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lfunc_lfunctions • Show schema
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{'Lhash': '1550259803141650034373688734259', 'a10': [4.403673748451237, -7.627386672274831], 'a2': [-2.341036478426952, -1.3515980410025343], 'a3': [0.1729745867612707, -0.29960077268875174], 'a4': [2.653634528883777, 4.596229828745804], 'a5': [0.0, 3.258123802239944], 'a6': [-0.8098796348979249, 0.4675842252195128], 'a7': [0.8660254037844386, -0.5], 'a8': [0.0, -8.94019675909385], 'a9': [1.4401595846695352, 2.4944295716549276], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-3.6055030607763165, 0.01864614524806625]]]], 'bad_primes': [7, 13], 'central_character': '91.43', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '2604397988583331922888385221422', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.341036478426952, 1.3515980410025343], [1.0, 1.7320508075688772]], 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'10.34453934857356329873789188469585', '11.68225469549773789298871611415687', '13.04813522200350616562662047122023', '14.61320508355478812822099678685332'], 'prelabel': '2-91-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.005728052950379216, 'root_number': '0.9998380905945923 - 0.017994237859934398*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00286402647519', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22293935163406960725887619243', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.92815942746469885708727773451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.23837485752598112880882444687', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.4', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/q/a/43/1'], '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': '2-91-13.4-c1-0-0', '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': '2-91-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.002864026475189608, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22293935163406960725887619243', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1550259803141650034373688734259', 'Lhash_array': ['1550259803141650034373688734259'], 'label': '2-91-13.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/q/a/43/1'}