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lfunc_lfunctions • Show schema
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{'Lhash': '3871684755627350882531049607697', 'a10': 2, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': 2, 'a6': 0, 'a7': -1, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, 1]]], 'bad_primes': [3, 7], 'central_character': '63.1', 'coefficient_field': '1.1.1.1', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1, -2, 5], [1, 1], [1, 4, 11], [1, 2, 13], [1, -6, 17], [1, -4, 19], [1, 0, 23], [1, -2, 29], [1, 0, 31], [1, -6, 37], [1, 2, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, 2, 61], [1, -4, 67], [1, 0, 71], [1, 6, 73], [1, 16, 79], [1, -12, 83], [1, -14, 89], [1, -18, 97], [1, 14, 101], [1, -8, 103], [1, 4, 107], [1, 18, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [1], [[[1, -2, 5], 1]], [[[1, 1], 1]], [[[1, 4, 11], 1]], [[[1, 2, 13], 1]], [[[1, -6, 17], 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-1.1954406872453047, -1.2542385871474724, -1.0365127570551675, -0.6227461474865804, -0.13629404599178496, 0.28617753806582236], 'positive_zeros': ['3.05422074105458389777226041970596', '5.02709416296405066539370067618027', '5.94607665445287604157300008428852', '7.81295430367747747098376616892112', '9.457705101580370517739336150901024', '10.18331996404873608095625884352111', '12.02428486441375050992152755294222', '13.00543957503168228446980436667014', '13.77909280462587463511606590838620', '14.66963209598428447187514618323400'], 'prelabel': '2-63-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7092654881876508, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2278490076300767204, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.05422074105458389777226041971', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.02709416296405066539370067618', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.94607665445287604157300008429', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5030575327340666, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 2, 0, -1, -3, 0, 2, -4, 0, -2, -1, 0, -1, 6, 0, 4, -2, 0, -4, 0, 0, -1, -2, 0, 1, 2, 0, 0, 5, 0, 6, -2, 0, 6, 4, 0, -6, -2, 0, -4, 4, 0, 0, 0, 0, 1, -1, 0, 2, -6, 0, -8, 3, 0, 2, -12, 0, -2, 0, 0, 7, -4, 0, 4, -6, 0, -2, 0, 0, -6, 6, 0, -4, 4, 0, -16, -2, 0, -2, 12, 0, 12, -4, 0, 12, 14, 0, 2, 0, 0, 0, 8, 0, 18, 1, 0, 1], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, -1, 2], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, 16, 79], 'euler83': [1, -12, 83], 'euler89': [1, -14, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, -2, 5], [1, 1, 0], [1, 4, 11], [1, 2, 13], [1, -6, 17], [1, -4, 19], [1, 0, 23], [1, -2, 29], [1, 0, 31], [1, -6, 37], [1, 2, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, 2, 61], [1, -4, 67], [1, 0, 71], [1, 6, 73], [1, 16, 79], [1, -12, 83], [1, -14, 89], [1, -18, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/63/a', 'ModularForm/GL2/Q/holomorphic/63/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/63/2/a/a'], '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': '2-63-1.1-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-63-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7092654881876508, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2278490076300767204, 'z1': {'__RealLiteral__': 0, 'data': '3.05422074105458389777226041971', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9957642
{'Lhash': '3871684755627350882531049607697', 'Lhash_array': ['3871684755627350882531049607697'], 'label': '2-63-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/2/a/a'}
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id: 24546273
{'Lhash': '3871684755627350882531049607697', 'Lhash_array': ['3871684755627350882531049607697'], 'label': '2-63-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/2/a/a/1/1'}
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id: 22080
{'Lhash': '2278490076300767204', 'Lhash_array': ['2278490076300767204'], 'label': '2-63-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/63/a'}