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lfunc_lfunctions • Show schema
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{'Lhash': '1254591525501025345507518977559,1559965876423475518064432286322', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.59723219412907, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '864.1', 'coefficient_field': '1.1.1.1', 'conductor': 746496, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -3, 0, 25], [1, 0, 1, 0, 49], [1, 2, 23, 22, 121], [1, -8, 42, -104, 169], [1, 0, 34, 0, 289], [1, 0, -14, 0, 361], [1, -12, 82, -276, 529], [1, 0, 6, 0, 841], [1, 0, 49, 0, 961], [1, -20, 174, -740, 1369], [1, 0, 30, 0, 1681], [1, 0, 34, 0, 1849], [1, -20, 194, -940, 2209], [1, 0, 93, 0, 2809], [1, -8, 134, -472, 3481], [1, 0, 122, 0, 3721], [1, 0, 82, 0, 4489], [1, 16, 206, 1136, 5041], [1, 6, 155, 438, 5329], [1, 0, -50, 0, 6241], [1, 18, 247, 1494, 6889], [1, 0, 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'3.49977165664856287199112412590600', '4.13218273163520837512685375835270', '4.44082148729733690222942083923897', '5.12993293925237691320274525242676', '5.72670324801817356906859602296695', '5.89942799257367761273399751419860', '6.49335744037121874476973366301467', '6.95068919942131121681486334724084', '7.44872784047950347991868238865988', '7.78611273786181910275629725402229', '8.393739727683504466634359674695019', '8.830254827021835108430879729823351', '8.928035848704536448691635188714509', '9.452113455488338039701609058853213', '9.964840343938564478644416184462612', '10.61329130962769716821788550023478'], 'prelabel': '4-864e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6266089801564734, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 2271864651126298703, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.989698206489348970590235414714', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.23059609338931193515469368251', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67852308830331863665695825763', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.59723219412907, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 746496, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0], 'euler11': [1, 2, 23, 22, 121], 'euler13': [1, -8, 42, -104, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, -14, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -12, 82, -276, 529], 'euler29': [1, 0, 6, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 49, 0, 961], 'euler37': [1, -20, 174, -740, 1369], 'euler41': [1, 0, 30, 0, 1681], 'euler43': [1, 0, 34, 0, 1849], 'euler47': [1, -20, 194, -940, 2209], 'euler5': [1, 0, -3, 0, 25], 'euler53': [1, 0, 93, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 0, 122, 0, 3721], 'euler67': [1, 0, 82, 0, 4489], 'euler7': [1, 0, 1, 0, 49], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, 6, 155, 438, 5329], 'euler79': [1, 0, -50, 0, 6241], 'euler83': [1, 18, 247, 1494, 6889], 'euler89': [1, 0, 126, 0, 7921], 'euler97': [1, -14, 243, -1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -3, 0, 25], [1, 0, 1, 0, 49], [1, 2, 23, 22, 121], [1, -8, 42, -104, 169], [1, 0, 34, 0, 289], [1, 0, -14, 0, 361], [1, -12, 82, -276, 529], [1, 0, 6, 0, 841], [1, 0, 49, 0, 961], [1, -20, 174, -740, 1369], [1, 0, 30, 0, 1681], [1, 0, 34, 0, 1849], [1, -20, 194, -940, 2209], [1, 0, 93, 0, 2809], [1, -8, 134, -472, 3481], [1, 0, 122, 0, 3721], [1, 0, 82, 0, 4489], [1, 16, 206, 1136, 5041], [1, 6, 155, 438, 5329], [1, 0, -50, 0, 6241], [1, 18, 247, 1494, 6889], [1, 0, 126, 0, 7921], [1, -14, 243, -1358, 9409]], 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/864/2/a/m'], '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': '4-864e2-1.1-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': '4-864e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6266089801564734, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2271864651126298703, 'z1': {'__RealLiteral__': 0, 'data': '0.989698206489348970590235414714', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1254591525501025345507518977559,1559965876423475518064432286322', 'Lhash_array': ['1254591525501025345507518977559', '1559965876423475518064432286322'], 'label': '4-864e2-1.1-c1e2-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/864/2/a/m'}