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lfunc_lfunctions • Show schema
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{'Lhash': '2718741024722871530907121405575', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.23606797749979, 0], 'a4': [0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [0, -9.797958971132712], 'a8': [0, 0], 'a9': [-4.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.643084266317778, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [19.0, -21.908902300206645]]]], 'bad_primes': [2, 29], 'central_character': '464.463', 'coefficient_field': 'CDF', 'conductor': 464, 'conductor_radical': 58, 'conjugate': '507356159178040997808356929348', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.23606797749979, 0], [9.0, 0]], [[1.0, 0], [1.0, 0], [25.0, 0]], [[1.0, 0], [0, 9.797958971132712], [-49.0, 0]], [[1.0, 0], [6.708203932499369, 0], [121.0, 0]], [[1.0, 0], [5.0, 0], [169.0, 0]], [[1.0, 0], [0, 21.908902300206645], [-289.0, 0]], [[1.0, 0], [13.416407864998739, 0], [361.0, 0]], [[1.0, 0], 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'5.61263173017018409296044504505605', '6.35088942601619210889828790582786', '8.078769420845042877241601825855239', '8.212334584306326314916249840380302', '9.247967832994511810656937441430491', '10.10463655194870474895529871694350', '11.26249538700673638014257273843872'], 'prelabel': '2-464-116.115-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.555711499308933, 'root_angle': 0.7274040254119775, 'root_number': '-0.6551724137931034482758620689655172413793103448275862069 + 0.7554793896622980875268548728286925985555099241351493162*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3637020127059888', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14470850582438567239106206626', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91341728651881546473606179830', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29717751501363784530427031168', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.643084266317778, 'bad_primes': [2, 29], 'central_character': '116.115', 'conductor': 464, 'conductor_radical': 58, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/464/3/h/a/463/3'], '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': '2-464-116.115-c2-0-27', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-464-116.115-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.555711499308933, 'root_angle': 0.36370201270598873, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14470850582438567239106206626', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2718741024722871530907121405575', 'Lhash_array': ['2718741024722871530907121405575'], 'label': '2-464-116.115-c2-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/464/3/h/a/463/3'}