Database - inv_ops ((description not yet updated on this server))

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Query: /api/inv_ops/?_offset=0

Column	Type
content	jsonb
isa	text
scan_date	timestamp without time zone

0. id: 0
   {'content': {'gone': {'colls_gone': {'num': 0, 'items': []}}, 'fields': None, 'latest': {'latest_scan': {'_id': 56, 'INFO': {}, 'name': 'mwf_tables', 'NOTES': {}, 'db_id': 23, 'status': 0, 'nice_name': 'Display data for Maass forms', 'scan_date': {'data': '2018-09-26 17:21:31.772464', '__date__': 0}}}, 'scrapes': {'scrapes_run': 0, 'scrapes_hung': False}, 'connection': {'inv_ok': False, 'can_write': False, 'global_lock': False}}, 'isa': 'report', 'scan_date': {'__date__': 0, 'data': '2019-05-21 17:37:53.875881'}}
1. id: 1
   {'content': {'gone': {'colls_gone': {'num': 0, 'items': []}}, 'fields': {'table_match': {'num': 0, 'items': []}, 'human_missing': {'num': 65, 'items': [['artin_field_data', 0, [[{'_id': 0, 'data': {'type': "List(Dict{u'Size': Z, u'Representative': List(Z), u'Order': Z}) ", 'example': None, 'description': '(list of dicts): for each conjugacy class of the group: its Order (int), Representative (list of ints giving a permutation), and Size (int)'}, 'name': 'ConjClasses', 'table_id': 0}, 'c_name'], [{'_id': 1, 'data': {'type': 'String ', 'example': None, 'description': "name for the Galois group, but we usually substitute a latex'ed name from the Galois group database, but this is a fallback"}, 'name': 'G-Name', 'table_id': 0}, 'c_name'], [{'_id': 2, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'coefficients for a defining polynomial over Qp used for explicitly writing roots. The first coefficient is the constant term'}, 'name': 'QpRts-minpoly', 'table_id': 0}, 'c_name'], [{'_id': 3, 'data': {'type': 'Z ', 'example': None, 'description': 'index for ConjClasses to say where complex conjugation lies'}, 'name': 'ComplexConjugation', 'table_id': 0}, 'c_name'], [{'_id': 4, 'data': {'type': "List(Dict({u'Classes': Z, u'Data': Z, u'Algorithm': String, u'CycleType': List(Z)})) ", 'example': None, 'description': None}, 'name': 'FrobResolvents', 'table_id': 0}, 'c_name'], [{'_id': 6, 'data': {'type': "List(Dict{u'GalConj': Z, u'Character': List(List(Z)), u'CharacterField': Z, u'Baselabel': String}) ", 'example': None, 'description': ' (list of pairs, [string, int]): the string is the baselabel of an entry from the Artin representation database, and the int is the GalOrbIndex for a particular character with that Baselabel'}, 'name': 'ArtinReps', 'table_id': 0}, 'c_name'], [{'_id': 7, 'data': {'type': 'List(List(Z)) ', 'example': None, 'description': 'inner lists are permutations given as lists which generate the Galois group'}, 'name': 'G-Gens', 'table_id': 0}, 'c_name'], [{'_id': 8, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'coefficients of a polynomial defining this field, the comma-separated list of coefficients as a string. This is the main identifier for this field from the representations collection, and also matches entries in the number field database.'}, 'name': 'Polynomial', 'table_id': 0}, 'c_name'], [{'_id': 9, 'data': {'type': 'List(List(Z)) ', 'example': None, 'description': 'each entry is a p-adic root, where entries in the list give the coefficients of powers of p in the p-adic approximation. They are themselves polynomials in a, where a is a root of the QpRts-minpoly'}, 'name': 'QpRts', 'table_id': 0}, 'c_name'], [{'_id': 10, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'if the i-th entry is j, then the Frobenius for the i-th prime lies in the j-th conjugacy class'}, 'name': 'Frobs', 'table_id': 0}, 'c_name'], [{'_id': 11, 'data': {'type': 'Z ', 'example': None, 'description': 'the prime p used for computing the roots p-adicly'}, 'name': 'QpRts-p', 'table_id': 0}, 'c_name'], [{'_id': 12, 'data': {'type': 'Z ', 'example': None, 'description': 'degree of the polynomial'}, 'name': 'TransitiveDegree', 'table_id': 0}, 'c_name'], [{'_id': 13, 'data': {'type': 'Z ', 'example': None, 'description': 'order of the Galois group'}, 'name': 'Size', 'table_id': 0}, 'c_name'], [{'_id': 5, 'data': {'type': 'Z ', 'example': None, 'description': 'p-adic roots are computed up to (p^prec)'}, 'name': 'QpRts-prec', 'table_id': 0}, 'c_name']]], ['artin_reps', 1, [[{'_id': 14, 'data': {'type': 'String ', 'example': None, 'description': None}, 'name': 'Baselabel', 'table_id': 1}, 'c_name'], [{'_id': 15, 'data': {'type': 'Z ', 'example': None, 'description': 'dimension'}, 'name': 'Dim', 'table_id': 1}, 'c_name'], [{'_id': 16, 'data': {'type': 'Z ', 'example': None, 'description': 'conductor'}, 'name': 'Conductor', 'table_id': 1}, 'c_name'], [{'_id': 17, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Galn', 'table_id': 1}, 'c_name'], [{'_id': 18, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Galt', 'table_id': 1}, 'c_name'], [{'_id': 19, 'data': {'type': None, 'example': '`4t3 or 32`', 'description': 'Smallest permutation representation which has this representation as a factor. Permutation representations are ordered by degree, and then by T-number. If the degree is 32 or greater than 47, we just give the degree.'}, 'name': 'Container', 'table_id': 1}, 'c_name'], [{'_id': 20, 'data': {'type': 'Z ', 'example': None, 'description': 'Frobenius-Schur indicator, 1 for orthogonal, -1 for symplectic, and 0 for other'}, 'name': 'Indicator', 'table_id': 1}, 'c_name'], [{'_id': 21, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'list of bad primes, i.e., primes dividing the conductor. Stored as strings since they may get too big'}, 'name': 'BadPrimes', 'table_id': 1}, 'c_name'], [{'_id': 22, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'primes dividing the polynomial discriminant for the defining field. These include the Bad Primes'}, 'name': 'HardPrimes', 'table_id': 1}, 'c_name'], [{'_id': 23, 'data': {'type': "List(Dict{u'Character': List(List(Z)), u'GalOrbIndex': Z, u'HardFactors': List(Z), u'LocalFactors': List(List(List(Z))) u'Sign': Z} ", 'example': None, 'description': 'list of Galois conjugate character information.\n\nEach entry in the GaloisConjugates list is a dictionary with the following entries\n\n * *LocalFactors* (list of list of int-as-strings): local factors for the L-function \n\n * *Character* (list of list of ints): character for this representation. Each sublist are coefficients for the character value written on a power basis for Z[zeta_n]\n\n * *Sign* (int): sign of the functional equation when we know it is 1 or -1, otherwise we give 0.\n\n * *HardFactors* : local factors for bad primes\n\n * *GalOrbIndex*(ints): an index assigned to the given character'}, 'name': 'GaloisConjugates', 'table_id': 1}, 'c_name'], [{'_id': 24, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'GalConjSigns', 'table_id': 1}, 'c_name'], [{'_id': 25, 'data': {'type': 'Z ', 'example': None, 'description': 'the n for writing the character'}, 'name': 'CharacterField', 'table_id': 1}, 'c_name'], [{'_id': 26, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'list of Galois conjugate character information'}, 'name': 'NFGal', 'table_id': 1}, 'c_name'], [{'_id': 27, 'data': {'type': 'Boolean ', 'example': None, 'description': "0 if we should show it when searching for Artin rep'ns, 1 if not. The representations are invariants of the Galois closure of the given field. More than one field can have the same Galois closure. We pick a best/minimal one and show that. We have data for others for linking to the number field database."}, 'name': 'Hide', 'table_id': 1}, 'c_name']]], ['av_fqisog', 2, [[{'_id': 28, 'data': {'type': 'String', 'example': None, 'description': 'LMFDB Label. http://beta.lmfdb.org/Variety/Abelian/Fq/Labels[Labeling Scheme]'}, 'name': 'label', 'table_id': 2}, 'c_name'], [{'_id': 29, 'data': {'type': 'Z', 'example': None, 'description': 'Genus. The degree of the Weil L-polynomial is 2g'}, 'name': 'g', 'table_id': 2}, 'c_name'], [{'_id': 30, 'data': {'type': 'Z', 'example': None, 'description': 'Cardinality of Field. All of the roots of the Weil L-polynomial have absolute value $1/\\sqrt{q}$.'}, 'name': 'q', 'table_id': 2}, 'c_name'], [{'_id': 31, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'poly', 'table_id': 2}, 'c_name'], [{'_id': 32, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'poly_str', 'table_id': 2}, 'c_name'], [{'_id': 33, 'data': {'type': 'List(R)', 'example': None, 'description': None}, 'name': 'angles', 'table_id': 2}, 'c_name'], [{'_id': 34, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'ang_rank', 'table_id': 2}, 'c_name'], [{'_id': 35, 'data': {'type': 'N', 'example': None, 'description': 'The $p$-rank of the abelian variety. The rank of the $p$-torsion subgroup of the abelian variety. Equal to the number of occurences of the slope 0 in the Newton slopes.'}, 'name': 'p_rank', 'table_id': 2}, 'c_name'], [{'_id': 36, 'data': {'type': 'List(Q)', 'example': None, 'description': None}, 'name': 'slps', 'table_id': 2}, 'c_name'], [{'_id': 37, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'A_cnts', 'table_id': 2}, 'c_name'], [{'_id': 38, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A_cnts_str', 'table_id': 2}, 'c_name'], [{'_id': 39, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'C_cnts', 'table_id': 2}, 'c_name'], [{'_id': 40, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C_cnts_str', 'table_id': 2}, 'c_name'], [{'_id': 41, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'pt_cnt', 'table_id': 2}, 'c_name'], [{'_id': 42, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'is_jac', 'table_id': 2}, 'c_name'], [{'_id': 43, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'is_pp', 'table_id': 2}, 'c_name'], [{'_id': 44, 'data': {'type': 'List(String*Z)', 'example': None, 'description': None}, 'name': 'decomp', 'table_id': 2}, 'c_name'], [{'_id': 45, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'simple_factors', 'table_id': 2}, 'c_name'], [{'_id': 46, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'simple_distinct', 'table_id': 2}, 'c_name'], [{'_id': 47, 'data': {'type': 'Boolean', 'example': None, 'description': None}, 'name': 'is_simp', 'table_id': 2}, 'c_name'], [{'_id': 48, 'data': {'type': 'List(Q)', 'example': None, 'description': None}, 'name': 'brauer_invs', 'table_id': 2}, 'c_name'], [{'_id': 49, 'data': {'type': 'List(List(List(Q)))', 'example': None, 'description': 'The ideals corresponding to the Brauer invariants of the endomorphism algebra. The outer set of lists corresponds to the simple factors of the isogeny class (so in the example, this isogeny class is a product of two simple isogeny classes). For each simple factor, the list contains one list per prime above p in the number field defined by the Weil polynomial. This list describes the prime ideal above p by giving the second generator of the ideal (the first generator is p), as a list of the coefficients of the generator when written in terms of a specific basis for the number field. This basis contains the powers of a root of the P-polynomial (which is the Weil polynomial but reversed)'}, 'name': 'places', 'table_id': 2}, 'c_name'], [{'_id': 50, 'data': {'type': 'List(String)', 'example': None, 'description': None}, 'name': 'prim_models', 'table_id': 2}, 'c_name'], [{'_id': 51, 'data': {'type': 'Boolean', 'example': None, 'description': None}, 'name': 'is_prim', 'table_id': 2}, 'c_name'], [{'_id': 52, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'nf', 'table_id': 2}, 'c_name'], [{'_id': 53, 'data': {'type': 'Z', 'example': None, 'description': 'The transitive label of the Galois group of the Weil polynomial. If the number field was not in the database when the isogeny class was added to the database, this string is empty. If the isogeny class is not simple, this is also an empty string.'}, 'name': 'galois_t', 'table_id': 2}, 'c_name'], [{'_id': 54, 'data': {'type': 'Z', 'example': None, 'description': 'The degree label of the Galois group of the Weil polynomial. If the number field was not in the database when the isogeny class was added to the database, this string is empty. If the isogeny class is not simple, this is also an empty string.'}, 'name': 'galois_n', 'table_id': 2}, 'c_name'], [{'_id': 55, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim1_factors', 'table_id': 2}, 'c_name'], [{'_id': 56, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim2_factors', 'table_id': 2}, 'c_name'], [{'_id': 57, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim3_factors', 'table_id': 2}, 'c_name'], [{'_id': 58, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim4_factors', 'table_id': 2}, 'c_name'], [{'_id': 59, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim5_factors', 'table_id': 2}, 'c_name'], [{'_id': 60, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim1_distinct', 'table_id': 2}, 'c_name'], [{'_id': 61, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim2_distinct', 'table_id': 2}, 'c_name'], [{'_id': 62, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim3_distinct', 'table_id': 2}, 'c_name'], [{'_id': 63, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim4_distinct', 'table_id': 2}, 'c_name'], [{'_id': 64, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim5_distinct', 'table_id': 2}, 'c_name']]], ['belyi_galmaps', 3, [[{'_id': 65, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'geomtype', 'table_id': 3}, 'c_name'], [{'_id': 66, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'map', 'table_id': 3}, 'c_name'], [{'_id': 67, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'abc', 'table_id': 3}, 'c_name'], [{'_id': 68, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'base_field', 'table_id': 3}, 'c_name'], [{'_id': 69, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'triples_cyc', 'table_id': 3}, 'c_name'], [{'_id': 70, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'g', 'table_id': 3}, 'c_name'], [{'_id': 71, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'curve', 'table_id': 3}, 'c_name'], [{'_id': 72, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'orbit_size', 'table_id': 3}, 'c_name'], [{'_id': 73, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 3}, 'c_name'], [{'_id': 74, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a_s', 'table_id': 3}, 'c_name'], [{'_id': 75, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'pass_size', 'table_id': 3}, 'c_name'], [{'_id': 76, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'c_s', 'table_id': 3}, 'c_name'], [{'_id': 77, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'aut_group', 'table_id': 3}, 'c_name'], [{'_id': 78, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'deg', 'table_id': 3}, 'c_name'], [{'_id': 79, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'group_num', 'table_id': 3}, 'c_name'], [{'_id': 80, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'embeddings', 'table_id': 3}, 'c_name'], [{'_id': 81, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'group', 'table_id': 3}, 'c_name'], [{'_id': 82, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'triples', 'table_id': 3}, 'c_name'], [{'_id': 83, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'b_s', 'table_id': 3}, 'c_name'], [{'_id': 84, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'plabel', 'table_id': 3}, 'c_name'], [{'_id': 85, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'lambdas', 'table_id': 3}, 'c_name']]], ['belyi_passports', 4, [[{'_id': 86, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'geomtype', 'table_id': 4}, 'c_name'], [{'_id': 87, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'pass_size', 'table_id': 4}, 'c_name'], [{'_id': 88, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'abc', 'table_id': 4}, 'c_name'], [{'_id': 89, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'group', 'table_id': 4}, 'c_name'], [{'_id': 90, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'g', 'table_id': 4}, 'c_name'], [{'_id': 91, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'maxdegbf', 'table_id': 4}, 'c_name'], [{'_id': 92, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'lambdas', 'table_id': 4}, 'c_name'], [{'_id': 93, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'plabel', 'table_id': 4}, 'c_name'], [{'_id': 94, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'num_orbits', 'table_id': 4}, 'c_name'], [{'_id': 95, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'deg', 'table_id': 4}, 'c_name']]], ['bmf_dims', 5, [[{'_id': 96, 'data': {'type': "FiniteMap(Z, Dict{u'cuspidal_dim': Z, u'new_dim': Z})", 'example': None, 'description': 'Dictionary keyed by weight with values dictionaries holding the cuspidal and new dimensions for the GL(2) level'}, 'name': 'gl2_dims', 'table_id': 5}, 'c_name'], [{'_id': 97, 'data': {'type': "FiniteMap(Z, Dict{u'cuspidal_dim': Z, u'new_dim': Z})", 'example': None, 'description': 'Dictionary keyed by weight with values dictionaries holding the cuspidal and new dimensions for the SL(2) level'}, 'name': 'sl2_dims', 'table_id': 5}, 'c_name'], [{'_id': 98, 'data': {'type': 'Z', 'example': None, 'description': 'absolute value of field discriminant'}, 'name': 'field_absdisc', 'table_id': 5}, 'c_name'], [{'_id': 99, 'data': {'type': 'String', 'example': None, 'description': 'Full label of level (including base field)'}, 'name': 'label', 'table_id': 5}, 'c_name'], [{'_id': 100, 'data': {'type': 'String', 'example': None, 'description': 'LMFDB label of base field'}, 'name': 'field_label', 'table_id': 5}, 'c_name'], [{'_id': 101, 'data': {'type': 'Z', 'example': None, 'description': 'Level norm'}, 'name': 'level_norm', 'table_id': 5}, 'c_name'], [{'_id': 102, 'data': {'type': 'String', 'example': None, 'description': 'Level label (excluding base field)'}, 'name': 'level_label', 'table_id': 5}, 'c_name']]], ['bmf_forms', 6, [[{'_id': 103, 'data': {'type': 'Z', 'example': None, 'description': 'discriminant of base field'}, 'name': 'field_disc', 'table_id': 6}, 'c_name'], [{'_id': 104, 'data': {'type': 'Z', 'example': None, 'description': 'Sign of functional equation'}, 'name': 'sfe', 'table_id': 6}, 'c_name'], [{'_id': 105, 'data': {'type': 'C', 'example': None, 'description': 'generator of the level ideal'}, 'name': 'level_gen', 'table_id': 6}, 'c_name'], [{'_id': 106, 'data': {'type': 'Z', 'example': None, 'description': 'weight'}, 'name': 'weight', 'table_id': 6}, 'c_name'], [{'_id': 107, 'data': {'type': 'Z', 'example': None, 'description': 'Complex Multiplication flag: a negative discriminant, or 0 if not CM'}, 'name': 'CM', 'table_id': 6}, 'c_name'], [{'_id': 108, 'data': {'type': 'Z', 'example': None, 'description': 'Base change flag: d>0 if form is base change from Q with eigs in Q(sqrt(d)), 0 if not base-change'}, 'name': 'bc', 'table_id': 6}, 'c_name'], [{'_id': 109, 'data': {'type': 'Z', 'example': None, 'description': 'degree of base field'}, 'name': 'field_deg', 'table_id': 6}, 'c_name'], [{'_id': 110, 'data': {'type': 'String', 'example': None, 'description': 'Full label: field, level, suffix'}, 'name': 'label', 'table_id': 6}, 'c_name'], [{'_id': 111, 'data': {'type': 'String', 'example': None, 'description': 'letter code label suffix'}, 'name': 'label_suffix', 'table_id': 6}, 'c_name'], [{'_id': 112, 'data': {'type': "Poly('x', Z)", 'example': None, 'description': 'Polynomial defining the Hecke field (x if rational)'}, 'name': 'hecke_poly', 'table_id': 6}, 'c_name'], [{'_id': 113, 'data': {'type': 'String', 'example': None, 'description': 'LMFDB label of base field'}, 'name': 'field_label', 'table_id': 6}, 'c_name'], [{'_id': 114, 'data': {'type': 'List(Z)', 'example': None, 'description': 'Atkin-Lehner eigenvalues'}, 'name': 'AL_eigs', 'table_id': 6}, 'c_name'], [{'_id': 115, 'data': {'type': 'R', 'example': None, 'description': 'L(F,1) divided by the real period'}, 'name': 'Lratio', 'table_id': 6}, 'c_name'], [{'_id': 116, 'data': {'type': 'Z', 'example': None, 'description': 'level norm'}, 'name': 'level_norm', 'table_id': 6}, 'c_name'], [{'_id': 117, 'data': {'type': 'List(R)', 'example': None, 'description': 'Hecke eigenvalues as integers or strings if not rational'}, 'name': 'hecke_eigs', 'table_id': 6}, 'c_name'], [{'_id': 118, 'data': {'type': 'String', 'example': None, 'description': 'Short form of label (omitting field)'}, 'name': 'short_label', 'table_id': 6}, 'c_name'], [{'_id': 119, 'data': {'type': 'String', 'example': None, 'description': 'label of the level ideal'}, 'name': 'level_label', 'table_id': 6}, 'c_name'], [{'_id': 120, 'data': {'type': 'Z', 'example': None, 'description': 'numerical version of label_suffix (1 for a, 2 for b etc) for sorting'}, 'name': 'label_nsuffix', 'table_id': 6}, 'c_name'], [{'_id': 121, 'data': {'type': 'Z', 'example': None, 'description': 'dimension of the Galois orbit, i.e. degree of the Hecke eigenvalue field'}, 'name': 'dimension', 'table_id': 6}, 'c_name'], [{'_id': 122, 'data': {'type': 'String', 'example': None, 'description': 'defining data of the level ideal'}, 'name': 'level_ideal', 'table_id': 6}, 'c_name']]], ['char_dir_orbits', 7, [[{'_id': 123, 'data': {'type': 'text', 'description': '(N.i)'}, 'name': 'orbit_label', 'table_id': 7}, 'c_name'], [{'_id': 123, 'data': {'type': 'text', 'description': '(N.i)'}, 'name': 'orbit_label', 'table_id': 7}, 'example'], [{'_id': 124, 'data': {'type': 'smallint', 'description': '(i) Index in the list of traces down to Q of the values of all characters of modulus N'}, 'name': 'orbit_index', 'table_id': 7}, 'c_name'], [{'_id': 124, 'data': {'type': 'smallint', 'description': '(i) Index in the list of traces down to Q of the values of all characters of modulus N'}, 'name': 'orbit_index', 'table_id': 7}, 'example'], [{'_id': 125, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'modulus', 'table_id': 7}, 'c_name'], [{'_id': 126, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'conductor', 'table_id': 7}, 'c_name'], [{'_id': 127, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'order', 'table_id': 7}, 'c_name'], [{'_id': 128, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'parity', 'table_id': 7}, 'c_name'], [{'_id': 129, 'data': {'type': 'jsonb', 'description': 'sorted list of conrey_labels in the same galois orbit'}, 'name': 'galois_orbit', 'table_id': 7}, 'c_name'], [{'_id': 129, 'data': {'type': 'jsonb', 'description': 'sorted list of conrey_labels in the same galois orbit'}, 'name': 'galois_orbit', 'table_id': 7}, 'example'], [{'_id': 130, 'data': {'type': 'boolean', 'description': 'if quadratic or trivial'}, 'name': 'is_real', 'table_id': 7}, 'c_name'], [{'_id': 130, 'data': {'type': 'boolean', 'description': 'if quadratic or trivial'}, 'name': 'is_real', 'table_id': 7}, 'example'], [{'_id': 131, 'data': {'type': 'boolean', 'description': 'if modulus = conductor'}, 'name': 'is_primitive', 'table_id': 7}, 'c_name'], [{'_id': 131, 'data': {'type': 'boolean', 'description': 'if modulus = conductor'}, 'name': 'is_primitive', 'table_id': 7}, 'example'], [{'_id': 132, 'data': {'type': 'smallint', 'description': 'degree of the cyclotomic field containing the image, ie Euler phi of the order; this is the same as the size of the Galois orbit'}, 'name': 'char_degree', 'table_id': 7}, 'c_name'], [{'_id': 132, 'data': {'type': 'smallint', 'description': 'degree of the cyclotomic field containing the image, ie Euler phi of the order; this is the same as the size of the Galois orbit'}, 'name': 'char_degree', 'table_id': 7}, 'example']]], ['char_dir_values', 8, [[{'_id': 133, 'data': {'type': 'text', 'description': 'N.n where N is the modulus and n is the conrey label'}, 'name': 'label', 'table_id': 8}, 'c_name'], [{'_id': 133, 'data': {'type': 'text', 'description': 'N.n where N is the modulus and n is the conrey label'}, 'name': 'label', 'table_id': 8}, 'example'], [{'_id': 134, 'data': {'type': 'text', 'description': 'N.i where N is the modulus and i is the orbit_index'}, 'name': 'orbit_label', 'table_id': 8}, 'c_name'], [{'_id': 134, 'data': {'type': 'text', 'description': 'N.i where N is the modulus and i is the orbit_index'}, 'name': 'orbit_label', 'table_id': 8}, 'example'], [{'_id': 135, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'order', 'table_id': 8}, 'c_name'], [{'_id': 136, 'data': {'type': 'jsonb', 'description': 'list of the first twelve values on -1,1, then the next ten integers relatively prime to the modulus'}, 'name': 'values', 'table_id': 8}, 'c_name'], [{'_id': 136, 'data': {'type': 'jsonb', 'description': 'list of the first twelve values on -1,1, then the next ten integers relatively prime to the modulus'}, 'name': 'values', 'table_id': 8}, 'example'], [{'_id': 137, 'data': {'type': 'jsonb', 'description': 'list of pairs [n, chi(n)] for n generating the unit group'}, 'name': 'values_gens', 'table_id': 8}, 'c_name'], [{'_id': 137, 'data': {'type': 'jsonb', 'description': 'list of pairs [n, chi(n)] for n generating the unit group'}, 'name': 'values_gens', 'table_id': 8}, 'example'], [{'_id': 138, 'data': {'type': 'text', 'description': 'the label of primitive character inducing this one'}, 'name': 'prim_label', 'table_id': 8}, 'c_name'], [{'_id': 138, 'data': {'type': 'text', 'description': 'the label of primitive character inducing this one'}, 'name': 'prim_label', 'table_id': 8}, 'example']]], ['ec_iqf_labels', 10, [[{'_id': 189, 'data': {'type': 'string (period-separated pair of integers)', 'example': None, 'description': 'Standard ideal label'}, 'name': 'new', 'table_id': 10}, 'c_name'], [{'_id': 190, 'data': {'type': 'string (period-separated triple of integers)', 'example': None, 'description': 'Old-style ideal label'}, 'name': 'old', 'table_id': 10}, 'c_name'], [{'_id': 191, 'data': {'type': None, 'example': None, 'description': 'Field label (for an imaginary quadratic field)'}, 'name': 'fld', 'table_id': 10}, 'c_name']]], ['ec_nfcurves', 11, [[{'_id': 192, 'data': {'type': None, 'example': None, 'description': 'invariants of torsion subgroup'}, 'name': 'torsion_structure', 'table_id': 11}, 'c_name'], [{'_id': 193, 'data': {'type': 'string (semicolon-separated list of comma-separated lists of integers)', 'example': None, 'description': '5 Weierstrass coefficients (a-invariants) as a single string'}, 'name': 'ainvs', 'table_id': 11}, 'c_name'], [{'_id': 194, 'data': {'type': None, 'example': None, 'description': 'CM code. Either 0 for no CM, or a negative discriminant.'}, 'name': 'cm', 'table_id': 11}, 'c_name'], [{'_id': 195, 'data': {'type': None, 'example': None, 'description': 'torsion generators'}, 'name': 'torsion_gens', 'table_id': 11}, 'c_name'], [{'_id': 196, 'data': {'type': None, 'example': None, 'description': 'index of curve in isogeny class. starts at 1'}, 'name': 'number', 'table_id': 11}, 'c_name'], [{'_id': 197, 'data': {'type': None, 'example': None, 'description': 'rank'}, 'name': 'rank', 'table_id': 11}, 'c_name'], [{'_id': 198, 'data': {'type': 'string (period-separated list of 4 integers)', 'example': None, 'description': 'Base field label'}, 'name': 'field_label', 'table_id': 11}, 'c_name'], [{'_id': 199, 'data': {'type': 'list of strings', 'example': None, 'description': 'Sutherland codes for non-maximal mod p Galois images'}, 'name': 'galois_images', 'table_id': 11}, 'c_name'], [{'_id': 200, 'data': {'type': None, 'example': None, 'description': 'norm of the conductor'}, 'name': 'conductor_norm', 'table_id': 11}, 'c_name'], [{'_id': 201, 'data': {'type': None, 'example': None, 'description': 'absolute value of discriminant of base field'}, 'name': 'abs_disc', 'table_id': 11}, 'c_name'], [{'_id': 202, 'data': {'type': None, 'example': None, 'description': 'heights of generators'}, 'name': 'heights', 'table_id': 11}, 'c_name'], [{'_id': 203, 'data': {'type': None, 'example': None, 'description': 'isogeny class index'}, 'name': 'iso_nlabel', 'table_id': 11}, 'c_name'], [{'_id': 204, 'data': {'type': None, 'example': None, 'description': 'lower and upper rank bounds'}, 'name': 'rank_bounds', 'table_id': 11}, 'c_name'], [{'_id': 205, 'data': {'type': None, 'example': None, 'description': 'data defining the conductor'}, 'name': 'conductor_ideal', 'table_id': 11}, 'c_name'], [{'_id': 206, 'data': {'type': 'list of strings', 'example': None, 'description': 'labels of base change source curves'}, 'name': 'base_change', 'table_id': 11}, 'c_name'], [{'_id': 207, 'data': {'type': None, 'example': None, 'description': 'List of local data at bad primes'}, 'name': 'local_data', 'table_id': 11}, 'c_name'], [{'_id': 208, 'data': {'type': None, 'example': None, 'description': 'analytic rank'}, 'name': 'analytic_rank', 'table_id': 11}, 'c_name'], [{'_id': 209, 'data': {'type': None, 'example': None, 'description': 'minimal discriminant ideal'}, 'name': 'minD', 'table_id': 11}, 'c_name'], [{'_id': 210, 'data': {'type': None, 'example': None, 'description': 'full label'}, 'name': 'label', 'table_id': 11}, 'c_name'], [{'_id': 211, 'data': {'type': None, 'example': None, 'description': 'j-invariant'}, 'name': 'jinv', 'table_id': 11}, 'c_name'], [{'_id': 212, 'data': {'type': 'string (period-separated pair of integers)', 'example': None, 'description': 'label of the conductor'}, 'name': 'conductor_label', 'table_id': 11}, 'c_name'], [{'_id': 213, 'data': {'type': None, 'example': None, 'description': 'LCM of isogeny degrees within this class'}, 'name': 'class_deg', 'table_id': 11}, 'c_name'], [{'_id': 214, 'data': {'type': None, 'example': None, 'description': 'regulator'}, 'name': 'reg', 'table_id': 11}, 'c_name'], [{'_id': 215, 'data': {'type': None, 'example': None, 'description': 'Number of curves in the isogeny class'}, 'name': 'class_size', 'table_id': 11}, 'c_name'], [{'_id': 216, 'data': {'type': None, 'example': None, 'description': 'Degrees of rational cyclic isogenies'}, 'name': 'isogeny_degrees', 'table_id': 11}, 'c_name'], [{'_id': 217, 'data': {'type': None, 'example': None, 'description': 'full label of the isogeny class'}, 'name': 'class_label', 'table_id': 11}, 'c_name'], [{'_id': 218, 'data': {'type': None, 'example': None, 'description': 'isogeny class label'}, 'name': 'iso_label', 'table_id': 11}, 'c_name'], [{'_id': 219, 'data': {'type': None, 'example': None, 'description': 'Base field degree'}, 'name': 'degree', 'table_id': 11}, 'c_name'], [{'_id': 220, 'data': {'type': None, 'example': None, 'description': 'Non-minimal primes'}, 'name': 'non_min_p', 'table_id': 11}, 'c_name'], [{'_id': 221, 'data': {'type': None, 'example': None, 'description': 'Q-curve flag'}, 'name': 'q_curve', 'table_id': 11}, 'c_name'], [{'_id': 222, 'data': {'type': None, 'example': None, 'description': 'short label (excludes field)'}, 'name': 'short_label', 'table_id': 11}, 'c_name'], [{'_id': 223, 'data': {'type': None, 'example': None, 'description': 'short label of isogeny class (excludes field)'}, 'name': 'short_class_label', 'table_id': 11}, 'c_name'], [{'_id': 224, 'data': {'type': 'list of lists of integers', 'example': None, 'description': 'Matrix of isogeny degrees between curves in the isogeny class'}, 'name': 'isogeny_matrix', 'table_id': 11}, 'c_name'], [{'_id': 225, 'data': {'type': None, 'example': None, 'description': 'torsion order'}, 'name': 'torsion_order', 'table_id': 11}, 'c_name'], [{'_id': 226, 'data': {'type': None, 'example': None, 'description': 'List of primes p for which the mod p Galois representation does not have maximal image'}, 'name': 'non-surjective_primes', 'table_id': 11}, 'c_name'], [{'_id': 227, 'data': {'type': None, 'example': None, 'description': 'Weierstrass equation (LaTeX)'}, 'name': 'equation', 'table_id': 11}, 'c_name'], [{'_id': 228, 'data': {'type': None, 'example': None, 'description': 'generators of infinite order'}, 'name': 'gens', 'table_id': 11}, 'c_name'], [{'_id': 229, 'data': {'type': None, 'example': None, 'description': 'Number of generators of infinite order stored'}, 'name': 'ngens', 'table_id': 11}, 'c_name'], [{'_id': 230, 'data': {'type': None, 'example': None, 'description': 'Base field signature'}, 'name': 'signature', 'table_id': 11}, 'c_name']]], ['ec_padic', 12, [[{'_id': 231, 'data': {'type': None, 'example': None, 'description': 'LMFDB label of isogeny class'}, 'name': 'lmfdb_iso', 'table_id': 12}, 'c_name'], [{'_id': 232, 'data': {'type': None, 'example': None, 'description': 'prime'}, 'name': 'p', 'table_id': 12}, 'c_name'], [{'_id': 233, 'data': {'type': None, 'example': None, 'description': 'p-adic precision'}, 'name': 'prec', 'table_id': 12}, 'c_name'], [{'_id': 234, 'data': {'type': None, 'example': None, 'description': 'unit factor of regulator'}, 'name': 'unit', 'table_id': 12}, 'c_name'], [{'_id': 235, 'data': {'type': None, 'example': None, 'description': 'valuation of p-adic regulator'}, 'name': 'val', 'table_id': 12}, 'c_name']]], ['fq_fields', 13, [[{'_id': 236, 'data': {'type': None, 'example': None, 'description': 'Coefficients of the defining polynomial over the prime field'}, 'name': 'polynomial', 'table_id': 13}, 'c_name'], [{'_id': 237, 'data': {'type': 'integer (prime)', 'example': None, 'description': 'The characteristic of the field'}, 'name': 'characteristic', 'table_id': 13}, 'c_name'], [{'_id': 238, 'data': {'type': None, 'example': None, 'description': 'The degree of the field over its prime field'}, 'name': 'degree', 'table_id': 13}, 'c_name'], [{'_id': 239, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'conway', 'table_id': 13}, 'c_name']]], ['g2c_curves', 14, [[{'_id': 240, 'data': {'type': None, 'example': None, 'description': 'geometric automorphism group (shorthand)'}, 'name': 'geom_aut_grp_id', 'table_id': 14}, 'c_name'], [{'_id': 241, 'data': {'type': None, 'example': None, 'description': 'Igusa invariants'}, 'name': 'igusa_inv', 'table_id': 14}, 'c_name'], [{'_id': 242, 'data': {'type': None, 'example': None, 'description': 'number of rational Weierstrass points'}, 'name': 'num_rat_wpts', 'table_id': 14}, 'c_name'], [{'_id': 243, 'data': {'type': None, 'example': None, 'description': 'whether the curve is simple over the base field'}, 'name': 'is_simple_base', 'table_id': 14}, 'c_name'], [{'_id': 244, 'data': {'type': None, 'example': None, 'description': 'whether the curve is simple over the algebraic closure'}, 'name': 'is_simple_geom', 'table_id': 14}, 'c_name'], [{'_id': 245, 'data': {'type': None, 'example': None, 'description': 'rational torsion order of the Jacobian'}, 'name': 'torsion_order', 'table_id': 14}, 'c_name'], [{'_id': 246, 'data': {'type': None, 'example': None, 'description': 'G2 invariants'}, 'name': 'g2_inv', 'table_id': 14}, 'c_name'], [{'_id': 247, 'data': {'type': None, 'example': None, 'description': 'conductor'}, 'name': 'cond', 'table_id': 14}, 'c_name'], [{'_id': 248, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Lhash', 'table_id': 14}, 'c_name'], [{'_id': 249, 'data': {'type': None, 'example': None, 'description': 'absolute discriminant'}, 'name': 'abs_disc', 'table_id': 14}, 'c_name'], [{'_id': 250, 'data': {'type': None, 'example': None, 'description': 'assuming Sha is finite, true if the order of Sha is a square, false otherwise (in which case it is 2 times a square, by a result of Poonen-Stoll 1999)'}, 'name': 'has_square_sha', 'table_id': 14}, 'c_name'], [{'_id': 251, 'data': {'type': None, 'example': None, 'description': '2-Selmer rank'}, 'name': 'two_selmer_rank', 'table_id': 14}, 'c_name'], [{'_id': 252, 'data': {'type': None, 'example': None, 'description': 'analytic rank upper bound that is believed to be tight (known for rank 0 or 1)'}, 'name': 'analytic_rank', 'table_id': 14}, 'c_name'], [{'_id': 253, 'data': {'type': None, 'example': None, 'description': 'LMFDB label'}, 'name': 'label', 'table_id': 14}, 'c_name'], [{'_id': 254, 'data': {'type': None, 'example': None, 'description': 'Sato-Tate group over base field'}, 'name': 'st_group', 'table_id': 14}, 'c_name'], [{'_id': 255, 'data': {'type': None, 'example': None, 'description': 'automorphism group (specified by GAP id)'}, 'name': 'aut_grp_id', 'table_id': 14}, 'c_name'], [{'_id': 256, 'data': {'type': None, 'example': None, 'description': 'coefficients of minimal equation y^2+h(x)y=f(x)'}, 'name': 'eqn', 'table_id': 14}, 'c_name'], [{'_id': 257, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'num_rat_pts', 'table_id': 14}, 'c_name'], [{'_id': 258, 'data': {'type': None, 'example': None, 'description': 'true if the curve has rational points locally everywhere (i.e. over every completion of Q, including R)'}, 'name': 'locally_solvable', 'table_id': 14}, 'c_name'], [{'_id': 259, 'data': {'type': 'string encoding list of pairs [p,c] where p is a bad prime and c is a list of the coefficients of the Euler factor at p', 'example': None, 'description': 'bad primes and the corresponding L-factors'}, 'name': 'bad_lfactors', 'table_id': 14}, 'c_name'], [{'_id': 260, 'data': {'type': None, 'example': None, 'description': 'whether the curve is of GL2-type over its base field'}, 'name': 'is_gl2_type', 'table_id': 14}, 'c_name'], [{'_id': 261, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'non_solvable_places', 'table_id': 14}, 'c_name'], [{'_id': 262, 'data': {'type': None, 'example': None, 'description': 'sign of the discriminant'}, 'name': 'disc_sign', 'table_id': 14}, 'c_name'], [{'_id': 263, 'data': {'type': None, 'example': None, 'description': 'isogeny class'}, 'name': 'class', 'table_id': 14}, 'c_name'], [{'_id': 264, 'data': {'type': None, 'example': None, 'description': 'Igusa-Clebsch invariants'}, 'name': 'igusa_clebsch_inv', 'table_id': 14}, 'c_name'], [{'_id': 265, 'data': {'type': None, 'example': None, 'description': '1 if known to have rational points, 0 if known to have no rational points, -1 if unknown'}, 'name': 'globally_solvable', 'table_id': 14}, 'c_name'], [{'_id': 266, 'data': {'type': None, 'example': None, 'description': 'endomorphism ring over base field tensored with RR'}, 'name': 'real_geom_end_alg', 'table_id': 14}, 'c_name'], [{'_id': 267, 'data': {'type': None, 'example': None, 'description': 'rational torsion group of the Jacobian, represented by the invariant factors [d_1, d_2, ...] for which this torsion group is isomorphic to ZZ / d_1 ZZ x ZZ / d_2 ZZ x ...'}, 'name': 'torsion_subgroup', 'table_id': 14}, 'c_name'], [{'_id': 268, 'data': {'type': None, 'example': None, 'description': 'root number'}, 'name': 'root_number', 'table_id': 14}, 'c_name'], [{'_id': 269, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'two_torsion_field', 'table_id': 14}, 'c_name']]], ['g2c_endomorphisms', 15, [[{'_id': 270, 'data': {'type': None, 'example': None, 'description': 'endomorphism algebra factors over the base field tensored with RR'}, 'name': 'factorsRR_base', 'table_id': 15}, 'c_name'], [{'_id': 271, 'data': {'type': None, 'example': None, 'description': 'conductor norms of the elliptic curves obtained by splitting the Jacobian'}, 'name': 'spl_facs_condnorms', 'table_id': 15}, 'c_name'], [{'_id': 272, 'data': {'type': None, 'example': None, 'description': 'description of endomorphism algebra factors over the algebraic closure'}, 'name': 'factorsQQ_geom', 'table_id': 15}, 'c_name'], [{'_id': 273, 'data': {'type': None, 'example': None, 'description': 'LMFDB labels of the elliptic curves obtained by splitting the Jacobian'}, 'name': 'spl_facs_labels', 'table_id': 15}, 'c_name'], [{'_id': 274, 'data': {'type': None, 'example': None, 'description': 'whether the curve is simple over the base field'}, 'name': 'is_simple_base', 'table_id': 15}, 'c_name'], [{'_id': 275, 'data': {'type': None, 'example': None, 'description': 'LMFDB label of a field of minimal degree over which a splitting of the Jacobian is defined'}, 'name': 'spl_fod_label', 'table_id': 15}, 'c_name'], [{'_id': 276, 'data': {'type': None, 'example': None, 'description': 'endomorphism ring over the algebraic closure as a subring of the endomorphism algebra'}, 'name': 'ring_geom', 'table_id': 15}, 'c_name'], [{'_id': 277, 'data': {'type': None, 'example': None, 'description': 'Sato-Tate group over the base field'}, 'name': 'st_group_base', 'table_id': 15}, 'c_name'], [{'_id': 278, 'data': {'type': None, 'example': None, 'description': 'defining coefficients of the elliptic curves obtained by splitting the Jacobian'}, 'name': 'spl_facs_coeffs', 'table_id': 15}, 'c_name'], [{'_id': 279, 'data': {'type': None, 'example': None, 'description': 'description of endomorphism algebra factors over the base field'}, 'name': 'factorsQQ_base', 'table_id': 15}, 'c_name'], [{'_id': 280, 'data': {'type': None, 'example': None, 'description': 'LMFDB label of the smallest field over which all endomorphisms are defined'}, 'name': 'fod_label', 'table_id': 15}, 'c_name'], [{'_id': 281, 'data': {'type': None, 'example': None, 'description': 'defining polynomial of the smallest field over which all endomorphisms are defined'}, 'name': 'fod_coeffs', 'table_id': 15}, 'c_name'], [{'_id': 282, 'data': {'type': None, 'example': None, 'description': 'defining polynomial of a field of minimal degree over which a splitting of the Jacobian is defined'}, 'name': 'spl_fod_coeffs', 'table_id': 15}, 'c_name'], [{'_id': 283, 'data': {'type': None, 'example': None, 'description': 'whether the curve is simple over the algebraic closure'}, 'name': 'is_simple_geom', 'table_id': 15}, 'c_name'], [{'_id': 284, 'data': {'type': None, 'example': None, 'description': 'endomorphism lattice. See notes section'}, 'name': 'lattice', 'table_id': 15}, 'c_name'], [{'_id': 285, 'data': {'type': None, 'example': None, 'description': 'Sato-Tate group over the algebraic closure (equivalently, its identity component)'}, 'name': 'st_group_geom', 'table_id': 15}, 'c_name'], [{'_id': 286, 'data': {'type': None, 'example': None, 'description': 'LMFDB label'}, 'name': 'label', 'table_id': 15}, 'c_name'], [{'_id': 287, 'data': {'type': None, 'example': None, 'description': 'endomorphism ring over the base field as a subring of the endomorphism algebra'}, 'name': 'ring_base', 'table_id': 15}, 'c_name'], [{'_id': 288, 'data': {'type': None, 'example': None, 'description': 'generator of a field of minimal degree over which a splitting of the Jacobian is defined, as a subfield of the smallest field over which all endomorphisms are defined'}, 'name': 'spl_fod_gen', 'table_id': 15}, 'c_name'], [{'_id': 289, 'data': {'type': None, 'example': None, 'description': 'endomorphism algebra factors over the algebraic closure tensored with RR'}, 'name': 'factorsRR_geom', 'table_id': 15}, 'c_name']]], ['g2c_ratpts', 16, [[{'_id': 290, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'num_rat_pts', 'table_id': 16}, 'c_name'], [{'_id': 291, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'rat_pts', 'table_id': 16}, 'c_name'], [{'_id': 292, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'rat_pts_v', 'table_id': 16}, 'c_name'], [{'_id': 293, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 16}, 'c_name']]], ['g2c_tamagawa', 17, [[{'_id': 294, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'p', 'table_id': 17}, 'c_name'], [{'_id': 295, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'tamagawa_number', 'table_id': 17}, 'c_name'], [{'_id': 296, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 17}, 'c_name']]], ['gps_gmodules', 18, [[{'_id': 297, 'data': {'type': None, 'example': None, 'description': 'dimension of lattice'}, 'name': 'dim', 'table_id': 18}, 'c_name'], [{'_id': 298, 'data': {'type': None, 'example': None, 'description': 'Do we have complete information, 1 for yes, 0 for no'}, 'name': 'complete', 'table_id': 18}, 'c_name'], [{'_id': 299, 'data': {'type': None, 'example': None, 'description': 'index to identify the G-module'}, 'name': 'index', 'table_id': 18}, 'c_name'], [{'_id': 300, 'data': {'type': 'pair [string of cycle type, matrix for action]', 'example': None, 'description': 'generators of group and matrix for their actions'}, 'name': 'gens', 'table_id': 18}, 'c_name'], [{'_id': 301, 'data': {'type': None, 'example': None, 'description': 'for Galois group in form nTt'}, 'name': 'n', 'table_id': 18}, 'c_name'], [{'_id': 302, 'data': {'type': None, 'example': None, 'description': 'for Galois group in form nTt'}, 'name': 't', 'table_id': 18}, 'c_name'], [{'_id': 303, 'data': {'type': None, 'example': None, 'description': 'name of this G-module'}, 'name': 'name', 'table_id': 18}, 'c_name']]], ['gps_sato_tate', 19, [[{'_id': 304, 'data': {'type': None, 'example': None, 'description': 'dimension of the identity component as a connected compact real Lie group (positive integer)'}, 'name': 'real_dimension', 'table_id': 19}, 'c_name'], [{'_id': 305, 'data': {'type': None, 'example': None, 'description': 'proportion of components on which the trace is identically zero, rational number encoded as a string'}, 'name': 'trace_zero_density', 'table_id': 19}, 'c_name'], [{'_id': 306, 'data': {'type': None, 'example': None, 'description': 'label of the identity component'}, 'name': 'identity_component', 'table_id': 19}, 'c_name'], [{'_id': 307, 'data': {'type': None, 'example': None, 'description': 'string naming the Sato-Tate group unique within its weight and degree'}, 'name': 'name', 'table_id': 19}, 'c_name'], [{'_id': 308, 'data': {'type': None, 'example': None, 'description': 'degree of the Sato-Tate group (cohomological dimension), a positive integer'}, 'name': 'degree', 'table_id': 19}, 'c_name'], [{'_id': 309, 'data': {'type': None, 'example': None, 'description': 'b64 encoded .png file containing 220x124 trace histogram plot'}, 'name': 'trace_histogram', 'table_id': 19}, 'c_name'], [{'_id': 310, 'data': {'type': 'list of lists [*x*,*m_1*, *m_2*,..., ]', 'example': None, 'description': 'where *x* is a class function (elementary symmetric or power sum function of eigenvalues), and *m_n* is the *n*th moment of *x*'}, 'name': 'moments', 'table_id': 19}, 'c_name'], [{'_id': 311, 'data': {'type': None, 'example': None, 'description': 'number of components (equal to _a_ in the GAP id of the component group), stored as an integer'}, 'name': 'components', 'table_id': 19}, 'c_name'], [{'_id': 312, 'data': {'type': 'list of matrices', 'example': None, 'description': 'generators, stored as a list of *d*-by-*d* matrices whose entries are strings, where *d* is the degree; together with the identity component, they generate the group.'}, 'name': 'gens', 'table_id': 19}, 'c_name'], [{'_id': 313, 'data': {'type': None, 'example': None, 'description': 'weight of the Sato-Tate group (nonnegative integer)'}, 'name': 'weight', 'table_id': 19}, 'c_name'], [{'_id': 314, 'data': {'type': None, 'example': None, 'description': 'label of the form *wt*.*deg*.*dim*.*a.bc* (string) where *wt* is the weight, *deg* is the degree, *dim* is the real dimension, *a.b* is the GAP id of the component group, and *c* is a letter or string of letters used to break ties; uniquely identifies the Sato-Tate group.'}, 'name': 'label', 'table_id': 19}, 'c_name'], [{'_id': 315, 'data': {'type': None, 'example': None, 'description': 'list of labels of minimal proper super group'}, 'name': 'supgroups', 'table_id': 19}, 'c_name'], [{'_id': 316, 'data': {'type': None, 'example': None, 'description': 'boolean indicating whether the Sato-Tate group satisfies the rationality axiom (currently always True)'}, 'name': 'rational', 'table_id': 19}, 'c_name'], [{'_id': 317, 'data': {'type': 'list of pairs [*name*,*value_list*]', 'example': None, 'description': 'where *x* is a class function (*a_n* denotes the nth elementary symmetric function of the eigenvalues and *s_n* denotes the nth power sum), and *value_list* is a list of pairs [_v_,_n_] where _v_ is an integer value and _n_ is the number of components for which _x_=_v_.'}, 'name': 'counts', 'table_id': 19}, 'c_name'], [{'_id': 318, 'data': {'type': None, 'example': None, 'description': 'pretty-print version of name in latex math mode'}, 'name': 'pretty', 'table_id': 19}, 'c_name'], [{'_id': 319, 'data': {'type': 'GAP id string', 'example': None, 'description': "encoded as GAP id string '_a_._b_', where _a_ and _b_ are integers; _a_ is the order of the group and _b_ distinguishes groups of the same order"}, 'name': 'component_group', 'table_id': 19}, 'c_name'], [{'_id': 320, 'data': {'type': None, 'example': None, 'description': 'list of labels of maximal proper subgroups'}, 'name': 'subgroups', 'table_id': 19}, 'c_name']]], ['gps_sato_tate0', 20, [[{'_id': 321, 'data': {'type': '(latex math mode string)', 'example': None, 'description': 'mathematical description of the identity component as a set of d-by-d matrices'}, 'name': 'description', 'table_id': 20}, 'c_name'], [{'_id': 322, 'data': {'type': None, 'example': None, 'description': 'degree of the corresponding Sato-Tate group (positive integer)'}, 'name': 'degree', 'table_id': 20}, 'c_name'], [{'_id': 323, 'data': {'type': None, 'example': None, 'description': 'label of the identity component, currently of the form w.d.r, where w is the weight, d is the degree, and r is the real dimension (this is sufficient to uniquely identify the identity component for w=1 and d=0,2,4) but in other cases more information will be required (so the label format may need to vary with w and d).'}, 'name': 'label', 'table_id': 20}, 'c_name'], [{'_id': 324, 'data': {'type': None, 'example': None, 'description': 'pretty-print version of the name in latex math mode'}, 'name': 'pretty', 'table_id': 20}, 'c_name'], [{'_id': 325, 'data': {'type': None, 'example': None, 'description': 'dimension of the identity component as a connected compact real Lie group (positive integer)'}, 'name': 'real_dimension', 'table_id': 20}, 'c_name'], [{'_id': 326, 'data': {'type': None, 'example': None, 'description': 'text name of the identity component, used for displaying in scrolled input boxes where latex is not supported'}, 'name': 'name', 'table_id': 20}, 'c_name']]], ['gps_small', 21, [[{'_id': 327, 'data': {'type': None, 'example': None, 'description': 'true if the group is perfect, false otherwise'}, 'name': 'perfect', 'table_id': 21}, 'c_name'], [{'_id': 328, 'data': {'type': None, 'example': None, 'description': 'true if the group is abelian, false otherwise'}, 'name': 'abelian', 'table_id': 21}, 'c_name'], [{'_id': 329, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'derived_group', 'table_id': 21}, 'c_name'], [{'_id': 330, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'exponent', 'table_id': 21}, 'c_name'], [{'_id': 331, 'data': {'type': None, 'example': None, 'description': 'text discription of the group'}, 'name': 'name', 'table_id': 21}, 'c_name'], [{'_id': 332, 'data': {'type': None, 'example': None, 'description': 'true if the group is cyclic, false otherwise'}, 'name': 'cyclic', 'table_id': 21}, 'c_name'], [{'_id': 333, 'data': {'type': None, 'example': None, 'description': 'true if the group is simple, false otherwise'}, 'name': 'simple', 'table_id': 21}, 'c_name'], [{'_id': 334, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'center', 'table_id': 21}, 'c_name'], [{'_id': 335, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'maximal_subgroups', 'table_id': 21}, 'c_name'], [{'_id': 336, 'data': {'type': None, 'example': None, 'description': ''}, 'name': 'abelian_quotient', 'table_id': 21}, 'c_name'], [{'_id': 337, 'data': {'type': None, 'example': None, 'description': "GAP ID encoded as a string u'N.n', where N is the order of the group and n distinguishes groups of the same order (as determined in GAP)."}, 'name': 'label', 'table_id': 21}, 'c_name'], [{'_id': 338, 'data': {'type': None, 'example': None, 'description': 'pretty-print version of the name in latex math mode'}, 'name': 'pretty', 'table_id': 21}, 'c_name'], [{'_id': 339, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'normal_subgroups', 'table_id': 21}, 'c_name'], [{'_id': 340, 'data': {'type': None, 'example': None, 'description': 'true if the group is solvable, false otherwise'}, 'name': 'solvable', 'table_id': 21}, 'c_name'], [{'_id': 341, 'data': {'type': None, 'example': None, 'description': 'order of the group (positive integer)'}, 'name': 'order', 'table_id': 21}, 'c_name'], [{'_id': 342, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'clases', 'table_id': 21}, 'c_name']]], ['gps_transitive', 22, [[{'_id': 343, 'data': {'type': None, 'example': None, 'description': '1 if the group is a subgroup of A_n, otherwise -1'}, 'name': 'parity', 'table_id': 22}, 'c_name'], [{'_id': 344, 'data': {'type': None, 'example': None, 'description': 'Whether or not the group is abelian: 1 if yes, 0 if no'}, 'name': 'ab', 'table_id': 22}, 'c_name'], [{'_id': 345, 'data': {'type': None, 'example': None, 'description': 'whether or not the permutation representation is primitive, 1 for yes, 0 for no'}, 'name': 'prim', 'table_id': 22}, 'c_name'], [{'_id': 346, 'data': {'type': None, 'example': None, 'description': 'the name given by gap (also used by pari, magma, sage, etc)'}, 'name': 'name', 'table_id': 22}, 'c_name'], [{'_id': 347, 'data': {'type': None, 'example': None, 'description': 'The gap id for the group, 0 if not known'}, 'name': 'gapid', 'table_id': 22}, 'c_name'], [{'_id': 348, 'data': {'type': 'comma separated list of integer stored as string', 'example': None, 'description': 'Gap id of the group as a pair [order, number], or empty string if it is not available'}, 'name': 'gapidfull', 'table_id': 22}, 'c_name'], [{'_id': 349, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'moddecompuniq', 'table_id': 22}, 'c_name'], [{'_id': 350, 'data': {'type': None, 'example': None, 'description': 'label is of the form nTt where n is the degree and t is the "t-number"'}, 'name': 'label', 'table_id': 22}, 'c_name'], [{'_id': 351, 'data': {'type': None, 'example': None, 'description': '1 if the group is cyclic, otherwise 0'}, 'name': 'cyc', 'table_id': 22}, 'c_name'], [{'_id': 352, 'data': {'type': None, 'example': None, 'description': 'number of arithmetically equivalent fields for number fields with this Galois group'}, 'name': 'arith_equiv', 'table_id': 22}, 'c_name'], [{'_id': 353, 'data': {'type': 'list of pairs [n,t]', 'example': None, 'description': 'Low degree resolvents, up to isomorphism, for the a field with this Galois group'}, 'name': 'resolve', 'table_id': 22}, 'c_name'], [{'_id': 354, 'data': {'type': None, 'example': None, 'description': 'the number of automorphisms a degree n field with this as its Galois group'}, 'name': 'auts', 'table_id': 22}, 'c_name'], [{'_id': 355, 'data': {'type': None, 'example': None, 'description': 'latex of a nicer name for this group'}, 'name': 'pretty', 'table_id': 22}, 'c_name'], [{'_id': 356, 'data': {'type': 'list of pairs [n,t]', 'example': None, 'description': 'if K is a degree n field with this Galois group, this gives other small degree fields with the same Galois closure, up to isomorphism, in terms of their Galois groups'}, 'name': 'repns', 'table_id': 22}, 'c_name'], [{'_id': 357, 'data': {'type': None, 'example': None, 'description': '1 if the group is solvable, otherwise 0'}, 'name': 'solv', 'table_id': 22}, 'c_name'], [{'_id': 358, 'data': {'type': None, 'example': None, 'description': 'the t-number, a standard index for conjugacy classes of subgroups of S_n'}, 'name': 't', 'table_id': 22}, 'c_name'], [{'_id': 359, 'data': {'type': None, 'example': None, 'description': 'the degree (n from S_n)'}, 'name': 'n', 'table_id': 22}, 'c_name'], [{'_id': 360, 'data': {'type': None, 'example': None, 'description': 'the size of the group'}, 'name': 'order', 'table_id': 22}, 'c_name'], [{'_id': 361, 'data': {'type': 'list of pairs [n,t]', 'example': None, 'description': ' if K is a degree n field with this Galois group, this gives the subfields up to isomorphism in terms of their Galois groups'}, 'name': 'subs', 'table_id': 22}, 'c_name']]], ['halfmf_forms', 23, [[{'_id': 362, 'data': {'type': None, 'example': None, 'description': 'dimension of the space'}, 'name': 'dim', 'table_id': 23}, 'c_name'], [{'_id': 363, 'data': {'type': None, 'example': None, 'description': 'double of the weight of the forms'}, 'name': 'weight', 'table_id': 23}, 'c_name'], [{'_id': 364, 'data': {'type': None, 'example': None, 'description': 'label of the characters appearing in the S0 subspace'}, 'name': 'thetas', 'table_id': 23}, 'c_name'], [{'_id': 365, 'data': {'type': None, 'example': None, 'description': 'Level'}, 'name': 'level', 'table_id': 23}, 'c_name'], [{'_id': 366, 'data': {'type': None, 'example': None, 'description': 'character label in the LMFDB notation'}, 'name': 'character', 'table_id': 23}, 'c_name'], [{'_id': 367, 'data': {'type': None, 'example': None, 'description': 'LMFDB label'}, 'name': 'label', 'table_id': 23}, 'c_name'], [{'_id': 368, 'data': {'type': None, 'example': None, 'description': 'dimension of the S0 subspace (see the shimura decomposition knowl http://beta.lmfdb.org/knowledge/show/mf.half_integral_weight.shimura_decomposition[here])'}, 'name': 'dimtheta', 'table_id': 23}, 'c_name'], [{'_id': 369, 'data': {'type': None, 'example': None, 'description': 'description of the subspace corresponding to the image of the shimura map. The entries of the dictionary contain the following fields:\n\n * *dim_image* (int) the dimension of the subspace given by the image\n\n * *half_forms* (list of lists of strings) the coefficients (algebraic integers) of the q-expansions of the half integral weight newforms in the image\n\n * *mf_label* (string) the label of the classical newform which is mapped into this space of half integral weight cuspforms\n\n * *nf_label* (string) the label of the number field where the coefficients of the q-expansion belong to (this will be changed into the list of coefficients of a polynomial)'}, 'name': 'newpart', 'table_id': 23}, 'c_name']]], ['hecke_algebras', 24, [[{'_id': 370, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 24}, 'c_name'], [{'_id': 371, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'num_orbits', 'table_id': 24}, 'c_name'], [{'_id': 372, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'weight', 'table_id': 24}, 'c_name'], [{'_id': 373, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'level', 'table_id': 24}, 'c_name']]], ['hecke_ladic', 25, [[{'_id': 374, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'index', 'table_id': 25}, 'c_name'], [{'_id': 375, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'weight', 'table_id': 25}, 'c_name'], [{'_id': 376, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'ell', 'table_id': 25}, 'c_name'], [{'_id': 377, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'level', 'table_id': 25}, 'c_name'], [{'_id': 378, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label_l', 'table_id': 25}, 'c_name'], [{'_id': 379, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'operators', 'table_id': 25}, 'c_name'], [{'_id': 380, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'idempotent', 'table_id': 25}, 'c_name'], [{'_id': 381, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'field', 'table_id': 25}, 'c_name'], [{'_id': 382, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'orbit_label', 'table_id': 25}, 'c_name'], [{'_id': 383, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'num_charpoly_ql', 'table_id': 25}, 'c_name'], [{'_id': 384, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'properties', 'table_id': 25}, 'c_name'], [{'_id': 385, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'structure', 'table_id': 25}, 'c_name']]], ['hecke_orbits', 26, [[{'_id': 386, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'disc_fac', 'table_id': 26}, 'c_name'], [{'_id': 387, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Zbasis', 'table_id': 26}, 'c_name'], [{'_id': 388, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'weight', 'table_id': 26}, 'c_name'], [{'_id': 389, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'discriminant', 'table_id': 26}, 'c_name'], [{'_id': 390, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Qalg_gen', 'table_id': 26}, 'c_name'], [{'_id': 391, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'parent_label', 'table_id': 26}, 'c_name'], [{'_id': 392, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'orbit', 'table_id': 26}, 'c_name'], [{'_id': 393, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'hecke_op', 'table_id': 26}, 'c_name'], [{'_id': 394, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'orbit_label', 'table_id': 26}, 'c_name'], [{'_id': 395, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Qbasis', 'table_id': 26}, 'c_name'], [{'_id': 396, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'level', 'table_id': 26}, 'c_name'], [{'_id': 397, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'num_hecke_op', 'table_id': 26}, 'c_name']]], ['hgcwa_passports', 27, [[{'_id': 398, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'ndim', 'table_id': 27}, 'c_name'], [{'_id': 399, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'jacobian_decomp', 'table_id': 27}, 'c_name'], [{'_id': 400, 'data': {'type': None, 'example': None, 'description': 'ordered pair of positive integers where first number is which refined passport and second is which generating vector for that conjugacy class list'}, 'name': 'cc', 'table_id': 27}, 'c_name'], [{'_id': 401, 'data': {'type': None, 'example': None, 'description': 'group id for the full automorphism group for this family, as string representing a pair of integers encoding the GAP/Magma group id'}, 'name': 'full_auto', 'table_id': 27}, 'c_name'], [{'_id': 402, 'data': {'type': None, 'example': None, 'description': "label for the passport (numbered by conjugacy class), string of form 'g.a-b.g0.m1-m2-...-mr.x' where x is a positive integer representing the conjugacy class list, and assigned when the data is initially generated by increasing numeric values of the conjugacy classes"}, 'name': 'passport_label', 'table_id': 27}, 'c_name'], [{'_id': 403, 'data': {'type': None, 'example': None, 'description': 'automorphism group, string representing a pair of integers encoding the GAP/Magma group id'}, 'name': 'group', 'table_id': 27}, 'c_name'], [{'_id': 404, 'data': {'type': None, 'example': None, 'description': 'signature of full action, a string representing a list of positive integers for the action of the full automorphism group of this family'}, 'name': 'signH', 'table_id': 27}, 'c_name'], [{'_id': 405, 'data': {'type': None, 'example': None, 'description': "label for whole family, string of form 'g.a-b.g0.m1-m2-...-mr' where g is genus, a-b is group, g0 is quotient genus, and m1, ..., mr are remaining r entries in signature"}, 'name': 'label', 'table_id': 27}, 'c_name'], [{'_id': 406, 'data': {'type': None, 'example': None, 'description': 'hyperelliptic involution (if hyperelliptic), stored as list of positive integers representing a permutation'}, 'name': 'hyp_involution', 'table_id': 27}, 'c_name'], [{'_id': 407, 'data': {'type': None, 'example': None, 'description': 'label for full automorphism group, in same form as label but for full automorphism group data'}, 'name': 'full_label', 'table_id': 27}, 'c_name'], [{'_id': 408, 'data': {'type': None, 'example': None, 'description': 'string representing an equation for the family, given in LaTeX notation'}, 'name': 'eqn', 'table_id': 27}, 'c_name'], [{'_id': 409, 'data': {'type': None, 'example': None, 'description': 'trigonal automorphism (if cyclic trigonal), sotred as a list of positive intgers representing a permutation'}, 'name': 'cinv', 'table_id': 27}, 'c_name'], [{'_id': 410, 'data': {'type': None, 'example': None, 'description': 'True/False whether curve is hyperelliptic'}, 'name': 'hyperelliptic', 'table_id': 27}, 'c_name'], [{'_id': 411, 'data': {'type': None, 'example': None, 'description': 'generating vector for this action, stored as r lists of positive integers representing permutations'}, 'name': 'gen_vectors', 'table_id': 27}, 'c_name'], [{'_id': 412, 'data': {'type': None, 'example': None, 'description': "label including which generating vector, string of form 'g.a-b.g0.m1-m2-...-mr.x.y' where y is a positive integer representing the particular generating vector for a given refined passport, the value is assigned when the data is initially generated in the order the generating vectors are found"}, 'name': 'total_label', 'table_id': 27}, 'c_name'], [{'_id': 413, 'data': {'type': None, 'example': None, 'description': 'quotient genus, this is a non-negative integer'}, 'name': 'g0', 'table_id': 27}, 'c_name'], [{'_id': 414, 'data': {'type': None, 'example': None, 'description': 'dimension of the family of curves, this is a non-negative integer'}, 'name': 'dim', 'table_id': 27}, 'c_name'], [{'_id': 415, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'group_order', 'table_id': 27}, 'c_name'], [{'_id': 416, 'data': {'type': None, 'example': None, 'description': 'True/False whether curve is cyclic trigonal'}, 'name': 'cyclic_trigonal', 'table_id': 27}, 'c_name'], [{'_id': 417, 'data': {'type': None, 'example': None, 'description': 'number of branch points of the cover, positive integer'}, 'name': 'r', 'table_id': 27}, 'c_name'], [{'_id': 418, 'data': {'type': None, 'example': None, 'description': 'a string representing a list of non-negative integers [g0,m1,...,mr] where g0 is the quotient genus, and the mi represent the orders of the generators of the monodromy group'}, 'name': 'signature', 'table_id': 27}, 'c_name'], [{'_id': 419, 'data': {'type': None, 'example': None, 'description': 'genus of the family of curves, this is a positive integer > 1'}, 'name': 'genus', 'table_id': 27}, 'c_name'], [{'_id': 420, 'data': {'type': None, 'example': None, 'description': 'list of conjugacy classes where the action for this particular refined passport occurs, stored as a string representing a list of positive integers'}, 'name': 'con', 'table_id': 27}, 'c_name']]], ['hgm_families', 28, [[{'_id': 421, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'snf', 'table_id': 28}, 'c_name'], [{'_id': 422, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu2rev', 'table_id': 28}, 'c_name'], [{'_id': 423, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'weight', 'table_id': 28}, 'c_name'], [{'_id': 424, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A5rev', 'table_id': 28}, 'c_name'], [{'_id': 425, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au3rev', 'table_id': 28}, 'c_name'], [{'_id': 426, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Arev', 'table_id': 28}, 'c_name'], [{'_id': 427, 'data': {'type': None, 'example': None, 'description': 'A test description'}, 'name': 'A', 'table_id': 28}, 'c_name'], [{'_id': 428, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A7', 'table_id': 28}, 'c_name'], [{'_id': 429, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au2rev', 'table_id': 28}, 'c_name'], [{'_id': 430, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A2rev', 'table_id': 28}, 'c_name'], [{'_id': 431, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 28}, 'c_name'], [{'_id': 432, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A3', 'table_id': 28}, 'c_name'], [{'_id': 433, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A2', 'table_id': 28}, 'c_name'], [{'_id': 434, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A5', 'table_id': 28}, 'c_name'], [{'_id': 435, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au7rev', 'table_id': 28}, 'c_name'], [{'_id': 436, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C3', 'table_id': 28}, 'c_name'], [{'_id': 437, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C2', 'table_id': 28}, 'c_name'], [{'_id': 438, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C7', 'table_id': 28}, 'c_name'], [{'_id': 439, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A7rev', 'table_id': 28}, 'c_name'], [{'_id': 440, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu3', 'table_id': 28}, 'c_name'], [{'_id': 441, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Cu7', 'table_id': 28}, 'c_name'], [{'_id': 442, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Cu5', 'table_id': 28}, 'c_name'], [{'_id': 443, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B', 'table_id': 28}, 'c_name'], [{'_id': 444, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Cu3', 'table_id': 28}, 'c_name'], [{'_id': 445, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Cu2', 'table_id': 28}, 'c_name'], [{'_id': 446, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'degree', 'table_id': 28}, 'c_name'], [{'_id': 447, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B3', 'table_id': 28}, 'c_name'], [{'_id': 448, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au3', 'table_id': 28}, 'c_name'], [{'_id': 449, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au2', 'table_id': 28}, 'c_name'], [{'_id': 450, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au5', 'table_id': 28}, 'c_name'], [{'_id': 451, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B3rev', 'table_id': 28}, 'c_name'], [{'_id': 452, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au7', 'table_id': 28}, 'c_name'], [{'_id': 453, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu7rev', 'table_id': 28}, 'c_name'], [{'_id': 454, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Brev', 'table_id': 28}, 'c_name'], [{'_id': 455, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B5rev', 'table_id': 28}, 'c_name'], [{'_id': 456, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B7rev', 'table_id': 28}, 'c_name'], [{'_id': 457, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'imprim', 'table_id': 28}, 'c_name'], [{'_id': 458, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu5rev', 'table_id': 28}, 'c_name'], [{'_id': 459, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu2', 'table_id': 28}, 'c_name'], [{'_id': 460, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'mono', 'table_id': 28}, 'c_name'], [{'_id': 461, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'det', 'table_id': 28}, 'c_name'], [{'_id': 462, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu7', 'table_id': 28}, 'c_name'], [{'_id': 463, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu5', 'table_id': 28}, 'c_name'], [{'_id': 464, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au5rev', 'table_id': 28}, 'c_name'], [{'_id': 465, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B5', 'table_id': 28}, 'c_name'], [{'_id': 466, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B7', 'table_id': 28}, 'c_name'], [{'_id': 467, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C5', 'table_id': 28}, 'c_name'], [{'_id': 468, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B2', 'table_id': 28}, 'c_name'], [{'_id': 469, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'bezout', 'table_id': 28}, 'c_name'], [{'_id': 470, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu3rev', 'table_id': 28}, 'c_name'], [{'_id': 471, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A3rev', 'table_id': 28}, 'c_name'], [{'_id': 472, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'famhodge', 'table_id': 28}, 'c_name'], [{'_id': 473, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B2rev', 'table_id': 28}, 'c_name']]], ['hgm_motives', 29, [[{'_id': 474, 'data': {'type': None, 'example': None, 'description': 'A test description'}, 'name': 'A', 'table_id': 29}, 'c_name'], [{'_id': 475, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu2rev', 'table_id': 29}, 'c_name'], [{'_id': 476, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'weight', 'table_id': 29}, 'c_name'], [{'_id': 477, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A5rev', 'table_id': 29}, 'c_name'], [{'_id': 478, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au3rev', 'table_id': 29}, 'c_name'], [{'_id': 479, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'sign', 'table_id': 29}, 'c_name'], [{'_id': 480, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Arev', 'table_id': 29}, 'c_name'], [{'_id': 481, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'centralval', 'table_id': 29}, 'c_name'], [{'_id': 482, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'cond', 'table_id': 29}, 'c_name'], [{'_id': 483, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A7', 'table_id': 29}, 'c_name'], [{'_id': 484, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au2rev', 'table_id': 29}, 'c_name'], [{'_id': 485, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A2rev', 'table_id': 29}, 'c_name'], [{'_id': 486, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'locinfo', 'table_id': 29}, 'c_name'], [{'_id': 487, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'req', 'table_id': 29}, 'c_name'], [{'_id': 488, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'hodge', 'table_id': 29}, 'c_name'], [{'_id': 489, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 29}, 'c_name'], [{'_id': 490, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C5', 'table_id': 29}, 'c_name'], [{'_id': 491, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A3', 'table_id': 29}, 'c_name'], [{'_id': 492, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A2', 'table_id': 29}, 'c_name'], [{'_id': 493, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A5', 'table_id': 29}, 'c_name'], [{'_id': 494, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au7rev', 'table_id': 29}, 'c_name'], [{'_id': 495, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C3', 'table_id': 29}, 'c_name'], [{'_id': 496, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C2', 'table_id': 29}, 'c_name'], [{'_id': 497, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C7', 'table_id': 29}, 'c_name'], [{'_id': 498, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A7rev', 'table_id': 29}, 'c_name'], [{'_id': 499, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Cu7', 'table_id': 29}, 'c_name'], [{'_id': 500, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Cu5', 'table_id': 29}, 'c_name'], [{'_id': 501, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B', 'table_id': 29}, 'c_name'], [{'_id': 502, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Cu3', 'table_id': 29}, 'c_name'], [{'_id': 503, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Cu2', 'table_id': 29}, 'c_name'], [{'_id': 504, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'degree', 'table_id': 29}, 'c_name'], [{'_id': 505, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au3', 'table_id': 29}, 'c_name'], [{'_id': 506, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au2', 'table_id': 29}, 'c_name'], [{'_id': 507, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au5', 'table_id': 29}, 'c_name'], [{'_id': 508, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B3rev', 'table_id': 29}, 'c_name'], [{'_id': 509, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au7', 'table_id': 29}, 'c_name'], [{'_id': 510, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu7rev', 'table_id': 29}, 'c_name'], [{'_id': 511, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Brev', 'table_id': 29}, 'c_name'], [{'_id': 512, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B5rev', 'table_id': 29}, 'c_name'], [{'_id': 513, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B7rev', 'table_id': 29}, 'c_name'], [{'_id': 514, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu5rev', 'table_id': 29}, 'c_name'], [{'_id': 515, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu2', 'table_id': 29}, 'c_name'], [{'_id': 516, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu3', 'table_id': 29}, 'c_name'], [{'_id': 517, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'sig', 'table_id': 29}, 'c_name'], [{'_id': 518, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu7', 'table_id': 29}, 'c_name'], [{'_id': 519, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu5', 'table_id': 29}, 'c_name'], [{'_id': 520, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Au5rev', 'table_id': 29}, 'c_name'], [{'_id': 521, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B5', 'table_id': 29}, 'c_name'], [{'_id': 522, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B7', 'table_id': 29}, 'c_name'], [{'_id': 523, 'data': {'type': None, 'example': None, 'description': None}, 'name': 't', 'table_id': 29}, 'c_name'], [{'_id': 524, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B2', 'table_id': 29}, 'c_name'], [{'_id': 525, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B3', 'table_id': 29}, 'c_name'], [{'_id': 526, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'coeffs', 'table_id': 29}, 'c_name'], [{'_id': 527, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Bu3rev', 'table_id': 29}, 'c_name'], [{'_id': 528, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A3rev', 'table_id': 29}, 'c_name'], [{'_id': 529, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'famhodge', 'table_id': 29}, 'c_name'], [{'_id': 530, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'B2rev', 'table_id': 29}, 'c_name'], [{'_id': 531, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'lcms', 'table_id': 29}, 'c_name']]], ['hmf_fields', 30, [[{'_id': 532, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'degree', 'table_id': 30}, 'c_name'], [{'_id': 534, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'label', 'table_id': 30}, 'c_name'], [{'_id': 535, 'data': {'type': "List(List(Poly('w', Z)))", 'example': None, 'description': None}, 'name': 'ideals', 'table_id': 30}, 'c_name'], [{'_id': 536, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'narrow_class_no', 'table_id': 30}, 'c_name'], [{'_id': 537, 'data': {'type': "List(List(Poly('w', Z)))", 'example': None, 'description': None}, 'name': 'primes', 'table_id': 30}, 'c_name'], [{'_id': 533, 'data': {'type': 'Z', 'example': None, 'description': 'field discriminant '}, 'name': 'discriminant', 'table_id': 30}, 'c_name']]], ['hmf_forms', 31, [[{'_id': 538, 'data': {'type': 'Boolean', 'example': None, 'description': None}, 'name': 'is_base_change', 'table_id': 31}, 'c_name'], [{'_id': 539, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'weight', 'table_id': 31}, 'c_name'], [{'_id': 540, 'data': {'type': 'Boolean', 'example': None, 'description': None}, 'name': 'is_CM', 'table_id': 31}, 'c_name'], [{'_id': 541, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'label_suffix', 'table_id': 31}, 'c_name'], [{'_id': 542, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'label', 'table_id': 31}, 'c_name'], [{'_id': 543, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'field_label', 'table_id': 31}, 'c_name'], [{'_id': 544, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'level_norm', 'table_id': 31}, 'c_name'], [{'_id': 545, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'disc', 'table_id': 31}, 'c_name'], [{'_id': 546, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'deg', 'table_id': 31}, 'c_name'], [{'_id': 547, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'short_label', 'table_id': 31}, 'c_name'], [{'_id': 548, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'level_label', 'table_id': 31}, 'c_name'], [{'_id': 549, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'label_nsuffix', 'table_id': 31}, 'c_name'], [{'_id': 550, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'dimension', 'table_id': 31}, 'c_name'], [{'_id': 551, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'parallel_weight', 'table_id': 31}, 'c_name'], [{'_id': 552, 'data': {'type': "List(Poly(Q, 'w'))", 'example': None, 'description': None}, 'name': 'level_ideal', 'table_id': 31}, 'c_name']]], ['hmf_hecke', 32, [[{'_id': 553, 'data': {'type': "Poly('x', Z)", 'example': None, 'description': None}, 'name': 'hecke_polynomial', 'table_id': 32}, 'c_name'], [{'_id': 554, 'data': {'type': "List(List(Poly('w', Z)*Z))", 'example': None, 'description': None}, 'name': 'AL_eigenvalues', 'table_id': 32}, 'c_name'], [{'_id': 555, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'hecke_eigenvalues', 'table_id': 32}, 'c_name'], [{'_id': 556, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'label', 'table_id': 32}, 'c_name']]], ['inv_dbs', 33, [[{'_id': 557, 'data': {'type': None, 'example': None, 'description': None}, 'name': '_id', 'table_id': 33}, 'c_name'], [{'_id': 558, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'name', 'table_id': 33}, 'c_name'], [{'_id': 559, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'nice_name', 'table_id': 33}, 'c_name']]], ['inv_fields_auto', 34, [[{'_id': 560, 'data': {'type': None, 'example': None, 'description': None}, 'name': '_id', 'table_id': 34}, 'c_name'], [{'_id': 561, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'table_id', 'table_id': 34}, 'c_name'], [{'_id': 562, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'name', 'table_id': 34}, 'c_name'], [{'_id': 563, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'data', 'table_id': 34}, 'c_name']]], ['inv_fields_human', 35, [[{'_id': 564, 'data': {'type': None, 'example': None, 'description': None}, 'name': '_id', 'table_id': 35}, 'c_name'], [{'_id': 565, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'table_id', 'table_id': 35}, 'c_name'], [{'_id': 566, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'name', 'table_id': 35}, 'c_name'], [{'_id': 567, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'data', 'table_id': 35}, 'c_name']]], ['inv_ops', 36, [[{'_id': 568, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'time', 'table_id': 36}, 'c_name'], [{'_id': 569, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'isa', 'table_id': 36}, 'c_name'], [{'_id': 570, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'running', 'table_id': 36}, 'c_name'], [{'_id': 571, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'complete', 'table_id': 36}, 'c_name'], [{'_id': 572, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'uid', 'table_id': 36}, 'c_name'], [{'_id': 573, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'db_id', 'table_id': 36}, 'c_name'], [{'_id': 574, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'table_id', 'table_id': 36}, 'c_name'], [{'_id': 575, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'report', 'table_id': 36}, 'c_name'], [{'_id': 576, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'orphans', 'table_id': 36}, 'c_name'], [{'_id': 577, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'lockout', 'table_id': 36}, 'c_name']]], ['inv_rollback', 37, [[{'_id': 578, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'diff', 'table_id': 37}, 'c_name']]], ['inv_tables', 38, [[{'_id': 579, 'data': {'type': None, 'example': None, 'description': None}, 'name': '_id', 'table_id': 38}, 'c_name'], [{'_id': 580, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'db_id', 'table_id': 38}, 'c_name'], [{'_id': 581, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'name', 'table_id': 38}, 'c_name'], [{'_id': 582, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'nice_name', 'table_id': 38}, 'c_name'], [{'_id': 583, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'INFO', 'table_id': 38}, 'c_name'], [{'_id': 584, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'scan_date', 'table_id': 38}, 'c_name'], [{'_id': 585, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'status', 'table_id': 38}, 'c_name'], [{'_id': 586, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'NOTES', 'table_id': 38}, 'c_name']]], ['lat_lattices', 39, [[{'_id': 587, 'data': {'type': None, 'example': None, 'description': 'dimension of a lattice'}, 'name': 'dim', 'table_id': 39}, 'c_name'], [{'_id': 588, 'data': {'type': None, 'example': None, 'description': 'list of known names of a given lattice'}, 'name': 'name', 'table_id': 39}, 'c_name'], [{'_id': 589, 'data': {'type': None, 'example': None, 'description': 'part of the *label* which is completely deterministic'}, 'name': 'base_label', 'table_id': 39}, 'c_name'], [{'_id': 590, 'data': {'type': None, 'example': None, 'description': 'density of a lattice'}, 'name': 'density', 'table_id': 39}, 'c_name'], [{'_id': 591, 'data': {'type': None, 'example': None, 'description': 'coefficients of the q-expansion of the theta series associated to a lattice (for the Leech lattice it is a list of strings)'}, 'name': 'theta_series', 'table_id': 39}, 'c_name'], [{'_id': 592, 'data': {'type': None, 'example': None, 'description': 'Hermite number of a lattice'}, 'name': 'hermite', 'table_id': 39}, 'c_name'], [{'_id': 593, 'data': {'type': None, 'example': None, 'description': 'list of genus representatives (matrices)'}, 'name': 'genus_reps', 'table_id': 39}, 'c_name'], [{'_id': 594, 'data': {'type': None, 'example': None, 'description': 'determinant of a lattice'}, 'name': 'det', 'table_id': 39}, 'c_name'], [{'_id': 595, 'data': {'type': None, 'example': None, 'description': 'comments and historical remarks'}, 'name': 'comments', 'table_id': 39}, 'c_name'], [{'_id': 596, 'data': {'type': None, 'example': None, 'description': 'LMFDB label of a lattice'}, 'name': 'label', 'table_id': 39}, 'c_name'], [{'_id': 597, 'data': {'type': None, 'example': None, 'description': 'length of the shortest vector'}, 'name': 'minimum', 'table_id': 39}, 'c_name'], [{'_id': 598, 'data': {'type': None, 'example': None, 'description': 'index of a lattice'}, 'name': 'index', 'table_id': 39}, 'c_name'], [{'_id': 599, 'data': {'type': None, 'example': None, 'description': 'size of automorphism group'}, 'name': 'aut', 'table_id': 39}, 'c_name'], [{'_id': 600, 'data': {'type': None, 'example': None, 'description': 'Kissing number of a lattice'}, 'name': 'kissing', 'table_id': 39}, 'c_name'], [{'_id': 601, 'data': {'type': None, 'example': None, 'description': 'level of a lattice'}, 'name': 'level', 'table_id': 39}, 'c_name'], [{'_id': 602, 'data': {'type': None, 'example': None, 'description': 'class number or genus of a lattice'}, 'name': 'class_number', 'table_id': 39}, 'c_name'], [{'_id': 603, 'data': {'type': None, 'example': None, 'description': 'list of shortest vectors (for the Leech lattice it is a list of strings)'}, 'name': 'shortest', 'table_id': 39}, 'c_name'], [{'_id': 604, 'data': {'type': None, 'example': None, 'description': 'Gram matrix of a lattice'}, 'name': 'gram', 'table_id': 39}, 'c_name']]], ['lf_fields', 40, [[{'_id': 605, 'data': {'type': 'Z', 'example': None, 'description': 'the T-number for the Galois group'}, 'name': 'galT', 'table_id': 40}, 'c_name'], [{'_id': 606, 'data': {'type': 'String', 'example': None, 'description': 'label'}, 'name': 'label', 'table_id': 40}, 'c_name'], [{'_id': 607, 'data': {'type': 'List(Z)', 'example': None, 'description': 'root field'}, 'name': 'rf', 'table_id': 40}, 'c_name'], [{'_id': 608, 'data': {'type': 'Z', 'example': None, 'description': 'number of automorphisms of the field'}, 'name': 'aut', 'table_id': 40}, 'c_name'], [{'_id': 609, 'data': {'type': 'Z', 'example': None, 'description': 'Galois mean slope'}, 'name': 'gms', 'table_id': 40}, 'c_name'], [{'_id': 610, 'data': {'type': 'List(Q)', 'example': None, 'description': 'wild ramification slopes'}, 'name': 'slopes', 'table_id': 40}, 'c_name'], [{'_id': 611, 'data': {'type': 'List(List(Z)*Z)', 'example': None, 'description': None}, 'name': 'subfields', 'table_id': 40}, 'c_name'], [{'_id': 612, 'data': {'type': 'Q', 'example': None, 'description': None}, 'name': 'top_slope', 'table_id': 40}, 'c_name'], [{'_id': 613, 'data': {'type': 'String', 'example': None, 'description': 'Hasse-Witt invariant as a string'}, 'name': 'hw', 'table_id': 40}, 'c_name'], [{'_id': 614, 'data': {'type': 'List(Z)', 'example': None, 'description': 'the Galois group [n, t] for nTt'}, 'name': 'gal', 'table_id': 40}, 'c_name'], [{'_id': 615, 'data': {'type': 'String*List(Z)', 'example': None, 'description': 'inertia subgroup'}, 'name': 'inertia', 'table_id': 40}, 'c_name'], [{'_id': 616, 'data': {'type': 'Z', 'example': None, 'description': 'valuation of the discriminant'}, 'name': 'c', 'table_id': 40}, 'c_name'], [{'_id': 617, 'data': {'type': 'Z', 'example': None, 'description': 'ramification degree'}, 'name': 'e', 'table_id': 40}, 'c_name'], [{'_id': 618, 'data': {'type': 'Z', 'example': None, 'description': 'residue field degree'}, 'name': 'f', 'table_id': 40}, 'c_name'], [{'_id': 619, 'data': {'type': "Poly('t', Z)", 'example': None, 'description': 'polynomial defining maximal unramified subfield'}, 'name': 'unram', 'table_id': 40}, 'c_name'], [{'_id': 620, 'data': {'type': 'Z', 'example': None, 'description': 'degree'}, 'name': 'n', 'table_id': 40}, 'c_name'], [{'_id': 621, 'data': {'type': 'Z', 'example': None, 'description': 'prime p for the base \\Q_p'}, 'name': 'p', 'table_id': 40}, 'c_name'], [{'_id': 622, 'data': {'type': 'Z', 'example': None, 'description': 'degree of maximal unramified subfield of the Galois closure'}, 'name': 'u', 'table_id': 40}, 'c_name'], [{'_id': 623, 'data': {'type': 'Z', 'example': None, 'description': 'tame degree for the Galois closure'}, 'name': 't', 'table_id': 40}, 'c_name'], [{'_id': 624, 'data': {'type': 'List(Z)', 'example': None, 'description': 'coefficients of a defining polynomial, starting with the constant term'}, 'name': 'coeffs', 'table_id': 40}, 'c_name'], [{'_id': 625, 'data': {'type': "Poly('y', Z)", 'example': None, 'description': 'Eisenstein polynomial defining relative extension of this field over the maxmial unramified subfield'}, 'name': 'eisen', 'table_id': 40}, 'c_name'], [{'_id': 626, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'gsm', 'table_id': 40}, 'c_name']]], ['lfunc_instances', 41, [[{'_id': 627, 'data': {'type': None, 'example': None, 'description': 'lookup by object homepage URL'}, 'name': 'url', 'table_id': 41}, 'c_name'], [{'_id': 628, 'data': {'type': None, 'example': None, 'description': 'lookup by L-function hash (used to find all objects with the same L-function)'}, 'name': 'Lhash', 'table_id': 41}, 'c_name'], [{'_id': 629, 'data': {'type': None, 'example': None, 'description': 'used to filter instances by type'}, 'name': 'type', 'table_id': 41}, 'c_name']]], ['lfunc_lfunctions', 42, [[{'_id': 684, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'coefficient_field', 'table_id': 42}, 'c_name'], [{'_id': 630, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'origin', 'table_id': 42}, 'c_name'], [{'_id': 631, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'primitive', 'table_id': 42}, 'c_name'], [{'_id': 632, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'conductor', 'table_id': 42}, 'c_name'], [{'_id': 633, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'central_character', 'table_id': 42}, 'c_name'], [{'_id': 634, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'load_key', 'table_id': 42}, 'c_name'], [{'_id': 635, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'self_dual', 'table_id': 42}, 'c_name'], [{'_id': 636, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a9', 'table_id': 42}, 'c_name'], [{'_id': 637, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'motivic_weight', 'table_id': 42}, 'c_name'], [{'_id': 638, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'conjugate', 'table_id': 42}, 'c_name'], [{'_id': 639, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'types', 'table_id': 42}, 'c_name'], [{'_id': 640, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Lhash', 'table_id': 42}, 'c_name'], [{'_id': 641, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'symmetry_type', 'table_id': 42}, 'c_name'], [{'_id': 642, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'group', 'table_id': 42}, 'c_name'], [{'_id': 643, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'degree', 'table_id': 42}, 'c_name'], [{'_id': 644, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'st_group', 'table_id': 42}, 'c_name'], [{'_id': 645, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'plot_delta', 'table_id': 42}, 'c_name'], [{'_id': 646, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'selfdual', 'table_id': 42}, 'c_name'], [{'_id': 647, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'analytic_normalization', 'table_id': 42}, 'c_name'], [{'_id': 648, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A3', 'table_id': 42}, 'c_name'], [{'_id': 649, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'euler_factors', 'table_id': 42}, 'c_name'], [{'_id': 650, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A5', 'table_id': 42}, 'c_name'], [{'_id': 651, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A4', 'table_id': 42}, 'c_name'], [{'_id': 652, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A7', 'table_id': 42}, 'c_name'], [{'_id': 653, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A6', 'table_id': 42}, 'c_name'], [{'_id': 654, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A9', 'table_id': 42}, 'c_name'], [{'_id': 655, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A8', 'table_id': 42}, 'c_name'], [{'_id': 656, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'z3', 'table_id': 42}, 'c_name'], [{'_id': 657, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A2', 'table_id': 42}, 'c_name'], [{'_id': 658, 'data': {'type': None, 'example': None, 'description': ' '}, 'name': 'accuracy', 'table_id': 42}, 'c_name'], [{'_id': 659, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'order_of_vanishing', 'table_id': 42}, 'c_name'], [{'_id': 660, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'bad_lfactors', 'table_id': 42}, 'c_name'], [{'_id': 661, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a10', 'table_id': 42}, 'c_name'], [{'_id': 662, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'sign_arg', 'table_id': 42}, 'c_name'], [{'_id': 663, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'plot_values', 'table_id': 42}, 'c_name'], [{'_id': 664, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'precision', 'table_id': 42}, 'c_name'], [{'_id': 665, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'algebraic', 'table_id': 42}, 'c_name'], [{'_id': 666, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a3', 'table_id': 42}, 'c_name'], [{'_id': 667, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a2', 'table_id': 42}, 'c_name'], [{'_id': 668, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a5', 'table_id': 42}, 'c_name'], [{'_id': 669, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a4', 'table_id': 42}, 'c_name'], [{'_id': 670, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a7', 'table_id': 42}, 'c_name'], [{'_id': 671, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a6', 'table_id': 42}, 'c_name'], [{'_id': 672, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'coeff_info', 'table_id': 42}, 'c_name'], [{'_id': 673, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a8', 'table_id': 42}, 'c_name'], [{'_id': 674, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'leading_term', 'table_id': 42}, 'c_name'], [{'_id': 675, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'z1', 'table_id': 42}, 'c_name'], [{'_id': 676, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'z2', 'table_id': 42}, 'c_name'], [{'_id': 677, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A10', 'table_id': 42}, 'c_name'], [{'_id': 678, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'root_number', 'table_id': 42}, 'c_name'], [{'_id': 679, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'positive_zeros', 'table_id': 42}, 'c_name'], [{'_id': 680, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'credit', 'table_id': 42}, 'c_name'], [{'_id': 681, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'gamma_factors', 'table_id': 42}, 'c_name'], [{'_id': 682, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'values', 'table_id': 42}, 'c_name'], [{'_id': 683, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dirichlet_coefficients', 'table_id': 42}, 'c_name']]], ['lfunc_zeros', 43, [[{'_id': 685, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'degree', 'table_id': 43}, 'c_name'], [{'_id': 686, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'level', 'table_id': 43}, 'c_name'], [{'_id': 687, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'signature', 'table_id': 43}, 'c_name'], [{'_id': 688, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'first_zero', 'table_id': 43}, 'c_name'], [{'_id': 689, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'description', 'table_id': 43}, 'c_name'], [{'_id': 690, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'coeffs', 'table_id': 43}, 'c_name'], [{'_id': 691, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'eta', 'table_id': 43}, 'c_name'], [{'_id': 692, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'mu', 'table_id': 43}, 'c_name'], [{'_id': 693, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'special', 'table_id': 43}, 'c_name']]], ['mf_gamma1_subspaces', 44, [[{'_id': 694, 'data': {'type': 'integer', 'description': 'level N of the cuspidal space S_k(Gamma_1(N))'}, 'name': 'level', 'table_id': 44}, 'c_name'], [{'_id': 694, 'data': {'type': 'integer', 'description': 'level N of the cuspidal space S_k(Gamma_1(N))'}, 'name': 'level', 'table_id': 44}, 'example'], [{'_id': 695, 'data': {'type': 'smallint', 'description': 'weight k of the cuspidal space S_k(Gamma_1(N))'}, 'name': 'weight', 'table_id': 44}, 'c_name'], [{'_id': 695, 'data': {'type': 'smallint', 'description': 'weight k of the cuspidal space S_k(Gamma_1(N))'}, 'name': 'weight', 'table_id': 44}, 'example'], [{'_id': 696, 'data': {'type': 'integer', 'description': 'dimension of S_k(Gamma_1(N))'}, 'name': 'dim', 'table_id': 44}, 'c_name'], [{'_id': 696, 'data': {'type': 'integer', 'description': 'dimension of S_k(Gamma_1(N))'}, 'name': 'dim', 'table_id': 44}, 'example'], [{'_id': 697, 'data': {'type': 'integer', 'description': 'level M of the newspace S_k^{new}(Gamma_1(M)) that embed in S^k(Gamma_1(N))'}, 'name': 'sub_level', 'table_id': 44}, 'c_name'], [{'_id': 697, 'data': {'type': 'integer', 'description': 'level M of the newspace S_k^{new}(Gamma_1(M)) that embed in S^k(Gamma_1(N))'}, 'name': 'sub_level', 'table_id': 44}, 'example'], [{'_id': 698, 'data': {'type': 'integer', 'description': 'dimension of S_k^{new}(Gamma_1(M))'}, 'name': 'sub_dim', 'table_id': 44}, 'c_name'], [{'_id': 698, 'data': {'type': 'integer', 'description': 'dimension of S_k^{new}(Gamma_1(M))'}, 'name': 'sub_dim', 'table_id': 44}, 'example'], [{'_id': 699, 'data': {'type': 'integer', 'description': 'multiplicity of S_k^{new}(Gamma_1(M)) as a direct summand of S_k^{Gamma_1(N)). Summing dimensions of embedded newspaces S_k^{new}(Gamma_1(M)) with multiplicity gives the dimension of the cusp space S_k(Gamma_1(N).'}, 'name': 'sub_mult', 'table_id': 44}, 'c_name'], [{'_id': 699, 'data': {'type': 'integer', 'description': 'multiplicity of S_k^{new}(Gamma_1(M)) as a direct summand of S_k^{Gamma_1(N)). Summing dimensions of embedded newspaces S_k^{new}(Gamma_1(M)) with multiplicity gives the dimension of the cusp space S_k(Gamma_1(N).'}, 'name': 'sub_mult', 'table_id': 44}, 'example']]], ['mf_hecke_cc', 45, [[{'_id': 700, 'data': {'type': 'bigint', 'description': 'encoding of the tuple (N.k.i.x) into 64 bits'}, 'name': 'hecke_orbit_code', 'table_id': 45}, 'c_name'], [{'_id': 700, 'data': {'type': 'bigint', 'description': 'encoding of the tuple (N.k.i.x) into 64 bits'}, 'name': 'hecke_orbit_code', 'table_id': 45}, 'example'], [{'_id': 701, 'data': {'type': 'integer', 'description': 'enumeration of which embedding (shows up in L-function link) for the given conrey label'}, 'name': 'embedding_index', 'table_id': 45}, 'c_name'], [{'_id': 701, 'data': {'type': 'integer', 'description': 'enumeration of which embedding (shows up in L-function link) for the given conrey label'}, 'name': 'embedding_index', 'table_id': 45}, 'example'], [{'_id': 702, 'data': {'type': 'jsonb', 'description': 'list of pairs [x,y] of doubles x, y so that `a_n = x + iy`'}, 'name': 'an', 'table_id': 45}, 'c_name'], [{'_id': 702, 'data': {'type': 'jsonb', 'description': 'list of pairs [x,y] of doubles x, y so that `a_n = x + iy`'}, 'name': 'an', 'table_id': 45}, 'example'], [{'_id': 703, 'data': {'type': 'jsonb', 'description': 'list of pairs [p, `\\theta_p`] where `a_p = p^{(k-1)/2} (e^{2\\pi i \\theta_p} + chi(p)e^{-2\\pi i \\theta_p})`; it will range over good primes p, with `\\theta_p` between -0.5 and 0.5'}, 'name': 'angles', 'table_id': 45}, 'c_name'], [{'_id': 703, 'data': {'type': 'jsonb', 'description': 'list of pairs [p, `\\theta_p`] where `a_p = p^{(k-1)/2} (e^{2\\pi i \\theta_p} + chi(p)e^{-2\\pi i \\theta_p})`; it will range over good primes p, with `\\theta_p` between -0.5 and 0.5'}, 'name': 'angles', 'table_id': 45}, 'example'], [{'_id': 704, 'data': {'type': 'text', 'description': '(N.k.c.x.n) where N.c is the Conrey label of the restriction to the cyclotomic field and n enumerates the embeddings with the same character (starting at 1)'}, 'name': 'lfunction_label', 'table_id': 45}, 'c_name'], [{'_id': 704, 'data': {'type': 'text', 'description': '(N.k.c.x.n) where N.c is the Conrey label of the restriction to the cyclotomic field and n enumerates the embeddings with the same character (starting at 1)'}, 'name': 'lfunction_label', 'table_id': 45}, 'example'], [{'_id': 705, 'data': {'type': 'integer', 'description': 'the Conrey label for the restriction of the embedding to the character field'}, 'name': 'conrey_label', 'table_id': 45}, 'c_name'], [{'_id': 705, 'data': {'type': 'integer', 'description': 'the Conrey label for the restriction of the embedding to the character field'}, 'name': 'conrey_label', 'table_id': 45}, 'example'], [{'_id': 706, 'data': {'type': 'real', 'description': 'real part of the root corresponding to this embedding'}, 'name': 'embedding_root_real', 'table_id': 45}, 'c_name'], [{'_id': 706, 'data': {'type': 'real', 'description': 'real part of the root corresponding to this embedding'}, 'name': 'embedding_root_real', 'table_id': 45}, 'example'], [{'_id': 707, 'data': {'type': 'real', 'description': 'imaginary part of the root corresponding to this embedding'}, 'name': 'embedding_root_imag', 'table_id': 45}, 'c_name'], [{'_id': 707, 'data': {'type': 'real', 'description': 'imaginary part of the root corresponding to this embedding'}, 'name': 'embedding_root_imag', 'table_id': 45}, 'example']]], ['mf_hecke_nf', 46, [[{'_id': 708, 'data': {'type': 'bigint', 'description': 'encoding of the tuple (N.k.i.x) into 64 bits'}, 'name': 'hecke_orbit_code', 'table_id': 46}, 'c_name'], [{'_id': 708, 'data': {'type': 'bigint', 'description': 'encoding of the tuple (N.k.i.x) into 64 bits'}, 'name': 'hecke_orbit_code', 'table_id': 46}, 'example'], [{'_id': 709, 'data': {'type': 'integer', 'description': ''}, 'name': 'n', 'table_id': 46}, 'c_name'], [{'_id': 709, 'data': {'type': 'integer', 'description': ''}, 'name': 'n', 'table_id': 46}, 'example'], [{'_id': 710, 'data': {'type': 'jsonb', 'description': 'list of integers, giving the Hecke eigenvalue as a linear combination of the basis specified in the orbit table'}, 'name': 'an', 'table_id': 46}, 'c_name'], [{'_id': 710, 'data': {'type': 'jsonb', 'description': 'list of integers, giving the Hecke eigenvalue as a linear combination of the basis specified in the orbit table'}, 'name': 'an', 'table_id': 46}, 'example'], [{'_id': 711, 'data': {'type': 'numeric', 'description': 'trace of a_n down to Z'}, 'name': 'trace_an', 'table_id': 46}, 'c_name'], [{'_id': 711, 'data': {'type': 'numeric', 'description': 'trace of a_n down to Z'}, 'name': 'trace_an', 'table_id': 46}, 'example']]], ['mf_newform_portraits', 47, [[{'_id': 712, 'data': {'type': 'text', 'description': 'label (N.k.i.x) of the newform'}, 'name': 'label', 'table_id': 47}, 'c_name'], [{'_id': 712, 'data': {'type': 'text', 'description': 'label (N.k.i.x) of the newform'}, 'name': 'label', 'table_id': 47}, 'example'], [{'_id': 713, 'data': {'type': 'text', 'description': 'base-64 encoded image of the newform (plot created by portrait.sage) to display in the properties box'}, 'name': 'portrait', 'table_id': 47}, 'c_name'], [{'_id': 713, 'data': {'type': 'text', 'description': 'base-64 encoded image of the newform (plot created by portrait.sage) to display in the properties box'}, 'name': 'portrait', 'table_id': 47}, 'example']]], ['mf_newforms', 48, [[{'_id': 714, 'data': {'type': 'text', 'description': '(N.k.i.x)'}, 'name': 'label', 'table_id': 48}, 'c_name'], [{'_id': 714, 'data': {'type': 'text', 'description': '(N.k.i.x)'}, 'name': 'label', 'table_id': 48}, 'example'], [{'_id': 715, 'data': {'type': 'text', 'description': '(N.k.i)'}, 'name': 'space_label', 'table_id': 48}, 'c_name'], [{'_id': 715, 'data': {'type': 'text', 'description': '(N.k.i)'}, 'name': 'space_label', 'table_id': 48}, 'example'], [{'_id': 716, 'data': {'type': 'integer', 'description': '(N)'}, 'name': 'level', 'table_id': 48}, 'c_name'], [{'_id': 716, 'data': {'type': 'integer', 'description': '(N)'}, 'name': 'level', 'table_id': 48}, 'example'], [{'_id': 717, 'data': {'type': 'smallint', 'description': '(k)'}, 'name': 'weight', 'table_id': 48}, 'c_name'], [{'_id': 717, 'data': {'type': 'smallint', 'description': '(k)'}, 'name': 'weight', 'table_id': 48}, 'example'], [{'_id': 718, 'data': {'type': 'integer', 'description': '(i) As above'}, 'name': 'char_orbit_index', 'table_id': 48}, 'c_name'], [{'_id': 718, 'data': {'type': 'integer', 'description': '(i) As above'}, 'name': 'char_orbit_index', 'table_id': 48}, 'example'], [{'_id': 719, 'data': {'type': 'integer', 'description': '(X) An integer that is encoded into x in the label via 1=a, 2=b, 26=z, 27=ba, 28=bb. Note the shift: the letter is the Cremona code for X-1.'}, 'name': 'hecke_orbit', 'table_id': 48}, 'c_name'], [{'_id': 719, 'data': {'type': 'integer', 'description': '(X) An integer that is encoded into x in the label via 1=a, 2=b, 26=z, 27=ba, 28=bb. Note the shift: the letter is the Cremona code for X-1.'}, 'name': 'hecke_orbit', 'table_id': 48}, 'example'], [{'_id': 720, 'data': {'type': 'bigint', 'description': 'encoding of the tuple (N.k.i.x) into 64 bits, used in eigenvalue tables. N + (k<<24) + ((i-1)<<36) + ((X-1)<<52).'}, 'name': 'hecke_orbit_code', 'table_id': 48}, 'c_name'], [{'_id': 720, 'data': {'type': 'bigint', 'description': 'encoding of the tuple (N.k.i.x) into 64 bits, used in eigenvalue tables. N + (k<<24) + ((i-1)<<36) + ((X-1)<<52).'}, 'name': 'hecke_orbit_code', 'table_id': 48}, 'example'], [{'_id': 721, 'data': {'type': 'integer', 'description': 'the dimension of this Hecke orbit'}, 'name': 'dim', 'table_id': 48}, 'c_name'], [{'_id': 721, 'data': {'type': 'integer', 'description': 'the dimension of this Hecke orbit'}, 'name': 'dim', 'table_id': 48}, 'example'], [{'_id': 722, 'data': {'type': 'jsonb', 'description': 'list of integers giving defining polynomial for the Hecke field (standard Sage order of coefficients)'}, 'name': 'field_poly', 'table_id': 48}, 'c_name'], [{'_id': 722, 'data': {'type': 'jsonb', 'description': 'list of integers giving defining polynomial for the Hecke field (standard Sage order of coefficients)'}, 'name': 'field_poly', 'table_id': 48}, 'example'], [{'_id': 723, 'data': {'type': 'boolean', 'description': "whether the polynomial has been reduced by Pari's `polredabs`"}, 'name': 'is_polredabs', 'table_id': 48}, 'c_name'], [{'_id': 723, 'data': {'type': 'boolean', 'description': "whether the polynomial has been reduced by Pari's `polredabs`"}, 'name': 'is_polredabs', 'table_id': 48}, 'example'], [{'_id': 724, 'data': {'type': 'text', 'description': 'LMFDB label for the corresponding number field (can be NULL)'}, 'name': 'nf_label', 'table_id': 48}, 'c_name'], [{'_id': 724, 'data': {'type': 'text', 'description': 'LMFDB label for the corresponding number field (can be NULL)'}, 'name': 'nf_label', 'table_id': 48}, 'example'], [{'_id': 725, 'data': {'type': 'jsonb', 'description': 'List of lists of integers, giving the numerators of a basis for the Hecke order in terms of the field generator specified by the field polynomial'}, 'name': 'hecke_ring_numerators', 'table_id': 48}, 'c_name'], [{'_id': 725, 'data': {'type': 'jsonb', 'description': 'List of lists of integers, giving the numerators of a basis for the Hecke order in terms of the field generator specified by the field polynomial'}, 'name': 'hecke_ring_numerators', 'table_id': 48}, 'example'], [{'_id': 726, 'data': {'type': 'jsonb', 'description': 'List of integers, giving the denominators of the basis'}, 'name': 'hecke_ring_denominators', 'table_id': 48}, 'c_name'], [{'_id': 726, 'data': {'type': 'jsonb', 'description': 'List of integers, giving the denominators of the basis'}, 'name': 'hecke_ring_denominators', 'table_id': 48}, 'example'], [{'_id': 727, 'data': {'type': 'boolean', 'description': 'whether the index has been proven correct (computing the maximal order may not be possible)'}, 'name': 'hecke_ring_index_proven', 'table_id': 48}, 'c_name'], [{'_id': 727, 'data': {'type': 'boolean', 'description': 'whether the index has been proven correct (computing the maximal order may not be possible)'}, 'name': 'hecke_ring_index_proven', 'table_id': 48}, 'example'], [{'_id': 728, 'data': {'type': 'bigint', 'description': 'appropriate linear combination of the a_p between 2^12 and 2^13'}, 'name': 'trace_hash', 'table_id': 48}, 'c_name'], [{'_id': 728, 'data': {'type': 'bigint', 'description': 'appropriate linear combination of the a_p between 2^12 and 2^13'}, 'name': 'trace_hash', 'table_id': 48}, 'example'], [{'_id': 729, 'data': {'type': 'smallint', 'description': 'n so that q-expansion is known to precision O(q^n).'}, 'name': 'qexp_prec', 'table_id': 48}, 'c_name'], [{'_id': 729, 'data': {'type': 'smallint', 'description': 'n so that q-expansion is known to precision O(q^n).'}, 'name': 'qexp_prec', 'table_id': 48}, 'example'], [{'_id': 730, 'data': {'type': 'smallint', 'description': ''}, 'name': 'analytic_rank', 'table_id': 48}, 'c_name'], [{'_id': 730, 'data': {'type': 'smallint', 'description': ''}, 'name': 'analytic_rank', 'table_id': 48}, 'example'], [{'_id': 731, 'data': {'type': 'smallint', 'description': 'The (negative) discriminant of the order by which we have CM (1 if no CM, 0 if CM status is not known)'}, 'name': 'cm_disc', 'table_id': 48}, 'c_name'], [{'_id': 731, 'data': {'type': 'smallint', 'description': 'The (negative) discriminant of the order by which we have CM (1 if no CM, 0 if CM status is not known)'}, 'name': 'cm_disc', 'table_id': 48}, 'example'], [{'_id': 732, 'data': {'type': 'text', 'description': 'label for the Hecke character giving the CM'}, 'name': 'cm_hecke_char', 'table_id': 48}, 'c_name'], [{'_id': 732, 'data': {'type': 'text', 'description': 'label for the Hecke character giving the CM'}, 'name': 'cm_hecke_char', 'table_id': 48}, 'example'], [{'_id': 733, 'data': {'type': 'boolean', 'description': 'whether the cm columns are provably correct'}, 'name': 'cm_proved', 'table_id': 48}, 'c_name'], [{'_id': 733, 'data': {'type': 'boolean', 'description': 'whether the cm columns are provably correct'}, 'name': 'cm_proved', 'table_id': 48}, 'example'], [{'_id': 734, 'data': {'type': 'boolean', 'description': ''}, 'name': 'is_twist_minimal', 'table_id': 48}, 'c_name'], [{'_id': 734, 'data': {'type': 'boolean', 'description': ''}, 'name': 'is_twist_minimal', 'table_id': 48}, 'example'], [{'_id': 735, 'data': {'type': 'jsonb', 'description': 'List of integers giving the char_orbit values for the nontrivial Dirichlet characters that give inner twists'}, 'name': 'inner_twist', 'table_id': 48}, 'c_name'], [{'_id': 735, 'data': {'type': 'jsonb', 'description': 'List of integers giving the char_orbit values for the nontrivial Dirichlet characters that give inner twists'}, 'name': 'inner_twist', 'table_id': 48}, 'example'], [{'_id': 736, 'data': {'type': 'jsonb', 'description': 'a list of pairs [p, ev] where ev is 1 or -1, the Atkin-Lehner eigenvalue for each p dividing N (NULL overall if nontrivial character)'}, 'name': 'atkin_lehner_eigenvals', 'table_id': 48}, 'c_name'], [{'_id': 736, 'data': {'type': 'jsonb', 'description': 'a list of pairs [p, ev] where ev is 1 or -1, the Atkin-Lehner eigenvalue for each p dividing N (NULL overall if nontrivial character)'}, 'name': 'atkin_lehner_eigenvals', 'table_id': 48}, 'example'], [{'_id': 737, 'data': {'type': 'jsonb', 'description': 'a list of pairs [p, F_p] where F_p is a list of integers encoding a polynomial; the intersection of the kernels of F_p(T_p) is this Hecke orbit'}, 'name': 'hecke_cutters', 'table_id': 48}, 'c_name'], [{'_id': 737, 'data': {'type': 'jsonb', 'description': 'a list of pairs [p, F_p] where F_p is a list of integers encoding a polynomial; the intersection of the kernels of F_p(T_p) is this Hecke orbit'}, 'name': 'hecke_cutters', 'table_id': 48}, 'example'], [{'_id': 738, 'data': {'type': 'text', 'description': 'latexed string for display on search page results'}, 'name': 'qexp_display', 'table_id': 48}, 'c_name'], [{'_id': 738, 'data': {'type': 'text', 'description': 'latexed string for display on search page results'}, 'name': 'qexp_display', 'table_id': 48}, 'example'], [{'_id': 739, 'data': {'type': 'jsonb', 'description': 'list of the first four a_n traces for display on search page results'}, 'name': 'trace_display', 'table_id': 48}, 'c_name'], [{'_id': 739, 'data': {'type': 'jsonb', 'description': 'list of the first four a_n traces for display on search page results'}, 'name': 'trace_display', 'table_id': 48}, 'example'], [{'_id': 740, 'data': {'type': 'boolean', 'description': 'whether k is odd'}, 'name': 'odd_weight', 'table_id': 48}, 'c_name'], [{'_id': 740, 'data': {'type': 'boolean', 'description': 'whether k is odd'}, 'name': 'odd_weight', 'table_id': 48}, 'example'], [{'_id': 741, 'data': {'type': 'integer', 'description': 'the order of the character'}, 'name': 'char_order', 'table_id': 48}, 'c_name'], [{'_id': 741, 'data': {'type': 'integer', 'description': 'the order of the character'}, 'name': 'char_order', 'table_id': 48}, 'example'], [{'_id': 742, 'data': {'type': 'smallint', 'description': 'whether there is an inner twist. 1=yes, -1=no, 0=unknown'}, 'name': 'has_inner_twist', 'table_id': 48}, 'c_name'], [{'_id': 742, 'data': {'type': 'smallint', 'description': 'whether there is an inner twist. 1=yes, -1=no, 0=unknown'}, 'name': 'has_inner_twist', 'table_id': 48}, 'example'], [{'_id': 743, 'data': {'type': 'jsonb', 'description': '(a divisor of) the index of the order generated by the Hecke eigenvalues in the maximal order. Stored as its factorization, as a list of pairs [p,e].'}, 'name': 'hecke_ring_index', 'table_id': 48}, 'c_name'], [{'_id': 743, 'data': {'type': 'jsonb', 'description': '(a divisor of) the index of the order generated by the Hecke eigenvalues in the maximal order. Stored as its factorization, as a list of pairs [p,e].'}, 'name': 'hecke_ring_index', 'table_id': 48}, 'example'], [{'_id': 744, 'data': {'type': 'smallint', 'description': '1 or -1, depending on the parity of the character'}, 'name': 'char_parity', 'table_id': 48}, 'c_name'], [{'_id': 744, 'data': {'type': 'smallint', 'description': '1 or -1, depending on the parity of the character'}, 'name': 'char_parity', 'table_id': 48}, 'example'], [{'_id': 745, 'data': {'type': 'jsonb', 'description': 'Sorted list of Conrey indexes of characters in this Galois orbit'}, 'name': 'char_labels', 'table_id': 48}, 'c_name'], [{'_id': 745, 'data': {'type': 'jsonb', 'description': 'Sorted list of Conrey indexes of characters in this Galois orbit'}, 'name': 'char_labels', 'table_id': 48}, 'example'], [{'_id': 746, 'data': {'type': 'text', 'description': 'the isogeny class label of the corresponding elliptic curve or modular abelian variety (could be null if not yet in the database)'}, 'name': 'isogeny_class_label', 'table_id': 48}, 'c_name'], [{'_id': 746, 'data': {'type': 'text', 'description': 'the isogeny class label of the corresponding elliptic curve or modular abelian variety (could be null if not yet in the database)'}, 'name': 'isogeny_class_label', 'table_id': 48}, 'example'], [{'_id': 747, 'data': {'type': 'integer', 'description': 'Degree of the (cyclotomic) character field'}, 'name': 'char_degree', 'table_id': 48}, 'c_name'], [{'_id': 747, 'data': {'type': 'integer', 'description': 'Degree of the (cyclotomic) character field'}, 'name': 'char_degree', 'table_id': 48}, 'example'], [{'_id': 748, 'data': {'type': 'integer', 'description': 'char_orbit for the primitive version of this character'}, 'name': 'prim_orbit_index', 'table_id': 48}, 'c_name'], [{'_id': 748, 'data': {'type': 'integer', 'description': 'char_orbit for the primitive version of this character'}, 'name': 'prim_orbit_index', 'table_id': 48}, 'example'], [{'_id': 749, 'data': {'type': 'integer', 'description': 'Conductor of the Dirichlet character'}, 'name': 'char_conductor', 'table_id': 48}, 'c_name'], [{'_id': 749, 'data': {'type': 'integer', 'description': 'Conductor of the Dirichlet character'}, 'name': 'char_conductor', 'table_id': 48}, 'example'], [{'_id': 750, 'data': {'type': 'boolean', 'description': 'whether the inner twist columns are provably correct'}, 'name': 'inner_twist_proved', 'table_id': 48}, 'c_name'], [{'_id': 750, 'data': {'type': 'boolean', 'description': 'whether the inner twist columns are provably correct'}, 'name': 'inner_twist_proved', 'table_id': 48}, 'example'], [{'_id': 751, 'data': {'type': 'smallint', 'description': 'whether there is cm. 1=yes, -1=no, 0=unknown'}, 'name': 'is_cm', 'table_id': 48}, 'c_name'], [{'_id': 751, 'data': {'type': 'smallint', 'description': 'whether there is cm. 1=yes, -1=no, 0=unknown'}, 'name': 'is_cm', 'table_id': 48}, 'example'], [{'_id': 752, 'data': {'type': 'text', 'description': 'letter encoded version of (i)'}, 'name': 'char_orbit_label', 'table_id': 48}, 'c_name'], [{'_id': 752, 'data': {'type': 'text', 'description': 'letter encoded version of (i)'}, 'name': 'char_orbit_label', 'table_id': 48}, 'example'], [{'_id': 753, 'data': {'type': 'boolean', 'description': 'whether the character'}, 'name': 'char_is_real', 'table_id': 48}, 'c_name'], [{'_id': 753, 'data': {'type': 'boolean', 'description': 'whether the character'}, 'name': 'char_is_real', 'table_id': 48}, 'example'], [{'_id': 754, 'data': {'type': 'integer', 'description': 'N*k^2'}, 'name': 'Nk2', 'table_id': 48}, 'c_name'], [{'_id': 754, 'data': {'type': 'integer', 'description': 'N*k^2'}, 'name': 'Nk2', 'table_id': 48}, 'example'], [{'_id': 755, 'data': {'type': 'smallint', 'description': 'product of the Atkin-Lehner eigenvalues (NULL if nontrivial character)'}, 'name': 'fricke_eigenval', 'table_id': 48}, 'c_name'], [{'_id': 755, 'data': {'type': 'smallint', 'description': 'product of the Atkin-Lehner eigenvalues (NULL if nontrivial character)'}, 'name': 'fricke_eigenval', 'table_id': 48}, 'example']]], ['mf_newspaces', 49, [[{'_id': 756, 'data': {'type': 'text', 'description': '(N.k.i)'}, 'name': 'label', 'table_id': 49}, 'c_name'], [{'_id': 756, 'data': {'type': 'text', 'description': '(N.k.i)'}, 'name': 'label', 'table_id': 49}, 'example'], [{'_id': 757, 'data': {'type': 'integer', 'description': '(N)'}, 'name': 'level', 'table_id': 49}, 'c_name'], [{'_id': 757, 'data': {'type': 'integer', 'description': '(N)'}, 'name': 'level', 'table_id': 49}, 'example'], [{'_id': 758, 'data': {'type': 'smallint', 'description': '(k)'}, 'name': 'weight', 'table_id': 49}, 'c_name'], [{'_id': 758, 'data': {'type': 'smallint', 'description': '(k)'}, 'name': 'weight', 'table_id': 49}, 'example'], [{'_id': 759, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'char_orbit_index', 'table_id': 49}, 'c_name'], [{'_id': 760, 'data': {'type': 'jsonb', 'description': 'Sorted list of Conrey indexes of characters in this Galois orbit'}, 'name': 'char_labels', 'table_id': 49}, 'c_name'], [{'_id': 760, 'data': {'type': 'jsonb', 'description': 'Sorted list of Conrey indexes of characters in this Galois orbit'}, 'name': 'char_labels', 'table_id': 49}, 'example'], [{'_id': 761, 'data': {'type': 'integer', 'description': 'Conductor of the Dirichlet character'}, 'name': 'char_conductor', 'table_id': 49}, 'c_name'], [{'_id': 761, 'data': {'type': 'integer', 'description': 'Conductor of the Dirichlet character'}, 'name': 'char_conductor', 'table_id': 49}, 'example'], [{'_id': 762, 'data': {'type': 'integer', 'description': 'the degree of the (cyclotomic) character field'}, 'name': 'char_degree', 'table_id': 49}, 'c_name'], [{'_id': 762, 'data': {'type': 'integer', 'description': 'the degree of the (cyclotomic) character field'}, 'name': 'char_degree', 'table_id': 49}, 'example'], [{'_id': 763, 'data': {'type': 'smallint', 'description': '1 or -1, depending on the parity of the character'}, 'name': 'char_parity', 'table_id': 49}, 'c_name'], [{'_id': 763, 'data': {'type': 'smallint', 'description': '1 or -1, depending on the parity of the character'}, 'name': 'char_parity', 'table_id': 49}, 'example'], [{'_id': 764, 'data': {'type': 'integer', 'description': ''}, 'name': 'sturm_bound', 'table_id': 49}, 'c_name'], [{'_id': 764, 'data': {'type': 'integer', 'description': ''}, 'name': 'sturm_bound', 'table_id': 49}, 'example'], [{'_id': 765, 'data': {'type': 'integer', 'description': 'Q-dimension of this newspace'}, 'name': 'dim', 'table_id': 49}, 'c_name'], [{'_id': 765, 'data': {'type': 'integer', 'description': 'Q-dimension of this newspace'}, 'name': 'dim', 'table_id': 49}, 'example'], [{'_id': 766, 'data': {'type': 'integer', 'description': 'Q-dimension of the eisenstein subspace of the corresponding `M_k(N, \\chi)`'}, 'name': 'eis_dim', 'table_id': 49}, 'c_name'], [{'_id': 766, 'data': {'type': 'integer', 'description': 'Q-dimension of the eisenstein subspace of the corresponding `M_k(N, \\chi)`'}, 'name': 'eis_dim', 'table_id': 49}, 'example'], [{'_id': 767, 'data': {'type': 'integer', 'description': 'Q-dimension of the new eisenstein subspace of the corresponding `M_k(N, \\chi)`'}, 'name': 'eis_new_dim', 'table_id': 49}, 'c_name'], [{'_id': 767, 'data': {'type': 'integer', 'description': 'Q-dimension of the new eisenstein subspace of the corresponding `M_k(N, \\chi)`'}, 'name': 'eis_new_dim', 'table_id': 49}, 'example'], [{'_id': 768, 'data': {'type': 'integer', 'description': 'Q-dimension of the cuspidal space `S_k(N, \\chi)`'}, 'name': 'cusp_dim', 'table_id': 49}, 'c_name'], [{'_id': 768, 'data': {'type': 'integer', 'description': 'Q-dimension of the cuspidal space `S_k(N, \\chi)`'}, 'name': 'cusp_dim', 'table_id': 49}, 'example'], [{'_id': 769, 'data': {'type': 'integer', 'description': 'Q-dimension of `M_k(N, \\chi)`'}, 'name': 'mf_dim', 'table_id': 49}, 'c_name'], [{'_id': 769, 'data': {'type': 'integer', 'description': 'Q-dimension of `M_k(N, \\chi)`'}, 'name': 'mf_dim', 'table_id': 49}, 'example'], [{'_id': 770, 'data': {'type': 'jsonb', 'description': 'Sorted list of dimensions of Hecke orbits (irreducible Galois stable subspaces)'}, 'name': 'hecke_orbit_dims', 'table_id': 49}, 'c_name'], [{'_id': 770, 'data': {'type': 'jsonb', 'description': 'Sorted list of dimensions of Hecke orbits (irreducible Galois stable subspaces)'}, 'name': 'hecke_orbit_dims', 'table_id': 49}, 'example'], [{'_id': 771, 'data': {'type': 'boolean', 'description': 'whether k is odd'}, 'name': 'odd_weight', 'table_id': 49}, 'c_name'], [{'_id': 771, 'data': {'type': 'boolean', 'description': 'whether k is odd'}, 'name': 'odd_weight', 'table_id': 49}, 'example'], [{'_id': 772, 'data': {'type': 'integer', 'description': 'the order of the character'}, 'name': 'char_order', 'table_id': 49}, 'c_name'], [{'_id': 772, 'data': {'type': 'integer', 'description': 'the order of the character'}, 'name': 'char_order', 'table_id': 49}, 'example'], [{'_id': 773, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'prim_orbit_index', 'table_id': 49}, 'c_name'], [{'_id': 774, 'data': {'type': 'text', 'description': 'letter encoded version of (i)'}, 'name': 'char_orbit_label', 'table_id': 49}, 'c_name'], [{'_id': 774, 'data': {'type': 'text', 'description': 'letter encoded version of (i)'}, 'name': 'char_orbit_label', 'table_id': 49}, 'example'], [{'_id': 775, 'data': {'type': 'boolean', 'description': 'whether the character takes only real values (trivial or quadratic)'}, 'name': 'char_is_real', 'table_id': 49}, 'c_name'], [{'_id': 775, 'data': {'type': 'boolean', 'description': 'whether the character takes only real values (trivial or quadratic)'}, 'name': 'char_is_real', 'table_id': 49}, 'example'], [{'_id': 776, 'data': {'type': 'integer', 'description': 'the integer n so that the traces from 1 up to n distinguish all forms in this space (e.g. 1 if the dimensions are all distinct)'}, 'name': 'trace_bound', 'table_id': 49}, 'c_name'], [{'_id': 776, 'data': {'type': 'integer', 'description': 'the integer n so that the traces from 1 up to n distinguish all forms in this space (e.g. 1 if the dimensions are all distinct)'}, 'name': 'trace_bound', 'table_id': 49}, 'example'], [{'_id': 777, 'data': {'type': 'smallint', 'description': 'number of Hecke orbits (each corresponds to a Galois conjugacy class of modular forms)'}, 'name': 'num_forms', 'table_id': 49}, 'c_name'], [{'_id': 777, 'data': {'type': 'smallint', 'description': 'number of Hecke orbits (each corresponds to a Galois conjugacy class of modular forms)'}, 'name': 'num_forms', 'table_id': 49}, 'example'], [{'_id': 778, 'data': {'type': 'integer', 'description': 'N*k^2'}, 'name': 'Nk2', 'table_id': 49}, 'c_name'], [{'_id': 778, 'data': {'type': 'integer', 'description': 'N*k^2'}, 'name': 'Nk2', 'table_id': 49}, 'example']]], ['mf_subspaces', 50, [[{'_id': 779, 'data': {'type': 'text', 'description': 'label N.k.i for the cuspidal space `S_k(N, [\\chi])` (same as the label for `S_k^{new}(N, [\\chi])`)'}, 'name': 'label', 'table_id': 50}, 'c_name'], [{'_id': 779, 'data': {'type': 'text', 'description': 'label N.k.i for the cuspidal space `S_k(N, [\\chi])` (same as the label for `S_k^{new}(N, [\\chi])`)'}, 'name': 'label', 'table_id': 50}, 'example'], [{'_id': 780, 'data': {'type': 'integer', 'description': 'level N of the cuspidal space `S_k(N, [\\chi])`'}, 'name': 'level', 'table_id': 50}, 'c_name'], [{'_id': 780, 'data': {'type': 'integer', 'description': 'level N of the cuspidal space `S_k(N, [\\chi])`'}, 'name': 'level', 'table_id': 50}, 'example'], [{'_id': 781, 'data': {'type': 'smallint', 'description': 'weight k of the cuspidal space `S_k(N, [\\chi])`'}, 'name': 'weight', 'table_id': 50}, 'c_name'], [{'_id': 781, 'data': {'type': 'smallint', 'description': 'weight k of the cuspidal space `S_k(N, [\\chi])`'}, 'name': 'weight', 'table_id': 50}, 'example'], [{'_id': 782, 'data': {'type': 'jsonb', 'description': 'list of Conrey indexes n of the characters N.n in the Galois orbit indexed by i'}, 'name': 'char_labels', 'table_id': 50}, 'c_name'], [{'_id': 782, 'data': {'type': 'jsonb', 'description': 'list of Conrey indexes n of the characters N.n in the Galois orbit indexed by i'}, 'name': 'char_labels', 'table_id': 50}, 'example'], [{'_id': 783, 'data': {'type': 'integer', 'description': 'dimension of `S_k(N, [\\psi])`'}, 'name': 'dim', 'table_id': 50}, 'c_name'], [{'_id': 783, 'data': {'type': 'integer', 'description': 'dimension of `S_k(N, [\\psi])`'}, 'name': 'dim', 'table_id': 50}, 'example'], [{'_id': 784, 'data': {'type': 'text', 'description': 'The label of the newspace `S_k^{new}(M, [\\psi])` that appears as a non-trivial subspace of`S_k(N, [\\chi])`'}, 'name': 'sub_label', 'table_id': 50}, 'c_name'], [{'_id': 784, 'data': {'type': 'text', 'description': 'The label of the newspace `S_k^{new}(M, [\\psi])` that appears as a non-trivial subspace of`S_k(N, [\\chi])`'}, 'name': 'sub_label', 'table_id': 50}, 'example'], [{'_id': 785, 'data': {'type': 'integer', 'description': '(M)'}, 'name': 'sub_level', 'table_id': 50}, 'c_name'], [{'_id': 785, 'data': {'type': 'integer', 'description': '(M)'}, 'name': 'sub_level', 'table_id': 50}, 'example'], [{'_id': 786, 'data': {'type': 'jsonb', 'description': 'list of Conrey indexes n of the characters M.n in the Galois orrbit indexed by j.'}, 'name': 'sub_char_labels', 'table_id': 50}, 'c_name'], [{'_id': 786, 'data': {'type': 'jsonb', 'description': 'list of Conrey indexes n of the characters M.n in the Galois orrbit indexed by j.'}, 'name': 'sub_char_labels', 'table_id': 50}, 'example'], [{'_id': 787, 'data': {'type': 'integer', 'description': 'the dimension of `S_k^{new}(M, [\\psi])`'}, 'name': 'sub_dim', 'table_id': 50}, 'c_name'], [{'_id': 787, 'data': {'type': 'integer', 'description': 'the dimension of `S_k^{new}(M, [\\psi])`'}, 'name': 'sub_dim', 'table_id': 50}, 'example'], [{'_id': 788, 'data': {'type': 'integer', 'description': 'Multiplicity of`S_k^{new}(M, [\\psi])` as a direct summand of `S_k(N, [\\chi])` (this is just the number of divisors of N/M). Summing dimensions of embedded newspaces with multiplicity gives the dimension of the cusp space.'}, 'name': 'sub_mult', 'table_id': 50}, 'c_name'], [{'_id': 788, 'data': {'type': 'integer', 'description': 'Multiplicity of`S_k^{new}(M, [\\psi])` as a direct summand of `S_k(N, [\\chi])` (this is just the number of divisors of N/M). Summing dimensions of embedded newspaces with multiplicity gives the dimension of the cusp space.'}, 'name': 'sub_mult', 'table_id': 50}, 'example'], [{'_id': 789, 'data': {'type': 'integer', 'description': 'index i of the character orbit `[\\chi]` in the sorted list of character orbits of modulus N'}, 'name': 'char_orbit_index', 'table_id': 50}, 'c_name'], [{'_id': 789, 'data': {'type': 'integer', 'description': 'index i of the character orbit `[\\chi]` in the sorted list of character orbits of modulus N'}, 'name': 'char_orbit_index', 'table_id': 50}, 'example'], [{'_id': 790, 'data': {'type': 'integer', 'description': '(j) index of `[\\psi]` in sorted list of character orbits of modulus M'}, 'name': 'sub_char_orbit_index', 'table_id': 50}, 'c_name'], [{'_id': 790, 'data': {'type': 'integer', 'description': '(j) index of `[\\psi]` in sorted list of character orbits of modulus M'}, 'name': 'sub_char_orbit_index', 'table_id': 50}, 'example']]], ['modlgal_reps', 51, [[{'_id': 791, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'image_order', 'table_id': 51}, 'c_name'], [{'_id': 792, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'rep_type', 'table_id': 51}, 'c_name'], [{'_id': 793, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'weight', 'table_id': 51}, 'c_name'], [{'_id': 794, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'primes_conductor', 'table_id': 51}, 'c_name'], [{'_id': 795, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'field_char', 'table_id': 51}, 'c_name'], [{'_id': 796, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'degree_proj_field', 'table_id': 51}, 'c_name'], [{'_id': 797, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'index', 'table_id': 51}, 'c_name'], [{'_id': 798, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'field_order', 'table_id': 51}, 'c_name'], [{'_id': 799, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'image_type', 'table_id': 51}, 'c_name'], [{'_id': 800, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'good_prime_list', 'table_id': 51}, 'c_name'], [{'_id': 801, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'poly_ker', 'table_id': 51}, 'c_name'], [{'_id': 802, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 51}, 'c_name'], [{'_id': 803, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'field', 'table_id': 51}, 'c_name'], [{'_id': 804, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'projective_type', 'table_id': 51}, 'c_name'], [{'_id': 805, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'bad_prime_list', 'table_id': 51}, 'c_name'], [{'_id': 806, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'conductor', 'table_id': 51}, 'c_name'], [{'_id': 807, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'field_deg', 'table_id': 51}, 'c_name'], [{'_id': 808, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'poly_proj_ker', 'table_id': 51}, 'c_name'], [{'_id': 809, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'abs_irr', 'table_id': 51}, 'c_name'], [{'_id': 810, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'image_at', 'table_id': 51}, 'c_name'], [{'_id': 811, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim', 'table_id': 51}, 'c_name'], [{'_id': 812, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'base_field', 'table_id': 51}, 'c_name'], [{'_id': 813, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'base_label', 'table_id': 51}, 'c_name'], [{'_id': 814, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'projective_label', 'table_id': 51}, 'c_name'], [{'_id': 815, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'image_label', 'table_id': 51}, 'c_name']]], ['modlmf_forms', 52, [[{'_id': 816, 'data': {'type': None, 'example': None, 'description': 'minimum weight in a theta cycle'}, 'name': 'min_theta_weight', 'table_id': 52}, 'c_name'], [{'_id': 817, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'index', 'table_id': 52}, 'c_name'], [{'_id': 818, 'data': {'type': None, 'example': None, 'description': 'label of the mod ell Dirichlet character'}, 'name': 'dirchar', 'table_id': 52}, 'c_name'], [{'_id': 819, 'data': {'type': None, 'example': None, 'description': 'the number of Fourier coefficients'}, 'name': 'n_coeffs', 'table_id': 52}, 'c_name'], [{'_id': 820, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'base_label', 'table_id': 52}, 'c_name'], [{'_id': 821, 'data': {'type': None, 'example': None, 'description': 'minimal level of the form, that is the smallest level in which the eigenvalue system does occurr. If the associated representation is irreducible this is the Artin conductor away from l'}, 'name': 'level', 'table_id': 52}, 'c_name'], [{'_id': 822, 'data': {'type': None, 'example': None, 'description': 'the characteristic of the base ring of the form'}, 'name': 'characteristic', 'table_id': 52}, 'c_name'], [{'_id': 823, 'data': {'type': 'list [integer, string, string, string]', 'example': None, 'description': 'description of the characteristic zero cuspidal lift of smallest weight and smallest Galois orbit (alphabetical order).\n\n This consists of\n\n * *(int)* the weight of the newform\n\n * *(string)* the label of the newform \n\n * *(string)* the polynomial giving the Hecke eigenvalue field \n\n * *(string)* the ideal used for the reduction, in terms of the generators'}, 'name': 'cuspidal_lift', 'table_id': 52}, 'c_name'], [{'_id': 824, 'data': {'type': 'list of tuples [int, str]', 'example': None, 'description': 'theta cycle, formattes as list of [weight, label of the Galois orbit]'}, 'name': 'theta_cycle', 'table_id': 52}, 'c_name'], [{'_id': 825, 'data': {'type': None, 'example': None, 'description': '[[int(p^e), int(W_{p^e})] for p^e exactly dividing N]'}, 'name': 'atkinlehner', 'table_id': 52}, 'c_name'], [{'_id': 826, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 52}, 'c_name'], [{'_id': 827, 'data': {'type': None, 'example': None, 'description': 'coefficients of the q-expansion. The finite field where the coefficients belongs is represented using Conway polynomials.'}, 'name': 'coeffs', 'table_id': 52}, 'c_name'], [{'_id': 828, 'data': {'type': 'list [string, integer, string, integer, integer]', 'example': None, 'description': 'this means that the associated representation is reducible of the form \n\n chi_1 cycl^a + chi_2 cycl^b, with a < b \n\n where chi_1, chi_2 are mod ell Dirichlet characters and cycl is the mod ell cyclotomic character. This is the format \n\n [dirchar_label(chi_1), power of cyclotomic a, dirchar_label(chi_2), power of cyclotomic b, eisenstein_weight] \n\n The dirchar_label is the *full* label of the character. The eisenstein_weight is the minimal weight of the Eisenstein lift of smallest weight'}, 'name': 'reducible', 'table_id': 52}, 'c_name'], [{'_id': 829, 'data': {'type': None, 'example': None, 'description': '1 means ordinary'}, 'name': 'ordinary', 'table_id': 52}, 'c_name'], [{'_id': 830, 'data': {'type': None, 'example': None, 'description': '@@weight of the form modulo ell-1'}, 'name': 'weight_grading', 'table_id': 52}, 'c_name'], [{'_id': 831, 'data': {'type': None, 'example': None, 'description': 'degree of base field over prime field'}, 'name': 'deg', 'table_id': 52}, 'c_name']]], ['mwf_coeffs', 53, [[{'_id': 832, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 53}, 'c_name'], [{'_id': 833, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Numc', 'table_id': 53}, 'c_name'], [{'_id': 834, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'coefficients', 'table_id': 53}, 'c_name']]], ['mwf_forms', 54, [[{'_id': 835, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'maass_id', 'table_id': 54}, 'c_name'], [{'_id': 836, 'data': {'type': None, 'example': None, 'description': 'Spectral parameter R corresponding to this Maass form, s.t. the actual eigenvalue is lambda=1/4+R^2'}, 'name': 'Eigenvalue', 'table_id': 54}, 'c_name'], [{'_id': 837, 'data': {'type': None, 'example': None, 'description': 'character number in Conrey numbering if Conrey is set to 1 else in Sage ordering'}, 'name': 'Character', 'table_id': 54}, 'c_name'], [{'_id': 838, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'date', 'table_id': 54}, 'c_name'], [{'_id': 839, 'data': {'type': None, 'example': None, 'description': 'the M0 which was used as input to the algorithm for computing the eigenvalue (if set correctly it should be > 0)'}, 'name': 'M0', 'table_id': 54}, 'c_name'], [{'_id': 840, 'data': {'type': None, 'example': None, 'description': 'describes the normalisation used for the coefficients, 1.0 means Hecke normalisation so c(1)=1, other} alternatives (not used currently) would be L2-normalisation'}, 'name': 'Norm', 'table_id': 54}, 'c_name'], [{'_id': 841, 'data': {'type': None, 'example': None, 'description': 'A short list of Fourier coefficients c(1),c(2),...'}, 'name': 'Coefficient', 'table_id': 54}, 'c_name'], [{'_id': 842, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'ObjectUrl', 'table_id': 54}, 'c_name'], [{'_id': 843, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Precision', 'table_id': 54}, 'c_name'], [{'_id': 844, 'data': {'type': None, 'example': None, 'description': 'number of coefficients available for this form'}, 'name': 'Numc', 'table_id': 54}, 'c_name'], [{'_id': 845, 'data': {'type': None, 'example': None, 'description': "list of (complex) numbers such that the Fourier coefficients at that cusp are proportional to the ones at infinity with this constant. Such constants exists if the corresponding Atkin-Lehner operators are cusp normalisers. The first '1' corresponds to the cusp at infinity"}, 'name': 'Cusp_evs', 'table_id': 54}, 'c_name'], [{'_id': 846, 'data': {'type': None, 'example': None, 'description': 'dimension of the eigenspace containing this Maass form (estimated heuristically / numerically)'}, 'name': 'Dim', 'table_id': 54}, 'c_name'], [{'_id': 847, 'data': {'type': None, 'example': None, 'description': 'level'}, 'name': 'Level', 'table_id': 54}, 'c_name'], [{'_id': 848, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Newform', 'table_id': 54}, 'c_name'], [{'_id': 849, 'data': {'type': None, 'example': None, 'description': 'estimate of the error in the eigenvalue'}, 'name': 'Error', 'table_id': 54}, 'c_name'], [{'_id': 850, 'data': {'type': None, 'example': None, 'description': 'the Y which was used as input to the algorithm for computing the eigenvalue (if set correctly it should be > 0)'}, 'name': 'Y', 'table_id': 54}, 'c_name'], [{'_id': 851, 'data': {'type': None, 'example': None, 'description': 'probably a duplicate of Dim'}, 'name': 'Dimension', 'table_id': 54}, 'c_name'], [{'_id': 852, 'data': {'type': None, 'example': None, 'description': "probably a third duplicate of 'Dim' and 'Dimension'"}, 'name': 'dim', 'table_id': 54}, 'c_name'], [{'_id': 853, 'data': {'type': None, 'example': None, 'description': '1 if this Maass form is even and 0 if it is odd'}, 'name': 'Symmetry', 'table_id': 54}, 'c_name'], [{'_id': 854, 'data': {'type': None, 'example': None, 'description': 'the weight of the Maass form'}, 'name': 'Weight', 'table_id': 54}, 'c_name'], [{'_id': 855, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Fricke', 'table_id': 54}, 'c_name'], [{'_id': 856, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'ObjectLabel', 'table_id': 54}, 'c_name'], [{'_id': 857, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Sign', 'table_id': 54}, 'c_name'], [{'_id': 858, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'coeff_label', 'table_id': 54}, 'c_name'], [{'_id': 859, 'data': {'type': None, 'example': None, 'description': "identifier of person who originally submitted this data, e.g. 'HT' is Holger Then, FS is Fredrik Stromberg etc. (coefficients may have been added later by other contributors, identified in the corresponding coefficient record)"}, 'name': 'Contributor', 'table_id': 54}, 'c_name'], [{'_id': 860, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'software', 'table_id': 54}, 'c_name']]], ['mwf_plots', 55, [[{'_id': 861, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'eigenvalue', 'table_id': 55}, 'c_name'], [{'_id': 862, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'plot', 'table_id': 55}, 'c_name'], [{'_id': 863, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'level', 'table_id': 55}, 'c_name'], [{'_id': 864, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'maass_id', 'table_id': 55}, 'c_name'], [{'_id': 865, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'num_pts', 'table_id': 55}, 'c_name'], [{'_id': 866, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dpi', 'table_id': 55}, 'c_name']]], ['mwf_tables', 56, [[{'_id': 867, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'ncols', 'table_id': 56}, 'c_name'], [{'_id': 868, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'nrows', 'table_id': 56}, 'c_name'], [{'_id': 869, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'levels', 'table_id': 56}, 'c_name'], [{'_id': 870, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'characters', 'table_id': 56}, 'c_name'], [{'_id': 871, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'weights', 'table_id': 56}, 'c_name'], [{'_id': 872, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'keylist', 'table_id': 56}, 'c_name'], [{'_id': 873, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'data', 'table_id': 56}, 'c_name']]], ['mwfp_forms', 57, [[{'_id': 874, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'maass_id', 'table_id': 57}, 'c_name'], [{'_id': 875, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'ev', 'table_id': 57}, 'c_name'], [{'_id': 876, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'prec', 'table_id': 57}, 'c_name'], [{'_id': 877, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'sym', 'table_id': 57}, 'c_name'], [{'_id': 878, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'coef', 'table_id': 57}, 'c_name']]], ['nf_fields', 58, [[{'_id': 879, 'data': {'type': None, 'example': None, 'description': "LMFDB label, formed by joining the degree, number of real places, absolute discriminant, and index with '.'. The index is a counter to distinguish fields which would otherwise have the same label"}, 'name': 'label', 'table_id': 58}, 'c_name'], [{'_id': 880, 'data': {'type': None, 'example': None, 'description': 'coefficients of our defining polynomial starting with the constant term.'}, 'name': 'coeffs', 'table_id': 58}, 'c_name'], [{'_id': 881, 'data': {'type': None, 'example': '`3`', 'description': 'degree of the field over *Q*'}, 'name': 'degree', 'table_id': 58}, 'c_name'], [{'_id': 882, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'r2', 'table_id': 58}, 'c_name'], [{'_id': 883, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'cm', 'table_id': 58}, 'c_name'], [{'_id': 884, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'iso_number', 'table_id': 58}, 'c_name'], [{'_id': 885, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'disc_abs', 'table_id': 58}, 'c_name'], [{'_id': 886, 'data': {'type': None, 'example': None, 'description': '1 or -1 depending on the sign of the discriminant'}, 'name': 'disc_sign', 'table_id': 58}, 'c_name'], [{'_id': 887, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'disc_rad', 'table_id': 58}, 'c_name'], [{'_id': 888, 'data': {'type': None, 'example': None, 'description': 'the ramified primes in a list. Stored as strings because they may be too big'}, 'name': 'ramps', 'table_id': 58}, 'c_name'], [{'_id': 889, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'galt', 'table_id': 58}, 'c_name'], [{'_id': 890, 'data': {'type': None, 'example': None, 'description': 'class number'}, 'name': 'class_number', 'table_id': 58}, 'c_name'], [{'_id': 891, 'data': {'type': 'comma separated list of integer stored as string', 'example': '`10,5`', 'description': 'invariant factors for the class group, in descending order'}, 'name': 'class_group', 'table_id': 58}, 'c_name'], [{'_id': 892, 'data': {'type': None, 'example': None, 'description': 'True if class group/unit computation assumed GRH. If missing, assume false'}, 'name': 'used_grh', 'table_id': 58}, 'c_name'], [{'_id': 893, 'data': {'type': None, 'example': "`['1','a']`", 'description': "an integral basis in terms of 'a', a root of the defining polynomial"}, 'name': 'zk', 'table_id': 58}, 'c_name'], [{'_id': 894, 'data': {'type': 'collection of latex strings', 'example': None, 'description': 'list of generators of the units modulo torsion, stored as latex ready strings. If there is no class number, assume units are too hard to compute. If there is a class number but no units, units can be computed on the fly'}, 'name': 'units', 'table_id': 58}, 'c_name'], [{'_id': 895, 'data': {'type': 'float or string', 'example': None, 'description': 'regulator, computed if we have fundamental units. It is stored as a float, unless it is so large that there are precision issues, in which case we store it as a string.'}, 'name': 'reg', 'table_id': 58}, 'c_name'], [{'_id': 896, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'subs', 'table_id': 58}, 'c_name'], [{'_id': 897, 'data': {'type': 'List of list of integers', 'example': None, 'description': 'in some cases we have data on the units modulo torsion as an integral Galois module. In each pair, the first coordinate is an index to the database of integral representations of the finite group, and the second is the multiplicity with which this representation appears'}, 'name': 'unitsGmodule', 'table_id': 58}, 'c_name'], [{'_id': 898, 'data': {'type': None, 'example': None, 'description': 'Type of unit group, modulo torsion, as a G-module where G is the Galois group'}, 'name': 'unitsType', 'table_id': 58}, 'c_name'], [{'_id': 899, 'data': {'type': None, 'example': None, 'description': "Resolvent information. Currently, only certain types of siblings are represented. Each key is a type and the value is a list of coefficients of polredabs'ed polynomials. The types are 'gal' for Galois closure, 'ae' for arithmetically equivalent field, 'sex' for twin sextic algebra (for degree 6 fields only), and 'sib' for other siblings."}, 'name': 'res', 'table_id': 58}, 'c_name'], [{'_id': 900, 'data': {'type': None, 'example': "`{'3': 'x^2+3'}`", 'description': 'Local algebras for small prime and degree. Indeces are primes dividing the discriminant, values are lists of polynomials from the local database, separated by commas.'}, 'name': 'loc_algebras', 'table_id': 58}, 'c_name']]], ['sl2z_subgroups', 59, [[{'_id': 901, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'index', 'table_id': 59}, 'c_name'], [{'_id': 902, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'domain', 'table_id': 59}, 'c_name'], [{'_id': 903, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'type', 'table_id': 59}, 'c_name'], [{'_id': 904, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'G', 'table_id': 59}, 'c_name'], [{'_id': 905, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'level', 'table_id': 59}, 'c_name']]], ['smf_dims', 60, [[{'_id': 906, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '111111', 'table_id': 60}, 'c_name'], [{'_id': 907, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '2211', 'table_id': 60}, 'c_name'], [{'_id': 908, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '21111', 'table_id': 60}, 'c_name'], [{'_id': 909, 'data': {'type': None, 'example': None, 'description': "name of the modular group, string (currently always 'Gamma(2)')"}, 'name': 'group', 'table_id': 60}, 'c_name'], [{'_id': 910, 'data': {'type': None, 'example': None, 'description': 'string describing the space'}, 'name': 'description', 'table_id': 60}, 'c_name'], [{'_id': 911, 'data': {'type': None, 'example': None, 'description': 'string naming the author(s)'}, 'name': 'author', 'table_id': 60}, 'c_name'], [{'_id': 912, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '33', 'table_id': 60}, 'c_name'], [{'_id': 913, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '42', 'table_id': 60}, 'c_name'], [{'_id': 914, 'data': {'type': None, 'example': None, 'description': 'string describing the type of the space (either "total" or "cusp")'}, 'name': 'space', 'table_id': 60}, 'c_name'], [{'_id': 915, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '51', 'table_id': 60}, 'c_name'], [{'_id': 916, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '3111', 'table_id': 60}, 'c_name'], [{'_id': 917, 'data': {'type': None, 'example': None, 'description': 'string containing a latex note'}, 'name': 'note', 'table_id': 60}, 'c_name'], [{'_id': 918, 'data': {'type': None, 'example': None, 'description': 'string encoding a nonnegative even integer (currently in [0,100])'}, 'name': 'sym_power', 'table_id': 60}, 'c_name'], [{'_id': 919, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '321', 'table_id': 60}, 'c_name'], [{'_id': 920, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '411', 'table_id': 60}, 'c_name'], [{'_id': 921, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '6', 'table_id': 60}, 'c_name'], [{'_id': 922, 'data': {'type': None, 'example': None, 'description': 'string (currently always set to "Hilbert Poincare series")'}, 'name': 'title', 'table_id': 60}, 'c_name'], [{'_id': 923, 'data': {'type': None, 'example': None, 'description': 'string encoding a rational function in Q(t)'}, 'name': '222', 'table_id': 60}, 'c_name']]], ['smf_ev', 61, [[{'_id': 924, 'data': {'type': None, 'example': None, 'description': 'Object(id) equal to the _id attribute of the sample to which this eigenvalue data belongs'}, 'name': 'owner_id', 'table_id': 61}, 'c_name'], [{'_id': 925, 'data': {'type': None, 'example': None, 'description': 'string encoding the integer index of the eigenvalue (currently an integer in [2..100]). This uniquely identifies the eigenvalue among other eigenvalues with the same owner_id.'}, 'name': 'index', 'table_id': 61}, 'c_name'], [{'_id': 926, 'data': {'type': None, 'example': None, 'description': '"ev" records::\n\n string encoding the eigenvalue as an element of the number field Q(a) of the sample (as defined by field_poly)\n\n "fc" records::\n\n dictionary whose keys are strings encoding integer vectors and whose values are strings encoding (possibly constant) polynomials in Q(a)[x,y]\n\n'}, 'name': 'data', 'table_id': 61}, 'c_name']]], ['smf_families', 62, [[{'_id': 927, 'data': {'type': None, 'example': None, 'description': 'for families with dimension formulas, a dictionary with default values for k and j'}, 'name': 'dim_args_default', 'table_id': 62}, 'c_name'], [{'_id': 928, 'data': {'type': None, 'example': None, 'description': 'latex string for displaying the name'}, 'name': 'latex_name', 'table_id': 62}, 'c_name'], [{'_id': 929, 'data': {'type': None, 'example': None, 'description': 'string identifying the family (e.g. "Sp4Z")'}, 'name': 'name', 'table_id': 62}, 'c_name'], [{'_id': 930, 'data': {'type': None, 'example': None, 'description': 'integer degree of the famly (currently 2, 3, or 4)'}, 'name': 'degree', 'table_id': 62}, 'c_name'], [{'_id': 931, 'data': {'type': None, 'example': None, 'description': 'integer used to control the ordering of the families for display purposes'}, 'name': 'order', 'table_id': 62}, 'c_name']]], ['smf_fc', 63, [[{'_id': 932, 'data': {'type': None, 'example': None, 'description': 'Object(id) equal to the _id attribute of the sample to which this eigenvalue data belongs'}, 'name': 'owner_id', 'table_id': 63}, 'c_name'], [{'_id': 933, 'data': {'type': None, 'example': None, 'description': 'string encoding an integer that uniquely identifies this Fourier coefficient data record among others with the same owner_id (currently an integer in [0..2999])'}, 'name': 'det', 'table_id': 63}, 'c_name'], [{'_id': 934, 'data': {'type': None, 'example': None, 'description': '"ev" records::\n\n string encoding the eigenvalue as an element of the number field Q(a) of the sample (as defined by field_poly)\n\n "fc" records::\n\n dictionary whose keys are strings encoding integer vectors and whose values are strings encoding (possibly constant) polynomials in Q(a)[x,y]\n\n'}, 'name': 'data', 'table_id': 63}, 'c_name']]], ['smf_samples', 64, [[{'_id': 939, 'data': {'type': None, 'example': None, 'description': 'string encoding a monic polynomial f(x) in Z[x] defining a number field Q(a):=Q[x]/(f(x)) (x is used for Q)'}, 'name': 'field_poly', 'table_id': 64}, 'c_name'], [{'_id': 942, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Fourier_coefficients', 'table_id': 64}, 'c_name'], [{'_id': 940, 'data': {'type': None, 'example': None, 'description': 'integer degree of field_poly (current an integer in [1..29])'}, 'name': 'fdeg', 'table_id': 64}, 'c_name'], [{'_id': 941, 'data': {'type': None, 'example': None, 'description': 'boolean'}, 'name': 'is_integral', 'table_id': 64}, 'c_name'], [{'_id': 935, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'id_link', 'table_id': 64}, 'c_name'], [{'_id': 936, 'data': {'type': None, 'example': None, 'description': 'name uniquely identifying the sample within any of the collections it belongs to'}, 'name': 'name', 'table_id': 64}, 'c_name'], [{'_id': 937, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'weight', 'table_id': 64}, 'c_name'], [{'_id': 938, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'degree', 'table_id': 64}, 'c_name'], [{'_id': 943, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'field', 'table_id': 64}, 'c_name'], [{'_id': 944, 'data': {'type': None, 'example': None, 'description': "string describing the type of sample (e.g. 'Ikeda lift, cusp form')"}, 'name': 'type', 'table_id': 64}, 'c_name'], [{'_id': 945, 'data': {'type': None, 'example': None, 'description': 'array of strings identifying families of spaces of Siegel modular forms that contain this sample (the families currently defined are not disjoint, so the same sample may appear in multiple families)'}, 'name': 'collection', 'table_id': 64}, 'c_name'], [{'_id': 946, 'data': {'type': None, 'example': None, 'description': 'string identifying the source of the sample (e.g. authors and date)'}, 'name': 'courtesy_of', 'table_id': 64}, 'c_name'], [{'_id': 947, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'eigenvalues', 'table_id': 64}, 'c_name'], [{'_id': 948, 'data': {'type': None, 'example': None, 'description': 'boolean'}, 'name': 'is_eigenform', 'table_id': 64}, 'c_name'], [{'_id': 949, 'data': {'type': None, 'example': None, 'description': 'string encoding an integer (currently an element of {0,2})'}, 'name': 'representation', 'table_id': 64}, 'c_name'], [{'_id': 950, 'data': {'type': None, 'example': None, 'description': 'string encoding a polynomial in Q(a)[A,B,C,D]'}, 'name': 'explicit_formula', 'table_id': 64}, 'c_name']]], ['ec_curves', 9, [[{'_id': 139, 'data': {'type': None, 'example': None, 'description': 'Cremona label'}, 'name': 'label', 'table_id': 9}, 'c_name'], [{'_id': 140, 'data': {'type': None, 'example': None, 'description': 'LMFDB label'}, 'name': 'lmfdb_label', 'table_id': 9}, 'c_name'], [{'_id': 141, 'data': {'type': None, 'example': None, 'description': 'Cremona isogeny class code'}, 'name': 'iso', 'table_id': 9}, 'c_name'], [{'_id': 142, 'data': {'type': None, 'example': None, 'description': 'LMFDB isogeny class code'}, 'name': 'lmfdb_iso', 'table_id': 9}, 'c_name'], [{'_id': 143, 'data': {'type': None, 'example': None, 'description': 'numerical version of the LMFDB isogeny class label'}, 'name': 'iso_nlabel', 'table_id': 9}, 'c_name'], [{'_id': 144, 'data': {'type': None, 'example': None, 'description': 'Cremona curve number within its class'}, 'name': 'number', 'table_id': 9}, 'c_name'], [{'_id': 145, 'data': {'type': None, 'example': None, 'description': 'LMFDB curve number within its class'}, 'name': 'lmfdb_number', 'table_id': 9}, 'c_name'], [{'_id': 147, 'data': {'type': 'string representing rational', 'example': None, 'description': 'j-invariant'}, 'name': 'jinv', 'table_id': 9}, 'c_name'], [{'_id': 148, 'data': {'type': None, 'example': None, 'description': 'Conductor'}, 'name': 'conductor', 'table_id': 9}, 'c_name'], [{'_id': 149, 'data': {'type': None, 'example': None, 'description': 'torsion order'}, 'name': 'torsion', 'table_id': 9}, 'c_name'], [{'_id': 150, 'data': {'type': None, 'example': None, 'description': 'rank'}, 'name': 'rank', 'table_id': 9}, 'c_name'], [{'_id': 151, 'data': {'type': None, 'example': None, 'description': 'analytic order of sha (rounded value of sha_an)'}, 'name': 'sha', 'table_id': 9}, 'c_name'], [{'_id': 152, 'data': {'type': 'list of integers stored as string', 'example': None, 'description': 'invariants of torsion subgroup'}, 'name': 'torsion_structure', 'table_id': 9}, 'c_name'], [{'_id': 153, 'data': {'type': None, 'example': None, 'description': 'CM code. 0 (for no CM), or a negative discriminant'}, 'name': 'cm', 'table_id': 9}, 'c_name'], [{'_id': 154, 'data': {'type': 'list of integers', 'example': None, 'description': 'Degrees of cyclic isogenies for this curve'}, 'name': 'isogeny_degrees', 'table_id': 9}, 'c_name'], [{'_id': 155, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'nonmax_primes', 'table_id': 9}, 'c_name'], [{'_id': 156, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'nonmax_rad', 'table_id': 9}, 'c_name'], [{'_id': 157, 'data': {'type': None, 'example': None, 'description': 'Weierstrass equation (LaTeX)'}, 'name': 'equation', 'table_id': 9}, 'c_name'], [{'_id': 158, 'data': {'type': None, 'example': None, 'description': 'sign of Discriminant in {-1,+1}'}, 'name': 'signD', 'table_id': 9}, 'c_name'], [{'_id': 159, 'data': {'type': 'list of strings encoding coordinates of points', 'example': None, 'description': 'generators of torsion subgroup'}, 'name': 'torsion_generators', 'table_id': 9}, 'c_name'], [{'_id': 160, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'xcoord_integral_points', 'table_id': 9}, 'c_name'], [{'_id': 161, 'data': {'type': 'list of strings representing homogeneous coordinates of points', 'example': None, 'description': 'Generators of infinite order i projective coordinates.'}, 'name': 'gens', 'table_id': 9}, 'c_name'], [{'_id': 162, 'data': {'type': 'list of reals', 'example': None, 'description': 'Heights of generators.'}, 'name': 'heights', 'table_id': 9}, 'c_name'], [{'_id': 163, 'data': {'type': 'real', 'example': None, 'description': 'Regulator. May be missing; Approximate if rank>0'}, 'name': 'regulator', 'table_id': 9}, 'c_name'], [{'_id': 164, 'data': {'type': None, 'example': None, 'description': 'Product of Tamagawa numbers at all primes'}, 'name': 'tamagawa_product', 'table_id': 9}, 'c_name'], [{'_id': 165, 'data': {'type': None, 'example': None, 'description': "approximate special value of r'th derivative of L-function (divided by r!)"}, 'name': 'special_value', 'table_id': 9}, 'c_name'], [{'_id': 166, 'data': {'type': None, 'example': None, 'description': 'Real period (approximate)'}, 'name': 'real_period', 'table_id': 9}, 'c_name'], [{'_id': 167, 'data': {'type': None, 'example': None, 'description': 'degree of modular parametrization'}, 'name': 'degree', 'table_id': 9}, 'c_name'], [{'_id': 169, 'data': {'type': None, 'example': None, 'description': 'Rouse label of the associated modular curve (null for CM curves). Based on Rouse, Zureik-Brown classification'}, 'name': '2adic_label', 'table_id': 9}, 'c_name'], [{'_id': 170, 'data': {'type': None, 'example': None, 'description': 'index in GL(2,Z2) of the 2-adicrepresentation (or 0 for CM curves)'}, 'name': '2adic_index', 'table_id': 9}, 'c_name'], [{'_id': 171, 'data': {'type': None, 'example': None, 'description': 'the smallest n such that the image contains the kernel of reduction modulo 2^n'}, 'name': '2adic_log_level', 'table_id': 9}, 'c_name'], [{'_id': 172, 'data': {'type': None, 'example': None, 'description': 'list of matrices in GL(2,Z/2^nZ) generating the image (null for CM curves).'}, 'name': '2adic_gens', 'table_id': 9}, 'c_name'], [{'_id': 173, 'data': {'type': 'list of lists of integers', 'example': None, 'description': 'isogeny matrix'}, 'name': 'isogeny_matrix', 'table_id': 9}, 'c_name'], [{'_id': 174, 'data': {'type': None, 'example': None, 'description': 'LCM of isogeny degrees in the isogeny class'}, 'name': 'class_deg', 'table_id': 9}, 'c_name'], [{'_id': 175, 'data': {'type': None, 'example': None, 'description': 'Number of curves in the isogeny class'}, 'name': 'class_size', 'table_id': 9}, 'c_name'], [{'_id': 176, 'data': {'type': 'real', 'example': None, 'description': 'analytic order of Sha, approximate unless rank<2'}, 'name': 'sha_an', 'table_id': 9}, 'c_name'], [{'_id': 177, 'data': {'type': 'list of integers', 'example': None, 'description': 'primes dividing order of Tate-Shafarevich group.'}, 'name': 'sha_primes', 'table_id': 9}, 'c_name'], [{'_id': 178, 'data': {'type': 'list of integers', 'example': None, 'description': 'primes dividing torsion'}, 'name': 'torsion_primes', 'table_id': 9}, 'c_name'], [{'_id': 179, 'data': {'type': None, 'example': None, 'description': 'Degrees of fields in which torsion grows'}, 'name': 'tor_degs', 'table_id': 9}, 'c_name'], [{'_id': 180, 'data': {'type': None, 'example': None, 'description': 'Fields of small degree in which the torsion grows'}, 'name': 'tor_fields', 'table_id': 9}, 'c_name'], [{'_id': 181, 'data': {'type': None, 'example': None, 'description': 'Fields of small degree in which the torsion grows, with the new torsion structure constants'}, 'name': 'tor_gro', 'table_id': 9}, 'c_name'], [{'_id': 182, 'data': {'type': "list of dicts, one per prime, each with keys 'p' (value:int),'ord_cond' (value: int), 'ord_disc' (value: int), 'ord_den_j' (value:int), 'red' (value: int), 'cp' (value: int), 'kod' (value:string), 'rootno' (value:int)'", 'example': None, 'description': 'reduction data at bad primes'}, 'name': 'local_data', 'table_id': 9}, 'c_name'], [{'_id': 183, 'data': {'type': "dict with keys 'disc' (value: int), 'label' (value: string)", 'example': None, 'description': 'minimal quadratic twist'}, 'name': 'min_quad_twist', 'table_id': 9}, 'c_name'], [{'_id': 184, 'data': {'type': 'list of integers', 'example': None, 'description': 'Traces of Frobenius. a_p for p < 100'}, 'name': 'aplist', 'table_id': 9}, 'c_name'], [{'_id': 185, 'data': {'type': 'list of integers', 'example': None, 'description': 'L-series coefficients. a_n for 0 <= n < 20'}, 'name': 'anlist', 'table_id': 9}, 'c_name'], [{'_id': 186, 'data': {'type': 'dictionary with keys ints, values either list of ints, or string', 'example': None, 'description': "Iwasawa invariants. Keys are primes, including all bad multiplicative primes and all primes up to some bound. Values are '?' (unknown), 'a' (additive reduction) or a list of ints: either [lambda,mu] for good ordinary or bad multiplicative reduction, or [lambda+,lambda-,mu] for good supersingular."}, 'name': 'iwdata', 'table_id': 9}, 'c_name'], [{'_id': 187, 'data': {'type': None, 'example': None, 'description': 'Iwasawa prime. if nonzero, a prime p0 such that lambda=mu=0 for all good p>=p0'}, 'name': 'iwp0', 'table_id': 9}, 'c_name'], [{'_id': 188, 'data': {'type': 'list of strings', 'example': None, 'description': "OBSOLETE: see 'mod-p_images'"}, 'name': 'galois_images', 'table_id': 9}, 'c_name'], [{'_id': 146, 'data': {'type': None, 'example': None, 'description': ' '}, 'name': 'ainvs', 'table_id': 9}, 'c_name'], [{'_id': 168, 'data': {'type': None, 'example': None, 'description': '(Description not yet populated)'}, 'name': 'modp_images', 'table_id': 9}, 'c_name']]]]}}, 'latest': {'latest_scan': {'_id': 56, 'INFO': {}, 'name': 'mwf_tables', 'NOTES': {}, 'db_id': 23, 'status': 0, 'nice_name': 'Display data for Maass forms', 'scan_date': {'data': '2018-09-26 17:21:31.772464', '__date__': 0}}}, 'scrapes': {'scrapes_run': 0, 'scrapes_hung': False}, 'connection': {'inv_ok': False, 'can_write': False, 'global_lock': False}}, 'isa': 'report', 'scan_date': {'__date__': 0, 'data': '2019-05-21 17:47:07.114963'}}