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lfunc_lfunctions • Show schema
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{'Lhash': '1599988830517897128367818516663', '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': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1654473714078107092313259306361', 'degree': 2, 'euler_factors': 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0], [-2.732961768595094, 4.73362863835], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-585-117.103-c1-0-28', '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/571/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4045786801474855, 1.356875080824046, 1.2972966630291405, 1.2220689423704003, 1.126162012486019, 1.0048132317062421, 0.8549441225142774, 0.6763080028459446, 0.4722958813482474, 0.25036223157403764, 0.022030741690109615, -0.19756547978311625, -0.39064455610154875, -0.5382399240081048, -0.6221169163200574, -0.6270231436728778, -0.5430812502600751, -0.3680661696854061, -0.10926108167084865, 0.2154310936924268, 0.5774204454471789, 0.9386362779046845, 1.254117389698471, 1.4759366373151939, 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'5.86976541189051419831518895843960', '7.85199107264057582607264494583054', '7.910677176840745021631588250397804', '8.701931342310324421609310202046226', '9.543458625721087010876420658865222', '10.63168036169244347623604601715771'], 'prelabel': '2-585-117.103-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': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26216863718585636745249912273', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29448567333412523826339275853', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49367042222112343199042105407', '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': '117.103', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/17'], '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': '2-585-117.103-c1-0-28', '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': '2-585-117.103-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': '1.26216863718585636745249912273', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1599988830517897128367818516663', 'Lhash_array': ['1599988830517897128367818516663'], 'label': '2-585-117.103-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/17'}