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lfunc_lfunctions • Show schema
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{'Lhash': '717519288467540734488728033823', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.5646021430912047, 1.7376667208456675], 'a8': [0.0, 0.0], 'a9': [-0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6853425476616493, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0.10452846326765347, 0.9945218953682733]]], [307, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 307], 'central_character': '3377.1841', 'coefficient_field': 'CDF', 'conductor': 3377, 'conductor_radical': 3377, 'conjugate': '2433644537910584405389810363830', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.5646021430912047, 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'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56602291541404048029509275790', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86543762897333228799099958594', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.65125267424124137105933239616', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6853425476616493, 'bad_primes': [11, 307], 'central_character': '3377.1841', 'conductor': 3377, 'conductor_radical': 3377, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3377/1/m/b/1841/2'], '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': '2-3377-3377.1841-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3377-3377.1841-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2982074362988565, 'root_angle': -0.3704504037688384, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56602291541404048029509275790', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '717519288467540734488728033823', 'Lhash_array': ['717519288467540734488728033823'], 'label': '2-3377-3377.1841-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3377/1/m/b/1841/2'}