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{'Lhash': '404390949423358667032010704079,1019439480466785646392877525298,2098072724811633556028349993460,2629309452632479425516582551572', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 2, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4848.122555883773, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 4, 14, 20, 25]], [11, [1, 4, 6, 4, 1]], [19, [1, -4, 6, -4, 1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.1', 'coefficient_field': '1.1.1.1', 'conductor': 1192518600625, 'conductor_radical': 1045, 'degree': 8, 'euler_factors': [[1, 0, -2, 0, 1, 0, -8, 0, 16], [1, 0, -4, 0, 22, 0, -36, 0, 81], [1, 4, 14, 20, 25], [1, 0, -4, 0, -26, 0, -196, 0, 2401], [1, 4, 6, 4, 1], [1, 0, -4, 0, -170, 0, -676, 0, 28561], [1, 0, -20, 0, 166, 0, -5780, 0, 83521], [1, -4, 6, -4, 1], [1, 0, -20, 0, 646, 0, -10580, 0, 279841], [1, -8, 124, -664, 5526, -19256, 104284, -195112, 707281], [1, 16, 204, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4848.122555883773, 'bad_primes': [5, 11, 19], 'central_character': '1.1', 'conductor': 1192518600625, 'conductor_radical': 1045, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 2, -4, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 3, 0, 0, 4, -8, 0, 0, 0, 0, 2, 0, 0, 0, 8, 0, -16, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, 0, 0, -8, -16, 0, 0, 0, 4, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -8, 0, 0, 12, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 8, 0, 0, 0, -12, -6, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -16, 0, 0, 0, -16, 4], 'euler11': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler13': [1, 0, -4, 0, -170, 0, -676, 0, 28561], 'euler17': [1, 0, -20, 0, 166, 0, -5780, 0, 83521], 'euler19': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler2': [1, 0, -2, 0, 1, 0, -8, 0, 16], 'euler23': [1, 0, -20, 0, 646, 0, -10580, 0, 279841], 'euler29': [1, -8, 124, -664, 5526, -19256, 104284, -195112, 707281], 'euler3': [1, 0, -4, 0, 22, 0, -36, 0, 81], 'euler31': [1, 16, 204, 1616, 10790, 50096, 196044, 476656, 923521], 'euler37': [1, 0, -4, 0, 2742, 0, -5476, 0, 1874161], 'euler41': [1, 8, 44, 440, 4870, 18040, 73964, 551368, 2825761], 'euler43': [1, 0, -148, 0, 9046, 0, -273652, 0, 3418801], 'euler47': [1, 0, -52, 0, 486, 0, -114868, 0, 4879681], 'euler5': [1, 4, 14, 20, 25, 0, 0, 0, 0], 'euler53': [1, 0, -68, 0, 4726, 0, -191012, 0, 7890481], 'euler59': [1, 0, 220, 0, 19062, 0, 765820, 0, 12117361], 'euler61': [1, 8, 268, 1496, 25270, 91256, 997228, 1815848, 13845841], 'euler67': [1, 0, -196, 0, 18582, 0, -879844, 0, 20151121], 'euler7': [1, 0, -4, 0, -26, 0, -196, 0, 2401], 'euler71': [1, 48, 1132, 16752, 169158, 1189392, 5706412, 17179728, 25411681], 'euler73': [1, 0, -244, 0, 25030, 0, -1300276, 0, 28398241], 'euler79': [1, 0, 252, 0, 28358, 0, 1572732, 0, 38950081], 'euler83': [1, 0, -180, 0, 20726, 0, -1240020, 0, 47458321], 'euler89': [1, -40, 892, -13400, 147558, -1192600, 7065532, -28198760, 62742241], 'euler97': [1, 0, -340, 0, 47206, 0, -3199060, 0, 88529281], 'euler_factors': [[1, 0, -2, 0, 1, 0, -8, 0, 16], [1, 0, -4, 0, 22, 0, -36, 0, 81], [1, 4, 14, 20, 25, 0, 0, 0, 0], [1, 0, -4, 0, -26, 0, -196, 0, 2401], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 0, -4, 0, -170, 0, -676, 0, 28561], [1, 0, -20, 0, 166, 0, -5780, 0, 83521], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 0, -20, 0, 646, 0, -10580, 0, 279841], [1, -8, 124, -664, 5526, -19256, 104284, -195112, 707281], [1, 16, 204, 1616, 10790, 50096, 196044, 476656, 923521], [1, 0, -4, 0, 2742, 0, -5476, 0, 1874161], [1, 8, 44, 440, 4870, 18040, 73964, 551368, 2825761], [1, 0, -148, 0, 9046, 0, -273652, 0, 3418801], [1, 0, -52, 0, 486, 0, -114868, 0, 4879681], [1, 0, -68, 0, 4726, 0, -191012, 0, 7890481], [1, 0, 220, 0, 19062, 0, 765820, 0, 12117361], [1, 8, 268, 1496, 25270, 91256, 997228, 1815848, 13845841], [1, 0, -196, 0, 18582, 0, -879844, 0, 20151121], [1, 48, 1132, 16752, 169158, 1189392, 5706412, 17179728, 25411681], [1, 0, -244, 0, 25030, 0, -1300276, 0, 28398241], [1, 0, 252, 0, 28358, 0, 1572732, 0, 38950081], [1, 0, -180, 0, 20726, 0, -1240020, 0, 47458321], [1, -40, 892, -13400, 147558, -1192600, 7065532, -28198760, 62742241], [1, 0, -340, 0, 47206, 0, -3199060, 0, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/2/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': '8-1045e4-1.1-c1e4-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1045e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.888661802846398, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1969039609964933447, 'z1': {'__RealLiteral__': 0, 'data': '0.31900821042529512003868514157', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '404390949423358667032010704079,1019439480466785646392877525298,2098072724811633556028349993460,2629309452632479425516582551572', 'Lhash_array': ['404390949423358667032010704079', '1019439480466785646392877525298', '2098072724811633556028349993460', '2629309452632479425516582551572'], 'label': '8-1045e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/2/b/a'}