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lfunc_lfunctions • Show schema
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{'Lhash': '4261528175825625988770814566311,5980817723622454958701276511852', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -8, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.24055540206937767, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '18.1', 'coefficient_field': '1.1.1.1', 'conductor': 324, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, 0, 2], [1], [1, 0, -32, 0, 625], [1, 8, 114, 392, 2401], [1, 0, 46, 0, 14641], [1, -16, 402, -2704, 28561], [1, 0, -416, 0, 83521], [1, 32, 978, 11552, 130321], [1, 0, -770, 0, 279841], [1, 0, -1664, 0, 707281], [1, -88, 3858, -84568, 923521], [1, 68, 3894, 93092, 1874161], [1, 0, -1184, 0, 2825761], [1, 80, 5298, 147920, 3418801], [1, 0, 2782, 0, 4879681], [1, 0, -4160, 0, 7890481], [1, 0, -5810, 0, 12117361], [1, -100, 9942, -372100, 13845841], [1, -16, 9042, -71824, 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'root_analytic_conductor': 0.7003316898788277, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 305516784036938827, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.36175297440665047564543646315', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.71803328341868101997909002331', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.24803028236882973923729368575', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.24055540206937767, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 324, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, -8, 0, 0, 0, 0, 0, 16, 0, 0, 4, 0, 0, -32, 0, 0, 0, 0, 0, 32, 0, 0, 16, 0, 0, 88, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -50, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, -8, 0, 0, 16, 0, 0, 0, 0, 0, -32, 0, 0, 64, 0, 0, -152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 352, 0, 0, -64], 'euler11': [1, 0, 46, 0, 14641], 'euler13': [1, -16, 402, -2704, 28561], 'euler17': [1, 0, -416, 0, 83521], 'euler19': [1, 32, 978, 11552, 130321], 'euler2': [1, 0, 2, 0, 0], 'euler23': [1, 0, -770, 0, 279841], 'euler29': [1, 0, -1664, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -88, 3858, -84568, 923521], 'euler37': [1, 68, 3894, 93092, 1874161], 'euler41': [1, 0, -1184, 0, 2825761], 'euler43': [1, 80, 5298, 147920, 3418801], 'euler47': [1, 0, 2782, 0, 4879681], 'euler5': [1, 0, -32, 0, 625], 'euler53': [1, 0, -4160, 0, 7890481], 'euler59': [1, 0, -5810, 0, 12117361], 'euler61': [1, -100, 9942, -372100, 13845841], 'euler67': [1, -16, 9042, -71824, 20151121], 'euler7': [1, 8, 114, 392, 2401], 'euler71': [1, 0, -7490, 0, 25411681], 'euler73': [1, 32, 10914, 170528, 28398241], 'euler79': [1, 152, 18258, 948632, 38950081], 'euler83': [1, 0, 334, 0, 47458321], 'euler89': [1, 0, -15680, 0, 62742241], 'euler97': [1, -352, 49794, -3311968, 88529281], 'euler_factors': [[1, 0, 2, 0, 0], [1, 0, 0, 0, 0], [1, 0, -32, 0, 625], [1, 8, 114, 392, 2401], [1, 0, 46, 0, 14641], [1, -16, 402, -2704, 28561], [1, 0, -416, 0, 83521], [1, 32, 978, 11552, 130321], [1, 0, -770, 0, 279841], [1, 0, -1664, 0, 707281], [1, -88, 3858, -84568, 923521], [1, 68, 3894, 93092, 1874161], [1, 0, -1184, 0, 2825761], [1, 80, 5298, 147920, 3418801], [1, 0, 2782, 0, 4879681], [1, 0, -4160, 0, 7890481], [1, 0, -5810, 0, 12117361], [1, -100, 9942, -372100, 13845841], [1, -16, 9042, -71824, 20151121], [1, 0, -7490, 0, 25411681], [1, 32, 10914, 170528, 28398241], [1, 152, 18258, 948632, 38950081], [1, 0, 334, 0, 47458321], [1, 0, -15680, 0, 62742241], [1, -352, 49794, -3311968, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/3/b/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': '4-18e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-18e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 305516784036938827, 'z1': {'__RealLiteral__': 0, 'data': '3.36175297440665047564543646315', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4261528175825625988770814566311,5980817723622454958701276511852', 'Lhash_array': ['4261528175825625988770814566311', '5980817723622454958701276511852'], 'label': '4-18e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/3/b/a'}