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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': 0, 'A8': 1, 'A9': 3, 'Lhash': '543686406688323108,1400156825977793489', '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': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.90782426131276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -2, 1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '720000.1', 'coefficient_field': '1.1.1.1', 'conductor': 720000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, -1], [1, -2, 1], [1], [1, 0, 10, 0, 49], [1, 0, 18, 0, 121], [1, 12, 62, 156, 169], [1, 0, 30, 0, 289], [1, 0, 38, 0, 361], [1, 0, 30, 0, 529], [1, 0, 58, 0, 841], [1, 16, 126, 496, 961], [1, 4, 78, 148, 1369], [1, -4, 86, -164, 1681], [1, -8, 102, -344, 1849], [1, 0, 30, 0, 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9.608587512018438, 8.076206229959894, 6.408334334456705, 4.748569427925743, 3.224875824381893], 'positive_zeros': ['1.62764325671716933168154276530197', '2.36879858490653300083733004582647', '2.45815773509881651106722995928754', '3.22247217757406603059726753652096', '3.79143046769365773246334925916511', '4.21329681476984441450446373249835', '4.98557453494780998363680778314877', '5.13544146251726925083565635926013', '5.51306797780401171163763542733378', '6.62229130807727725313447057116889', '6.64959962043719359186062300669398', '7.47947512213883760565427163250650', '7.50083844850222126920204719803466', '7.82425125324178640900965713696061'], 'prelabel': '4-720000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6029850729434325, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1943843232666116597, 'z1': {'__RealLiteral__': 0, 'data': '1.62764325671716933168154276530197', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.36879858490653300083733004582647', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.45815773509881651106722995928754', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.90782426131276, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 1, 2, 1, 0, 2, 0, 1, 3, 0, 0, 2, -12, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 2, 0, -12, 4, 0, 0, 0, -16, 1, 0, 0, 0, 3, -4, 0, -24, 0, 4, 0, 8, 0, 0, 0, 0, 2, -10, 0, 0, -12, -12, 4, 0, 0, 0, 0, 0, 0, 0, -16, 0, 1, 0, 0, 16, 0, 0, 0, 24, 3, 0, -4, 0, 0, 0, -24, 0, 0, 5, 4, 8, 0, 0, 8, 0, 0, -20, 0, 0, 0, -32, 0, 0, 2, 0, -10, 0, 0], 'euler11': [1, 0, 18, 0, 121], 'euler13': [1, 12, 62, 156, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, 18, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, 0, 130, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, -8, 182, -664, 6889], 'euler89': [1, 20, 278, 1780, 7921], 'euler97': [1, 0, 130, 0, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 10, 0, 49], [1, 0, 18, 0, 121], [1, 12, 62, 156, 169], [1, 0, 30, 0, 289], [1, 0, 38, 0, 361], [1, 0, 30, 0, 529], [1, 0, 58, 0, 841], [1, 16, 126, 496, 961], [1, 4, 78, 148, 1369], [1, -4, 86, -164, 1681], [1, -8, 102, -344, 1849], [1, 0, 30, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 18, 0, 3481], [1, 0, 118, 0, 3721], [1, -16, 198, -1072, 4489], [1, -24, 286, -1704, 5041], [1, 0, 130, 0, 5329], [1, 0, 158, 0, 6241], [1, -8, 182, -664, 6889], [1, 20, 278, 1780, 7921], [1, 0, 130, 0, 9409]], 'index': 81, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-450.1-bh', 'EllipticCurve/2.2.40.1/450.1/bh'], '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': '4-720000-1.1-c1e2-0-81', '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': '4-720000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6029850729434325, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1943843232666116597, 'z1': {'__RealLiteral__': 0, 'data': '1.62764325671716933168154276530197', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9496140
{'Lhash': '543686406688323108,1400156825977793489', 'Lhash_array': ['543686406688323108', '1400156825977793489'], 'label': '4-720000-1.1-c1e2-0-81', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/450.1/bh'}
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id: 9497001
{'Lhash': '543686406688323108,1400156825977793489', 'Lhash_array': ['543686406688323108', '1400156825977793489'], 'label': '4-720000-1.1-c1e2-0-81', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-450.1-bh'}