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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -1, 'A4': -1, 'A5': 0, 'A6': -1, 'A7': 0, 'A8': -1, 'A9': -3, 'Lhash': '880919496577043453908530828533', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [-0.5773502691896257, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [-0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.143842869655057, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 2, -2]], [37, [1, 6, 30, -37]], [73, [1, 1, 73]]], 'bad_primes': [2, 37, 73], 'central_character': '394346.1', 'coefficient_field': '1.1.1.1', 'conductor': 394346, 'conductor_radical': 5402, 'degree': 4, 'euler_factors': [[1, -1, 2, -2], [1, 1, 4, 3, 9], [1, 0, 4, 0, 25], [1, 0, 1, 0, 49], [1, 0, -8, 0, 121], [1, 0, -2, 0, 169], [1, 0, 13, 0, 289], [1, -13, 78, -247, 361], [1, -6, 19, -138, 529], [1, 0, -26, 0, 841], [1, 0, -35, 0, 961], [1, 6, 30, -37], [1, -3, 64, 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-1.3063852100078077, -0.8595843853833938, -0.3020714026674725, 0.262352405392756, 0.7380314998839136, 1.0535144132195817, 1.1726614212396755], 'positive_zeros': ['0.69492295149660450963549283238400', '1.58658837797378256130982737558293', '2.82479441600697525056608599738176', '3.26014569386235684543905560057874', '3.58246380990593374585114064963635', '4.49843372419212924829576875109604', '4.94888849357542036568799303220423', '5.27137362701715745273215893230857', '5.76680915485167472518108581786463', '5.98815946080522635058800089725300', '6.72369795752143691886044933551977', '7.42511600390410125587361210613856', '7.59342064983623174686754349685258', '8.087785635283753567499403527680726', '8.877138158879103659681076892803290'], 'prelabel': '4-394346-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.239277485151306, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 521484318922995619, 'z1': {'__RealLiteral__': 0, 'data': '0.69492295149660450963549283238400', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.58658837797378256130982737558293', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.82479441600697525056608599738176', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.143842869655057, 'bad_primes': [2, 37, 73], 'central_character': '1.1', 'conductor': 394346, 'conductor_radical': 5402, 'degree': 4, 'dirichlet_coefficients': [1, 1, -1, -1, 0, -1, 0, -1, -3, 0, 0, 1, 0, 0, 0, 3, 0, -3, 13, 0, 0, 0, 6, 1, -4, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 3, -6, 13, 0, 0, 3, 0, 0, 0, 0, 6, 0, -3, -1, -4, 0, 0, 0, 4, 0, 0, -13, 0, 0, 0, -17, 0, 0, -5, 0, 0, -5, 0, -6, 0, -6, 3, -1, -6, 4, -13, 0, 0, 16, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -3, 4, -1, 0, 4], 'euler11': [1, 0, -8, 0, 121], 'euler13': [1, 0, -2, 0, 169], 'euler17': [1, 0, 13, 0, 289], 'euler19': [1, -13, 78, -247, 361], 'euler2': [1, -1, 2, -2, 0], 'euler23': [1, -6, 19, -138, 529], 'euler29': [1, 0, -26, 0, 841], 'euler3': [1, 1, 4, 3, 9], 'euler31': [1, 0, -35, 0, 961], 'euler37': [1, 6, 30, -37, 0], 'euler41': [1, -3, 64, -123, 1681], 'euler43': [1, 0, 40, 0, 1849], 'euler47': [1, 0, -59, 0, 2209], 'euler5': [1, 0, 4, 0, 25], 'euler53': [1, 0, -38, 0, 2809], 'euler59': [1, 0, -44, 0, 3481], 'euler61': [1, 17, 192, 1037, 3721], 'euler67': [1, 5, 84, 335, 4489], 'euler7': [1, 0, 1, 0, 49], 'euler71': [1, 6, 115, 426, 5041], 'euler73': [1, 1, 73, 0, 0], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 28, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, -1, 2, -2, 0], [1, 1, 4, 3, 9], [1, 0, 4, 0, 25], [1, 0, 1, 0, 49], [1, 0, -8, 0, 121], [1, 0, -2, 0, 169], [1, 0, 13, 0, 289], [1, -13, 78, -247, 361], [1, -6, 19, -138, 529], [1, 0, -26, 0, 841], [1, 0, -35, 0, 961], [1, 6, 30, -37, 0], [1, -3, 64, -123, 1681], [1, 0, 40, 0, 1849], [1, 0, -59, 0, 2209], [1, 0, -38, 0, 2809], [1, 0, -44, 0, 3481], [1, 17, 192, 1037, 3721], [1, 5, 84, 335, 4489], [1, 6, 115, 426, 5041], [1, 1, 73, 0, 0], [1, -16, 222, -1264, 6241], [1, 0, 28, 0, 6889], [1, 0, 142, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 0, 'instance_types': ['ECNF', 'HMF', 'HMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.2.73.1/74.4/a', 'ModularForm/GL2/TotallyReal/2.2.73.1/holomorphic/2.2.73.1-74.4-a', 'ModularForm/GL2/TotallyReal/2.2.73.1/holomorphic/2.2.73.1-74.1-a', 'EllipticCurve/2.2.73.1/74.1/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': '4-394346-1.1-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': '4-394346-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.239277485151306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 521484318922995619, 'z1': {'__RealLiteral__': 0, 'data': '0.69492295149660450963549283238400', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9475588
{'Lhash': '880919496577043453908530828533', 'Lhash_array': ['880919496577043453908530828533'], 'label': '4-394346-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.73.1/74.1/a'}
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id: 9475551
{'Lhash': '880919496577043453908530828533', 'Lhash_array': ['880919496577043453908530828533'], 'label': '4-394346-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.73.1/holomorphic/2.2.73.1-74.1-a'}
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id: 9475516
{'Lhash': '880919496577043453908530828533', 'Lhash_array': ['880919496577043453908530828533'], 'label': '4-394346-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.73.1/holomorphic/2.2.73.1-74.4-a'}
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id: 9475496
{'Lhash': '880919496577043453908530828533', 'Lhash_array': ['880919496577043453908530828533'], 'label': '4-394346-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.73.1/74.4/a'}