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lfunc_lfunctions • Show schema
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{'Lhash': '2552379967176575523425479233695', 'a10': [2.004251648554301, 0.9914511229845713], 'a2': [-0.25881904510252074, 0.9659258262890683], 'a3': [-0.6848175932188154, 1.5909195026832719], 'a4': [-0.8660254037844386, -0.5], 'a5': [0.4389297473701196, -2.1925648626377288], 'a6': [-1.3594663996424328, -1.073243266106637], 'a7': [1.8259682031486628, 1.914638378673645], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-2.062049728035978, -2.178979329664866], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [0.6848175932188154, -1.5909195026832719]]], [5, [[1.0, 0], [-0.4389297473701196, 2.1925648626377288]]], [7, [[1.0, 0], [-1.8259682031486628, -1.914638378673645]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '630.517', 'coefficient_field': 'CDF', 'conductor': 630, 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['2.01347277137488976685269570044457', '2.58065419661238726833228525453630', '4.38199447827784741917013314258193', '5.23550385822371262524280969485721', '6.74390696977365087507838495291259', '7.31352773471259934144748768852428', '7.951535631981476585501202790711303', '9.313964904348944288808244162084752', '10.35425547798053009706277910930185', '10.80623925198398853639296993345388'], 'prelabel': '2-630-315.202-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.5974453477600222, 'root_number': '-0.301374252114538 + 0.9535059308480482*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.29872267388', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01347277137488976685269570044', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58065419661238726833228525454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38199447827784741917013314258', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.030575327340666, 'bad_primes': [2, 3, 5, 7], 'central_character': '315.202', 'conductor': 630, 'conductor_radical': 210, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/630/2/bz/a/517/10'], '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': '2-630-315.202-c1-0-38', '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': '2-630-315.202-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.2987226738800111, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01347277137488976685269570044', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2552379967176575523425479233695', 'Lhash_array': ['2552379967176575523425479233695'], 'label': '2-630-315.202-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/630/2/bz/a/517/10'}