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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': 0, 'Lhash': '401333918892878,86041466291751017', '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': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.66180841000206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [19, [1, 0, -1]]], 'bad_primes': [2, 3, 19], 'central_character': '935712.1', 'coefficient_field': '1.1.1.1', 'conductor': 935712, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, 1], [1], [1, 0, 10, 0, 25], [1, 0, -2, 0, 49], [1, 0, 22, 0, 121], [1, 8, 42, 104, 169], [1, 12, 70, 204, 289], [1, 0, -1], [1, 0, 10, 0, 529], [1, 12, 94, 348, 841], [1, 0, 58, 0, 961], [1, 8, 90, 296, 1369], [1, 12, 118, 492, 1681], [1, 0, 70, 0, 1849], [1, 0, 58, 0, 2209], [1, 12, 142, 636, 2809], [1, 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0.03433586420461978, -0.07190784396494691, 0.11664494320982534, 0.5938140847056864], 'positive_zeros': ['1.81801100280978906223857531825842', '2.27147129954073815802695201167592', '2.34092707995523044468378525917048', '3.58677867797817326821260752741140', '3.81156610301665935267786910206756', '4.54790713149621293279441185277973', '5.21083603966480863402338802043475', '5.21403289865941834256074312934092', '6.07507983377375758209992822317017', '6.59547283064248335138694127148131', '7.06756557503064388001592546480541', '7.10678703287277123493279316153107', '7.72795819597559924442133345233762'], 'prelabel': '4-935712-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.779227531268646, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 86442800210643895, 'z1': {'__RealLiteral__': 0, 'data': '1.81801100280978906223857531825842', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.27147129954073815802695201167592', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.34092707995523044468378525917048', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.66180841000206, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 935712, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -8, 0, 0, 1, -12, 0, 0, 0, 0, 0, 0, 0, -10, 8, 0, 0, -12, 0, 0, -1, 0, 12, 0, 0, -8, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 2, 10, 0, -8, -12, 0, 0, 0, 0, 12, 0, 0, 28, 0, 0, 1, 0, 0, 0, -12, 0, 0, 0, 0, 28, 8, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -20, -2, 0, -10], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 0, -1, 0, 0], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 58, 0, 961], 'euler37': [1, 8, 90, 296, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 58, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, -28, 318, -1708, 3721], 'euler67': [1, 0, 70, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -28, 342, -2044, 5329], 'euler79': [1, 0, 58, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, 0, -2, 0, 49], [1, 0, 22, 0, 121], [1, 8, 42, 104, 169], [1, 12, 70, 204, 289], [1, 0, -1, 0, 0], [1, 0, 10, 0, 529], [1, 12, 94, 348, 841], [1, 0, 58, 0, 961], [1, 8, 90, 296, 1369], [1, 12, 118, 492, 1681], [1, 0, 70, 0, 1849], [1, 0, 58, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -26, 0, 3481], [1, -28, 318, -1708, 3721], [1, 0, 70, 0, 4489], [1, 0, 142, 0, 5041], [1, -28, 342, -2044, 5329], [1, 0, 58, 0, 6241], [1, 0, 22, 0, 6889], [1, -12, 214, -1068, 7921], [1, 20, 294, 1940, 9409]], 'index': 32, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/58482.1/c', 'EllipticCurve/2.0.4.1/58482.1/c'], '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': '4-935712-1.1-c1e2-0-32', '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': 2, 'prelabel': '4-935712-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.779227531268646, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 86442800210643895, 'z1': {'__RealLiteral__': 0, 'data': '1.81801100280978906223857531825842', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9711944
{'Lhash': '401333918892878,86041466291751017', 'Lhash_array': ['401333918892878', '86041466291751017'], 'label': '4-935712-1.1-c1e2-0-32', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/58482.1/c'}
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id: 9712455
{'Lhash': '401333918892878,86041466291751017', 'Lhash_array': ['401333918892878', '86041466291751017'], 'label': '4-935712-1.1-c1e2-0-32', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/58482.1/c'}