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lfunc_lfunctions • Show schema
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{'Lhash': '606730543890964013116608278539,704347242854870365225777843068,1004548667163406025946787643687,1534812093218635437621673280668', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6820690.199037971, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '6400.1', 'coefficient_field': '1.1.1.1', 'conductor': 1677721600000000, 'conductor_radical': 10, 'degree': 8, 'euler_factors': [[1], [1, 0, 2, 0, 19, 0, 18, 0, 81], [1], [1, 0, 12, 0, 134, 0, 588, 0, 2401], [1, 0, 34, 0, 531, 0, 4114, 0, 14641], [1, 0, -28, 0, 534, 0, -4732, 0, 28561], [1, -20, 218, -1520, 7459, -25840, 63002, -98260, 83521], [1, 0, 66, 0, 1811, 0, 23826, 0, 130321], [1, 0, 28, 0, 1254, 0, 14812, 0, 279841], [1, 0, 36, 0, 2006, 0, 30276, 0, 707281], [1, 0, 124, 0, 5766, 0, 119164, 0, 923521], [1, 0, 68, 0, 3894, 0, 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'0.792449170917085375064566359672', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6820690.199037971, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1677721600000000, 'conductor_radical': 10, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0], 'euler11': [1, 0, 34, 0, 531, 0, 4114, 0, 14641], 'euler13': [1, 0, -28, 0, 534, 0, -4732, 0, 28561], 'euler17': [1, -20, 218, -1520, 7459, -25840, 63002, -98260, 83521], 'euler19': [1, 0, 66, 0, 1811, 0, 23826, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 28, 0, 1254, 0, 14812, 0, 279841], 'euler29': [1, 0, 36, 0, 2006, 0, 30276, 0, 707281], 'euler3': [1, 0, 2, 0, 19, 0, 18, 0, 81], 'euler31': [1, 0, 124, 0, 5766, 0, 119164, 0, 923521], 'euler37': [1, 0, 68, 0, 3894, 0, 93092, 0, 1874161], 'euler41': [1, 12, 218, 1584, 14595, 64944, 366458, 827052, 2825761], 'euler43': [1, 0, 12, 0, 3734, 0, 22188, 0, 3418801], 'euler47': [1, 0, 172, 0, 11814, 0, 379948, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -108, 0, 8534, 0, -303372, 0, 7890481], 'euler59': [1, 0, 76, 0, 8406, 0, 264556, 0, 12117361], 'euler61': [1, 0, 164, 0, 14166, 0, 610244, 0, 13845841], 'euler67': [1, 0, 18, 0, 9059, 0, 80802, 0, 20151121], 'euler7': [1, 0, 12, 0, 134, 0, 588, 0, 2401], 'euler71': [1, 0, -116, 0, 13446, 0, -584756, 0, 25411681], 'euler73': [1, -60, 1642, -26640, 279699, -1944720, 8750218, -23341020, 28398241], 'euler79': [1, 0, -84, 0, 14246, 0, -524244, 0, 38950081], 'euler83': [1, 0, 242, 0, 28419, 0, 1667138, 0, 47458321], 'euler89': [1, 4, 362, 1072, 48595, 95408, 2867402, 2819876, 62742241], 'euler97': [1, 40, 988, 15640, 182854, 1517080, 9296092, 36506920, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 0, 19, 0, 18, 0, 81], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 12, 0, 134, 0, 588, 0, 2401], [1, 0, 34, 0, 531, 0, 4114, 0, 14641], [1, 0, -28, 0, 534, 0, -4732, 0, 28561], [1, -20, 218, -1520, 7459, -25840, 63002, -98260, 83521], [1, 0, 66, 0, 1811, 0, 23826, 0, 130321], [1, 0, 28, 0, 1254, 0, 14812, 0, 279841], [1, 0, 36, 0, 2006, 0, 30276, 0, 707281], [1, 0, 124, 0, 5766, 0, 119164, 0, 923521], [1, 0, 68, 0, 3894, 0, 93092, 0, 1874161], [1, 12, 218, 1584, 14595, 64944, 366458, 827052, 2825761], [1, 0, 12, 0, 3734, 0, 22188, 0, 3418801], [1, 0, 172, 0, 11814, 0, 379948, 0, 4879681], [1, 0, -108, 0, 8534, 0, -303372, 0, 7890481], [1, 0, 76, 0, 8406, 0, 264556, 0, 12117361], [1, 0, 164, 0, 14166, 0, 610244, 0, 13845841], [1, 0, 18, 0, 9059, 0, 80802, 0, 20151121], [1, 0, -116, 0, 13446, 0, -584756, 0, 25411681], [1, -60, 1642, -26640, 279699, -1944720, 8750218, -23341020, 28398241], [1, 0, -84, 0, 14246, 0, -524244, 0, 38950081], [1, 0, 242, 0, 28419, 0, 1667138, 0, 47458321], [1, 4, 362, 1072, 48595, 95408, 2867402, 2819876, 62742241], [1, 40, 988, 15640, 182854, 1517080, 9296092, 36506920, 88529281]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6400/2/a/cs'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '8-80e8-1.1-c1e4-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-80e8-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.148724172439406, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 179886823250784259, 'z1': {'__RealLiteral__': 0, 'data': '0.47862600607906270561338145322', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '606730543890964013116608278539,704347242854870365225777843068,1004548667163406025946787643687,1534812093218635437621673280668', 'Lhash_array': ['606730543890964013116608278539', '704347242854870365225777843068', '1004548667163406025946787643687', '1534812093218635437621673280668'], 'label': '8-80e8-1.1-c1e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6400/2/a/cs'}