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lfunc_lfunctions • Show schema
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{'Lhash': '1630789102670111653933747499397,1825963640898571879501472704227', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2482.695136051794, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 1]], [5, [1, 2, 1]], [13, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '6240.1', 'coefficient_field': '1.1.1.1', 'conductor': 38937600, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, -2, 1], [1, 2, 1], [1, 3, 8, 21, 49], [1, -3, 16, -33, 121], [1, 2, 1], [1, 5, 32, 85, 289], [1, 4, 42, 76, 361], [1, -1, 38, -23, 529], [1, -6, 34, -174, 841], [1, -2, 30, -62, 961], [1, -3, 68, -111, 1369], [1, -5, 80, -205, 1681], [1, 2, 54, 86, 1849], [1, 6, 70, 282, 2209], [1, 21, 208, 1113, 2809], [1, -6, 94, -354, 3481], [1, 1, 48, 61, 3721], [1, -14, 150, -938, 4489], [1, -3, 136, -213, 5041], [1, 12, 182, 876, 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'1.44043133065990194696224928942587', '2.40479157068419456330073465136165', '2.56182931708867292820606685710279', '3.10888672306195319454915802463411', '3.20792184020664322468012143804707', '3.98674035312219027409459734044990', '4.10707421330271105895252393809274', '4.44439984543876444517338429022867', '4.71289872935930689991358443695156', '5.34780925261638376154217830821294', '5.81532768465000277304388660322916', '6.38843838440150210586119062885843', '6.63782722916762836552082879153918', '6.87614989520827523125175693593761', '6.94309427515614049687156616942188', '7.65850080870521988519817595890410', '7.944402474334000709144354697253869'], 'prelabel': '4-6240e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.058799534005693, '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': 1578962886913946829, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28646576775690583960011701612', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.44043133065990194696224928943', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.40479157068419456330073465136', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2482.695136051794, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 38937600, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, -2, 0, -3, 0, 3, 0, 3, 0, -2, 0, -4, 0, -5, 0, -4, 0, -6, 0, 1, 0, 3, 0, 4, 0, 6, 0, 2, 0, 6, 0, 6, 0, 3, 0, -4, 0, 5, 0, -2, 0, -6, 0, -6, 0, 1, 0, -10, 0, -21, 0, -6, 0, -8, 0, 6, 0, -1, 0, -9, 0, 4, 0, 14, 0, 2, 0, 3, 0, -12, 0, 6, 0, -9, 0, -25, 0, 5, 0, -18, 0, 10, 0, 12, 0, -9, 0, 6, 0, 4, 0, 8, 0, 1, 0, 9, 0], 'euler11': [1, -3, 16, -33, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, 5, 32, 85, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -1, 38, -23, 529], 'euler29': [1, -6, 34, -174, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, -2, 30, -62, 961], 'euler37': [1, -3, 68, -111, 1369], 'euler41': [1, -5, 80, -205, 1681], 'euler43': [1, 2, 54, 86, 1849], 'euler47': [1, 6, 70, 282, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 21, 208, 1113, 2809], 'euler59': [1, -6, 94, -354, 3481], 'euler61': [1, 1, 48, 61, 3721], 'euler67': [1, -14, 150, -938, 4489], 'euler7': [1, 3, 8, 21, 49], 'euler71': [1, -3, 136, -213, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 25, 306, 1975, 6241], 'euler83': [1, 18, 214, 1494, 6889], 'euler89': [1, 9, 124, 801, 7921], 'euler97': [1, -1, 120, -97, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, 3, 8, 21, 49], [1, -3, 16, -33, 121], [1, 2, 1, 0, 0], [1, 5, 32, 85, 289], [1, 4, 42, 76, 361], [1, -1, 38, -23, 529], [1, -6, 34, -174, 841], [1, -2, 30, -62, 961], [1, -3, 68, -111, 1369], [1, -5, 80, -205, 1681], [1, 2, 54, 86, 1849], [1, 6, 70, 282, 2209], [1, 21, 208, 1113, 2809], [1, -6, 94, -354, 3481], [1, 1, 48, 61, 3721], [1, -14, 150, -938, 4489], [1, -3, 136, -213, 5041], [1, 12, 182, 876, 5329], [1, 25, 306, 1975, 6241], [1, 18, 214, 1494, 6889], [1, 9, 124, 801, 7921], [1, -1, 120, -97, 9409]], 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6240/2/a/bo'], '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': '4-6240e2-1.1-c1e2-0-15', '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': '4-6240e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1578962886913946829, 'z1': {'__RealLiteral__': 0, 'data': '1.28646576775690583960011701612', 'prec': 103}}
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{'Lhash': '1630789102670111653933747499397,1825963640898571879501472704227', 'Lhash_array': ['1630789102670111653933747499397', '1825963640898571879501472704227'], 'label': '4-6240e2-1.1-c1e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/bo'}