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lfunc_lfunctions • Show schema
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{'Lhash': '1304569131508299822909572965466', 'a10': [-1.645784998019215, 0.052134407337384406], 'a2': [0.5822927083652505, 1.2887727502491126], 'a3': [0.0, 0.0], 'a4': [-1.3218704035693227, 1.5008859504197765], 'a5': [-0.4455696001783493, 1.0757001717317283], 'a6': [0.0, 0.0], 'a7': [2.5753346501981658, 2.5753346501981658], 'a8': [-2.704016411534996, -0.8296356104636557], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.299691578212876, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5822927083652505, -1.2887727502491126]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '288.181', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '3260824220544882563097241100921', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5822927083652505, -1.2887727502491126]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.4455696001783493, -1.0757001717317283], 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'4.76194605068771651066074520265909', '6.30916427872838444612131147804361', '7.87070605535392467176862727264558', '8.563312080357444463888710973825396', '10.04485764748582549181340376520081', '10.50012040032001181839329033543573', '11.54520429258729116408396489872340'], 'prelabel': '2-288-32.21-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.516473401749228, 'root_angle': -0.7378995048566219, 'root_number': '-0.6797218452707735 - 0.7334699810228736*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.368949752428', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02912358600502659235084555587', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71123061938271715878048781220', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42817331253519942756834702676', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.299691578212876, 'bad_primes': [2, 3], 'central_character': '32.21', 'conductor': 288, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/288/2/v/c/181/6'], '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': '2-288-32.21-c1-0-3', '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': '2-288-32.21-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.516473401749228, 'root_angle': -0.36894975242831096, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02912358600502659235084555587', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1304569131508299822909572965466', 'Lhash_array': ['1304569131508299822909572965466'], 'label': '2-288-32.21-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/288/2/v/c/181/6'}