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  • lfunc_lfunctions • Show schema
    {'Lhash': '6999306331500799189943033973487', 'a10': [0.0, 0.0], 'a2': [-0.5, -0.8660254037844386], 'a3': [-1.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [1.5, 0.8660254037844386], 'a7': [-1.0, -1.7320508075688772], 'a8': [1.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.14373072363830475, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]]], 'bad_primes': [2, 3], 'central_character': '18.13', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '5529231308959443969539426230047', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [1.0, 1.7320508075688772], [-3.5, 6.06217782649107]], [[1.0, 0], [-1.5, -2.598076211353316], 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-0.27354443724568916], 'positive_zeros': ['5.52147912858687978615646302052609', '6.92583624002767656428145584124702', '8.790108040571259251135981778049433', '10.66744030764575546769971244074087', '12.18420205922030737509979676104717', '13.60256088276205419926735569180859', '15.36554110674836471808657271020734', '16.50555445570130060214767610978446', '17.58588719176622164211034015698087', '18.65330191638767616820202141857877'], 'prelabel': '2-18-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.379118350437307, 'root_angle': 0.05555555555555555, 'root_number': '0.9396926207859084 + 0.3420201433256687*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0555555555556', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.52147912858687978615646302053', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '6.92583624002767656428145584125', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '8.790108040571259251135981778049', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.14373072363830475, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/2/c/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': '2-18-9.4-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-18-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.379118350437307, 'root_angle': 0.05555555555555555, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '5.52147912858687978615646302053', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '6999306331500799189943033973487', 'Lhash_array': ['6999306331500799189943033973487'], 'factors': ['2-18-9.4-c1-0-0'], 'label': '2-18-9.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/2/c/a/13/1'}