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  • lfunc_lfunctions • Show schema
    {'Lhash': '2058074275490167205995222551942,3351446753840818614971340229788', 'a10': 0, 'a2': 0, 'a3': 14, 'a4': -26, 'a5': -38, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -339, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 376.60999875988864, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '121.1', 'coefficient_field': '1.1.1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'euler_factors': [[1, 0, 26, 0, 1024], [1, -14, 535, -3402, 59049], [1, 38, 6611, 118750, 9765625], [1, 0, 31182, 0, 282475249], [1], [1, 0, 195386, 0, 137858491849], [1, 0, -489694, 0, 2015993900449], [1, 0, 455430, 0, 6131066257801], [1, -6142, 22303727, -39532018706, 41426511213649], [1, 0, 40779098, 0, 420707233300201], [1, 3162, 59757863, 90525375462, 819628286980801], [1, 18290, 222318939, 1268300973530, 4808584372417849], [1, 0, -71336686, 0, 13422659310152401], [1, 0, 95089014, 0, 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'11.31926463724405542552456793463151', '11.51115705876298014244318773415968', '12.36924908140251050916223362136927'], 'prelabel': '4-11e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.405274361191442, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e2-0', 'trace_hash': 988565109733380088, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62353433597525133202022977064', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.64382532003488969635477437109', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.46437978352597760446699600659', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 376.60999875988864, 'bad_primes': [11], 'central_character': '1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'dirichlet_coefficients': [1, 0, 14, -26, -38, 0, 0, 0, -339, 0, 0, -364, 0, 0, -532, -348, 0, 0, 0, 988, 0, 0, 6142, 0, -5167, 0, -8834, 0, 0, 0, -3162, 0, 0, 0, 0, 8814, -18290, 0, 0, 0, 0, 0, 0, 0, 12882, 0, -33272, -4872, -31182, 0, 0, 0, -32532, 0, 0, 0, 0, 0, 29010, 13832, 0, 0, 0, 35672, 0, 0, -21270, 0, 85988, 0, 62090, 0, 0, 0, -72338, 0, 0, 0, 0, 13224, 46268, 0, 0, 0, 0, 0, 0, 0, -218962, 0, 0, -159692, -44268, 0, 0, 0, -27230, 0, 0, 134342], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 0, 195386, 0, 137858491849], 'euler17': [1, 0, -489694, 0, 2015993900449], 'euler19': [1, 0, 455430, 0, 6131066257801], 'euler2': [1, 0, 26, 0, 1024], 'euler23': [1, -6142, 22303727, -39532018706, 41426511213649], 'euler29': [1, 0, 40779098, 0, 420707233300201], 'euler3': [1, -14, 535, -3402, 59049], 'euler31': [1, 3162, 59757863, 90525375462, 819628286980801], 'euler37': [1, 18290, 222318939, 1268300973530, 4808584372417849], 'euler41': [1, 0, -71336686, 0, 13422659310152401], 'euler43': [1, 0, 95089014, 0, 21611482313284249], 'euler47': [1, 33272, 735446510, 7630767072904, 52599132235830049], 'euler5': [1, 38, 6611, 118750, 9765625], 'euler53': [1, 32532, 1100973742, 13604735778276, 174887470365513049], 'euler59': [1, -29010, 1640243623, -20739953913990, 511116753300641401], 'euler61': [1, 0, 1628480154, 0, 713342911662882601], 'euler67': [1, 21270, 2813353439, 28717161025890, 1822837804551761449], 'euler7': [1, 0, 31182, 0, 282475249], 'euler71': [1, -62090, 4572250727, -112024600403590, 3255243551009881201], 'euler73': [1, 0, 3011641938, 0, 4297625829703557649], 'euler79': [1, 0, -857839330, 0, 9468276082626847201], 'euler83': [1, 0, 683252486, 0, 15516041187205853449], 'euler89': [1, 218962, 23154208259, 1222696825071938, 31181719929966183601], 'euler97': [1, 27230, 17360048739, 233833275198110, 73742412689492826049], 'euler_factors': [[1, 0, 26, 0, 1024], [1, -14, 535, -3402, 59049], [1, 38, 6611, 118750, 9765625], [1, 0, 31182, 0, 282475249], [1, 0, 0, 0, 0], [1, 0, 195386, 0, 137858491849], [1, 0, -489694, 0, 2015993900449], [1, 0, 455430, 0, 6131066257801], [1, -6142, 22303727, -39532018706, 41426511213649], [1, 0, 40779098, 0, 420707233300201], [1, 3162, 59757863, 90525375462, 819628286980801], [1, 18290, 222318939, 1268300973530, 4808584372417849], [1, 0, -71336686, 0, 13422659310152401], [1, 0, 95089014, 0, 21611482313284249], [1, 33272, 735446510, 7630767072904, 52599132235830049], [1, 32532, 1100973742, 13604735778276, 174887470365513049], [1, -29010, 1640243623, -20739953913990, 511116753300641401], [1, 0, 1628480154, 0, 713342911662882601], [1, 21270, 2813353439, 28717161025890, 1822837804551761449], [1, -62090, 4572250727, -112024600403590, 3255243551009881201], [1, 0, 3011641938, 0, 4297625829703557649], [1, 0, -857839330, 0, 9468276082626847201], [1, 0, 683252486, 0, 15516041187205853449], [1, 218962, 23154208259, 1222696825071938, 31181719929966183601], [1, 27230, 17360048739, 233833275198110, 73742412689492826049]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/121/6/a/c'], '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': '4-11e4-1.1-c5e2-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 2, 'prelabel': '4-11e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.405274361191442, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 988565109733380088, 'z1': {'__RealLiteral__': 0, 'data': '1.62353433597525133202022977064', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2058074275490167205995222551942,3351446753840818614971340229788', 'Lhash_array': ['2058074275490167205995222551942', '3351446753840818614971340229788'], 'factors': ['2-11e2-1.1-c5-0-23', '2-11e2-1.1-c5-0-37'], 'label': '4-11e4-1.1-c5e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/121/6/a/c'}