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lfunc_lfunctions • Show schema
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{'Lhash': '5788557714178803616600571713821', 'a10': [313.9357993524145, -5.064044465790468e-60], 'a2': [-2.0, -3.4641016151377544], 'a3': [-8.580658306350605, -13.014311469672776], 'a4': [-8.0, 13.856406460551018], 'a5': [-39.24197491905181, 67.96909434914133], 'a6': [-27.921580769298057, 55.752895237319876], 'a7': [-110.56553164997244, -191.50511838361703], 'a8': [64.0, 0.0], 'a9': [-95.74460605931273, 223.34271962736332], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 3.4641016151377544]]], [3, [[1.0, 0], [8.580658306350605, 13.014311469672776]]]], 'bad_primes': [2, 3], 'central_character': '18.13', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '401048577870575634892913280023', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 3.4641016151377544]], [[1.0, 0], [8.580658306350605, 13.014311469672776]], [[1.0, 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[-114672503.5, 198618602.2931199]], [[1.0, 0], [32589.215599417046, 0], [418195493.0, 0]], [[1.0, 0], [-11916.05085721017, 20639.205510262687], [-357462149.5, -619142604.7167817]], [[1.0, 0], [18804.42052329282, 32570.211753234104], [-422298150.5, 731441852.6083683]], [[1.0, 0], [-11525.56795773748, 19962.869288889175], [-675062553.5, -1169242640.9491835]], [[1.0, 0], [66050.35647168152, 0], [1804229351.0, 0]], [[1.0, 0], [-65129.951108527624, 0], [2073071593.0, 0]], [[1.0, 0], [-35433.70686664393, -61372.980593529486], [-1538528199.5, 2664809010.4114656]], [[1.0, 0], [27643.50723961285, 47879.95903840754], [-1969520321.5, 3411309263.37739]], [[1.0, 0], [-10598.562950992131, 0], [5584059449.0, 0]], [[1.0, 0], [-41409.92361818453, -71724.09164424204], [-4293670128.5, 7436854813.50279]], [[1.0, 0], [10604.122086159758, 18366.878222891974], [-5255050250.5, 9102014030.193556]], [[1.0, 0], [65877.38071934725, -114102.9704754678], [-5796370371.5, -10039607982.924889]], [[1.0, 0], [-54796.486125190575, 0], [14025517307.0, 0]], [[1.0, 0], [-160569.5777603651, 0], [15386239549.0, 0]], [[1.0, 0], [-33217.81160674912, 57534.93741914064], [-9212175896.5, -15955956700.99937]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-18-9.4-c5-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/18/6/c/b/13/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.345588580814907, 0.5449796824101462, 0.749397254634412, 0.9585378117531527, 1.171807984386723, 1.388163431538811, 1.6059632776522812, 1.8228478664171084, 2.03564829266815, 2.2403368621418656, 2.432028131834739, 2.605040225658695, 2.7530253881055886, 2.869176926370665, 2.946516545571479, 2.9782614469630833, 2.9582644191687533, 2.88151266649844, 2.7446626491996993, 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'8.669307454575246483405434428531367', '9.475077200999163593879622889208985', '11.58187056062167237461055623628125', '12.76934449698440983994196314706907', '15.12463477000219797347209011206610', '15.96915799238770267109285130680539', '16.57129365209708683263168774577861', '18.13779546372517718252372260422562'], 'prelabel': '2-18-9.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': -0.9266428346758557, 'root_number': '-0.9735618034217984 - 0.2284237617195186*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.463321417338', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.56636687833116194394944606844', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.13191726385951281914000296910', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.669307454575246483405434428531', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/6/c/b/13/1'], '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': '2-18-9.4-c5-0-4', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-18-9.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': -0.46332141733792787, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '4.56636687833116194394944606844', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5788557714178803616600571713821', 'Lhash_array': ['5788557714178803616600571713821'], 'label': '2-18-9.4-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/6/c/b/13/1'}