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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '181107016944194544,2035702147213998194', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.7755095539803, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [11, [1, 0, -1]]], 'bad_primes': [2, 3, 11], 'central_character': '278784.1', 'coefficient_field': '1.1.1.1', 'conductor': 278784, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 0, 6, 0, 25], [1, -4, 18, -28, 49], [1, 0, -1], [1, 0, -10, 0, 169], [1, 8, 50, 136, 289], [1, 0, 34, 0, 361], [1, 16, 110, 368, 529], [1, 0, 58, 0, 841], [1, 0, 62, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -14, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, -90, 0, 2809], [1, 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-1.9712543629879962, -3.0265005711045765, -4.137687548779541], 'positive_zeros': ['1.78475197427395493967428855416163', '1.86785039249087723872477729693992', '2.68960361520115551828286024783972', '3.88983618093726006470154183680335', '4.18020563951979381603420573913561', '4.48203045992240111424037022492938', '5.31071889191422752331035379139921', '5.62860857478680063008223727074516', '6.41893627610765861044252902088497', '6.58959743419791195955338690324513', '7.34210915134896326470286525975562', '8.017674089261979349140094913787647', '8.051105786605775860607404181361143', '8.409015033356692865444976169403682'], 'prelabel': '4-528e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.053314692569945, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2216809164158192738, 'z1': {'__RealLiteral__': 0, 'data': '1.78475197427395493967428855416163', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.86785039249087723872477729693992', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.68960361520115551828286024783972', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.7755095539803, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 278784, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -16, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, -1, 0, 0], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 8, 50, 136, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 16, 110, 368, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 0, 38, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, -14, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 0, -90, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, -74, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, -4, 18, -28, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -12, 182, -876, 5329], 'euler79': [1, -4, 162, -316, 6241], 'euler83': [1, 0, -90, 0, 6889], 'euler89': [1, 28, 374, 2492, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 6, 0, 25], [1, -4, 18, -28, 49], [1, 0, -1, 0, 0], [1, 0, -10, 0, 169], [1, 8, 50, 136, 289], [1, 0, 34, 0, 361], [1, 16, 110, 368, 529], [1, 0, 58, 0, 841], [1, 0, 62, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -14, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, -90, 0, 2809], [1, 0, -26, 0, 3481], [1, 0, -74, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, -12, 182, -876, 5329], [1, -4, 162, -316, 6241], [1, 0, -90, 0, 6889], [1, 28, 374, 2492, 7921], [1, 4, 198, 388, 9409]], 'index': 82, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-4356.1-a', 'EllipticCurve/2.2.8.1/4356.1/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': '4-528e2-1.1-c1e2-0-82', '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': '4-528e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.053314692569945, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2216809164158192738, 'z1': {'__RealLiteral__': 0, 'data': '1.78475197427395493967428855416163', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9563663
{'Lhash': '181107016944194544,2035702147213998194', 'Lhash_array': ['181107016944194544', '2035702147213998194'], 'label': '4-528e2-1.1-c1e2-0-82', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/4356.1/a'}
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id: 9563188
{'Lhash': '181107016944194544,2035702147213998194', 'Lhash_array': ['181107016944194544', '2035702147213998194'], 'label': '4-528e2-1.1-c1e2-0-82', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-4356.1-a'}