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lfunc_lfunctions • Show schema
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{'Lhash': '2407443352086954721230035442360', 'a10': -3, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': -3, 'a6': 0, 'a7': 1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.079495851085733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [7, [1, -1]], [13, [1, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.1', 'coefficient_field': '1.1.1.1', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 3, 5], [1, -1], [1, 1, 11], [1, 1], [1, 5, 17], [1, 1, 19], [1, -1, 23], [1, 7, 29], [1, 2, 31], [1, -1, 37], [1, 6, 41], [1, 3, 43], [1, 8, 47], [1, 2, 53], [1, -6, 59], [1, 5, 61], [1, -8, 67], [1, -6, 71], [1, 11, 73], [1, 14, 79], [1, -2, 83], [1, 14, 89], [1, 10, 97], [1, -6, 101], [1, -9, 103], [1, 10, 107], [1, -15, 109], [1, 4, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 3, 5], 1]], [[[1, -1], 1]], [[[1, 1, 11], 1]], [[[1, 1], 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-1.26128358802807, -0.9548829877491256, -0.6338586367047829, -0.3160440391308386, -0.01942307564707188, 0.2388176268852401, 0.44320822814072847, 0.5808386055019502, 0.6420795925316176], 'positive_zeros': ['1.89913794199562214175475004948885', '3.11346507231815676323880972931047', '4.01680586816339694050615224273799', '4.66162486191056383154167071598321', '5.51931339869349074764387757966780', '6.69061749873854041708189827768702', '7.31743211521265601126957812632636', '8.087399671123924969643801147843255', '8.753348500037287827964908129271785'], 'prelabel': '2-1638-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.6165585645867444, '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': 2156674998835385028, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89913794199562214175475004949', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11346507231815676323880972931', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01680586816339694050615224274', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.079495851085733, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -3, 0, 1, 1, 0, -3, -1, 0, -1, 1, 0, 1, -5, 0, -1, -3, 0, -1, 1, 0, 4, -1, 0, 1, -7, 0, -2, 1, 0, -5, -3, 0, 1, -1, 0, -3, -6, 0, -3, -1, 0, 1, -8, 0, 1, 4, 0, -1, -2, 0, 3, 1, 0, -7, 6, 0, -5, -2, 0, 1, 3, 0, 8, -5, 0, -3, 6, 0, -11, 1, 0, -1, -1, 0, -14, -3, 0, -6, 2, 0, 15, -3, 0, -1, -14, 0, -1, 1, 0, -8, 3, 0, -10, 1, 0, 4], 'euler11': [1, 1, 11], 'euler13': [1, 1, 0], 'euler17': [1, 5, 17], 'euler19': [1, 1, 19], 'euler2': [1, -1, 0], 'euler23': [1, -1, 23], 'euler29': [1, 7, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -1, 37], 'euler41': [1, 6, 41], 'euler43': [1, 3, 43], 'euler47': [1, 8, 47], 'euler5': [1, 3, 5], 'euler53': [1, 2, 53], 'euler59': [1, -6, 59], 'euler61': [1, 5, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, -6, 71], 'euler73': [1, 11, 73], 'euler79': [1, 14, 79], 'euler83': [1, -2, 83], 'euler89': [1, 14, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 3, 5], [1, -1, 0], [1, 1, 11], [1, 1, 0], [1, 5, 17], [1, 1, 19], [1, -1, 23], [1, 7, 29], [1, 2, 31], [1, -1, 37], [1, 6, 41], [1, 3, 43], [1, 8, 47], [1, 2, 53], [1, -6, 59], [1, 5, 61], [1, -8, 67], [1, -6, 71], [1, 11, 73], [1, 14, 79], [1, -2, 83], [1, 14, 89], [1, 10, 97]], 'index': 27, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1638/m', 'ModularForm/GL2/Q/holomorphic/1638/2/a/m/1/1', 'ModularForm/GL2/Q/holomorphic/1638/2/a/m'], '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': '2-1638-1.1-c1-0-27', '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': '2-1638-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2156674998835385028, 'z1': {'__RealLiteral__': 0, 'data': '1.89913794199562214175475004949', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20641991
{'Lhash': '2407443352086954721230035442360', 'Lhash_array': ['2407443352086954721230035442360'], 'label': '2-1638-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/2/a/m'}
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id: 24553905
{'Lhash': '2407443352086954721230035442360', 'Lhash_array': ['2407443352086954721230035442360'], 'label': '2-1638-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/2/a/m/1/1'}
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id: 26166
{'Lhash': '2156674998835385028', 'Lhash_array': ['2156674998835385028'], 'label': '2-1638-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1638/m'}