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lfunc_lfunctions • Show schema
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{'Lhash': '1572522890679931539862184553494', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.10425729361947, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '6400.1', 'coefficient_field': '1.1.1.1', 'conductor': 6400, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1], [1, 0, 7], [1, 0, 11], [1, 6, 13], [1, -8, 17], [1, 0, 19], [1, 0, 23], [1, -4, 29], [1, 0, 31], [1, 2, 37], [1, -10, 41], [1, 0, 43], [1, 0, 47], [1, -14, 53], [1, 0, 59], [1, 12, 61], [1, 0, 67], [1, 0, 71], [1, 16, 73], [1, 0, 79], [1, 0, 83], [1, 10, 89], [1, 8, 97], [1, 20, 101], [1, 0, 103], [1, 0, 107], [1, 20, 109], [1, -16, 113]], 'euler_factors_factorization': [[1], [[[1, 0, 3], 1]], [1], [[[1, 0, 7], 1]], [[[1, 0, 11], 1]], [[[1, 6, 13], 1]], [[[1, -8, 17], 1]], [[[1, 0, 19], 1]], 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0.4751523390995556, 0.08787947013734744, -0.24090299023507009, -0.49615817864004025, -0.6677971314937432, -0.751252861999787, -0.747740888253423], 'positive_zeros': ['1.24050183102253298299416842270166', '2.56689996206740720789053854014398', '2.97502285542379453811613298150596', '4.00876466448291688011441820104766', '4.95105732336230764748666309509341', '5.50747642148206340848918452264418', '6.12996629302168141583867226312408', '7.14473555825159979633317300338335', '7.65439923191156272025601402743625'], 'prelabel': '2-80e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.1487241724394055, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2221561011013866710, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24050183102253298299416842270', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56689996206740720789053854014', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97502285542379453811613298151', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.10425729361947, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 6400, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 6, 13], 'euler17': [1, -8, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 3], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, -10, 41], 'euler43': [1, 0, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -14, 53], 'euler59': [1, 0, 59], 'euler61': [1, 12, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 16, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, 10, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 0, 0], [1, 0, 7], [1, 0, 11], [1, 6, 13], [1, -8, 17], [1, 0, 19], [1, 0, 23], [1, -4, 29], [1, 0, 31], [1, 2, 37], [1, -10, 41], [1, 0, 43], [1, 0, 47], [1, -14, 53], [1, 0, 59], [1, 12, 61], [1, 0, 67], [1, 0, 71], [1, 16, 73], [1, 0, 79], [1, 0, 83], [1, 10, 89], [1, 8, 97]], 'index': 98, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6400/k', 'ModularForm/GL2/Q/holomorphic/6400/2/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/6400/2/a/k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-80e2-1.1-c1-0-98', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-80e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.1487241724394055, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2221561011013866710, 'z1': {'__RealLiteral__': 0, 'data': '1.24050183102253298299416842270', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21712696
{'Lhash': '1572522890679931539862184553494', 'Lhash_array': ['1572522890679931539862184553494'], 'label': '2-80e2-1.1-c1-0-98', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6400/2/a/k'}
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id: 24574821
{'Lhash': '1572522890679931539862184553494', 'Lhash_array': ['1572522890679931539862184553494'], 'label': '2-80e2-1.1-c1-0-98', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6400/2/a/k/1/1'}
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id: 100225
{'Lhash': '2221561011013866710', 'Lhash_array': ['2221561011013866710'], 'label': '2-80e2-1.1-c1-0-98', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6400/k'}