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lfunc_lfunctions • Show schema
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{'Lhash': '437808048549324113233032599653', 'a10': [-352.0, -936.0], 'a2': [0.0, 8.0], 'a3': [0.0, 0.0], 'a4': [-64.0, 0.0], 'a5': [-117.0, 44.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, -512.0], 'a9': [-729.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6010816723970205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -8.0]]], [5, [[1.0, 0], [117.0, -44.0]]]], 'bad_primes': [2, 5], 'central_character': '20.19', 'coefficient_field': 'CDF', 'conductor': 20, 'conductor_radical': 10, 'conjugate': '5010307366358491601192750163728', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -8.0]], [[1.0, 0], [0, 0], [729.0, 0]], [[1.0, 0], [117.0, -44.0]], [[1.0, 0], [0, 0], [117649.0, 0]], [[1.0, 0], [0, 0], [-1771561.0, 0]], [[1.0, 0], [0, -1656.0], [-4826809.0, 0]], [[1.0, 0], [0, -9776.0], [-24137569.0, 0]], [[1.0, 0], [0, 0], [-47045881.0, 0]], [[1.0, 0], [0, 0], [148035889.0, 0]], [[1.0, 0], [31878.0, 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'2-20-20.19-c6-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/20/7/d/c/19/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.53554739413289, 0.25763885669837094, -0.009172750943654691, -0.26139402544066664, -0.4953764452703577, -0.7072451812404182, -0.8928783181584383, -1.0479464706872066, -1.1680201914425086, -1.2487492503093962, -1.2861136980351189, -1.276741543473201, -1.2182818861205287, -1.1098155962082723, -0.9522784320744628, -0.748864326634757, -0.5053701508516373, -0.23043842934729758, 0.06434778685410117, 0.36456239196013, 0.6532647691696143, 0.9115871863806206, 1.1195923823444738, 1.2573909533119076, 1.3064819961471783, 1.2512514863445297, 1.0805334276791707, 0.7891119457998206, 0.3790217509856966, -0.1395064945925712, -0.7476068696657306, 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'14.79672026095810305901821197089570', '16.41309310941420722358276692430395'], 'prelabel': '2-20-20.19-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.145013210308277, 'root_angle': 0.8855017059025997, 'root_number': '-0.936 + 0.3519999999999998*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.442750852951', 'prec': 47}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34536965349166450433700440595', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12628350211487746483549995409', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05351961884906686195943630547', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6010816723970205, 'bad_primes': [2, 5], 'central_character': '20.19', 'conductor': 20, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/20/7/d/c/19/2'], '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': '2-20-20.19-c6-0-1', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-20-20.19-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.145013210308277, 'root_angle': 0.44275085295129984, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34536965349166450433700440595', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '437808048549324113233032599653', 'Lhash_array': ['437808048549324113233032599653'], 'label': '2-20-20.19-c6-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/20/7/d/c/19/2'}