Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,6,Mod(1,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.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: | \(44.1055504486\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 352 x^{12} + 47255 x^{10} - 3018020 x^{8} + 93670492 x^{6} - 1312532272 x^{4} + \cdots - 10706454784 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-10.3818\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.3818 | −1.83526 | −0.917629 | − | 0.397438i | \(-0.869899\pi\) | ||||
−0.917629 | + | 0.397438i | \(0.869899\pi\) | |||||||
\(3\) | −3.25402 | −0.208745 | −0.104373 | − | 0.994538i | \(-0.533283\pi\) | ||||
−0.104373 | + | 0.994538i | \(0.533283\pi\) | |||||||
\(4\) | 75.7815 | 2.36817 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 33.7825 | 0.383102 | ||||||||
\(7\) | −50.5985 | −0.390294 | −0.195147 | − | 0.980774i | \(-0.562518\pi\) | ||||
−0.195147 | + | 0.980774i | \(0.562518\pi\) | |||||||
\(8\) | −454.530 | −2.51095 | ||||||||
\(9\) | −232.411 | −0.956425 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −246.594 | −0.494345 | ||||||||
\(13\) | −990.313 | −1.62523 | −0.812614 | − | 0.582803i | \(-0.801956\pi\) | ||||
−0.812614 | + | 0.582803i | \(0.801956\pi\) | |||||||
\(14\) | 525.303 | 0.716291 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2293.83 | 2.24007 | ||||||||
\(17\) | −427.441 | −0.358719 | −0.179359 | − | 0.983784i | \(-0.557402\pi\) | ||||
−0.179359 | + | 0.983784i | \(0.557402\pi\) | |||||||
\(18\) | 2412.85 | 1.75529 | ||||||||
\(19\) | 2338.79 | 1.48630 | 0.743150 | − | 0.669124i | \(-0.233331\pi\) | ||||
0.743150 | + | 0.669124i | \(0.233331\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 164.648 | 0.0814721 | ||||||||
\(22\) | 1256.20 | 0.553351 | ||||||||
\(23\) | −4201.10 | −1.65593 | −0.827967 | − | 0.560777i | \(-0.810502\pi\) | ||||
−0.827967 | + | 0.560777i | \(0.810502\pi\) | |||||||
\(24\) | 1479.05 | 0.524149 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10281.2 | 2.98271 | ||||||||
\(27\) | 1547.00 | 0.408395 | ||||||||
\(28\) | −3834.43 | −0.924284 | ||||||||
\(29\) | 1541.00 | 0.340257 | 0.170128 | − | 0.985422i | \(-0.445582\pi\) | ||||
0.170128 | + | 0.985422i | \(0.445582\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6335.60 | −1.18409 | −0.592044 | − | 0.805906i | \(-0.701679\pi\) | ||||
−0.592044 | + | 0.805906i | \(0.701679\pi\) | |||||||
\(32\) | −9269.08 | −1.60015 | ||||||||
\(33\) | 393.736 | 0.0629391 | ||||||||
\(34\) | 4437.60 | 0.658341 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17612.5 | −2.26498 | ||||||||
\(37\) | 1212.35 | 0.145587 | 0.0727935 | − | 0.997347i | \(-0.476809\pi\) | ||||
0.0727935 | + | 0.997347i | \(0.476809\pi\) | |||||||
\(38\) | −24280.8 | −2.72775 | ||||||||
\(39\) | 3222.50 | 0.339259 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14978.1 | −1.39154 | −0.695771 | − | 0.718264i | \(-0.744937\pi\) | ||||
−0.695771 | + | 0.718264i | \(0.744937\pi\) | |||||||
\(42\) | −1709.34 | −0.149522 | ||||||||
\(43\) | 1792.48 | 0.147837 | 0.0739185 | − | 0.997264i | \(-0.476450\pi\) | ||||
0.0739185 | + | 0.997264i | \(0.476450\pi\) | |||||||
\(44\) | −9169.56 | −0.714031 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 43614.9 | 3.03907 | ||||||||
\(47\) | 1669.75 | 0.110257 | 0.0551286 | − | 0.998479i | \(-0.482443\pi\) | ||||
0.0551286 | + | 0.998479i | \(0.482443\pi\) | |||||||
\(48\) | −7464.16 | −0.467604 | ||||||||
\(49\) | −14246.8 | −0.847670 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1390.90 | 0.0748808 | ||||||||
\(52\) | −75047.4 | −3.84882 | ||||||||
\(53\) | −11936.6 | −0.583702 | −0.291851 | − | 0.956464i | \(-0.594271\pi\) | ||||
−0.291851 | + | 0.956464i | \(0.594271\pi\) | |||||||
\(54\) | −16060.6 | −0.749510 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22998.5 | 0.980009 | ||||||||
\(57\) | −7610.45 | −0.310258 | ||||||||
\(58\) | −15998.3 | −0.624459 | ||||||||
\(59\) | −16390.0 | −0.612982 | −0.306491 | − | 0.951874i | \(-0.599155\pi\) | ||||
−0.306491 | + | 0.951874i | \(0.599155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6937.73 | −0.238722 | −0.119361 | − | 0.992851i | \(-0.538085\pi\) | ||||
−0.119361 | + | 0.992851i | \(0.538085\pi\) | |||||||
\(62\) | 65774.9 | 2.17311 | ||||||||
\(63\) | 11759.7 | 0.373287 | ||||||||
\(64\) | 22827.1 | 0.696627 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4087.68 | −0.115509 | ||||||||
\(67\) | −4862.12 | −0.132324 | −0.0661620 | − | 0.997809i | \(-0.521075\pi\) | ||||
−0.0661620 | + | 0.997809i | \(0.521075\pi\) | |||||||
\(68\) | −32392.1 | −0.849507 | ||||||||
\(69\) | 13670.4 | 0.345668 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −18827.8 | −0.443255 | −0.221628 | − | 0.975131i | \(-0.571137\pi\) | ||||
−0.221628 | + | 0.975131i | \(0.571137\pi\) | |||||||
\(72\) | 105638. | 2.40154 | ||||||||
\(73\) | 66194.3 | 1.45383 | 0.726914 | − | 0.686728i | \(-0.240954\pi\) | ||||
0.726914 | + | 0.686728i | \(0.240954\pi\) | |||||||
\(74\) | −12586.3 | −0.267190 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 177237. | 3.51982 | ||||||||
\(77\) | 6122.41 | 0.117678 | ||||||||
\(78\) | −33455.3 | −0.622627 | ||||||||
\(79\) | 83073.7 | 1.49760 | 0.748800 | − | 0.662796i | \(-0.230630\pi\) | ||||
0.748800 | + | 0.662796i | \(0.230630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 51442.0 | 0.871175 | ||||||||
\(82\) | 155499. | 2.55384 | ||||||||
\(83\) | −5982.11 | −0.0953145 | −0.0476573 | − | 0.998864i | \(-0.515176\pi\) | ||||
−0.0476573 | + | 0.998864i | \(0.515176\pi\) | |||||||
\(84\) | 12477.3 | 0.192940 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −18609.1 | −0.271319 | ||||||||
\(87\) | −5014.43 | −0.0710271 | ||||||||
\(88\) | 54998.2 | 0.757080 | ||||||||
\(89\) | 48499.0 | 0.649019 | 0.324510 | − | 0.945882i | \(-0.394801\pi\) | ||||
0.324510 | + | 0.945882i | \(0.394801\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50108.3 | 0.634317 | ||||||||
\(92\) | −318365. | −3.92154 | ||||||||
\(93\) | 20616.2 | 0.247173 | ||||||||
\(94\) | −17335.0 | −0.202351 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 30161.7 | 0.334025 | ||||||||
\(97\) | −109206. | −1.17847 | −0.589236 | − | 0.807961i | \(-0.700571\pi\) | ||||
−0.589236 | + | 0.807961i | \(0.700571\pi\) | |||||||
\(98\) | 147907. | 1.55569 | ||||||||
\(99\) | 28121.8 | 0.288373 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −82441.8 | −0.804163 | −0.402081 | − | 0.915604i | \(-0.631713\pi\) | ||||
−0.402081 | + | 0.915604i | \(0.631713\pi\) | |||||||
\(102\) | −14440.0 | −0.137426 | ||||||||
\(103\) | 166529. | 1.54666 | 0.773332 | − | 0.634001i | \(-0.218589\pi\) | ||||
0.773332 | + | 0.634001i | \(0.218589\pi\) | |||||||
\(104\) | 450127. | 4.08086 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 123923. | 1.07124 | ||||||||
\(107\) | 145595. | 1.22938 | 0.614690 | − | 0.788769i | \(-0.289281\pi\) | ||||
0.614690 | + | 0.788769i | \(0.289281\pi\) | |||||||
\(108\) | 117234. | 0.967149 | ||||||||
\(109\) | −227065. | −1.83056 | −0.915282 | − | 0.402814i | \(-0.868032\pi\) | ||||
−0.915282 | + | 0.402814i | \(0.868032\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3945.00 | −0.0303906 | ||||||||
\(112\) | −116064. | −0.874286 | ||||||||
\(113\) | −179567. | −1.32291 | −0.661454 | − | 0.749986i | \(-0.730060\pi\) | ||||
−0.661454 | + | 0.749986i | \(0.730060\pi\) | |||||||
\(114\) | 79010.1 | 0.569404 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 116779. | 0.805787 | ||||||||
\(117\) | 230160. | 1.55441 | ||||||||
\(118\) | 170157. | 1.12498 | ||||||||
\(119\) | 21627.9 | 0.140006 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 72026.0 | 0.438117 | ||||||||
\(123\) | 48738.9 | 0.290478 | ||||||||
\(124\) | −480122. | −2.80412 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −122086. | −0.685079 | ||||||||
\(127\) | 217036. | 1.19405 | 0.597026 | − | 0.802222i | \(-0.296349\pi\) | ||||
0.597026 | + | 0.802222i | \(0.296349\pi\) | |||||||
\(128\) | 59624.8 | 0.321664 | ||||||||
\(129\) | −5832.76 | −0.0308603 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −187469. | −0.954444 | −0.477222 | − | 0.878783i | \(-0.658356\pi\) | ||||
−0.477222 | + | 0.878783i | \(0.658356\pi\) | |||||||
\(132\) | 29837.9 | 0.149051 | ||||||||
\(133\) | −118339. | −0.580095 | ||||||||
\(134\) | 50477.5 | 0.242849 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 194285. | 0.900724 | ||||||||
\(137\) | 175520. | 0.798959 | 0.399479 | − | 0.916742i | \(-0.369191\pi\) | ||||
0.399479 | + | 0.916742i | \(0.369191\pi\) | |||||||
\(138\) | −141924. | −0.634391 | ||||||||
\(139\) | 343197. | 1.50663 | 0.753316 | − | 0.657659i | \(-0.228453\pi\) | ||||
0.753316 | + | 0.657659i | \(0.228453\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5433.40 | −0.0230157 | ||||||||
\(142\) | 195466. | 0.813488 | ||||||||
\(143\) | 119828. | 0.490024 | ||||||||
\(144\) | −533112. | −2.14246 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −687215. | −2.66815 | ||||||||
\(147\) | 46359.3 | 0.176947 | ||||||||
\(148\) | 91873.5 | 0.344775 | ||||||||
\(149\) | −307566. | −1.13494 | −0.567470 | − | 0.823394i | \(-0.692078\pi\) | ||||
−0.567470 | + | 0.823394i | \(0.692078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 355275. | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(152\) | −1.06305e6 | −3.73203 | ||||||||
\(153\) | 99342.1 | 0.343088 | ||||||||
\(154\) | −63561.6 | −0.215970 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 244206. | 0.803423 | ||||||||
\(157\) | 165270. | 0.535113 | 0.267557 | − | 0.963542i | \(-0.413784\pi\) | ||||
0.267557 | + | 0.963542i | \(0.413784\pi\) | |||||||
\(158\) | −862454. | −2.74848 | ||||||||
\(159\) | 38841.9 | 0.121845 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 212569. | 0.646302 | ||||||||
\(162\) | −534060. | −1.59883 | ||||||||
\(163\) | −379294. | −1.11817 | −0.559085 | − | 0.829111i | \(-0.688847\pi\) | ||||
−0.559085 | + | 0.829111i | \(0.688847\pi\) | |||||||
\(164\) | −1.13506e6 | −3.29541 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 62105.0 | 0.174927 | ||||||||
\(167\) | 32375.9 | 0.0898319 | 0.0449159 | − | 0.998991i | \(-0.485698\pi\) | ||||
0.0449159 | + | 0.998991i | \(0.485698\pi\) | |||||||
\(168\) | −74837.6 | −0.204572 | ||||||||
\(169\) | 609427. | 1.64136 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −543561. | −1.42154 | ||||||||
\(172\) | 135837. | 0.350103 | ||||||||
\(173\) | −50258.6 | −0.127672 | −0.0638360 | − | 0.997960i | \(-0.520333\pi\) | ||||
−0.0638360 | + | 0.997960i | \(0.520333\pi\) | |||||||
\(174\) | 52058.8 | 0.130353 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −277553. | −0.675406 | ||||||||
\(177\) | 53333.2 | 0.127957 | ||||||||
\(178\) | −503506. | −1.19112 | ||||||||
\(179\) | −384940. | −0.897967 | −0.448984 | − | 0.893540i | \(-0.648214\pi\) | ||||
−0.448984 | + | 0.893540i | \(0.648214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 724705. | 1.64424 | 0.822120 | − | 0.569315i | \(-0.192791\pi\) | ||||
0.822120 | + | 0.569315i | \(0.192791\pi\) | |||||||
\(182\) | −520214. | −1.16414 | ||||||||
\(183\) | 22575.5 | 0.0498321 | ||||||||
\(184\) | 1.90953e6 | 4.15797 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −214033. | −0.453626 | ||||||||
\(187\) | 51720.4 | 0.108158 | ||||||||
\(188\) | 126536. | 0.261108 | ||||||||
\(189\) | −78275.7 | −0.159394 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15927.2 | −0.0315905 | −0.0157952 | − | 0.999875i | \(-0.505028\pi\) | ||||
−0.0157952 | + | 0.999875i | \(0.505028\pi\) | |||||||
\(192\) | −74279.7 | −0.145418 | ||||||||
\(193\) | 492233. | 0.951212 | 0.475606 | − | 0.879658i | \(-0.342229\pi\) | ||||
0.475606 | + | 0.879658i | \(0.342229\pi\) | |||||||
\(194\) | 1.13376e6 | 2.16280 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.07964e6 | −2.00743 | ||||||||
\(197\) | 435505. | 0.799517 | 0.399758 | − | 0.916621i | \(-0.369094\pi\) | ||||
0.399758 | + | 0.916621i | \(0.369094\pi\) | |||||||
\(198\) | −291954. | −0.529239 | ||||||||
\(199\) | 590146. | 1.05640 | 0.528198 | − | 0.849121i | \(-0.322868\pi\) | ||||
0.528198 | + | 0.849121i | \(0.322868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15821.4 | 0.0276220 | ||||||||
\(202\) | 855893. | 1.47585 | ||||||||
\(203\) | −77972.1 | −0.132800 | ||||||||
\(204\) | 105405. | 0.177331 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.72887e6 | −2.83853 | ||||||||
\(207\) | 976382. | 1.58378 | ||||||||
\(208\) | −2.27161e6 | −3.64062 | ||||||||
\(209\) | −282993. | −0.448137 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 218014. | 0.337116 | 0.168558 | − | 0.985692i | \(-0.446089\pi\) | ||||
0.168558 | + | 0.985692i | \(0.446089\pi\) | |||||||
\(212\) | −904575. | −1.38231 | ||||||||
\(213\) | 61266.0 | 0.0925275 | ||||||||
\(214\) | −1.51153e6 | −2.25623 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −703157. | −1.02546 | ||||||||
\(217\) | 320572. | 0.462142 | ||||||||
\(218\) | 2.35735e6 | 3.35956 | ||||||||
\(219\) | −215397. | −0.303480 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 423300. | 0.582999 | ||||||||
\(222\) | 40956.1 | 0.0557746 | ||||||||
\(223\) | 614763. | 0.827838 | 0.413919 | − | 0.910314i | \(-0.364160\pi\) | ||||
0.413919 | + | 0.910314i | \(0.364160\pi\) | |||||||
\(224\) | 469001. | 0.624531 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.86422e6 | 2.42788 | ||||||||
\(227\) | −1.07088e6 | −1.37935 | −0.689675 | − | 0.724119i | \(-0.742247\pi\) | ||||
−0.689675 | + | 0.724119i | \(0.742247\pi\) | |||||||
\(228\) | −576732. | −0.734745 | ||||||||
\(229\) | −134715. | −0.169757 | −0.0848784 | − | 0.996391i | \(-0.527050\pi\) | ||||
−0.0848784 | + | 0.996391i | \(0.527050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19922.4 | −0.0245648 | ||||||||
\(232\) | −700430. | −0.854368 | ||||||||
\(233\) | 17916.1 | 0.0216199 | 0.0108099 | − | 0.999942i | \(-0.496559\pi\) | ||||
0.0108099 | + | 0.999942i | \(0.496559\pi\) | |||||||
\(234\) | −2.38947e6 | −2.85274 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.24206e6 | −1.45165 | ||||||||
\(237\) | −270323. | −0.312617 | ||||||||
\(238\) | −224536. | −0.256947 | ||||||||
\(239\) | 878276. | 0.994572 | 0.497286 | − | 0.867587i | \(-0.334330\pi\) | ||||
0.497286 | + | 0.867587i | \(0.334330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 480494. | 0.532900 | 0.266450 | − | 0.963849i | \(-0.414149\pi\) | ||||
0.266450 | + | 0.963849i | \(0.414149\pi\) | |||||||
\(242\) | −152000. | −0.166842 | ||||||||
\(243\) | −543313. | −0.590248 | ||||||||
\(244\) | −525751. | −0.565335 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −505997. | −0.533102 | ||||||||
\(247\) | −2.31613e6 | −2.41558 | ||||||||
\(248\) | 2.87972e6 | 2.97318 | ||||||||
\(249\) | 19465.9 | 0.0198965 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −873829. | −0.875472 | −0.437736 | − | 0.899104i | \(-0.644220\pi\) | ||||
−0.437736 | + | 0.899104i | \(0.644220\pi\) | |||||||
\(252\) | 891165. | 0.884009 | ||||||||
\(253\) | 508333. | 0.499283 | ||||||||
\(254\) | −2.25322e6 | −2.19139 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.34948e6 | −1.28696 | ||||||||
\(257\) | 1.69731e6 | 1.60298 | 0.801491 | − | 0.598007i | \(-0.204040\pi\) | ||||
0.801491 | + | 0.598007i | \(0.204040\pi\) | |||||||
\(258\) | 60554.5 | 0.0566366 | ||||||||
\(259\) | −61342.9 | −0.0568218 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −358145. | −0.325430 | ||||||||
\(262\) | 1.94626e6 | 1.75165 | ||||||||
\(263\) | 793063. | 0.706998 | 0.353499 | − | 0.935435i | \(-0.384992\pi\) | ||||
0.353499 | + | 0.935435i | \(0.384992\pi\) | |||||||
\(264\) | −178965. | −0.158037 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.22857e6 | 1.06462 | ||||||||
\(267\) | −157817. | −0.135480 | ||||||||
\(268\) | −368459. | −0.313366 | ||||||||
\(269\) | 641402. | 0.540442 | 0.270221 | − | 0.962798i | \(-0.412903\pi\) | ||||
0.270221 | + | 0.962798i | \(0.412903\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 678036. | 0.560828 | 0.280414 | − | 0.959879i | \(-0.409528\pi\) | ||||
0.280414 | + | 0.959879i | \(0.409528\pi\) | |||||||
\(272\) | −980477. | −0.803554 | ||||||||
\(273\) | −163053. | −0.132411 | ||||||||
\(274\) | −1.82221e6 | −1.46630 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.03597e6 | 0.818602 | ||||||||
\(277\) | 1.79159e6 | 1.40294 | 0.701469 | − | 0.712700i | \(-0.252528\pi\) | ||||
0.701469 | + | 0.712700i | \(0.252528\pi\) | |||||||
\(278\) | −3.56300e6 | −2.76506 | ||||||||
\(279\) | 1.47247e6 | 1.13249 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −199237. | −0.150524 | −0.0752619 | − | 0.997164i | \(-0.523979\pi\) | ||||
−0.0752619 | + | 0.997164i | \(0.523979\pi\) | |||||||
\(282\) | 56408.4 | 0.0422397 | ||||||||
\(283\) | −8539.72 | −0.00633837 | −0.00316918 | − | 0.999995i | \(-0.501009\pi\) | ||||
−0.00316918 | + | 0.999995i | \(0.501009\pi\) | |||||||
\(284\) | −1.42680e6 | −1.04971 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.24403e6 | −0.899321 | ||||||||
\(287\) | 757868. | 0.543111 | ||||||||
\(288\) | 2.15424e6 | 1.53043 | ||||||||
\(289\) | −1.23715e6 | −0.871321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 355360. | 0.246000 | ||||||||
\(292\) | 5.01630e6 | 3.44292 | ||||||||
\(293\) | 1.35528e6 | 0.922277 | 0.461139 | − | 0.887328i | \(-0.347441\pi\) | ||||
0.461139 | + | 0.887328i | \(0.347441\pi\) | |||||||
\(294\) | −481293. | −0.324744 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −551049. | −0.365562 | ||||||||
\(297\) | −187187. | −0.123136 | ||||||||
\(298\) | 3.19309e6 | 2.08291 | ||||||||
\(299\) | 4.16040e6 | 2.69127 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −90696.7 | −0.0576999 | ||||||||
\(302\) | −3.68839e6 | −2.32712 | ||||||||
\(303\) | 268267. | 0.167865 | ||||||||
\(304\) | 5.36478e6 | 3.32942 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.03135e6 | −0.629654 | ||||||||
\(307\) | −1.04893e6 | −0.635183 | −0.317592 | − | 0.948228i | \(-0.602874\pi\) | ||||
−0.317592 | + | 0.948228i | \(0.602874\pi\) | |||||||
\(308\) | 463966. | 0.278682 | ||||||||
\(309\) | −541887. | −0.322859 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 540559. | 0.316915 | 0.158457 | − | 0.987366i | \(-0.449348\pi\) | ||||
0.158457 | + | 0.987366i | \(0.449348\pi\) | |||||||
\(312\) | −1.46472e6 | −0.851861 | ||||||||
\(313\) | −1.13973e6 | −0.657569 | −0.328784 | − | 0.944405i | \(-0.606639\pi\) | ||||
−0.328784 | + | 0.944405i | \(0.606639\pi\) | |||||||
\(314\) | −1.71580e6 | −0.982071 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.29545e6 | 3.54658 | ||||||||
\(317\) | 1.80634e6 | 1.00961 | 0.504803 | − | 0.863235i | \(-0.331565\pi\) | ||||
0.504803 | + | 0.863235i | \(0.331565\pi\) | |||||||
\(318\) | −403249. | −0.223617 | ||||||||
\(319\) | −186461. | −0.102591 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −473768. | −0.256627 | ||||||||
\(322\) | −2.20685e6 | −1.18613 | ||||||||
\(323\) | −999694. | −0.533164 | ||||||||
\(324\) | 3.89835e6 | 2.06309 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.93775e6 | 2.05213 | ||||||||
\(327\) | 738875. | 0.382122 | ||||||||
\(328\) | 6.80799e6 | 3.49409 | ||||||||
\(329\) | −84486.9 | −0.0430328 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.76943e6 | −1.89106 | −0.945531 | − | 0.325533i | \(-0.894456\pi\) | ||||
−0.945531 | + | 0.325533i | \(0.894456\pi\) | |||||||
\(332\) | −453333. | −0.225721 | ||||||||
\(333\) | −281763. | −0.139243 | ||||||||
\(334\) | −336120. | −0.164865 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 377675. | 0.182503 | ||||||||
\(337\) | −4.09543e6 | −1.96438 | −0.982189 | − | 0.187898i | \(-0.939833\pi\) | ||||
−0.982189 | + | 0.187898i | \(0.939833\pi\) | |||||||
\(338\) | −6.32694e6 | −3.01233 | ||||||||
\(339\) | 584313. | 0.276151 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 766608. | 0.357016 | ||||||||
\(342\) | 5.64313e6 | 2.60889 | ||||||||
\(343\) | 1.57127e6 | 0.721135 | ||||||||
\(344\) | −814736. | −0.371211 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 521774. | 0.234311 | ||||||||
\(347\) | −590909. | −0.263449 | −0.131725 | − | 0.991286i | \(-0.542051\pi\) | ||||
−0.131725 | + | 0.991286i | \(0.542051\pi\) | |||||||
\(348\) | −380001. | −0.168204 | ||||||||
\(349\) | 3.61334e6 | 1.58798 | 0.793991 | − | 0.607930i | \(-0.208000\pi\) | ||||
0.793991 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.53201e6 | −0.663734 | ||||||||
\(352\) | 1.12156e6 | 0.482464 | ||||||||
\(353\) | −3.14648e6 | −1.34396 | −0.671982 | − | 0.740567i | \(-0.734557\pi\) | ||||
−0.671982 | + | 0.740567i | \(0.734557\pi\) | |||||||
\(354\) | −553694. | −0.234834 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.67533e6 | 1.53699 | ||||||||
\(357\) | −70377.4 | −0.0292256 | ||||||||
\(358\) | 3.99637e6 | 1.64800 | ||||||||
\(359\) | −1.08362e6 | −0.443754 | −0.221877 | − | 0.975075i | \(-0.571218\pi\) | ||||
−0.221877 | + | 0.975075i | \(0.571218\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.99383e6 | 1.20909 | ||||||||
\(362\) | −7.52374e6 | −3.01760 | ||||||||
\(363\) | −47642.1 | −0.0189768 | ||||||||
\(364\) | 3.79728e6 | 1.50217 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −234374. | −0.0914548 | ||||||||
\(367\) | −3.15625e6 | −1.22322 | −0.611612 | − | 0.791158i | \(-0.709479\pi\) | ||||
−0.611612 | + | 0.791158i | \(0.709479\pi\) | |||||||
\(368\) | −9.63660e6 | −3.70940 | ||||||||
\(369\) | 3.48108e6 | 1.33091 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 603974. | 0.227816 | ||||||||
\(372\) | 1.56232e6 | 0.585347 | ||||||||
\(373\) | −2.03193e6 | −0.756202 | −0.378101 | − | 0.925764i | \(-0.623423\pi\) | ||||
−0.378101 | + | 0.925764i | \(0.623423\pi\) | |||||||
\(374\) | −536950. | −0.198497 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −758953. | −0.276850 | ||||||||
\(377\) | −1.52607e6 | −0.552995 | ||||||||
\(378\) | 812641. | 0.292529 | ||||||||
\(379\) | −998682. | −0.357132 | −0.178566 | − | 0.983928i | \(-0.557146\pi\) | ||||
−0.178566 | + | 0.983928i | \(0.557146\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −706240. | −0.249253 | ||||||||
\(382\) | 165353. | 0.0579767 | ||||||||
\(383\) | −1.89593e6 | −0.660427 | −0.330214 | − | 0.943906i | \(-0.607121\pi\) | ||||
−0.330214 | + | 0.943906i | \(0.607121\pi\) | |||||||
\(384\) | −194020. | −0.0671458 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.11026e6 | −1.74572 | ||||||||
\(387\) | −416593. | −0.141395 | ||||||||
\(388\) | −8.27583e6 | −2.79082 | ||||||||
\(389\) | −1.84597e6 | −0.618514 | −0.309257 | − | 0.950978i | \(-0.600080\pi\) | ||||
−0.309257 | + | 0.950978i | \(0.600080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.79572e6 | 0.594014 | ||||||||
\(392\) | 6.47560e6 | 2.12846 | ||||||||
\(393\) | 610026. | 0.199236 | ||||||||
\(394\) | −4.52132e6 | −1.46732 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.13111e6 | 0.682917 | ||||||||
\(397\) | −180968. | −0.0576270 | −0.0288135 | − | 0.999585i | \(-0.509173\pi\) | ||||
−0.0288135 | + | 0.999585i | \(0.509173\pi\) | |||||||
\(398\) | −6.12677e6 | −1.93876 | ||||||||
\(399\) | 385077. | 0.121092 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.73198e6 | 1.15899 | 0.579493 | − | 0.814978i | \(-0.303251\pi\) | ||||
0.579493 | + | 0.814978i | \(0.303251\pi\) | |||||||
\(402\) | −164255. | −0.0506936 | ||||||||
\(403\) | 6.27423e6 | 1.92441 | ||||||||
\(404\) | −6.24756e6 | −1.90440 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 809490. | 0.243723 | ||||||||
\(407\) | −146694. | −0.0438961 | ||||||||
\(408\) | −632206. | −0.188022 | ||||||||
\(409\) | −2.93967e6 | −0.868940 | −0.434470 | − | 0.900686i | \(-0.643064\pi\) | ||||
−0.434470 | + | 0.900686i | \(0.643064\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −571144. | −0.166779 | ||||||||
\(412\) | 1.26198e7 | 3.66277 | ||||||||
\(413\) | 829307. | 0.239243 | ||||||||
\(414\) | −1.01366e7 | −2.90664 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.17929e6 | 2.60061 | ||||||||
\(417\) | −1.11677e6 | −0.314502 | ||||||||
\(418\) | 2.93798e6 | 0.822446 | ||||||||
\(419\) | −2.38197e6 | −0.662830 | −0.331415 | − | 0.943485i | \(-0.607526\pi\) | ||||
−0.331415 | + | 0.943485i | \(0.607526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −663533. | −0.182456 | −0.0912279 | − | 0.995830i | \(-0.529079\pi\) | ||||
−0.0912279 | + | 0.995830i | \(0.529079\pi\) | |||||||
\(422\) | −2.26338e6 | −0.618694 | ||||||||
\(423\) | −388069. | −0.105453 | ||||||||
\(424\) | 5.42555e6 | 1.46565 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −636051. | −0.169812 | ||||||||
\(427\) | 351038. | 0.0931719 | ||||||||
\(428\) | 1.10334e7 | 2.91138 | ||||||||
\(429\) | −389922. | −0.102290 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.80832e6 | −0.468903 | −0.234451 | − | 0.972128i | \(-0.575329\pi\) | ||||
−0.234451 | + | 0.972128i | \(0.575329\pi\) | |||||||
\(432\) | 3.54855e6 | 0.914832 | ||||||||
\(433\) | −6.02055e6 | −1.54318 | −0.771590 | − | 0.636121i | \(-0.780538\pi\) | ||||
−0.771590 | + | 0.636121i | \(0.780538\pi\) | |||||||
\(434\) | −3.32811e6 | −0.848151 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.72074e7 | −4.33509 | ||||||||
\(437\) | −9.82547e6 | −2.46122 | ||||||||
\(438\) | 2.23621e6 | 0.556964 | ||||||||
\(439\) | −3.14357e6 | −0.778507 | −0.389253 | − | 0.921131i | \(-0.627267\pi\) | ||||
−0.389253 | + | 0.921131i | \(0.627267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.31112e6 | 0.810733 | ||||||||
\(442\) | −4.39461e6 | −1.06995 | ||||||||
\(443\) | −5.58480e6 | −1.35207 | −0.676034 | − | 0.736871i | \(-0.736303\pi\) | ||||
−0.676034 | + | 0.736871i | \(0.736303\pi\) | |||||||
\(444\) | −298958. | −0.0719702 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.38234e6 | −1.51930 | ||||||||
\(447\) | 1.00083e6 | 0.236913 | ||||||||
\(448\) | −1.15501e6 | −0.271889 | ||||||||
\(449\) | 7.04017e6 | 1.64804 | 0.824019 | − | 0.566562i | \(-0.191727\pi\) | ||||
0.824019 | + | 0.566562i | \(0.191727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.81235e6 | 0.419566 | ||||||||
\(452\) | −1.36078e7 | −3.13287 | ||||||||
\(453\) | −1.15607e6 | −0.264691 | ||||||||
\(454\) | 1.11176e7 | 2.53146 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.45918e6 | 0.779043 | ||||||||
\(457\) | 249299. | 0.0558379 | 0.0279190 | − | 0.999610i | \(-0.491112\pi\) | ||||
0.0279190 | + | 0.999610i | \(0.491112\pi\) | |||||||
\(458\) | 1.39858e6 | 0.311548 | ||||||||
\(459\) | −661250. | −0.146499 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.02575e6 | 1.53971 | 0.769857 | − | 0.638216i | \(-0.220327\pi\) | ||||
0.769857 | + | 0.638216i | \(0.220327\pi\) | |||||||
\(462\) | 206831. | 0.0450827 | ||||||||
\(463\) | 200249. | 0.0434127 | 0.0217064 | − | 0.999764i | \(-0.493090\pi\) | ||||
0.0217064 | + | 0.999764i | \(0.493090\pi\) | |||||||
\(464\) | 3.53479e6 | 0.762199 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −186001. | −0.0396780 | ||||||||
\(467\) | −2.10125e6 | −0.445847 | −0.222923 | − | 0.974836i | \(-0.571560\pi\) | ||||
−0.222923 | + | 0.974836i | \(0.571560\pi\) | |||||||
\(468\) | 1.74419e7 | 3.68111 | ||||||||
\(469\) | 246016. | 0.0516453 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −537792. | −0.111702 | ||||||||
\(472\) | 7.44973e6 | 1.53917 | ||||||||
\(473\) | −216890. | −0.0445745 | ||||||||
\(474\) | 2.80644e6 | 0.573733 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.63899e6 | 0.331558 | ||||||||
\(477\) | 2.77420e6 | 0.558268 | ||||||||
\(478\) | −9.11808e6 | −1.82530 | ||||||||
\(479\) | −303525. | −0.0604443 | −0.0302222 | − | 0.999543i | \(-0.509621\pi\) | ||||
−0.0302222 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.20060e6 | −0.236612 | ||||||||
\(482\) | −4.98839e6 | −0.978008 | ||||||||
\(483\) | −691703. | −0.134912 | ||||||||
\(484\) | 1.10952e6 | 0.215288 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.64056e6 | 1.08326 | ||||||||
\(487\) | 847330. | 0.161894 | 0.0809469 | − | 0.996718i | \(-0.474206\pi\) | ||||
0.0809469 | + | 0.996718i | \(0.474206\pi\) | |||||||
\(488\) | 3.15341e6 | 0.599419 | ||||||||
\(489\) | 1.23423e6 | 0.233413 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.46005e6 | 0.647708 | 0.323854 | − | 0.946107i | \(-0.395021\pi\) | ||||
0.323854 | + | 0.946107i | \(0.395021\pi\) | |||||||
\(492\) | 3.69351e6 | 0.687902 | ||||||||
\(493\) | −658686. | −0.122057 | ||||||||
\(494\) | 2.40456e7 | 4.43321 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.45328e7 | −2.65244 | ||||||||
\(497\) | 952659. | 0.173000 | ||||||||
\(498\) | −202091. | −0.0365151 | ||||||||
\(499\) | 3.44516e6 | 0.619381 | 0.309691 | − | 0.950837i | \(-0.399775\pi\) | ||||
0.309691 | + | 0.950837i | \(0.399775\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −105352. | −0.0187520 | ||||||||
\(502\) | 9.07191e6 | 1.60672 | ||||||||
\(503\) | −5.30250e6 | −0.934459 | −0.467230 | − | 0.884136i | \(-0.654748\pi\) | ||||
−0.467230 | + | 0.884136i | \(0.654748\pi\) | |||||||
\(504\) | −5.34512e6 | −0.937306 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.27740e6 | −0.916313 | ||||||||
\(507\) | −1.98309e6 | −0.342627 | ||||||||
\(508\) | 1.64473e7 | 2.82772 | ||||||||
\(509\) | −1.18529e6 | −0.202783 | −0.101391 | − | 0.994847i | \(-0.532329\pi\) | ||||
−0.101391 | + | 0.994847i | \(0.532329\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.34933e6 | −0.567421 | ||||||||
\(512\) | 1.21020e7 | 2.04024 | ||||||||
\(513\) | 3.61810e6 | 0.606997 | ||||||||
\(514\) | −1.76211e7 | −2.94189 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −442015. | −0.0730824 | ||||||||
\(517\) | −202040. | −0.0332438 | ||||||||
\(518\) | 636849. | 0.104283 | ||||||||
\(519\) | 163542. | 0.0266509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.10974e6 | −1.47032 | −0.735159 | − | 0.677894i | \(-0.762893\pi\) | ||||
−0.735159 | + | 0.677894i | \(0.762893\pi\) | |||||||
\(522\) | 3.71819e6 | 0.597249 | ||||||||
\(523\) | 6.68845e6 | 1.06923 | 0.534615 | − | 0.845096i | \(-0.320457\pi\) | ||||
0.534615 | + | 0.845096i | \(0.320457\pi\) | |||||||
\(524\) | −1.42067e7 | −2.26029 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.23341e6 | −1.29752 | ||||||||
\(527\) | 2.70810e6 | 0.424754 | ||||||||
\(528\) | 903164. | 0.140988 | ||||||||
\(529\) | 1.12129e7 | 1.74212 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.80921e6 | 0.586272 | ||||||||
\(532\) | −8.96791e6 | −1.37376 | ||||||||
\(533\) | 1.48330e7 | 2.26157 | ||||||||
\(534\) | 1.63842e6 | 0.248640 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.20998e6 | 0.332259 | ||||||||
\(537\) | 1.25260e6 | 0.187446 | ||||||||
\(538\) | −6.65890e6 | −0.991851 | ||||||||
\(539\) | 1.72386e6 | 0.255582 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.79737e6 | −0.851605 | −0.425802 | − | 0.904816i | \(-0.640008\pi\) | ||||
−0.425802 | + | 0.904816i | \(0.640008\pi\) | |||||||
\(542\) | −7.03923e6 | −1.02926 | ||||||||
\(543\) | −2.35820e6 | −0.343227 | ||||||||
\(544\) | 3.96198e6 | 0.574005 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.69279e6 | 0.243008 | ||||||||
\(547\) | 1.31793e7 | 1.88332 | 0.941660 | − | 0.336566i | \(-0.109266\pi\) | ||||
0.941660 | + | 0.336566i | \(0.109266\pi\) | |||||||
\(548\) | 1.33011e7 | 1.89207 | ||||||||
\(549\) | 1.61241e6 | 0.228320 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.60407e6 | 0.505724 | ||||||||
\(552\) | −6.21363e6 | −0.867956 | ||||||||
\(553\) | −4.20340e6 | −0.584505 | ||||||||
\(554\) | −1.85999e7 | −2.57476 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.60080e7 | 3.56796 | ||||||||
\(557\) | 3.17990e6 | 0.434286 | 0.217143 | − | 0.976140i | \(-0.430326\pi\) | ||||
0.217143 | + | 0.976140i | \(0.430326\pi\) | |||||||
\(558\) | −1.52868e7 | −2.07841 | ||||||||
\(559\) | −1.77512e6 | −0.240269 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −168299. | −0.0225774 | ||||||||
\(562\) | 2.06844e6 | 0.276250 | ||||||||
\(563\) | −5.49194e6 | −0.730222 | −0.365111 | − | 0.930964i | \(-0.618969\pi\) | ||||
−0.365111 | + | 0.930964i | \(0.618969\pi\) | |||||||
\(564\) | −411751. | −0.0545051 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 88657.6 | 0.0116325 | ||||||||
\(567\) | −2.60289e6 | −0.340015 | ||||||||
\(568\) | 8.55782e6 | 1.11299 | ||||||||
\(569\) | −2.24494e6 | −0.290686 | −0.145343 | − | 0.989381i | \(-0.546429\pi\) | ||||
−0.145343 | + | 0.989381i | \(0.546429\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.92316e6 | −0.760262 | −0.380131 | − | 0.924933i | \(-0.624121\pi\) | ||||
−0.380131 | + | 0.924933i | \(0.624121\pi\) | |||||||
\(572\) | 9.08074e6 | 1.16046 | ||||||||
\(573\) | 51827.4 | 0.00659436 | ||||||||
\(574\) | −7.86802e6 | −0.996749 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.30527e6 | −0.666272 | ||||||||
\(577\) | −1.72233e6 | −0.215366 | −0.107683 | − | 0.994185i | \(-0.534343\pi\) | ||||
−0.107683 | + | 0.994185i | \(0.534343\pi\) | |||||||
\(578\) | 1.28438e7 | 1.59910 | ||||||||
\(579\) | −1.60173e6 | −0.198561 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 302686. | 0.0372007 | ||||||||
\(582\) | −3.68927e6 | −0.451474 | ||||||||
\(583\) | 1.44433e6 | 0.175993 | ||||||||
\(584\) | −3.00873e7 | −3.65049 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.40703e7 | −1.69262 | ||||||||
\(587\) | −4.01191e6 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(588\) | 3.51318e6 | 0.419041 | ||||||||
\(589\) | −1.48176e7 | −1.75991 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.41714e6 | −0.166895 | ||||||||
\(592\) | 2.78092e6 | 0.326125 | ||||||||
\(593\) | −1.81663e6 | −0.212143 | −0.106072 | − | 0.994358i | \(-0.533827\pi\) | ||||
−0.106072 | + | 0.994358i | \(0.533827\pi\) | |||||||
\(594\) | 1.94333e6 | 0.225986 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.33078e7 | −2.68773 | ||||||||
\(597\) | −1.92035e6 | −0.220518 | ||||||||
\(598\) | −4.31924e7 | −4.93917 | ||||||||
\(599\) | −7.43101e6 | −0.846215 | −0.423108 | − | 0.906079i | \(-0.639061\pi\) | ||||
−0.423108 | + | 0.906079i | \(0.639061\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.83570e6 | −0.320239 | −0.160119 | − | 0.987098i | \(-0.551188\pi\) | ||||
−0.160119 | + | 0.987098i | \(0.551188\pi\) | |||||||
\(602\) | 941594. | 0.105894 | ||||||||
\(603\) | 1.13001e6 | 0.126558 | ||||||||
\(604\) | 2.69232e7 | 3.00286 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.78509e6 | −0.308076 | ||||||||
\(607\) | −1.58704e7 | −1.74830 | −0.874151 | − | 0.485654i | \(-0.838581\pi\) | ||||
−0.874151 | + | 0.485654i | \(0.838581\pi\) | |||||||
\(608\) | −2.16784e7 | −2.37831 | ||||||||
\(609\) | 253723. | 0.0277215 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.65358e6 | −0.179193 | ||||||||
\(612\) | 7.52830e6 | 0.812490 | ||||||||
\(613\) | −1.07890e6 | −0.115965 | −0.0579827 | − | 0.998318i | \(-0.518467\pi\) | ||||
−0.0579827 | + | 0.998318i | \(0.518467\pi\) | |||||||
\(614\) | 1.08897e7 | 1.16573 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.78282e6 | −0.295484 | ||||||||
\(617\) | 4.90715e6 | 0.518940 | 0.259470 | − | 0.965751i | \(-0.416452\pi\) | ||||
0.259470 | + | 0.965751i | \(0.416452\pi\) | |||||||
\(618\) | 5.62576e6 | 0.592529 | ||||||||
\(619\) | 6.37999e6 | 0.669258 | 0.334629 | − | 0.942350i | \(-0.391389\pi\) | ||||
0.334629 | + | 0.942350i | \(0.391389\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.49908e6 | −0.676274 | ||||||||
\(622\) | −5.61197e6 | −0.581620 | ||||||||
\(623\) | −2.45397e6 | −0.253308 | ||||||||
\(624\) | 7.39186e6 | 0.759962 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.18324e7 | 1.20681 | ||||||||
\(627\) | 920865. | 0.0935464 | ||||||||
\(628\) | 1.25244e7 | 1.26724 | ||||||||
\(629\) | −518207. | −0.0522248 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.34499e6 | −0.434426 | −0.217213 | − | 0.976124i | \(-0.569697\pi\) | ||||
−0.217213 | + | 0.976124i | \(0.569697\pi\) | |||||||
\(632\) | −3.77595e7 | −3.76040 | ||||||||
\(633\) | −709422. | −0.0703713 | ||||||||
\(634\) | −1.87530e7 | −1.85289 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.94350e6 | 0.288550 | ||||||||
\(637\) | 1.41088e7 | 1.37766 | ||||||||
\(638\) | 1.93580e6 | 0.188282 | ||||||||
\(639\) | 4.37580e6 | 0.423941 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.84166e7 | 1.77037 | 0.885184 | − | 0.465241i | \(-0.154032\pi\) | ||||
0.885184 | + | 0.465241i | \(0.154032\pi\) | |||||||
\(642\) | 4.91856e6 | 0.470977 | ||||||||
\(643\) | −8.94487e6 | −0.853192 | −0.426596 | − | 0.904442i | \(-0.640287\pi\) | ||||
−0.426596 | + | 0.904442i | \(0.640287\pi\) | |||||||
\(644\) | 1.61088e7 | 1.53055 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.03786e7 | 0.978493 | ||||||||
\(647\) | 7.92058e6 | 0.743869 | 0.371934 | − | 0.928259i | \(-0.378695\pi\) | ||||
0.371934 | + | 0.928259i | \(0.378695\pi\) | |||||||
\(648\) | −2.33820e7 | −2.18748 | ||||||||
\(649\) | 1.98319e6 | 0.184821 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.04315e6 | −0.0964701 | ||||||||
\(652\) | −2.87435e7 | −2.64802 | ||||||||
\(653\) | 1.28235e7 | 1.17685 | 0.588426 | − | 0.808551i | \(-0.299748\pi\) | ||||
0.588426 | + | 0.808551i | \(0.299748\pi\) | |||||||
\(654\) | −7.67084e6 | −0.701292 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.43572e7 | −3.11715 | ||||||||
\(657\) | −1.53843e7 | −1.39048 | ||||||||
\(658\) | 877125. | 0.0789763 | ||||||||
\(659\) | −4.40034e6 | −0.394705 | −0.197353 | − | 0.980333i | \(-0.563234\pi\) | ||||
−0.197353 | + | 0.980333i | \(0.563234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.25957e6 | 0.112129 | 0.0560647 | − | 0.998427i | \(-0.482145\pi\) | ||||
0.0560647 | + | 0.998427i | \(0.482145\pi\) | |||||||
\(662\) | 3.91334e7 | 3.47059 | ||||||||
\(663\) | −1.37743e6 | −0.121698 | ||||||||
\(664\) | 2.71905e6 | 0.239330 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.92521e6 | 0.255547 | ||||||||
\(667\) | −6.47388e6 | −0.563443 | ||||||||
\(668\) | 2.45349e6 | 0.212737 | ||||||||
\(669\) | −2.00045e6 | −0.172807 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 839465. | 0.0719774 | ||||||||
\(672\) | −1.52614e6 | −0.130368 | ||||||||
\(673\) | 304612. | 0.0259244 | 0.0129622 | − | 0.999916i | \(-0.495874\pi\) | ||||
0.0129622 | + | 0.999916i | \(0.495874\pi\) | |||||||
\(674\) | 4.25179e7 | 3.60514 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.61833e7 | 3.88703 | ||||||||
\(677\) | 3.54969e6 | 0.297659 | 0.148829 | − | 0.988863i | \(-0.452449\pi\) | ||||
0.148829 | + | 0.988863i | \(0.452449\pi\) | |||||||
\(678\) | −6.06621e6 | −0.506808 | ||||||||
\(679\) | 5.52568e6 | 0.459951 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.48465e6 | 0.287933 | ||||||||
\(682\) | −7.95876e6 | −0.655216 | ||||||||
\(683\) | 1.80415e7 | 1.47986 | 0.739932 | − | 0.672681i | \(-0.234858\pi\) | ||||
0.739932 | + | 0.672681i | \(0.234858\pi\) | |||||||
\(684\) | −4.11919e7 | −3.36644 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.63126e7 | −1.32347 | ||||||||
\(687\) | 438365. | 0.0354359 | ||||||||
\(688\) | 4.11164e6 | 0.331165 | ||||||||
\(689\) | 1.18210e7 | 0.948649 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.76063e7 | 1.40273 | 0.701365 | − | 0.712802i | \(-0.252574\pi\) | ||||
0.701365 | + | 0.712802i | \(0.252574\pi\) | |||||||
\(692\) | −3.80868e6 | −0.302349 | ||||||||
\(693\) | −1.42292e6 | −0.112550 | ||||||||
\(694\) | 6.13469e6 | 0.483497 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.27921e6 | 0.178345 | ||||||||
\(697\) | 6.40224e6 | 0.499172 | ||||||||
\(698\) | −3.75129e7 | −2.91436 | ||||||||
\(699\) | −58299.2 | −0.00451304 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.97597e6 | −0.459318 | −0.229659 | − | 0.973271i | \(-0.573761\pi\) | ||||
−0.229659 | + | 0.973271i | \(0.573761\pi\) | |||||||
\(702\) | 1.59050e7 | 1.21812 | ||||||||
\(703\) | 2.83542e6 | 0.216386 | ||||||||
\(704\) | −2.76208e6 | −0.210041 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.26660e7 | 2.46652 | ||||||||
\(707\) | 4.17143e6 | 0.313860 | ||||||||
\(708\) | 4.04167e6 | 0.303025 | ||||||||
\(709\) | 4.89639e6 | 0.365814 | 0.182907 | − | 0.983130i | \(-0.441449\pi\) | ||||
0.182907 | + | 0.983130i | \(0.441449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.93073e7 | −1.43234 | ||||||||
\(712\) | −2.20443e7 | −1.62965 | ||||||||
\(713\) | 2.66165e7 | 1.96077 | ||||||||
\(714\) | 730643. | 0.0536364 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.91713e7 | −2.12654 | ||||||||
\(717\) | −2.85793e6 | −0.207612 | ||||||||
\(718\) | 1.12500e7 | 0.814403 | ||||||||
\(719\) | −2.14209e7 | −1.54531 | −0.772653 | − | 0.634828i | \(-0.781071\pi\) | ||||
−0.772653 | + | 0.634828i | \(0.781071\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.42610e6 | −0.603654 | ||||||||
\(722\) | −3.10813e7 | −2.21899 | ||||||||
\(723\) | −1.56354e6 | −0.111240 | ||||||||
\(724\) | 5.49193e7 | 3.89384 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 494610. | 0.0348274 | ||||||||
\(727\) | 2.80489e7 | 1.96825 | 0.984125 | − | 0.177479i | \(-0.0567941\pi\) | ||||
0.984125 | + | 0.177479i | \(0.0567941\pi\) | |||||||
\(728\) | −2.27758e7 | −1.59274 | ||||||||
\(729\) | −1.07325e7 | −0.747963 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −766179. | −0.0530319 | ||||||||
\(732\) | 1.71080e6 | 0.118011 | ||||||||
\(733\) | −1.26781e7 | −0.871553 | −0.435776 | − | 0.900055i | \(-0.643526\pi\) | ||||
−0.435776 | + | 0.900055i | \(0.643526\pi\) | |||||||
\(734\) | 3.27675e7 | 2.24493 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.89403e7 | 2.64975 | ||||||||
\(737\) | 588317. | 0.0398972 | ||||||||
\(738\) | −3.61398e7 | −2.44256 | ||||||||
\(739\) | 1.14208e7 | 0.769284 | 0.384642 | − | 0.923066i | \(-0.374325\pi\) | ||||
0.384642 | + | 0.923066i | \(0.374325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.53673e6 | 0.504240 | ||||||||
\(742\) | −6.27033e6 | −0.418101 | ||||||||
\(743\) | −2.69184e6 | −0.178887 | −0.0894433 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894433 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(744\) | −9.37067e6 | −0.620638 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.10951e7 | 1.38783 | ||||||||
\(747\) | 1.39031e6 | 0.0911612 | ||||||||
\(748\) | 3.91945e6 | 0.256136 | ||||||||
\(749\) | −7.36687e6 | −0.479820 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.39859e6 | 0.155187 | 0.0775935 | − | 0.996985i | \(-0.475276\pi\) | ||||
0.0775935 | + | 0.996985i | \(0.475276\pi\) | |||||||
\(752\) | 3.83013e6 | 0.246984 | ||||||||
\(753\) | 2.84346e6 | 0.182751 | ||||||||
\(754\) | 1.58433e7 | 1.01489 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.93185e6 | −0.377473 | ||||||||
\(757\) | 1.21139e7 | 0.768324 | 0.384162 | − | 0.923266i | \(-0.374490\pi\) | ||||
0.384162 | + | 0.923266i | \(0.374490\pi\) | |||||||
\(758\) | 1.03681e7 | 0.655430 | ||||||||
\(759\) | −1.65412e6 | −0.104223 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.03382e6 | −0.502875 | −0.251438 | − | 0.967873i | \(-0.580903\pi\) | ||||
−0.251438 | + | 0.967873i | \(0.580903\pi\) | |||||||
\(762\) | 7.33203e6 | 0.457443 | ||||||||
\(763\) | 1.14892e7 | 0.714459 | ||||||||
\(764\) | −1.20699e6 | −0.0748117 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.96831e7 | 1.21205 | ||||||||
\(767\) | 1.62312e7 | 0.996235 | ||||||||
\(768\) | 4.39122e6 | 0.268647 | ||||||||
\(769\) | −4.58340e6 | −0.279494 | −0.139747 | − | 0.990187i | \(-0.544629\pi\) | ||||
−0.139747 | + | 0.990187i | \(0.544629\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.52308e6 | −0.334615 | ||||||||
\(772\) | 3.73022e7 | 2.25263 | ||||||||
\(773\) | −1.69473e7 | −1.02012 | −0.510062 | − | 0.860138i | \(-0.670377\pi\) | ||||
−0.510062 | + | 0.860138i | \(0.670377\pi\) | |||||||
\(774\) | 4.32498e6 | 0.259496 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.96377e7 | 2.95908 | ||||||||
\(777\) | 199611. | 0.0118613 | ||||||||
\(778\) | 1.91644e7 | 1.13513 | ||||||||
\(779\) | −3.50305e7 | −2.06825 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.27817e6 | 0.133647 | ||||||||
\(782\) | −1.86428e7 | −1.09017 | ||||||||
\(783\) | 2.38392e6 | 0.138959 | ||||||||
\(784\) | −3.26797e7 | −1.89884 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.33316e6 | −0.365649 | ||||||||
\(787\) | 4.01619e6 | 0.231141 | 0.115571 | − | 0.993299i | \(-0.463130\pi\) | ||||
0.115571 | + | 0.993299i | \(0.463130\pi\) | |||||||
\(788\) | 3.30032e7 | 1.89339 | ||||||||
\(789\) | −2.58064e6 | −0.147583 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.08579e6 | 0.516323 | ||||||||
\(792\) | −1.27822e7 | −0.724090 | ||||||||
\(793\) | 6.87052e6 | 0.387978 | ||||||||
\(794\) | 1.87877e6 | 0.105760 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.47222e7 | 2.50173 | ||||||||
\(797\) | 2.36467e7 | 1.31863 | 0.659317 | − | 0.751865i | \(-0.270845\pi\) | ||||
0.659317 | + | 0.751865i | \(0.270845\pi\) | |||||||
\(798\) | −3.99779e6 | −0.222235 | ||||||||
\(799\) | −713720. | −0.0395513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.12717e7 | −0.620738 | ||||||||
\(802\) | −3.87446e7 | −2.12704 | ||||||||
\(803\) | −8.00951e6 | −0.438346 | ||||||||
\(804\) | 1.19897e6 | 0.0654137 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.51377e7 | −3.53179 | ||||||||
\(807\) | −2.08713e6 | −0.112815 | ||||||||
\(808\) | 3.74723e7 | 2.01921 | ||||||||
\(809\) | 1.06140e7 | 0.570174 | 0.285087 | − | 0.958502i | \(-0.407978\pi\) | ||||
0.285087 | + | 0.958502i | \(0.407978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.28249e6 | 0.175247 | 0.0876236 | − | 0.996154i | \(-0.472073\pi\) | ||||
0.0876236 | + | 0.996154i | \(0.472073\pi\) | |||||||
\(812\) | −5.90885e6 | −0.314494 | ||||||||
\(813\) | −2.20634e6 | −0.117070 | ||||||||
\(814\) | 1.52295e6 | 0.0805607 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.19049e6 | 0.167738 | ||||||||
\(817\) | 4.19223e6 | 0.219730 | ||||||||
\(818\) | 3.05190e7 | 1.59473 | ||||||||
\(819\) | −1.16457e7 | −0.606677 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.61250e6 | 0.445935 | 0.222967 | − | 0.974826i | \(-0.428426\pi\) | ||||
0.222967 | + | 0.974826i | \(0.428426\pi\) | |||||||
\(822\) | 5.92949e6 | 0.306082 | ||||||||
\(823\) | −1.41290e7 | −0.727131 | −0.363565 | − | 0.931569i | \(-0.618441\pi\) | ||||
−0.363565 | + | 0.931569i | \(0.618441\pi\) | |||||||
\(824\) | −7.56924e7 | −3.88360 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.60969e6 | −0.439074 | ||||||||
\(827\) | 597955. | 0.0304022 | 0.0152011 | − | 0.999884i | \(-0.495161\pi\) | ||||
0.0152011 | + | 0.999884i | \(0.495161\pi\) | |||||||
\(828\) | 7.39917e7 | 3.75066 | ||||||||
\(829\) | 1.66755e7 | 0.842736 | 0.421368 | − | 0.906890i | \(-0.361550\pi\) | ||||
0.421368 | + | 0.906890i | \(0.361550\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.82986e6 | −0.292857 | ||||||||
\(832\) | −2.26059e7 | −1.13218 | ||||||||
\(833\) | 6.08966e6 | 0.304075 | ||||||||
\(834\) | 1.15941e7 | 0.577193 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.14457e7 | −1.06126 | ||||||||
\(837\) | −9.80116e6 | −0.483575 | ||||||||
\(838\) | 2.47291e7 | 1.21646 | ||||||||
\(839\) | −1.15062e7 | −0.564322 | −0.282161 | − | 0.959367i | \(-0.591051\pi\) | ||||
−0.282161 | + | 0.959367i | \(0.591051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.81365e7 | −0.884225 | ||||||||
\(842\) | 6.88866e6 | 0.334853 | ||||||||
\(843\) | 648322. | 0.0314211 | ||||||||
\(844\) | 1.65215e7 | 0.798348 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.02885e6 | 0.193533 | ||||||||
\(847\) | −740812. | −0.0354813 | ||||||||
\(848\) | −2.73806e7 | −1.30753 | ||||||||
\(849\) | 27788.4 | 0.00132310 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.09319e6 | −0.241082 | ||||||||
\(852\) | 4.64283e6 | 0.219121 | ||||||||
\(853\) | −1.62039e7 | −0.762513 | −0.381257 | − | 0.924469i | \(-0.624509\pi\) | ||||
−0.381257 | + | 0.924469i | \(0.624509\pi\) | |||||||
\(854\) | −3.64440e6 | −0.170994 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.61772e7 | −3.08691 | ||||||||
\(857\) | 9.97322e6 | 0.463856 | 0.231928 | − | 0.972733i | \(-0.425497\pi\) | ||||
0.231928 | + | 0.972733i | \(0.425497\pi\) | |||||||
\(858\) | 4.04809e6 | 0.187729 | ||||||||
\(859\) | −3.22135e7 | −1.48955 | −0.744774 | − | 0.667316i | \(-0.767443\pi\) | ||||
−0.744774 | + | 0.667316i | \(0.767443\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.46611e6 | −0.113372 | ||||||||
\(862\) | 1.87736e7 | 0.860558 | ||||||||
\(863\) | −1.41832e7 | −0.648257 | −0.324128 | − | 0.946013i | \(-0.605071\pi\) | ||||
−0.324128 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(864\) | −1.43392e7 | −0.653494 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.25041e7 | 2.83213 | ||||||||
\(867\) | 4.02571e6 | 0.181884 | ||||||||
\(868\) | 2.42934e7 | 1.09443 | ||||||||
\(869\) | −1.00519e7 | −0.451544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.81502e6 | 0.215057 | ||||||||
\(872\) | 1.03208e8 | 4.59645 | ||||||||
\(873\) | 2.53808e7 | 1.12712 | ||||||||
\(874\) | 1.02006e8 | 4.51697 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.63231e7 | −0.718693 | ||||||||
\(877\) | −1.87883e7 | −0.824875 | −0.412437 | − | 0.910986i | \(-0.635322\pi\) | ||||
−0.412437 | + | 0.910986i | \(0.635322\pi\) | |||||||
\(878\) | 3.26359e7 | 1.42876 | ||||||||
\(879\) | −4.41012e6 | −0.192521 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.00458e7 | 1.30420 | 0.652099 | − | 0.758134i | \(-0.273889\pi\) | ||||
0.652099 | + | 0.758134i | \(0.273889\pi\) | |||||||
\(882\) | −3.43753e7 | −1.48791 | ||||||||
\(883\) | −4.10805e7 | −1.77310 | −0.886552 | − | 0.462629i | \(-0.846906\pi\) | ||||
−0.886552 | + | 0.462629i | \(0.846906\pi\) | |||||||
\(884\) | 3.20783e7 | 1.38064 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.79802e7 | 2.48139 | ||||||||
\(887\) | 1.64567e7 | 0.702316 | 0.351158 | − | 0.936316i | \(-0.385788\pi\) | ||||
0.351158 | + | 0.936316i | \(0.385788\pi\) | |||||||
\(888\) | 1.79312e6 | 0.0763093 | ||||||||
\(889\) | −1.09817e7 | −0.466031 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.22448e6 | −0.262669 | ||||||||
\(892\) | 4.65877e7 | 1.96046 | ||||||||
\(893\) | 3.90519e6 | 0.163875 | ||||||||
\(894\) | −1.03904e7 | −0.434797 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.01692e6 | −0.125543 | ||||||||
\(897\) | −1.35380e7 | −0.561790 | ||||||||
\(898\) | −7.30896e7 | −3.02458 | ||||||||
\(899\) | −9.76315e6 | −0.402894 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.10220e6 | 0.209385 | ||||||||
\(902\) | −1.88154e7 | −0.770012 | ||||||||
\(903\) | 295129. | 0.0120446 | ||||||||
\(904\) | 8.16185e7 | 3.32175 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.20021e7 | 0.485776 | ||||||||
\(907\) | −1.72342e6 | −0.0695621 | −0.0347810 | − | 0.999395i | \(-0.511073\pi\) | ||||
−0.0347810 | + | 0.999395i | \(0.511073\pi\) | |||||||
\(908\) | −8.11526e7 | −3.26654 | ||||||||
\(909\) | 1.91604e7 | 0.769122 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.98387e7 | −1.59041 | −0.795206 | − | 0.606340i | \(-0.792637\pi\) | ||||
−0.795206 | + | 0.606340i | \(0.792637\pi\) | |||||||
\(912\) | −1.74571e7 | −0.695000 | ||||||||
\(913\) | 723835. | 0.0287384 | ||||||||
\(914\) | −2.58816e6 | −0.102477 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.02089e7 | −0.402013 | ||||||||
\(917\) | 9.48563e6 | 0.372514 | ||||||||
\(918\) | 6.86496e6 | 0.268863 | ||||||||
\(919\) | 309349. | 0.0120826 | 0.00604129 | − | 0.999982i | \(-0.498077\pi\) | ||||
0.00604129 | + | 0.999982i | \(0.498077\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.41322e6 | 0.132592 | ||||||||
\(922\) | −7.29398e7 | −2.82577 | ||||||||
\(923\) | 1.86454e7 | 0.720391 | ||||||||
\(924\) | −1.50975e6 | −0.0581736 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.07894e6 | −0.0796736 | ||||||||
\(927\) | −3.87032e7 | −1.47927 | ||||||||
\(928\) | −1.42836e7 | −0.544463 | ||||||||
\(929\) | 3.31582e7 | 1.26053 | 0.630263 | − | 0.776382i | \(-0.282947\pi\) | ||||
0.630263 | + | 0.776382i | \(0.282947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.33202e7 | −1.25989 | ||||||||
\(932\) | 1.35771e6 | 0.0511995 | ||||||||
\(933\) | −1.75899e6 | −0.0661545 | ||||||||
\(934\) | 2.18147e7 | 0.818244 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.04615e8 | −3.90304 | ||||||||
\(937\) | −5.04047e7 | −1.87552 | −0.937760 | − | 0.347283i | \(-0.887104\pi\) | ||||
−0.937760 | + | 0.347283i | \(0.887104\pi\) | |||||||
\(938\) | −2.55409e6 | −0.0947825 | ||||||||
\(939\) | 3.70870e6 | 0.137264 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.93209e7 | 0.711299 | 0.355649 | − | 0.934619i | \(-0.384260\pi\) | ||||
0.355649 | + | 0.934619i | \(0.384260\pi\) | |||||||
\(942\) | 5.58325e6 | 0.205003 | ||||||||
\(943\) | 6.29243e7 | 2.30430 | ||||||||
\(944\) | −3.75958e7 | −1.37312 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.25171e6 | 0.0818057 | ||||||||
\(947\) | −6.05379e6 | −0.219358 | −0.109679 | − | 0.993967i | \(-0.534982\pi\) | ||||
−0.109679 | + | 0.993967i | \(0.534982\pi\) | |||||||
\(948\) | −2.04855e7 | −0.740331 | ||||||||
\(949\) | −6.55530e7 | −2.36280 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.87786e6 | −0.210750 | ||||||||
\(952\) | −9.83052e6 | −0.351548 | ||||||||
\(953\) | 2.45689e7 | 0.876302 | 0.438151 | − | 0.898901i | \(-0.355634\pi\) | ||||
0.438151 | + | 0.898901i | \(0.355634\pi\) | |||||||
\(954\) | −2.88012e7 | −1.02457 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.65571e7 | 2.35532 | ||||||||
\(957\) | 606747. | 0.0214155 | ||||||||
\(958\) | 3.15113e6 | 0.110931 | ||||||||
\(959\) | −8.88102e6 | −0.311829 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.15107e7 | 0.402062 | ||||||||
\(962\) | 1.24644e7 | 0.434244 | ||||||||
\(963\) | −3.38379e7 | −1.17581 | ||||||||
\(964\) | 3.64126e7 | 1.26200 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7.18111e6 | 0.247599 | ||||||||
\(967\) | 4.76945e7 | 1.64022 | 0.820110 | − | 0.572206i | \(-0.193912\pi\) | ||||
0.820110 | + | 0.572206i | \(0.193912\pi\) | |||||||
\(968\) | −6.65478e6 | −0.228268 | ||||||||
\(969\) | 3.25302e6 | 0.111295 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39483.8 | −0.00134391 | −0.000671957 | − | 1.00000i | \(-0.500214\pi\) | ||||
−0.000671957 | 1.00000i | \(0.500214\pi\) | ||||||||
\(972\) | −4.11731e7 | −1.39781 | ||||||||
\(973\) | −1.73653e7 | −0.588030 | ||||||||
\(974\) | −8.79680e6 | −0.297117 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.59140e7 | −0.534754 | ||||||||
\(977\) | −3.06451e7 | −1.02713 | −0.513564 | − | 0.858051i | \(-0.671675\pi\) | ||||
−0.513564 | + | 0.858051i | \(0.671675\pi\) | |||||||
\(978\) | −1.28135e7 | −0.428372 | ||||||||
\(979\) | −5.86838e6 | −0.195687 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.27726e7 | 1.75080 | ||||||||
\(982\) | −3.59215e7 | −1.18871 | ||||||||
\(983\) | 2.19736e7 | 0.725300 | 0.362650 | − | 0.931925i | \(-0.381872\pi\) | ||||
0.362650 | + | 0.931925i | \(0.381872\pi\) | |||||||
\(984\) | −2.21533e7 | −0.729375 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.83833e6 | 0.224005 | ||||||||
\(987\) | 274922. | 0.00898289 | ||||||||
\(988\) | −1.75520e8 | −5.72050 | ||||||||
\(989\) | −7.53038e6 | −0.244808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.06580e6 | −0.163857 | −0.0819284 | − | 0.996638i | \(-0.526108\pi\) | ||||
−0.0819284 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(992\) | 5.87252e7 | 1.89472 | ||||||||
\(993\) | 1.22658e7 | 0.394750 | ||||||||
\(994\) | −9.89030e6 | −0.317500 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.47515e6 | 0.0471183 | ||||||||
\(997\) | 1.77819e7 | 0.566552 | 0.283276 | − | 0.959038i | \(-0.408579\pi\) | ||||
0.283276 | + | 0.959038i | \(0.408579\pi\) | |||||||
\(998\) | −3.57669e7 | −1.13672 | ||||||||
\(999\) | 1.87550e6 | 0.0594570 |
(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 | 275.6.a.l.1.1 | 14 | ||
5.2 | odd | 4 | 55.6.b.b.34.1 | ✓ | 14 | ||
5.3 | odd | 4 | 55.6.b.b.34.14 | yes | 14 | ||
5.4 | even | 2 | inner | 275.6.a.l.1.14 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.6.b.b.34.1 | ✓ | 14 | 5.2 | odd | 4 | ||
55.6.b.b.34.14 | yes | 14 | 5.3 | odd | 4 | ||
275.6.a.l.1.1 | 14 | 1.1 | even | 1 | trivial | ||
275.6.a.l.1.14 | 14 | 5.4 | even | 2 | inner |