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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -3, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 3, 'Lhash': '1048509029722223405', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.030927835051546393, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.030927835051546393, 0.0], 'a8': [0.0, 0.0], 'a9': [0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 0.42643267869397183, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1]], [11, [1, 0, 10, -11]], [19, [1, 5, 13, -19]]], 'bad_primes': [2, 11, 19], 'central_character': '6688.1', 'coefficient_field': '1.1.1.1', 'conductor': 6688, 'conductor_radical': 418, 'degree': 4, 'euler_factors': [[1], [1, 3, 6, 9, 9], [1, 0, -7, 0, 25], [1, 3, 10, 21, 49], [1, 0, 10, -11], [1, 6, 26, 78, 169], [1, -1, -22, -17, 289], [1, 5, 13, -19], [1, 5, 38, 115, 529], [1, 4, -10, 116, 841], [1, -5, 48, -155, 961], [1, 3, 58, 111, 1369], [1, 6, 34, 246, 1681], [1, -1, 28, -43, 1849], [1, 1, -6, 47, 2209], [1, 0, 78, 0, 2809], [1, -5, 48, -295, 3481], [1, 3, 82, 183, 3721], [1, -13, 144, -871, 4489], [1, -3, 20, -213, 5041], [1, -7, 128, -511, 5329], [1, -4, -58, -316, 6241], [1, 14, 174, 1162, 6889], [1, -25, 332, -2225, 7921], [1, 15, 190, 1455, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 2, 'label': '4-6688-1.1-c1e2-0-2', 'leading_term': '0.688201853552', 'load_key': 'G2Q', '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, 'origin': 'Genus2Curve/Q/6688/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.1335202540320911, 0.2936370110910603, 0.505145606325491, 0.787877212560062, 1.151243648476964, 1.586479002113558, 2.057988341665077, 2.496945200212077, 2.801773034119127, 2.85047587200404, 2.527880379064803, 1.766048828678956, 0.5889049025534496, 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4.891796024381061, 5.267210211576843, 6.192116699811432, 6.528408709707267, 7.119868208013743, 8.005631625104812, 8.783515868037368, 9.703249399536787, 9.934017859351984, 10.62876402149878, 11.04183346510727, 11.83406110168837, 12.09698536893821, 12.62483436709619, 12.9596376810644, 13.72333852605951, 14.46996697883075, 14.8553947554659, 15.51048508283991, 16.08581279547442, 16.52990611967538, 16.95401372273537, 17.21726073365934, 17.56550632800315, 18.28577122930426, 18.80647717279663, 19.12423949076353, 19.78073164273233], 'prelabel': '4-6688-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.808095372123941, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1048509029722223405, 'z1': {'__RealLiteral__': 0, 'data': '2.51647120272', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.76798168984', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.89179602438', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.42643267869397183, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 6688, 'conductor_radical': 418, 'degree': 4, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, -3, 0, 3, 0, 0, 0, -6, 0, 0, 0, 1, 0, -5, 0, 9, 0, -5, 0, 7, 0, 0, 0, -4, 0, 5, 0, 0, 0, 0, 0, -3, 0, 18, 0, -6, 0, 1, 0, 0, 0, -1, 0, -1, 0, -3, 0, 0, 0, 0, 0, 15, 0, 5, 0, -3, 0, -9, 0, 0, 0, 13, 0, 15, 0, 3, 0, 7, 0, -21, 0, 0, 0, 4, 0, 0, 0, -14, 0, 0, 0, 12, 0, 25, 0, 18, 0, -15, 0, 0, 0, -15, 0, 0, 0], 'euler11': [1, 0, 10, -11, 0], 'euler13': [1, 6, 26, 78, 169], 'euler17': [1, -1, -22, -17, 289], 'euler19': [1, 5, 13, -19, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 5, 38, 115, 529], 'euler29': [1, 4, -10, 116, 841], 'euler3': [1, 3, 6, 9, 9], 'euler31': [1, -5, 48, -155, 961], 'euler37': [1, 3, 58, 111, 1369], 'euler41': [1, 6, 34, 246, 1681], 'euler43': [1, -1, 28, -43, 1849], 'euler47': [1, 1, -6, 47, 2209], 'euler5': [1, 0, -7, 0, 25], 'euler53': [1, 0, 78, 0, 2809], 'euler59': [1, -5, 48, -295, 3481], 'euler61': [1, 3, 82, 183, 3721], 'euler67': [1, -13, 144, -871, 4489], 'euler7': [1, 3, 10, 21, 49], 'euler71': [1, -3, 20, -213, 5041], 'euler73': [1, -7, 128, -511, 5329], 'euler79': [1, -4, -58, -316, 6241], 'euler83': [1, 14, 174, 1162, 6889], 'euler89': [1, -25, 332, -2225, 7921], 'euler97': [1, 15, 190, 1455, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 3, 6, 9, 9], [1, 0, -7, 0, 25], [1, 3, 10, 21, 49], [1, 0, 10, -11, 0], [1, 6, 26, 78, 169], [1, -1, -22, -17, 289], [1, 5, 13, -19, 0], [1, 5, 38, 115, 529], [1, 4, -10, 116, 841], [1, -5, 48, -155, 961], [1, 3, 58, 111, 1369], [1, 6, 34, 246, 1681], [1, -1, 28, -43, 1849], [1, 1, -6, 47, 2209], [1, 0, 78, 0, 2809], [1, -5, 48, -295, 3481], [1, 3, 82, 183, 3721], [1, -13, 144, -871, 4489], [1, -3, 20, -213, 5041], [1, -7, 128, -511, 5329], [1, -4, -58, -316, 6241], [1, 14, 174, 1162, 6889], [1, -25, 332, -2225, 7921], [1, 15, 190, 1455, 9409]], 'index': 2, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/6688/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-6688-1.1-c1e2-0-2', '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': '4-6688-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.808095372123941, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1048509029722223405, 'z1': {'__RealLiteral__': 0, 'data': '2.51647120272', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1048509029722223405', 'Lhash_array': ['1048509029722223405'], 'label': '4-6688-1.1-c1e2-0-2', 'type': 'G2Q', 'url': 'Genus2Curve/Q/6688/a'}