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lfunc_lfunctions • Show schema
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{'Lhash': '2186385025168023399422743322771', 'a10': [2.92521085907208, 0.0], 'a2': [0.929066844536504, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.1368347983829836, 0.0], 'a5': [3.148547250689394, 0.0], 'a6': [0.929066844536504, 0.0], 'a7': [-4.695090006612953, 0.0], 'a8': [-2.914329207965979, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.075906491948345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]], [103, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 13, 103], 'central_character': '4017.1', 'coefficient_field': 'CDF', 'conductor': 4017, 'conductor_radical': 4017, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.929066844536504, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.148547250689394, 0], [5.0, 0]], [[1.0, 0], [4.695090006612953, 0], [7.0, 0]], [[1.0, 0], [-3.6659721179375993, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.3848039349473957, 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[[1.0, 0], [-15.957915598275312, 0], [109.0, 0]], [[1.0, 0], [5.024183151275034, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 181, 'label': '2-4017-1.1-c1-0-181', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4017/2/a/f/1/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.7283452588122155e-60, 0.26952985405229524, 0.5385031214536141, 0.8062923749877772, 1.0721329997686955, 1.335065465588413, 1.5938896680413512, 1.8471339031398135, 2.093040066870977, 2.329565720373628, 2.554402816525536, 2.765012191395409, 2.9586723956769028, 3.13254106183902, 3.283726742349161, 3.4093689789199404, 3.5067242420938936, 3.5732552926458476, 3.60672144889575, 3.605267193600482, 3.5675065241258745, 3.492600448270072, 3.3803250660678406, 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'5.08935817066572150404482216457976', '6.10608120131953679346560424891396', '6.33660122113497051034416452139751', '6.91820471093713195101017260213356', '8.583142732214355969195798524845158'], 'prelabel': '2-4017-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.66355952488789, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72475367011571161766735422454', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62573526004537422219664050015', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58729189923423453414050083821', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.075906491948345, 'bad_primes': [3, 13, 103], 'central_character': '1.1', 'conductor': 4017, 'conductor_radical': 4017, 'degree': 2, 'index': 181, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4017/2/a/f/1/14'], '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': '2-4017-1.1-c1-0-181', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4017-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.66355952488789, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72475367011571161766735422454', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2186385025168023399422743322771', 'Lhash_array': ['2186385025168023399422743322771'], 'label': '2-4017-1.1-c1-0-181', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4017/2/a/f/1/14'}