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lfunc_lfunctions • Show schema
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{'Lhash': '694943311192309297121307029566', 'a10': [-1.7196841097631028, -0.5513945209206229], 'a2': [-2.724898719974978, -0.03523044763379193], 'a3': [-1.5100179371770965, -0.8484372866649759], 'a4': [5.424500382901421, 0.14029110616057813], 'a5': [0.6336105323268871, 0.1941621295363667], 'a6': [4.08475511875472, 2.3651042842742402], 'a7': [1.090348946805598, -2.7189281765622884], 'a8': [-9.330117562087112, -0.3620510519266157], 'a9': [1.5603083411931473, 2.562311042867959], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5100179371770965, 0.8484372866649759]]]], 'bad_primes': [3], 'central_character': '729.4', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1591011919052946308085967857789', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.724898719974978, 0.03523044763379193], [1.999331466779375, 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[[1.0, 0], [0.6467578625877654, 3.9672010735742202], [-78.70234714303434, 26.36172517452742]], [[1.0, 0], [-2.9508061368835574, -1.2055369629704558], [63.53974637565302, 62.319343951278]], [[1.0, 0], [0.5164407462365233, -2.243566332836715], [-87.23792361025203, -42.40925234158027]], [[1.0, 0], [0.47191154264311047, -3.1506675678401344], [-96.56767173916185, -29.591971459797712]], [[1.0, 0], [-1.4286545376472124, -4.00557202660965], [-79.75190974812564, 65.18153796533818]], [[1.0, 0], [0.5933890908717264, 10.188097231457958], [-106.2765042783879, 12.421941811399634]], [[1.0, 0], [0.24562832655183328, -4.217275497994197], [-108.26298099387179, -12.654127639650095]], [[1.0, 0], [2.403710623721575, -1.765461780096439], [33.8055497893235, -107.82478751864791]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-3e6-729.4-c1-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 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2.4126944081982997, 'root_angle': -0.24728480737189226, 'root_number': '0.7131126246591977 - 0.7010494879476556*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.123642403686', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54821360954445241703244515047', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95119456717149328270109391587', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38479314213522479926645147943', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '729.4', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/k/a/4/1'], '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': '2-3e6-729.4-c1-0-17', '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': '2-3e6-729.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.12364240368594613, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54821360954445241703244515047', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '694943311192309297121307029566', 'Lhash_array': ['694943311192309297121307029566'], 'label': '2-3e6-729.4-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/k/a/4/1'}