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lfunc_lfunctions • Show schema
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{'Lhash': '547468486549632532898552589376', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.104887622889267, -2.104887622889267], 'a6': [0, 0], 'a7': [-4.407312528553695, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.863', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1297773066956225809908157154420', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.104887622889267, 2.104887622889267], [0, 5.0]], [[1.0, 0], [4.407312528553695, 0], [7.0, 0]], [[1.0, 0], [-0.21558931531378753, 0.21558931531378753], [0, -11.0]], [[1.0, 0], [-2.735441238611917, -2.735441238611917], [0, 13.0]], [[1.0, 0], [0, -2.364383052777864], [-17.0, 0]], [[1.0, 0], 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3.12872303503928, 2.790145035024747, 2.366347809055562, 1.8863882407745176, 1.3817163015827971], 'positive_zeros': ['0.43187648587952044593815539153249', '2.70945029373442735440338302334781', '3.36464225285713083830308551842345', '4.12623879689587553022592120047905', '5.65045941457947302062463721997572', '6.44475986082914161511367928974042', '7.15417467104354003007615789142535', '7.85284762719194779579822779522066', '8.972471008821949923749124915348635', '9.683233825834395170528487847190494'], 'prelabel': '2-1152-48.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.2955045391608562, 'root_number': '0.5991519262248317474060100169773079709617444466879756481 - 0.8006353535168639897130482384543020139070179639390436577*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1477522695804281', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43187648587952044593815539153', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70945029373442735440338302335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36464225285713083830308551842', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '48.35', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/l/a/863/2'], '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': '2-1152-48.35-c1-0-2', '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': '2-1152-48.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.1477522695804281, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43187648587952044593815539153', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '547468486549632532898552589376', 'Lhash_array': ['547468486549632532898552589376'], 'label': '2-1152-48.35-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/l/a/863/2'}