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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -2, 'A4': 1, 'A5': 0, 'A6': -2, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '1365580332666206487,1422146765026648502', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.8164965809277259, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.3535533905932738, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.194213954608443, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 2, 3]], [7, [1, -1]]], 'bad_primes': [2, 3, 7], 'central_character': '395136.1', 'coefficient_field': '1.1.1.1', 'conductor': 395136, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, -1], [1, 2, 3], [1, 0, 10, 0, 25], [1, -1], [1, 0, 22, 0, 121], [1, 8, 42, 104, 169], [1, 12, 70, 204, 289], [1, -4, 42, -76, 361], [1, 0, 46, 0, 529], [1, -12, 94, -348, 841], [1, 0, 46, 0, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 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'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 481884088479161038, 'z1': {'__RealLiteral__': 0, 'data': '0.51891811197874657341665639572198', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.99280794987984862469967531446206', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.39101862347891857041372548490334', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.194213954608443, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 395136, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 1, -2, 1, 0, -2, 1, 1, 1, 0, 0, -2, -8, 1, 0, 1, -12, 1, 4, 0, -2, 0, 0, -2, -10, -8, 4, 1, 12, 0, 0, 1, 0, -12, 0, 1, 0, 4, 16, 0, -12, -2, 0, 0, 0, 0, 24, -2, 1, -10, 24, -8, -12, 4, 0, 1, -8, 12, 0, 0, 16, 0, 1, 1, 0, 0, 0, -12, 0, 0, 0, 1, 0, 0, 20, 4, 0, 16, 16, 0, -11, -12, 0, -2, 0, 0, -24, 0, 12, 0, -8, 0, 0, 24, 0, -2, 0, 1, 0, -10], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, -24, 238, -1128, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, -1, 0, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 142, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 2, 3, 0, 0], [1, 0, 10, 0, 25], [1, -1, 0, 0, 0], [1, 0, 22, 0, 121], [1, 8, 42, 104, 169], [1, 12, 70, 204, 289], [1, -4, 42, -76, 361], [1, 0, 46, 0, 529], [1, -12, 94, -348, 841], [1, 0, 46, 0, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 22, 0, 1849], [1, -24, 238, -1128, 2209], [1, 12, 142, 636, 2809], [1, 0, 82, 0, 3481], [1, -16, 186, -976, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 142, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, 130, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, 94, 0, 9409]], 'index': 1, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.168.1/14.1/b', 'ModularForm/GL2/TotallyReal/2.2.168.1/holomorphic/2.2.168.1-14.1-b'], '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': '4-395136-1.1-c1e2-0-1', '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': '4-395136-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.240398139216447, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 481884088479161038, 'z1': {'__RealLiteral__': 0, 'data': '0.51891811197874657341665639572198', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9461888
{'Lhash': '1365580332666206487,1422146765026648502', 'Lhash_array': ['1365580332666206487', '1422146765026648502'], 'label': '4-395136-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.168.1/holomorphic/2.2.168.1-14.1-b'}
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id: 9461802
{'Lhash': '1365580332666206487,1422146765026648502', 'Lhash_array': ['1365580332666206487', '1422146765026648502'], 'label': '4-395136-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.168.1/14.1/b'}