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lfunc_lfunctions • Show schema
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{'Lhash': '4168254501877967604740399358023', 'a10': [-2.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, -3.0204479180442196], 'a4': [1.0, 0.0], 'a5': [-2.0, 0.0], 'a6': [0.0, -3.0204479180442196], 'a7': [-2.5615528128088303, -0.6621534468619564], 'a8': [1.0, 0.0], 'a9': [-6.123105625617661, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [2.5615528128088303, 0.6621534468619564]]], [23, [[1.0, 0], [-2.5615528128088303, 4.05443549550257]]]], 'bad_primes': [2, 7, 23], 'central_character': '322.321', 'coefficient_field': 'CDF', 'conductor': 322, 'conductor_radical': 322, 'conjugate': '1094165520303362329975874479834', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 3.0204479180442196], [-3.0, 0]], [[1.0, 0], [2.0, 0], [5.0, 0]], [[1.0, 0], [2.5615528128088303, 0.6621534468619564]], [[1.0, 0], [0, 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'5.57865861726097544518528573131562', '7.11357815209502445875749596586011', '8.246959339265266843378266238274190', '9.732374449302687945881902930171236', '9.877863475371695219259409470647689', '11.09704286163543972026624220765158', '11.93301164861121264666560866468848'], 'prelabel': '2-322-161.160-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': 0.7598767571027192, 'root_number': '-0.7287035305383611 + 0.6848292959423741*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.379938378551', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.28817301954301117711180868348', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56189248689979180419366785891', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92389216227506731130061848997', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'bad_primes': [2, 7, 23], 'central_character': '161.160', 'conductor': 322, 'conductor_radical': 322, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/322/2/c/c/321/1'], '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': '2-322-161.160-c1-0-15', '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': '2-322-161.160-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': 0.3799383785513596, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.28817301954301117711180868348', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4168254501877967604740399358023', 'Lhash_array': ['4168254501877967604740399358023'], 'label': '2-322-161.160-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/322/2/c/c/321/1'}