Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,4,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.a (trivial) |
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: | yes |
Analytic conductor: | \(33.6310887033\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 410x^{2} + 4362x - 12540 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.43713\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −15.8571 | −0.856204 | −0.428102 | − | 0.903730i | \(-0.640818\pi\) | ||||
−0.428102 | + | 0.903730i | \(0.640818\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | 50.7314 | 1.39055 | 0.695277 | − | 0.718742i | \(-0.255282\pi\) | ||||
0.695277 | + | 0.718742i | \(0.255282\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 22.2003 | 0.473635 | 0.236818 | − | 0.971554i | \(-0.423896\pi\) | ||||
0.236818 | + | 0.971554i | \(0.423896\pi\) | |||||||
\(14\) | −31.7142 | −0.605428 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −55.0234 | −0.785008 | −0.392504 | − | 0.919750i | \(-0.628391\pi\) | ||||
−0.392504 | + | 0.919750i | \(0.628391\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | −47.5714 | −0.494330 | ||||||||
\(22\) | 101.463 | 0.983270 | ||||||||
\(23\) | 148.394 | 1.34532 | 0.672661 | − | 0.739951i | \(-0.265151\pi\) | ||||
0.672661 | + | 0.739951i | \(0.265151\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 44.4006 | 0.334911 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −63.4285 | −0.428102 | ||||||||
\(29\) | 47.8615 | 0.306471 | 0.153236 | − | 0.988190i | \(-0.451031\pi\) | ||||
0.153236 | + | 0.988190i | \(0.451031\pi\) | |||||||
\(30\) | 30.0000 | 0.182574 | ||||||||
\(31\) | −8.22219 | −0.0476371 | −0.0238185 | − | 0.999716i | \(-0.507582\pi\) | ||||
−0.0238185 | + | 0.999716i | \(0.507582\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 152.194 | 0.802836 | ||||||||
\(34\) | −110.047 | −0.555085 | ||||||||
\(35\) | −79.2856 | −0.382906 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −226.589 | −1.00678 | −0.503391 | − | 0.864059i | \(-0.667914\pi\) | ||||
−0.503391 | + | 0.864059i | \(0.667914\pi\) | |||||||
\(38\) | 38.0000 | 0.162221 | ||||||||
\(39\) | 66.6009 | 0.273453 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | 284.264 | 1.08279 | 0.541396 | − | 0.840767i | \(-0.317896\pi\) | ||||
0.541396 | + | 0.840767i | \(0.317896\pi\) | |||||||
\(42\) | −95.1427 | −0.349544 | ||||||||
\(43\) | 341.182 | 1.20999 | 0.604996 | − | 0.796228i | \(-0.293175\pi\) | ||||
0.604996 | + | 0.796228i | \(0.293175\pi\) | |||||||
\(44\) | 202.926 | 0.695277 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 296.789 | 0.951286 | ||||||||
\(47\) | 561.047 | 1.74122 | 0.870608 | − | 0.491977i | \(-0.163726\pi\) | ||||
0.870608 | + | 0.491977i | \(0.163726\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −91.5518 | −0.266915 | ||||||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | −165.070 | −0.453225 | ||||||||
\(52\) | 88.8012 | 0.236818 | ||||||||
\(53\) | 430.176 | 1.11489 | 0.557446 | − | 0.830213i | \(-0.311781\pi\) | ||||
0.557446 | + | 0.830213i | \(0.311781\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 253.657 | 0.621874 | ||||||||
\(56\) | −126.857 | −0.302714 | ||||||||
\(57\) | 57.0000 | 0.132453 | ||||||||
\(58\) | 95.7231 | 0.216708 | ||||||||
\(59\) | −537.166 | −1.18531 | −0.592653 | − | 0.805458i | \(-0.701919\pi\) | ||||
−0.592653 | + | 0.805458i | \(0.701919\pi\) | |||||||
\(60\) | 60.0000 | 0.129099 | ||||||||
\(61\) | −767.733 | −1.61144 | −0.805722 | − | 0.592294i | \(-0.798223\pi\) | ||||
−0.805722 | + | 0.592294i | \(0.798223\pi\) | |||||||
\(62\) | −16.4444 | −0.0336845 | ||||||||
\(63\) | −142.714 | −0.285401 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 111.002 | 0.211816 | ||||||||
\(66\) | 304.388 | 0.567691 | ||||||||
\(67\) | −457.125 | −0.833532 | −0.416766 | − | 0.909014i | \(-0.636837\pi\) | ||||
−0.416766 | + | 0.909014i | \(0.636837\pi\) | |||||||
\(68\) | −220.094 | −0.392504 | ||||||||
\(69\) | 445.183 | 0.776722 | ||||||||
\(70\) | −158.571 | −0.270755 | ||||||||
\(71\) | −28.3320 | −0.0473576 | −0.0236788 | − | 0.999720i | \(-0.507538\pi\) | ||||
−0.0236788 | + | 0.999720i | \(0.507538\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 663.799 | 1.06427 | 0.532135 | − | 0.846659i | \(-0.321390\pi\) | ||||
0.532135 | + | 0.846659i | \(0.321390\pi\) | |||||||
\(74\) | −453.177 | −0.711903 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 76.0000 | 0.114708 | ||||||||
\(77\) | −804.454 | −1.19060 | ||||||||
\(78\) | 133.202 | 0.193361 | ||||||||
\(79\) | −220.526 | −0.314064 | −0.157032 | − | 0.987593i | \(-0.550193\pi\) | ||||
−0.157032 | + | 0.987593i | \(0.550193\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 568.527 | 0.765650 | ||||||||
\(83\) | −316.427 | −0.418462 | −0.209231 | − | 0.977866i | \(-0.567096\pi\) | ||||
−0.209231 | + | 0.977866i | \(0.567096\pi\) | |||||||
\(84\) | −190.285 | −0.247165 | ||||||||
\(85\) | −275.117 | −0.351066 | ||||||||
\(86\) | 682.363 | 0.855594 | ||||||||
\(87\) | 143.585 | 0.176941 | ||||||||
\(88\) | 405.851 | 0.491635 | ||||||||
\(89\) | −1428.33 | −1.70115 | −0.850574 | − | 0.525855i | \(-0.823745\pi\) | ||||
−0.850574 | + | 0.525855i | \(0.823745\pi\) | |||||||
\(90\) | 90.0000 | 0.105409 | ||||||||
\(91\) | −352.033 | −0.405528 | ||||||||
\(92\) | 593.578 | 0.672661 | ||||||||
\(93\) | −24.6666 | −0.0275033 | ||||||||
\(94\) | 1122.09 | 1.23123 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 1552.09 | 1.62465 | 0.812323 | − | 0.583208i | \(-0.198203\pi\) | ||||
0.812323 | + | 0.583208i | \(0.198203\pi\) | |||||||
\(98\) | −183.104 | −0.188737 | ||||||||
\(99\) | 456.582 | 0.463518 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 616.336 | 0.607205 | 0.303602 | − | 0.952799i | \(-0.401811\pi\) | ||||
0.303602 | + | 0.952799i | \(0.401811\pi\) | |||||||
\(102\) | −330.141 | −0.320478 | ||||||||
\(103\) | −1795.44 | −1.71757 | −0.858784 | − | 0.512338i | \(-0.828780\pi\) | ||||
−0.858784 | + | 0.512338i | \(0.828780\pi\) | |||||||
\(104\) | 177.602 | 0.167455 | ||||||||
\(105\) | −237.857 | −0.221071 | ||||||||
\(106\) | 860.353 | 0.788348 | ||||||||
\(107\) | 933.758 | 0.843643 | 0.421821 | − | 0.906679i | \(-0.361391\pi\) | ||||
0.421821 | + | 0.906679i | \(0.361391\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 1867.99 | 1.64148 | 0.820738 | − | 0.571305i | \(-0.193563\pi\) | ||||
0.820738 | + | 0.571305i | \(0.193563\pi\) | |||||||
\(110\) | 507.314 | 0.439732 | ||||||||
\(111\) | −679.766 | −0.581266 | ||||||||
\(112\) | −253.714 | −0.214051 | ||||||||
\(113\) | −720.629 | −0.599921 | −0.299960 | − | 0.953952i | \(-0.596973\pi\) | ||||
−0.299960 | + | 0.953952i | \(0.596973\pi\) | |||||||
\(114\) | 114.000 | 0.0936586 | ||||||||
\(115\) | 741.972 | 0.601646 | ||||||||
\(116\) | 191.446 | 0.153236 | ||||||||
\(117\) | 199.803 | 0.157878 | ||||||||
\(118\) | −1074.33 | −0.838138 | ||||||||
\(119\) | 872.513 | 0.672127 | ||||||||
\(120\) | 120.000 | 0.0912871 | ||||||||
\(121\) | 1242.67 | 0.933639 | ||||||||
\(122\) | −1535.47 | −1.13946 | ||||||||
\(123\) | 852.791 | 0.625151 | ||||||||
\(124\) | −32.8888 | −0.0238185 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −285.428 | −0.201809 | ||||||||
\(127\) | −644.374 | −0.450228 | −0.225114 | − | 0.974332i | \(-0.572275\pi\) | ||||
−0.225114 | + | 0.974332i | \(0.572275\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 1023.54 | 0.698590 | ||||||||
\(130\) | 222.003 | 0.149777 | ||||||||
\(131\) | −901.698 | −0.601387 | −0.300694 | − | 0.953721i | \(-0.597218\pi\) | ||||
−0.300694 | + | 0.953721i | \(0.597218\pi\) | |||||||
\(132\) | 608.777 | 0.401418 | ||||||||
\(133\) | −301.285 | −0.196427 | ||||||||
\(134\) | −914.249 | −0.589396 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | −440.187 | −0.277542 | ||||||||
\(137\) | −1839.55 | −1.14718 | −0.573588 | − | 0.819144i | \(-0.694449\pi\) | ||||
−0.573588 | + | 0.819144i | \(0.694449\pi\) | |||||||
\(138\) | 890.367 | 0.549225 | ||||||||
\(139\) | −3084.12 | −1.88195 | −0.940976 | − | 0.338474i | \(-0.890089\pi\) | ||||
−0.940976 | + | 0.338474i | \(0.890089\pi\) | |||||||
\(140\) | −317.142 | −0.191453 | ||||||||
\(141\) | 1683.14 | 1.00529 | ||||||||
\(142\) | −56.6640 | −0.0334869 | ||||||||
\(143\) | 1126.25 | 0.658615 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 239.308 | 0.137058 | ||||||||
\(146\) | 1327.60 | 0.752553 | ||||||||
\(147\) | −274.656 | −0.154103 | ||||||||
\(148\) | −906.355 | −0.503391 | ||||||||
\(149\) | 911.565 | 0.501197 | 0.250598 | − | 0.968091i | \(-0.419373\pi\) | ||||
0.250598 | + | 0.968091i | \(0.419373\pi\) | |||||||
\(150\) | 150.000 | 0.0816497 | ||||||||
\(151\) | −2771.47 | −1.49364 | −0.746818 | − | 0.665028i | \(-0.768420\pi\) | ||||
−0.746818 | + | 0.665028i | \(0.768420\pi\) | |||||||
\(152\) | 152.000 | 0.0811107 | ||||||||
\(153\) | −495.211 | −0.261669 | ||||||||
\(154\) | −1608.91 | −0.841879 | ||||||||
\(155\) | −41.1109 | −0.0213039 | ||||||||
\(156\) | 266.404 | 0.136727 | ||||||||
\(157\) | 2546.36 | 1.29440 | 0.647202 | − | 0.762318i | \(-0.275939\pi\) | ||||
0.647202 | + | 0.762318i | \(0.275939\pi\) | |||||||
\(158\) | −441.051 | −0.222077 | ||||||||
\(159\) | 1290.53 | 0.643683 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | −2353.11 | −1.15187 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 2765.37 | 1.32884 | 0.664418 | − | 0.747361i | \(-0.268679\pi\) | ||||
0.664418 | + | 0.747361i | \(0.268679\pi\) | |||||||
\(164\) | 1137.05 | 0.541396 | ||||||||
\(165\) | 760.971 | 0.359039 | ||||||||
\(166\) | −632.854 | −0.295898 | ||||||||
\(167\) | −2551.63 | −1.18234 | −0.591170 | − | 0.806547i | \(-0.701334\pi\) | ||||
−0.591170 | + | 0.806547i | \(0.701334\pi\) | |||||||
\(168\) | −380.571 | −0.174772 | ||||||||
\(169\) | −1704.15 | −0.775670 | ||||||||
\(170\) | −550.234 | −0.248241 | ||||||||
\(171\) | 171.000 | 0.0764719 | ||||||||
\(172\) | 1364.73 | 0.604996 | ||||||||
\(173\) | 530.424 | 0.233106 | 0.116553 | − | 0.993184i | \(-0.462815\pi\) | ||||
0.116553 | + | 0.993184i | \(0.462815\pi\) | |||||||
\(174\) | 287.169 | 0.125116 | ||||||||
\(175\) | −396.428 | −0.171241 | ||||||||
\(176\) | 811.702 | 0.347638 | ||||||||
\(177\) | −1611.50 | −0.684337 | ||||||||
\(178\) | −2856.65 | −1.20289 | ||||||||
\(179\) | −304.410 | −0.127110 | −0.0635549 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635549 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(180\) | 180.000 | 0.0745356 | ||||||||
\(181\) | −1211.98 | −0.497710 | −0.248855 | − | 0.968541i | \(-0.580054\pi\) | ||||
−0.248855 | + | 0.968541i | \(0.580054\pi\) | |||||||
\(182\) | −704.066 | −0.286752 | ||||||||
\(183\) | −2303.20 | −0.930368 | ||||||||
\(184\) | 1187.16 | 0.475643 | ||||||||
\(185\) | −1132.94 | −0.450247 | ||||||||
\(186\) | −49.3331 | −0.0194477 | ||||||||
\(187\) | −2791.41 | −1.09160 | ||||||||
\(188\) | 2244.19 | 0.870608 | ||||||||
\(189\) | −428.142 | −0.164777 | ||||||||
\(190\) | 190.000 | 0.0725476 | ||||||||
\(191\) | −213.308 | −0.0808086 | −0.0404043 | − | 0.999183i | \(-0.512865\pi\) | ||||
−0.0404043 | + | 0.999183i | \(0.512865\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 86.5818 | 0.0322917 | 0.0161458 | − | 0.999870i | \(-0.494860\pi\) | ||||
0.0161458 | + | 0.999870i | \(0.494860\pi\) | |||||||
\(194\) | 3104.17 | 1.14880 | ||||||||
\(195\) | 333.005 | 0.122292 | ||||||||
\(196\) | −366.207 | −0.133458 | ||||||||
\(197\) | −4694.88 | −1.69795 | −0.848976 | − | 0.528432i | \(-0.822780\pi\) | ||||
−0.848976 | + | 0.528432i | \(0.822780\pi\) | |||||||
\(198\) | 913.165 | 0.327757 | ||||||||
\(199\) | 4206.05 | 1.49829 | 0.749143 | − | 0.662408i | \(-0.230466\pi\) | ||||
0.749143 | + | 0.662408i | \(0.230466\pi\) | |||||||
\(200\) | 200.000 | 0.0707107 | ||||||||
\(201\) | −1371.37 | −0.481240 | ||||||||
\(202\) | 1232.67 | 0.429359 | ||||||||
\(203\) | −758.946 | −0.262402 | ||||||||
\(204\) | −660.281 | −0.226612 | ||||||||
\(205\) | 1421.32 | 0.484240 | ||||||||
\(206\) | −3590.87 | −1.21450 | ||||||||
\(207\) | 1335.55 | 0.448440 | ||||||||
\(208\) | 355.205 | 0.118409 | ||||||||
\(209\) | 963.896 | 0.319015 | ||||||||
\(210\) | −475.714 | −0.156321 | ||||||||
\(211\) | 4148.47 | 1.35352 | 0.676759 | − | 0.736205i | \(-0.263384\pi\) | ||||
0.676759 | + | 0.736205i | \(0.263384\pi\) | |||||||
\(212\) | 1720.71 | 0.557446 | ||||||||
\(213\) | −84.9960 | −0.0273419 | ||||||||
\(214\) | 1867.52 | 0.596545 | ||||||||
\(215\) | 1705.91 | 0.541125 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 130.380 | 0.0407870 | ||||||||
\(218\) | 3735.98 | 1.16070 | ||||||||
\(219\) | 1991.40 | 0.614457 | ||||||||
\(220\) | 1014.63 | 0.310937 | ||||||||
\(221\) | −1221.54 | −0.371808 | ||||||||
\(222\) | −1359.53 | −0.411017 | ||||||||
\(223\) | −4745.76 | −1.42511 | −0.712555 | − | 0.701616i | \(-0.752462\pi\) | ||||
−0.712555 | + | 0.701616i | \(0.752462\pi\) | |||||||
\(224\) | −507.428 | −0.151357 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −1441.26 | −0.424208 | ||||||||
\(227\) | −4213.15 | −1.23188 | −0.615940 | − | 0.787793i | \(-0.711224\pi\) | ||||
−0.615940 | + | 0.787793i | \(0.711224\pi\) | |||||||
\(228\) | 228.000 | 0.0662266 | ||||||||
\(229\) | −2596.66 | −0.749310 | −0.374655 | − | 0.927164i | \(-0.622239\pi\) | ||||
−0.374655 | + | 0.927164i | \(0.622239\pi\) | |||||||
\(230\) | 1483.94 | 0.425428 | ||||||||
\(231\) | −2413.36 | −0.687392 | ||||||||
\(232\) | 382.892 | 0.108354 | ||||||||
\(233\) | −3787.12 | −1.06482 | −0.532408 | − | 0.846488i | \(-0.678713\pi\) | ||||
−0.532408 | + | 0.846488i | \(0.678713\pi\) | |||||||
\(234\) | 399.606 | 0.111637 | ||||||||
\(235\) | 2805.24 | 0.778696 | ||||||||
\(236\) | −2148.66 | −0.592653 | ||||||||
\(237\) | −661.577 | −0.181325 | ||||||||
\(238\) | 1745.03 | 0.475266 | ||||||||
\(239\) | 2701.41 | 0.731128 | 0.365564 | − | 0.930786i | \(-0.380876\pi\) | ||||
0.365564 | + | 0.930786i | \(0.380876\pi\) | |||||||
\(240\) | 240.000 | 0.0645497 | ||||||||
\(241\) | −5098.72 | −1.36281 | −0.681405 | − | 0.731906i | \(-0.738631\pi\) | ||||
−0.681405 | + | 0.731906i | \(0.738631\pi\) | |||||||
\(242\) | 2485.35 | 0.660182 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −3070.93 | −0.805722 | ||||||||
\(245\) | −457.759 | −0.119368 | ||||||||
\(246\) | 1705.58 | 0.442048 | ||||||||
\(247\) | 421.806 | 0.108659 | ||||||||
\(248\) | −65.7775 | −0.0168422 | ||||||||
\(249\) | −949.281 | −0.241599 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | −5480.82 | −1.37827 | −0.689136 | − | 0.724632i | \(-0.742010\pi\) | ||||
−0.689136 | + | 0.724632i | \(0.742010\pi\) | |||||||
\(252\) | −570.856 | −0.142701 | ||||||||
\(253\) | 7528.26 | 1.87074 | ||||||||
\(254\) | −1288.75 | −0.318359 | ||||||||
\(255\) | −825.351 | −0.202688 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1287.94 | −0.312605 | −0.156303 | − | 0.987709i | \(-0.549957\pi\) | ||||
−0.156303 | + | 0.987709i | \(0.549957\pi\) | |||||||
\(258\) | 2047.09 | 0.493978 | ||||||||
\(259\) | 3593.04 | 0.862011 | ||||||||
\(260\) | 444.006 | 0.105908 | ||||||||
\(261\) | 430.754 | 0.102157 | ||||||||
\(262\) | −1803.40 | −0.425245 | ||||||||
\(263\) | −4069.55 | −0.954141 | −0.477070 | − | 0.878865i | \(-0.658301\pi\) | ||||
−0.477070 | + | 0.878865i | \(0.658301\pi\) | |||||||
\(264\) | 1217.55 | 0.283846 | ||||||||
\(265\) | 2150.88 | 0.498595 | ||||||||
\(266\) | −602.570 | −0.138895 | ||||||||
\(267\) | −4284.98 | −0.982159 | ||||||||
\(268\) | −1828.50 | −0.416766 | ||||||||
\(269\) | −2303.24 | −0.522049 | −0.261024 | − | 0.965332i | \(-0.584060\pi\) | ||||
−0.261024 | + | 0.965332i | \(0.584060\pi\) | |||||||
\(270\) | 270.000 | 0.0608581 | ||||||||
\(271\) | −4575.49 | −1.02561 | −0.512807 | − | 0.858504i | \(-0.671394\pi\) | ||||
−0.512807 | + | 0.858504i | \(0.671394\pi\) | |||||||
\(272\) | −880.375 | −0.196252 | ||||||||
\(273\) | −1056.10 | −0.234132 | ||||||||
\(274\) | −3679.10 | −0.811176 | ||||||||
\(275\) | 1268.28 | 0.278111 | ||||||||
\(276\) | 1780.73 | 0.388361 | ||||||||
\(277\) | 2257.26 | 0.489623 | 0.244812 | − | 0.969571i | \(-0.421274\pi\) | ||||
0.244812 | + | 0.969571i | \(0.421274\pi\) | |||||||
\(278\) | −6168.23 | −1.33074 | ||||||||
\(279\) | −73.9997 | −0.0158790 | ||||||||
\(280\) | −634.285 | −0.135378 | ||||||||
\(281\) | 4461.98 | 0.947257 | 0.473628 | − | 0.880725i | \(-0.342944\pi\) | ||||
0.473628 | + | 0.880725i | \(0.342944\pi\) | |||||||
\(282\) | 3366.28 | 0.710849 | ||||||||
\(283\) | 1315.17 | 0.276251 | 0.138125 | − | 0.990415i | \(-0.455892\pi\) | ||||
0.138125 | + | 0.990415i | \(0.455892\pi\) | |||||||
\(284\) | −113.328 | −0.0236788 | ||||||||
\(285\) | 285.000 | 0.0592349 | ||||||||
\(286\) | 2252.51 | 0.465711 | ||||||||
\(287\) | −4507.60 | −0.927091 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −1885.42 | −0.383762 | ||||||||
\(290\) | 478.615 | 0.0969147 | ||||||||
\(291\) | 4656.26 | 0.937989 | ||||||||
\(292\) | 2655.19 | 0.532135 | ||||||||
\(293\) | 4905.15 | 0.978026 | 0.489013 | − | 0.872276i | \(-0.337357\pi\) | ||||
0.489013 | + | 0.872276i | \(0.337357\pi\) | |||||||
\(294\) | −549.311 | −0.108968 | ||||||||
\(295\) | −2685.83 | −0.530085 | ||||||||
\(296\) | −1812.71 | −0.355951 | ||||||||
\(297\) | 1369.75 | 0.267612 | ||||||||
\(298\) | 1823.13 | 0.354400 | ||||||||
\(299\) | 3294.40 | 0.637191 | ||||||||
\(300\) | 300.000 | 0.0577350 | ||||||||
\(301\) | −5410.16 | −1.03600 | ||||||||
\(302\) | −5542.94 | −1.05616 | ||||||||
\(303\) | 1849.01 | 0.350570 | ||||||||
\(304\) | 304.000 | 0.0573539 | ||||||||
\(305\) | −3838.66 | −0.720660 | ||||||||
\(306\) | −990.422 | −0.185028 | ||||||||
\(307\) | −1871.47 | −0.347917 | −0.173958 | − | 0.984753i | \(-0.555656\pi\) | ||||
−0.173958 | + | 0.984753i | \(0.555656\pi\) | |||||||
\(308\) | −3217.81 | −0.595299 | ||||||||
\(309\) | −5386.31 | −0.991639 | ||||||||
\(310\) | −82.2219 | −0.0150642 | ||||||||
\(311\) | −5183.32 | −0.945077 | −0.472539 | − | 0.881310i | \(-0.656662\pi\) | ||||
−0.472539 | + | 0.881310i | \(0.656662\pi\) | |||||||
\(312\) | 532.807 | 0.0966804 | ||||||||
\(313\) | 6174.73 | 1.11507 | 0.557534 | − | 0.830154i | \(-0.311748\pi\) | ||||
0.557534 | + | 0.830154i | \(0.311748\pi\) | |||||||
\(314\) | 5092.72 | 0.915282 | ||||||||
\(315\) | −713.570 | −0.127635 | ||||||||
\(316\) | −882.103 | −0.157032 | ||||||||
\(317\) | 60.0596 | 0.0106413 | 0.00532064 | − | 0.999986i | \(-0.498306\pi\) | ||||
0.00532064 | + | 0.999986i | \(0.498306\pi\) | |||||||
\(318\) | 2581.06 | 0.455153 | ||||||||
\(319\) | 2428.08 | 0.426165 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | 2801.27 | 0.487077 | ||||||||
\(322\) | −4706.22 | −0.814494 | ||||||||
\(323\) | −1045.45 | −0.180093 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 555.008 | 0.0947270 | ||||||||
\(326\) | 5530.74 | 0.939629 | ||||||||
\(327\) | 5603.96 | 0.947706 | ||||||||
\(328\) | 2274.11 | 0.382825 | ||||||||
\(329\) | −8896.59 | −1.49084 | ||||||||
\(330\) | 1521.94 | 0.253879 | ||||||||
\(331\) | −5472.36 | −0.908726 | −0.454363 | − | 0.890817i | \(-0.650133\pi\) | ||||
−0.454363 | + | 0.890817i | \(0.650133\pi\) | |||||||
\(332\) | −1265.71 | −0.209231 | ||||||||
\(333\) | −2039.30 | −0.335594 | ||||||||
\(334\) | −5103.26 | −0.836041 | ||||||||
\(335\) | −2285.62 | −0.372767 | ||||||||
\(336\) | −761.142 | −0.123582 | ||||||||
\(337\) | −5752.93 | −0.929917 | −0.464959 | − | 0.885332i | \(-0.653931\pi\) | ||||
−0.464959 | + | 0.885332i | \(0.653931\pi\) | |||||||
\(338\) | −3408.29 | −0.548481 | ||||||||
\(339\) | −2161.89 | −0.346364 | ||||||||
\(340\) | −1100.47 | −0.175533 | ||||||||
\(341\) | −417.123 | −0.0662419 | ||||||||
\(342\) | 342.000 | 0.0540738 | ||||||||
\(343\) | 6890.74 | 1.08474 | ||||||||
\(344\) | 2729.45 | 0.427797 | ||||||||
\(345\) | 2225.92 | 0.347360 | ||||||||
\(346\) | 1060.85 | 0.164831 | ||||||||
\(347\) | −1904.93 | −0.294704 | −0.147352 | − | 0.989084i | \(-0.547075\pi\) | ||||
−0.147352 | + | 0.989084i | \(0.547075\pi\) | |||||||
\(348\) | 574.338 | 0.0884706 | ||||||||
\(349\) | 6389.95 | 0.980075 | 0.490038 | − | 0.871701i | \(-0.336983\pi\) | ||||
0.490038 | + | 0.871701i | \(0.336983\pi\) | |||||||
\(350\) | −792.856 | −0.121086 | ||||||||
\(351\) | 599.408 | 0.0911511 | ||||||||
\(352\) | 1623.40 | 0.245817 | ||||||||
\(353\) | −10230.2 | −1.54249 | −0.771246 | − | 0.636537i | \(-0.780366\pi\) | ||||
−0.771246 | + | 0.636537i | \(0.780366\pi\) | |||||||
\(354\) | −3223.00 | −0.483899 | ||||||||
\(355\) | −141.660 | −0.0211790 | ||||||||
\(356\) | −5713.30 | −0.850574 | ||||||||
\(357\) | 2617.54 | 0.388053 | ||||||||
\(358\) | −608.819 | −0.0898802 | ||||||||
\(359\) | −581.945 | −0.0855540 | −0.0427770 | − | 0.999085i | \(-0.513620\pi\) | ||||
−0.0427770 | + | 0.999085i | \(0.513620\pi\) | |||||||
\(360\) | 360.000 | 0.0527046 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −2423.95 | −0.351934 | ||||||||
\(363\) | 3728.02 | 0.539037 | ||||||||
\(364\) | −1408.13 | −0.202764 | ||||||||
\(365\) | 3318.99 | 0.475956 | ||||||||
\(366\) | −4606.40 | −0.657869 | ||||||||
\(367\) | 10047.4 | 1.42907 | 0.714535 | − | 0.699599i | \(-0.246638\pi\) | ||||
0.714535 | + | 0.699599i | \(0.246638\pi\) | |||||||
\(368\) | 2374.31 | 0.336330 | ||||||||
\(369\) | 2558.37 | 0.360931 | ||||||||
\(370\) | −2265.89 | −0.318372 | ||||||||
\(371\) | −6821.36 | −0.954575 | ||||||||
\(372\) | −98.6663 | −0.0137516 | ||||||||
\(373\) | 14080.4 | 1.95457 | 0.977285 | − | 0.211927i | \(-0.0679741\pi\) | ||||
0.977285 | + | 0.211927i | \(0.0679741\pi\) | |||||||
\(374\) | −5582.83 | −0.771875 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 4488.38 | 0.615613 | ||||||||
\(377\) | 1062.54 | 0.145156 | ||||||||
\(378\) | −856.284 | −0.116515 | ||||||||
\(379\) | 5515.37 | 0.747507 | 0.373754 | − | 0.927528i | \(-0.378071\pi\) | ||||
0.373754 | + | 0.927528i | \(0.378071\pi\) | |||||||
\(380\) | 380.000 | 0.0512989 | ||||||||
\(381\) | −1933.12 | −0.259939 | ||||||||
\(382\) | −426.616 | −0.0571403 | ||||||||
\(383\) | 3365.31 | 0.448980 | 0.224490 | − | 0.974476i | \(-0.427928\pi\) | ||||
0.224490 | + | 0.974476i | \(0.427928\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −4022.27 | −0.532451 | ||||||||
\(386\) | 173.164 | 0.0228337 | ||||||||
\(387\) | 3070.63 | 0.403331 | ||||||||
\(388\) | 6208.35 | 0.812323 | ||||||||
\(389\) | 5391.60 | 0.702737 | 0.351369 | − | 0.936237i | \(-0.385716\pi\) | ||||
0.351369 | + | 0.936237i | \(0.385716\pi\) | |||||||
\(390\) | 666.009 | 0.0864736 | ||||||||
\(391\) | −8165.17 | −1.05609 | ||||||||
\(392\) | −732.415 | −0.0943687 | ||||||||
\(393\) | −2705.10 | −0.347211 | ||||||||
\(394\) | −9389.76 | −1.20063 | ||||||||
\(395\) | −1102.63 | −0.140454 | ||||||||
\(396\) | 1826.33 | 0.231759 | ||||||||
\(397\) | 4380.78 | 0.553816 | 0.276908 | − | 0.960896i | \(-0.410690\pi\) | ||||
0.276908 | + | 0.960896i | \(0.410690\pi\) | |||||||
\(398\) | 8412.10 | 1.05945 | ||||||||
\(399\) | −903.856 | −0.113407 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −9635.17 | −1.19989 | −0.599947 | − | 0.800040i | \(-0.704812\pi\) | ||||
−0.599947 | + | 0.800040i | \(0.704812\pi\) | |||||||
\(402\) | −2742.75 | −0.340288 | ||||||||
\(403\) | −182.535 | −0.0225626 | ||||||||
\(404\) | 2465.34 | 0.303602 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −1517.89 | −0.185546 | ||||||||
\(407\) | −11495.2 | −1.39998 | ||||||||
\(408\) | −1320.56 | −0.160239 | ||||||||
\(409\) | −1837.81 | −0.222186 | −0.111093 | − | 0.993810i | \(-0.535435\pi\) | ||||
−0.111093 | + | 0.993810i | \(0.535435\pi\) | |||||||
\(410\) | 2842.64 | 0.342409 | ||||||||
\(411\) | −5518.64 | −0.662323 | ||||||||
\(412\) | −7181.74 | −0.858784 | ||||||||
\(413\) | 8517.91 | 1.01486 | ||||||||
\(414\) | 2671.10 | 0.317095 | ||||||||
\(415\) | −1582.14 | −0.187142 | ||||||||
\(416\) | 710.410 | 0.0837277 | ||||||||
\(417\) | −9252.35 | −1.08655 | ||||||||
\(418\) | 1927.79 | 0.225578 | ||||||||
\(419\) | 5812.61 | 0.677720 | 0.338860 | − | 0.940837i | \(-0.389959\pi\) | ||||
0.338860 | + | 0.940837i | \(0.389959\pi\) | |||||||
\(420\) | −951.427 | −0.110535 | ||||||||
\(421\) | 8992.63 | 1.04103 | 0.520516 | − | 0.853852i | \(-0.325740\pi\) | ||||
0.520516 | + | 0.853852i | \(0.325740\pi\) | |||||||
\(422\) | 8296.94 | 0.957082 | ||||||||
\(423\) | 5049.43 | 0.580406 | ||||||||
\(424\) | 3441.41 | 0.394174 | ||||||||
\(425\) | −1375.59 | −0.157002 | ||||||||
\(426\) | −169.992 | −0.0193337 | ||||||||
\(427\) | 12174.0 | 1.37972 | ||||||||
\(428\) | 3735.03 | 0.421821 | ||||||||
\(429\) | 3378.76 | 0.380252 | ||||||||
\(430\) | 3411.82 | 0.382633 | ||||||||
\(431\) | 147.925 | 0.0165320 | 0.00826601 | − | 0.999966i | \(-0.497369\pi\) | ||||
0.00826601 | + | 0.999966i | \(0.497369\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 9308.09 | 1.03307 | 0.516534 | − | 0.856267i | \(-0.327222\pi\) | ||||
0.516534 | + | 0.856267i | \(0.327222\pi\) | |||||||
\(434\) | 260.760 | 0.0288408 | ||||||||
\(435\) | 717.923 | 0.0791305 | ||||||||
\(436\) | 7471.95 | 0.820738 | ||||||||
\(437\) | 2819.49 | 0.308638 | ||||||||
\(438\) | 3982.79 | 0.434487 | ||||||||
\(439\) | −832.727 | −0.0905327 | −0.0452664 | − | 0.998975i | \(-0.514414\pi\) | ||||
−0.0452664 | + | 0.998975i | \(0.514414\pi\) | |||||||
\(440\) | 2029.26 | 0.219866 | ||||||||
\(441\) | −823.967 | −0.0889717 | ||||||||
\(442\) | −2443.07 | −0.262908 | ||||||||
\(443\) | −156.708 | −0.0168068 | −0.00840339 | − | 0.999965i | \(-0.502675\pi\) | ||||
−0.00840339 | + | 0.999965i | \(0.502675\pi\) | |||||||
\(444\) | −2719.06 | −0.290633 | ||||||||
\(445\) | −7141.63 | −0.760777 | ||||||||
\(446\) | −9491.52 | −1.00771 | ||||||||
\(447\) | 2734.70 | 0.289366 | ||||||||
\(448\) | −1014.86 | −0.107025 | ||||||||
\(449\) | −4607.38 | −0.484266 | −0.242133 | − | 0.970243i | \(-0.577847\pi\) | ||||
−0.242133 | + | 0.970243i | \(0.577847\pi\) | |||||||
\(450\) | 450.000 | 0.0471405 | ||||||||
\(451\) | 14421.1 | 1.50568 | ||||||||
\(452\) | −2882.51 | −0.299960 | ||||||||
\(453\) | −8314.41 | −0.862351 | ||||||||
\(454\) | −8426.30 | −0.871070 | ||||||||
\(455\) | −1760.16 | −0.181358 | ||||||||
\(456\) | 456.000 | 0.0468293 | ||||||||
\(457\) | 7656.99 | 0.783762 | 0.391881 | − | 0.920016i | \(-0.371825\pi\) | ||||
0.391881 | + | 0.920016i | \(0.371825\pi\) | |||||||
\(458\) | −5193.32 | −0.529842 | ||||||||
\(459\) | −1485.63 | −0.151075 | ||||||||
\(460\) | 2967.89 | 0.300823 | ||||||||
\(461\) | −12317.8 | −1.24447 | −0.622234 | − | 0.782832i | \(-0.713775\pi\) | ||||
−0.622234 | + | 0.782832i | \(0.713775\pi\) | |||||||
\(462\) | −4826.72 | −0.486059 | ||||||||
\(463\) | 10751.8 | 1.07922 | 0.539608 | − | 0.841916i | \(-0.318572\pi\) | ||||
0.539608 | + | 0.841916i | \(0.318572\pi\) | |||||||
\(464\) | 765.785 | 0.0766178 | ||||||||
\(465\) | −123.333 | −0.0122998 | ||||||||
\(466\) | −7574.23 | −0.752939 | ||||||||
\(467\) | −11618.8 | −1.15129 | −0.575647 | − | 0.817699i | \(-0.695250\pi\) | ||||
−0.575647 | + | 0.817699i | \(0.695250\pi\) | |||||||
\(468\) | 799.211 | 0.0789392 | ||||||||
\(469\) | 7248.68 | 0.713674 | ||||||||
\(470\) | 5610.47 | 0.550621 | ||||||||
\(471\) | 7639.08 | 0.747325 | ||||||||
\(472\) | −4297.33 | −0.419069 | ||||||||
\(473\) | 17308.6 | 1.68256 | ||||||||
\(474\) | −1323.15 | −0.128216 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | 3490.05 | 0.336064 | ||||||||
\(477\) | 3871.59 | 0.371631 | ||||||||
\(478\) | 5402.82 | 0.516986 | ||||||||
\(479\) | 2195.73 | 0.209448 | 0.104724 | − | 0.994501i | \(-0.466604\pi\) | ||||
0.104724 | + | 0.994501i | \(0.466604\pi\) | |||||||
\(480\) | 480.000 | 0.0456435 | ||||||||
\(481\) | −5030.34 | −0.476848 | ||||||||
\(482\) | −10197.4 | −0.963653 | ||||||||
\(483\) | −7059.33 | −0.665032 | ||||||||
\(484\) | 4970.69 | 0.466820 | ||||||||
\(485\) | 7760.44 | 0.726563 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −1633.07 | −0.151954 | −0.0759769 | − | 0.997110i | \(-0.524208\pi\) | ||||
−0.0759769 | + | 0.997110i | \(0.524208\pi\) | |||||||
\(488\) | −6141.86 | −0.569732 | ||||||||
\(489\) | 8296.10 | 0.767204 | ||||||||
\(490\) | −915.518 | −0.0844059 | ||||||||
\(491\) | −8508.71 | −0.782063 | −0.391031 | − | 0.920377i | \(-0.627882\pi\) | ||||
−0.391031 | + | 0.920377i | \(0.627882\pi\) | |||||||
\(492\) | 3411.16 | 0.312575 | ||||||||
\(493\) | −2633.51 | −0.240582 | ||||||||
\(494\) | 843.612 | 0.0768338 | ||||||||
\(495\) | 2282.91 | 0.207291 | ||||||||
\(496\) | −131.555 | −0.0119093 | ||||||||
\(497\) | 449.264 | 0.0405478 | ||||||||
\(498\) | −1898.56 | −0.170837 | ||||||||
\(499\) | −5631.15 | −0.505181 | −0.252590 | − | 0.967573i | \(-0.581282\pi\) | ||||
−0.252590 | + | 0.967573i | \(0.581282\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | −7654.88 | −0.682625 | ||||||||
\(502\) | −10961.6 | −0.974585 | ||||||||
\(503\) | 14035.5 | 1.24416 | 0.622078 | − | 0.782955i | \(-0.286289\pi\) | ||||
0.622078 | + | 0.782955i | \(0.286289\pi\) | |||||||
\(504\) | −1141.71 | −0.100905 | ||||||||
\(505\) | 3081.68 | 0.271550 | ||||||||
\(506\) | 15056.5 | 1.32281 | ||||||||
\(507\) | −5112.44 | −0.447833 | ||||||||
\(508\) | −2577.49 | −0.225114 | ||||||||
\(509\) | 16758.0 | 1.45930 | 0.729650 | − | 0.683821i | \(-0.239683\pi\) | ||||
0.729650 | + | 0.683821i | \(0.239683\pi\) | |||||||
\(510\) | −1650.70 | −0.143322 | ||||||||
\(511\) | −10525.9 | −0.911233 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 513.000 | 0.0441511 | ||||||||
\(514\) | −2575.88 | −0.221045 | ||||||||
\(515\) | −8977.18 | −0.768120 | ||||||||
\(516\) | 4094.18 | 0.349295 | ||||||||
\(517\) | 28462.7 | 2.42125 | ||||||||
\(518\) | 7186.08 | 0.609534 | ||||||||
\(519\) | 1591.27 | 0.134584 | ||||||||
\(520\) | 888.012 | 0.0748883 | ||||||||
\(521\) | 1472.09 | 0.123787 | 0.0618937 | − | 0.998083i | \(-0.480286\pi\) | ||||
0.0618937 | + | 0.998083i | \(0.480286\pi\) | |||||||
\(522\) | 861.508 | 0.0722359 | ||||||||
\(523\) | −10915.9 | −0.912656 | −0.456328 | − | 0.889812i | \(-0.650836\pi\) | ||||
−0.456328 | + | 0.889812i | \(0.650836\pi\) | |||||||
\(524\) | −3606.79 | −0.300694 | ||||||||
\(525\) | −1189.28 | −0.0988659 | ||||||||
\(526\) | −8139.09 | −0.674679 | ||||||||
\(527\) | 452.413 | 0.0373955 | ||||||||
\(528\) | 2435.11 | 0.200709 | ||||||||
\(529\) | 9853.92 | 0.809889 | ||||||||
\(530\) | 4301.76 | 0.352560 | ||||||||
\(531\) | −4834.49 | −0.395102 | ||||||||
\(532\) | −1205.14 | −0.0982133 | ||||||||
\(533\) | 6310.74 | 0.512849 | ||||||||
\(534\) | −8569.95 | −0.694491 | ||||||||
\(535\) | 4668.79 | 0.377288 | ||||||||
\(536\) | −3657.00 | −0.294698 | ||||||||
\(537\) | −913.229 | −0.0733869 | ||||||||
\(538\) | −4606.49 | −0.369144 | ||||||||
\(539\) | −4644.55 | −0.371160 | ||||||||
\(540\) | 540.000 | 0.0430331 | ||||||||
\(541\) | 195.388 | 0.0155275 | 0.00776377 | − | 0.999970i | \(-0.497529\pi\) | ||||
0.00776377 | + | 0.999970i | \(0.497529\pi\) | |||||||
\(542\) | −9150.98 | −0.725218 | ||||||||
\(543\) | −3635.93 | −0.287353 | ||||||||
\(544\) | −1760.75 | −0.138771 | ||||||||
\(545\) | 9339.94 | 0.734090 | ||||||||
\(546\) | −2112.20 | −0.165556 | ||||||||
\(547\) | −12927.8 | −1.01052 | −0.505259 | − | 0.862968i | \(-0.668603\pi\) | ||||
−0.505259 | + | 0.862968i | \(0.668603\pi\) | |||||||
\(548\) | −7358.19 | −0.573588 | ||||||||
\(549\) | −6909.60 | −0.537148 | ||||||||
\(550\) | 2536.57 | 0.196654 | ||||||||
\(551\) | 909.369 | 0.0703093 | ||||||||
\(552\) | 3561.47 | 0.274613 | ||||||||
\(553\) | 3496.90 | 0.268903 | ||||||||
\(554\) | 4514.52 | 0.346216 | ||||||||
\(555\) | −3398.83 | −0.259950 | ||||||||
\(556\) | −12336.5 | −0.940976 | ||||||||
\(557\) | 17152.6 | 1.30481 | 0.652407 | − | 0.757869i | \(-0.273759\pi\) | ||||
0.652407 | + | 0.757869i | \(0.273759\pi\) | |||||||
\(558\) | −147.999 | −0.0112282 | ||||||||
\(559\) | 7574.34 | 0.573095 | ||||||||
\(560\) | −1268.57 | −0.0957265 | ||||||||
\(561\) | −8374.24 | −0.630233 | ||||||||
\(562\) | 8923.95 | 0.669812 | ||||||||
\(563\) | 19714.9 | 1.47582 | 0.737909 | − | 0.674901i | \(-0.235814\pi\) | ||||
0.737909 | + | 0.674901i | \(0.235814\pi\) | |||||||
\(564\) | 6732.57 | 0.502646 | ||||||||
\(565\) | −3603.14 | −0.268293 | ||||||||
\(566\) | 2630.35 | 0.195339 | ||||||||
\(567\) | −1284.43 | −0.0951338 | ||||||||
\(568\) | −226.656 | −0.0167434 | ||||||||
\(569\) | 16286.4 | 1.19993 | 0.599964 | − | 0.800027i | \(-0.295181\pi\) | ||||
0.599964 | + | 0.800027i | \(0.295181\pi\) | |||||||
\(570\) | 570.000 | 0.0418854 | ||||||||
\(571\) | −19645.3 | −1.43981 | −0.719903 | − | 0.694075i | \(-0.755814\pi\) | ||||
−0.719903 | + | 0.694075i | \(0.755814\pi\) | |||||||
\(572\) | 4505.01 | 0.329308 | ||||||||
\(573\) | −639.925 | −0.0466549 | ||||||||
\(574\) | −9015.20 | −0.655553 | ||||||||
\(575\) | 3709.86 | 0.269064 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 5176.59 | 0.373491 | 0.186745 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186745 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(578\) | −3770.84 | −0.271361 | ||||||||
\(579\) | 259.745 | 0.0186436 | ||||||||
\(580\) | 957.231 | 0.0685290 | ||||||||
\(581\) | 5017.62 | 0.358289 | ||||||||
\(582\) | 9312.52 | 0.663259 | ||||||||
\(583\) | 21823.4 | 1.55032 | ||||||||
\(584\) | 5310.39 | 0.376277 | ||||||||
\(585\) | 999.014 | 0.0706054 | ||||||||
\(586\) | 9810.29 | 0.691569 | ||||||||
\(587\) | 18538.7 | 1.30353 | 0.651766 | − | 0.758420i | \(-0.274028\pi\) | ||||
0.651766 | + | 0.758420i | \(0.274028\pi\) | |||||||
\(588\) | −1098.62 | −0.0770517 | ||||||||
\(589\) | −156.222 | −0.0109287 | ||||||||
\(590\) | −5371.66 | −0.374827 | ||||||||
\(591\) | −14084.6 | −0.980313 | ||||||||
\(592\) | −3625.42 | −0.251696 | ||||||||
\(593\) | 16412.2 | 1.13654 | 0.568270 | − | 0.822842i | \(-0.307613\pi\) | ||||
0.568270 | + | 0.822842i | \(0.307613\pi\) | |||||||
\(594\) | 2739.49 | 0.189230 | ||||||||
\(595\) | 4362.56 | 0.300584 | ||||||||
\(596\) | 3646.26 | 0.250598 | ||||||||
\(597\) | 12618.1 | 0.865036 | ||||||||
\(598\) | 6588.81 | 0.450562 | ||||||||
\(599\) | −24397.0 | −1.66416 | −0.832082 | − | 0.554653i | \(-0.812851\pi\) | ||||
−0.832082 | + | 0.554653i | \(0.812851\pi\) | |||||||
\(600\) | 600.000 | 0.0408248 | ||||||||
\(601\) | 26547.9 | 1.80185 | 0.900926 | − | 0.433973i | \(-0.142889\pi\) | ||||
0.900926 | + | 0.433973i | \(0.142889\pi\) | |||||||
\(602\) | −10820.3 | −0.732563 | ||||||||
\(603\) | −4114.12 | −0.277844 | ||||||||
\(604\) | −11085.9 | −0.746818 | ||||||||
\(605\) | 6213.37 | 0.417536 | ||||||||
\(606\) | 3698.01 | 0.247890 | ||||||||
\(607\) | 3740.95 | 0.250149 | 0.125075 | − | 0.992147i | \(-0.460083\pi\) | ||||
0.125075 | + | 0.992147i | \(0.460083\pi\) | |||||||
\(608\) | 608.000 | 0.0405554 | ||||||||
\(609\) | −2276.84 | −0.151498 | ||||||||
\(610\) | −7677.33 | −0.509583 | ||||||||
\(611\) | 12455.4 | 0.824702 | ||||||||
\(612\) | −1980.84 | −0.130835 | ||||||||
\(613\) | 13449.2 | 0.886144 | 0.443072 | − | 0.896486i | \(-0.353889\pi\) | ||||
0.443072 | + | 0.896486i | \(0.353889\pi\) | |||||||
\(614\) | −3742.94 | −0.246014 | ||||||||
\(615\) | 4263.95 | 0.279576 | ||||||||
\(616\) | −6435.63 | −0.420940 | ||||||||
\(617\) | 13438.8 | 0.876866 | 0.438433 | − | 0.898764i | \(-0.355534\pi\) | ||||
0.438433 | + | 0.898764i | \(0.355534\pi\) | |||||||
\(618\) | −10772.6 | −0.701194 | ||||||||
\(619\) | −18146.7 | −1.17832 | −0.589159 | − | 0.808017i | \(-0.700541\pi\) | ||||
−0.589159 | + | 0.808017i | \(0.700541\pi\) | |||||||
\(620\) | −164.444 | −0.0106520 | ||||||||
\(621\) | 4006.65 | 0.258907 | ||||||||
\(622\) | −10366.6 | −0.668271 | ||||||||
\(623\) | 22649.1 | 1.45653 | ||||||||
\(624\) | 1065.61 | 0.0683634 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 12349.5 | 0.788472 | ||||||||
\(627\) | 2891.69 | 0.184183 | ||||||||
\(628\) | 10185.4 | 0.647202 | ||||||||
\(629\) | 12467.7 | 0.790332 | ||||||||
\(630\) | −1427.14 | −0.0902518 | ||||||||
\(631\) | −5015.02 | −0.316394 | −0.158197 | − | 0.987408i | \(-0.550568\pi\) | ||||
−0.158197 | + | 0.987408i | \(0.550568\pi\) | |||||||
\(632\) | −1764.21 | −0.111038 | ||||||||
\(633\) | 12445.4 | 0.781454 | ||||||||
\(634\) | 120.119 | 0.00752452 | ||||||||
\(635\) | −3221.87 | −0.201348 | ||||||||
\(636\) | 5162.12 | 0.321842 | ||||||||
\(637\) | −2032.48 | −0.126420 | ||||||||
\(638\) | 4856.16 | 0.301344 | ||||||||
\(639\) | −254.988 | −0.0157859 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | −17869.0 | −1.10107 | −0.550534 | − | 0.834813i | \(-0.685576\pi\) | ||||
−0.550534 | + | 0.834813i | \(0.685576\pi\) | |||||||
\(642\) | 5602.55 | 0.344416 | ||||||||
\(643\) | −10833.2 | −0.664419 | −0.332209 | − | 0.943206i | \(-0.607794\pi\) | ||||
−0.332209 | + | 0.943206i | \(0.607794\pi\) | |||||||
\(644\) | −9412.43 | −0.575935 | ||||||||
\(645\) | 5117.72 | 0.312419 | ||||||||
\(646\) | −2090.89 | −0.127345 | ||||||||
\(647\) | 2378.25 | 0.144511 | 0.0722555 | − | 0.997386i | \(-0.476980\pi\) | ||||
0.0722555 | + | 0.997386i | \(0.476980\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −27251.2 | −1.64823 | ||||||||
\(650\) | 1110.02 | 0.0669821 | ||||||||
\(651\) | 391.141 | 0.0235484 | ||||||||
\(652\) | 11061.5 | 0.664418 | ||||||||
\(653\) | −12759.1 | −0.764627 | −0.382314 | − | 0.924033i | \(-0.624873\pi\) | ||||
−0.382314 | + | 0.924033i | \(0.624873\pi\) | |||||||
\(654\) | 11207.9 | 0.670130 | ||||||||
\(655\) | −4508.49 | −0.268949 | ||||||||
\(656\) | 4548.22 | 0.270698 | ||||||||
\(657\) | 5974.19 | 0.354757 | ||||||||
\(658\) | −17793.2 | −1.05418 | ||||||||
\(659\) | 15189.7 | 0.897883 | 0.448942 | − | 0.893561i | \(-0.351801\pi\) | ||||
0.448942 | + | 0.893561i | \(0.351801\pi\) | |||||||
\(660\) | 3043.88 | 0.179520 | ||||||||
\(661\) | 4398.55 | 0.258826 | 0.129413 | − | 0.991591i | \(-0.458691\pi\) | ||||
0.129413 | + | 0.991591i | \(0.458691\pi\) | |||||||
\(662\) | −10944.7 | −0.642566 | ||||||||
\(663\) | −3664.61 | −0.214663 | ||||||||
\(664\) | −2531.42 | −0.147949 | ||||||||
\(665\) | −1506.43 | −0.0878447 | ||||||||
\(666\) | −4078.60 | −0.237301 | ||||||||
\(667\) | 7102.39 | 0.412302 | ||||||||
\(668\) | −10206.5 | −0.591170 | ||||||||
\(669\) | −14237.3 | −0.822788 | ||||||||
\(670\) | −4571.25 | −0.263586 | ||||||||
\(671\) | −38948.2 | −2.24080 | ||||||||
\(672\) | −1522.28 | −0.0873859 | ||||||||
\(673\) | 16170.9 | 0.926215 | 0.463108 | − | 0.886302i | \(-0.346734\pi\) | ||||
0.463108 | + | 0.886302i | \(0.346734\pi\) | |||||||
\(674\) | −11505.9 | −0.657551 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −6816.58 | −0.387835 | ||||||||
\(677\) | 17812.2 | 1.01120 | 0.505598 | − | 0.862769i | \(-0.331272\pi\) | ||||
0.505598 | + | 0.862769i | \(0.331272\pi\) | |||||||
\(678\) | −4323.77 | −0.244917 | ||||||||
\(679\) | −24611.6 | −1.39103 | ||||||||
\(680\) | −2200.94 | −0.124121 | ||||||||
\(681\) | −12639.5 | −0.711226 | ||||||||
\(682\) | −834.246 | −0.0468401 | ||||||||
\(683\) | 25203.8 | 1.41200 | 0.705999 | − | 0.708213i | \(-0.250498\pi\) | ||||
0.705999 | + | 0.708213i | \(0.250498\pi\) | |||||||
\(684\) | 684.000 | 0.0382360 | ||||||||
\(685\) | −9197.74 | −0.513033 | ||||||||
\(686\) | 13781.5 | 0.767025 | ||||||||
\(687\) | −7789.98 | −0.432615 | ||||||||
\(688\) | 5458.90 | 0.302498 | ||||||||
\(689\) | 9550.05 | 0.528052 | ||||||||
\(690\) | 4451.83 | 0.245621 | ||||||||
\(691\) | 10306.9 | 0.567430 | 0.283715 | − | 0.958909i | \(-0.408433\pi\) | ||||
0.283715 | + | 0.958909i | \(0.408433\pi\) | |||||||
\(692\) | 2121.70 | 0.116553 | ||||||||
\(693\) | −7240.08 | −0.396866 | ||||||||
\(694\) | −3809.87 | −0.208387 | ||||||||
\(695\) | −15420.6 | −0.841634 | ||||||||
\(696\) | 1148.68 | 0.0625582 | ||||||||
\(697\) | −15641.2 | −0.850001 | ||||||||
\(698\) | 12779.9 | 0.693018 | ||||||||
\(699\) | −11361.4 | −0.614772 | ||||||||
\(700\) | −1585.71 | −0.0856204 | ||||||||
\(701\) | 22781.9 | 1.22747 | 0.613737 | − | 0.789510i | \(-0.289665\pi\) | ||||
0.613737 | + | 0.789510i | \(0.289665\pi\) | |||||||
\(702\) | 1198.82 | 0.0644536 | ||||||||
\(703\) | −4305.18 | −0.230972 | ||||||||
\(704\) | 3246.81 | 0.173819 | ||||||||
\(705\) | 8415.71 | 0.449580 | ||||||||
\(706\) | −20460.5 | −1.09071 | ||||||||
\(707\) | −9773.31 | −0.519891 | ||||||||
\(708\) | −6445.99 | −0.342168 | ||||||||
\(709\) | −16970.4 | −0.898924 | −0.449462 | − | 0.893299i | \(-0.648384\pi\) | ||||
−0.449462 | + | 0.893299i | \(0.648384\pi\) | |||||||
\(710\) | −283.320 | −0.0149758 | ||||||||
\(711\) | −1984.73 | −0.104688 | ||||||||
\(712\) | −11426.6 | −0.601447 | ||||||||
\(713\) | −1220.13 | −0.0640871 | ||||||||
\(714\) | 5235.08 | 0.274395 | ||||||||
\(715\) | 5631.26 | 0.294542 | ||||||||
\(716\) | −1217.64 | −0.0635549 | ||||||||
\(717\) | 8104.23 | 0.422117 | ||||||||
\(718\) | −1163.89 | −0.0604958 | ||||||||
\(719\) | −7479.87 | −0.387972 | −0.193986 | − | 0.981004i | \(-0.562142\pi\) | ||||
−0.193986 | + | 0.981004i | \(0.562142\pi\) | |||||||
\(720\) | 720.000 | 0.0372678 | ||||||||
\(721\) | 28470.4 | 1.47059 | ||||||||
\(722\) | 722.000 | 0.0372161 | ||||||||
\(723\) | −15296.2 | −0.786819 | ||||||||
\(724\) | −4847.90 | −0.248855 | ||||||||
\(725\) | 1196.54 | 0.0612942 | ||||||||
\(726\) | 7456.04 | 0.381157 | ||||||||
\(727\) | −15908.9 | −0.811595 | −0.405797 | − | 0.913963i | \(-0.633006\pi\) | ||||
−0.405797 | + | 0.913963i | \(0.633006\pi\) | |||||||
\(728\) | −2816.26 | −0.143376 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 6637.99 | 0.336552 | ||||||||
\(731\) | −18773.0 | −0.949855 | ||||||||
\(732\) | −9212.79 | −0.465184 | ||||||||
\(733\) | 1892.84 | 0.0953804 | 0.0476902 | − | 0.998862i | \(-0.484814\pi\) | ||||
0.0476902 | + | 0.998862i | \(0.484814\pi\) | |||||||
\(734\) | 20094.8 | 1.01051 | ||||||||
\(735\) | −1373.28 | −0.0689172 | ||||||||
\(736\) | 4748.62 | 0.237821 | ||||||||
\(737\) | −23190.6 | −1.15907 | ||||||||
\(738\) | 5116.74 | 0.255217 | ||||||||
\(739\) | −1412.05 | −0.0702886 | −0.0351443 | − | 0.999382i | \(-0.511189\pi\) | ||||
−0.0351443 | + | 0.999382i | \(0.511189\pi\) | |||||||
\(740\) | −4531.77 | −0.225123 | ||||||||
\(741\) | 1265.42 | 0.0627345 | ||||||||
\(742\) | −13642.7 | −0.674986 | ||||||||
\(743\) | −29072.8 | −1.43550 | −0.717751 | − | 0.696300i | \(-0.754828\pi\) | ||||
−0.717751 | + | 0.696300i | \(0.754828\pi\) | |||||||
\(744\) | −197.333 | −0.00972387 | ||||||||
\(745\) | 4557.83 | 0.224142 | ||||||||
\(746\) | 28160.8 | 1.38209 | ||||||||
\(747\) | −2847.84 | −0.139487 | ||||||||
\(748\) | −11165.7 | −0.545798 | ||||||||
\(749\) | −14806.7 | −0.722330 | ||||||||
\(750\) | 750.000 | 0.0365148 | ||||||||
\(751\) | 12794.4 | 0.621668 | 0.310834 | − | 0.950464i | \(-0.399392\pi\) | ||||
0.310834 | + | 0.950464i | \(0.399392\pi\) | |||||||
\(752\) | 8976.76 | 0.435304 | ||||||||
\(753\) | −16442.5 | −0.795746 | ||||||||
\(754\) | 2125.08 | 0.102640 | ||||||||
\(755\) | −13857.4 | −0.667975 | ||||||||
\(756\) | −1712.57 | −0.0823883 | ||||||||
\(757\) | 3334.12 | 0.160080 | 0.0800401 | − | 0.996792i | \(-0.474495\pi\) | ||||
0.0800401 | + | 0.996792i | \(0.474495\pi\) | |||||||
\(758\) | 11030.7 | 0.528568 | ||||||||
\(759\) | 22584.8 | 1.08007 | ||||||||
\(760\) | 760.000 | 0.0362738 | ||||||||
\(761\) | 37410.1 | 1.78202 | 0.891009 | − | 0.453985i | \(-0.149998\pi\) | ||||
0.891009 | + | 0.453985i | \(0.149998\pi\) | |||||||
\(762\) | −3866.24 | −0.183805 | ||||||||
\(763\) | −29620.9 | −1.40544 | ||||||||
\(764\) | −853.233 | −0.0404043 | ||||||||
\(765\) | −2476.05 | −0.117022 | ||||||||
\(766\) | 6730.61 | 0.317476 | ||||||||
\(767\) | −11925.3 | −0.561403 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 15438.0 | 0.723941 | 0.361970 | − | 0.932190i | \(-0.382104\pi\) | ||||
0.361970 | + | 0.932190i | \(0.382104\pi\) | |||||||
\(770\) | −8044.54 | −0.376500 | ||||||||
\(771\) | −3863.82 | −0.180483 | ||||||||
\(772\) | 346.327 | 0.0161458 | ||||||||
\(773\) | −24903.7 | −1.15876 | −0.579381 | − | 0.815057i | \(-0.696706\pi\) | ||||
−0.579381 | + | 0.815057i | \(0.696706\pi\) | |||||||
\(774\) | 6141.27 | 0.285198 | ||||||||
\(775\) | −205.555 | −0.00952741 | ||||||||
\(776\) | 12416.7 | 0.574399 | ||||||||
\(777\) | 10779.1 | 0.497682 | ||||||||
\(778\) | 10783.2 | 0.496910 | ||||||||
\(779\) | 5401.01 | 0.248410 | ||||||||
\(780\) | 1332.02 | 0.0611460 | ||||||||
\(781\) | −1437.32 | −0.0658533 | ||||||||
\(782\) | −16330.3 | −0.746767 | ||||||||
\(783\) | 1292.26 | 0.0589804 | ||||||||
\(784\) | −1464.83 | −0.0667288 | ||||||||
\(785\) | 12731.8 | 0.578875 | ||||||||
\(786\) | −5410.19 | −0.245515 | ||||||||
\(787\) | −2237.73 | −0.101355 | −0.0506775 | − | 0.998715i | \(-0.516138\pi\) | ||||
−0.0506775 | + | 0.998715i | \(0.516138\pi\) | |||||||
\(788\) | −18779.5 | −0.848976 | ||||||||
\(789\) | −12208.6 | −0.550873 | ||||||||
\(790\) | −2205.26 | −0.0993158 | ||||||||
\(791\) | 11427.1 | 0.513654 | ||||||||
\(792\) | 3652.66 | 0.163878 | ||||||||
\(793\) | −17043.9 | −0.763237 | ||||||||
\(794\) | 8761.55 | 0.391607 | ||||||||
\(795\) | 6452.64 | 0.287864 | ||||||||
\(796\) | 16824.2 | 0.749143 | ||||||||
\(797\) | −9047.59 | −0.402111 | −0.201055 | − | 0.979580i | \(-0.564437\pi\) | ||||
−0.201055 | + | 0.979580i | \(0.564437\pi\) | |||||||
\(798\) | −1807.71 | −0.0801908 | ||||||||
\(799\) | −30870.8 | −1.36687 | ||||||||
\(800\) | 800.000 | 0.0353553 | ||||||||
\(801\) | −12854.9 | −0.567050 | ||||||||
\(802\) | −19270.3 | −0.848453 | ||||||||
\(803\) | 33675.4 | 1.47993 | ||||||||
\(804\) | −5485.50 | −0.240620 | ||||||||
\(805\) | −11765.5 | −0.515132 | ||||||||
\(806\) | −365.070 | −0.0159542 | ||||||||
\(807\) | −6909.73 | −0.301405 | ||||||||
\(808\) | 4930.69 | 0.214679 | ||||||||
\(809\) | −6467.14 | −0.281054 | −0.140527 | − | 0.990077i | \(-0.544880\pi\) | ||||
−0.140527 | + | 0.990077i | \(0.544880\pi\) | |||||||
\(810\) | 810.000 | 0.0351364 | ||||||||
\(811\) | −10840.0 | −0.469352 | −0.234676 | − | 0.972074i | \(-0.575403\pi\) | ||||
−0.234676 | + | 0.972074i | \(0.575403\pi\) | |||||||
\(812\) | −3035.78 | −0.131201 | ||||||||
\(813\) | −13726.5 | −0.592138 | ||||||||
\(814\) | −22990.3 | −0.989939 | ||||||||
\(815\) | 13826.8 | 0.594274 | ||||||||
\(816\) | −2641.12 | −0.113306 | ||||||||
\(817\) | 6482.45 | 0.277591 | ||||||||
\(818\) | −3675.62 | −0.157109 | ||||||||
\(819\) | −3168.30 | −0.135176 | ||||||||
\(820\) | 5685.27 | 0.242120 | ||||||||
\(821\) | −3920.48 | −0.166657 | −0.0833286 | − | 0.996522i | \(-0.526555\pi\) | ||||
−0.0833286 | + | 0.996522i | \(0.526555\pi\) | |||||||
\(822\) | −11037.3 | −0.468333 | ||||||||
\(823\) | 138.929 | 0.00588427 | 0.00294214 | − | 0.999996i | \(-0.499063\pi\) | ||||
0.00294214 | + | 0.999996i | \(0.499063\pi\) | |||||||
\(824\) | −14363.5 | −0.607252 | ||||||||
\(825\) | 3804.85 | 0.160567 | ||||||||
\(826\) | 17035.8 | 0.717617 | ||||||||
\(827\) | −23967.6 | −1.00778 | −0.503890 | − | 0.863768i | \(-0.668098\pi\) | ||||
−0.503890 | + | 0.863768i | \(0.668098\pi\) | |||||||
\(828\) | 5342.20 | 0.224220 | ||||||||
\(829\) | −26196.6 | −1.09752 | −0.548760 | − | 0.835980i | \(-0.684900\pi\) | ||||
−0.548760 | + | 0.835980i | \(0.684900\pi\) | |||||||
\(830\) | −3164.27 | −0.132329 | ||||||||
\(831\) | 6771.78 | 0.282684 | ||||||||
\(832\) | 1420.82 | 0.0592044 | ||||||||
\(833\) | 5037.50 | 0.209531 | ||||||||
\(834\) | −18504.7 | −0.768304 | ||||||||
\(835\) | −12758.1 | −0.528759 | ||||||||
\(836\) | 3855.59 | 0.159507 | ||||||||
\(837\) | −221.999 | −0.00916775 | ||||||||
\(838\) | 11625.2 | 0.479220 | ||||||||
\(839\) | 3239.87 | 0.133317 | 0.0666583 | − | 0.997776i | \(-0.478766\pi\) | ||||
0.0666583 | + | 0.997776i | \(0.478766\pi\) | |||||||
\(840\) | −1902.85 | −0.0781604 | ||||||||
\(841\) | −22098.3 | −0.906075 | ||||||||
\(842\) | 17985.3 | 0.736120 | ||||||||
\(843\) | 13385.9 | 0.546899 | ||||||||
\(844\) | 16593.9 | 0.676759 | ||||||||
\(845\) | −8520.73 | −0.346890 | ||||||||
\(846\) | 10098.9 | 0.410409 | ||||||||
\(847\) | −19705.2 | −0.799385 | ||||||||
\(848\) | 6882.82 | 0.278723 | ||||||||
\(849\) | 3945.52 | 0.159493 | ||||||||
\(850\) | −2751.17 | −0.111017 | ||||||||
\(851\) | −33624.5 | −1.35445 | ||||||||
\(852\) | −339.984 | −0.0136710 | ||||||||
\(853\) | −34062.5 | −1.36726 | −0.683632 | − | 0.729827i | \(-0.739601\pi\) | ||||
−0.683632 | + | 0.729827i | \(0.739601\pi\) | |||||||
\(854\) | 24348.1 | 0.975613 | ||||||||
\(855\) | 855.000 | 0.0341993 | ||||||||
\(856\) | 7470.06 | 0.298273 | ||||||||
\(857\) | 7779.69 | 0.310092 | 0.155046 | − | 0.987907i | \(-0.450447\pi\) | ||||
0.155046 | + | 0.987907i | \(0.450447\pi\) | |||||||
\(858\) | 6757.52 | 0.268879 | ||||||||
\(859\) | −17297.7 | −0.687068 | −0.343534 | − | 0.939140i | \(-0.611624\pi\) | ||||
−0.343534 | + | 0.939140i | \(0.611624\pi\) | |||||||
\(860\) | 6823.63 | 0.270563 | ||||||||
\(861\) | −13522.8 | −0.535256 | ||||||||
\(862\) | 295.850 | 0.0116899 | ||||||||
\(863\) | −14014.6 | −0.552796 | −0.276398 | − | 0.961043i | \(-0.589141\pi\) | ||||
−0.276398 | + | 0.961043i | \(0.589141\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 2652.12 | 0.104248 | ||||||||
\(866\) | 18616.2 | 0.730489 | ||||||||
\(867\) | −5656.27 | −0.221565 | ||||||||
\(868\) | 521.521 | 0.0203935 | ||||||||
\(869\) | −11187.6 | −0.436723 | ||||||||
\(870\) | 1435.85 | 0.0559537 | ||||||||
\(871\) | −10148.3 | −0.394790 | ||||||||
\(872\) | 14943.9 | 0.580349 | ||||||||
\(873\) | 13968.8 | 0.541548 | ||||||||
\(874\) | 5638.99 | 0.218240 | ||||||||
\(875\) | −1982.14 | −0.0765812 | ||||||||
\(876\) | 7965.58 | 0.307229 | ||||||||
\(877\) | 34301.0 | 1.32071 | 0.660355 | − | 0.750954i | \(-0.270406\pi\) | ||||
0.660355 | + | 0.750954i | \(0.270406\pi\) | |||||||
\(878\) | −1665.45 | −0.0640163 | ||||||||
\(879\) | 14715.4 | 0.564664 | ||||||||
\(880\) | 4058.51 | 0.155469 | ||||||||
\(881\) | 4025.57 | 0.153944 | 0.0769721 | − | 0.997033i | \(-0.475475\pi\) | ||||
0.0769721 | + | 0.997033i | \(0.475475\pi\) | |||||||
\(882\) | −1647.93 | −0.0629125 | ||||||||
\(883\) | 12216.0 | 0.465573 | 0.232786 | − | 0.972528i | \(-0.425216\pi\) | ||||
0.232786 | + | 0.972528i | \(0.425216\pi\) | |||||||
\(884\) | −4886.15 | −0.185904 | ||||||||
\(885\) | −8057.49 | −0.306045 | ||||||||
\(886\) | −313.415 | −0.0118842 | ||||||||
\(887\) | 14443.0 | 0.546728 | 0.273364 | − | 0.961911i | \(-0.411864\pi\) | ||||
0.273364 | + | 0.961911i | \(0.411864\pi\) | |||||||
\(888\) | −5438.13 | −0.205509 | ||||||||
\(889\) | 10217.9 | 0.385487 | ||||||||
\(890\) | −14283.3 | −0.537950 | ||||||||
\(891\) | 4109.24 | 0.154506 | ||||||||
\(892\) | −18983.0 | −0.712555 | ||||||||
\(893\) | 10659.9 | 0.399462 | ||||||||
\(894\) | 5469.39 | 0.204613 | ||||||||
\(895\) | −1522.05 | −0.0568452 | ||||||||
\(896\) | −2029.71 | −0.0756784 | ||||||||
\(897\) | 9883.21 | 0.367883 | ||||||||
\(898\) | −9214.75 | −0.342428 | ||||||||
\(899\) | −393.527 | −0.0145994 | ||||||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | −23669.8 | −0.875199 | ||||||||
\(902\) | 28842.2 | 1.06468 | ||||||||
\(903\) | −16230.5 | −0.598135 | ||||||||
\(904\) | −5765.03 | −0.212104 | ||||||||
\(905\) | −6059.88 | −0.222583 | ||||||||
\(906\) | −16628.8 | −0.609775 | ||||||||
\(907\) | 16427.3 | 0.601387 | 0.300693 | − | 0.953721i | \(-0.402782\pi\) | ||||
0.300693 | + | 0.953721i | \(0.402782\pi\) | |||||||
\(908\) | −16852.6 | −0.615940 | ||||||||
\(909\) | 5547.02 | 0.202402 | ||||||||
\(910\) | −3520.33 | −0.128239 | ||||||||
\(911\) | 7719.97 | 0.280762 | 0.140381 | − | 0.990098i | \(-0.455167\pi\) | ||||
0.140381 | + | 0.990098i | \(0.455167\pi\) | |||||||
\(912\) | 912.000 | 0.0331133 | ||||||||
\(913\) | −16052.8 | −0.581894 | ||||||||
\(914\) | 15314.0 | 0.554203 | ||||||||
\(915\) | −11516.0 | −0.416073 | ||||||||
\(916\) | −10386.6 | −0.374655 | ||||||||
\(917\) | 14298.3 | 0.514910 | ||||||||
\(918\) | −2971.27 | −0.106826 | ||||||||
\(919\) | −36761.3 | −1.31953 | −0.659763 | − | 0.751474i | \(-0.729343\pi\) | ||||
−0.659763 | + | 0.751474i | \(0.729343\pi\) | |||||||
\(920\) | 5935.78 | 0.212714 | ||||||||
\(921\) | −5614.41 | −0.200870 | ||||||||
\(922\) | −24635.7 | −0.879971 | ||||||||
\(923\) | −628.979 | −0.0224302 | ||||||||
\(924\) | −9653.44 | −0.343696 | ||||||||
\(925\) | −5664.72 | −0.201356 | ||||||||
\(926\) | 21503.5 | 0.763121 | ||||||||
\(927\) | −16158.9 | −0.572523 | ||||||||
\(928\) | 1531.57 | 0.0541770 | ||||||||
\(929\) | 7843.88 | 0.277018 | 0.138509 | − | 0.990361i | \(-0.455769\pi\) | ||||
0.138509 | + | 0.990361i | \(0.455769\pi\) | |||||||
\(930\) | −246.666 | −0.00869730 | ||||||||
\(931\) | −1739.49 | −0.0612345 | ||||||||
\(932\) | −15148.5 | −0.532408 | ||||||||
\(933\) | −15550.0 | −0.545641 | ||||||||
\(934\) | −23237.6 | −0.814087 | ||||||||
\(935\) | −13957.1 | −0.488177 | ||||||||
\(936\) | 1598.42 | 0.0558184 | ||||||||
\(937\) | −49214.3 | −1.71586 | −0.857930 | − | 0.513767i | \(-0.828250\pi\) | ||||
−0.857930 | + | 0.513767i | \(0.828250\pi\) | |||||||
\(938\) | 14497.4 | 0.504643 | ||||||||
\(939\) | 18524.2 | 0.643785 | ||||||||
\(940\) | 11220.9 | 0.389348 | ||||||||
\(941\) | 8370.20 | 0.289969 | 0.144984 | − | 0.989434i | \(-0.453687\pi\) | ||||
0.144984 | + | 0.989434i | \(0.453687\pi\) | |||||||
\(942\) | 15278.2 | 0.528439 | ||||||||
\(943\) | 42183.1 | 1.45670 | ||||||||
\(944\) | −8594.66 | −0.296327 | ||||||||
\(945\) | −2140.71 | −0.0736903 | ||||||||
\(946\) | 34617.2 | 1.18975 | ||||||||
\(947\) | −31820.3 | −1.09189 | −0.545945 | − | 0.837821i | \(-0.683829\pi\) | ||||
−0.545945 | + | 0.837821i | \(0.683829\pi\) | |||||||
\(948\) | −2646.31 | −0.0906625 | ||||||||
\(949\) | 14736.5 | 0.504076 | ||||||||
\(950\) | 950.000 | 0.0324443 | ||||||||
\(951\) | 180.179 | 0.00614374 | ||||||||
\(952\) | 6980.10 | 0.237633 | ||||||||
\(953\) | −53391.9 | −1.81483 | −0.907415 | − | 0.420235i | \(-0.861948\pi\) | ||||
−0.907415 | + | 0.420235i | \(0.861948\pi\) | |||||||
\(954\) | 7743.17 | 0.262783 | ||||||||
\(955\) | −1066.54 | −0.0361387 | ||||||||
\(956\) | 10805.6 | 0.365564 | ||||||||
\(957\) | 7284.25 | 0.246046 | ||||||||
\(958\) | 4391.47 | 0.148102 | ||||||||
\(959\) | 29169.9 | 0.982217 | ||||||||
\(960\) | 960.000 | 0.0322749 | ||||||||
\(961\) | −29723.4 | −0.997731 | ||||||||
\(962\) | −10060.7 | −0.337182 | ||||||||
\(963\) | 8403.82 | 0.281214 | ||||||||
\(964\) | −20394.9 | −0.681405 | ||||||||
\(965\) | 432.909 | 0.0144413 | ||||||||
\(966\) | −14118.7 | −0.470249 | ||||||||
\(967\) | 12889.7 | 0.428650 | 0.214325 | − | 0.976762i | \(-0.431245\pi\) | ||||
0.214325 | + | 0.976762i | \(0.431245\pi\) | |||||||
\(968\) | 9941.39 | 0.330091 | ||||||||
\(969\) | −3136.34 | −0.103977 | ||||||||
\(970\) | 15520.9 | 0.513758 | ||||||||
\(971\) | −51052.1 | −1.68727 | −0.843636 | − | 0.536916i | \(-0.819589\pi\) | ||||
−0.843636 | + | 0.536916i | \(0.819589\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 48905.2 | 1.61133 | ||||||||
\(974\) | −3266.14 | −0.107448 | ||||||||
\(975\) | 1665.02 | 0.0546907 | ||||||||
\(976\) | −12283.7 | −0.402861 | ||||||||
\(977\) | −26920.8 | −0.881548 | −0.440774 | − | 0.897618i | \(-0.645296\pi\) | ||||
−0.440774 | + | 0.897618i | \(0.645296\pi\) | |||||||
\(978\) | 16592.2 | 0.542495 | ||||||||
\(979\) | −72460.9 | −2.36554 | ||||||||
\(980\) | −1831.04 | −0.0596840 | ||||||||
\(981\) | 16811.9 | 0.547158 | ||||||||
\(982\) | −17017.4 | −0.553002 | ||||||||
\(983\) | 10536.9 | 0.341886 | 0.170943 | − | 0.985281i | \(-0.445319\pi\) | ||||
0.170943 | + | 0.985281i | \(0.445319\pi\) | |||||||
\(984\) | 6822.32 | 0.221024 | ||||||||
\(985\) | −23474.4 | −0.759347 | ||||||||
\(986\) | −5267.01 | −0.170117 | ||||||||
\(987\) | −26689.8 | −0.860735 | ||||||||
\(988\) | 1687.22 | 0.0543297 | ||||||||
\(989\) | 50629.5 | 1.62783 | ||||||||
\(990\) | 4565.82 | 0.146577 | ||||||||
\(991\) | −14974.1 | −0.479987 | −0.239994 | − | 0.970774i | \(-0.577145\pi\) | ||||
−0.239994 | + | 0.970774i | \(0.577145\pi\) | |||||||
\(992\) | −263.110 | −0.00842112 | ||||||||
\(993\) | −16417.1 | −0.524653 | ||||||||
\(994\) | 898.528 | 0.0286716 | ||||||||
\(995\) | 21030.2 | 0.670054 | ||||||||
\(996\) | −3797.12 | −0.120800 | ||||||||
\(997\) | −26765.1 | −0.850210 | −0.425105 | − | 0.905144i | \(-0.639763\pi\) | ||||
−0.425105 | + | 0.905144i | \(0.639763\pi\) | |||||||
\(998\) | −11262.3 | −0.357217 | ||||||||
\(999\) | −6117.89 | −0.193755 |
(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 | 570.4.a.s.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 1710.4.a.bc.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.4.a.s.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1710.4.a.bc.1.1 | 4 | 3.2 | odd | 2 |