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lfunc_lfunctions • Show schema
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{'Lhash': '1692393954062354722824899368047', 'a10': [-2.7386127875258306, -1.5811388300841898], 'a2': [-0.7071067811865476, -1.224744871391589], 'a3': [2.7386127875258306, 1.5811388300841898], 'a4': [-1.0, 1.7320508075688772], 'a5': [1.9364916731037085, -1.118033988749895], 'a6': [-1.805395977730913e-60, -4.47213595499958], 'a7': [0.0, 0.0], 'a8': [2.8284271247461903, 0.0], 'a9': [3.5, 6.06217782649107], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 1.224744871391589]]], [5, [[1.0, 0], [-1.9364916731037085, 1.118033988749895]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '980.619', 'coefficient_field': 'CDF', 'conductor': 980, 'conductor_radical': 70, 'conjugate': '2014925284209180904143035120124', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 1.224744871391589]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '0.010086476527', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33506342659219661633388930645', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33429581462068515509876420701', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42879814922958629516428684232', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'bad_primes': [2, 5, 7], 'central_character': '140.59', 'conductor': 980, 'conductor_radical': 70, 'degree': 2, 'index': 62, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/980/2/s/b/619/2'], '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': '2-980-140.59-c1-0-62', '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': '2-980-140.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.797380810344827, 'root_angle': 0.010086476526973061, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33506342659219661633388930645', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1692393954062354722824899368047', 'Lhash_array': ['1692393954062354722824899368047'], 'label': '2-980-140.59-c1-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/980/2/s/b/619/2'}