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lfunc_lfunctions • Show schema
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{'Lhash': '5562648234821014015675298051467', 'a10': [0.0, -2.0], 'a2': [-1.0, 1.0], 'a3': [-1.0, -1.0], 'a4': [0.0, -2.0], 'a5': [-1.0, 1.0], 'a6': [2.0, 0.0], 'a7': [0.0, 2.0], 'a8': [2.0, 2.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.12776064323404868, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.0]]]], 'bad_primes': [2], 'central_character': '16.13', 'coefficient_field': 'CDF', 'conductor': 16, 'conductor_radical': 2, 'conjugate': '7449057628237973576081451745090', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.0]], [[1.0, 0], [1.0, 1.0], [0, 3.0]], [[1.0, 0], [1.0, -1.0], [0, -5.0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -11.0]], [[1.0, 0], [1.0, 1.0], [0, 13.0]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [-3.0, -3.0], [0, 19.0]], [[1.0, 0], [0, 6.0], [-23.0, 0]], [[1.0, 0], [-3.0, -3.0], [0, 29.0]], [[1.0, 0], [8.0, 0], [31.0, 0]], [[1.0, 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'0.9238795325112867 - 0.38268343236508984*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0625', 'prec': 24}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.38815572194696855867145714346', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.55228244623799316615009824381', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '9.422303413938473441171880689948', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.12776064323404868, 'bad_primes': [2], 'central_character': '16.13', 'conductor': 16, 'conductor_radical': 2, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/16/2/e/a/13/1'], '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': '2-2e4-16.13-c1-0-0', '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': '2-2e4-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3574362086219703, 'root_angle': -0.06250000000000001, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.38815572194696855867145714346', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5562648234821014015675298051467', 'Lhash_array': ['5562648234821014015675298051467'], 'label': '2-2e4-16.13-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/16/2/e/a/13/1'}