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lfunc_lfunctions • Show schema
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{'Lhash': '1357603208401529827131375549399', 'a10': [1.4422418509696662, -2.4980361626816427], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.16993844331159128, -0.29434201797483955], 'a4': [0.5, 0.8660254037844386], 'a5': [-2.8844837019393323, 0.0], 'a6': [0.16993844331159128, 0.29434201797483955], 'a7': [1.7723034076580748, 3.069719548491242], 'a8': [-3.0, 0.0], 'a9': [1.4422418509696662, 2.4980361626816427], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.14186074890431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-1.6699384433115914, 3.195513353993386]]]], 'bad_primes': [11, 13], 'central_character': '143.100', 'coefficient_field': 'CDF', 'conductor': 143, 'conductor_radical': 143, 'conjugate': '3399777218432765863601922591361', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386], [-1.0, -1.7320508075688772]], [[1.0, 0], [-0.16993844331159128, 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[[1.0, 0], [-7.054422145250924, -12.218617573613635], [-29.5, 51.09549882328188]], [[1.0, 0], [2.009815329934774, 3.4811022652778347], [-30.5, 52.827549630850754]], [[1.0, 0], [6.054422145250924, -10.486566766044756], [-33.5, -58.023702053557386]], [[1.0, 0], [3.0, 5.196152422706632], [-35.5, 61.48780366869514]], [[1.0, 0], [16.082541623073478, 0], [73.0, 0]], [[1.0, 0], [-0.9041143618088799, 0], [79.0, 0]], [[1.0, 0], [-4.90411436180888, 0], [83.0, 0]], [[1.0, 0], [-2.8267255529089983, 4.896032276691612], [-44.5, -77.07626093681505]], [[1.0, 0], [1.3976350356535163, 2.42077489219023], [-48.5, 84.00446416709055]], [[1.0, 0], [-4.932426521034892, 8.543213339032633], [-50.5, -87.4685657822283]], [[1.0, 0], [-5.35950754649273, 0], [103.0, 0]], [[1.0, 0], [1.6567871095974072, -2.8696394511478953], [-53.5, -92.66471820493493]], [[1.0, 0], [-2.154777617799763, 0], [109.0, 0]], [[1.0, 0], [1.8976350356535163, 3.2868002959746683], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-143-13.9-c1-0-2', '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/143/2/e/a/100/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8629585811892763, 0.7839396682463029, 0.7094283465556536, 0.6345330518345624, 0.5541315867720285, 0.46334619437409247, 0.3579220812456797, 0.23451332529747004, 0.09090730702805373, -0.07378347999537793, -0.25894976267461445, -0.46233886131498547, -0.679950607170245, -0.9060002425418607, -1.1329747820655467, -1.351807341267303, -1.552188510096017, -1.7230252934628065, -1.8530467658247751, -1.93154185848451, -1.9491993548943192, -1.8990042720538691, -1.7771297306937008, -1.583750789961971, -1.3236983063763266, -1.0068684094134466, -0.6483081825642585, -0.2679116739411499, 0.1103171486410789, 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'11.68390435241481062027274935685565', '12.33278938642137365649833878982710'], 'prelabel': '2-143-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0685788454317773, 'root_angle': -0.5946754400820123, 'root_number': '-0.2930656124885866 - 0.9560923317215182*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.297337720041', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07096009591058075893692776287', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46295341241537849987082325893', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.51667750288562432253196531162', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.14186074890431, 'bad_primes': [11, 13], 'central_character': '13.9', 'conductor': 143, 'conductor_radical': 143, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/143/2/e/a/100/2'], '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': '2-143-13.9-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': '2-143-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0685788454317773, 'root_angle': -0.29733772004100617, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07096009591058075893692776287', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1357603208401529827131375549399', 'Lhash_array': ['1357603208401529827131375549399'], 'label': '2-143-13.9-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/143/2/e/a/100/2'}