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lfunc_lfunctions • Show schema
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{'Lhash': '1636928871654503374108495923659', 'a10': [-4.065112149013191, -5.7857465564908175], 'a2': [-0.36602540378443865, 1.3660254037844386], 'a3': [2.6677357514397397, -1.372292228532337], 'a4': [-1.7320508075688772, -1.0], 'a5': [-3.2077712301266073, 3.835388342159374], 'a6': [0.8981269899802192, 4.146488624109449], 'a7': [6.794181470652108, -1.6849623568043157], 'a8': [2.0, -2.0], 'a9': [5.233628079019504, -7.321826078957258], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.722085551566235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.36602540378443865, -1.3660254037844386]]], [3, [[1.0, 0], [-2.6677357514397397, 1.372292228532337]]], [5, [[1.0, 0], [3.2077712301266073, -3.835388342159374]]], [7, [[1.0, 0], [-6.794181470652108, 1.6849623568043157]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.143', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 'conjugate': 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'positive_zeros': ['1.29130919147578098427972716541304', '3.04523485663267272321604302358409', '4.25796543026745948109591254606961', '5.15450432353875463326934715725202', '7.36318655538365359062404228306037', '8.450782829146424456575089051924581', '8.872467486928959157649672612828167', '9.916419388452118656659615573996313', '11.20996462746719870874809054303916', '11.79827972018468622500136269452765'], 'prelabel': '2-210-105.38-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': -0.287704452557952, 'root_number': '0.6185894073482329 - 0.7857144170222168*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.143852226279', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29130919147578098427972716541', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04523485663267272321604302358', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25796543026745948109591254607', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.722085551566235, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.38', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/3/w/b/143/13'], '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': '2-210-105.38-c2-0-14', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-210-105.38-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': -0.143852226278976, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29130919147578098427972716541', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1636928871654503374108495923659', 'Lhash_array': ['1636928871654503374108495923659'], 'label': '2-210-105.38-c2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/3/w/b/143/13'}