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lfunc_lfunctions • Show schema
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{'Lhash': '2597636871091774853854823403998', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.3689911778989208, -0.42583851982929477], 'a4': [0.0, 0.0], 'a5': [0.14231483827328514, -0.9898214418809327], 'a6': [0.0, 0.0], 'a7': [-0.7557495743542583, -1.654860733945285], 'a8': [0.0, 0.0], 'a9': [0.0971308826701135, 0.6755601278278439], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9182796232447245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.14231483827328514, 0.9898214418809327]]], [23, [[1.0, 0], [-0.28173255684142967, 0.9594929736144974]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.639', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '1026790592261239648877910129159', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3689911778989208, 0.42583851982929477], [-0.14231483827328514, -0.9898214418809327]], [[1.0, 0], 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'3.08390670842130696582390605449835', '3.43767824944645185418180576849278', '4.82339160126138421484413947235465', '5.97409383065353476489264334566345', '6.27895850458588596782871492746617', '7.25881208343963790104250460147036', '8.281654823437477102932476162242576', '9.113616421640308653336459627588084', '9.622884724189096992273836417322700'], 'prelabel': '2-1840-460.179-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9582690766401285, 'root_angle': 0.6290199860047564, 'root_number': '-0.39432042549281560584771836056593 + 0.91897301485906802249697254598524*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3145099930023782', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04917417356493426395222551226', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08390670842130696582390605450', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43767824944645185418180576849', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9182796232447245, 'bad_primes': [2, 5, 23], 'central_character': '460.179', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/1/bq/a/639/2'], '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': '2-1840-460.179-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1840-460.179-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9582690766401285, 'root_angle': 0.3145099930023782, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04917417356493426395222551226', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2597636871091774853854823403998', 'Lhash_array': ['2597636871091774853854823403998'], 'label': '2-1840-460.179-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/1/bq/a/639/2'}