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lfunc_lfunctions • Show schema
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{'Lhash': '3039598782808431638644332303311', 'a10': [0.0, 0.0], 'a2': [0.0, 1.0], 'a3': [1.4142135623730951, -1.4142135623730951], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [1.4142135623730951, 1.4142135623730951], 'a7': [-2.8284271247461903, -2.8284271247461903], 'a8': [0.0, -1.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.615353236830009, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 17], 'central_character': '578.327', 'coefficient_field': 'CDF', 'conductor': 578, 'conductor_radical': 34, 'conjugate': '672745749953408971127587153692', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [-1.4142135623730951, 1.4142135623730951], [0, -3.0]], [[1.0, 0], [0, 0], [0, -5.0]], [[1.0, 0], [2.8284271247461903, 2.8284271247461903], [0, 7.0]], [[1.0, 0], [4.242640687119285, 4.242640687119285], [0, 11.0]], [[1.0, 0], [2.0, 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'6.29941707747763324660347934192714', '7.72670709491563663215781400088470', '8.604299210363705363873879879387695', '9.562538574596311137043234309225555', '9.885624896950080306771177854859867', '10.57786440423496178388431453277030'], 'prelabel': '2-578-17.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.14833731914474, 'root_angle': 0.5483570281982233, 'root_number': '-0.15133440293091135 + 0.9884826242729533*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.274178514099', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39782064731494503880738504547', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.92508762724022476591227108172', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16518240900301913280902737550', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.615353236830009, 'bad_primes': [2, 17], 'central_character': '17.4', 'conductor': 578, 'conductor_radical': 34, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/578/2/c/e/327/2'], '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': '2-578-17.4-c1-0-19', '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': '2-578-17.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.14833731914474, 'root_angle': 0.27417851409911165, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39782064731494503880738504547', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3039598782808431638644332303311', 'Lhash_array': ['3039598782808431638644332303311'], 'label': '2-578-17.4-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/578/2/c/e/327/2'}