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lfunc_lfunctions • Show schema
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{'Lhash': '3584563397767987350441970269804', 'a10': [-1.224744871391589, -0.7071067811865476], 'a2': [-0.5, -0.8660254037844386], 'a3': [1.0, -1.4142135623730951], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.224744871391589, -0.7071067811865476], 'a6': [-1.724744871391589, -0.15891862259789113], 'a7': [-0.4494897427831781, 0.0], 'a8': [1.0, 0.0], 'a9': [-1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-1.0, 1.4142135623730951]]], [19, [[1.0, 0], [-3.1742346141747673, -2.987345747344081]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.107', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '2135558697206700431773727263989', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, 1.4142135623730951]], [[1.0, 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[-29.5, 51.09549882328188]], [[1.0, 0], [-0.775255128608411, 1.342781271578112], [-30.5, -52.827549630850754]], [[1.0, 0], [-2.1742346141747673, -1.255294939775204], [33.5, 58.023702053557386]], [[1.0, 0], [3.0, 5.196152422706632], [-35.5, 61.48780366869514]], [[1.0, 0], [4.398979485566356, 7.619255970454132], [-36.5, 63.21985447626402]], [[1.0, 0], [7.3484692283495345, -4.242640687119285], [39.5, -68.41600689897065]], [[1.0, 0], [0, -17.002670830492992], [-83.0, 0]], [[1.0, 0], [3.550510257216822, -6.149664158293978], [-44.5, -77.07626093681505]], [[1.0, 0], [-2.848469228349534, 1.6445644757659692], [48.5, -84.00446416709055]], [[1.0, 0], [8.573214099741124, 4.949747468305833], [50.5, 87.4685657822283]], [[1.0, 0], [0, 5.021179759100816], [-103.0, 0]], [[1.0, 0], [-4.898979485566356, 0], [107.0, 0]], [[1.0, 0], [0, 0], [54.5, -94.39676901250381]], [[1.0, 0], [-18.79795897113271, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-114-57.50-c1-0-6', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.4674215666035548, 'root_number': '0.10216957523404308 + 0.9947669967869336*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.233710783302', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.82772192678536030945170781749', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.65012206407404933622648897726', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.95679877052569384345613007563', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '57.50', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/h/e/107/1'], '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': '2-114-57.50-c1-0-6', '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': '2-114-57.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.2337107833017774, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.82772192678536030945170781749', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3584563397767987350441970269804', 'Lhash_array': ['3584563397767987350441970269804'], 'label': '2-114-57.50-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/h/e/107/1'}