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lfunc_lfunctions • Show schema
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{'Lhash': '945182427454691211968451526724', 'a10': [-1.6132298433924508, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.6132298433924508, 0.0], 'a6': [-1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.82362001368209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '3234.1', 'coefficient_field': 'CDF', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.6132298433924508, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [7.342059571206135, 0], [17.0, 0]], [[1.0, 0], [-1.1710297856030671, 0], [19.0, 0]], [[1.0, 0], [-3.5577999422106164, 0], [23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-3234-1.1-c1-0-11', 'leading_term': '1.8551059703210467174468554442743', '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/3234/2/a/bf/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.8551059703210466, 1.8470849059551413, 1.822946872499171, 1.782474731577902, 1.7253307239661309, 1.6510910822853015, 1.559291482303999, 1.449480713136168, 1.3212796633336217, 1.1744426608972245, 1.0089183266700479, 0.8249073448196471, 0.6229148642490191, 0.4037955747827438, 0.16878982156343753, -0.08045058422606056, -0.34184793212512593, -0.612896382225416, -0.8906725243577107, -1.1718590709908445, -1.4527817738061712, -1.7294593803946898, -1.99766615196189, -2.253006146180423, -2.4909981357493214, 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'4.63538443336979284942494968148626', '5.51603538273905658558150676923729', '6.53097533673180727057813588424540', '6.83537775653755787055218829841758', '7.84553452701584066735953834707627', '8.473650396790543273812909141405860'], 'prelabel': '2-3234-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74561746532090103070418096808', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24077992026809123306857026515', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14767287423707492032674949862', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.82362001368209, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3234/2/a/bf/1/2'], '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': '2-3234-1.1-c1-0-11', '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': '2-3234-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74561746532090103070418096808', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '945182427454691211968451526724', 'Lhash_array': ['945182427454691211968451526724'], 'label': '2-3234-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3234/2/a/bf/1/2'}