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lfunc_lfunctions • Show schema
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{'Lhash': '560360501118970549193841589315,2176277994588058080837216161658', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -6, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 536.2288917189449, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [29, [1, 4, 29]]], 'bad_primes': [2, 5, 29], 'central_character': '2900.1', 'coefficient_field': '1.1.1.1', 'conductor': 8410000, 'conductor_radical': 290, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1], [1, 6, 18, 42, 49], [1, -4, 8, -44, 121], [1, 4, 8, 52, 169], [1, -12, 70, -204, 289], [1, 8, 32, 152, 361], [1, -10, 50, -230, 529], [1, 4, 29], [1, 12, 72, 372, 961], [1, 0, -38, 0, 1369], [1, -14, 98, -574, 1681], [1, 0, -70, 0, 1849], [1, 0, -30, 0, 2209], [1, -8, 32, -424, 2809], [1, 0, -102, 0, 3481], [1, -18, 162, -1098, 3721], [1, 6, 18, 402, 4489], [1, 0, 2, 0, 5041], [1, 28, 342, 2044, 5329], [1, 16, 128, 1264, 6241], [1, 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'2.58166436293935809995596778844627', '2.90102209465193200658671914853097', '3.38524268383881273635851517533328', '3.70798527963776588288731338273282', '4.27967073720307300271273431834842', '4.34333822966742514393820838721546', '5.43582126961429306085295709243747', '5.54661094904062123309254949361150', '5.76657296274509949119021804799223', '6.39807696666865248092829321780299', '6.86538486156140705656128655941979', '6.96433189869470152212222528860182', '7.37921140321126875248277844209648', '7.58515957344434026104251885666589', '8.193529009059072443594106182959270', '8.880613867348480001755859510985311', '9.379768314640414115649867775724755'], 'prelabel': '4-2900e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.812132228666552, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 742635950777787247, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44204649216281090613912552256', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.14984765122851659209047568091', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.71678062882330372850353226323', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 536.2288917189449, 'bad_primes': [2, 5, 29], 'central_character': '1.1', 'conductor': 8410000, 'conductor_radical': 290, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -6, 0, 2, 0, 4, 0, -4, 0, 0, 0, 12, 0, -8, 0, 0, 0, 10, 0, 0, 0, 0, 0, -4, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 18, 0, -12, 0, 0, 0, -6, 0, 0, 0, 0, 0, -28, 0, 0, 0, -24, 0, -16, 0, -5, 0, 6, 0, 0, 0, 0, 0, 14, 0, 24, 0, 0, 0, 0, 0, 0, 0, 8, 0], 'euler11': [1, -4, 8, -44, 121], 'euler13': [1, 4, 8, 52, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 8, 32, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -10, 50, -230, 529], 'euler29': [1, 4, 29, 0, 0], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 12, 72, 372, 961], 'euler37': [1, 0, -38, 0, 1369], 'euler41': [1, -14, 98, -574, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -8, 32, -424, 2809], 'euler59': [1, 0, -102, 0, 3481], 'euler61': [1, -18, 162, -1098, 3721], 'euler67': [1, 6, 18, 402, 4489], 'euler7': [1, 6, 18, 42, 49], 'euler71': [1, 0, 2, 0, 5041], 'euler73': [1, 28, 342, 2044, 5329], 'euler79': [1, 16, 128, 1264, 6241], 'euler83': [1, -6, 18, -498, 6889], 'euler89': [1, -14, 98, -1246, 7921], 'euler97': [1, 0, -190, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, 0, 0, 0], [1, 6, 18, 42, 49], [1, -4, 8, -44, 121], [1, 4, 8, 52, 169], [1, -12, 70, -204, 289], [1, 8, 32, 152, 361], [1, -10, 50, -230, 529], [1, 4, 29, 0, 0], [1, 12, 72, 372, 961], [1, 0, -38, 0, 1369], [1, -14, 98, -574, 1681], [1, 0, -70, 0, 1849], [1, 0, -30, 0, 2209], [1, -8, 32, -424, 2809], [1, 0, -102, 0, 3481], [1, -18, 162, -1098, 3721], [1, 6, 18, 402, 4489], [1, 0, 2, 0, 5041], [1, 28, 342, 2044, 5329], [1, 16, 128, 1264, 6241], [1, -6, 18, -498, 6889], [1, -14, 98, -1246, 7921], [1, 0, -190, 0, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2900/2/j/a'], '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': '4-2900e2-1.1-c1e2-0-4', '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': '4-2900e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.812132228666552, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 742635950777787247, 'z1': {'__RealLiteral__': 0, 'data': '0.44204649216281090613912552256', 'prec': 103}}
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{'Lhash': '560360501118970549193841589315,2176277994588058080837216161658', 'Lhash_array': ['560360501118970549193841589315', '2176277994588058080837216161658'], 'factors': ['2-2900-145.128-c1-0-9', '2-2900-145.17-c1-0-41'], 'label': '4-2900e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2900/2/j/a'}