-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1896764292577002014721750160371', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -2, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.222721433457888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1, 1]], [7, [1, -1]], [11, [1, -1]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '1155.1', 'coefficient_field': '1.1.1.1', 'conductor': 1155, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 1], [1, 1], [1, -1], [1, -1], [1, 0, 13], [1, -3, 17], [1, 3, 19], [1, 1, 23], [1, 7, 29], [1, -6, 31], [1, 8, 37], [1, 2, 41], [1, 5, 43], [1, 6, 47], [1, 3, 53], [1, 5, 59], [1, 7, 61], [1, -6, 67], [1, 10, 71], [1, -12, 73], [1, 16, 79], [1, 3, 83], [1, -3, 89], [1, 1, 97], [1, 14, 101], [1, 5, 103], [1, -6, 107], [1, 2, 109], [1, 19, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 0, 13], 1]], [[[1, -3, 17], 1]], [[[1, 3, 19], 1]], [[[1, 1, 23], 1]], [[[1, 7, 29], 1]], [[[1, -6, 31], 1]], [[[1, 8, 37], 1]], [[[1, 2, 41], 1]], [[[1, 5, 43], 1]], [[[1, 6, 47], 1]], [[[1, 3, 53], 1]], [[[1, 5, 59], 1]], [[[1, 7, 61], 1]], [[[1, -6, 67], 1]], [[[1, 10, 71], 1]], [[[1, -12, 73], 1]], [[[1, 16, 79], 1]], [[[1, 3, 83], 1]], [[[1, -3, 89], 1]], [[[1, 1, 97], 1]], [[[1, 14, 101], 1]], [[[1, 5, 103], 1]], [[[1, -6, 107], 1]], [[[1, 2, 109], 1]], [[[1, 19, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-1155-1.1-c1-0-26', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1155/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.0075936846380638e-60, 0.11036118732768202, 0.2205684900435472, 0.33041053229077316, 0.4395644547106067, 0.5475485579870368, 0.6536840754516502, 0.757067776591259, 0.8565563073405897, 0.9507624863165649, 1.0380632608296496, 1.116618691765867, 1.1844011521718154, 1.2392338407806611, 1.2788376767897482, 1.300885613225909, 1.303063354775581, 1.2831353780088042, 1.2390150254108945, 1.1688372860113434, 1.0710326964686285, 0.9444006118502095, 0.7881799206770183, 0.6021151295493199, 0.3865156333685496, 0.1423059309069412, -0.1289354464719791, -0.4249504436257974, -0.7427914169563986, -1.0788282392899429, -1.4287739861304298, -1.7877302006997493, -2.1502522430937083, -2.5104346680904572, -2.8620159590938816, -3.1985012881952986, -3.5133012933300725, -3.799884184667106, -4.051937837581651, -4.263537924245071, -4.429317606171418, -4.54463388195749, -4.605725382714857, -4.609856254833222, -4.555440784899023, -4.442143619567533, -4.270950823276812, -4.044207601916125, -3.7656192969073126, -3.440213210068944, -3.074259935750134, -2.6751541259104115, -2.251255961524642, -1.8116960086034422, -1.366147552210939, -0.9245718757277757, -0.49694323111841393, -0.09296137417865812, 0.2782395369657363, 0.6083762115239276, 0.8902858231271326, 1.118170055627969, 1.2878040408676512, 1.3967013271489823, 1.4442270860291582, 1.4316531923933433, 1.3621505682986699, 1.2407162191668566, 1.0740346512806174, 0.8702757686420054, 0.6388338202582544, 0.39001441242473633, 0.13467891583168154, -0.11614231601537915, -0.35165474036082484, -0.5617079113647447, -0.7371918942831074, -0.8704061600226396, -0.9553856370734184, -0.9881695533197236, -0.9670002848159722, -0.8924416139709856, -0.7674085302614351, -0.5971039005906714, -0.38886088695446186, -0.15189376765054477, 0.10303632120996017, 0.3640304230554705, 0.6185217331395924, 0.8537895235266757, 1.0574974608631027, 1.2182348803848768, 1.3260385218612243, 1.3728720829248944, 1.3530417561585208, 1.2635277026054648, 1.1042141478316236, 0.8780043954057267, 0.5908114218715822, 0.25141969193479435, -0.12878077778097938, -0.5361814926356547, -0.9554515360568789, -1.370125204257888, -1.7632591109699953, -2.1181327287682534, -2.4189634025223206, -2.651605111712684, -2.8041998051319985, -2.867751063356696, -2.8365921804973673, -2.7087244519278917, -2.48600639824294, -2.174180673296083, -1.782732263016049, -1.3245789986582193, -0.8156030608304908, -0.2740396909227862, 0.2802536038741396, 0.8266178187304604, 1.3444685626454673, 1.8141892240760094, 2.2180009098677087, 2.540768712037783, 2.770705597373616, 2.8999388489446307, 2.92490941256255, 2.846581519448108, 2.6704482873988153, 2.4063282894089553, 2.0679579025735575, 1.6723941498924426, 1.2392522403212738, 0.7898106168500477, 0.3460235833081524, -0.0705129071237647, -0.43959328753161364, -0.743382112736523, -0.9672927128384593, -1.100719790289516, -1.1375871452657424, -1.076679989040987, -0.9217413427531634, -0.681323363912922, -0.36839655687402817, 0.00026789010172028314, 0.404915565023891, 0.8237882556529922, 1.2342184078315301, 1.6137847790191233, 1.9414711421618138, 2.198768495270926, 2.3706628938773338, 2.446455746203111, 2.4203710316492617, 2.2919141002082544, 2.0659590146523414, 1.7525552128455535, 1.3664588992187106, 0.9264092624733165, 0.4541835753427671, -0.0265223077313417, -0.49133128871841936, -0.916476004298472, -1.280075115957982, -1.563326056224559, -1.7515485737555838, -1.8350202628299301, -1.809555465809905, -1.6767920225031518, -1.4441656573477368, -1.1245685514634807, -0.7357059476548942, -0.2991815336583329, 0.16064210924431338, 0.6179484193964566, 1.0468673247217848, 1.4228949318791702, 1.72425371742819, 1.9331165066516225, 2.036623896978536, 2.0276352592010034, 1.905167525957691, 1.6744929292626431, 1.346885769804868, 0.9390281470196591, 0.4721042280813933, -0.029369052493331025, -0.538911081598225, -1.0295701721951236, -1.4754551167161702, -1.8532175963096587, -2.1433989023387534, -2.3315610657344665, -2.409133933966706, -2.373925408960844, -2.2302611226990066, -1.9887412201688763, -1.665624418277341, -1.281871796751696, -0.8619035178589838, -0.4321395932787403, -0.01940978655268995, 0.35067316142485283, 0.6552792146047756, 0.8757701245618251, 0.9988644923901994, 1.0174849223226121, 0.9312316467299449, 0.746448981765733, 0.4758753947846558, 0.13789338056292574, -0.24457978803659935, -0.6454965895681922, -1.037295973995007, -1.3926347343318193, -1.686127327230061, -1.8959857137990805, -2.005455270162191, -2.0039538539069994, -1.8878381492260625, -1.6607435041632517, -1.3334693347066617, -0.9234102546863698, -0.45356167647095796, 0.04884407449459474, 0.55399082523678, 1.031320859479724, 1.451452845271763, 1.7880550425146, 2.0195542282997123, 2.130569167196103, 2.112973066290436, 1.9665114374235582, 1.698928863290372, 1.325588698895462, 0.8686018485646604, 0.35551241446396115, -0.182382824169716, -0.7119793921207546, -1.2004541901628198, -1.617367034105808, -1.9366400537694521, -2.138285979420926, -2.2097703915829787, -2.1469147179757715, -1.95427486221929, -1.6449631359173054, -1.239916593941836, -0.7666506859551643, -0.25757101146640443, 0.2520543396952575, 0.7263358733096874, 1.1310755366834495, 1.4360029636561888, 1.6167896329753597, 1.6567078656258443], 'positive_zeros': ['1.49628319683318589226316651231880', '3.35399164298404557991082474165654', '4.24991801630843389574934371776531', '5.01570492177079781617268790956125', '5.84009967093002728684369364894770', '6.88447028715167810681872577779388', '7.899830020151268989852881692338816', '8.496053516320620371043593499931160', '9.430337462578200218062202779039136'], 'prelabel': '2-1155-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 74338796896976785, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49628319683318589226316651232', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35399164298404557991082474166', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24991801630843389574934371777', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.222721433457888, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 1155, 'conductor_radical': 1155, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, -2, -1, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 4, 3, 0, -3, 2, -1, 0, -1, 0, 1, 0, -1, -2, -7, 0, 6, 0, -1, 0, -1, -2, -8, 0, 0, 0, -2, 0, -5, -2, -1, 0, -6, -4, 1, 0, -3, 0, -3, 0, -1, 0, 3, 0, -5, -2, -7, 0, 1, -8, 0, 0, 6, -6, 1, 0, -10, 0, 12, 0, -1, 6, 1, 0, -16, -4, 1, 0, -3, 2, -3, 0, 7, 0, 3, 0, 0, 2, -6, 0, 3, 0, -1, 0, 1, -2], 'euler11': [1, -1, 0], 'euler13': [1, 0, 13], 'euler17': [1, -3, 17], 'euler19': [1, 3, 19], 'euler2': [1, 0, 2], 'euler23': [1, 1, 23], 'euler29': [1, 7, 29], 'euler3': [1, 1, 0], 'euler31': [1, -6, 31], 'euler37': [1, 8, 37], 'euler41': [1, 2, 41], 'euler43': [1, 5, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, 3, 53], 'euler59': [1, 5, 59], 'euler61': [1, 7, 61], 'euler67': [1, -6, 67], 'euler7': [1, -1, 0], 'euler71': [1, 10, 71], 'euler73': [1, -12, 73], 'euler79': [1, 16, 79], 'euler83': [1, 3, 83], 'euler89': [1, -3, 89], 'euler97': [1, 1, 97], 'euler_factors': [[1, 0, 2], [1, 1, 0], [1, 1, 0], [1, -1, 0], [1, -1, 0], [1, 0, 13], [1, -3, 17], [1, 3, 19], [1, 1, 23], [1, 7, 29], [1, -6, 31], [1, 8, 37], [1, 2, 41], [1, 5, 43], [1, 6, 47], [1, 3, 53], [1, 5, 59], [1, 7, 61], [1, -6, 67], [1, 10, 71], [1, -12, 73], [1, 16, 79], [1, 3, 83], [1, -3, 89], [1, 1, 97]], 'index': 26, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1155/g', 'ModularForm/GL2/Q/holomorphic/1155/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/1155/2/a/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-1155-1.1-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1155-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 74338796896976785, 'z1': {'__RealLiteral__': 0, 'data': '1.49628319683318589226316651232', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20575456
{'Lhash': '1896764292577002014721750160371', 'Lhash_array': ['1896764292577002014721750160371'], 'label': '2-1155-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/a/g'}
-
id: 24552007
{'Lhash': '1896764292577002014721750160371', 'Lhash_array': ['1896764292577002014721750160371'], 'label': '2-1155-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/a/g/1/1'}
-
id: 41729
{'Lhash': '74338796896976785', 'Lhash_array': ['74338796896976785'], 'label': '2-1155-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1155/g'}