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lfunc_lfunctions • Show schema
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{'Lhash': '2453617827845595248834891895765', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [-1.3228756555322954, -2.29128784747792], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [1.3228756555322954, 2.29128784747792]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '420.361', 'coefficient_field': 'CDF', 'conductor': 420, 'conductor_radical': 210, 'conjugate': '670398909707132201179265942806', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.3228756555322954, 2.29128784747792]], [[1.0, 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[0.3228756555322953, -0.5592370399090427], [-33.5, -58.023702053557386]], [[1.0, 0], [-13.64575131106459, 0], [71.0, 0]], [[1.0, 0], [6.614378277661476, -11.4564392373896], [-36.5, -63.21985447626402]], [[1.0, 0], [1.1457513110645905, 1.984499483602524], [-39.5, 68.41600689897065]], [[1.0, 0], [10.937253933193771, 0], [83.0, 0]], [[1.0, 0], [-7.114378277661476, -12.322464641174038], [-44.5, 77.07626093681505]], [[1.0, 0], [-8.0, 0], [97.0, 0]], [[1.0, 0], [-2.468626966596886, 4.275787331080444], [-50.5, -87.4685657822283]], [[1.0, 0], [4.677124344467705, 8.101016997935345], [-51.5, 89.20061658979718]], [[1.0, 0], [-8.468626966596887, -14.668092176493708], [-53.5, 92.66471820493493]], [[1.0, 0], [-6.5, 11.258330249197702], [-54.5, -94.39676901250381]], [[1.0, 0], [-6.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-420-7.4-c1-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 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'root_analytic_conductor': 1.8313156158602968, 'root_angle': 0.5201729530539462, 'root_number': '-0.06333278610434481 + 0.9979924640017385*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.260086476527', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93556318074068897418215183173', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23440761245805510457951021020', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69085356341645749707963176647', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.4', 'conductor': 420, 'conductor_radical': 210, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/420/2/q/c/361/1'], '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': '2-420-7.4-c1-0-5', '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': '2-420-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': 0.2600864765269731, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93556318074068897418215183173', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2453617827845595248834891895765', 'Lhash_array': ['2453617827845595248834891895765'], 'label': '2-420-7.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/420/2/q/c/361/1'}