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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': 2, 'A3': -1, 'A4': 2, 'A5': -1, 'A6': -2, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '1967133585660478719855365747076', 'a10': [-0.632455532033676, 0], 'a2': [1.4142135623730951, 0], 'a3': [-0.5773502691896257, 0], 'a4': [1.0, 0], 'a5': [-0.447213595499958, 0], 'a6': [-0.8164965809277259, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.772347278393827, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 2]], [3, [1, 1, 3]], [5, [1, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '216000.1', 'coefficient_field': '1.1.1.1', 'conductor': 216000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, -2, 2], [1, 1, 3], [1, 1], [1, 0, 10, 0, 49], [1, 0, -12, 0, 121], [1, -3, 8, -39, 169], [1, 0, 2, 0, 289], [1, 0, -13, 0, 361], [1, 0, -21, 0, 529], [1, 0, -32, 0, 841], [1, 2, 54, 62, 961], [1, 12, 94, 444, 1369], [1, 3, 72, 123, 1681], 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2074159565763643499, 'z1': {'__RealLiteral__': 0, 'data': '1.55179478107478001093121490032727', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.57128120301065922656290658012387', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.31251437718625774347934014905574', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.772347278393827, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 216000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 2, -1, 2, -1, -2, 0, 0, -2, -2, 0, -2, 3, 0, 1, -4, 0, -4, 0, -2, 0, 0, 0, 0, 1, 6, 5, 0, 0, 2, -2, -8, 0, 0, 0, -4, -12, 0, -3, 0, -3, 0, 3, 0, 2, 0, 0, 4, -10, 2, 0, 6, -7, 10, 0, 0, 0, 0, 0, 2, 0, -4, 0, -8, -3, 0, 9, 0, 0, 0, -9, 0, 0, -24, -1, 0, 0, -6, -10, 4, 1, -6, 18, 0, 0, 6, 0, 0, -21, 4, 0, 0, 2, 0, 0, 8, 0, -20, 0, 2], 'euler11': [1, 0, -12, 0, 121], 'euler13': [1, -3, 8, -39, 169], 'euler17': [1, 0, 2, 0, 289], 'euler19': [1, 0, -13, 0, 361], 'euler2': [1, -2, 2, 0, 0], 'euler23': [1, 0, -21, 0, 529], 'euler29': [1, 0, -32, 0, 841], 'euler3': [1, 1, 3, 0, 0], 'euler31': [1, 2, 54, 62, 961], 'euler37': [1, 12, 94, 444, 1369], 'euler41': [1, 3, 72, 123, 1681], 'euler43': [1, -3, 88, -129, 1849], 'euler47': [1, 0, -15, 0, 2209], 'euler5': [1, 1, 0, 0, 0], 'euler53': [1, 7, 8, 371, 2809], 'euler59': [1, 0, -90, 0, 3481], 'euler61': [1, 0, 95, 0, 3721], 'euler67': [1, -9, 98, -603, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 9, 72, 639, 5041], 'euler73': [1, 0, 100, 0, 5329], 'euler79': [1, 10, 102, 790, 6241], 'euler83': [1, -18, 238, -1494, 6889], 'euler89': [1, 21, 288, 1869, 7921], 'euler97': [1, 0, -176, 0, 9409], 'euler_factors': [[1, -2, 2, 0, 0], [1, 1, 3, 0, 0], [1, 1, 0, 0, 0], [1, 0, 10, 0, 49], [1, 0, -12, 0, 121], [1, -3, 8, -39, 169], [1, 0, 2, 0, 289], [1, 0, -13, 0, 361], [1, 0, -21, 0, 529], [1, 0, -32, 0, 841], [1, 2, 54, 62, 961], [1, 12, 94, 444, 1369], [1, 3, 72, 123, 1681], [1, -3, 88, -129, 1849], [1, 0, -15, 0, 2209], [1, 7, 8, 371, 2809], [1, 0, -90, 0, 3481], [1, 0, 95, 0, 3721], [1, -9, 98, -603, 4489], [1, 9, 72, 639, 5041], [1, 0, 100, 0, 5329], [1, 10, 102, 790, 6241], [1, -18, 238, -1494, 6889], [1, 21, 288, 1869, 7921], [1, 0, -176, 0, 9409]], 'index': 26, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-135.4-h', 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-135.3-h', 'EllipticCurve/2.2.40.1/135.4/h', 'EllipticCurve/2.2.40.1/135.3/h'], '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': '4-60e3-1.1-c1e2-0-26', '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': '4-60e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9264244928355312, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2074159565763643499, 'z1': {'__RealLiteral__': 0, 'data': '1.55179478107478001093121490032727', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9494828
{'Lhash': '1967133585660478719855365747076', 'Lhash_array': ['1967133585660478719855365747076'], 'label': '4-60e3-1.1-c1e2-0-26', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/135.3/h'}
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id: 9494757
{'Lhash': '1967133585660478719855365747076', 'Lhash_array': ['1967133585660478719855365747076'], 'label': '4-60e3-1.1-c1e2-0-26', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/135.4/h'}
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id: 9494488
{'Lhash': '1967133585660478719855365747076', 'Lhash_array': ['1967133585660478719855365747076'], 'label': '4-60e3-1.1-c1e2-0-26', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-135.3-h'}
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id: 9494361
{'Lhash': '1967133585660478719855365747076', 'Lhash_array': ['1967133585660478719855365747076'], 'label': '4-60e3-1.1-c1e2-0-26', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-135.4-h'}