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'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 801070386121121035, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32653171371801238870142165391', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.51120410345282507646669023921', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.19396089585866482458430720296', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1523769.0003069295, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 374809600000000, 'conductor_radical': 110, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 2, 0, -12, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0], 'euler11': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler13': [1, 0, -50, 0, 963, 0, -8450, 0, 28561], 'euler17': [1, 0, -53, 0, 1233, 0, -15317, 0, 83521], 'euler19': [1, -8, 58, -320, 1771, -6080, 20938, -54872, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -77, 0, 2493, 0, -40733, 0, 279841], 'euler29': [1, 18, 227, 1836, 11709, 53244, 190907, 439002, 707281], 'euler3': [1, 0, -1, 0, 13, 0, -9, 0, 81], 'euler31': [1, -16, 178, -1408, 9139, -43648, 171058, -476656, 923521], 'euler37': [1, 0, -98, 0, 4803, 0, -134162, 0, 1874161], 'euler41': [1, 24, 338, 3312, 24579, 135792, 568178, 1654104, 2825761], 'euler43': [1, 0, 28, 0, 3894, 0, 51772, 0, 3418801], 'euler47': [1, 0, -74, 0, 2763, 0, -163466, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -77, 0, 3273, 0, -216293, 0, 7890481], 'euler59': [1, 24, 410, 4608, 41643, 271872, 1427210, 4929096, 12117361], 'euler61': [1, -26, 487, -5720, 53341, -348920, 1812127, -5901506, 13845841], 'euler67': [1, 0, -236, 0, 22902, 0, -1059404, 0, 20151121], 'euler7': [1, 0, -5, 0, -27, 0, -245, 0, 2401], 'euler71': [1, 12, -40, 396, 16638, 28116, -201640, 4294932, 25411681], 'euler73': [1, 0, -221, 0, 22233, 0, -1177709, 0, 28398241], 'euler79': [1, -2, -197, 40, 22441, 3160, -1229477, -986078, 38950081], 'euler83': [1, 0, -65, 0, 13653, 0, -447785, 0, 47458321], 'euler89': [1, 6, 359, 1584, 48069, 140976, 2843639, 4229814, 62742241], 'euler97': [1, 0, -233, 0, 30873, 0, -2192297, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 13, 0, -9, 0, 81], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -5, 0, -27, 0, -245, 0, 2401], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 0, -50, 0, 963, 0, -8450, 0, 28561], [1, 0, -53, 0, 1233, 0, -15317, 0, 83521], [1, -8, 58, -320, 1771, -6080, 20938, -54872, 130321], [1, 0, -77, 0, 2493, 0, -40733, 0, 279841], [1, 18, 227, 1836, 11709, 53244, 190907, 439002, 707281], [1, -16, 178, -1408, 9139, -43648, 171058, -476656, 923521], [1, 0, -98, 0, 4803, 0, -134162, 0, 1874161], [1, 24, 338, 3312, 24579, 135792, 568178, 1654104, 2825761], [1, 0, 28, 0, 3894, 0, 51772, 0, 3418801], [1, 0, -74, 0, 2763, 0, -163466, 0, 4879681], [1, 0, -77, 0, 3273, 0, -216293, 0, 7890481], [1, 24, 410, 4608, 41643, 271872, 1427210, 4929096, 12117361], [1, -26, 487, -5720, 53341, -348920, 1812127, -5901506, 13845841], [1, 0, -236, 0, 22902, 0, -1059404, 0, 20151121], [1, 12, -40, 396, 16638, 28116, -201640, 4294932, 25411681], [1, 0, -221, 0, 22233, 0, -1177709, 0, 28398241], [1, -2, -197, 40, 22441, 3160, -1229477, -986078, 38950081], [1, 0, -65, 0, 13653, 0, -447785, 0, 47458321], [1, 6, 359, 1584, 48069, 140976, 2843639, 4229814, 62742241], [1, 0, -233, 0, 30873, 0, -2192297, 0, 88529281]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4400/2/b/s'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '8-4400e4-1.1-c1e4-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-4400e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.927408952431356, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 801070386121121035, 'z1': {'__RealLiteral__': 0, 'data': '0.32653171371801238870142165391', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '413928122888190772936345179671,648028188581107586451742777491,1513525246284270960755482434054,2122785223983120161186445658306', 'Lhash_array': ['413928122888190772936345179671', '648028188581107586451742777491', '1513525246284270960755482434054', '2122785223983120161186445658306'], 'label': '8-4400e4-1.1-c1e4-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/b/s'}