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lfunc_lfunctions • Show schema
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{'Lhash': '1511912158561115076600142683152', 'a10': [-0.08475266882205465, 0.14679592847685738], 'a2': [-0.9135454576426009, -0.4067366430758002], 'a3': [0.9781476007338057, 0.20791169081775934], 'a4': [0.6691306063588582, 0.7431448254773942], 'a5': [0.017718132459603478, -0.1685767696688587], 'a6': [-0.8090169943749475, -0.5877852522924731], 'a7': [2.4618963628731945, 0.9690543320535415], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [0.9135454576426009, 0.4067366430758002], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9135454576426009, 0.4067366430758002]]], [3, [[1.0, 0], [-0.9781476007338057, -0.20791169081775934]]], [7, [[1.0, 0], [-2.4618963628731945, -0.9690543320535415]]], [11, [[1.0, 0], [-0.32490667277626306, -3.3006720003637833]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.25', 'coefficient_field': 'CDF', 'conductor': 462, 'conductor_radical': 462, 'conjugate': '2024002897837137148819074010117', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [-0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [-0.017718132459603478, 0.1685767696688587], [-4.8907380036690284, -1.0395584540887968]], [[1.0, 0], [-2.4618963628731945, -0.9690543320535415]], [[1.0, 0], [-0.32490667277626306, -3.3006720003637833]], [[1.0, 0], [-0.62198969005725, 0.45190196180746534], [4.017220926874317, -12.363734711836996]], [[1.0, 0], [3.7277428057884134, -1.6596980285895293], [11.37522030810059, -12.633462033115702]], [[1.0, 0], [-2.4272708391922166, 2.695757370886833], [-1.986040802085416, -18.895916011997194]], [[1.0, 0], [-0.7178303887444271, -1.243318704522266], [-11.5, 19.91858428704209]], [[1.0, 0], [-1.0258166390931627, 3.157138982297475], [-23.461492836873475, -17.04577231648172]], [[1.0, 0], [-0.54163170185196, -5.153281411380373], [-30.322575622747976, 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'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/462/2/y/a/25/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.392271359190917, 1.3491225693168962, 1.2966887173318655, 1.2294748557969548, 1.1403666500753655, 1.0219108856987416, 0.867608447857067, 0.6730927863847536, 0.4371419566887044, 0.16249497717638137, -0.1435709458832033, -0.4689695466571496, -0.7969224946153989, -1.106541862509212, -1.3739314096022215, -1.5738167384441697, -1.6816556489876944, -1.6761113833232157, -1.5417004434829282, -1.2713624997028905, -0.8686528690106112, -0.34923839492367803, 0.25860587588657424, 0.9147432438030373, 1.5693073246937028, 2.166221094053816, 2.6479364000634944, 2.9610485339597554, 3.062273312420312, 2.9241436677645667, 2.5397136164810705, 1.925570257140594, 1.1225617442170965, 0.19385222292457205, -0.7797989748964452, -1.7072937590345425, -2.496387470772331, -3.0638888303159364, -3.3456946857873575, 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'root_number': '0.9652770184246359 - 0.2612284014062121*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0420637878365', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19268839401717517292346854993', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69854345833482901066283301270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14998683137625231818221907003', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '77.25', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/2/y/a/25/3'], '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': '2-462-77.25-c1-0-6', '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': '2-462-77.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': -0.04206378783651261, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19268839401717517292346854993', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1511912158561115076600142683152', 'Lhash_array': ['1511912158561115076600142683152'], 'label': '2-462-77.25-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/y/a/25/3'}