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lfunc_lfunctions • Show schema
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{'Lhash': '692432823712997555306394244225,2044001334341525037229018635576', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 428.3750897471616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '2592.1', 'coefficient_field': '1.1.1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, -1, -10, 25], [1, 4, 9, 28, 49], [1, 4, 5, 44, 121], [1, -2, -9, -26, 169], [1, -12, 70, -204, 289], [1, -8, 54, -152, 361], [1, 0, -23, 0, 529], [1, -2, -25, -58, 841], [1, -4, -15, -124, 961], [1, 4, 78, 148, 1369], [1, -2, -37, -82, 1681], [1, -4, -27, -172, 1849], [1, 8, 17, 376, 2209], [1, 20, 206, 1060, 2809], [1, -4, -43, -236, 3481], [1, 6, -25, 366, 3721], [1, -4, -51, -268, 4489], [1, 32, 398, 2272, 5041], [1, 12, 182, 876, 5329], [1, -4, -63, -316, 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'2.75777918642639635223666845749864', '3.11210321750689923638245189346373', '3.11594811809659479814376814324550', '3.49839209218241177546766190159782', '4.51376439229060954432598363816086', '4.71883769099416620556295262356760', '5.51606420923729636508185604889699', '5.53378037272390217592388190966938', '6.01006486638016017582975513081965', '6.10979780039144253905857067493210', '6.86166440945316610047332621941698', '7.18481242833963500625169124498180', '7.55126874611262419808969959610884', '7.82563842306841597038728593252195', '8.466770107578634234459457748071287', '8.523196761884638693677920060892979', '9.353773918829635163119583115158524'], 'prelabel': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1510606611075848379, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54623318411897654023694048051', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.33153106367843797436547517728', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.61243274288161144511544500488', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 428.3750897471616, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, -4, 0, 0, 0, -4, 0, 2, 0, 0, 0, 12, 0, 8, 0, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0, 4, 0, 0, 0, -8, 0, -4, 0, 0, 0, 2, 0, 4, 0, 0, 0, -8, 0, 7, 0, 0, 0, -20, 0, -8, 0, 0, 0, 4, 0, -6, 0, 0, 0, 4, 0, 4, 0, 0, 0, -32, 0, -12, 0, 0, 0, 16, 0, 4, 0, 0, 0, -12, 0, 24, 0, 0, 0, -20, 0, -8, 0, 0, 0, 16, 0, 14, 0, 0, 0], 'euler11': [1, 4, 5, 44, 121], 'euler13': [1, -2, -9, -26, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -23, 0, 529], 'euler29': [1, -2, -25, -58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, -15, -124, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, -2, -37, -82, 1681], 'euler43': [1, -4, -27, -172, 1849], 'euler47': [1, 8, 17, 376, 2209], 'euler5': [1, -2, -1, -10, 25], 'euler53': [1, 20, 206, 1060, 2809], 'euler59': [1, -4, -43, -236, 3481], 'euler61': [1, 6, -25, 366, 3721], 'euler67': [1, -4, -51, -268, 4489], 'euler7': [1, 4, 9, 28, 49], 'euler71': [1, 32, 398, 2272, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, -4, -63, -316, 6241], 'euler83': [1, 12, 61, 996, 6889], 'euler89': [1, 20, 278, 1780, 7921], 'euler97': [1, -14, 99, -1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, -1, -10, 25], [1, 4, 9, 28, 49], [1, 4, 5, 44, 121], [1, -2, -9, -26, 169], [1, -12, 70, -204, 289], [1, -8, 54, -152, 361], [1, 0, -23, 0, 529], [1, -2, -25, -58, 841], [1, -4, -15, -124, 961], [1, 4, 78, 148, 1369], [1, -2, -37, -82, 1681], [1, -4, -27, -172, 1849], [1, 8, 17, 376, 2209], [1, 20, 206, 1060, 2809], [1, -4, -43, -236, 3481], [1, 6, -25, 366, 3721], [1, -4, -51, -268, 4489], [1, 32, 398, 2272, 5041], [1, 12, 182, 876, 5329], [1, -4, -63, -316, 6241], [1, 12, 61, 996, 6889], [1, 20, 278, 1780, 7921], [1, -14, 99, -1358, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/i/q'], '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': '4-2592e2-1.1-c1e2-0-9', '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': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1510606611075848379, 'z1': {'__RealLiteral__': 0, 'data': '0.54623318411897654023694048051', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '692432823712997555306394244225,2044001334341525037229018635576', 'Lhash_array': ['692432823712997555306394244225', '2044001334341525037229018635576'], 'label': '4-2592e2-1.1-c1e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/i/q'}