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lfunc_lfunctions • Show schema
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{'Lhash': '1737768238296143268329069832976', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 68.86298670315223, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 7, 11], 'central_character': '8624.1', 'coefficient_field': '1.1.1.1', 'conductor': 8624, 'conductor_radical': 154, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 2, 5], [1], [1, 1], [1, -2, 13], [1, 0, 17], [1, -2, 19], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, -8, 41], [1, 12, 43], [1, 12, 47], [1, 2, 53], [1, 10, 59], [1, 10, 61], [1, -12, 67], [1, 4, 71], [1, -12, 73], [1, 0, 79], [1, -18, 83], [1, 0, 89], [1, 12, 97], [1, -6, 101], [1, 12, 103], [1, 12, 107], [1, 10, 109], [1, 10, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, 2, 5], 1]], [1], [[[1, 1], 1]], [[[1, -2, 13], 1]], [[[1, 0, 17], 1]], 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-3.0977517861387986, -2.755795631282306, -2.3092545176462074, -1.7822389695322862, -1.203551578259421, -0.6050871897213328, -0.0200550087204831, 0.5188778401716979], 'positive_zeros': ['1.37085742552661853239671743806932', '2.37777618848739236526734684859507', '3.23400828637191869712477583111469', '3.60662757255630072193242606932961', '4.46334868900367902524257023299301', '5.21957456919730061256036186750834', '6.17954231644219072510468276327257', '6.88420472227818731407746511895875', '7.82619487448678845685486744928255'], 'prelabel': '2-8624-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.298372533403898, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1635921487093872686, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37085742552661853239671743807', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37777618848739236526734684860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23400828637191869712477583111', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 68.86298670315223, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 8624, 'conductor_radical': 154, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -2, 0, 0, 0, 1, 0, -1, 0, 2, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, -4, 0, 6, 0, -4, 0, -2, 0, 0, 0, 2, 0, 4, 0, 8, 0, -12, 0, -2, 0, -12, 0, 0, 0, 0, 0, -2, 0, 2, 0, 4, 0, -10, 0, -10, 0, 0, 0, -4, 0, 12, 0, 0, 0, -4, 0, 12, 0, -2, 0, 0, 0, 0, 0, -11, 0, 18, 0, 0, 0, 12, 0, 0, 0, 0, 0, -8, 0, -4, 0, -12, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 0, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -2, 3], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -8, 41], 'euler43': [1, 12, 43], 'euler47': [1, 12, 47], 'euler5': [1, 2, 5], 'euler53': [1, 2, 53], 'euler59': [1, 10, 59], 'euler61': [1, 10, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, 4, 71], 'euler73': [1, -12, 73], 'euler79': [1, 0, 79], 'euler83': [1, -18, 83], 'euler89': [1, 0, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 2, 5], [1, 0, 0], [1, 1, 0], [1, -2, 13], [1, 0, 17], [1, -2, 19], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, -8, 41], [1, 12, 43], [1, 12, 47], [1, 2, 53], [1, 10, 59], [1, 10, 61], [1, -12, 67], [1, 4, 71], [1, -12, 73], [1, 0, 79], [1, -18, 83], [1, 0, 89], [1, 12, 97]], 'index': 172, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/8624/y', 'ModularForm/GL2/Q/holomorphic/8624/2/a/y/1/1', 'ModularForm/GL2/Q/holomorphic/8624/2/a/y'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-8624-1.1-c1-0-172', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8624-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.298372533403898, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1635921487093872686, 'z1': {'__RealLiteral__': 0, 'data': '1.37085742552661853239671743807', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22328724
{'Lhash': '1737768238296143268329069832976', 'Lhash_array': ['1737768238296143268329069832976'], 'label': '2-8624-1.1-c1-0-172', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8624/2/a/y'}
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id: 24584853
{'Lhash': '1737768238296143268329069832976', 'Lhash_array': ['1737768238296143268329069832976'], 'label': '2-8624-1.1-c1-0-172', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8624/2/a/y/1/1'}
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id: 98159
{'Lhash': '1635921487093872686', 'Lhash_array': ['1635921487093872686'], 'label': '2-8624-1.1-c1-0-172', 'type': 'ECQ', 'url': 'EllipticCurve/Q/8624/y'}