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lfunc_lfunctions • Show schema
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{'Lhash': '3595602839824675577413265302540', 'a10': [-0.8660254037844386, 1.5], 'a2': [-0.8660254037844386, -0.5], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, -1.7320508075688772], 'a6': [-0.8660254037844386, 0.5], 'a7': [1.098076211353316, -0.6339745962155614], 'a8': [0.0, -1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-1.598076211353316, -3.232050807568877]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.43', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '2156996828402040268542707969861', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.7320508075688772], [-5.0, 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[-30.5, 52.827549630850754]], [[1.0, 0], [-6.294228634059948, -3.633974596215561], [33.5, 58.023702053557386]], [[1.0, 0], [-1.901923788646684, 1.098076211353316], [35.5, -61.48780366869514]], [[1.0, 0], [0, -12.12435565298214], [-73.0, 0]], [[1.0, 0], [-8.392304845413264, 0], [79.0, 0]], [[1.0, 0], [0, 5.660254037844386], [-83.0, 0]], [[1.0, 0], [8.196152422706632, 4.732050807568878], [44.5, 77.07626093681505]], [[1.0, 0], [5.196152422706632, -3.0], [48.5, -84.00446416709055]], [[1.0, 0], [-9.696152422706632, 16.794228634059948], [-50.5, -87.4685657822283]], [[1.0, 0], [6.196152422706632, 0], [103.0, 0]], [[1.0, 0], [-1.098076211353316, 1.901923788646684], [-53.5, -92.66471820493493]], [[1.0, 0], [0, -4.392304845413264], [-109.0, 0]], [[1.0, 0], [0.40192378864668404, 0.6961524227066319], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-78-13.4-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 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'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.3497518056925321, 'root_number': '0.4546851020925263 + 0.890652265440957*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.174875902846', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.83643051103933429250281585704', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.98937760909974793030923450180', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.56786227303523526596374036781', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '13.4', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/i/b/43/1'], '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': '2-78-13.4-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': '2-78-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.17487590284626606, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.83643051103933429250281585704', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3595602839824675577413265302540', 'Lhash_array': ['3595602839824675577413265302540'], 'label': '2-78-13.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/i/b/43/1'}