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lfunc_lfunctions • Show schema
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{'Lhash': '1250810552862983998641800064037,1541368808090315305387272176999', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 147.5070039818273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, -3, 0, 4], [1], [1, 0, -6, 0, 25], [1, 0, 2, 0, 49], [1, 0, -6, 0, 121], [1], [1, -4, 38, -68, 289], [1, 0, -38, 0, 361], [1, 0, 46, 0, 529], [1, -20, 158, -580, 841], [1, 0, -46, 0, 961], [1, 0, -70, 0, 1369], [1, 0, -46, 0, 1681], [1, -24, 230, -1032, 1849], [1, 0, -94, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 26, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -70, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -142, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, -150, 0, 6889], [1, 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4.916396545820869, 5.061617509420142, 5.027564176594174], 'positive_zeros': ['0.986715544991487796685379614942073', '1.21592559322955815662451966161818', '2.24083217726722598682601865848030', '2.66683722585971036089659170776910', '2.99835845276749615904355331951632', '3.44424116905537115240067014072816', '4.35761070343197201943379184790386', '4.55083173295707621349601812298583', '5.15244582722234115187458525947014', '5.75401838951053768388123523619562', '6.05535666758222217048917172905871', '6.48650284417218830676544772662897', '6.93849291761639245410735055018585', '7.02005853911333667455607411882500', '7.81781235133689436226841505767763', '7.918147403743473727379022895859484', '8.334248954155828532794708635045634', '8.835438824409376606960205624596687', '9.384373766189590463031197894900426', '9.632329551395308856333565239859451'], 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 370287143599892497, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.986715544991487796685379614942', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.21592559322955815662451966162', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.24083217726722598682601865848', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 147.5070039818273, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -2, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 3, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18], 'euler11': [1, 0, -6, 0, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, -38, 0, 361], 'euler2': [1, 0, -3, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, -20, 158, -580, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -46, 0, 961], 'euler37': [1, 0, -70, 0, 1369], 'euler41': [1, 0, -46, 0, 1681], 'euler43': [1, -24, 230, -1032, 1849], 'euler47': [1, 0, -94, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, 26, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -70, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, -142, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, -150, 0, 6889], 'euler89': [1, 0, -174, 0, 7921], 'euler97': [1, 0, -94, 0, 9409], 'euler_factors': [[1, 0, -3, 0, 4], [1, 0, 0, 0, 0], [1, 0, -6, 0, 25], [1, 0, 2, 0, 49], [1, 0, -6, 0, 121], [1, 0, 0, 0, 0], [1, -4, 38, -68, 289], [1, 0, -38, 0, 361], [1, 0, 46, 0, 529], [1, -20, 158, -580, 841], [1, 0, -46, 0, 961], [1, 0, -70, 0, 1369], [1, 0, -46, 0, 1681], [1, -24, 230, -1032, 1849], [1, 0, -94, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 26, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -70, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -142, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, -150, 0, 6889], [1, 0, -174, 0, 7921], [1, 0, -94, 0, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/2/b/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': '4-39e4-1.1-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': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 370287143599892497, 'z1': {'__RealLiteral__': 0, 'data': '0.986715544991487796685379614942', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1250810552862983998641800064037,1541368808090315305387272176999', 'Lhash_array': ['1250810552862983998641800064037', '1541368808090315305387272176999'], 'label': '4-39e4-1.1-c1e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/2/b/b'}