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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': -5, 'Lhash': '576127386404918798,1461279149926245527', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [-1.6666666666666667, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.896119675908043, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, 0, -1]], [13, [1, -2, 1]]], 'bad_primes': [2, 7, 13], 'central_character': '264992.1', 'coefficient_field': '1.1.1.1', 'conductor': 264992, 'conductor_radical': 182, 'degree': 4, 'euler_factors': [[1, -1], [1, 0, 5, 0, 9], [1, 0, 10, 0, 25], [1, 0, -1], [1, 0, 13, 0, 121], [1, -2, 1], [1, 0, 34, 0, 289], [1, 0, 34, 0, 361], [1, 0, 37, 0, 529], [1, 0, 58, 0, 841], [1, 0, 37, 0, 961], [1, 14, 123, 518, 1369], [1, -6, 91, -246, 1681], [1, 0, 22, 0, 1849], [1, 0, 85, 0, 2209], 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{'__RealLiteral__': 0, 'data': '1.60256072097181437267558889267176', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.33000973337707432224237511882728', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.03438118997979637652891820124270', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.896119675908043, 'bad_primes': [2, 7, 13], 'central_character': '1.1', 'conductor': 264992, 'conductor_radical': 182, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, -5, 0, 0, 0, 2, 0, 0, 1, 0, -5, 0, 0, 0, 0, 0, 0, -10, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5, -14, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 1, -10, 0, 2, -24, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -5, 22, -14, 0, 0, 0, 0, 0, 0, 16, 6, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 34, 1, 0, -10], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 37, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 5, 0, 9], 'euler31': [1, 0, 37, 0, 961], 'euler37': [1, 14, 123, 518, 1369], 'euler41': [1, -6, 91, -246, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 85, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 24, 250, 1272, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, 2, 123, 122, 3721], 'euler67': [1, 0, 109, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 0, 157, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 36, 502, 3204, 7921], 'euler97': [1, -34, 483, -3298, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 5, 0, 9], [1, 0, 10, 0, 25], [1, 0, -1, 0, 0], [1, 0, 13, 0, 121], [1, -2, 1, 0, 0], [1, 0, 34, 0, 289], [1, 0, 34, 0, 361], [1, 0, 37, 0, 529], [1, 0, 58, 0, 841], [1, 0, 37, 0, 961], [1, 14, 123, 518, 1369], [1, -6, 91, -246, 1681], [1, 0, 22, 0, 1849], [1, 0, 85, 0, 2209], [1, 24, 250, 1272, 2809], [1, 0, 82, 0, 3481], [1, 2, 123, 122, 3721], [1, 0, 109, 0, 4489], [1, 0, -2, 0, 5041], [1, -22, 267, -1606, 5329], [1, 0, 157, 0, 6241], [1, 0, 22, 0, 6889], [1, 36, 502, 3204, 7921], [1, -34, 483, -3298, 9409]], 'index': 20, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/16562.2/d', 'EllipticCurve/2.0.4.1/16562.2/d'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-264992-1.1-c1e2-0-20', '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': 1, 'prelabel': '4-264992-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.027434088344075, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2037406536331164325, 'z1': {'__RealLiteral__': 0, 'data': '1.60256072097181437267558889267176', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9654069
{'Lhash': '576127386404918798,1461279149926245527', 'Lhash_array': ['576127386404918798', '1461279149926245527'], 'label': '4-264992-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/16562.2/d'}
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id: 9653976
{'Lhash': '576127386404918798,1461279149926245527', 'Lhash_array': ['576127386404918798', '1461279149926245527'], 'label': '4-264992-1.1-c1e2-0-20', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/16562.2/d'}