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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': -2, 'Lhash': '930465999513371460,1428752966040989219', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.06943558419523554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1, 3]], [11, [1, 0, -1]]], 'bad_primes': [3, 11], 'central_character': '1089.1', 'coefficient_field': '1.1.1.1', 'conductor': 1089, 'conductor_radical': 33, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1, 1, 3], [1, 0, 9, 0, 25], [1, 4, 18, 28, 49], [1, 0, -1], [1, -8, 42, -104, 169], [1, 0, 30, 0, 289], [1, 0, 38, 0, 361], [1, 0, 45, 0, 529], [1, 0, 58, 0, 841], [1, -14, 111, -434, 961], [1, -6, 83, -222, 1369], [1, 0, 18, 0, 1681], [1, 12, 122, 516, 1849], [1, 0, 30, 0, 2209], 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'symplectic', 'trace_hash': 53375956340666728, 'z1': {'__RealLiteral__': 0, 'data': '3.09000916592887094247460325416532', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '4.19085115174357929506261869806169', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.66407660024727617127120629680543', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.06943558419523554, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 1089, 'conductor_radical': 33, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -4, 0, -2, 0, 0, 0, 8, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, -9, 0, 5, 0, 0, 0, 14, 0, 0, 0, 0, 0, 6, 0, -8, 0, 0, 0, -12, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 8, 0, 0, 0, -14, 0, 0, 0, 0, 0, 8, 0, 9, 0, 0, 0, -20, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, -14, 0, 0, 0, -14, 0, 0, 0], 'euler11': [1, 0, -1, 0, 0], 'euler13': [1, -8, 42, -104, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 0, 45, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 1, 3, 0, 0], 'euler31': [1, -14, 111, -434, 961], 'euler37': [1, -6, 83, -222, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, 12, 122, 516, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 9, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, 93, 0, 3481], 'euler61': [1, -24, 266, -1464, 3721], 'euler67': [1, 14, 183, 938, 4489], 'euler7': [1, 4, 18, 28, 49], 'euler71': [1, 0, 133, 0, 5041], 'euler73': [1, -8, 162, -584, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, 0, -47, 0, 7921], 'euler97': [1, 14, 243, 1358, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 1, 3, 0, 0], [1, 0, 9, 0, 25], [1, 4, 18, 28, 49], [1, 0, -1, 0, 0], [1, -8, 42, -104, 169], [1, 0, 30, 0, 289], [1, 0, 38, 0, 361], [1, 0, 45, 0, 529], [1, 0, 58, 0, 841], [1, -14, 111, -434, 961], [1, -6, 83, -222, 1369], [1, 0, 18, 0, 1681], [1, 12, 122, 516, 1849], [1, 0, 30, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, 93, 0, 3481], [1, -24, 266, -1464, 3721], [1, 14, 183, 938, 4489], [1, 0, 133, 0, 5041], [1, -8, 162, -584, 5329], [1, 20, 258, 1580, 6241], [1, 0, 130, 0, 6889], [1, 0, -47, 0, 7921], [1, 14, 243, 1358, 9409]], 'index': 0, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/121.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/121.1/a'], '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': '4-33e2-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-33e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5133286731424862, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 53375956340666728, 'z1': {'__RealLiteral__': 0, 'data': '3.09000916592887094247460325416532', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9696789
{'Lhash': '930465999513371460,1428752966040989219', 'Lhash_array': ['930465999513371460', '1428752966040989219'], 'label': '4-33e2-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/121.1/a'}
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id: 9695852
{'Lhash': '930465999513371460,1428752966040989219', 'Lhash_array': ['930465999513371460', '1428752966040989219'], 'label': '4-33e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/121.1/a'}