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lfunc_lfunctions • Show schema
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{'Lhash': '944282176960075201745123680309,1208803490672709311658304460940', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3529.393529209725, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 1]], [5, [1, -2, 1]], [31, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '7440.1', 'coefficient_field': '1.1.1.1', 'conductor': 55353600, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1], [1, -2, 1], [1, -2, 1], [1, 1, 10, 7, 49], [1, 1, 18, 11, 121], [1, -4, 30, -52, 169], [1, -2, 18, -34, 289], [1, -3, 2, -57, 361], [1, 7, 54, 161, 529], [1, -6, 50, -174, 841], [1, 2, 1], [1, -2, 58, -74, 1369], [1, -6, 74, -246, 1681], [1, 5, -14, 215, 1849], [1, 2, 78, 94, 2209], [1, -19, 192, -1007, 2809], [1, -18, 182, -1062, 3481], [1, -12, 158, -732, 3721], [1, -6, -10, -402, 4489], [1, -3, 106, -213, 5041], [1, 1, 40, 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'7.36637808857125504513710442176043', '7.953679186914090726885351048719336', '8.102653435309411881512184918512363'], 'prelabel': '4-7440e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.7077038801339945, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1260675585200591520, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74490729290079258126477942500', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.953577815886392368258272183956', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.86377409912771564889771108507', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3529.393529209725, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 55353600, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 2, 0, -1, 0, 3, 0, -1, 0, 4, 0, 4, 0, 2, 0, 3, 0, -2, 0, -7, 0, 3, 0, 4, 0, 6, 0, -2, 0, -2, 0, -2, 0, 2, 0, 8, 0, 6, 0, -5, 0, 6, 0, -2, 0, -9, 0, 4, 0, 19, 0, -2, 0, 6, 0, 18, 0, 12, 0, -3, 0, 8, 0, 6, 0, -14, 0, 3, 0, -1, 0, 6, 0, 1, 0, 21, 0, 5, 0, -12, 0, 4, 0, 12, 0, -15, 0, -4, 0, -4, 0, 6, 0, -12, 0, -3, 0], 'euler11': [1, 1, 18, 11, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -2, 18, -34, 289], 'euler19': [1, -3, 2, -57, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 7, 54, 161, 529], 'euler29': [1, -6, 50, -174, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 2, 1, 0, 0], 'euler37': [1, -2, 58, -74, 1369], 'euler41': [1, -6, 74, -246, 1681], 'euler43': [1, 5, -14, 215, 1849], 'euler47': [1, 2, 78, 94, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -19, 192, -1007, 2809], 'euler59': [1, -18, 182, -1062, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, -6, -10, -402, 4489], 'euler7': [1, 1, 10, 7, 49], 'euler71': [1, -3, 106, -213, 5041], 'euler73': [1, 1, 40, 73, 5329], 'euler79': [1, -21, 230, -1659, 6241], 'euler83': [1, 12, 134, 996, 6889], 'euler89': [1, 15, 196, 1335, 7921], 'euler97': [1, 12, 230, 1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 1, 10, 7, 49], [1, 1, 18, 11, 121], [1, -4, 30, -52, 169], [1, -2, 18, -34, 289], [1, -3, 2, -57, 361], [1, 7, 54, 161, 529], [1, -6, 50, -174, 841], [1, 2, 1, 0, 0], [1, -2, 58, -74, 1369], [1, -6, 74, -246, 1681], [1, 5, -14, 215, 1849], [1, 2, 78, 94, 2209], [1, -19, 192, -1007, 2809], [1, -18, 182, -1062, 3481], [1, -12, 158, -732, 3721], [1, -6, -10, -402, 4489], [1, -3, 106, -213, 5041], [1, 1, 40, 73, 5329], [1, -21, 230, -1659, 6241], [1, 12, 134, 996, 6889], [1, 15, 196, 1335, 7921], [1, 12, 230, 1164, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7440/2/a/bl'], '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': '4-7440e2-1.1-c1e2-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-7440e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.7077038801339945, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1260675585200591520, 'z1': {'__RealLiteral__': 0, 'data': '0.74490729290079258126477942500', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '944282176960075201745123680309,1208803490672709311658304460940', 'Lhash_array': ['944282176960075201745123680309', '1208803490672709311658304460940'], 'label': '4-7440e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7440/2/a/bl'}