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lfunc_lfunctions • Show schema
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{'Lhash': '519864744099987812252575301432', 'a10': [-946096.6553358294, -1775241.8197183837], 'a2': [-86.5801515635805, -26.379487395084624], 'a3': [913.8847049461316, -913.8847049461316], 'a4': [6800.245289545143, 4567.880033671976], 'a5': [15715.717897858995, 15715.717897858995], 'a6': [-103232.08632056123, 55016.46621118701], 'a7': [0.0, 356100.47037856333], 'a8': [-468267.9340678342, -574874.7305386126], 'a9': [0.0, -76047.5078689558], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.15694863230604, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [86.5801515635805, 26.379487395084624]]]], 'bad_primes': [2], 'central_character': '16.5', 'coefficient_field': 'CDF', 'conductor': 16, 'conductor_radical': 2, 'conjugate': '2445777602334402344474974331569', 'degree': 2, 'euler_factors': [[[1.0, 0], [86.5801515635805, 26.379487395084624]], [[1.0, 0], [-913.8847049461316, 913.8847049461316], [0, -1594323.0]], [[1.0, 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'6.99356903850022080486895785120333', '8.503602168901020984825594254373706', '9.791555660326998501361665650229955', '10.62210565325073686094091495041667', '12.97827213265828735657151753702591', '14.68946894937730779496484939742592', '15.59942757376916055424964922194639'], 'prelabel': '2-2e4-16.5-c13-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.142094715516056, 'root_angle': -0.49844267505802203, 'root_number': '0.004892461078958849 - 0.999988031840677*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.249221337529', 'prec': 50}, 'spectral_label': 'c13-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41010097262320604172598121296', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45297505233538578131822577228', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70765015338230226516595351289', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.15694863230604, 'bad_primes': [2], 'central_character': '16.5', 'conductor': 16, 'conductor_radical': 2, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/16/14/e/a/5/2'], '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': '2-2e4-16.5-c13-0-3', 'motivic_weight': 13, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [13], 'order_of_vanishing': 0, 'prelabel': '2-2e4-16.5-c13-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.142094715516056, 'root_angle': -0.24922133752901102, 'self_dual': False, 'spectral_label': 'c13-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41010097262320604172598121296', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '519864744099987812252575301432', 'Lhash_array': ['519864744099987812252575301432'], 'label': '2-2e4-16.5-c13-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/16/14/e/a/5/2'}