Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.16691 | −1.62050 | −0.810248 | − | 0.586087i | \(-0.800668\pi\) | ||||
−0.810248 | + | 0.586087i | \(0.800668\pi\) | |||||||
\(3\) | −28.2569 | −1.81268 | −0.906340 | − | 0.422549i | \(-0.861136\pi\) | ||||
−0.906340 | + | 0.422549i | \(0.861136\pi\) | |||||||
\(4\) | 52.0323 | 1.62601 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 259.028 | 2.93744 | ||||||||
\(7\) | 66.4323 | 0.512430 | 0.256215 | − | 0.966620i | \(-0.417525\pi\) | ||||
0.256215 | + | 0.966620i | \(0.417525\pi\) | |||||||
\(8\) | −183.634 | −1.01445 | ||||||||
\(9\) | 555.452 | 2.28581 | ||||||||
\(10\) | −229.173 | −0.724708 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −1470.27 | −2.94743 | ||||||||
\(13\) | 856.238 | 1.40519 | 0.702597 | − | 0.711588i | \(-0.252024\pi\) | ||||
0.702597 | + | 0.711588i | \(0.252024\pi\) | |||||||
\(14\) | −608.979 | −0.830390 | ||||||||
\(15\) | −706.422 | −0.810655 | ||||||||
\(16\) | 18.3254 | 0.0178959 | ||||||||
\(17\) | −2251.06 | −1.88914 | −0.944572 | − | 0.328303i | \(-0.893523\pi\) | ||||
−0.944572 | + | 0.328303i | \(0.893523\pi\) | |||||||
\(18\) | −5091.78 | −3.70415 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 1300.81 | 0.727173 | ||||||||
\(21\) | −1877.17 | −0.928871 | ||||||||
\(22\) | 1109.20 | 0.488598 | ||||||||
\(23\) | 2094.06 | 0.825410 | 0.412705 | − | 0.910865i | \(-0.364584\pi\) | ||||
0.412705 | + | 0.910865i | \(0.364584\pi\) | |||||||
\(24\) | 5188.93 | 1.83886 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −7849.06 | −2.27711 | ||||||||
\(27\) | −8828.93 | −2.33076 | ||||||||
\(28\) | 3456.62 | 0.833215 | ||||||||
\(29\) | −3557.08 | −0.785414 | −0.392707 | − | 0.919664i | \(-0.628461\pi\) | ||||
−0.392707 | + | 0.919664i | \(0.628461\pi\) | |||||||
\(30\) | 6475.71 | 1.31366 | ||||||||
\(31\) | −6117.12 | −1.14325 | −0.571627 | − | 0.820514i | \(-0.693688\pi\) | ||||
−0.571627 | + | 0.820514i | \(0.693688\pi\) | |||||||
\(32\) | 5708.31 | 0.985445 | ||||||||
\(33\) | 3419.08 | 0.546544 | ||||||||
\(34\) | 20635.3 | 3.06135 | ||||||||
\(35\) | 1660.81 | 0.229165 | ||||||||
\(36\) | 28901.4 | 3.71675 | ||||||||
\(37\) | 11878.1 | 1.42640 | 0.713202 | − | 0.700959i | \(-0.247244\pi\) | ||||
0.713202 | + | 0.700959i | \(0.247244\pi\) | |||||||
\(38\) | 3309.26 | 0.371767 | ||||||||
\(39\) | −24194.6 | −2.54717 | ||||||||
\(40\) | −4590.85 | −0.453674 | ||||||||
\(41\) | −4115.68 | −0.382368 | −0.191184 | − | 0.981554i | \(-0.561233\pi\) | ||||
−0.191184 | + | 0.981554i | \(0.561233\pi\) | |||||||
\(42\) | 17207.9 | 1.50523 | ||||||||
\(43\) | −15128.1 | −1.24771 | −0.623854 | − | 0.781541i | \(-0.714434\pi\) | ||||
−0.623854 | + | 0.781541i | \(0.714434\pi\) | |||||||
\(44\) | −6295.91 | −0.490260 | ||||||||
\(45\) | 13886.3 | 1.02225 | ||||||||
\(46\) | −19196.1 | −1.33757 | ||||||||
\(47\) | 29205.4 | 1.92849 | 0.964247 | − | 0.265003i | \(-0.0853731\pi\) | ||||
0.964247 | + | 0.265003i | \(0.0853731\pi\) | |||||||
\(48\) | −517.818 | −0.0324395 | ||||||||
\(49\) | −12393.7 | −0.737416 | ||||||||
\(50\) | −5729.32 | −0.324099 | ||||||||
\(51\) | 63608.0 | 3.42442 | ||||||||
\(52\) | 44552.0 | 2.28486 | ||||||||
\(53\) | 8106.51 | 0.396410 | 0.198205 | − | 0.980161i | \(-0.436489\pi\) | ||||
0.198205 | + | 0.980161i | \(0.436489\pi\) | |||||||
\(54\) | 80934.0 | 3.77700 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | −12199.2 | −0.519832 | ||||||||
\(57\) | 10200.7 | 0.415857 | ||||||||
\(58\) | 32607.4 | 1.27276 | ||||||||
\(59\) | 35327.2 | 1.32123 | 0.660615 | − | 0.750725i | \(-0.270295\pi\) | ||||
0.660615 | + | 0.750725i | \(0.270295\pi\) | |||||||
\(60\) | −36756.8 | −1.31813 | ||||||||
\(61\) | 13703.0 | 0.471512 | 0.235756 | − | 0.971812i | \(-0.424243\pi\) | ||||
0.235756 | + | 0.971812i | \(0.424243\pi\) | |||||||
\(62\) | 56075.1 | 1.85264 | ||||||||
\(63\) | 36900.0 | 1.17132 | ||||||||
\(64\) | −52914.0 | −1.61481 | ||||||||
\(65\) | 21406.0 | 0.628422 | ||||||||
\(66\) | −31342.4 | −0.885672 | ||||||||
\(67\) | −23511.0 | −0.639859 | −0.319930 | − | 0.947441i | \(-0.603659\pi\) | ||||
−0.319930 | + | 0.947441i | \(0.603659\pi\) | |||||||
\(68\) | −117128. | −3.07177 | ||||||||
\(69\) | −59171.7 | −1.49621 | ||||||||
\(70\) | −15224.5 | −0.371362 | ||||||||
\(71\) | 22933.3 | 0.539909 | 0.269954 | − | 0.962873i | \(-0.412991\pi\) | ||||
0.269954 | + | 0.962873i | \(0.412991\pi\) | |||||||
\(72\) | −102000. | −2.31883 | ||||||||
\(73\) | −53346.6 | −1.17165 | −0.585827 | − | 0.810436i | \(-0.699230\pi\) | ||||
−0.585827 | + | 0.810436i | \(0.699230\pi\) | |||||||
\(74\) | −108885. | −2.31148 | ||||||||
\(75\) | −17660.6 | −0.362536 | ||||||||
\(76\) | −18783.7 | −0.373032 | ||||||||
\(77\) | −8038.31 | −0.154503 | ||||||||
\(78\) | 221790. | 4.12768 | ||||||||
\(79\) | −37921.0 | −0.683615 | −0.341808 | − | 0.939770i | \(-0.611039\pi\) | ||||
−0.341808 | + | 0.939770i | \(0.611039\pi\) | |||||||
\(80\) | 458.134 | 0.00800327 | ||||||||
\(81\) | 114503. | 1.93912 | ||||||||
\(82\) | 37728.0 | 0.619626 | ||||||||
\(83\) | 65371.2 | 1.04158 | 0.520788 | − | 0.853686i | \(-0.325638\pi\) | ||||
0.520788 | + | 0.853686i | \(0.325638\pi\) | |||||||
\(84\) | −97673.5 | −1.51035 | ||||||||
\(85\) | −56276.6 | −0.844851 | ||||||||
\(86\) | 138678. | 2.02191 | ||||||||
\(87\) | 100512. | 1.42370 | ||||||||
\(88\) | 22219.7 | 0.305867 | ||||||||
\(89\) | 81398.5 | 1.08929 | 0.544643 | − | 0.838668i | \(-0.316665\pi\) | ||||
0.544643 | + | 0.838668i | \(0.316665\pi\) | |||||||
\(90\) | −127295. | −1.65655 | ||||||||
\(91\) | 56881.9 | 0.720063 | ||||||||
\(92\) | 108959. | 1.34212 | ||||||||
\(93\) | 172851. | 2.07235 | ||||||||
\(94\) | −267723. | −3.12512 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −161299. | −1.78630 | ||||||||
\(97\) | 57974.2 | 0.625613 | 0.312806 | − | 0.949817i | \(-0.398731\pi\) | ||||
0.312806 | + | 0.949817i | \(0.398731\pi\) | |||||||
\(98\) | 113612. | 1.19498 | ||||||||
\(99\) | −67209.7 | −0.689198 | ||||||||
\(100\) | 32520.2 | 0.325202 | ||||||||
\(101\) | −46127.7 | −0.449944 | −0.224972 | − | 0.974365i | \(-0.572229\pi\) | ||||
−0.224972 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(102\) | −583089. | −5.54925 | ||||||||
\(103\) | −74583.5 | −0.692708 | −0.346354 | − | 0.938104i | \(-0.612580\pi\) | ||||
−0.346354 | + | 0.938104i | \(0.612580\pi\) | |||||||
\(104\) | −157235. | −1.42549 | ||||||||
\(105\) | −46929.3 | −0.415404 | ||||||||
\(106\) | −74311.7 | −0.642381 | ||||||||
\(107\) | 192930. | 1.62907 | 0.814536 | − | 0.580113i | \(-0.196992\pi\) | ||||
0.814536 | + | 0.580113i | \(0.196992\pi\) | |||||||
\(108\) | −459389. | −3.78984 | ||||||||
\(109\) | −129162. | −1.04128 | −0.520639 | − | 0.853777i | \(-0.674306\pi\) | ||||
−0.520639 | + | 0.853777i | \(0.674306\pi\) | |||||||
\(110\) | 27729.9 | 0.218508 | ||||||||
\(111\) | −335638. | −2.58561 | ||||||||
\(112\) | 1217.40 | 0.00917037 | ||||||||
\(113\) | −115751. | −0.852766 | −0.426383 | − | 0.904543i | \(-0.640212\pi\) | ||||
−0.426383 | + | 0.904543i | \(0.640212\pi\) | |||||||
\(114\) | −93509.3 | −0.673896 | ||||||||
\(115\) | 52351.6 | 0.369135 | ||||||||
\(116\) | −185083. | −1.27709 | ||||||||
\(117\) | 475599. | 3.21201 | ||||||||
\(118\) | −323841. | −2.14105 | ||||||||
\(119\) | −149543. | −0.968054 | ||||||||
\(120\) | 129723. | 0.822365 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −125615. | −0.764083 | ||||||||
\(123\) | 116296. | 0.693111 | ||||||||
\(124\) | −318288. | −1.85894 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −338259. | −1.89812 | ||||||||
\(127\) | 254354. | 1.39936 | 0.699681 | − | 0.714456i | \(-0.253326\pi\) | ||||
0.699681 | + | 0.714456i | \(0.253326\pi\) | |||||||
\(128\) | 302392. | 1.63134 | ||||||||
\(129\) | 427473. | 2.26170 | ||||||||
\(130\) | −196226. | −1.01836 | ||||||||
\(131\) | −124646. | −0.634601 | −0.317301 | − | 0.948325i | \(-0.602776\pi\) | ||||
−0.317301 | + | 0.948325i | \(0.602776\pi\) | |||||||
\(132\) | 177903. | 0.888685 | ||||||||
\(133\) | −23982.1 | −0.117559 | ||||||||
\(134\) | 215524. | 1.03689 | ||||||||
\(135\) | −220723. | −1.04235 | ||||||||
\(136\) | 413372. | 1.91643 | ||||||||
\(137\) | −96720.4 | −0.440268 | −0.220134 | − | 0.975470i | \(-0.570649\pi\) | ||||
−0.220134 | + | 0.975470i | \(0.570649\pi\) | |||||||
\(138\) | 542422. | 2.42460 | ||||||||
\(139\) | −216501. | −0.950436 | −0.475218 | − | 0.879868i | \(-0.657631\pi\) | ||||
−0.475218 | + | 0.879868i | \(0.657631\pi\) | |||||||
\(140\) | 86415.6 | 0.372625 | ||||||||
\(141\) | −825254. | −3.49575 | ||||||||
\(142\) | −210227. | −0.874920 | ||||||||
\(143\) | −103605. | −0.423682 | ||||||||
\(144\) | 10178.9 | 0.0409066 | ||||||||
\(145\) | −88927.0 | −0.351248 | ||||||||
\(146\) | 489023. | 1.89866 | ||||||||
\(147\) | 350209. | 1.33670 | ||||||||
\(148\) | 618044. | 2.31934 | ||||||||
\(149\) | −335609. | −1.23842 | −0.619209 | − | 0.785226i | \(-0.712547\pi\) | ||||
−0.619209 | + | 0.785226i | \(0.712547\pi\) | |||||||
\(150\) | 161893. | 0.587489 | ||||||||
\(151\) | 117542. | 0.419520 | 0.209760 | − | 0.977753i | \(-0.432732\pi\) | ||||
0.209760 | + | 0.977753i | \(0.432732\pi\) | |||||||
\(152\) | 66291.9 | 0.232730 | ||||||||
\(153\) | −1.25036e6 | −4.31823 | ||||||||
\(154\) | 73686.5 | 0.250372 | ||||||||
\(155\) | −152928. | −0.511279 | ||||||||
\(156\) | −1.25890e6 | −4.14172 | ||||||||
\(157\) | −355619. | −1.15143 | −0.575713 | − | 0.817652i | \(-0.695275\pi\) | ||||
−0.575713 | + | 0.817652i | \(0.695275\pi\) | |||||||
\(158\) | 347618. | 1.10780 | ||||||||
\(159\) | −229065. | −0.718564 | ||||||||
\(160\) | 142708. | 0.440704 | ||||||||
\(161\) | 139113. | 0.422965 | ||||||||
\(162\) | −1.04964e6 | −3.14234 | ||||||||
\(163\) | 364837. | 1.07555 | 0.537774 | − | 0.843089i | \(-0.319265\pi\) | ||||
0.537774 | + | 0.843089i | \(0.319265\pi\) | |||||||
\(164\) | −214148. | −0.621734 | ||||||||
\(165\) | 85477.1 | 0.244422 | ||||||||
\(166\) | −599252. | −1.68787 | ||||||||
\(167\) | 171652. | 0.476275 | 0.238137 | − | 0.971231i | \(-0.423463\pi\) | ||||
0.238137 | + | 0.971231i | \(0.423463\pi\) | |||||||
\(168\) | 344713. | 0.942289 | ||||||||
\(169\) | 361851. | 0.974569 | ||||||||
\(170\) | 515882. | 1.36908 | ||||||||
\(171\) | −200518. | −0.524401 | ||||||||
\(172\) | −787149. | −2.02878 | ||||||||
\(173\) | 245690. | 0.624126 | 0.312063 | − | 0.950061i | \(-0.398980\pi\) | ||||
0.312063 | + | 0.950061i | \(0.398980\pi\) | |||||||
\(174\) | −921385. | −2.30711 | ||||||||
\(175\) | 41520.2 | 0.102486 | ||||||||
\(176\) | −2217.37 | −0.00539581 | ||||||||
\(177\) | −998236. | −2.39497 | ||||||||
\(178\) | −746173. | −1.76518 | ||||||||
\(179\) | −348150. | −0.812146 | −0.406073 | − | 0.913841i | \(-0.633102\pi\) | ||||
−0.406073 | + | 0.913841i | \(0.633102\pi\) | |||||||
\(180\) | 722536. | 1.66218 | ||||||||
\(181\) | −62340.8 | −0.141441 | −0.0707206 | − | 0.997496i | \(-0.522530\pi\) | ||||
−0.0707206 | + | 0.997496i | \(0.522530\pi\) | |||||||
\(182\) | −521431. | −1.16686 | ||||||||
\(183\) | −387205. | −0.854700 | ||||||||
\(184\) | −384541. | −0.837334 | ||||||||
\(185\) | 296952. | 0.637907 | ||||||||
\(186\) | −1.58451e6 | −3.35824 | ||||||||
\(187\) | 272379. | 0.569599 | ||||||||
\(188\) | 1.51962e6 | 3.13575 | ||||||||
\(189\) | −586526. | −1.19435 | ||||||||
\(190\) | 82731.4 | 0.166259 | ||||||||
\(191\) | 604468. | 1.19892 | 0.599459 | − | 0.800405i | \(-0.295382\pi\) | ||||
0.599459 | + | 0.800405i | \(0.295382\pi\) | |||||||
\(192\) | 1.49518e6 | 2.92713 | ||||||||
\(193\) | 53159.1 | 0.102727 | 0.0513635 | − | 0.998680i | \(-0.483643\pi\) | ||||
0.0513635 | + | 0.998680i | \(0.483643\pi\) | |||||||
\(194\) | −531444. | −1.01380 | ||||||||
\(195\) | −604866. | −1.13913 | ||||||||
\(196\) | −644875. | −1.19904 | ||||||||
\(197\) | −960324. | −1.76300 | −0.881500 | − | 0.472184i | \(-0.843466\pi\) | ||||
−0.881500 | + | 0.472184i | \(0.843466\pi\) | |||||||
\(198\) | 616105. | 1.11684 | ||||||||
\(199\) | −132861. | −0.237829 | −0.118914 | − | 0.992905i | \(-0.537941\pi\) | ||||
−0.118914 | + | 0.992905i | \(0.537941\pi\) | |||||||
\(200\) | −114771. | −0.202889 | ||||||||
\(201\) | 664349. | 1.15986 | ||||||||
\(202\) | 422849. | 0.729133 | ||||||||
\(203\) | −236305. | −0.402469 | ||||||||
\(204\) | 3.30967e6 | 5.56813 | ||||||||
\(205\) | −102892. | −0.171000 | ||||||||
\(206\) | 683701. | 1.12253 | ||||||||
\(207\) | 1.16315e6 | 1.88673 | ||||||||
\(208\) | 15690.9 | 0.0251471 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | 430196. | 0.673160 | ||||||||
\(211\) | −412287. | −0.637519 | −0.318760 | − | 0.947836i | \(-0.603266\pi\) | ||||
−0.318760 | + | 0.947836i | \(0.603266\pi\) | |||||||
\(212\) | 421800. | 0.644566 | ||||||||
\(213\) | −648023. | −0.978682 | ||||||||
\(214\) | −1.76857e6 | −2.63991 | ||||||||
\(215\) | −378202. | −0.557992 | ||||||||
\(216\) | 1.62129e6 | 2.36443 | ||||||||
\(217\) | −406374. | −0.585837 | ||||||||
\(218\) | 1.18401e6 | 1.68739 | ||||||||
\(219\) | 1.50741e6 | 2.12383 | ||||||||
\(220\) | −157398. | −0.219251 | ||||||||
\(221\) | −1.92745e6 | −2.65461 | ||||||||
\(222\) | 3.07676e6 | 4.18998 | ||||||||
\(223\) | 1.17182e6 | 1.57796 | 0.788982 | − | 0.614416i | \(-0.210608\pi\) | ||||
0.788982 | + | 0.614416i | \(0.210608\pi\) | |||||||
\(224\) | 379216. | 0.504971 | ||||||||
\(225\) | 347158. | 0.457162 | ||||||||
\(226\) | 1.06108e6 | 1.38190 | ||||||||
\(227\) | 626009. | 0.806336 | 0.403168 | − | 0.915126i | \(-0.367909\pi\) | ||||
0.403168 | + | 0.915126i | \(0.367909\pi\) | |||||||
\(228\) | 530768. | 0.676188 | ||||||||
\(229\) | 403204. | 0.508084 | 0.254042 | − | 0.967193i | \(-0.418240\pi\) | ||||
0.254042 | + | 0.967193i | \(0.418240\pi\) | |||||||
\(230\) | −479902. | −0.598182 | ||||||||
\(231\) | 227138. | 0.280065 | ||||||||
\(232\) | 653201. | 0.796759 | ||||||||
\(233\) | 518044. | 0.625139 | 0.312570 | − | 0.949895i | \(-0.398810\pi\) | ||||
0.312570 | + | 0.949895i | \(0.398810\pi\) | |||||||
\(234\) | −4.35978e6 | −5.20505 | ||||||||
\(235\) | 730135. | 0.862449 | ||||||||
\(236\) | 1.83815e6 | 2.14833 | ||||||||
\(237\) | 1.07153e6 | 1.23918 | ||||||||
\(238\) | 1.37085e6 | 1.56873 | ||||||||
\(239\) | 1.34862e6 | 1.52720 | 0.763598 | − | 0.645691i | \(-0.223431\pi\) | ||||
0.763598 | + | 0.645691i | \(0.223431\pi\) | |||||||
\(240\) | −12945.4 | −0.0145074 | ||||||||
\(241\) | 613835. | 0.680784 | 0.340392 | − | 0.940284i | \(-0.389440\pi\) | ||||
0.340392 | + | 0.940284i | \(0.389440\pi\) | |||||||
\(242\) | −134213. | −0.147318 | ||||||||
\(243\) | −1.09007e6 | −1.18424 | ||||||||
\(244\) | 713000. | 0.766682 | ||||||||
\(245\) | −309844. | −0.329782 | ||||||||
\(246\) | −1.06608e6 | −1.12318 | ||||||||
\(247\) | −309102. | −0.322374 | ||||||||
\(248\) | 1.12331e6 | 1.15977 | ||||||||
\(249\) | −1.84719e6 | −1.88805 | ||||||||
\(250\) | −143233. | −0.144942 | ||||||||
\(251\) | −689394. | −0.690690 | −0.345345 | − | 0.938476i | \(-0.612238\pi\) | ||||
−0.345345 | + | 0.938476i | \(0.612238\pi\) | |||||||
\(252\) | 1.91999e6 | 1.90457 | ||||||||
\(253\) | −253382. | −0.248871 | ||||||||
\(254\) | −2.33164e6 | −2.26766 | ||||||||
\(255\) | 1.59020e6 | 1.53145 | ||||||||
\(256\) | −1.07875e6 | −1.02878 | ||||||||
\(257\) | 564460. | 0.533089 | 0.266545 | − | 0.963823i | \(-0.414118\pi\) | ||||
0.266545 | + | 0.963823i | \(0.414118\pi\) | |||||||
\(258\) | −3.91861e6 | −3.66507 | ||||||||
\(259\) | 789089. | 0.730931 | ||||||||
\(260\) | 1.11380e6 | 1.02182 | ||||||||
\(261\) | −1.97579e6 | −1.79531 | ||||||||
\(262\) | 1.14262e6 | 1.02837 | ||||||||
\(263\) | −1.73353e6 | −1.54541 | −0.772703 | − | 0.634768i | \(-0.781096\pi\) | ||||
−0.772703 | + | 0.634768i | \(0.781096\pi\) | |||||||
\(264\) | −627861. | −0.554439 | ||||||||
\(265\) | 202663. | 0.177280 | ||||||||
\(266\) | 219841. | 0.190505 | ||||||||
\(267\) | −2.30007e6 | −1.97453 | ||||||||
\(268\) | −1.22333e6 | −1.04042 | ||||||||
\(269\) | 570898. | 0.481036 | 0.240518 | − | 0.970645i | \(-0.422683\pi\) | ||||
0.240518 | + | 0.970645i | \(0.422683\pi\) | |||||||
\(270\) | 2.02335e6 | 1.68912 | ||||||||
\(271\) | 689745. | 0.570513 | 0.285256 | − | 0.958451i | \(-0.407921\pi\) | ||||
0.285256 | + | 0.958451i | \(0.407921\pi\) | |||||||
\(272\) | −41251.5 | −0.0338079 | ||||||||
\(273\) | −1.60730e6 | −1.30524 | ||||||||
\(274\) | 886627. | 0.713452 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | −3.07884e6 | −2.43284 | ||||||||
\(277\) | −1.22302e6 | −0.957710 | −0.478855 | − | 0.877894i | \(-0.658948\pi\) | ||||
−0.478855 | + | 0.877894i | \(0.658948\pi\) | |||||||
\(278\) | 1.98465e6 | 1.54018 | ||||||||
\(279\) | −3.39777e6 | −2.61326 | ||||||||
\(280\) | −304981. | −0.232476 | ||||||||
\(281\) | 2.38326e6 | 1.80055 | 0.900275 | − | 0.435322i | \(-0.143366\pi\) | ||||
0.900275 | + | 0.435322i | \(0.143366\pi\) | |||||||
\(282\) | 7.56503e6 | 5.66484 | ||||||||
\(283\) | −270350. | −0.200659 | −0.100330 | − | 0.994954i | \(-0.531990\pi\) | ||||
−0.100330 | + | 0.994954i | \(0.531990\pi\) | |||||||
\(284\) | 1.19327e6 | 0.877896 | ||||||||
\(285\) | 255018. | 0.185977 | ||||||||
\(286\) | 949736. | 0.686575 | ||||||||
\(287\) | −273414. | −0.195937 | ||||||||
\(288\) | 3.17069e6 | 2.25254 | ||||||||
\(289\) | 3.64742e6 | 2.56887 | ||||||||
\(290\) | 815186. | 0.569196 | ||||||||
\(291\) | −1.63817e6 | −1.13404 | ||||||||
\(292\) | −2.77574e6 | −1.90512 | ||||||||
\(293\) | −1.92919e6 | −1.31282 | −0.656412 | − | 0.754403i | \(-0.727927\pi\) | ||||
−0.656412 | + | 0.754403i | \(0.727927\pi\) | |||||||
\(294\) | −3.21033e6 | −2.16612 | ||||||||
\(295\) | 883179. | 0.590872 | ||||||||
\(296\) | −2.18122e6 | −1.44701 | ||||||||
\(297\) | 1.06830e6 | 0.702752 | ||||||||
\(298\) | 3.07649e6 | 2.00685 | ||||||||
\(299\) | 1.79302e6 | 1.15986 | ||||||||
\(300\) | −918919. | −0.589487 | ||||||||
\(301\) | −1.00499e6 | −0.639363 | ||||||||
\(302\) | −1.07750e6 | −0.679830 | ||||||||
\(303\) | 1.30343e6 | 0.815605 | ||||||||
\(304\) | −6615.46 | −0.00410559 | ||||||||
\(305\) | 342576. | 0.210866 | ||||||||
\(306\) | 1.14619e7 | 6.99767 | ||||||||
\(307\) | −1.51935e6 | −0.920050 | −0.460025 | − | 0.887906i | \(-0.652160\pi\) | ||||
−0.460025 | + | 0.887906i | \(0.652160\pi\) | |||||||
\(308\) | −418252. | −0.251224 | ||||||||
\(309\) | 2.10750e6 | 1.25566 | ||||||||
\(310\) | 1.40188e6 | 0.828525 | ||||||||
\(311\) | −2.51623e6 | −1.47519 | −0.737597 | − | 0.675241i | \(-0.764040\pi\) | ||||
−0.737597 | + | 0.675241i | \(0.764040\pi\) | |||||||
\(312\) | 4.44296e6 | 2.58396 | ||||||||
\(313\) | −545024. | −0.314452 | −0.157226 | − | 0.987563i | \(-0.550255\pi\) | ||||
−0.157226 | + | 0.987563i | \(0.550255\pi\) | |||||||
\(314\) | 3.25993e6 | 1.86588 | ||||||||
\(315\) | 922499. | 0.523829 | ||||||||
\(316\) | −1.97311e6 | −1.11156 | ||||||||
\(317\) | 133688. | 0.0747214 | 0.0373607 | − | 0.999302i | \(-0.488105\pi\) | ||||
0.0373607 | + | 0.999302i | \(0.488105\pi\) | |||||||
\(318\) | 2.09982e6 | 1.16443 | ||||||||
\(319\) | 430406. | 0.236811 | ||||||||
\(320\) | −1.32285e6 | −0.722163 | ||||||||
\(321\) | −5.45160e6 | −2.95299 | ||||||||
\(322\) | −1.27524e6 | −0.685413 | ||||||||
\(323\) | 812634. | 0.433400 | ||||||||
\(324\) | 5.95786e6 | 3.15303 | ||||||||
\(325\) | 535149. | 0.281039 | ||||||||
\(326\) | −3.34443e6 | −1.74292 | ||||||||
\(327\) | 3.64970e6 | 1.88751 | ||||||||
\(328\) | 755779. | 0.387891 | ||||||||
\(329\) | 1.94018e6 | 0.988218 | ||||||||
\(330\) | −783561. | −0.396085 | ||||||||
\(331\) | −3.12617e6 | −1.56835 | −0.784175 | − | 0.620539i | \(-0.786914\pi\) | ||||
−0.784175 | + | 0.620539i | \(0.786914\pi\) | |||||||
\(332\) | 3.40141e6 | 1.69361 | ||||||||
\(333\) | 6.59771e6 | 3.26049 | ||||||||
\(334\) | −1.57352e6 | −0.771802 | ||||||||
\(335\) | −587776. | −0.286154 | ||||||||
\(336\) | −34399.8 | −0.0166229 | ||||||||
\(337\) | 2.05851e6 | 0.987365 | 0.493683 | − | 0.869642i | \(-0.335650\pi\) | ||||
0.493683 | + | 0.869642i | \(0.335650\pi\) | |||||||
\(338\) | −3.31705e6 | −1.57929 | ||||||||
\(339\) | 3.27077e6 | 1.54579 | ||||||||
\(340\) | −2.92820e6 | −1.37374 | ||||||||
\(341\) | 740172. | 0.344704 | ||||||||
\(342\) | 1.83813e6 | 0.849790 | ||||||||
\(343\) | −1.93987e6 | −0.890303 | ||||||||
\(344\) | 2.77803e6 | 1.26573 | ||||||||
\(345\) | −1.47929e6 | −0.669123 | ||||||||
\(346\) | −2.25222e6 | −1.01139 | ||||||||
\(347\) | 3.98161e6 | 1.77515 | 0.887574 | − | 0.460665i | \(-0.152389\pi\) | ||||
0.887574 | + | 0.460665i | \(0.152389\pi\) | |||||||
\(348\) | 5.22987e6 | 2.31496 | ||||||||
\(349\) | −2.24411e6 | −0.986237 | −0.493119 | − | 0.869962i | \(-0.664143\pi\) | ||||
−0.493119 | + | 0.869962i | \(0.664143\pi\) | |||||||
\(350\) | −380612. | −0.166078 | ||||||||
\(351\) | −7.55966e6 | −3.27518 | ||||||||
\(352\) | −690705. | −0.297123 | ||||||||
\(353\) | 307957. | 0.131539 | 0.0657694 | − | 0.997835i | \(-0.479050\pi\) | ||||
0.0657694 | + | 0.997835i | \(0.479050\pi\) | |||||||
\(354\) | 9.15074e6 | 3.88104 | ||||||||
\(355\) | 573332. | 0.241455 | ||||||||
\(356\) | 4.23535e6 | 1.77119 | ||||||||
\(357\) | 4.22563e6 | 1.75477 | ||||||||
\(358\) | 3.19146e6 | 1.31608 | ||||||||
\(359\) | −1.11335e6 | −0.455929 | −0.227964 | − | 0.973669i | \(-0.573207\pi\) | ||||
−0.227964 | + | 0.973669i | \(0.573207\pi\) | |||||||
\(360\) | −2.55000e6 | −1.03701 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 571473. | 0.229205 | ||||||||
\(363\) | −413709. | −0.164789 | ||||||||
\(364\) | 2.95969e6 | 1.17083 | ||||||||
\(365\) | −1.33366e6 | −0.523979 | ||||||||
\(366\) | 3.54948e6 | 1.38504 | ||||||||
\(367\) | −25188.1 | −0.00976180 | −0.00488090 | − | 0.999988i | \(-0.501554\pi\) | ||||
−0.00488090 | + | 0.999988i | \(0.501554\pi\) | |||||||
\(368\) | 38374.4 | 0.0147714 | ||||||||
\(369\) | −2.28606e6 | −0.874021 | ||||||||
\(370\) | −2.72214e6 | −1.03373 | ||||||||
\(371\) | 538534. | 0.203132 | ||||||||
\(372\) | 8.99382e6 | 3.36967 | ||||||||
\(373\) | 4.83284e6 | 1.79858 | 0.899292 | − | 0.437349i | \(-0.144082\pi\) | ||||
0.899292 | + | 0.437349i | \(0.144082\pi\) | |||||||
\(374\) | −2.49687e6 | −0.923032 | ||||||||
\(375\) | −441514. | −0.162131 | ||||||||
\(376\) | −5.36311e6 | −1.95635 | ||||||||
\(377\) | −3.04571e6 | −1.10366 | ||||||||
\(378\) | 5.37663e6 | 1.93544 | ||||||||
\(379\) | 2.02328e6 | 0.723534 | 0.361767 | − | 0.932269i | \(-0.382174\pi\) | ||||
0.361767 | + | 0.932269i | \(0.382174\pi\) | |||||||
\(380\) | −469591. | −0.166825 | ||||||||
\(381\) | −7.18726e6 | −2.53659 | ||||||||
\(382\) | −5.54110e6 | −1.94284 | ||||||||
\(383\) | −2.05417e6 | −0.715549 | −0.357775 | − | 0.933808i | \(-0.616464\pi\) | ||||
−0.357775 | + | 0.933808i | \(0.616464\pi\) | |||||||
\(384\) | −8.54465e6 | −2.95710 | ||||||||
\(385\) | −200958. | −0.0690960 | ||||||||
\(386\) | −487305. | −0.166469 | ||||||||
\(387\) | −8.40293e6 | −2.85202 | ||||||||
\(388\) | 3.01653e6 | 1.01725 | ||||||||
\(389\) | 2.43820e6 | 0.816950 | 0.408475 | − | 0.912770i | \(-0.366061\pi\) | ||||
0.408475 | + | 0.912770i | \(0.366061\pi\) | |||||||
\(390\) | 5.54475e6 | 1.84595 | ||||||||
\(391\) | −4.71386e6 | −1.55932 | ||||||||
\(392\) | 2.27592e6 | 0.748068 | ||||||||
\(393\) | 3.52212e6 | 1.15033 | ||||||||
\(394\) | 8.80321e6 | 2.85694 | ||||||||
\(395\) | −948024. | −0.305722 | ||||||||
\(396\) | −3.49707e6 | −1.12064 | ||||||||
\(397\) | −3.58215e6 | −1.14069 | −0.570345 | − | 0.821405i | \(-0.693191\pi\) | ||||
−0.570345 | + | 0.821405i | \(0.693191\pi\) | |||||||
\(398\) | 1.21792e6 | 0.385401 | ||||||||
\(399\) | 677659. | 0.213098 | ||||||||
\(400\) | 11453.4 | 0.00357917 | ||||||||
\(401\) | −2.46752e6 | −0.766301 | −0.383150 | − | 0.923686i | \(-0.625161\pi\) | ||||
−0.383150 | + | 0.923686i | \(0.625161\pi\) | |||||||
\(402\) | −6.09003e6 | −1.87955 | ||||||||
\(403\) | −5.23771e6 | −1.60649 | ||||||||
\(404\) | −2.40013e6 | −0.731613 | ||||||||
\(405\) | 2.86258e6 | 0.867201 | ||||||||
\(406\) | 2.16619e6 | 0.652200 | ||||||||
\(407\) | −1.43725e6 | −0.430077 | ||||||||
\(408\) | −1.16806e7 | −3.47388 | ||||||||
\(409\) | −4.63675e6 | −1.37058 | −0.685292 | − | 0.728269i | \(-0.740325\pi\) | ||||
−0.685292 | + | 0.728269i | \(0.740325\pi\) | |||||||
\(410\) | 943201. | 0.277105 | ||||||||
\(411\) | 2.73302e6 | 0.798064 | ||||||||
\(412\) | −3.88075e6 | −1.12635 | ||||||||
\(413\) | 2.34686e6 | 0.677038 | ||||||||
\(414\) | −1.06625e7 | −3.05744 | ||||||||
\(415\) | 1.63428e6 | 0.465807 | ||||||||
\(416\) | 4.88767e6 | 1.38474 | ||||||||
\(417\) | 6.11765e6 | 1.72284 | ||||||||
\(418\) | −400420. | −0.112092 | ||||||||
\(419\) | 3.35416e6 | 0.933359 | 0.466680 | − | 0.884426i | \(-0.345450\pi\) | ||||
0.466680 | + | 0.884426i | \(0.345450\pi\) | |||||||
\(420\) | −2.44184e6 | −0.675450 | ||||||||
\(421\) | −6.02799e6 | −1.65755 | −0.828777 | − | 0.559580i | \(-0.810963\pi\) | ||||
−0.828777 | + | 0.559580i | \(0.810963\pi\) | |||||||
\(422\) | 3.77940e6 | 1.03310 | ||||||||
\(423\) | 1.62222e7 | 4.40817 | ||||||||
\(424\) | −1.48863e6 | −0.402136 | ||||||||
\(425\) | −1.40691e6 | −0.377829 | ||||||||
\(426\) | 5.94037e6 | 1.58595 | ||||||||
\(427\) | 910324. | 0.241616 | ||||||||
\(428\) | 1.00386e7 | 2.64889 | ||||||||
\(429\) | 2.92755e6 | 0.768000 | ||||||||
\(430\) | 3.46695e6 | 0.904224 | ||||||||
\(431\) | 2.57138e6 | 0.666766 | 0.333383 | − | 0.942792i | \(-0.391810\pi\) | ||||
0.333383 | + | 0.942792i | \(0.391810\pi\) | |||||||
\(432\) | −161793. | −0.0417110 | ||||||||
\(433\) | −2.38192e6 | −0.610532 | −0.305266 | − | 0.952267i | \(-0.598745\pi\) | ||||
−0.305266 | + | 0.952267i | \(0.598745\pi\) | |||||||
\(434\) | 3.72520e6 | 0.949347 | ||||||||
\(435\) | 2.51280e6 | 0.636700 | ||||||||
\(436\) | −6.72057e6 | −1.69313 | ||||||||
\(437\) | −755956. | −0.189362 | ||||||||
\(438\) | −1.38183e7 | −3.44167 | ||||||||
\(439\) | −4.98108e6 | −1.23357 | −0.616783 | − | 0.787134i | \(-0.711564\pi\) | ||||
−0.616783 | + | 0.787134i | \(0.711564\pi\) | |||||||
\(440\) | 555493. | 0.136788 | ||||||||
\(441\) | −6.88413e6 | −1.68559 | ||||||||
\(442\) | 1.76687e7 | 4.30179 | ||||||||
\(443\) | −943151. | −0.228335 | −0.114167 | − | 0.993462i | \(-0.536420\pi\) | ||||
−0.114167 | + | 0.993462i | \(0.536420\pi\) | |||||||
\(444\) | −1.74640e7 | −4.20423 | ||||||||
\(445\) | 2.03496e6 | 0.487143 | ||||||||
\(446\) | −1.07419e7 | −2.55709 | ||||||||
\(447\) | 9.48325e6 | 2.24486 | ||||||||
\(448\) | −3.51520e6 | −0.827474 | ||||||||
\(449\) | −358465. | −0.0839133 | −0.0419567 | − | 0.999119i | \(-0.513359\pi\) | ||||
−0.0419567 | + | 0.999119i | \(0.513359\pi\) | |||||||
\(450\) | −3.18236e6 | −0.740830 | ||||||||
\(451\) | 497997. | 0.115288 | ||||||||
\(452\) | −6.02280e6 | −1.38660 | ||||||||
\(453\) | −3.32139e6 | −0.760455 | ||||||||
\(454\) | −5.73857e6 | −1.30667 | ||||||||
\(455\) | 1.42205e6 | 0.322022 | ||||||||
\(456\) | −1.87320e6 | −0.421865 | ||||||||
\(457\) | −4.58896e6 | −1.02784 | −0.513918 | − | 0.857839i | \(-0.671806\pi\) | ||||
−0.513918 | + | 0.857839i | \(0.671806\pi\) | |||||||
\(458\) | −3.69613e6 | −0.823349 | ||||||||
\(459\) | 1.98745e7 | 4.40315 | ||||||||
\(460\) | 2.72397e6 | 0.600216 | ||||||||
\(461\) | 6.80506e6 | 1.49135 | 0.745675 | − | 0.666310i | \(-0.232127\pi\) | ||||
0.745675 | + | 0.666310i | \(0.232127\pi\) | |||||||
\(462\) | −2.08215e6 | −0.453845 | ||||||||
\(463\) | 5.76634e6 | 1.25011 | 0.625054 | − | 0.780581i | \(-0.285077\pi\) | ||||
0.625054 | + | 0.780581i | \(0.285077\pi\) | |||||||
\(464\) | −65184.8 | −0.0140557 | ||||||||
\(465\) | 4.32127e6 | 0.926785 | ||||||||
\(466\) | −4.74886e6 | −1.01304 | ||||||||
\(467\) | −2.25580e6 | −0.478640 | −0.239320 | − | 0.970941i | \(-0.576925\pi\) | ||||
−0.239320 | + | 0.970941i | \(0.576925\pi\) | |||||||
\(468\) | 2.47465e7 | 5.22275 | ||||||||
\(469\) | −1.56189e6 | −0.327883 | ||||||||
\(470\) | −6.69308e6 | −1.39760 | ||||||||
\(471\) | 1.00487e7 | 2.08717 | ||||||||
\(472\) | −6.48727e6 | −1.34032 | ||||||||
\(473\) | 1.83050e6 | 0.376198 | ||||||||
\(474\) | −9.82261e6 | −2.00808 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −7.78108e6 | −1.57406 | ||||||||
\(477\) | 4.50278e6 | 0.906118 | ||||||||
\(478\) | −1.23627e7 | −2.47482 | ||||||||
\(479\) | 5.82530e6 | 1.16006 | 0.580029 | − | 0.814596i | \(-0.303041\pi\) | ||||
0.580029 | + | 0.814596i | \(0.303041\pi\) | |||||||
\(480\) | −4.03248e6 | −0.798856 | ||||||||
\(481\) | 1.01705e7 | 2.00437 | ||||||||
\(482\) | −5.62697e6 | −1.10321 | ||||||||
\(483\) | −3.93091e6 | −0.766700 | ||||||||
\(484\) | 761805. | 0.147819 | ||||||||
\(485\) | 1.44936e6 | 0.279782 | ||||||||
\(486\) | 9.99262e6 | 1.91906 | ||||||||
\(487\) | −2.83168e6 | −0.541030 | −0.270515 | − | 0.962716i | \(-0.587194\pi\) | ||||
−0.270515 | + | 0.962716i | \(0.587194\pi\) | |||||||
\(488\) | −2.51635e6 | −0.478323 | ||||||||
\(489\) | −1.03092e7 | −1.94963 | ||||||||
\(490\) | 2.84031e6 | 0.534411 | ||||||||
\(491\) | −5.25571e6 | −0.983846 | −0.491923 | − | 0.870639i | \(-0.663706\pi\) | ||||
−0.491923 | + | 0.870639i | \(0.663706\pi\) | |||||||
\(492\) | 6.05116e6 | 1.12700 | ||||||||
\(493\) | 8.00721e6 | 1.48376 | ||||||||
\(494\) | 2.83351e6 | 0.522405 | ||||||||
\(495\) | −1.68024e6 | −0.308219 | ||||||||
\(496\) | −112098. | −0.0204595 | ||||||||
\(497\) | 1.52351e6 | 0.276665 | ||||||||
\(498\) | 1.69330e7 | 3.05957 | ||||||||
\(499\) | −4.86665e6 | −0.874941 | −0.437471 | − | 0.899233i | \(-0.644126\pi\) | ||||
−0.437471 | + | 0.899233i | \(0.644126\pi\) | |||||||
\(500\) | 813004. | 0.145435 | ||||||||
\(501\) | −4.85035e6 | −0.863334 | ||||||||
\(502\) | 6.31962e6 | 1.11926 | ||||||||
\(503\) | −5.00425e6 | −0.881899 | −0.440949 | − | 0.897532i | \(-0.645358\pi\) | ||||
−0.440949 | + | 0.897532i | \(0.645358\pi\) | |||||||
\(504\) | −6.77609e6 | −1.18824 | ||||||||
\(505\) | −1.15319e6 | −0.201221 | ||||||||
\(506\) | 2.32273e6 | 0.403294 | ||||||||
\(507\) | −1.02248e7 | −1.76658 | ||||||||
\(508\) | 1.32346e7 | 2.27537 | ||||||||
\(509\) | −76974.8 | −0.0131690 | −0.00658452 | − | 0.999978i | \(-0.502096\pi\) | ||||
−0.00658452 | + | 0.999978i | \(0.502096\pi\) | |||||||
\(510\) | −1.45772e7 | −2.48170 | ||||||||
\(511\) | −3.54393e6 | −0.600390 | ||||||||
\(512\) | 212292. | 0.0357898 | ||||||||
\(513\) | 3.18724e6 | 0.534714 | ||||||||
\(514\) | −5.17435e6 | −0.863870 | ||||||||
\(515\) | −1.86459e6 | −0.309788 | ||||||||
\(516\) | 2.22424e7 | 3.67754 | ||||||||
\(517\) | −3.53385e6 | −0.581463 | ||||||||
\(518\) | −7.23351e6 | −1.18447 | ||||||||
\(519\) | −6.94243e6 | −1.13134 | ||||||||
\(520\) | −3.93086e6 | −0.637499 | ||||||||
\(521\) | 6.10975e6 | 0.986119 | 0.493059 | − | 0.869996i | \(-0.335878\pi\) | ||||
0.493059 | + | 0.869996i | \(0.335878\pi\) | |||||||
\(522\) | 1.81119e7 | 2.90929 | ||||||||
\(523\) | 7.63002e6 | 1.21975 | 0.609876 | − | 0.792497i | \(-0.291219\pi\) | ||||
0.609876 | + | 0.792497i | \(0.291219\pi\) | |||||||
\(524\) | −6.48563e6 | −1.03187 | ||||||||
\(525\) | −1.17323e6 | −0.185774 | ||||||||
\(526\) | 1.58911e7 | 2.50433 | ||||||||
\(527\) | 1.37700e7 | 2.15977 | ||||||||
\(528\) | 62656.0 | 0.00978087 | ||||||||
\(529\) | −2.05125e6 | −0.318698 | ||||||||
\(530\) | −1.85779e6 | −0.287281 | ||||||||
\(531\) | 1.96225e7 | 3.02008 | ||||||||
\(532\) | −1.24784e6 | −0.191153 | ||||||||
\(533\) | −3.52400e6 | −0.537301 | ||||||||
\(534\) | 2.10845e7 | 3.19971 | ||||||||
\(535\) | 4.82325e6 | 0.728543 | ||||||||
\(536\) | 4.31743e6 | 0.649102 | ||||||||
\(537\) | 9.83764e6 | 1.47216 | ||||||||
\(538\) | −5.23337e6 | −0.779518 | ||||||||
\(539\) | 1.49964e6 | 0.222339 | ||||||||
\(540\) | −1.14847e7 | −1.69487 | ||||||||
\(541\) | 1.73668e6 | 0.255110 | 0.127555 | − | 0.991832i | \(-0.459287\pi\) | ||||
0.127555 | + | 0.991832i | \(0.459287\pi\) | |||||||
\(542\) | −6.32283e6 | −0.924514 | ||||||||
\(543\) | 1.76156e6 | 0.256388 | ||||||||
\(544\) | −1.28498e7 | −1.86165 | ||||||||
\(545\) | −3.22904e6 | −0.465674 | ||||||||
\(546\) | 1.47340e7 | 2.11514 | ||||||||
\(547\) | −7.51122e6 | −1.07335 | −0.536676 | − | 0.843788i | \(-0.680320\pi\) | ||||
−0.536676 | + | 0.843788i | \(0.680320\pi\) | |||||||
\(548\) | −5.03258e6 | −0.715879 | ||||||||
\(549\) | 7.61138e6 | 1.07779 | ||||||||
\(550\) | 693248. | 0.0977196 | ||||||||
\(551\) | 1.28411e6 | 0.180186 | ||||||||
\(552\) | 1.08659e7 | 1.51782 | ||||||||
\(553\) | −2.51918e6 | −0.350305 | ||||||||
\(554\) | 1.12113e7 | 1.55196 | ||||||||
\(555\) | −8.39095e6 | −1.15632 | ||||||||
\(556\) | −1.12650e7 | −1.54542 | ||||||||
\(557\) | −1.34726e7 | −1.83998 | −0.919990 | − | 0.391942i | \(-0.871803\pi\) | ||||
−0.919990 | + | 0.391942i | \(0.871803\pi\) | |||||||
\(558\) | 3.11470e7 | 4.23478 | ||||||||
\(559\) | −1.29532e7 | −1.75327 | ||||||||
\(560\) | 30434.9 | 0.00410111 | ||||||||
\(561\) | −7.69657e6 | −1.03250 | ||||||||
\(562\) | −2.18471e7 | −2.91778 | ||||||||
\(563\) | 4.28186e6 | 0.569327 | 0.284663 | − | 0.958628i | \(-0.408118\pi\) | ||||
0.284663 | + | 0.958628i | \(0.408118\pi\) | |||||||
\(564\) | −4.29398e7 | −5.68411 | ||||||||
\(565\) | −2.89378e6 | −0.381368 | ||||||||
\(566\) | 2.47827e6 | 0.325168 | ||||||||
\(567\) | 7.60671e6 | 0.993663 | ||||||||
\(568\) | −4.21133e6 | −0.547708 | ||||||||
\(569\) | −1.24720e7 | −1.61494 | −0.807471 | − | 0.589907i | \(-0.799164\pi\) | ||||
−0.807471 | + | 0.589907i | \(0.799164\pi\) | |||||||
\(570\) | −2.33773e6 | −0.301375 | ||||||||
\(571\) | 1.26377e7 | 1.62210 | 0.811049 | − | 0.584978i | \(-0.198897\pi\) | ||||
0.811049 | + | 0.584978i | \(0.198897\pi\) | |||||||
\(572\) | −5.39079e6 | −0.688910 | ||||||||
\(573\) | −1.70804e7 | −2.17326 | ||||||||
\(574\) | 2.50636e6 | 0.317515 | ||||||||
\(575\) | 1.30879e6 | 0.165082 | ||||||||
\(576\) | −2.93912e7 | −3.69114 | ||||||||
\(577\) | 1.20353e6 | 0.150494 | 0.0752470 | − | 0.997165i | \(-0.476025\pi\) | ||||
0.0752470 | + | 0.997165i | \(0.476025\pi\) | |||||||
\(578\) | −3.34356e7 | −4.16284 | ||||||||
\(579\) | −1.50211e6 | −0.186211 | ||||||||
\(580\) | −4.62707e6 | −0.571132 | ||||||||
\(581\) | 4.34276e6 | 0.533735 | ||||||||
\(582\) | 1.50170e7 | 1.83770 | ||||||||
\(583\) | −980888. | −0.119522 | ||||||||
\(584\) | 9.79625e6 | 1.18858 | ||||||||
\(585\) | 1.18900e7 | 1.43645 | ||||||||
\(586\) | 1.76847e7 | 2.12743 | ||||||||
\(587\) | 690137. | 0.0826685 | 0.0413342 | − | 0.999145i | \(-0.486839\pi\) | ||||
0.0413342 | + | 0.999145i | \(0.486839\pi\) | |||||||
\(588\) | 1.82222e7 | 2.17349 | ||||||||
\(589\) | 2.20828e6 | 0.262280 | ||||||||
\(590\) | −8.09602e6 | −0.957506 | ||||||||
\(591\) | 2.71358e7 | 3.19576 | ||||||||
\(592\) | 217670. | 0.0255267 | ||||||||
\(593\) | −3.51525e6 | −0.410506 | −0.205253 | − | 0.978709i | \(-0.565802\pi\) | ||||
−0.205253 | + | 0.978709i | \(0.565802\pi\) | |||||||
\(594\) | −9.79301e6 | −1.13881 | ||||||||
\(595\) | −3.73858e6 | −0.432927 | ||||||||
\(596\) | −1.74625e7 | −2.01368 | ||||||||
\(597\) | 3.75423e6 | 0.431108 | ||||||||
\(598\) | −1.64364e7 | −1.87955 | ||||||||
\(599\) | 8.04943e6 | 0.916638 | 0.458319 | − | 0.888788i | \(-0.348452\pi\) | ||||
0.458319 | + | 0.888788i | \(0.348452\pi\) | |||||||
\(600\) | 3.24308e6 | 0.367773 | ||||||||
\(601\) | −3.27785e6 | −0.370171 | −0.185085 | − | 0.982722i | \(-0.559256\pi\) | ||||
−0.185085 | + | 0.982722i | \(0.559256\pi\) | |||||||
\(602\) | 9.21269e6 | 1.03608 | ||||||||
\(603\) | −1.30592e7 | −1.46260 | ||||||||
\(604\) | 6.11600e6 | 0.682143 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | −1.19484e7 | −1.32168 | ||||||||
\(607\) | −678553. | −0.0747502 | −0.0373751 | − | 0.999301i | \(-0.511900\pi\) | ||||
−0.0373751 | + | 0.999301i | \(0.511900\pi\) | |||||||
\(608\) | −2.06070e6 | −0.226077 | ||||||||
\(609\) | 6.67724e6 | 0.729548 | ||||||||
\(610\) | −3.14036e6 | −0.341708 | ||||||||
\(611\) | 2.50068e7 | 2.70991 | ||||||||
\(612\) | −6.50589e7 | −7.02148 | ||||||||
\(613\) | −1.28758e7 | −1.38395 | −0.691977 | − | 0.721920i | \(-0.743260\pi\) | ||||
−0.691977 | + | 0.721920i | \(0.743260\pi\) | |||||||
\(614\) | 1.39277e7 | 1.49094 | ||||||||
\(615\) | 2.90741e6 | 0.309969 | ||||||||
\(616\) | 1.47611e6 | 0.156735 | ||||||||
\(617\) | −1.72087e7 | −1.81985 | −0.909924 | − | 0.414776i | \(-0.863860\pi\) | ||||
−0.909924 | + | 0.414776i | \(0.863860\pi\) | |||||||
\(618\) | −1.93193e7 | −2.03479 | ||||||||
\(619\) | 6.64082e6 | 0.696619 | 0.348309 | − | 0.937380i | \(-0.386756\pi\) | ||||
0.348309 | + | 0.937380i | \(0.386756\pi\) | |||||||
\(620\) | −7.95719e6 | −0.831344 | ||||||||
\(621\) | −1.84883e7 | −1.92384 | ||||||||
\(622\) | 2.30661e7 | 2.39055 | ||||||||
\(623\) | 5.40749e6 | 0.558182 | ||||||||
\(624\) | −443375. | −0.0455837 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 4.99619e6 | 0.509569 | ||||||||
\(627\) | −1.23429e6 | −0.125386 | ||||||||
\(628\) | −1.85037e7 | −1.87223 | ||||||||
\(629\) | −2.67383e7 | −2.69468 | ||||||||
\(630\) | −8.45647e6 | −0.848863 | ||||||||
\(631\) | 5.84026e6 | 0.583927 | 0.291964 | − | 0.956429i | \(-0.405691\pi\) | ||||
0.291964 | + | 0.956429i | \(0.405691\pi\) | |||||||
\(632\) | 6.96359e6 | 0.693490 | ||||||||
\(633\) | 1.16499e7 | 1.15562 | ||||||||
\(634\) | −1.22551e6 | −0.121086 | ||||||||
\(635\) | 6.35886e6 | 0.625813 | ||||||||
\(636\) | −1.19188e7 | −1.16839 | ||||||||
\(637\) | −1.06120e7 | −1.03621 | ||||||||
\(638\) | −3.94550e6 | −0.383752 | ||||||||
\(639\) | 1.27383e7 | 1.23413 | ||||||||
\(640\) | 7.55980e6 | 0.729558 | ||||||||
\(641\) | −2.49949e6 | −0.240274 | −0.120137 | − | 0.992757i | \(-0.538333\pi\) | ||||
−0.120137 | + | 0.992757i | \(0.538333\pi\) | |||||||
\(642\) | 4.99744e7 | 4.78531 | ||||||||
\(643\) | 7.25773e6 | 0.692267 | 0.346134 | − | 0.938185i | \(-0.387494\pi\) | ||||
0.346134 | + | 0.938185i | \(0.387494\pi\) | |||||||
\(644\) | 7.23839e6 | 0.687744 | ||||||||
\(645\) | 1.06868e7 | 1.01146 | ||||||||
\(646\) | −7.44934e6 | −0.702322 | ||||||||
\(647\) | 1.21058e7 | 1.13692 | 0.568462 | − | 0.822709i | \(-0.307539\pi\) | ||||
0.568462 | + | 0.822709i | \(0.307539\pi\) | |||||||
\(648\) | −2.10267e7 | −1.96713 | ||||||||
\(649\) | −4.27459e6 | −0.398366 | ||||||||
\(650\) | −4.90566e6 | −0.455422 | ||||||||
\(651\) | 1.14829e7 | 1.06194 | ||||||||
\(652\) | 1.89833e7 | 1.74885 | ||||||||
\(653\) | 2.08897e7 | 1.91712 | 0.958561 | − | 0.284888i | \(-0.0919563\pi\) | ||||
0.958561 | + | 0.284888i | \(0.0919563\pi\) | |||||||
\(654\) | −3.34565e7 | −3.05870 | ||||||||
\(655\) | −3.11616e6 | −0.283802 | ||||||||
\(656\) | −75421.3 | −0.00684280 | ||||||||
\(657\) | −2.96315e7 | −2.67818 | ||||||||
\(658\) | −1.77855e7 | −1.60140 | ||||||||
\(659\) | −4.46750e6 | −0.400729 | −0.200365 | − | 0.979721i | \(-0.564213\pi\) | ||||
−0.200365 | + | 0.979721i | \(0.564213\pi\) | |||||||
\(660\) | 4.44757e6 | 0.397432 | ||||||||
\(661\) | 1.70197e6 | 0.151512 | 0.0757560 | − | 0.997126i | \(-0.475863\pi\) | ||||
0.0757560 | + | 0.997126i | \(0.475863\pi\) | |||||||
\(662\) | 2.86574e7 | 2.54151 | ||||||||
\(663\) | 5.44636e7 | 4.81197 | ||||||||
\(664\) | −1.20044e7 | −1.05662 | ||||||||
\(665\) | −599551. | −0.0525742 | ||||||||
\(666\) | −6.04806e7 | −5.28361 | ||||||||
\(667\) | −7.44874e6 | −0.648289 | ||||||||
\(668\) | 8.93144e6 | 0.774427 | ||||||||
\(669\) | −3.31119e7 | −2.86035 | ||||||||
\(670\) | 5.38809e6 | 0.463711 | ||||||||
\(671\) | −1.65807e6 | −0.142166 | ||||||||
\(672\) | −1.07155e7 | −0.915351 | ||||||||
\(673\) | 1.82947e7 | 1.55699 | 0.778496 | − | 0.627649i | \(-0.215983\pi\) | ||||
0.778496 | + | 0.627649i | \(0.215983\pi\) | |||||||
\(674\) | −1.88702e7 | −1.60002 | ||||||||
\(675\) | −5.51808e6 | −0.466153 | ||||||||
\(676\) | 1.88279e7 | 1.58466 | ||||||||
\(677\) | 5.79481e6 | 0.485923 | 0.242961 | − | 0.970036i | \(-0.421881\pi\) | ||||
0.242961 | + | 0.970036i | \(0.421881\pi\) | |||||||
\(678\) | −2.99829e7 | −2.50495 | ||||||||
\(679\) | 3.85136e6 | 0.320582 | ||||||||
\(680\) | 1.03343e7 | 0.857055 | ||||||||
\(681\) | −1.76891e7 | −1.46163 | ||||||||
\(682\) | −6.78509e6 | −0.558592 | ||||||||
\(683\) | −5.53455e6 | −0.453973 | −0.226987 | − | 0.973898i | \(-0.572887\pi\) | ||||
−0.226987 | + | 0.973898i | \(0.572887\pi\) | |||||||
\(684\) | −1.04334e7 | −0.852681 | ||||||||
\(685\) | −2.41801e6 | −0.196894 | ||||||||
\(686\) | 1.77826e7 | 1.44273 | ||||||||
\(687\) | −1.13933e7 | −0.920994 | ||||||||
\(688\) | −277228. | −0.0223288 | ||||||||
\(689\) | 6.94110e6 | 0.557032 | ||||||||
\(690\) | 1.35605e7 | 1.08431 | ||||||||
\(691\) | 8.62709e6 | 0.687336 | 0.343668 | − | 0.939091i | \(-0.388331\pi\) | ||||
0.343668 | + | 0.939091i | \(0.388331\pi\) | |||||||
\(692\) | 1.27838e7 | 1.01483 | ||||||||
\(693\) | −4.46489e6 | −0.353165 | ||||||||
\(694\) | −3.64990e7 | −2.87662 | ||||||||
\(695\) | −5.41252e6 | −0.425048 | ||||||||
\(696\) | −1.84574e7 | −1.44427 | ||||||||
\(697\) | 9.26464e6 | 0.722348 | ||||||||
\(698\) | 2.05716e7 | 1.59819 | ||||||||
\(699\) | −1.46383e7 | −1.13318 | ||||||||
\(700\) | 2.16039e6 | 0.166643 | ||||||||
\(701\) | 2.57068e7 | 1.97584 | 0.987922 | − | 0.154952i | \(-0.0495224\pi\) | ||||
0.987922 | + | 0.154952i | \(0.0495224\pi\) | |||||||
\(702\) | 6.92988e7 | 5.30741 | ||||||||
\(703\) | −4.28799e6 | −0.327239 | ||||||||
\(704\) | 6.40259e6 | 0.486882 | ||||||||
\(705\) | −2.06313e7 | −1.56334 | ||||||||
\(706\) | −2.82302e6 | −0.213158 | ||||||||
\(707\) | −3.06437e6 | −0.230565 | ||||||||
\(708\) | −5.19405e7 | −3.89424 | ||||||||
\(709\) | 5.87521e6 | 0.438943 | 0.219471 | − | 0.975619i | \(-0.429567\pi\) | ||||
0.219471 | + | 0.975619i | \(0.429567\pi\) | |||||||
\(710\) | −5.25568e6 | −0.391276 | ||||||||
\(711\) | −2.10633e7 | −1.56262 | ||||||||
\(712\) | −1.49476e7 | −1.10502 | ||||||||
\(713\) | −1.28096e7 | −0.943654 | ||||||||
\(714\) | −3.87360e7 | −2.84360 | ||||||||
\(715\) | −2.59012e6 | −0.189476 | ||||||||
\(716\) | −1.81150e7 | −1.32056 | ||||||||
\(717\) | −3.81078e7 | −2.76832 | ||||||||
\(718\) | 1.02060e7 | 0.738831 | ||||||||
\(719\) | −2.20444e7 | −1.59029 | −0.795143 | − | 0.606422i | \(-0.792604\pi\) | ||||
−0.795143 | + | 0.606422i | \(0.792604\pi\) | |||||||
\(720\) | 254472. | 0.0182940 | ||||||||
\(721\) | −4.95476e6 | −0.354964 | ||||||||
\(722\) | −1.19464e6 | −0.0852893 | ||||||||
\(723\) | −1.73451e7 | −1.23404 | ||||||||
\(724\) | −3.24374e6 | −0.229985 | ||||||||
\(725\) | −2.22317e6 | −0.157083 | ||||||||
\(726\) | 3.79244e6 | 0.267040 | ||||||||
\(727\) | 1.69303e7 | 1.18803 | 0.594015 | − | 0.804454i | \(-0.297542\pi\) | ||||
0.594015 | + | 0.804454i | \(0.297542\pi\) | |||||||
\(728\) | −1.04455e7 | −0.730464 | ||||||||
\(729\) | 2.97786e6 | 0.207532 | ||||||||
\(730\) | 1.22256e7 | 0.849107 | ||||||||
\(731\) | 3.40543e7 | 2.35710 | ||||||||
\(732\) | −2.01472e7 | −1.38975 | ||||||||
\(733\) | 2.50996e7 | 1.72547 | 0.862733 | − | 0.505661i | \(-0.168751\pi\) | ||||
0.862733 | + | 0.505661i | \(0.168751\pi\) | |||||||
\(734\) | 230897. | 0.0158190 | ||||||||
\(735\) | 8.75522e6 | 0.597790 | ||||||||
\(736\) | 1.19535e7 | 0.813397 | ||||||||
\(737\) | 2.84483e6 | 0.192925 | ||||||||
\(738\) | 2.09561e7 | 1.41635 | ||||||||
\(739\) | 2.29213e7 | 1.54393 | 0.771967 | − | 0.635662i | \(-0.219273\pi\) | ||||
0.771967 | + | 0.635662i | \(0.219273\pi\) | |||||||
\(740\) | 1.54511e7 | 1.03724 | ||||||||
\(741\) | 8.73426e6 | 0.584360 | ||||||||
\(742\) | −4.93670e6 | −0.329175 | ||||||||
\(743\) | 2.72611e7 | 1.81164 | 0.905820 | − | 0.423662i | \(-0.139255\pi\) | ||||
0.905820 | + | 0.423662i | \(0.139255\pi\) | |||||||
\(744\) | −3.17413e7 | −2.10229 | ||||||||
\(745\) | −8.39021e6 | −0.553837 | ||||||||
\(746\) | −4.43023e7 | −2.91460 | ||||||||
\(747\) | 3.63106e7 | 2.38085 | ||||||||
\(748\) | 1.41725e7 | 0.926172 | ||||||||
\(749\) | 1.28168e7 | 0.834785 | ||||||||
\(750\) | 4.04732e6 | 0.262733 | ||||||||
\(751\) | −3.04081e7 | −1.96739 | −0.983693 | − | 0.179854i | \(-0.942437\pi\) | ||||
−0.983693 | + | 0.179854i | \(0.942437\pi\) | |||||||
\(752\) | 535200. | 0.0345121 | ||||||||
\(753\) | 1.94801e7 | 1.25200 | ||||||||
\(754\) | 2.79197e7 | 1.78847 | ||||||||
\(755\) | 2.93856e6 | 0.187615 | ||||||||
\(756\) | −3.05183e7 | −1.94203 | ||||||||
\(757\) | −2.16756e6 | −0.137478 | −0.0687388 | − | 0.997635i | \(-0.521898\pi\) | ||||
−0.0687388 | + | 0.997635i | \(0.521898\pi\) | |||||||
\(758\) | −1.85473e7 | −1.17248 | ||||||||
\(759\) | 7.15977e6 | 0.451123 | ||||||||
\(760\) | 1.65730e6 | 0.104080 | ||||||||
\(761\) | −1.27130e7 | −0.795765 | −0.397882 | − | 0.917436i | \(-0.630255\pi\) | ||||
−0.397882 | + | 0.917436i | \(0.630255\pi\) | |||||||
\(762\) | 6.58850e7 | 4.11054 | ||||||||
\(763\) | −8.58050e6 | −0.533582 | ||||||||
\(764\) | 3.14518e7 | 1.94945 | ||||||||
\(765\) | −3.12589e7 | −1.93117 | ||||||||
\(766\) | 1.88304e7 | 1.15955 | ||||||||
\(767\) | 3.02485e7 | 1.85658 | ||||||||
\(768\) | 3.04822e7 | 1.86485 | ||||||||
\(769\) | 8.41597e6 | 0.513202 | 0.256601 | − | 0.966517i | \(-0.417397\pi\) | ||||
0.256601 | + | 0.966517i | \(0.417397\pi\) | |||||||
\(770\) | 1.84216e6 | 0.111970 | ||||||||
\(771\) | −1.59499e7 | −0.966321 | ||||||||
\(772\) | 2.76599e6 | 0.167035 | ||||||||
\(773\) | 1.79031e7 | 1.07765 | 0.538827 | − | 0.842416i | \(-0.318868\pi\) | ||||
0.538827 | + | 0.842416i | \(0.318868\pi\) | |||||||
\(774\) | 7.70289e7 | 4.62170 | ||||||||
\(775\) | −3.82320e6 | −0.228651 | ||||||||
\(776\) | −1.06460e7 | −0.634650 | ||||||||
\(777\) | −2.22972e7 | −1.32495 | ||||||||
\(778\) | −2.23508e7 | −1.32386 | ||||||||
\(779\) | 1.48576e6 | 0.0877212 | ||||||||
\(780\) | −3.14725e7 | −1.85223 | ||||||||
\(781\) | −2.77493e6 | −0.162789 | ||||||||
\(782\) | 4.32116e7 | 2.52687 | ||||||||
\(783\) | 3.14052e7 | 1.83061 | ||||||||
\(784\) | −227120. | −0.0131967 | ||||||||
\(785\) | −8.89047e6 | −0.514933 | ||||||||
\(786\) | −3.22869e7 | −1.86410 | ||||||||
\(787\) | 2.59120e7 | 1.49130 | 0.745648 | − | 0.666340i | \(-0.232140\pi\) | ||||
0.745648 | + | 0.666340i | \(0.232140\pi\) | |||||||
\(788\) | −4.99679e7 | −2.86665 | ||||||||
\(789\) | 4.89843e7 | 2.80133 | ||||||||
\(790\) | 8.69046e6 | 0.495421 | ||||||||
\(791\) | −7.68962e6 | −0.436982 | ||||||||
\(792\) | 1.23420e7 | 0.699153 | ||||||||
\(793\) | 1.17331e7 | 0.662565 | ||||||||
\(794\) | 3.28373e7 | 1.84849 | ||||||||
\(795\) | −5.72662e6 | −0.321352 | ||||||||
\(796\) | −6.91305e6 | −0.386712 | ||||||||
\(797\) | 1.67109e7 | 0.931866 | 0.465933 | − | 0.884820i | \(-0.345719\pi\) | ||||
0.465933 | + | 0.884820i | \(0.345719\pi\) | |||||||
\(798\) | −6.21204e6 | −0.345324 | ||||||||
\(799\) | −6.57432e7 | −3.64321 | ||||||||
\(800\) | 3.56769e6 | 0.197089 | ||||||||
\(801\) | 4.52130e7 | 2.48990 | ||||||||
\(802\) | 2.26195e7 | 1.24179 | ||||||||
\(803\) | 6.45493e6 | 0.353267 | ||||||||
\(804\) | 3.45676e7 | 1.88594 | ||||||||
\(805\) | 3.47783e6 | 0.189156 | ||||||||
\(806\) | 4.80136e7 | 2.60332 | ||||||||
\(807\) | −1.61318e7 | −0.871965 | ||||||||
\(808\) | 8.47063e6 | 0.456444 | ||||||||
\(809\) | −1.13038e7 | −0.607229 | −0.303614 | − | 0.952795i | \(-0.598193\pi\) | ||||
−0.303614 | + | 0.952795i | \(0.598193\pi\) | |||||||
\(810\) | −2.62410e7 | −1.40530 | ||||||||
\(811\) | −3.69748e7 | −1.97403 | −0.987015 | − | 0.160630i | \(-0.948647\pi\) | ||||
−0.987015 | + | 0.160630i | \(0.948647\pi\) | |||||||
\(812\) | −1.22955e7 | −0.654418 | ||||||||
\(813\) | −1.94901e7 | −1.03416 | ||||||||
\(814\) | 1.31751e7 | 0.696938 | ||||||||
\(815\) | 9.12093e6 | 0.481000 | ||||||||
\(816\) | 1.16564e6 | 0.0612829 | ||||||||
\(817\) | 5.46124e6 | 0.286244 | ||||||||
\(818\) | 4.25047e7 | 2.22103 | ||||||||
\(819\) | 3.15951e7 | 1.64593 | ||||||||
\(820\) | −5.35370e6 | −0.278048 | ||||||||
\(821\) | −3.01143e7 | −1.55924 | −0.779622 | − | 0.626250i | \(-0.784589\pi\) | ||||
−0.779622 | + | 0.626250i | \(0.784589\pi\) | |||||||
\(822\) | −2.50533e7 | −1.29326 | ||||||||
\(823\) | −2.11678e7 | −1.08937 | −0.544685 | − | 0.838641i | \(-0.683351\pi\) | ||||
−0.544685 | + | 0.838641i | \(0.683351\pi\) | |||||||
\(824\) | 1.36961e7 | 0.702714 | ||||||||
\(825\) | 2.13693e6 | 0.109309 | ||||||||
\(826\) | −2.15135e7 | −1.09714 | ||||||||
\(827\) | 2.42006e7 | 1.23044 | 0.615222 | − | 0.788354i | \(-0.289066\pi\) | ||||
0.615222 | + | 0.788354i | \(0.289066\pi\) | |||||||
\(828\) | 6.05214e7 | 3.06784 | ||||||||
\(829\) | 2.15825e7 | 1.09073 | 0.545364 | − | 0.838199i | \(-0.316391\pi\) | ||||
0.545364 | + | 0.838199i | \(0.316391\pi\) | |||||||
\(830\) | −1.49813e7 | −0.754839 | ||||||||
\(831\) | 3.45587e7 | 1.73602 | ||||||||
\(832\) | −4.53069e7 | −2.26911 | ||||||||
\(833\) | 2.78991e7 | 1.39309 | ||||||||
\(834\) | −5.60799e7 | −2.79185 | ||||||||
\(835\) | 4.29130e6 | 0.212997 | ||||||||
\(836\) | 2.27282e6 | 0.112473 | ||||||||
\(837\) | 5.40076e7 | 2.66466 | ||||||||
\(838\) | −3.07473e7 | −1.51251 | ||||||||
\(839\) | −1.13438e6 | −0.0556355 | −0.0278178 | − | 0.999613i | \(-0.508856\pi\) | ||||
−0.0278178 | + | 0.999613i | \(0.508856\pi\) | |||||||
\(840\) | 8.61782e6 | 0.421404 | ||||||||
\(841\) | −7.85834e6 | −0.383125 | ||||||||
\(842\) | 5.52581e7 | 2.68606 | ||||||||
\(843\) | −6.73434e7 | −3.26382 | ||||||||
\(844\) | −2.14522e7 | −1.03661 | ||||||||
\(845\) | 9.04627e6 | 0.435840 | ||||||||
\(846\) | −1.48707e8 | −7.14343 | ||||||||
\(847\) | 972635. | 0.0465845 | ||||||||
\(848\) | 148555. | 0.00709409 | ||||||||
\(849\) | 7.63924e6 | 0.363732 | ||||||||
\(850\) | 1.28971e7 | 0.612270 | ||||||||
\(851\) | 2.48735e7 | 1.17737 | ||||||||
\(852\) | −3.37181e7 | −1.59135 | ||||||||
\(853\) | −6.38506e6 | −0.300464 | −0.150232 | − | 0.988651i | \(-0.548002\pi\) | ||||
−0.150232 | + | 0.988651i | \(0.548002\pi\) | |||||||
\(854\) | −8.34486e6 | −0.391539 | ||||||||
\(855\) | −5.01295e6 | −0.234519 | ||||||||
\(856\) | −3.54285e7 | −1.65260 | ||||||||
\(857\) | −3.31421e7 | −1.54144 | −0.770722 | − | 0.637172i | \(-0.780104\pi\) | ||||
−0.770722 | + | 0.637172i | \(0.780104\pi\) | |||||||
\(858\) | −2.68366e7 | −1.24454 | ||||||||
\(859\) | 2.29603e7 | 1.06168 | 0.530840 | − | 0.847472i | \(-0.321876\pi\) | ||||
0.530840 | + | 0.847472i | \(0.321876\pi\) | |||||||
\(860\) | −1.96787e7 | −0.907300 | ||||||||
\(861\) | 7.72583e6 | 0.355171 | ||||||||
\(862\) | −2.35716e7 | −1.08049 | ||||||||
\(863\) | −1.01302e7 | −0.463010 | −0.231505 | − | 0.972834i | \(-0.574365\pi\) | ||||
−0.231505 | + | 0.972834i | \(0.574365\pi\) | |||||||
\(864\) | −5.03982e7 | −2.29684 | ||||||||
\(865\) | 6.14225e6 | 0.279118 | ||||||||
\(866\) | 2.18349e7 | 0.989364 | ||||||||
\(867\) | −1.03065e8 | −4.65654 | ||||||||
\(868\) | −2.11446e7 | −0.952576 | ||||||||
\(869\) | 4.58844e6 | 0.206118 | ||||||||
\(870\) | −2.30346e7 | −1.03177 | ||||||||
\(871\) | −2.01310e7 | −0.899126 | ||||||||
\(872\) | 2.37185e7 | 1.05632 | ||||||||
\(873\) | 3.22019e7 | 1.43003 | ||||||||
\(874\) | 6.92979e6 | 0.306861 | ||||||||
\(875\) | 1.03800e6 | 0.0458331 | ||||||||
\(876\) | 7.84339e7 | 3.45337 | ||||||||
\(877\) | −2.12082e7 | −0.931119 | −0.465559 | − | 0.885017i | \(-0.654147\pi\) | ||||
−0.465559 | + | 0.885017i | \(0.654147\pi\) | |||||||
\(878\) | 4.56611e7 | 1.99899 | ||||||||
\(879\) | 5.45130e7 | 2.37973 | ||||||||
\(880\) | −55434.2 | −0.00241308 | ||||||||
\(881\) | 4.48994e7 | 1.94895 | 0.974475 | − | 0.224494i | \(-0.0720731\pi\) | ||||
0.974475 | + | 0.224494i | \(0.0720731\pi\) | |||||||
\(882\) | 6.31063e7 | 2.73150 | ||||||||
\(883\) | 4.21540e6 | 0.181943 | 0.0909717 | − | 0.995853i | \(-0.471003\pi\) | ||||
0.0909717 | + | 0.995853i | \(0.471003\pi\) | |||||||
\(884\) | −1.00289e8 | −4.31643 | ||||||||
\(885\) | −2.49559e7 | −1.07106 | ||||||||
\(886\) | 8.64578e6 | 0.370015 | ||||||||
\(887\) | 1.47395e7 | 0.629035 | 0.314518 | − | 0.949252i | \(-0.398157\pi\) | ||||
0.314518 | + | 0.949252i | \(0.398157\pi\) | |||||||
\(888\) | 6.16346e7 | 2.62296 | ||||||||
\(889\) | 1.68973e7 | 0.717074 | ||||||||
\(890\) | −1.86543e7 | −0.789414 | ||||||||
\(891\) | −1.38549e7 | −0.584667 | ||||||||
\(892\) | 6.09723e7 | 2.56578 | ||||||||
\(893\) | −1.05431e7 | −0.442427 | ||||||||
\(894\) | −8.69322e7 | −3.63778 | ||||||||
\(895\) | −8.70375e6 | −0.363203 | ||||||||
\(896\) | 2.00886e7 | 0.835948 | ||||||||
\(897\) | −5.06651e7 | −2.10246 | ||||||||
\(898\) | 3.28602e6 | 0.135981 | ||||||||
\(899\) | 2.17591e7 | 0.897927 | ||||||||
\(900\) | 1.80634e7 | 0.743350 | ||||||||
\(901\) | −1.82483e7 | −0.748875 | ||||||||
\(902\) | −4.56509e6 | −0.186824 | ||||||||
\(903\) | 2.83980e7 | 1.15896 | ||||||||
\(904\) | 2.12559e7 | 0.865084 | ||||||||
\(905\) | −1.55852e6 | −0.0632545 | ||||||||
\(906\) | 3.04468e7 | 1.23232 | ||||||||
\(907\) | −6.63616e6 | −0.267854 | −0.133927 | − | 0.990991i | \(-0.542759\pi\) | ||||
−0.133927 | + | 0.990991i | \(0.542759\pi\) | |||||||
\(908\) | 3.25727e7 | 1.31111 | ||||||||
\(909\) | −2.56217e7 | −1.02849 | ||||||||
\(910\) | −1.30358e7 | −0.521835 | ||||||||
\(911\) | 2.09681e7 | 0.837074 | 0.418537 | − | 0.908200i | \(-0.362543\pi\) | ||||
0.418537 | + | 0.908200i | \(0.362543\pi\) | |||||||
\(912\) | 186932. | 0.00744213 | ||||||||
\(913\) | −7.90992e6 | −0.314047 | ||||||||
\(914\) | 4.20666e7 | 1.66560 | ||||||||
\(915\) | −9.68013e6 | −0.382233 | ||||||||
\(916\) | 2.09796e7 | 0.826149 | ||||||||
\(917\) | −8.28054e6 | −0.325188 | ||||||||
\(918\) | −1.82187e8 | −7.13529 | ||||||||
\(919\) | 8.30744e6 | 0.324473 | 0.162236 | − | 0.986752i | \(-0.448129\pi\) | ||||
0.162236 | + | 0.986752i | \(0.448129\pi\) | |||||||
\(920\) | −9.61353e6 | −0.374467 | ||||||||
\(921\) | 4.29321e7 | 1.66776 | ||||||||
\(922\) | −6.23814e7 | −2.41673 | ||||||||
\(923\) | 1.96363e7 | 0.758676 | ||||||||
\(924\) | 1.18185e7 | 0.455388 | ||||||||
\(925\) | 7.42381e6 | 0.285281 | ||||||||
\(926\) | −5.28595e7 | −2.02580 | ||||||||
\(927\) | −4.14276e7 | −1.58340 | ||||||||
\(928\) | −2.03049e7 | −0.773982 | ||||||||
\(929\) | −2.68907e7 | −1.02226 | −0.511132 | − | 0.859502i | \(-0.670774\pi\) | ||||
−0.511132 | + | 0.859502i | \(0.670774\pi\) | |||||||
\(930\) | −3.96127e7 | −1.50185 | ||||||||
\(931\) | 4.47414e6 | 0.169175 | ||||||||
\(932\) | 2.69550e7 | 1.01648 | ||||||||
\(933\) | 7.11008e7 | 2.67406 | ||||||||
\(934\) | 2.06788e7 | 0.775635 | ||||||||
\(935\) | 6.80946e6 | 0.254732 | ||||||||
\(936\) | −8.73363e7 | −3.25840 | ||||||||
\(937\) | −1.95375e7 | −0.726975 | −0.363488 | − | 0.931599i | \(-0.618414\pi\) | ||||
−0.363488 | + | 0.931599i | \(0.618414\pi\) | |||||||
\(938\) | 1.43177e7 | 0.531333 | ||||||||
\(939\) | 1.54007e7 | 0.570002 | ||||||||
\(940\) | 3.79906e7 | 1.40235 | ||||||||
\(941\) | 3.68525e7 | 1.35673 | 0.678364 | − | 0.734726i | \(-0.262689\pi\) | ||||
0.678364 | + | 0.734726i | \(0.262689\pi\) | |||||||
\(942\) | −9.21154e7 | −3.38225 | ||||||||
\(943\) | −8.61848e6 | −0.315611 | ||||||||
\(944\) | 647383. | 0.0236446 | ||||||||
\(945\) | −1.46631e7 | −0.534131 | ||||||||
\(946\) | −1.67800e7 | −0.609628 | ||||||||
\(947\) | −151048. | −0.00547318 | −0.00273659 | − | 0.999996i | \(-0.500871\pi\) | ||||
−0.00273659 | + | 0.999996i | \(0.500871\pi\) | |||||||
\(948\) | 5.57541e7 | 2.01491 | ||||||||
\(949\) | −4.56774e7 | −1.64640 | ||||||||
\(950\) | 2.06828e6 | 0.0743535 | ||||||||
\(951\) | −3.77761e6 | −0.135446 | ||||||||
\(952\) | 2.74613e7 | 0.982037 | ||||||||
\(953\) | 1.04441e7 | 0.372509 | 0.186255 | − | 0.982501i | \(-0.440365\pi\) | ||||
0.186255 | + | 0.982501i | \(0.440365\pi\) | |||||||
\(954\) | −4.12766e7 | −1.46836 | ||||||||
\(955\) | 1.51117e7 | 0.536173 | ||||||||
\(956\) | 7.01718e7 | 2.48324 | ||||||||
\(957\) | −1.21620e7 | −0.429263 | ||||||||
\(958\) | −5.34001e7 | −1.87987 | ||||||||
\(959\) | −6.42536e6 | −0.225606 | ||||||||
\(960\) | 3.73796e7 | 1.30905 | ||||||||
\(961\) | 8.79001e6 | 0.307030 | ||||||||
\(962\) | −9.32319e7 | −3.24808 | ||||||||
\(963\) | 1.07163e8 | 3.72375 | ||||||||
\(964\) | 3.19393e7 | 1.10696 | ||||||||
\(965\) | 1.32898e6 | 0.0459409 | ||||||||
\(966\) | 3.60343e7 | 1.24243 | ||||||||
\(967\) | −2.27014e7 | −0.780704 | −0.390352 | − | 0.920666i | \(-0.627647\pi\) | ||||
−0.390352 | + | 0.920666i | \(0.627647\pi\) | |||||||
\(968\) | −2.68859e6 | −0.0922223 | ||||||||
\(969\) | −2.29625e7 | −0.785615 | ||||||||
\(970\) | −1.32861e7 | −0.453387 | ||||||||
\(971\) | 2.51537e7 | 0.856158 | 0.428079 | − | 0.903741i | \(-0.359191\pi\) | ||||
0.428079 | + | 0.903741i | \(0.359191\pi\) | |||||||
\(972\) | −5.67191e7 | −1.92559 | ||||||||
\(973\) | −1.43827e7 | −0.487031 | ||||||||
\(974\) | 2.59577e7 | 0.876737 | ||||||||
\(975\) | −1.51216e7 | −0.509433 | ||||||||
\(976\) | 251113. | 0.00843810 | ||||||||
\(977\) | 3.04134e7 | 1.01936 | 0.509681 | − | 0.860363i | \(-0.329763\pi\) | ||||
0.509681 | + | 0.860363i | \(0.329763\pi\) | |||||||
\(978\) | 9.45032e7 | 3.15936 | ||||||||
\(979\) | −9.84922e6 | −0.328432 | ||||||||
\(980\) | −1.61219e7 | −0.536229 | ||||||||
\(981\) | −7.17430e7 | −2.38017 | ||||||||
\(982\) | 4.81786e7 | 1.59432 | ||||||||
\(983\) | −6.43832e6 | −0.212515 | −0.106257 | − | 0.994339i | \(-0.533887\pi\) | ||||
−0.106257 | + | 0.994339i | \(0.533887\pi\) | |||||||
\(984\) | −2.13560e7 | −0.703123 | ||||||||
\(985\) | −2.40081e7 | −0.788437 | ||||||||
\(986\) | −7.34014e7 | −2.40443 | ||||||||
\(987\) | −5.48235e7 | −1.79132 | ||||||||
\(988\) | −1.60833e7 | −0.524182 | ||||||||
\(989\) | −3.16792e7 | −1.02987 | ||||||||
\(990\) | 1.54026e7 | 0.499467 | ||||||||
\(991\) | 2.37565e7 | 0.768418 | 0.384209 | − | 0.923246i | \(-0.374474\pi\) | ||||
0.384209 | + | 0.923246i | \(0.374474\pi\) | |||||||
\(992\) | −3.49184e7 | −1.12661 | ||||||||
\(993\) | 8.83360e7 | 2.84292 | ||||||||
\(994\) | −1.39659e7 | −0.448335 | ||||||||
\(995\) | −3.32152e6 | −0.106360 | ||||||||
\(996\) | −9.61134e7 | −3.06998 | ||||||||
\(997\) | 4.00676e7 | 1.27660 | 0.638301 | − | 0.769787i | \(-0.279638\pi\) | ||||
0.638301 | + | 0.769787i | \(0.279638\pi\) | |||||||
\(998\) | 4.46122e7 | 1.41784 | ||||||||
\(999\) | −1.04871e8 | −3.32461 |
(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 | 1045.6.a.f.1.4 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.f.1.4 | ✓ | 38 | 1.1 | even | 1 | trivial |