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lfunc_lfunctions • Show schema
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{'Lhash': '5053490450368440596582197569998', 'a10': -418860, 'a2': 78, 'a3': -243, 'a4': 4036, 'a5': -5370, 'a6': -18954, 'a7': -27760, 'a8': 155064, 'a9': 59049, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.305029541678767, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 243]]], 'bad_primes': [3], 'central_character': '3.1', 'coefficient_field': '1.1.1.1', 'conductor': 3, 'conductor_radical': 3, 'degree': 2, 'euler_factors': [[1, -78, 2048], [1, 243], [1, 5370, 48828125], [1, 27760, 1977326743], [1, -637836, 285311670611], [1, -766214, 1792160394037], [1, -3084354, 34271896307633], [1, 19511404, 116490258898219], [1, -15312360, 952809757913927], [1, -10751262, 12200509765705829], [1, 50937400, 25408476896404831], [1, -664740830, 177917621779460413], [1, -898833450, 550329031716248441], [1, 957947188, 929293739471222707], [1, 1555741344, 2472159215084012303], [1, -3792417030, 9269035929372191597], [1, -555306924, 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177917621779460413], 1]], [[[1, -898833450, 550329031716248441], 1]], [[[1, 957947188, 929293739471222707], 1]], [[[1, 1555741344, 2472159215084012303], 1]], [[[1, -3792417030, 9269035929372191597], 1]], [[[1, -555306924, 30155888444737842659], 1]], [[[1, -4950420998, 43513917611435838661], 1]], [[[1, -5292399284, 122130132904968017083], 1]], [[[1, 14831086248, 231122292121701565271], 1]], [[[1, -13971005210, 313726685568359708377], 1]], [[[1, -3720542360, 747993810527520928879], 1]], [[[1, -8768454036, 1287831418538085836267], 1]], [[[1, 25472769174, 2775173073766990340489], 1]], [[[1, 39092494846, 7153014030880804126753], 1]], [[[1, -9310781526, 11156683466653165551101], 1]], [[[1, -48575052512, 13842338707244455781047], 1]], [[[1, -225595713276, 21048519522998348950643], 1]], [[[1, 69451179514, 25804264053054077850709], 1]], [[[1, 359664575694, 38358611506121121577937], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3-1.1-c11-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3/12/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [2.317708444208957, 2.313085242962998, 2.299195381914941, 2.2759795049616582, 2.2433434049048784, 2.201165102230305, 2.1493047488889747, 2.0876173386477186, 2.0159681835061627, 1.9342510814410636, 1.8424090521726977, 1.7404574529909491, 1.6285092047028369, 1.5068017579270592, 1.3757253125789093, 1.2358516698091635, 1.0879629484459907, 0.9330792410850637, 0.7724841238516256, 0.60774677561817, 0.44073931586793197, 0.27364784583610835, 0.10897558690201357, -0.05046353348560423, -0.20156248093477028, -0.3409514388440665, -0.4650422188272649, -0.5700878358705275, -0.6522579360035858, -0.7077302567843805, -0.7327976760874942, -0.72398966760843, -0.6782061445730992, 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'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5182323740714947, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c11-0', 'trace_hash': 890658222227714411, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.98650105120338668052543062604', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.38978670338428742867669092804', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '11.44100936879895756795295476050', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.305029541678767, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 3, 'conductor_radical': 3, 'degree': 2, 'dirichlet_coefficients': [1, 78, -243, 4036, -5370, -18954, -27760, 155064, 59049, -418860, 637836, -980748, 766214, -2165280, 1304910, 3829264, 3084354, 4605822, -19511404, -21673320, 6745680, 49751208, 15312360, -37680552, -19991225, 59764692, -14348907, -112039360, 10751262, 101782980, -50937400, -18888480, -154994148, 240579612, 149071200, 238321764, 664740830, -1521889512, -186190002, -832693680, 898833450, 526163040, -957947188, 2574306096, -317093130, 1194364080, -1555741344, -930511152, -1206709143, -1559315550, -749498022, 3092439704, 3792417030, -1119214746, -3425179320, -4304576640, 4741271172, 838598436, 555306924, 5266616760, 4950420998, -3973117200, -1639200240, -9315634112, -4114569180, -12089543544, 5292399284, 12448452744, -3720903480, 11627553600, -14831086248, 9156374136, 13971005210, 51849784740, 4857867675, -78748026544, -17706327360, -14522820156, 3720542360, -20563147680, 3486784401, 70109009100, 8768454036, 27225564480, -16562980980, -74719880664, -2612556666, 98905401504, -25472769174, -24733264140, -21270100640, 61800684960, 12377788200, -121347824832, 104776239480, 4589900640, -39092494846, -94123313154, 37663577964, -80684584100], 'euler11': [1, -637836, 285311670611], 'euler13': [1, -766214, 1792160394037], 'euler17': [1, -3084354, 34271896307633], 'euler19': [1, 19511404, 116490258898219], 'euler2': [1, -78, 2048], 'euler23': [1, -15312360, 952809757913927], 'euler29': [1, -10751262, 12200509765705829], 'euler3': [1, 243, 0], 'euler31': [1, 50937400, 25408476896404831], 'euler37': [1, -664740830, 177917621779460413], 'euler41': [1, -898833450, 550329031716248441], 'euler43': [1, 957947188, 929293739471222707], 'euler47': [1, 1555741344, 2472159215084012303], 'euler5': [1, 5370, 48828125], 'euler53': [1, -3792417030, 9269035929372191597], 'euler59': [1, -555306924, 30155888444737842659], 'euler61': [1, -4950420998, 43513917611435838661], 'euler67': [1, -5292399284, 122130132904968017083], 'euler7': [1, 27760, 1977326743], 'euler71': [1, 14831086248, 231122292121701565271], 'euler73': [1, -13971005210, 313726685568359708377], 'euler79': [1, -3720542360, 747993810527520928879], 'euler83': [1, -8768454036, 1287831418538085836267], 'euler89': [1, 25472769174, 2775173073766990340489], 'euler97': [1, 39092494846, 7153014030880804126753], 'euler_factors': [[1, -78, 2048], [1, 243, 0], [1, 5370, 48828125], [1, 27760, 1977326743], [1, -637836, 285311670611], [1, -766214, 1792160394037], [1, -3084354, 34271896307633], [1, 19511404, 116490258898219], [1, -15312360, 952809757913927], [1, -10751262, 12200509765705829], [1, 50937400, 25408476896404831], [1, -664740830, 177917621779460413], [1, -898833450, 550329031716248441], [1, 957947188, 929293739471222707], [1, 1555741344, 2472159215084012303], [1, -3792417030, 9269035929372191597], [1, -555306924, 30155888444737842659], [1, -4950420998, 43513917611435838661], [1, -5292399284, 122130132904968017083], [1, 14831086248, 231122292121701565271], [1, -13971005210, 313726685568359708377], [1, -3720542360, 747993810527520928879], [1, -8768454036, 1287831418538085836267], [1, 25472769174, 2775173073766990340489], [1, 39092494846, 7153014030880804126753]], 'index': 0, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3/12/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/3/12/a/a'], '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': '2-3-1.1-c11-0-0', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-3-1.1-c11-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5182323740714947, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11-0', 'trace_hash': 890658222227714411, 'z1': {'__RealLiteral__': 0, 'data': '3.98650105120338668052543062604', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9966882
{'Lhash': '5053490450368440596582197569998', 'Lhash_array': ['5053490450368440596582197569998'], 'label': '2-3-1.1-c11-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3/12/a/a'}
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id: 24548888
{'Lhash': '5053490450368440596582197569998', 'Lhash_array': ['5053490450368440596582197569998'], 'label': '2-3-1.1-c11-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3/12/a/a/1/1'}