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lfunc_lfunctions • Show schema
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{'Lhash': '152270401567538949672304301447', 'a10': [0.3231676980780795, 0.5597428724363127], 'a2': [0.030036955716369204, -0.1703480408709069], 'a3': [0.0, 0.0], 'a4': [1.8512690052519678, 0.6738068135313181], 'a5': [-2.862372974181598, 2.401816106927593], 'a6': [0.0, 0.0], 'a7': [-2.8486760421714368, 1.036833286417656], 'a8': [0.3433640897232882, -0.5947240488953737], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.649', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '3262422005028958771050049299172', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.030036955716369204, 0.1703480408709069], [-1.8793852415718169, -0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.862372974181598, -2.401816106927593], [0.8682408883346517, 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3.613925871112111, 3.752345045876265, 3.182250288881149, 2.135268533590043, 0.9944778624498724], 'positive_zeros': ['0.12012016681893575082245411132219', '1.88913286529967702402153895365064', '3.48402520877320597201429315940537', '4.30031986562471751465470205454505', '5.51397813814039058029563747473994', '6.47535412340687073546986428866708', '7.45034794592814035355060386283114', '7.990426988817516971589820277456707', '9.070642041370740357088405122943212', '10.04865187376510803649149408683243'], 'prelabel': '2-3e6-27.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.9629629629629629, 'root_number': '-0.993238357741943 + 0.11609291412523036*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.481481481481', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12012016681893575082245411132', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.25', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/s/649/2'], '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': '2-3e6-27.25-c1-0-1', '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': '2-3e6-27.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.48148148148148145, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12012016681893575082245411132', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '152270401567538949672304301447', 'Lhash_array': ['152270401567538949672304301447'], 'label': '2-3e6-27.25-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/s/649/2'}