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lfunc_lfunctions • Show schema
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{'Lhash': '882345563330440092286428301736', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-4.5, 7.794228634059948], 'a4': [0, 0], 'a5': [15.980796695811302, 27.679551822574012], 'a6': [0, 0], 'a7': [-85.70432793268174, 97.27162059720888], 'a8': [0, 0], 'a9': [-40.5, -70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.8889634571615, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [4.5, -7.794228634059948]]], [7, [[1.0, 0], [85.70432793268174, -97.27162059720888]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.193', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '1249585917143654695995741114942', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [4.5, -7.794228634059948]], [[1.0, 0], [-15.980796695811302, -27.679551822574012], [-1562.5, 2706.329386826371]], [[1.0, 0], [85.70432793268174, -97.27162059720888]], [[1.0, 0], 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'4.47404019280169835613789429965426', '5.83416751007355185983749496671149', '6.57053559713282391449863277460486', '7.60261354095062906589696762030562', '8.643343104445163386981360272890380', '9.634514542939558864015076525016304', '10.56224726641397445752971538146708'], 'prelabel': '2-336-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.3409102608029135, 'root_angle': -0.20829487241374584, 'root_number': '0.2590524603623376966360229398361721637837889962641726913 - 0.9658632526295942772568240878057414371443744714564210231*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.20829487241374584', 'prec': 67}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69604791980659457119804459844', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62680222066596273511391430440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35109684308924565263732609691', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.8889634571615, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/6/q/i/193/3'], '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': '2-336-7.4-c5-0-17', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-336-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.3409102608029135, 'root_angle': -0.20829487241374584, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69604791980659457119804459844', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '882345563330440092286428301736', 'Lhash_array': ['882345563330440092286428301736'], 'factors': ['2-336-7.4-c5-0-17'], 'label': '2-336-7.4-c5-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/6/q/i/193/3'}