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lfunc_lfunctions • Show schema
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{'Lhash': '3816018971598620405390500187413', 'a10': [0.6460838219953816, 0.0], 'a2': [0.0, 1.0], 'a3': [0.0, -3.09557356477856], 'a4': [-1.0, 0.0], 'a5': [0.0, -0.6460838219953816], 'a6': [3.09557356477856, 0.0], 'a7': [-2.449489742783178, -1.0], 'a8': [0.0, -1.0], 'a9': [-6.58257569495584, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2296961911277184, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [7, [[1.0, 0], [2.449489742783178, 1.0]]], [11, [[1.0, 0], [-2.79128784747792, 1.79128784747792]]]], 'bad_primes': [2, 7, 11], 'central_character': '154.153', 'coefficient_field': 'CDF', 'conductor': 154, 'conductor_radical': 154, 'conjugate': '1341004958771033263546511639993', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 3.09557356477856], [-3.0, 0]], [[1.0, 0], [0, 0.6460838219953816], [-5.0, 0]], [[1.0, 0], [2.449489742783178, 1.0]], [[1.0, 0], [-2.79128784747792, 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'6.52142185537106594181065793047480', '8.686325028583903411631354757139798', '9.412583555625762001907199884216057', '10.06362438232702606717641000161799', '11.08586651728769404271460757127532', '11.79299309669127043446451957900746', '13.16980065844479182833777197969795'], 'prelabel': '2-154-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1089166745647385, 'root_angle': 0.4417646831273614, 'root_number': '0.18193274534369486 + 0.9833109763303297*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.220882341564', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.01030818027584223214623570382', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.92954665589412620179875441003', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.12777921881293340631834055990', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2296961911277184, 'bad_primes': [2, 7, 11], 'central_character': '77.76', 'conductor': 154, 'conductor_radical': 154, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/154/2/c/a/153/5'], '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': '2-154-77.76-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': '2-154-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1089166745647385, 'root_angle': 0.2208823415636807, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.01030818027584223214623570382', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3816018971598620405390500187413', 'Lhash_array': ['3816018971598620405390500187413'], 'label': '2-154-77.76-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/154/2/c/a/153/5'}