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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': -3, 'A9': -2, 'Lhash': '724848311995249020988528103857', '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': [-1.0606601717798214, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.469073839217806, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 2]], [3, [1, 0, 2, 3]], [103, [1, -12, 103]]], 'bad_primes': [2, 3, 103], 'central_character': '509232.1', 'coefficient_field': '1.1.1.1', 'conductor': 509232, 'conductor_radical': 618, 'degree': 4, 'euler_factors': [[1, -1, 2], [1, 0, 2, 3], [1, 0, 2, 0, 25], [1, 0, -1, 0, 49], [1, -1, 16, -11, 121], [1, -1, 20, -13, 169], [1, 3, 30, 51, 289], [1, 0, -5, 0, 361], [1, 0, 16, 0, 529], [1, -7, 64, -203, 841], [1, 6, 46, 186, 961], [1, 0, -7, 0, 1369], [1, 9, 46, 369, 1681], [1, -2, -13, -86, 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'symmetry_type': 'symplectic', 'trace_hash': 699884245339196659, 'z1': {'__RealLiteral__': 0, 'data': '0.57180449554849453248108816772518', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.82746422605243952409172203860244', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.49827631201068496843971761003991', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.469073839217806, 'bad_primes': [2, 3, 103], 'central_character': '1.1', 'conductor': 509232, 'conductor_radical': 618, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, 0, -3, -2, 0, 1, 0, 1, 0, 0, -1, -3, -2, 0, 0, 0, 1, 0, 0, -2, 1, -3, 0, 7, 0, -6, 5, 0, -3, 0, 2, 0, 0, 0, 0, -9, 0, 2, -1, 0, 0, -9, 0, 1, -2, 0, -1, 0, -3, 0, 0, 0, 7, 0, 0, 4, -6, 0, 7, 0, 0, 20, 3, 0, 0, 11, 6, 0, 0, 0, 0, 0, 0, 0, 0, 4, -9, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, 0, -9, 0, 0, 11, 1, -2, 2], 'euler11': [1, -1, 16, -11, 121], 'euler13': [1, -1, 20, -13, 169], 'euler17': [1, 3, 30, 51, 289], 'euler19': [1, 0, -5, 0, 361], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, 0, 16, 0, 529], 'euler29': [1, -7, 64, -203, 841], 'euler3': [1, 0, 2, 3, 0], 'euler31': [1, 6, 46, 186, 961], 'euler37': [1, 0, -7, 0, 1369], 'euler41': [1, 9, 46, 369, 1681], 'euler43': [1, -2, -13, -86, 1849], 'euler47': [1, 9, 108, 423, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, 44, 0, 2809], 'euler59': [1, 0, -18, 0, 3481], 'euler61': [1, -4, 26, -244, 3721], 'euler67': [1, -20, 234, -1340, 4489], 'euler7': [1, 0, -1, 0, 49], 'euler71': [1, -11, 166, -781, 5041], 'euler73': [1, 0, -18, 0, 5329], 'euler79': [1, 0, -71, 0, 6241], 'euler83': [1, 0, -88, 0, 6889], 'euler89': [1, 0, -10, 0, 7921], 'euler97': [1, -11, 68, -1067, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, 0, 2, 3, 0], [1, 0, 2, 0, 25], [1, 0, -1, 0, 49], [1, -1, 16, -11, 121], [1, -1, 20, -13, 169], [1, 3, 30, 51, 289], [1, 0, -5, 0, 361], [1, 0, 16, 0, 529], [1, -7, 64, -203, 841], [1, 6, 46, 186, 961], [1, 0, -7, 0, 1369], [1, 9, 46, 369, 1681], [1, -2, -13, -86, 1849], [1, 9, 108, 423, 2209], [1, 0, 44, 0, 2809], [1, 0, -18, 0, 3481], [1, -4, 26, -244, 3721], [1, -20, 234, -1340, 4489], [1, -11, 166, -781, 5041], [1, 0, -18, 0, 5329], [1, 0, -71, 0, 6241], [1, 0, -88, 0, 6889], [1, 0, -10, 0, 7921], [1, -11, 68, -1067, 9409]], 'index': 0, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.412.1/3.1/a', 'ModularForm/GL2/TotallyReal/2.2.412.1/holomorphic/2.2.412.1-3.1-a', 'EllipticCurve/2.2.412.1/3.2/a', 'ModularForm/GL2/TotallyReal/2.2.412.1/holomorphic/2.2.412.1-3.2-a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-509232-1.1-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': '4-509232-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.387082754366325, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 699884245339196659, 'z1': {'__RealLiteral__': 0, 'data': '0.57180449554849453248108816772518', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9459098
{'Lhash': '724848311995249020988528103857', 'Lhash_array': ['724848311995249020988528103857'], 'label': '4-509232-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.412.1/holomorphic/2.2.412.1-3.2-a'}
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id: 9459097
{'Lhash': '724848311995249020988528103857', 'Lhash_array': ['724848311995249020988528103857'], 'label': '4-509232-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.412.1/3.2/a'}
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id: 9459094
{'Lhash': '724848311995249020988528103857', 'Lhash_array': ['724848311995249020988528103857'], 'label': '4-509232-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.412.1/holomorphic/2.2.412.1-3.1-a'}
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id: 9459093
{'Lhash': '724848311995249020988528103857', 'Lhash_array': ['724848311995249020988528103857'], 'label': '4-509232-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.412.1/3.1/a'}