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lfunc_lfunctions • Show schema
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{'Lhash': '3034589281889065210097612953075', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, -3.302775637731995], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [-3.302775637731995, 0], 'a7': [0, -2.605551275463989], 'a8': [0, 1.0], 'a9': [-7.908326913195984, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.772324373936879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.149', 'coefficient_field': 'CDF', 'conductor': 1850, 'conductor_radical': 370, 'conjugate': '455053172555923147596329889755', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 3.302775637731995], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.605551275463989], [-7.0, 0]], [[1.0, 0], [2.302775637731995, 0], [11.0, 0]], [[1.0, 0], [0, 1.3027756377319946], [-13.0, 0]], [[1.0, 0], [0, 6.0], [-17.0, 0]], [[1.0, 0], [2.0, 0], 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[-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 53, 'label': '2-1850-5.4-c1-0-53', 'leading_term': '0.883634235590353249673431551064183421797680934168314809', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1850/2/b/i/149/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8836342355903533, 1.0781116104626332, 1.2881234977150762, 1.514282889464598, 1.7570824642985712, 2.016805241933386, 2.2934373828111263, 2.5865874778790054, 2.8954158432859196, 3.218576465077231, 3.554173471389004, 3.8997334162898056, 4.252194247285387, 4.607911559189141, 4.96268255074163, 5.311787935706007, 5.650051866850837, 5.971919675367815, 6.271552892833452, 6.542940605401059, 6.780025699528529, 6.9768440125766125, 7.1276738231776084, 7.227192532246244, 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'7.84454553961700542486236218613721', '8.527273918355052946531069953505967', '9.067297388263805762324121347359716', '9.750713744738748517869496790593915'], 'prelabel': '2-1850-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': -0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.89442719099991587856366946749251049417624734384461028971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39386884788498814711500129560', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.50602512263894727306296580840', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26247640333869065064156096916', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.772324373936879, 'bad_primes': [2, 5, 37], 'central_character': '5.4', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1850/2/b/i/149/1'], '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': '2-1850-5.4-c1-0-53', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1850-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39386884788498814711500129560', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3034589281889065210097612953075', 'Lhash_array': ['3034589281889065210097612953075'], 'label': '2-1850-5.4-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/b/i/149/1'}