Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.158155776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 24x^{3} + 81x^{2} + 54x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(-0.376763 - 0.376763i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.g.337.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.20905i | − 1.48812i | −0.668111 | − | 0.744062i | \(-0.732897\pi\) | ||||
0.668111 | − | 0.744062i | \(-0.267103\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −9.71610 | −1.21451 | ||||||||
\(5\) | 11.4322i | 1.02253i | 0.859424 | + | 0.511264i | \(0.170822\pi\) | ||||
−0.859424 | + | 0.511264i | \(0.829178\pi\) | |||||||
\(6\) | − 12.6271i | − 0.859169i | ||||||||
\(7\) | − 11.2543i | − 0.607675i | −0.952724 | − | 0.303838i | \(-0.901732\pi\) | ||||
0.952724 | − | 0.303838i | \(-0.0982680\pi\) | |||||||
\(8\) | 7.22315i | 0.319221i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 48.1187 | 1.52165 | ||||||||
\(11\) | 25.8785i | 0.709333i | 0.934993 | + | 0.354666i | \(0.115406\pi\) | ||||
−0.934993 | + | 0.354666i | \(0.884594\pi\) | |||||||
\(12\) | −29.1483 | −0.701199 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −47.3699 | −0.904296 | ||||||||
\(15\) | 34.2966i | 0.590356i | ||||||||
\(16\) | −47.3262 | −0.739472 | ||||||||
\(17\) | 20.3276 | 0.290010 | 0.145005 | − | 0.989431i | \(-0.453680\pi\) | ||||
0.145005 | + | 0.989431i | \(0.453680\pi\) | |||||||
\(18\) | − 37.8814i | − 0.496041i | ||||||||
\(19\) | − 154.712i | − 1.86807i | −0.357181 | − | 0.934035i | \(-0.616262\pi\) | ||||
0.357181 | − | 0.934035i | \(-0.383738\pi\) | |||||||
\(20\) | − 111.076i | − 1.24187i | ||||||||
\(21\) | − 33.7629i | − 0.350841i | ||||||||
\(22\) | 108.924 | 1.05558 | ||||||||
\(23\) | 180.418 | 1.63565 | 0.817823 | − | 0.575471i | \(-0.195181\pi\) | ||||
0.817823 | + | 0.575471i | \(0.195181\pi\) | |||||||
\(24\) | 21.6695i | 0.184302i | ||||||||
\(25\) | −5.69520 | −0.0455616 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 109.348i | 0.738029i | ||||||||
\(29\) | −20.4522 | −0.130961 | −0.0654806 | − | 0.997854i | \(-0.520858\pi\) | ||||
−0.0654806 | + | 0.997854i | \(0.520858\pi\) | |||||||
\(30\) | 144.356 | 0.878523 | ||||||||
\(31\) | − 266.424i | − 1.54359i | −0.635873 | − | 0.771794i | \(-0.719360\pi\) | ||||
0.635873 | − | 0.771794i | \(-0.280640\pi\) | |||||||
\(32\) | 256.984i | 1.41965i | ||||||||
\(33\) | 77.6355i | 0.409534i | ||||||||
\(34\) | − 85.5599i | − 0.431571i | ||||||||
\(35\) | 128.661 | 0.621364 | ||||||||
\(36\) | −87.4449 | −0.404837 | ||||||||
\(37\) | 115.984i | 0.515340i | 0.966233 | + | 0.257670i | \(0.0829548\pi\) | ||||
−0.966233 | + | 0.257670i | \(0.917045\pi\) | |||||||
\(38\) | −651.190 | −2.77992 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −82.5765 | −0.326412 | ||||||||
\(41\) | − 391.184i | − 1.49006i | −0.667029 | − | 0.745032i | \(-0.732434\pi\) | ||||
0.667029 | − | 0.745032i | \(-0.267566\pi\) | |||||||
\(42\) | −142.110 | −0.522095 | ||||||||
\(43\) | −151.407 | −0.536963 | −0.268482 | − | 0.963285i | \(-0.586522\pi\) | ||||
−0.268482 | + | 0.963285i | \(0.586522\pi\) | |||||||
\(44\) | − 251.438i | − 0.861494i | ||||||||
\(45\) | 102.890i | 0.340842i | ||||||||
\(46\) | − 759.390i | − 2.43404i | ||||||||
\(47\) | − 467.365i | − 1.45047i | −0.688500 | − | 0.725236i | \(-0.741731\pi\) | ||||
0.688500 | − | 0.725236i | \(-0.258269\pi\) | |||||||
\(48\) | −141.979 | −0.426934 | ||||||||
\(49\) | 216.341 | 0.630731 | ||||||||
\(50\) | 23.9714i | 0.0678012i | ||||||||
\(51\) | 60.9828 | 0.167437 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 79.9842 | 0.207296 | 0.103648 | − | 0.994614i | \(-0.466949\pi\) | ||||
0.103648 | + | 0.994614i | \(0.466949\pi\) | |||||||
\(54\) | − 113.644i | − 0.286390i | ||||||||
\(55\) | −295.848 | −0.725312 | ||||||||
\(56\) | 81.2915 | 0.193983 | ||||||||
\(57\) | − 464.136i | − 1.07853i | ||||||||
\(58\) | 86.0843i | 0.194887i | ||||||||
\(59\) | − 873.710i | − 1.92792i | −0.266045 | − | 0.963960i | \(-0.585717\pi\) | ||||
0.266045 | − | 0.963960i | \(-0.414283\pi\) | |||||||
\(60\) | − 333.229i | − 0.716995i | ||||||||
\(61\) | −187.068 | −0.392649 | −0.196325 | − | 0.980539i | \(-0.562901\pi\) | ||||
−0.196325 | + | 0.980539i | \(0.562901\pi\) | |||||||
\(62\) | −1121.39 | −2.29705 | ||||||||
\(63\) | − 101.289i | − 0.202558i | ||||||||
\(64\) | 703.047 | 1.37314 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 326.772 | 0.609437 | ||||||||
\(67\) | 609.204i | 1.11084i | 0.831571 | + | 0.555418i | \(0.187442\pi\) | ||||
−0.831571 | + | 0.555418i | \(0.812558\pi\) | |||||||
\(68\) | −197.505 | −0.352221 | ||||||||
\(69\) | 541.255 | 0.944340 | ||||||||
\(70\) | − 541.542i | − 0.924667i | ||||||||
\(71\) | − 248.038i | − 0.414601i | −0.978277 | − | 0.207301i | \(-0.933532\pi\) | ||||
0.978277 | − | 0.207301i | \(-0.0664679\pi\) | |||||||
\(72\) | 65.0084i | 0.106407i | ||||||||
\(73\) | 852.765i | 1.36724i | 0.729838 | + | 0.683621i | \(0.239596\pi\) | ||||
−0.729838 | + | 0.683621i | \(0.760404\pi\) | |||||||
\(74\) | 488.181 | 0.766890 | ||||||||
\(75\) | −17.0856 | −0.0263050 | ||||||||
\(76\) | 1503.20i | 2.26880i | ||||||||
\(77\) | 291.244 | 0.431044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −331.221 | −0.471712 | −0.235856 | − | 0.971788i | \(-0.575789\pi\) | ||||
−0.235856 | + | 0.971788i | \(0.575789\pi\) | |||||||
\(80\) | − 541.043i | − 0.756130i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1646.51 | −2.21740 | ||||||||
\(83\) | 435.432i | 0.575842i | 0.957654 | + | 0.287921i | \(0.0929641\pi\) | ||||
−0.957654 | + | 0.287921i | \(0.907036\pi\) | |||||||
\(84\) | 328.044i | 0.426101i | ||||||||
\(85\) | 232.389i | 0.296543i | ||||||||
\(86\) | 637.281i | 0.799067i | ||||||||
\(87\) | −61.3566 | −0.0756105 | ||||||||
\(88\) | −186.924 | −0.226434 | ||||||||
\(89\) | 259.233i | 0.308749i | 0.988012 | + | 0.154375i | \(0.0493362\pi\) | ||||
−0.988012 | + | 0.154375i | \(0.950664\pi\) | |||||||
\(90\) | 433.068 | 0.507216 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1752.96 | −1.98651 | ||||||||
\(93\) | − 799.273i | − 0.891191i | ||||||||
\(94\) | −1967.16 | −2.15848 | ||||||||
\(95\) | 1768.70 | 1.91015 | ||||||||
\(96\) | 770.951i | 0.819634i | ||||||||
\(97\) | − 1225.17i | − 1.28245i | −0.767355 | − | 0.641223i | \(-0.778428\pi\) | ||||
0.767355 | − | 0.641223i | \(-0.221572\pi\) | |||||||
\(98\) | − 910.589i | − 0.938606i | ||||||||
\(99\) | 232.907i | 0.236444i | ||||||||
\(100\) | 55.3351 | 0.0553351 | ||||||||
\(101\) | −645.416 | −0.635855 | −0.317927 | − | 0.948115i | \(-0.602987\pi\) | ||||
−0.317927 | + | 0.948115i | \(0.602987\pi\) | |||||||
\(102\) | − 256.680i | − 0.249167i | ||||||||
\(103\) | 511.137 | 0.488969 | 0.244484 | − | 0.969653i | \(-0.421381\pi\) | ||||
0.244484 | + | 0.969653i | \(0.421381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 385.984 | 0.358745 | ||||||||
\(106\) | − 336.657i | − 0.308482i | ||||||||
\(107\) | 608.195 | 0.549499 | 0.274750 | − | 0.961516i | \(-0.411405\pi\) | ||||
0.274750 | + | 0.961516i | \(0.411405\pi\) | |||||||
\(108\) | −262.335 | −0.233733 | ||||||||
\(109\) | 1300.04i | 1.14239i | 0.820813 | + | 0.571197i | \(0.193521\pi\) | ||||
−0.820813 | + | 0.571197i | \(0.806479\pi\) | |||||||
\(110\) | 1245.24i | 1.07935i | ||||||||
\(111\) | 347.951i | 0.297532i | ||||||||
\(112\) | 532.623i | 0.449359i | ||||||||
\(113\) | 42.1953 | 0.0351274 | 0.0175637 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175637 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(114\) | −1953.57 | −1.60499 | ||||||||
\(115\) | 2062.58i | 1.67249i | ||||||||
\(116\) | 198.716 | 0.159054 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3677.49 | −2.86899 | ||||||||
\(119\) | − 228.773i | − 0.176232i | ||||||||
\(120\) | −247.729 | −0.188454 | ||||||||
\(121\) | 661.303 | 0.496847 | ||||||||
\(122\) | 787.378i | 0.584311i | ||||||||
\(123\) | − 1173.55i | − 0.860289i | ||||||||
\(124\) | 2588.61i | 1.87471i | ||||||||
\(125\) | 1363.92i | 0.975939i | ||||||||
\(126\) | −426.329 | −0.301432 | ||||||||
\(127\) | 311.018 | 0.217310 | 0.108655 | − | 0.994080i | \(-0.465346\pi\) | ||||
0.108655 | + | 0.994080i | \(0.465346\pi\) | |||||||
\(128\) | − 903.291i | − 0.623753i | ||||||||
\(129\) | −454.222 | −0.310016 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2000.98 | 1.33456 | 0.667278 | − | 0.744809i | \(-0.267459\pi\) | ||||
0.667278 | + | 0.744809i | \(0.267459\pi\) | |||||||
\(132\) | − 754.314i | − 0.497384i | ||||||||
\(133\) | −1741.17 | −1.13518 | ||||||||
\(134\) | 2564.17 | 1.65306 | ||||||||
\(135\) | 308.669i | 0.196785i | ||||||||
\(136\) | 146.829i | 0.0925773i | ||||||||
\(137\) | 1038.53i | 0.647644i | 0.946118 | + | 0.323822i | \(0.104968\pi\) | ||||
−0.946118 | + | 0.323822i | \(0.895032\pi\) | |||||||
\(138\) | − 2278.17i | − 1.40529i | ||||||||
\(139\) | −2858.46 | −1.74426 | −0.872128 | − | 0.489277i | \(-0.837261\pi\) | ||||
−0.872128 | + | 0.489277i | \(0.837261\pi\) | |||||||
\(140\) | −1250.09 | −0.754655 | ||||||||
\(141\) | − 1402.09i | − 0.837430i | ||||||||
\(142\) | −1044.00 | −0.616978 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −425.936 | −0.246491 | ||||||||
\(145\) | − 233.814i | − 0.133911i | ||||||||
\(146\) | 3589.33 | 2.03462 | ||||||||
\(147\) | 649.022 | 0.364153 | ||||||||
\(148\) | − 1126.91i | − 0.625887i | ||||||||
\(149\) | − 743.479i | − 0.408780i | −0.978890 | − | 0.204390i | \(-0.934479\pi\) | ||||
0.978890 | − | 0.204390i | \(-0.0655211\pi\) | |||||||
\(150\) | 71.9141i | 0.0391451i | ||||||||
\(151\) | 2277.24i | 1.22728i | 0.789586 | + | 0.613640i | \(0.210295\pi\) | ||||
−0.789586 | + | 0.613640i | \(0.789705\pi\) | |||||||
\(152\) | 1117.51 | 0.596328 | ||||||||
\(153\) | 182.948 | 0.0966700 | ||||||||
\(154\) | − 1225.86i | − 0.641447i | ||||||||
\(155\) | 3045.82 | 1.57836 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3173.51 | 1.61321 | 0.806605 | − | 0.591091i | \(-0.201303\pi\) | ||||
0.806605 | + | 0.591091i | \(0.201303\pi\) | |||||||
\(158\) | 1394.12i | 0.701966i | ||||||||
\(159\) | 239.953 | 0.119682 | ||||||||
\(160\) | −2937.89 | −1.45163 | ||||||||
\(161\) | − 2030.48i | − 0.993941i | ||||||||
\(162\) | − 340.933i | − 0.165347i | ||||||||
\(163\) | − 2314.65i | − 1.11225i | −0.831098 | − | 0.556126i | \(-0.812287\pi\) | ||||
0.831098 | − | 0.556126i | \(-0.187713\pi\) | |||||||
\(164\) | 3800.78i | 1.80970i | ||||||||
\(165\) | −887.545 | −0.418759 | ||||||||
\(166\) | 1832.76 | 0.856925 | ||||||||
\(167\) | − 2665.65i | − 1.23517i | −0.786502 | − | 0.617587i | \(-0.788110\pi\) | ||||
0.786502 | − | 0.617587i | \(-0.211890\pi\) | |||||||
\(168\) | 243.874 | 0.111996 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 978.138 | 0.441293 | ||||||||
\(171\) | − 1392.41i | − 0.622690i | ||||||||
\(172\) | 1471.09 | 0.652148 | ||||||||
\(173\) | 165.243 | 0.0726198 | 0.0363099 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363099 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(174\) | 258.253i | 0.112518i | ||||||||
\(175\) | 64.0954i | 0.0276866i | ||||||||
\(176\) | − 1224.73i | − 0.524532i | ||||||||
\(177\) | − 2621.13i | − 1.11309i | ||||||||
\(178\) | 1091.13 | 0.459457 | ||||||||
\(179\) | −712.339 | −0.297446 | −0.148723 | − | 0.988879i | \(-0.547516\pi\) | ||||
−0.148723 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(180\) | − 999.688i | − 0.413957i | ||||||||
\(181\) | −2206.53 | −0.906133 | −0.453066 | − | 0.891477i | \(-0.649670\pi\) | ||||
−0.453066 | + | 0.891477i | \(0.649670\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −561.204 | −0.226696 | ||||||||
\(184\) | 1303.19i | 0.522132i | ||||||||
\(185\) | −1325.95 | −0.526949 | ||||||||
\(186\) | −3364.18 | −1.32620 | ||||||||
\(187\) | 526.048i | 0.205714i | ||||||||
\(188\) | 4540.96i | 1.76162i | ||||||||
\(189\) | − 303.866i | − 0.116947i | ||||||||
\(190\) | − 7444.54i | − 2.84254i | ||||||||
\(191\) | 1470.64 | 0.557129 | 0.278565 | − | 0.960417i | \(-0.410141\pi\) | ||||
0.278565 | + | 0.960417i | \(0.410141\pi\) | |||||||
\(192\) | 2109.14 | 0.792782 | ||||||||
\(193\) | 369.560i | 0.137832i | 0.997622 | + | 0.0689158i | \(0.0219540\pi\) | ||||
−0.997622 | + | 0.0689158i | \(0.978046\pi\) | |||||||
\(194\) | −5156.80 | −1.90844 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2101.99 | −0.766031 | ||||||||
\(197\) | 4273.41i | 1.54552i | 0.634697 | + | 0.772761i | \(0.281125\pi\) | ||||
−0.634697 | + | 0.772761i | \(0.718875\pi\) | |||||||
\(198\) | 980.315 | 0.351858 | ||||||||
\(199\) | −4154.31 | −1.47985 | −0.739927 | − | 0.672687i | \(-0.765140\pi\) | ||||
−0.739927 | + | 0.672687i | \(0.765140\pi\) | |||||||
\(200\) | − 41.1373i | − 0.0145442i | ||||||||
\(201\) | 1827.61i | 0.641342i | ||||||||
\(202\) | 2716.59i | 0.946230i | ||||||||
\(203\) | 230.175i | 0.0795819i | ||||||||
\(204\) | −592.515 | −0.203355 | ||||||||
\(205\) | 4472.09 | 1.52363 | ||||||||
\(206\) | − 2151.40i | − 0.727646i | ||||||||
\(207\) | 1623.77 | 0.545215 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4003.71 | 1.32508 | ||||||||
\(210\) | − 1624.63i | − 0.533857i | ||||||||
\(211\) | 1231.59 | 0.401830 | 0.200915 | − | 0.979609i | \(-0.435608\pi\) | ||||
0.200915 | + | 0.979609i | \(0.435608\pi\) | |||||||
\(212\) | −777.134 | −0.251763 | ||||||||
\(213\) | − 744.114i | − 0.239370i | ||||||||
\(214\) | − 2559.92i | − 0.817723i | ||||||||
\(215\) | − 1730.92i | − 0.549059i | ||||||||
\(216\) | 195.025i | 0.0614341i | ||||||||
\(217\) | −2998.42 | −0.938000 | ||||||||
\(218\) | 5471.92 | 1.70002 | ||||||||
\(219\) | 2558.30i | 0.789377i | ||||||||
\(220\) | 2874.49 | 0.880901 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1464.54 | 0.442764 | ||||||||
\(223\) | 2187.24i | 0.656809i | 0.944537 | + | 0.328404i | \(0.106511\pi\) | ||||
−0.944537 | + | 0.328404i | \(0.893489\pi\) | |||||||
\(224\) | 2892.17 | 0.862684 | ||||||||
\(225\) | −51.2568 | −0.0151872 | ||||||||
\(226\) | − 177.602i | − 0.0522739i | ||||||||
\(227\) | − 4138.67i | − 1.21010i | −0.796187 | − | 0.605051i | \(-0.793153\pi\) | ||||
0.796187 | − | 0.605051i | \(-0.206847\pi\) | |||||||
\(228\) | 4509.59i | 1.30989i | ||||||||
\(229\) | − 835.354i | − 0.241056i | −0.992710 | − | 0.120528i | \(-0.961541\pi\) | ||||
0.992710 | − | 0.120528i | \(-0.0384587\pi\) | |||||||
\(230\) | 8681.50 | 2.48887 | ||||||||
\(231\) | 873.733 | 0.248863 | ||||||||
\(232\) | − 147.729i | − 0.0418056i | ||||||||
\(233\) | −3685.51 | −1.03625 | −0.518124 | − | 0.855305i | \(-0.673370\pi\) | ||||
−0.518124 | + | 0.855305i | \(0.673370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5343.01 | 1.48315 | ||||||||
\(236\) | 8489.05i | 2.34148i | ||||||||
\(237\) | −993.662 | −0.272343 | ||||||||
\(238\) | −962.917 | −0.262255 | ||||||||
\(239\) | − 3026.21i | − 0.819034i | −0.912303 | − | 0.409517i | \(-0.865697\pi\) | ||||
0.912303 | − | 0.409517i | \(-0.134303\pi\) | |||||||
\(240\) | − 1623.13i | − 0.436552i | ||||||||
\(241\) | 3265.58i | 0.872839i | 0.899743 | + | 0.436420i | \(0.143754\pi\) | ||||
−0.899743 | + | 0.436420i | \(0.856246\pi\) | |||||||
\(242\) | − 2783.46i | − 0.739370i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1817.57 | 0.476877 | ||||||||
\(245\) | 2473.25i | 0.644940i | ||||||||
\(246\) | −4939.53 | −1.28022 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1924.42 | 0.492746 | ||||||||
\(249\) | 1306.30i | 0.332463i | ||||||||
\(250\) | 5740.79 | 1.45232 | ||||||||
\(251\) | 6363.16 | 1.60016 | 0.800078 | − | 0.599897i | \(-0.204792\pi\) | ||||
0.800078 | + | 0.599897i | \(0.204792\pi\) | |||||||
\(252\) | 984.131i | 0.246010i | ||||||||
\(253\) | 4668.96i | 1.16022i | ||||||||
\(254\) | − 1309.09i | − 0.323385i | ||||||||
\(255\) | 697.168i | 0.171209i | ||||||||
\(256\) | 1822.38 | 0.444917 | ||||||||
\(257\) | 6085.36 | 1.47702 | 0.738511 | − | 0.674242i | \(-0.235529\pi\) | ||||
0.738511 | + | 0.674242i | \(0.235529\pi\) | |||||||
\(258\) | 1911.84i | 0.461342i | ||||||||
\(259\) | 1305.31 | 0.313159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −184.070 | −0.0436538 | ||||||||
\(262\) | − 8422.24i | − 1.98598i | ||||||||
\(263\) | 123.227 | 0.0288916 | 0.0144458 | − | 0.999896i | \(-0.495402\pi\) | ||||
0.0144458 | + | 0.999896i | \(0.495402\pi\) | |||||||
\(264\) | −560.773 | −0.130732 | ||||||||
\(265\) | 914.395i | 0.211965i | ||||||||
\(266\) | 7328.69i | 1.68929i | ||||||||
\(267\) | 777.700i | 0.178256i | ||||||||
\(268\) | − 5919.08i | − 1.34913i | ||||||||
\(269\) | −1935.79 | −0.438763 | −0.219381 | − | 0.975639i | \(-0.570404\pi\) | ||||
−0.219381 | + | 0.975639i | \(0.570404\pi\) | |||||||
\(270\) | 1299.20 | 0.292841 | ||||||||
\(271\) | − 4612.69i | − 1.03395i | −0.856000 | − | 0.516976i | \(-0.827058\pi\) | ||||
0.856000 | − | 0.516976i | \(-0.172942\pi\) | |||||||
\(272\) | −962.028 | −0.214454 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4371.20 | 0.963774 | ||||||||
\(275\) | − 147.383i | − 0.0323183i | ||||||||
\(276\) | −5258.89 | −1.14691 | ||||||||
\(277\) | 5834.30 | 1.26552 | 0.632761 | − | 0.774347i | \(-0.281922\pi\) | ||||
0.632761 | + | 0.774347i | \(0.281922\pi\) | |||||||
\(278\) | 12031.4i | 2.59567i | ||||||||
\(279\) | − 2397.82i | − 0.514529i | ||||||||
\(280\) | 929.341i | 0.198353i | ||||||||
\(281\) | 4691.91i | 0.996071i | 0.867157 | + | 0.498036i | \(0.165945\pi\) | ||||
−0.867157 | + | 0.498036i | \(0.834055\pi\) | |||||||
\(282\) | −5901.49 | −1.24620 | ||||||||
\(283\) | −3465.60 | −0.727945 | −0.363973 | − | 0.931410i | \(-0.618580\pi\) | ||||
−0.363973 | + | 0.931410i | \(0.618580\pi\) | |||||||
\(284\) | 2409.96i | 0.503539i | ||||||||
\(285\) | 5306.09 | 1.10283 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4402.50 | −0.905475 | ||||||||
\(288\) | 2312.85i | 0.473216i | ||||||||
\(289\) | −4499.79 | −0.915894 | ||||||||
\(290\) | −984.133 | −0.199277 | ||||||||
\(291\) | − 3675.51i | − 0.740420i | ||||||||
\(292\) | − 8285.55i | − 1.66053i | ||||||||
\(293\) | 2677.31i | 0.533822i | 0.963721 | + | 0.266911i | \(0.0860030\pi\) | ||||
−0.963721 | + | 0.266911i | \(0.913997\pi\) | |||||||
\(294\) | − 2731.77i | − 0.541904i | ||||||||
\(295\) | 9988.43 | 1.97135 | ||||||||
\(296\) | −837.767 | −0.164507 | ||||||||
\(297\) | 698.720i | 0.136511i | ||||||||
\(298\) | −3129.34 | −0.608315 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 166.005 | 0.0319477 | ||||||||
\(301\) | 1703.98i | 0.326299i | ||||||||
\(302\) | 9585.02 | 1.82634 | ||||||||
\(303\) | −1936.25 | −0.367111 | ||||||||
\(304\) | 7321.93i | 1.38139i | ||||||||
\(305\) | − 2138.60i | − 0.401494i | ||||||||
\(306\) | − 770.039i | − 0.143857i | ||||||||
\(307\) | 471.915i | 0.0877316i | 0.999037 | + | 0.0438658i | \(0.0139674\pi\) | ||||
−0.999037 | + | 0.0438658i | \(0.986033\pi\) | |||||||
\(308\) | −2829.76 | −0.523508 | ||||||||
\(309\) | 1533.41 | 0.282306 | ||||||||
\(310\) | − 12820.0i | − 2.34880i | ||||||||
\(311\) | 1518.52 | 0.276872 | 0.138436 | − | 0.990371i | \(-0.455793\pi\) | ||||
0.138436 | + | 0.990371i | \(0.455793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4049.86 | 0.731348 | 0.365674 | − | 0.930743i | \(-0.380839\pi\) | ||||
0.365674 | + | 0.930743i | \(0.380839\pi\) | |||||||
\(314\) | − 13357.5i | − 2.40066i | ||||||||
\(315\) | 1157.95 | 0.207121 | ||||||||
\(316\) | 3218.17 | 0.572900 | ||||||||
\(317\) | − 3253.96i | − 0.576532i | −0.957550 | − | 0.288266i | \(-0.906921\pi\) | ||||
0.957550 | − | 0.288266i | \(-0.0930787\pi\) | |||||||
\(318\) | − 1009.97i | − 0.178102i | ||||||||
\(319\) | − 529.272i | − 0.0928951i | ||||||||
\(320\) | 8037.37i | 1.40407i | ||||||||
\(321\) | 1824.59 | 0.317254 | ||||||||
\(322\) | −8546.40 | −1.47911 | ||||||||
\(323\) | − 3144.92i | − 0.541759i | ||||||||
\(324\) | −787.004 | −0.134946 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9742.46 | −1.65517 | ||||||||
\(327\) | 3900.11i | 0.659561i | ||||||||
\(328\) | 2825.58 | 0.475660 | ||||||||
\(329\) | −5259.86 | −0.881415 | ||||||||
\(330\) | 3735.72i | 0.623165i | ||||||||
\(331\) | 3422.45i | 0.568322i | 0.958777 | + | 0.284161i | \(0.0917150\pi\) | ||||
−0.958777 | + | 0.284161i | \(0.908285\pi\) | |||||||
\(332\) | − 4230.71i | − 0.699368i | ||||||||
\(333\) | 1043.85i | 0.171780i | ||||||||
\(334\) | −11219.8 | −1.83809 | ||||||||
\(335\) | −6964.54 | −1.13586 | ||||||||
\(336\) | 1597.87i | 0.259437i | ||||||||
\(337\) | 9301.67 | 1.50354 | 0.751772 | − | 0.659423i | \(-0.229199\pi\) | ||||
0.751772 | + | 0.659423i | \(0.229199\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 126.586 | 0.0202808 | ||||||||
\(340\) | − 2257.92i | − 0.360155i | ||||||||
\(341\) | 6894.66 | 1.09492 | ||||||||
\(342\) | −5860.71 | −0.926640 | ||||||||
\(343\) | − 6294.99i | − 0.990955i | ||||||||
\(344\) | − 1093.64i | − 0.171410i | ||||||||
\(345\) | 6187.74i | 0.965613i | ||||||||
\(346\) | − 695.518i | − 0.108067i | ||||||||
\(347\) | 216.898 | 0.0335554 | 0.0167777 | − | 0.999859i | \(-0.494659\pi\) | ||||
0.0167777 | + | 0.999859i | \(0.494659\pi\) | |||||||
\(348\) | 596.147 | 0.0918299 | ||||||||
\(349\) | − 4809.84i | − 0.737721i | −0.929485 | − | 0.368861i | \(-0.879748\pi\) | ||||
0.929485 | − | 0.368861i | \(-0.120252\pi\) | |||||||
\(350\) | 269.781 | 0.0412011 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6650.35 | −1.00700 | ||||||||
\(353\) | 2859.64i | 0.431170i | 0.976485 | + | 0.215585i | \(0.0691659\pi\) | ||||
−0.976485 | + | 0.215585i | \(0.930834\pi\) | |||||||
\(354\) | −11032.5 | −1.65641 | ||||||||
\(355\) | 2835.62 | 0.423941 | ||||||||
\(356\) | − 2518.74i | − 0.374980i | ||||||||
\(357\) | − 686.319i | − 0.101747i | ||||||||
\(358\) | 2998.27i | 0.442636i | ||||||||
\(359\) | 3686.04i | 0.541899i | 0.962594 | + | 0.270949i | \(0.0873376\pi\) | ||||
−0.962594 | + | 0.270949i | \(0.912662\pi\) | |||||||
\(360\) | −743.188 | −0.108804 | ||||||||
\(361\) | −17076.8 | −2.48969 | ||||||||
\(362\) | 9287.39i | 1.34844i | ||||||||
\(363\) | 1983.91 | 0.286855 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9748.98 | −1.39804 | ||||||||
\(366\) | 2362.14i | 0.337352i | ||||||||
\(367\) | −3470.59 | −0.493633 | −0.246816 | − | 0.969062i | \(-0.579384\pi\) | ||||
−0.246816 | + | 0.969062i | \(0.579384\pi\) | |||||||
\(368\) | −8538.52 | −1.20951 | ||||||||
\(369\) | − 3520.65i | − 0.496688i | ||||||||
\(370\) | 5580.98i | 0.784166i | ||||||||
\(371\) | − 900.166i | − 0.125968i | ||||||||
\(372\) | 7765.82i | 1.08236i | ||||||||
\(373\) | −11963.4 | −1.66070 | −0.830352 | − | 0.557240i | \(-0.811860\pi\) | ||||
−0.830352 | + | 0.557240i | \(0.811860\pi\) | |||||||
\(374\) | 2214.16 | 0.306127 | ||||||||
\(375\) | 4091.75i | 0.563459i | ||||||||
\(376\) | 3375.85 | 0.463021 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1278.99 | −0.174032 | ||||||||
\(379\) | − 345.604i | − 0.0468403i | −0.999726 | − | 0.0234202i | \(-0.992544\pi\) | ||||
0.999726 | − | 0.0234202i | \(-0.00745555\pi\) | |||||||
\(380\) | −17184.8 | −2.31990 | ||||||||
\(381\) | 933.055 | 0.125464 | ||||||||
\(382\) | − 6189.99i | − 0.829078i | ||||||||
\(383\) | 3386.40i | 0.451793i | 0.974151 | + | 0.225897i | \(0.0725312\pi\) | ||||
−0.974151 | + | 0.225897i | \(0.927469\pi\) | |||||||
\(384\) | − 2709.87i | − 0.360124i | ||||||||
\(385\) | 3329.56i | 0.440754i | ||||||||
\(386\) | 1555.49 | 0.205110 | ||||||||
\(387\) | −1362.67 | −0.178988 | ||||||||
\(388\) | 11903.9i | 1.55755i | ||||||||
\(389\) | 1629.88 | 0.212438 | 0.106219 | − | 0.994343i | \(-0.466126\pi\) | ||||
0.106219 | + | 0.994343i | \(0.466126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3667.47 | 0.474353 | ||||||||
\(392\) | 1562.66i | 0.201343i | ||||||||
\(393\) | 6002.95 | 0.770506 | ||||||||
\(394\) | 17987.0 | 2.29993 | ||||||||
\(395\) | − 3786.58i | − 0.482338i | ||||||||
\(396\) | − 2262.94i | − 0.287165i | ||||||||
\(397\) | 7938.94i | 1.00364i | 0.864973 | + | 0.501819i | \(0.167336\pi\) | ||||
−0.864973 | + | 0.501819i | \(0.832664\pi\) | |||||||
\(398\) | 17485.7i | 2.20221i | ||||||||
\(399\) | −5223.52 | −0.655396 | ||||||||
\(400\) | 269.532 | 0.0336915 | ||||||||
\(401\) | 214.402i | 0.0267001i | 0.999911 | + | 0.0133500i | \(0.00424958\pi\) | ||||
−0.999911 | + | 0.0133500i | \(0.995750\pi\) | |||||||
\(402\) | 7692.51 | 0.954396 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6270.93 | 0.772253 | ||||||||
\(405\) | 926.008i | 0.113614i | ||||||||
\(406\) | 968.819 | 0.118428 | ||||||||
\(407\) | −3001.48 | −0.365548 | ||||||||
\(408\) | 440.488i | 0.0534495i | ||||||||
\(409\) | 4783.73i | 0.578338i | 0.957278 | + | 0.289169i | \(0.0933789\pi\) | ||||
−0.957278 | + | 0.289169i | \(0.906621\pi\) | |||||||
\(410\) | − 18823.2i | − 2.26735i | ||||||||
\(411\) | 3115.58i | 0.373917i | ||||||||
\(412\) | −4966.25 | −0.593859 | ||||||||
\(413\) | −9832.99 | −1.17155 | ||||||||
\(414\) | − 6834.51i | − 0.811347i | ||||||||
\(415\) | −4977.95 | −0.588815 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8575.39 | −1.00705 | ||||||||
\(418\) | − 16851.8i | − 1.97189i | ||||||||
\(419\) | −9903.67 | −1.15472 | −0.577358 | − | 0.816491i | \(-0.695916\pi\) | ||||
−0.577358 | + | 0.816491i | \(0.695916\pi\) | |||||||
\(420\) | −3750.26 | −0.435700 | ||||||||
\(421\) | 12120.6i | 1.40314i | 0.712598 | + | 0.701572i | \(0.247518\pi\) | ||||
−0.712598 | + | 0.701572i | \(0.752482\pi\) | |||||||
\(422\) | − 5183.82i | − 0.597973i | ||||||||
\(423\) | − 4206.28i | − 0.483491i | ||||||||
\(424\) | 577.738i | 0.0661732i | ||||||||
\(425\) | −115.770 | −0.0132133 | ||||||||
\(426\) | −3132.01 | −0.356213 | ||||||||
\(427\) | 2105.32i | 0.238603i | ||||||||
\(428\) | −5909.28 | −0.667374 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7285.53 | −0.817068 | ||||||||
\(431\) | 13672.6i | 1.52805i | 0.645189 | + | 0.764023i | \(0.276779\pi\) | ||||
−0.645189 | + | 0.764023i | \(0.723221\pi\) | |||||||
\(432\) | −1277.81 | −0.142311 | ||||||||
\(433\) | −7113.10 | −0.789455 | −0.394727 | − | 0.918798i | \(-0.629161\pi\) | ||||
−0.394727 | + | 0.918798i | \(0.629161\pi\) | |||||||
\(434\) | 12620.5i | 1.39586i | ||||||||
\(435\) | − 701.441i | − 0.0773138i | ||||||||
\(436\) | − 12631.3i | − 1.38745i | ||||||||
\(437\) | − 27912.9i | − 3.05550i | ||||||||
\(438\) | 10768.0 | 1.17469 | ||||||||
\(439\) | 6022.04 | 0.654707 | 0.327353 | − | 0.944902i | \(-0.393843\pi\) | ||||
0.327353 | + | 0.944902i | \(0.393843\pi\) | |||||||
\(440\) | − 2136.96i | − 0.231535i | ||||||||
\(441\) | 1947.07 | 0.210244 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12994.4 | −1.39364 | −0.696821 | − | 0.717245i | \(-0.745403\pi\) | ||||
−0.696821 | + | 0.717245i | \(0.745403\pi\) | |||||||
\(444\) | − 3380.72i | − 0.361356i | ||||||||
\(445\) | −2963.61 | −0.315704 | ||||||||
\(446\) | 9206.20 | 0.977413 | ||||||||
\(447\) | − 2230.44i | − 0.236009i | ||||||||
\(448\) | − 7912.30i | − 0.834422i | ||||||||
\(449\) | 10984.3i | 1.15452i | 0.816560 | + | 0.577260i | \(0.195878\pi\) | ||||
−0.816560 | + | 0.577260i | \(0.804122\pi\) | |||||||
\(450\) | 215.742i | 0.0226004i | ||||||||
\(451\) | 10123.2 | 1.05695 | ||||||||
\(452\) | −409.973 | −0.0426627 | ||||||||
\(453\) | 6831.72i | 0.708570i | ||||||||
\(454\) | −17419.9 | −1.80078 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3352.52 | 0.344290 | ||||||||
\(457\) | − 9834.10i | − 1.00661i | −0.864109 | − | 0.503304i | \(-0.832118\pi\) | ||||
0.864109 | − | 0.503304i | \(-0.167882\pi\) | |||||||
\(458\) | −3516.05 | −0.358721 | ||||||||
\(459\) | 548.845 | 0.0558124 | ||||||||
\(460\) | − 20040.2i | − 2.03126i | ||||||||
\(461\) | − 3401.42i | − 0.343644i | −0.985128 | − | 0.171822i | \(-0.945035\pi\) | ||||
0.985128 | − | 0.171822i | \(-0.0549653\pi\) | |||||||
\(462\) | − 3677.59i | − 0.370339i | ||||||||
\(463\) | 1739.42i | 0.174596i | 0.996182 | + | 0.0872979i | \(0.0278232\pi\) | ||||
−0.996182 | + | 0.0872979i | \(0.972177\pi\) | |||||||
\(464\) | 967.925 | 0.0968422 | ||||||||
\(465\) | 9137.45 | 0.911267 | ||||||||
\(466\) | 15512.5i | 1.54207i | ||||||||
\(467\) | 7958.82 | 0.788630 | 0.394315 | − | 0.918975i | \(-0.370982\pi\) | ||||
0.394315 | + | 0.918975i | \(0.370982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6856.16 | 0.675028 | ||||||||
\(470\) | − 22489.0i | − 2.20711i | ||||||||
\(471\) | 9520.54 | 0.931387 | ||||||||
\(472\) | 6310.94 | 0.615433 | ||||||||
\(473\) | − 3918.20i | − 0.380886i | ||||||||
\(474\) | 4182.37i | 0.405280i | ||||||||
\(475\) | 881.114i | 0.0851122i | ||||||||
\(476\) | 2222.78i | 0.214036i | ||||||||
\(477\) | 719.858 | 0.0690986 | ||||||||
\(478\) | −12737.5 | −1.21882 | ||||||||
\(479\) | 8431.98i | 0.804315i | 0.915570 | + | 0.402158i | \(0.131740\pi\) | ||||
−0.915570 | + | 0.402158i | \(0.868260\pi\) | |||||||
\(480\) | −8813.66 | −0.838097 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 13745.0 | 1.29889 | ||||||||
\(483\) | − 6091.45i | − 0.573852i | ||||||||
\(484\) | −6425.29 | −0.603427 | ||||||||
\(485\) | 14006.4 | 1.31133 | ||||||||
\(486\) | − 1022.80i | − 0.0954632i | ||||||||
\(487\) | 11684.7i | 1.08723i | 0.839334 | + | 0.543617i | \(0.182945\pi\) | ||||
−0.839334 | + | 0.543617i | \(0.817055\pi\) | |||||||
\(488\) | − 1351.22i | − 0.125342i | ||||||||
\(489\) | − 6943.94i | − 0.642159i | ||||||||
\(490\) | 10410.0 | 0.959750 | ||||||||
\(491\) | 3954.70 | 0.363489 | 0.181745 | − | 0.983346i | \(-0.441826\pi\) | ||||
0.181745 | + | 0.983346i | \(0.441826\pi\) | |||||||
\(492\) | 11402.3i | 1.04483i | ||||||||
\(493\) | −415.744 | −0.0379801 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2662.63 | −0.241771 | ||||||||
\(496\) | 12608.8i | 1.14144i | ||||||||
\(497\) | −2791.49 | −0.251943 | ||||||||
\(498\) | 5498.27 | 0.494746 | ||||||||
\(499\) | 5690.37i | 0.510493i | 0.966876 | + | 0.255246i | \(0.0821566\pi\) | ||||
−0.966876 | + | 0.255246i | \(0.917843\pi\) | |||||||
\(500\) | − 13251.9i | − 1.18529i | ||||||||
\(501\) | − 7996.95i | − 0.713128i | ||||||||
\(502\) | − 26782.8i | − 2.38123i | ||||||||
\(503\) | 10859.1 | 0.962595 | 0.481298 | − | 0.876557i | \(-0.340166\pi\) | ||||
0.481298 | + | 0.876557i | \(0.340166\pi\) | |||||||
\(504\) | 731.623 | 0.0646609 | ||||||||
\(505\) | − 7378.53i | − 0.650178i | ||||||||
\(506\) | 19651.9 | 1.72655 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3021.88 | −0.263926 | ||||||||
\(509\) | 18558.6i | 1.61610i | 0.589115 | + | 0.808049i | \(0.299476\pi\) | ||||
−0.589115 | + | 0.808049i | \(0.700524\pi\) | |||||||
\(510\) | 2934.41 | 0.254780 | ||||||||
\(511\) | 9597.27 | 0.830838 | ||||||||
\(512\) | − 14896.8i | − 1.28584i | ||||||||
\(513\) | − 4177.22i | − 0.359510i | ||||||||
\(514\) | − 25613.6i | − 2.19799i | ||||||||
\(515\) | 5843.42i | 0.499984i | ||||||||
\(516\) | 4413.27 | 0.376518 | ||||||||
\(517\) | 12094.7 | 1.02887 | ||||||||
\(518\) | − 5494.13i | − 0.466020i | ||||||||
\(519\) | 495.730 | 0.0419271 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17297.5 | 1.45454 | 0.727271 | − | 0.686350i | \(-0.240788\pi\) | ||||
0.727271 | + | 0.686350i | \(0.240788\pi\) | |||||||
\(522\) | 774.759i | 0.0649622i | ||||||||
\(523\) | −5016.11 | −0.419386 | −0.209693 | − | 0.977767i | \(-0.567247\pi\) | ||||
−0.209693 | + | 0.977767i | \(0.567247\pi\) | |||||||
\(524\) | −19441.8 | −1.62084 | ||||||||
\(525\) | 192.286i | 0.0159849i | ||||||||
\(526\) | − 518.667i | − 0.0429942i | ||||||||
\(527\) | − 5415.77i | − 0.447656i | ||||||||
\(528\) | − 3674.19i | − 0.302839i | ||||||||
\(529\) | 20383.8 | 1.67533 | ||||||||
\(530\) | 3848.73 | 0.315431 | ||||||||
\(531\) | − 7863.39i | − 0.642640i | ||||||||
\(532\) | 16917.4 | 1.37869 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3273.38 | 0.265268 | ||||||||
\(535\) | 6953.01i | 0.561878i | ||||||||
\(536\) | −4400.37 | −0.354603 | ||||||||
\(537\) | −2137.02 | −0.171730 | ||||||||
\(538\) | 8147.83i | 0.652933i | ||||||||
\(539\) | 5598.57i | 0.447398i | ||||||||
\(540\) | − 2999.06i | − 0.238998i | ||||||||
\(541\) | 17642.3i | 1.40204i | 0.713144 | + | 0.701018i | \(0.247271\pi\) | ||||
−0.713144 | + | 0.701018i | \(0.752729\pi\) | |||||||
\(542\) | −19415.0 | −1.53865 | ||||||||
\(543\) | −6619.59 | −0.523156 | ||||||||
\(544\) | 5223.86i | 0.411712i | ||||||||
\(545\) | −14862.3 | −1.16813 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18414.9 | −1.43943 | −0.719713 | − | 0.694271i | \(-0.755727\pi\) | ||||
−0.719713 | + | 0.694271i | \(0.755727\pi\) | |||||||
\(548\) | − 10090.4i | − 0.786571i | ||||||||
\(549\) | −1683.61 | −0.130883 | ||||||||
\(550\) | −620.343 | −0.0480937 | ||||||||
\(551\) | 3164.20i | 0.244645i | ||||||||
\(552\) | 3909.57i | 0.301453i | ||||||||
\(553\) | 3727.66i | 0.286648i | ||||||||
\(554\) | − 24556.9i | − 1.88325i | ||||||||
\(555\) | −3977.84 | −0.304234 | ||||||||
\(556\) | 27773.1 | 2.11842 | ||||||||
\(557\) | 8179.15i | 0.622193i | 0.950378 | + | 0.311096i | \(0.100696\pi\) | ||||
−0.950378 | + | 0.311096i | \(0.899304\pi\) | |||||||
\(558\) | −10092.5 | −0.765683 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6089.05 | −0.459481 | ||||||||
\(561\) | 1578.14i | 0.118769i | ||||||||
\(562\) | 19748.5 | 1.48228 | ||||||||
\(563\) | 1880.07 | 0.140738 | 0.0703690 | − | 0.997521i | \(-0.477582\pi\) | ||||
0.0703690 | + | 0.997521i | \(0.477582\pi\) | |||||||
\(564\) | 13622.9i | 1.01707i | ||||||||
\(565\) | 482.385i | 0.0359187i | ||||||||
\(566\) | 14586.9i | 1.08327i | ||||||||
\(567\) | − 911.598i | − 0.0675194i | ||||||||
\(568\) | 1791.62 | 0.132350 | ||||||||
\(569\) | −10118.3 | −0.745485 | −0.372743 | − | 0.927935i | \(-0.621583\pi\) | ||||
−0.372743 | + | 0.927935i | \(0.621583\pi\) | |||||||
\(570\) | − 22333.6i | − 1.64114i | ||||||||
\(571\) | −23428.9 | −1.71711 | −0.858555 | − | 0.512721i | \(-0.828638\pi\) | ||||
−0.858555 | + | 0.512721i | \(0.828638\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4411.92 | 0.321659 | ||||||||
\(574\) | 18530.3i | 1.34746i | ||||||||
\(575\) | −1027.52 | −0.0745225 | ||||||||
\(576\) | 6327.42 | 0.457713 | ||||||||
\(577\) | − 20508.1i | − 1.47966i | −0.672793 | − | 0.739831i | \(-0.734906\pi\) | ||||
0.672793 | − | 0.739831i | \(-0.265094\pi\) | |||||||
\(578\) | 18939.8i | 1.36296i | ||||||||
\(579\) | 1108.68i | 0.0795771i | ||||||||
\(580\) | 2271.76i | 0.162637i | ||||||||
\(581\) | 4900.49 | 0.349925 | ||||||||
\(582\) | −15470.4 | −1.10184 | ||||||||
\(583\) | 2069.87i | 0.147042i | ||||||||
\(584\) | −6159.65 | −0.436452 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11268.9 | 0.794394 | ||||||||
\(587\) | 5968.43i | 0.419665i | 0.977737 | + | 0.209833i | \(0.0672919\pi\) | ||||
−0.977737 | + | 0.209833i | \(0.932708\pi\) | |||||||
\(588\) | −6305.97 | −0.442268 | ||||||||
\(589\) | −41219.0 | −2.88353 | ||||||||
\(590\) | − 42041.8i | − 2.93361i | ||||||||
\(591\) | 12820.2i | 0.892308i | ||||||||
\(592\) | − 5489.06i | − 0.381080i | ||||||||
\(593\) | − 14659.5i | − 1.01517i | −0.861602 | − | 0.507584i | \(-0.830539\pi\) | ||||
0.861602 | − | 0.507584i | \(-0.169461\pi\) | |||||||
\(594\) | 2940.95 | 0.203146 | ||||||||
\(595\) | 2615.38 | 0.180202 | ||||||||
\(596\) | 7223.72i | 0.496468i | ||||||||
\(597\) | −12462.9 | −0.854394 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23635.9 | 1.61225 | 0.806125 | − | 0.591746i | \(-0.201561\pi\) | ||||
0.806125 | + | 0.591746i | \(0.201561\pi\) | |||||||
\(600\) | − 123.412i | − 0.00839711i | ||||||||
\(601\) | −11527.0 | −0.782356 | −0.391178 | − | 0.920315i | \(-0.627932\pi\) | ||||
−0.391178 | + | 0.920315i | \(0.627932\pi\) | |||||||
\(602\) | 7172.15 | 0.485573 | ||||||||
\(603\) | 5482.83i | 0.370279i | ||||||||
\(604\) | − 22125.9i | − 1.49055i | ||||||||
\(605\) | 7560.15i | 0.508039i | ||||||||
\(606\) | 8149.77i | 0.546306i | ||||||||
\(607\) | −5098.56 | −0.340930 | −0.170465 | − | 0.985364i | \(-0.554527\pi\) | ||||
−0.170465 | + | 0.985364i | \(0.554527\pi\) | |||||||
\(608\) | 39758.4 | 2.65200 | ||||||||
\(609\) | 690.525i | 0.0459466i | ||||||||
\(610\) | −9001.47 | −0.597473 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1777.55 | −0.117407 | ||||||||
\(613\) | − 1516.39i | − 0.0999128i | −0.998751 | − | 0.0499564i | \(-0.984092\pi\) | ||||
0.998751 | − | 0.0499564i | \(-0.0159082\pi\) | |||||||
\(614\) | 1986.31 | 0.130556 | ||||||||
\(615\) | 13416.3 | 0.879668 | ||||||||
\(616\) | 2103.70i | 0.137598i | ||||||||
\(617\) | − 18539.3i | − 1.20966i | −0.796353 | − | 0.604832i | \(-0.793240\pi\) | ||||
0.796353 | − | 0.604832i | \(-0.206760\pi\) | |||||||
\(618\) | − 6454.20i | − 0.420107i | ||||||||
\(619\) | 25684.9i | 1.66779i | 0.551920 | + | 0.833897i | \(0.313895\pi\) | ||||
−0.551920 | + | 0.833897i | \(0.686105\pi\) | |||||||
\(620\) | −29593.5 | −1.91694 | ||||||||
\(621\) | 4871.30 | 0.314780 | ||||||||
\(622\) | − 6391.51i | − 0.412020i | ||||||||
\(623\) | 2917.49 | 0.187619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16304.5 | −1.04349 | ||||||||
\(626\) | − 17046.1i | − 1.08834i | ||||||||
\(627\) | 12011.1 | 0.765038 | ||||||||
\(628\) | −30834.2 | −1.95926 | ||||||||
\(629\) | 2357.67i | 0.149454i | ||||||||
\(630\) | − 4873.88i | − 0.308222i | ||||||||
\(631\) | − 22410.9i | − 1.41389i | −0.707269 | − | 0.706945i | \(-0.750073\pi\) | ||||
0.707269 | − | 0.706945i | \(-0.249927\pi\) | |||||||
\(632\) | − 2392.46i | − 0.150580i | ||||||||
\(633\) | 3694.77 | 0.231997 | ||||||||
\(634\) | −13696.1 | −0.857950 | ||||||||
\(635\) | 3555.62i | 0.222206i | ||||||||
\(636\) | −2331.40 | −0.145356 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2227.73 | −0.138239 | ||||||||
\(639\) | − 2232.34i | − 0.138200i | ||||||||
\(640\) | 10326.6 | 0.637804 | ||||||||
\(641\) | −6827.81 | −0.420721 | −0.210361 | − | 0.977624i | \(-0.567464\pi\) | ||||
−0.210361 | + | 0.977624i | \(0.567464\pi\) | |||||||
\(642\) | − 7679.77i | − 0.472113i | ||||||||
\(643\) | 23264.3i | 1.42684i | 0.700738 | + | 0.713418i | \(0.252854\pi\) | ||||
−0.700738 | + | 0.713418i | \(0.747146\pi\) | |||||||
\(644\) | 19728.4i | 1.20715i | ||||||||
\(645\) | − 5192.76i | − 0.316999i | ||||||||
\(646\) | −13237.1 | −0.806204 | ||||||||
\(647\) | −14745.9 | −0.896014 | −0.448007 | − | 0.894030i | \(-0.647866\pi\) | ||||
−0.448007 | + | 0.894030i | \(0.647866\pi\) | |||||||
\(648\) | 585.075i | 0.0354690i | ||||||||
\(649\) | 22610.3 | 1.36754 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8995.26 | −0.541554 | ||||||||
\(652\) | 22489.3i | 1.35084i | ||||||||
\(653\) | 10909.0 | 0.653755 | 0.326878 | − | 0.945067i | \(-0.394003\pi\) | ||||
0.326878 | + | 0.945067i | \(0.394003\pi\) | |||||||
\(654\) | 16415.8 | 0.981509 | ||||||||
\(655\) | 22875.7i | 1.36462i | ||||||||
\(656\) | 18513.2i | 1.10186i | ||||||||
\(657\) | 7674.89i | 0.455747i | ||||||||
\(658\) | 22139.0i | 1.31166i | ||||||||
\(659\) | −4182.99 | −0.247263 | −0.123631 | − | 0.992328i | \(-0.539454\pi\) | ||||
−0.123631 | + | 0.992328i | \(0.539454\pi\) | |||||||
\(660\) | 8623.47 | 0.508588 | ||||||||
\(661\) | 2224.23i | 0.130881i | 0.997856 | + | 0.0654406i | \(0.0208453\pi\) | ||||
−0.997856 | + | 0.0654406i | \(0.979155\pi\) | |||||||
\(662\) | 14405.2 | 0.845734 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3145.19 | −0.183821 | ||||||||
\(665\) | − 19905.4i | − 1.16075i | ||||||||
\(666\) | 4393.63 | 0.255630 | ||||||||
\(667\) | −3689.95 | −0.214206 | ||||||||
\(668\) | 25899.7i | 1.50013i | ||||||||
\(669\) | 6561.72i | 0.379209i | ||||||||
\(670\) | 29314.1i | 1.69030i | ||||||||
\(671\) | − 4841.04i | − 0.278519i | ||||||||
\(672\) | 8676.51 | 0.498071 | ||||||||
\(673\) | 24152.5 | 1.38337 | 0.691687 | − | 0.722197i | \(-0.256868\pi\) | ||||
0.691687 | + | 0.722197i | \(0.256868\pi\) | |||||||
\(674\) | − 39151.2i | − 2.23746i | ||||||||
\(675\) | −153.770 | −0.00876833 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15310.7 | −0.869187 | −0.434593 | − | 0.900627i | \(-0.643108\pi\) | ||||
−0.434593 | + | 0.900627i | \(0.643108\pi\) | |||||||
\(678\) | − 532.806i | − 0.0301804i | ||||||||
\(679\) | −13788.4 | −0.779310 | ||||||||
\(680\) | −1678.58 | −0.0946628 | ||||||||
\(681\) | − 12416.0i | − 0.698652i | ||||||||
\(682\) | − 29020.0i | − 1.62937i | ||||||||
\(683\) | 11399.6i | 0.638646i | 0.947646 | + | 0.319323i | \(0.103455\pi\) | ||||
−0.947646 | + | 0.319323i | \(0.896545\pi\) | |||||||
\(684\) | 13528.8i | 0.756265i | ||||||||
\(685\) | −11872.6 | −0.662233 | ||||||||
\(686\) | −26495.9 | −1.47466 | ||||||||
\(687\) | − 2506.06i | − 0.139174i | ||||||||
\(688\) | 7165.54 | 0.397069 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 26044.5 | 1.43695 | ||||||||
\(691\) | 3323.23i | 0.182955i | 0.995807 | + | 0.0914773i | \(0.0291589\pi\) | ||||
−0.995807 | + | 0.0914773i | \(0.970841\pi\) | |||||||
\(692\) | −1605.52 | −0.0881976 | ||||||||
\(693\) | 2621.20 | 0.143681 | ||||||||
\(694\) | − 912.936i | − 0.0499345i | ||||||||
\(695\) | − 32678.5i | − 1.78355i | ||||||||
\(696\) | − 443.188i | − 0.0241365i | ||||||||
\(697\) | − 7951.82i | − 0.432133i | ||||||||
\(698\) | −20244.8 | −1.09782 | ||||||||
\(699\) | −11056.5 | −0.598279 | ||||||||
\(700\) | − 622.758i | − 0.0336257i | ||||||||
\(701\) | 12670.4 | 0.682673 | 0.341336 | − | 0.939941i | \(-0.389120\pi\) | ||||
0.341336 | + | 0.939941i | \(0.389120\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17944.0 | 0.962692 | ||||||||
\(704\) | 18193.8i | 0.974012i | ||||||||
\(705\) | 16029.0 | 0.856295 | ||||||||
\(706\) | 12036.4 | 0.641635 | ||||||||
\(707\) | 7263.71i | 0.386393i | ||||||||
\(708\) | 25467.2i | 1.35186i | ||||||||
\(709\) | 13075.2i | 0.692594i | 0.938125 | + | 0.346297i | \(0.112561\pi\) | ||||
−0.938125 | + | 0.346297i | \(0.887439\pi\) | |||||||
\(710\) | − 11935.3i | − 0.630877i | ||||||||
\(711\) | −2980.99 | −0.157237 | ||||||||
\(712\) | −1872.48 | −0.0985592 | ||||||||
\(713\) | − 48067.8i | − 2.52476i | ||||||||
\(714\) | −2888.75 | −0.151413 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6921.16 | 0.361251 | ||||||||
\(717\) | − 9078.62i | − 0.472869i | ||||||||
\(718\) | 15514.7 | 0.806412 | ||||||||
\(719\) | 2988.41 | 0.155005 | 0.0775026 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775026 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(720\) | − 4869.38i | − 0.252043i | ||||||||
\(721\) | − 5752.48i | − 0.297134i | ||||||||
\(722\) | 71877.0i | 3.70496i | ||||||||
\(723\) | 9796.73i | 0.503934i | ||||||||
\(724\) | 21438.9 | 1.10051 | ||||||||
\(725\) | 116.479 | 0.00596680 | ||||||||
\(726\) | − 8350.37i | − 0.426875i | ||||||||
\(727\) | 5507.46 | 0.280963 | 0.140482 | − | 0.990083i | \(-0.455135\pi\) | ||||
0.140482 | + | 0.990083i | \(0.455135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 41033.9i | 2.08046i | ||||||||
\(731\) | −3077.75 | −0.155725 | ||||||||
\(732\) | 5452.71 | 0.275325 | ||||||||
\(733\) | 36585.2i | 1.84353i | 0.387751 | + | 0.921764i | \(0.373252\pi\) | ||||
−0.387751 | + | 0.921764i | \(0.626748\pi\) | |||||||
\(734\) | 14607.9i | 0.734587i | ||||||||
\(735\) | 7419.75i | 0.372356i | ||||||||
\(736\) | 46364.6i | 2.32204i | ||||||||
\(737\) | −15765.3 | −0.787953 | ||||||||
\(738\) | −14818.6 | −0.739133 | ||||||||
\(739\) | 6425.89i | 0.319865i | 0.987128 | + | 0.159933i | \(0.0511277\pi\) | ||||
−0.987128 | + | 0.159933i | \(0.948872\pi\) | |||||||
\(740\) | 12883.0 | 0.639986 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3788.84 | −0.187457 | ||||||||
\(743\) | − 20411.0i | − 1.00782i | −0.863757 | − | 0.503908i | \(-0.831895\pi\) | ||||
0.863757 | − | 0.503908i | \(-0.168105\pi\) | |||||||
\(744\) | 5773.27 | 0.284487 | ||||||||
\(745\) | 8499.60 | 0.417988 | ||||||||
\(746\) | 50354.6i | 2.47133i | ||||||||
\(747\) | 3918.89i | 0.191947i | ||||||||
\(748\) | − 5111.13i | − 0.249842i | ||||||||
\(749\) | − 6844.81i | − 0.333917i | ||||||||
\(750\) | 17222.4 | 0.838496 | ||||||||
\(751\) | 24259.5 | 1.17875 | 0.589375 | − | 0.807860i | \(-0.299374\pi\) | ||||
0.589375 | + | 0.807860i | \(0.299374\pi\) | |||||||
\(752\) | 22118.6i | 1.07258i | ||||||||
\(753\) | 19089.5 | 0.923850 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26033.9 | −1.25493 | ||||||||
\(756\) | 2952.39i | 0.142034i | ||||||||
\(757\) | 9295.39 | 0.446297 | 0.223148 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223148 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(758\) | −1454.66 | −0.0697042 | ||||||||
\(759\) | 14006.9i | 0.669851i | ||||||||
\(760\) | 12775.6i | 0.609761i | ||||||||
\(761\) | − 21974.7i | − 1.04676i | −0.852101 | − | 0.523378i | \(-0.824672\pi\) | ||||
0.852101 | − | 0.523378i | \(-0.175328\pi\) | |||||||
\(762\) | − 3927.27i | − 0.186706i | ||||||||
\(763\) | 14631.0 | 0.694204 | ||||||||
\(764\) | −14288.9 | −0.676641 | ||||||||
\(765\) | 2091.50i | 0.0988476i | ||||||||
\(766\) | 14253.5 | 0.672324 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 5467.13 | 0.256873 | ||||||||
\(769\) | − 22987.4i | − 1.07795i | −0.842320 | − | 0.538977i | \(-0.818811\pi\) | ||||
0.842320 | − | 0.538977i | \(-0.181189\pi\) | |||||||
\(770\) | 14014.3 | 0.655897 | ||||||||
\(771\) | 18256.1 | 0.852759 | ||||||||
\(772\) | − 3590.68i | − 0.167398i | ||||||||
\(773\) | − 31970.9i | − 1.48760i | −0.668404 | − | 0.743799i | \(-0.733022\pi\) | ||||
0.668404 | − | 0.743799i | \(-0.266978\pi\) | |||||||
\(774\) | 5735.53i | 0.266356i | ||||||||
\(775\) | 1517.34i | 0.0703283i | ||||||||
\(776\) | 8849.59 | 0.409384 | ||||||||
\(777\) | 3915.94 | 0.180803 | ||||||||
\(778\) | − 6860.25i | − 0.316133i | ||||||||
\(779\) | −60520.8 | −2.78354 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6418.85 | 0.294090 | ||||||||
\(782\) | − 15436.6i | − 0.705896i | ||||||||
\(783\) | −552.209 | −0.0252035 | ||||||||
\(784\) | −10238.6 | −0.466408 | ||||||||
\(785\) | 36280.2i | 1.64955i | ||||||||
\(786\) | − 25266.7i | − 1.14661i | ||||||||
\(787\) | 6087.26i | 0.275715i | 0.990452 | + | 0.137857i | \(0.0440215\pi\) | ||||
−0.990452 | + | 0.137857i | \(0.955978\pi\) | |||||||
\(788\) | − 41520.9i | − 1.87706i | ||||||||
\(789\) | 369.680 | 0.0166805 | ||||||||
\(790\) | −15937.9 | −0.717779 | ||||||||
\(791\) | − 474.878i | − 0.0213460i | ||||||||
\(792\) | −1682.32 | −0.0754780 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 33415.4 | 1.49354 | ||||||||
\(795\) | 2743.19i | 0.122378i | ||||||||
\(796\) | 40363.6 | 1.79730 | ||||||||
\(797\) | −23080.0 | −1.02577 | −0.512883 | − | 0.858458i | \(-0.671423\pi\) | ||||
−0.512883 | + | 0.858458i | \(0.671423\pi\) | |||||||
\(798\) | 21986.1i | 0.975311i | ||||||||
\(799\) | − 9500.41i | − 0.420651i | ||||||||
\(800\) | − 1463.57i | − 0.0646813i | ||||||||
\(801\) | 2333.10i | 0.102916i | ||||||||
\(802\) | 902.429 | 0.0397330 | ||||||||
\(803\) | −22068.3 | −0.969829 | ||||||||
\(804\) | − 17757.3i | − 0.778918i | ||||||||
\(805\) | 23212.9 | 1.01633 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5807.37 | −0.253320 | ||||||||
\(808\) | − 4661.94i | − 0.202978i | ||||||||
\(809\) | −32377.8 | −1.40710 | −0.703550 | − | 0.710646i | \(-0.748403\pi\) | ||||
−0.703550 | + | 0.710646i | \(0.748403\pi\) | |||||||
\(810\) | 3897.61 | 0.169072 | ||||||||
\(811\) | − 26352.8i | − 1.14103i | −0.821288 | − | 0.570513i | \(-0.806744\pi\) | ||||
0.821288 | − | 0.570513i | \(-0.193256\pi\) | |||||||
\(812\) | − 2236.40i | − 0.0966532i | ||||||||
\(813\) | − 13838.1i | − 0.596952i | ||||||||
\(814\) | 12633.4i | 0.543980i | ||||||||
\(815\) | 26461.5 | 1.13731 | ||||||||
\(816\) | −2886.08 | −0.123815 | ||||||||
\(817\) | 23424.5i | 1.00308i | ||||||||
\(818\) | 20135.0 | 0.860638 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −43451.3 | −1.85047 | ||||||||
\(821\) | − 35355.3i | − 1.50294i | −0.659770 | − | 0.751468i | \(-0.729346\pi\) | ||||
0.659770 | − | 0.751468i | \(-0.270654\pi\) | |||||||
\(822\) | 13113.6 | 0.556435 | ||||||||
\(823\) | 12663.3 | 0.536347 | 0.268173 | − | 0.963371i | \(-0.413580\pi\) | ||||
0.268173 | + | 0.963371i | \(0.413580\pi\) | |||||||
\(824\) | 3692.02i | 0.156089i | ||||||||
\(825\) | − 442.149i | − 0.0186590i | ||||||||
\(826\) | 41387.6i | 1.74341i | ||||||||
\(827\) | − 16295.2i | − 0.685176i | −0.939486 | − | 0.342588i | \(-0.888697\pi\) | ||||
0.939486 | − | 0.342588i | \(-0.111303\pi\) | |||||||
\(828\) | −15776.7 | −0.662170 | ||||||||
\(829\) | −13638.9 | −0.571411 | −0.285705 | − | 0.958318i | \(-0.592228\pi\) | ||||
−0.285705 | + | 0.958318i | \(0.592228\pi\) | |||||||
\(830\) | 20952.4i | 0.876229i | ||||||||
\(831\) | 17502.9 | 0.730649 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4397.69 | 0.182918 | ||||||||
\(834\) | 36094.2i | 1.49861i | ||||||||
\(835\) | 30474.2 | 1.26300 | ||||||||
\(836\) | −38900.5 | −1.60933 | ||||||||
\(837\) | − 7193.46i | − 0.297064i | ||||||||
\(838\) | 41685.0i | 1.71836i | ||||||||
\(839\) | − 1890.31i | − 0.0777838i | −0.999243 | − | 0.0388919i | \(-0.987617\pi\) | ||||
0.999243 | − | 0.0388919i | \(-0.0123828\pi\) | |||||||
\(840\) | 2788.02i | 0.114519i | ||||||||
\(841\) | −23970.7 | −0.982849 | ||||||||
\(842\) | 51016.4 | 2.08805 | ||||||||
\(843\) | 14075.7i | 0.575082i | ||||||||
\(844\) | −11966.3 | −0.488028 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −17704.5 | −0.719494 | ||||||||
\(847\) | − 7442.50i | − 0.301921i | ||||||||
\(848\) | −3785.35 | −0.153289 | ||||||||
\(849\) | −10396.8 | −0.420279 | ||||||||
\(850\) | 487.280i | 0.0196630i | ||||||||
\(851\) | 20925.6i | 0.842914i | ||||||||
\(852\) | 7229.89i | 0.290718i | ||||||||
\(853\) | 1620.21i | 0.0650351i | 0.999471 | + | 0.0325175i | \(0.0103525\pi\) | ||||
−0.999471 | + | 0.0325175i | \(0.989648\pi\) | |||||||
\(854\) | 8861.39 | 0.355071 | ||||||||
\(855\) | 15918.3 | 0.636718 | ||||||||
\(856\) | 4393.08i | 0.175412i | ||||||||
\(857\) | 14508.4 | 0.578292 | 0.289146 | − | 0.957285i | \(-0.406629\pi\) | ||||
0.289146 | + | 0.957285i | \(0.406629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29639.8 | 1.17730 | 0.588648 | − | 0.808389i | \(-0.299660\pi\) | ||||
0.588648 | + | 0.808389i | \(0.299660\pi\) | |||||||
\(860\) | 16817.8i | 0.666839i | ||||||||
\(861\) | −13207.5 | −0.522776 | ||||||||
\(862\) | 57548.8 | 2.27392 | ||||||||
\(863\) | − 21528.8i | − 0.849186i | −0.905384 | − | 0.424593i | \(-0.860417\pi\) | ||||
0.905384 | − | 0.424593i | \(-0.139583\pi\) | |||||||
\(864\) | 6938.56i | 0.273211i | ||||||||
\(865\) | 1889.10i | 0.0742557i | ||||||||
\(866\) | 29939.4i | 1.17481i | ||||||||
\(867\) | −13499.4 | −0.528792 | ||||||||
\(868\) | 29132.9 | 1.13921 | ||||||||
\(869\) | − 8571.50i | − 0.334601i | ||||||||
\(870\) | −2952.40 | −0.115053 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −9390.36 | −0.364676 | ||||||||
\(873\) | − 11026.5i | − 0.427482i | ||||||||
\(874\) | −117487. | −4.54696 | ||||||||
\(875\) | 15349.9 | 0.593054 | ||||||||
\(876\) | − 24856.7i | − 0.958708i | ||||||||
\(877\) | − 14865.3i | − 0.572366i | −0.958175 | − | 0.286183i | \(-0.907613\pi\) | ||||
0.958175 | − | 0.286183i | \(-0.0923866\pi\) | |||||||
\(878\) | − 25347.1i | − 0.974285i | ||||||||
\(879\) | 8031.92i | 0.308202i | ||||||||
\(880\) | 14001.4 | 0.536348 | ||||||||
\(881\) | 21336.0 | 0.815921 | 0.407961 | − | 0.913000i | \(-0.366240\pi\) | ||||
0.407961 | + | 0.913000i | \(0.366240\pi\) | |||||||
\(882\) | − 8195.30i | − 0.312869i | ||||||||
\(883\) | −37538.2 | −1.43065 | −0.715323 | − | 0.698794i | \(-0.753720\pi\) | ||||
−0.715323 | + | 0.698794i | \(0.753720\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29965.3 | 1.13816 | ||||||||
\(886\) | 54694.1i | 2.07391i | ||||||||
\(887\) | 34575.0 | 1.30881 | 0.654406 | − | 0.756144i | \(-0.272919\pi\) | ||||
0.654406 | + | 0.756144i | \(0.272919\pi\) | |||||||
\(888\) | −2513.30 | −0.0949784 | ||||||||
\(889\) | − 3500.29i | − 0.132054i | ||||||||
\(890\) | 12474.0i | 0.469807i | ||||||||
\(891\) | 2096.16i | 0.0788148i | ||||||||
\(892\) | − 21251.4i | − 0.797703i | ||||||||
\(893\) | −72306.9 | −2.70958 | ||||||||
\(894\) | −9388.02 | −0.351211 | ||||||||
\(895\) | − 8143.61i | − 0.304146i | ||||||||
\(896\) | −10165.9 | −0.379039 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 46233.3 | 1.71807 | ||||||||
\(899\) | 5448.96i | 0.202150i | ||||||||
\(900\) | 498.016 | 0.0184450 | ||||||||
\(901\) | 1625.89 | 0.0601178 | ||||||||
\(902\) | − 42609.2i | − 1.57287i | ||||||||
\(903\) | 5111.95i | 0.188389i | ||||||||
\(904\) | 304.783i | 0.0112134i | ||||||||
\(905\) | − 25225.5i | − 0.926545i | ||||||||
\(906\) | 28755.0 | 1.05444 | ||||||||
\(907\) | 10424.8 | 0.381641 | 0.190820 | − | 0.981625i | \(-0.438885\pi\) | ||||
0.190820 | + | 0.981625i | \(0.438885\pi\) | |||||||
\(908\) | 40211.7i | 1.46968i | ||||||||
\(909\) | −5808.75 | −0.211952 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10961.8 | 0.398661 | 0.199331 | − | 0.979932i | \(-0.436123\pi\) | ||||
0.199331 | + | 0.979932i | \(0.436123\pi\) | |||||||
\(912\) | 21965.8i | 0.797543i | ||||||||
\(913\) | −11268.3 | −0.408464 | ||||||||
\(914\) | −41392.2 | −1.49796 | ||||||||
\(915\) | − 6415.80i | − 0.231803i | ||||||||
\(916\) | 8116.38i | 0.292765i | ||||||||
\(917\) | − 22519.7i | − 0.810976i | ||||||||
\(918\) | − 2310.12i | − 0.0830558i | ||||||||
\(919\) | −10779.2 | −0.386914 | −0.193457 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193457 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(920\) | −14898.3 | −0.533895 | ||||||||
\(921\) | 1415.74i | 0.0506519i | ||||||||
\(922\) | −14316.7 | −0.511384 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −8489.28 | −0.302248 | ||||||||
\(925\) | − 660.549i | − 0.0234797i | ||||||||
\(926\) | 7321.32 | 0.259820 | ||||||||
\(927\) | 4600.23 | 0.162990 | ||||||||
\(928\) | − 5255.88i | − 0.185919i | ||||||||
\(929\) | − 5429.07i | − 0.191735i | −0.995394 | − | 0.0958675i | \(-0.969437\pi\) | ||||
0.995394 | − | 0.0958675i | \(-0.0305625\pi\) | |||||||
\(930\) | − 38460.0i | − 1.35608i | ||||||||
\(931\) | − 33470.5i | − 1.17825i | ||||||||
\(932\) | 35808.8 | 1.25854 | ||||||||
\(933\) | 4555.55 | 0.159852 | ||||||||
\(934\) | − 33499.1i | − 1.17358i | ||||||||
\(935\) | −6013.88 | −0.210348 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21300.1 | −0.742631 | −0.371315 | − | 0.928507i | \(-0.621093\pi\) | ||||
−0.371315 | + | 0.928507i | \(0.621093\pi\) | |||||||
\(938\) | − 28857.9i | − 1.00453i | ||||||||
\(939\) | 12149.6 | 0.422244 | ||||||||
\(940\) | −51913.2 | −1.80130 | ||||||||
\(941\) | − 26851.2i | − 0.930207i | −0.885256 | − | 0.465103i | \(-0.846017\pi\) | ||||
0.885256 | − | 0.465103i | \(-0.153983\pi\) | |||||||
\(942\) | − 40072.4i | − 1.38602i | ||||||||
\(943\) | − 70576.7i | − 2.43722i | ||||||||
\(944\) | 41349.4i | 1.42564i | ||||||||
\(945\) | 3473.86 | 0.119582 | ||||||||
\(946\) | −16491.9 | −0.566805 | ||||||||
\(947\) | − 8021.68i | − 0.275258i | −0.990484 | − | 0.137629i | \(-0.956052\pi\) | ||||
0.990484 | − | 0.137629i | \(-0.0439482\pi\) | |||||||
\(948\) | 9654.52 | 0.330764 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3708.65 | 0.126658 | ||||||||
\(951\) | − 9761.88i | − 0.332861i | ||||||||
\(952\) | 1652.46 | 0.0562569 | ||||||||
\(953\) | −35715.0 | −1.21398 | −0.606990 | − | 0.794709i | \(-0.707623\pi\) | ||||
−0.606990 | + | 0.794709i | \(0.707623\pi\) | |||||||
\(954\) | − 3029.92i | − 0.102827i | ||||||||
\(955\) | 16812.6i | 0.569680i | ||||||||
\(956\) | 29402.9i | 0.994726i | ||||||||
\(957\) | − 1587.82i | − 0.0536330i | ||||||||
\(958\) | 35490.6 | 1.19692 | ||||||||
\(959\) | 11687.9 | 0.393557 | ||||||||
\(960\) | 24112.1i | 0.810641i | ||||||||
\(961\) | −41190.9 | −1.38266 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5473.76 | 0.183166 | ||||||||
\(964\) | − 31728.7i | − 1.06007i | ||||||||
\(965\) | −4224.88 | −0.140936 | ||||||||
\(966\) | −25639.2 | −0.853963 | ||||||||
\(967\) | − 53338.8i | − 1.77380i | −0.461965 | − | 0.886898i | \(-0.652855\pi\) | ||||
0.461965 | − | 0.886898i | \(-0.347145\pi\) | |||||||
\(968\) | 4776.69i | 0.158604i | ||||||||
\(969\) | − 9434.77i | − 0.312785i | ||||||||
\(970\) | − 58953.6i | − 1.95143i | ||||||||
\(971\) | 23112.9 | 0.763882 | 0.381941 | − | 0.924187i | \(-0.375256\pi\) | ||||
0.381941 | + | 0.924187i | \(0.375256\pi\) | |||||||
\(972\) | −2361.01 | −0.0779110 | ||||||||
\(973\) | 32170.0i | 1.05994i | ||||||||
\(974\) | 49181.3 | 1.61794 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8853.22 | 0.290353 | ||||||||
\(977\) | 52874.6i | 1.73143i | 0.500538 | + | 0.865715i | \(0.333136\pi\) | ||||
−0.500538 | + | 0.865715i | \(0.666864\pi\) | |||||||
\(978\) | −29227.4 | −0.955612 | ||||||||
\(979\) | −6708.57 | −0.219006 | ||||||||
\(980\) | − 24030.4i | − 0.783287i | ||||||||
\(981\) | 11700.3i | 0.380798i | ||||||||
\(982\) | − 16645.5i | − 0.540917i | ||||||||
\(983\) | 45173.1i | 1.46572i | 0.680381 | + | 0.732858i | \(0.261814\pi\) | ||||
−0.680381 | + | 0.732858i | \(0.738186\pi\) | |||||||
\(984\) | 8476.73 | 0.274622 | ||||||||
\(985\) | −48854.5 | −1.58034 | ||||||||
\(986\) | 1749.89i | 0.0565190i | ||||||||
\(987\) | −15779.6 | −0.508885 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27316.7 | −0.878281 | ||||||||
\(990\) | 11207.2i | 0.359785i | ||||||||
\(991\) | 60485.6 | 1.93884 | 0.969418 | − | 0.245414i | \(-0.0789239\pi\) | ||||
0.969418 | + | 0.245414i | \(0.0789239\pi\) | |||||||
\(992\) | 68466.7 | 2.19135 | ||||||||
\(993\) | 10267.3i | 0.328121i | ||||||||
\(994\) | 11749.5i | 0.374922i | ||||||||
\(995\) | − 47492.8i | − 1.51319i | ||||||||
\(996\) | − 12692.1i | − 0.403780i | ||||||||
\(997\) | −18108.1 | −0.575214 | −0.287607 | − | 0.957749i | \(-0.592860\pi\) | ||||
−0.287607 | + | 0.957749i | \(0.592860\pi\) | |||||||
\(998\) | 23951.1 | 0.759677 | ||||||||
\(999\) | 3131.56i | 0.0991773i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 507.4.b.g.337.1 | 6 | ||
13.5 | odd | 4 | 507.4.a.h.1.1 | 3 | |||
13.8 | odd | 4 | 39.4.a.c.1.3 | ✓ | 3 | ||
13.12 | even | 2 | inner | 507.4.b.g.337.6 | 6 | ||
39.5 | even | 4 | 1521.4.a.u.1.3 | 3 | |||
39.8 | even | 4 | 117.4.a.f.1.1 | 3 | |||
52.47 | even | 4 | 624.4.a.t.1.1 | 3 | |||
65.34 | odd | 4 | 975.4.a.l.1.1 | 3 | |||
91.34 | even | 4 | 1911.4.a.k.1.3 | 3 | |||
104.21 | odd | 4 | 2496.4.a.bl.1.3 | 3 | |||
104.99 | even | 4 | 2496.4.a.bp.1.3 | 3 | |||
156.47 | odd | 4 | 1872.4.a.bk.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.3 | ✓ | 3 | 13.8 | odd | 4 | ||
117.4.a.f.1.1 | 3 | 39.8 | even | 4 | |||
507.4.a.h.1.1 | 3 | 13.5 | odd | 4 | |||
507.4.b.g.337.1 | 6 | 1.1 | even | 1 | trivial | ||
507.4.b.g.337.6 | 6 | 13.12 | even | 2 | inner | ||
624.4.a.t.1.1 | 3 | 52.47 | even | 4 | |||
975.4.a.l.1.1 | 3 | 65.34 | odd | 4 | |||
1521.4.a.u.1.3 | 3 | 39.5 | even | 4 | |||
1872.4.a.bk.1.3 | 3 | 156.47 | odd | 4 | |||
1911.4.a.k.1.3 | 3 | 91.34 | even | 4 | |||
2496.4.a.bl.1.3 | 3 | 104.21 | odd | 4 | |||
2496.4.a.bp.1.3 | 3 | 104.99 | even | 4 |