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lfunc_lfunctions • Show schema
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{'Lhash': '996526800659376072029321691186,1081259094497997649893867472066', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, '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, 0, -5, 0, 25], [1, 0, -11, 0, 49], [1, 0, -10, 0, 121], [1, 9, 40, 117, 169], [1, -6, 19, -102, 289], [1, -8, 19], [1, 6, 35, 138, 529], [1, -6, 41, -174, 841], [1, 2, 63, 62, 961], [1, 0, 1, 0, 1369], [1, -12, 89, -492, 1681], [1, -9, 70, -387, 1849], [1, 18, 155, 846, 2209], [1, -18, 161, -954, 2809], [1, -12, 85, -708, 3481], [1, -5, -36, -305, 3721], [1, -13, 102, -871, 4489], [1, 0, -71, 0, 5041], [1, -5, -48, -365, 5329], [1, 1, -78, 79, 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'4.83290734180628388147737114802224', '5.25941528822827524071450067072983', '5.50477250889786655422677599115058', '5.64017647220150830120279371406535', '6.60200220926847288805960798665526', '6.66024461727532770436596887294728', '7.35477575038134391865709489961651', '7.42638838008225255422949644225826', '7.900214878427305859215813754000018', '7.994157510319160775047178642609514', '8.729005477227680919121108753120308', '9.022628458601438721490821584852239'], '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': 125391662893310889, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78612103404515419227129834160', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.852963028064141971376002733129', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.09276069764711930499708413975', '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, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 6, 0, 8, 0, 0, 0, -6, 0, 5, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 9, 0, 0, 0, -18, 0, 11, 0, 0, 0, 18, 0, 0, 0, 0, 0, 12, 0, 5, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 9, 40, 117, 169], 'euler17': [1, -6, 19, -102, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 35, 138, 529], 'euler29': [1, -6, 41, -174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 2, 63, 62, 961], 'euler37': [1, 0, 1, 0, 1369], 'euler41': [1, -12, 89, -492, 1681], 'euler43': [1, -9, 70, -387, 1849], 'euler47': [1, 18, 155, 846, 2209], 'euler5': [1, 0, -5, 0, 25], 'euler53': [1, -18, 161, -954, 2809], 'euler59': [1, -12, 85, -708, 3481], 'euler61': [1, -5, -36, -305, 3721], 'euler67': [1, -13, 102, -871, 4489], 'euler7': [1, 0, -11, 0, 49], 'euler71': [1, 0, -71, 0, 5041], 'euler73': [1, -5, -48, -365, 5329], 'euler79': [1, 1, -78, 79, 6241], 'euler83': [1, 0, 134, 0, 6889], 'euler89': [1, 0, 89, 0, 7921], 'euler97': [1, -24, 289, -2328, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5, 0, 25], [1, 0, -11, 0, 49], [1, 0, -10, 0, 121], [1, 9, 40, 117, 169], [1, -6, 19, -102, 289], [1, -8, 19, 0, 0], [1, 6, 35, 138, 529], [1, -6, 41, -174, 841], [1, 2, 63, 62, 961], [1, 0, 1, 0, 1369], [1, -12, 89, -492, 1681], [1, -9, 70, -387, 1849], [1, 18, 155, 846, 2209], [1, -18, 161, -954, 2809], [1, -12, 85, -708, 3481], [1, -5, -36, -305, 3721], [1, -13, 102, -871, 4489], [1, 0, -71, 0, 5041], [1, -5, -48, -365, 5329], [1, 1, -78, 79, 6241], [1, 0, 134, 0, 6889], [1, 0, 89, 0, 7921], [1, -24, 289, -2328, 9409]], 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/bm/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-c1e2-0-34', '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': 125391662893310889, 'z1': {'__RealLiteral__': 0, 'data': '0.78612103404515419227129834160', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '996526800659376072029321691186,1081259094497997649893867472066', 'Lhash_array': ['996526800659376072029321691186', '1081259094497997649893867472066'], 'label': '4-2736e2-1.1-c1e2-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/bm/b'}