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lfunc_lfunctions • Show schema
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{'Lhash': '194268316632577207025377345563,2184850692476218244286215945880', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -6, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 6, 19, 30, 25], [1, 0, -11, 0, 49], [1, 0, 5, 0, 121], [1, 0, 22, 0, 169], [1, 6, 43, 102, 289], [1, -8, 19], [1, 0, -34, 0, 529], [1, 0, -58, 0, 841], [1, 8, 78, 248, 961], [1, 0, -26, 0, 1369], [1, 0, -34, 0, 1681], [1, 0, -11, 0, 1849], [1, 0, -19, 0, 2209], [1, 0, -58, 0, 2809], [1, 24, 262, 1416, 3481], [1, -14, 171, -854, 3721], [1, -16, 198, -1072, 4489], [1, 24, 286, 1704, 5041], [1, 10, 171, 730, 5329], [1, 16, 222, 1264, 6241], [1, 0, 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'3.93691725114823921101828932160659', '4.24188192936261500795265067956298', '4.41426893708808648998914503636351', '5.13698122377714035576864543291153', '5.38686810365043352245533050438567', '5.93724806769214772529088030741373', '6.46924621122733409412709229247818', '7.05976695935073563409145620430414', '7.20448437257015446406325909787876', '7.60665540134120069815031270274122', '7.64507147202340724519181813768807', '8.288286964029819327067385635199842', '8.558571977932800597808796766576075', '9.212291945496614031425153989737367'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 857030278704521960, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15325068011453699940967475640', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.05701477312683819753789372682', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.72354329503954401126436974481', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 14, 0, 0, 0, 0, 0, 16, 0, 0, 0, -24, 0, -10, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0], 'euler11': [1, 0, 5, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 6, 43, 102, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -34, 0, 529], 'euler29': [1, 0, -58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, -34, 0, 1681], 'euler43': [1, 0, -11, 0, 1849], 'euler47': [1, 0, -19, 0, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, 0, -58, 0, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, -14, 171, -854, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 0, -11, 0, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 10, 171, 730, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, -154, 0, 6889], 'euler89': [1, 0, -130, 0, 7921], 'euler97': [1, 0, -146, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 6, 19, 30, 25], [1, 0, -11, 0, 49], [1, 0, 5, 0, 121], [1, 0, 22, 0, 169], [1, 6, 43, 102, 289], [1, -8, 19, 0, 0], [1, 0, -34, 0, 529], [1, 0, -58, 0, 841], [1, 8, 78, 248, 961], [1, 0, -26, 0, 1369], [1, 0, -34, 0, 1681], [1, 0, -11, 0, 1849], [1, 0, -19, 0, 2209], [1, 0, -58, 0, 2809], [1, 24, 262, 1416, 3481], [1, -14, 171, -854, 3721], [1, -16, 198, -1072, 4489], [1, 24, 286, 1704, 5041], [1, 10, 171, 730, 5329], [1, 16, 222, 1264, 6241], [1, 0, -154, 0, 6889], [1, 0, -130, 0, 7921], [1, 0, -146, 0, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/k/b'], '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': '4-2736e2-1.1-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': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 857030278704521960, 'z1': {'__RealLiteral__': 0, 'data': '0.15325068011453699940967475640', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '194268316632577207025377345563,2184850692476218244286215945880', 'Lhash_array': ['194268316632577207025377345563', '2184850692476218244286215945880'], 'label': '4-2736e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/k/b'}