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lfunc_lfunctions • Show schema
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{'Lhash': '2017780349875492747914152212364', 'a10': [-0.05211191988786391, 2.6016593683644576e-61], 'a2': [0.8660254037844386, 0.5], 'a3': [1.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [-0.04513024646286966, 0.026055959943931953], 'a6': [0.8660254037844386, 0.5], 'a7': [1.5177744798009505, -2.1671088178642424], 'a8': [0.0, 1.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-1.5177744798009505, 2.1671088178642424]]], [13, [[1.0, 0], [-1.3082515332232807, 3.3598330205263083]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.361', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '2172054510745545281419404848698', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-1.0, 0]], 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[6.328049860519925, -10.960503871249657], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-546-91.88-c1-0-11', '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/546/2/bd/b/361/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.603533090245162, 2.558991700037656, 2.513172783229124, 2.458584954712035, 2.3850077437514434, 2.281325655995113, 2.1373141464393606, 1.9451864571847164, 1.7008398680281287, 1.4047871275641506, 1.0627472760485963, 0.6858420418420513, 0.2903283002249177, -0.10319439937277446, -0.471128250912663, -0.7887452046536969, -1.032480462229158, -1.1824782454610665, -1.2251469392175645, -1.1554281360165892, -0.978460195762716, -0.7103314697160237, -0.377677571250326, -0.015981976777149742, 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'7.06524648315727991795937131820320', '8.258525461184112435118650068591268', '8.911407319642477997303015412340187', '9.827242886220920244653320273091477', '10.97834232255484033288237830036812'], 'prelabel': '2-546-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.16307223902962623, 'root_number': '0.8716161827523604 - 0.4901889737276878*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0815361195148', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59174803333995112449078696254', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88051173691563139356338375753', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82086525619526578146911635401', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '91.88', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bd/b/361/8'], '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': '2-546-91.88-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': '2-546-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.08153611951481311, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59174803333995112449078696254', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2017780349875492747914152212364', 'Lhash_array': ['2017780349875492747914152212364'], 'label': '2-546-91.88-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bd/b/361/8'}