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lfunc_lfunctions • Show schema
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{'Lhash': '2861995962987861709705467234720', 'a10': [-291.38602088003296, -504.6953927795429], 'a2': [3.5446655390623127, -6.139540809494449], 'a3': [0.0, 0.0], 'a4': [-9.129307567631828, -15.812424545061372], 'a5': [41.10204724098098, -71.19083411647526], 'a6': [0.0, 0.0], 'a7': [112.55556319283663, 64.32919395067344], 'a8': [97.4172267780467, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-112.55556319283663, -64.32919395067344]]]], 'bad_primes': [3, 7], 'central_character': '63.37', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '1594854687103078410946931843517', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.5446655390623127, 6.139540809494449], [-16.0, -27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-41.10204724098098, 71.19083411647526], [-1562.5, 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'7.70373413125957173246587058382780', '9.977601256732319963654106604356384', '10.67938760098802880160472721810769', '12.33741132667364789372114958256647', '13.88956751073263425312157135560282', '14.41004958346859163226376460456445'], 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.6451013919364462, 'root_number': '-0.44022519819820827 + 0.8978873954295985*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.322550695968', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25771672610148598719412816747', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.51191873812479901716679137682', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.75784843746866856448144743560', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.2', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/f/37/5'], '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': '2-63-7.2-c5-0-12', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.3225506959682231, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25771672610148598719412816747', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2861995962987861709705467234720', 'Lhash_array': ['2861995962987861709705467234720'], 'label': '2-63-7.2-c5-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/f/37/5'}