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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 3, 'Lhash': '2162753454406528587', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.020618556701030927, 0.0], 'a4': [0.0, 0.0], 'a5': [0.020618556701030927, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.010309278350515464, 0.0], 'a8': [0.0, 0.0], 'a9': [0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 0.12854190793167572, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [7, [1, 1, 7, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '2016.1', 'coefficient_field': '1.1.1.1', 'conductor': 2016, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, -2, 2, -10, 25], [1, 1, 7, 7], [1, -6, 30, -66, 121], [1, 8, 38, 104, 169], [1, 2, 26, 34, 289], [1, 8, 54, 152, 361], [1, 6, 30, 138, 529], [1, -4, 46, -116, 841], [1, -8, 62, -248, 961], [1, -8, 86, -296, 1369], [1, 6, 82, 246, 1681], [1, 0, 70, 0, 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4.253030286927965, 4.809169099166338, 6.057004801742162, 6.428971070727447, 6.962073557839571, 8.098990694093692, 9.094314662852254, 9.846442211058848, 9.964671915727173, 10.84044260103234, 11.58204746144152, 12.31725686074734, 12.33374621805755, 13.15717312296324, 14.18198826155077, 14.18271778304861, 15.18560086242639, 15.47325164750051, 16.62726100086659, 16.84909588946188, 17.12059670696826, 17.67075195000178, 17.96916217776553, 19.10038407439374, 19.15515379485895, 19.89343166445288], 'prelabel': '4-2016-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5987715890652723, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'G_{3,3}', 'trace_hash': 2162753454406528587, 'z1': {'__RealLiteral__': 0, 'data': '2.24239796256', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.25303028693', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.80916909917', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.12854190793167572, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 2016, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 2, 0, -1, 0, 3, 0, 6, 0, -8, 0, -4, 0, -2, 0, -8, 0, 2, 0, -6, 0, 2, 0, -4, 0, 4, 0, 8, 0, -12, 0, -2, 0, 8, 0, 16, 0, -6, 0, 0, 0, 6, 0, 12, 0, -6, 0, 4, 0, -8, 0, 12, 0, 16, 0, -4, 0, 4, 0, -3, 0, -16, 0, -12, 0, 12, 0, 22, 0, 8, 0, -4, 0, -6, 0, 4, 0, 5, 0, -8, 0, -4, 0, -8, 0, -6, 0, 8, 0, -16, 0, -16, 0, 0, 0, 18, 0], 'euler11': [1, -6, 30, -66, 121], 'euler13': [1, 8, 38, 104, 169], 'euler17': [1, 2, 26, 34, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 30, 138, 529], 'euler29': [1, -4, 46, -116, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -8, 62, -248, 961], 'euler37': [1, -8, 86, -296, 1369], 'euler41': [1, 6, 82, 246, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, -12, 94, -564, 2209], 'euler5': [1, -2, 2, -10, 25], 'euler53': [1, 8, 118, 424, 2809], 'euler59': [1, 4, 86, 236, 3481], 'euler61': [1, -4, 110, -244, 3721], 'euler67': [1, 12, 166, 804, 4489], 'euler7': [1, 1, 7, 7, 0], 'euler71': [1, -22, 254, -1562, 5041], 'euler73': [1, -8, 126, -584, 5329], 'euler79': [1, -4, 62, -316, 6241], 'euler83': [1, 8, 182, 664, 6889], 'euler89': [1, 6, 178, 534, 7921], 'euler97': [1, 0, 190, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, -2, 2, -10, 25], [1, 1, 7, 7, 0], [1, -6, 30, -66, 121], [1, 8, 38, 104, 169], [1, 2, 26, 34, 289], [1, 8, 54, 152, 361], [1, 6, 30, 138, 529], [1, -4, 46, -116, 841], [1, -8, 62, -248, 961], [1, -8, 86, -296, 1369], [1, 6, 82, 246, 1681], [1, 0, 70, 0, 1849], [1, -12, 94, -564, 2209], [1, 8, 118, 424, 2809], [1, 4, 86, 236, 3481], [1, -4, 110, -244, 3721], [1, 12, 166, 804, 4489], [1, -22, 254, -1562, 5041], [1, -8, 126, -584, 5329], [1, -4, 62, -316, 6241], [1, 8, 182, 664, 6889], [1, 6, 178, 534, 7921], [1, 0, 190, 0, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/2016/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-2016-1.1-c1e2-0-0', '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': '4-2016-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5987715890652723, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2162753454406528587, 'z1': {'__RealLiteral__': 0, 'data': '2.24239796256', 'prec': 44}}
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lfunc_instances • Show schema
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id: 9953093
{'Lhash': '2162753454406528587', 'Lhash_array': ['2162753454406528587'], 'label': '4-2016-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/24/a|EllipticCurve/Q/84/a'}
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id: 1222100
{'Lhash': '2162753454406528587', 'Lhash_array': ['2162753454406528587'], 'label': '4-2016-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/2016/a'}