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lfunc_lfunctions • Show schema
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{'Lhash': '464091262481858990206521551816', 'a10': [0.0, 0.0], 'a2': [-0.25881904510252074, 0.9659258262890683], 'a3': [-1.9318516525781366, -0.5176380902050415], 'a4': [-0.8660254037844386, -0.5], 'a5': [0.0, 0.0], 'a6': [1.0, -1.7320508075688772], 'a7': [-1.224744871391589, 1.224744871391589], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.58578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-2.598076211353316, 3.5]]]], 'bad_primes': [2, 5, 19], 'central_character': '950.943', 'coefficient_field': 'CDF', 'conductor': 950, 'conductor_radical': 190, 'conjugate': '1451508163652782105411318051597', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [1.9318516525781366, 0.5176380902050415], 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'rational': False, 'root_analytic_conductor': 2.7542309619967678, 'root_angle': -0.69178823644584, 'root_number': '-0.5667209481275931 - 0.8239098051081574*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.345894118223', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36610345342660147689362679311', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89881302387080737577765373873', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54069216300378697859445836982', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.58578819202164, 'bad_primes': [2, 5, 19], 'central_character': '95.88', 'conductor': 950, 'conductor_radical': 190, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/950/2/q/d/943/1'], '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': '2-950-95.88-c1-0-5', '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': '2-950-95.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7542309619967678, 'root_angle': -0.34589411822292, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36610345342660147689362679311', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '464091262481858990206521551816', 'Lhash_array': ['464091262481858990206521551816'], 'label': '2-950-95.88-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/950/2/q/d/943/1'}