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lfunc_lfunctions • Show schema
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{'Lhash': '1654473714078107092313259306361', 'a10': [1.2689993013165934, -6.5761031196582784e-62], 'a2': [-1.0989856323248732, -0.6344996506582967], 'a3': [1.583922787246021, -0.700848488649862], 'a4': [-0.1948203866289989, -0.33743880799163845], 'a5': [-0.8660254037844386, 0.5], 'a6': [-2.1853965071080768, -0.2347760357145156], 'a7': [4.162284709943296, 2.4030961977296252], 'a8': [0.0, 3.0324524716620433], 'a9': [2.0176227919144085, -2.2201797831589016], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.583922787246021, 0.700848488649862]]], [5, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-3.093931961509988, 1.851373818964435]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.376', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1599988830517897128367818516663', 'degree': 2, 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[[1.0, 0], [-2.732961768595094, -4.73362863835], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-585-117.25-c1-0-23', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/376/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4045786801474855, 1.4415786968249122, 1.4655974588494036, 1.470783689420199, 1.4483051545265015, 1.3874683295077181, 1.2771259350591424, 1.1071915653824453, 0.8701544892369124, 0.5625205658133043, 0.18609510176557675, -0.25100635063557375, -0.733759706950347, -1.2401952883773846, -1.7420532606347108, -2.2062172411867613, -2.596939362005299, -2.8787760348356777, -3.0200468695611553, -2.996522133284468, -2.7949520791437696, -2.415990969259576, -1.8760553535640616, -1.2077024005119905, 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'7.54308970464434492549558200590147', '8.406182690366082830352733317765266', '8.600526017261435181233524743011448', '9.823888254432741441432141276576279', '10.61800400772510556312755450191114'], 'prelabel': '2-585-117.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.28537586266991055, 'root_number': '0.6243206826579153 + 0.7811681542443693*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.142687931335', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30514963175202502408380672797', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07398082953193088928919089235', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46699893843248344838249883525', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '117.25', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/376/17'], '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': '2-585-117.25-c1-0-23', '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': '2-585-117.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.14268793133495528, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30514963175202502408380672797', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1654473714078107092313259306361', 'Lhash_array': ['1654473714078107092313259306361'], 'label': '2-585-117.25-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/376/17'}