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lfunc_lfunctions • Show schema
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{'Lhash': '2443247443349716526071527205105', 'a10': [14.615554986812256, -25.3148838179755], 'a2': [-0.7990272218884501, -1.3839557449414064], 'a3': [0.0, 0.0], 'a4': [2.723110997362451, -4.716566602081325], 'a5': [9.145842961563512, 15.841064687474214], 'a6': [0.0, 0.0], 'a7': [12.392443989449804, -13.763260223084842], 'a8': [-21.487794810680825, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7171203303616602, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-12.392443989449804, 13.763260223084842]]]], 'bad_primes': [3, 7], 'central_character': '63.46', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '1993950634406406947095909880728', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7990272218884501, 1.3839557449414064], [-4.0, 6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [-9.145842961563512, -15.841064687474214], [-62.5, 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[-2006.0881256883395, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-63-7.4-c3-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/63/4/e/d/46/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5685399596303515, 1.6093278474217096, 1.638121927710068, 1.6539780217002324, 1.6555055248262394, 1.6408996735407984, 1.6080067974879533, 1.554420724330733, 1.4776077672446422, 1.3750571337502047, 1.2444529654055028, 1.083863387464514, 0.8919408237625335, 0.6681264145419871, 0.4128497505260465, 0.12771346037583997, -0.18434933892745, -0.5189578743129194, -0.8702205310101314, -1.2307390856795632, -1.591692528654705, -1.943010237259073, -2.2736406382119565, -2.5719166679192473, -2.8260134148656477, -3.024486529811877, 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'12.36733958475721945634189472748732', '13.34642877200258760841220044648810', '14.83904175885881651841784752383985'], 'prelabel': '2-63-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9279834880936249, 'root_angle': 0.25350563271357, 'root_number': '0.6992764979232501 + 0.7148512988392725*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.126752816357', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92738238983978013877255190590', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.59905531405162958262248200220', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.98582912559248432474082167657', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.7171203303616602, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/4/e/d/46/2'], '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': '2-63-7.4-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-63-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9279834880936249, 'root_angle': 0.126752816356785, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92738238983978013877255190590', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2443247443349716526071527205105', 'Lhash_array': ['2443247443349716526071527205105'], 'label': '2-63-7.4-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/4/e/d/46/2'}