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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 8, 'A8': 0, 'A9': 1, 'Lhash': '991544551204295018,1065312699390175217', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [3.0237157840738176, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.017877822715063, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 0, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '172800.1', 'coefficient_field': '1.1.1.1', 'conductor': 172800, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 1], [1, 0, -1], [1, -8, 30, -56, 49], [1, 0, 22, 0, 121], [1, -4, 30, -52, 169], [1, 0, -2, 0, 289], [1, -8, 54, -152, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 16, 126, 496, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 94, 0, 2209], [1, 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-0.3801168661793326, -0.9682640561540016, -1.1840359162058738, -1.0903233849204927, -0.7925483854844474], 'positive_zeros': ['1.36243712364701817507861978801175', '1.44399343799308961081305068602321', '2.50374962358163435732612030838978', '3.62987230449253956202768748220969', '4.08471431361169401081275954744688', '4.95303891523898796353167575120123', '4.97026786036012165020386374879770', '5.76555679083117871916592673419048', '5.85236328773314391596499497567282', '6.96170559755127999142057961260937', '7.38482725826507043429631860665898', '7.88297907167905508023143292046630', '7.965215938754459889106897012613934', '8.713350404322888410914105544855016', '9.206120678796429021467253404807326'], 'prelabel': '4-172800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8218997994774022, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2056857250594470235, 'z1': {'__RealLiteral__': 0, 'data': '1.36243712364701817507861978801175', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.44399343799308961081305068602321', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.50374962358163435732612030838978', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.017877822715063, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 172800, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 8, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 1, 0, -1, 0, 0, 0, -16, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -20, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, -16, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 16, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, -8, 150, -536, 4489], 'euler7': [1, -8, 30, -56, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, -146, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, -1, 0, 0], [1, -8, 30, -56, 49], [1, 0, 22, 0, 121], [1, -4, 30, -52, 169], [1, 0, -2, 0, 289], [1, -8, 54, -152, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 16, 126, 496, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 94, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, 118, 0, 3481], [1, 20, 222, 1220, 3721], [1, -8, 150, -536, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 16, 222, 1264, 6241], [1, 0, 22, 0, 6889], [1, 0, -146, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 16, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/19200.1/e', 'EllipticCurve/2.0.3.1/19200.1/e'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, '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': '4-172800-1.1-c1e2-0-16', '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': '4-172800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8218997994774022, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2056857250594470235, 'z1': {'__RealLiteral__': 0, 'data': '1.36243712364701817507861978801175', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9738747
{'Lhash': '991544551204295018,1065312699390175217', 'Lhash_array': ['991544551204295018', '1065312699390175217'], 'label': '4-172800-1.1-c1e2-0-16', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/19200.1/e'}
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id: 9738335
{'Lhash': '991544551204295018,1065312699390175217', 'Lhash_array': ['991544551204295018', '1065312699390175217'], 'label': '4-172800-1.1-c1e2-0-16', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/19200.1/e'}