-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '777454960134180020337342404012', 'a10': [1.0, 0], 'a2': [-1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [0, 0.3763599724728831], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.14979241883209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [67, [[1.0, 0], [7.529577371201078, 3.210212549208645]]]], 'bad_primes': [2, 3, 5, 67], 'central_character': '6030.2411', 'coefficient_field': 'CDF', 'conductor': 6030, 'conductor_radical': 2010, 'conjugate': '1054590799840396103466183838783', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -0.3763599724728831], [-7.0, 0]], [[1.0, 0], [-3.4376585964023403, 0], [11.0, 0]], [[1.0, 0], [0, 3.040714941909713], [-13.0, 0]], [[1.0, 0], [0, -5.534920747752965], [-17.0, 0]], [[1.0, 0], [-4.4225824300481635, 0], [19.0, 0]], [[1.0, 0], [0, -2.1418436233186293], [-23.0, 0]], [[1.0, 0], [0, 1.985021563665532], [-29.0, 0]], [[1.0, 0], [0, -2.8672237931986997], [-31.0, 0]], [[1.0, 0], [0.23366214918855813, 0], [37.0, 0]], [[1.0, 0], [-1.7876762090710132, 0], [41.0, 0]], [[1.0, 0], [0, 9.772891129725712], [-43.0, 0]], [[1.0, 0], [0, 5.439076981813299], [-47.0, 0]], [[1.0, 0], [-5.1124586176206535, 0], [53.0, 0]], [[1.0, 0], [0, -14.970678430250308], [-59.0, 0]], [[1.0, 0], [0, -11.622241233030286], [-61.0, 0]], [[1.0, 0], [7.529577371201078, 3.210212549208645]], [[1.0, 0], [0, -9.675511417452794], [-71.0, 0]], [[1.0, 0], [9.52485367017311, 0], [73.0, 0]], [[1.0, 0], [0, 5.921233064434283], [-79.0, 0]], [[1.0, 0], [0, -5.4278948668162235], [-83.0, 0]], [[1.0, 0], [0, 3.008199808292136], [-89.0, 0]], [[1.0, 0], [0, 11.274623255667745], [-97.0, 0]], [[1.0, 0], [13.368704311020293, 0], [101.0, 0]], [[1.0, 0], [-2.948829151044865, 0], [103.0, 0]], [[1.0, 0], [0, 3.1084227986803157], [-107.0, 0]], [[1.0, 0], [0, 15.957971311635298], [-109.0, 0]], [[1.0, 0], [-15.911341417620314, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-6030-201.200-c1-0-33', 'leading_term': '1.340918755245369238521662586248330594520336793859852254', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6030/2/d/k/2411/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.3409187552453692, 1.2991523043271378, 1.2455750790478903, 1.1804685293453867, 1.1041391891420942, 1.0169443571727568, 0.9193222531104164, 0.8118245436951459, 0.6951490273853513, 0.5701702998988216, 0.43796637273502786, 0.29983945179414745, 0.15732937284525844, 0.012218508683883147, -0.1334727098689456, -0.27750019237690654, -0.41742072374747247, -0.550626546734158, -0.6743896060109725, -0.7859147787717584, -0.8824011351198303, -0.9611099982982786, -1.0194383130784253, -1.0549955853058153, -1.065682433306672, -1.0497686004615752, -1.0059681264188092, -0.9335092710649723, -0.8321967391353767, -0.7024637720763176, -0.5454117640260954, -0.36283522539097685, -0.1572301631583901, 0.06821572794538204, 0.3096522675608075, 0.5626161159443432, 0.822100418932073, 1.082644378122859, 1.338441727129799, 1.5834664482672096, 1.8116134157454877, 2.0168510221311697, 2.193382256498714, 2.335810177905779, 2.4393032889224697, 2.499755982300202, 2.513939029011946, 2.4796350146975694, 2.3957537273837834, 2.262422761346675, 2.081049034352406, 1.8543475169792463, 1.5863342361461341, 1.2822815271053247, 0.9486345496377244, 0.5928892297408866, 0.2234330069586703, -0.15064897591290607, -0.5197983492022505, -0.8742335565737162, -1.2042192340635982, -1.5003477120221154, -1.7538246074062782, -1.9567498707974944, -2.102385297550046, -2.1853994338142444, -2.2020810262262507, -2.1505126901444007, -2.0306973066580327, -1.8446307935737953, -1.5963163093449055, -1.2917166093822166, -0.9386431385144453, -0.546582458760874, -0.1264627166151183, 0.30963501965669205, 0.7488136478653726, 1.1777362934123983, 1.583031349588063, 1.9517142342261165, 2.2716126753588495, 2.5317816143274565, 2.722893538145982, 2.837590256856945, 2.8707828434592466, 2.81988765373665, 2.684988022690745, 2.468913356397142, 2.1772298478226544, 1.8181398701720946, 1.4022901540403288, 0.942492034558948, 0.4533602516914277, -0.04912011529973221, -0.5480861174198363, -1.0263337995139652, -1.4668823404248756, -1.8535467824312533, -2.171499710991446, -2.407801973241985, -2.5518829679537762, -2.5959522127737125, -2.5353257812630736, -2.3686537591659698, -2.0980380256045215, -1.7290333235843969, -1.2705286250365746, -0.7345100787349649, -0.13571120001213108, 0.5088397449605969, 1.1803611579256688, 1.8589306866727018, 2.524148240227196, 3.1558263402760476, 3.734683144528609, 4.243012815770043, 4.665308203602057, 4.988812071607602, 5.203975319861557, 5.304803761339762, 5.2890789129537, 5.158442824514897, 4.918342027763024, 4.577831053218486, 4.149241427260383, 3.647727407388336, 3.090704720443321, 2.4972030245544743, 1.8871565253847375, 1.2806599709924449, 0.6972189909034706, 0.15502433769400478, -0.32972101695476635, -0.7433947864433929, -1.0754440859769088, -1.318749783065574, -1.4698512165175497, -1.5290216474590614, -1.5001909255628378, -1.390718213016305, -1.2110239403153844, -0.9740961990958311, -0.6948922419806035, -0.38966041049583827, -0.07521143218639291, 0.23182955969513877, 0.5157578535895763, 0.7624787331809392, 0.9601214419791256, 1.0995502931384376, 1.1747500363709844, 1.1830680260845337, 1.12530201589801, 1.005629265463336, 0.8313797851410716, 0.6126636427382207, 0.3618689897727103, 0.09305351833979839, -0.178742855631783, -0.4382324213814857, -0.6706271054858677, -0.8623639048162781, -1.0017740457937232, -1.0796639365839706, -1.089779849332855, -1.029133511621101, -0.8981721743372476, -0.7007839726461635, -0.4441371766258067, -0.13835987563264865, 0.2039256223777214, 0.5681922436652819, 0.9386938087907604, 1.2992142985966582, 1.633844684653193, 1.9277495515102898, 2.167885828517999, 2.3436378870179198, 2.447336980271419, 2.474638355554435, 2.424736114021716, 2.3004037242843793, 2.107856640375293, 1.8564423213091479, 1.558171661964683, 1.2271139857162037, 0.8786849001717265, 0.5288621018498839, 0.19336831808086113, -0.11313724232908486, -0.37781743912477567, -0.5903262495275327, -0.7433528482391055, -0.833011162102996, -0.8590528649239527, -0.8248905557532497, -0.7374274713996793, -0.6067000433863431, -0.44534941534701444, -0.2679471805549603, -0.09020859594970469, 0.07186705727420103, 0.20288482900278695, 0.28892478286060724, 0.31834874364681987, 0.2824993907860055, 0.1762528560106658, -0.001607014438339581, -0.24821576933809847, -0.5566696901234833, -0.9162831631896912, -1.3130525367032508, -1.7303058397266289, -2.149507543535665, -2.551178777432302, -2.9158865669828016, -3.2252511433609983, -3.4629184658993286, -3.615445961293735, -3.6730531237558477, -3.6301949046853847, -3.4859244681968167, -3.244022487798058, -2.912882183988591, -2.505152138858031, -2.0371519010978085, -1.5280878198356362, -0.9991077391974663, -0.47224251937766465, 0.030710717775656027, 0.489304614753776, 0.8854968740909336, 1.2045870518109842, 1.4359824823163574, 1.5737493244603036, 1.6169156343708548, 1.569506307686328, 1.4403040315027718, 1.2423452946451516, 0.9921752235241008, 0.7088987314678367, 0.4130774195547295, 0.12553115309022328, -0.13389031480235253, -0.34749731419972996, -0.5008441813478774, -0.5836439534918959, -0.5904587049394446, -0.5211216693421932, -0.38086124849113556, -0.1801129363594571, 0.06597774299066549, 0.3383408877200444, 0.6150194881312683, 0.8724064161145229, 1.0866168233243867, 1.2349224806232317], 'positive_zeros': ['0.61330382362001489664179291792151', '1.53307523962305345393139594518703', '2.65299166696568579144678559319912', '3.48246038095189275638957275671170', '4.35480402758117036191314778204320', '5.07260581133815785569049415422888', '6.15495999901556644904844033888824', '6.76128515485560416392789580856167', '7.37534837231078324880568485049809', '7.941320876923277705154314746913571'], 'prelabel': '2-6030-201.200-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.939005146188616, 'root_angle': -0.1758043398671231, 'root_number': '0.85131713767702968392268411390047936192170221515062702486 - 0.5246514377159270552678677979307181662682237152889484897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.08790216993356155', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61330382362001489664179291792', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.53307523962305345393139594519', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.65299166696568579144678559320', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 48.14979241883209, 'bad_primes': [2, 3, 5, 67], 'central_character': '201.200', 'conductor': 6030, 'conductor_radical': 2010, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6030/2/d/k/2411/14'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-6030-201.200-c1-0-33', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6030-201.200-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.939005146188616, 'root_angle': -0.08790216993356155, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61330382362001489664179291792', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '777454960134180020337342404012', 'Lhash_array': ['777454960134180020337342404012'], 'label': '2-6030-201.200-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6030/2/d/k/2411/14'}