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lfunc_lfunctions • Show schema
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{'Lhash': '1681766597503706400701653775806,1839931881576455398938062693069', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3879.2111500809283, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 1]], [5, [1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': '1.1.1.1', 'conductor': 60840000, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, -2, 1], [1], [1, 2, 13, 14, 49], [1, 2, 21, 22, 121], [1, -2, 1], [1, 2, 27, 34, 289], [1, 4, 42, 76, 361], [1, 4, 42, 92, 529], [1, 6, 35, 174, 841], [1, -6, 69, -186, 961], [1, -4, 46, -148, 1369], [1, 0, 50, 0, 1681], [1, -4, 18, -172, 1849], [1, 10, 69, 470, 2209], [1, -6, 107, -318, 2809], [1, 10, 141, 590, 3481], [1, -2, 115, -122, 3721], [1, 10, 141, 670, 4489], [1, 4, 114, 284, 5041], [1, -4, 22, -292, 5329], [1, 12, 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['1.32667992047723484410723322671883', '1.45145032964540209968022734204198', '2.23760123399759453338661676653046', '2.46410789823083094832853069126315', '2.95835306723105811582039678931366', '3.16346027183524709894427240810186', '3.76168783065216142658572618837337', '4.08813232584514651253703421160603', '4.28478198181978196413609115378354', '4.75281748996854592338607619198233', '5.25548477135529600953360069664506', '5.59761566725366290860496508345072', '6.15197511404963312029320639392502', '6.29375670655904299077238619417148', '6.74447949523242070017567938095186', '6.86861963198206200584581146740824', '7.49662425583364825893154870057594', '7.85169013255085771952788934668181'], 'prelabel': '4-7800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, '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': 543150469833162386, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32667992047723484410723322672', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.45145032964540209968022734204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.23760123399759453338661676653', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3879.2111500809283, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 60840000, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, -2, 0, 3, 0, -2, 0, 2, 0, 0, 0, -2, 0, -4, 0, -4, 0, -4, 0, 0, 0, 4, 0, -6, 0, 6, 0, -4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, -10, 0, -9, 0, -4, 0, 6, 0, 0, 0, -8, 0, -10, 0, 2, 0, -6, 0, 0, 0, -10, 0, -8, 0, -4, 0, 4, 0, 0, 0, 4, 0, -12, 0, 5, 0, -2, 0, 0, 0, -12, 0, 0, 0, -4, 0, 12, 0, 0, 0, 4, 0, -6, 0], 'euler11': [1, 2, 21, 22, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 2, 27, 34, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, 42, 92, 529], 'euler29': [1, 6, 35, 174, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, -6, 69, -186, 961], 'euler37': [1, -4, 46, -148, 1369], 'euler41': [1, 0, 50, 0, 1681], 'euler43': [1, -4, 18, -172, 1849], 'euler47': [1, 10, 69, 470, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -6, 107, -318, 2809], 'euler59': [1, 10, 141, 590, 3481], 'euler61': [1, -2, 115, -122, 3721], 'euler67': [1, 10, 141, 670, 4489], 'euler7': [1, 2, 13, 14, 49], 'euler71': [1, 4, 114, 284, 5041], 'euler73': [1, -4, 22, -292, 5329], 'euler79': [1, 12, 186, 948, 6241], 'euler83': [1, 2, 5, 166, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, -4, -90, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 2, 13, 14, 49], [1, 2, 21, 22, 121], [1, -2, 1, 0, 0], [1, 2, 27, 34, 289], [1, 4, 42, 76, 361], [1, 4, 42, 92, 529], [1, 6, 35, 174, 841], [1, -6, 69, -186, 961], [1, -4, 46, -148, 1369], [1, 0, 50, 0, 1681], [1, -4, 18, -172, 1849], [1, 10, 69, 470, 2209], [1, -6, 107, -318, 2809], [1, 10, 141, 590, 3481], [1, -2, 115, -122, 3721], [1, 10, 141, 670, 4489], [1, 4, 114, 284, 5041], [1, -4, 22, -292, 5329], [1, 12, 186, 948, 6241], [1, 2, 5, 166, 6889], [1, 0, 178, 0, 7921], [1, -4, -90, -388, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/ba'], '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': '4-7800e2-1.1-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': 2, 'prelabel': '4-7800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 543150469833162386, 'z1': {'__RealLiteral__': 0, 'data': '1.32667992047723484410723322672', 'prec': 103}}
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{'Lhash': '1681766597503706400701653775806,1839931881576455398938062693069', 'Lhash_array': ['1681766597503706400701653775806', '1839931881576455398938062693069'], 'label': '4-7800e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/ba'}