Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.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: | \(170.562223914\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 86504x^{3} - 9117228x^{2} + 89606664x + 21810067776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(44.7350\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −12.1505 | −0.0434708 | −0.0217354 | − | 0.999764i | \(-0.506919\pi\) | ||||
−0.0217354 | + | 0.999764i | \(0.506919\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 97.2036 | 0.0307385 | ||||||||
\(11\) | 2351.17 | 0.532609 | 0.266305 | − | 0.963889i | \(-0.414197\pi\) | ||||
0.266305 | + | 0.963889i | \(0.414197\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | 2197.00 | 0.277350 | ||||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | −328.062 | −0.0250979 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −23753.6 | −1.17262 | −0.586310 | − | 0.810087i | \(-0.699420\pi\) | ||||
−0.586310 | + | 0.810087i | \(0.699420\pi\) | |||||||
\(18\) | −5832.00 | −0.235702 | ||||||||
\(19\) | 40958.6 | 1.36996 | 0.684980 | − | 0.728562i | \(-0.259811\pi\) | ||||
0.684980 | + | 0.728562i | \(0.259811\pi\) | |||||||
\(20\) | −777.629 | −0.0217354 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | −18809.3 | −0.376612 | ||||||||
\(23\) | −36727.0 | −0.629416 | −0.314708 | − | 0.949189i | \(-0.601907\pi\) | ||||
−0.314708 | + | 0.949189i | \(0.601907\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | −77977.4 | −0.998110 | ||||||||
\(26\) | −17576.0 | −0.196116 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | −145789. | −1.11002 | −0.555012 | − | 0.831842i | \(-0.687286\pi\) | ||||
−0.555012 | + | 0.831842i | \(0.687286\pi\) | |||||||
\(30\) | 2624.50 | 0.0177469 | ||||||||
\(31\) | −91087.9 | −0.549155 | −0.274577 | − | 0.961565i | \(-0.588538\pi\) | ||||
−0.274577 | + | 0.961565i | \(0.588538\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | 63481.5 | 0.307502 | ||||||||
\(34\) | 190028. | 0.829168 | ||||||||
\(35\) | −4167.60 | −0.0164304 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 389729. | 1.26490 | 0.632451 | − | 0.774601i | \(-0.282049\pi\) | ||||
0.632451 | + | 0.774601i | \(0.282049\pi\) | |||||||
\(38\) | −327669. | −0.968708 | ||||||||
\(39\) | 59319.0 | 0.160128 | ||||||||
\(40\) | 6221.03 | 0.0153692 | ||||||||
\(41\) | 592344. | 1.34224 | 0.671120 | − | 0.741349i | \(-0.265813\pi\) | ||||
0.671120 | + | 0.741349i | \(0.265813\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | −408257. | −0.783059 | −0.391530 | − | 0.920166i | \(-0.628054\pi\) | ||||
−0.391530 | + | 0.920166i | \(0.628054\pi\) | |||||||
\(44\) | 150475. | 0.266305 | ||||||||
\(45\) | −8857.68 | −0.0144903 | ||||||||
\(46\) | 293816. | 0.445064 | ||||||||
\(47\) | −1.19508e6 | −1.67901 | −0.839507 | − | 0.543349i | \(-0.817156\pi\) | ||||
−0.839507 | + | 0.543349i | \(0.817156\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 623819. | 0.705771 | ||||||||
\(51\) | −641346. | −0.677013 | ||||||||
\(52\) | 140608. | 0.138675 | ||||||||
\(53\) | −1.59585e6 | −1.47240 | −0.736201 | − | 0.676763i | \(-0.763382\pi\) | ||||
−0.736201 | + | 0.676763i | \(0.763382\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −28567.7 | −0.0231529 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | 1.10588e6 | 0.790946 | ||||||||
\(58\) | 1.16631e6 | 0.784906 | ||||||||
\(59\) | 697099. | 0.441888 | 0.220944 | − | 0.975286i | \(-0.429086\pi\) | ||||
0.220944 | + | 0.975286i | \(0.429086\pi\) | |||||||
\(60\) | −20996.0 | −0.0125489 | ||||||||
\(61\) | −2.63653e6 | −1.48723 | −0.743615 | − | 0.668609i | \(-0.766890\pi\) | ||||
−0.743615 | + | 0.668609i | \(0.766890\pi\) | |||||||
\(62\) | 728703. | 0.388311 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −26694.5 | −0.0120566 | ||||||||
\(66\) | −507852. | −0.217437 | ||||||||
\(67\) | 2.94033e6 | 1.19436 | 0.597179 | − | 0.802108i | \(-0.296288\pi\) | ||||
0.597179 | + | 0.802108i | \(0.296288\pi\) | |||||||
\(68\) | −1.52023e6 | −0.586310 | ||||||||
\(69\) | −991628. | −0.363393 | ||||||||
\(70\) | 33340.8 | 0.0116181 | ||||||||
\(71\) | 2.79525e6 | 0.926865 | 0.463432 | − | 0.886132i | \(-0.346618\pi\) | ||||
0.463432 | + | 0.886132i | \(0.346618\pi\) | |||||||
\(72\) | −373248. | −0.117851 | ||||||||
\(73\) | 3.60050e6 | 1.08326 | 0.541630 | − | 0.840617i | \(-0.317808\pi\) | ||||
0.541630 | + | 0.840617i | \(0.317808\pi\) | |||||||
\(74\) | −3.11783e6 | −0.894420 | ||||||||
\(75\) | −2.10539e6 | −0.576259 | ||||||||
\(76\) | 2.62135e6 | 0.684980 | ||||||||
\(77\) | 806450. | 0.201307 | ||||||||
\(78\) | −474552. | −0.113228 | ||||||||
\(79\) | −5.23592e6 | −1.19481 | −0.597404 | − | 0.801940i | \(-0.703801\pi\) | ||||
−0.597404 | + | 0.801940i | \(0.703801\pi\) | |||||||
\(80\) | −49768.2 | −0.0108677 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −4.73875e6 | −0.949107 | ||||||||
\(83\) | −3.05612e6 | −0.586675 | −0.293337 | − | 0.956009i | \(-0.594766\pi\) | ||||
−0.293337 | + | 0.956009i | \(0.594766\pi\) | |||||||
\(84\) | 592704. | 0.109109 | ||||||||
\(85\) | 288616. | 0.0509747 | ||||||||
\(86\) | 3.26606e6 | 0.553706 | ||||||||
\(87\) | −3.93631e6 | −0.640873 | ||||||||
\(88\) | −1.20380e6 | −0.188306 | ||||||||
\(89\) | −2.20102e6 | −0.330948 | −0.165474 | − | 0.986214i | \(-0.552915\pi\) | ||||
−0.165474 | + | 0.986214i | \(0.552915\pi\) | |||||||
\(90\) | 70861.4 | 0.0102462 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −2.35053e6 | −0.314708 | ||||||||
\(93\) | −2.45937e6 | −0.317055 | ||||||||
\(94\) | 9.56063e6 | 1.18724 | ||||||||
\(95\) | −497666. | −0.0595532 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −1.71655e7 | −1.90966 | −0.954830 | − | 0.297153i | \(-0.903963\pi\) | ||||
−0.954830 | + | 0.297153i | \(0.903963\pi\) | |||||||
\(98\) | −941192. | −0.101015 | ||||||||
\(99\) | 1.71400e6 | 0.177536 | ||||||||
\(100\) | −4.99055e6 | −0.499055 | ||||||||
\(101\) | −1.25438e7 | −1.21145 | −0.605723 | − | 0.795676i | \(-0.707116\pi\) | ||||
−0.605723 | + | 0.795676i | \(0.707116\pi\) | |||||||
\(102\) | 5.13077e6 | 0.478720 | ||||||||
\(103\) | 34707.7 | 0.00312965 | 0.00156482 | − | 0.999999i | \(-0.499502\pi\) | ||||
0.00156482 | + | 0.999999i | \(0.499502\pi\) | |||||||
\(104\) | −1.12486e6 | −0.0980581 | ||||||||
\(105\) | −112525. | −0.00948610 | ||||||||
\(106\) | 1.27668e7 | 1.04114 | ||||||||
\(107\) | 1.42610e7 | 1.12540 | 0.562700 | − | 0.826662i | \(-0.309763\pi\) | ||||
0.562700 | + | 0.826662i | \(0.309763\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −9.09132e6 | −0.672410 | −0.336205 | − | 0.941789i | \(-0.609143\pi\) | ||||
−0.336205 | + | 0.941789i | \(0.609143\pi\) | |||||||
\(110\) | 228542. | 0.0163716 | ||||||||
\(111\) | 1.05227e7 | 0.730291 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | 6.11807e6 | 0.398878 | 0.199439 | − | 0.979910i | \(-0.436088\pi\) | ||||
0.199439 | + | 0.979910i | \(0.436088\pi\) | |||||||
\(114\) | −8.84706e6 | −0.559284 | ||||||||
\(115\) | 446249. | 0.0273612 | ||||||||
\(116\) | −9.33051e6 | −0.555012 | ||||||||
\(117\) | 1.60161e6 | 0.0924500 | ||||||||
\(118\) | −5.57679e6 | −0.312462 | ||||||||
\(119\) | −8.14747e6 | −0.443209 | ||||||||
\(120\) | 167968. | 0.00887343 | ||||||||
\(121\) | −1.39592e7 | −0.716327 | ||||||||
\(122\) | 2.10922e7 | 1.05163 | ||||||||
\(123\) | 1.59933e7 | 0.774943 | ||||||||
\(124\) | −5.82963e6 | −0.274577 | ||||||||
\(125\) | 1.89671e6 | 0.0868594 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | 2.62050e7 | 1.13520 | 0.567598 | − | 0.823306i | \(-0.307873\pi\) | ||||
0.567598 | + | 0.823306i | \(0.307873\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | −1.10230e7 | −0.452099 | ||||||||
\(130\) | 213556. | 0.00852532 | ||||||||
\(131\) | 3.22701e7 | 1.25415 | 0.627077 | − | 0.778957i | \(-0.284251\pi\) | ||||
0.627077 | + | 0.778957i | \(0.284251\pi\) | |||||||
\(132\) | 4.06281e6 | 0.153751 | ||||||||
\(133\) | 1.40488e7 | 0.517796 | ||||||||
\(134\) | −2.35227e7 | −0.844539 | ||||||||
\(135\) | −239157. | −0.00836595 | ||||||||
\(136\) | 1.21618e7 | 0.414584 | ||||||||
\(137\) | 4.94777e6 | 0.164394 | 0.0821972 | − | 0.996616i | \(-0.473806\pi\) | ||||
0.0821972 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(138\) | 7.93303e6 | 0.256958 | ||||||||
\(139\) | 4.73278e7 | 1.49474 | 0.747368 | − | 0.664410i | \(-0.231317\pi\) | ||||
0.747368 | + | 0.664410i | \(0.231317\pi\) | |||||||
\(140\) | −266727. | −0.00821520 | ||||||||
\(141\) | −3.22671e7 | −0.969379 | ||||||||
\(142\) | −2.23620e7 | −0.655392 | ||||||||
\(143\) | 5.16551e6 | 0.147719 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 1.77140e6 | 0.0482536 | ||||||||
\(146\) | −2.88040e7 | −0.765980 | ||||||||
\(147\) | 3.17652e6 | 0.0824786 | ||||||||
\(148\) | 2.49426e7 | 0.632451 | ||||||||
\(149\) | −8.61144e6 | −0.213267 | −0.106634 | − | 0.994298i | \(-0.534007\pi\) | ||||
−0.106634 | + | 0.994298i | \(0.534007\pi\) | |||||||
\(150\) | 1.68431e7 | 0.407477 | ||||||||
\(151\) | −4.00833e7 | −0.947424 | −0.473712 | − | 0.880680i | \(-0.657086\pi\) | ||||
−0.473712 | + | 0.880680i | \(0.657086\pi\) | |||||||
\(152\) | −2.09708e7 | −0.484354 | ||||||||
\(153\) | −1.73163e7 | −0.390873 | ||||||||
\(154\) | −6.45160e6 | −0.142346 | ||||||||
\(155\) | 1.10676e6 | 0.0238722 | ||||||||
\(156\) | 3.79642e6 | 0.0800641 | ||||||||
\(157\) | 2.87214e6 | 0.0592320 | 0.0296160 | − | 0.999561i | \(-0.490572\pi\) | ||||
0.0296160 | + | 0.999561i | \(0.490572\pi\) | |||||||
\(158\) | 4.18874e7 | 0.844857 | ||||||||
\(159\) | −4.30879e7 | −0.850091 | ||||||||
\(160\) | 398146. | 0.00768462 | ||||||||
\(161\) | −1.25974e7 | −0.237897 | ||||||||
\(162\) | −4.25153e6 | −0.0785674 | ||||||||
\(163\) | 9.22930e7 | 1.66921 | 0.834607 | − | 0.550846i | \(-0.185695\pi\) | ||||
0.834607 | + | 0.550846i | \(0.185695\pi\) | |||||||
\(164\) | 3.79100e7 | 0.671120 | ||||||||
\(165\) | −771328. | −0.0133674 | ||||||||
\(166\) | 2.44490e7 | 0.414842 | ||||||||
\(167\) | −4.13487e7 | −0.686995 | −0.343498 | − | 0.939154i | \(-0.611612\pi\) | ||||
−0.343498 | + | 0.939154i | \(0.611612\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −2.30893e6 | −0.0360446 | ||||||||
\(171\) | 2.98588e7 | 0.456653 | ||||||||
\(172\) | −2.61285e7 | −0.391530 | ||||||||
\(173\) | −7.56258e7 | −1.11047 | −0.555237 | − | 0.831692i | \(-0.687372\pi\) | ||||
−0.555237 | + | 0.831692i | \(0.687372\pi\) | |||||||
\(174\) | 3.14905e7 | 0.453165 | ||||||||
\(175\) | −2.67462e7 | −0.377250 | ||||||||
\(176\) | 9.63037e6 | 0.133152 | ||||||||
\(177\) | 1.88217e7 | 0.255124 | ||||||||
\(178\) | 1.76082e7 | 0.234015 | ||||||||
\(179\) | −1.37316e8 | −1.78952 | −0.894759 | − | 0.446549i | \(-0.852653\pi\) | ||||
−0.894759 | + | 0.446549i | \(0.852653\pi\) | |||||||
\(180\) | −566891. | −0.00724513 | ||||||||
\(181\) | 1.35670e8 | 1.70063 | 0.850314 | − | 0.526276i | \(-0.176412\pi\) | ||||
0.850314 | + | 0.526276i | \(0.176412\pi\) | |||||||
\(182\) | −6.02857e6 | −0.0741249 | ||||||||
\(183\) | −7.11862e7 | −0.858652 | ||||||||
\(184\) | 1.88042e7 | 0.222532 | ||||||||
\(185\) | −4.73538e6 | −0.0549862 | ||||||||
\(186\) | 1.96750e7 | 0.224192 | ||||||||
\(187\) | −5.58485e7 | −0.624549 | ||||||||
\(188\) | −7.64851e7 | −0.839507 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | 3.98133e6 | 0.0421105 | ||||||||
\(191\) | −1.52695e6 | −0.0158565 | −0.00792825 | − | 0.999969i | \(-0.502524\pi\) | ||||
−0.00792825 | + | 0.999969i | \(0.502524\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | 1.63010e8 | 1.63216 | 0.816080 | − | 0.577939i | \(-0.196143\pi\) | ||||
0.816080 | + | 0.577939i | \(0.196143\pi\) | |||||||
\(194\) | 1.37324e8 | 1.35033 | ||||||||
\(195\) | −720753. | −0.00696090 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | −4.38681e7 | −0.408806 | −0.204403 | − | 0.978887i | \(-0.565525\pi\) | ||||
−0.204403 | + | 0.978887i | \(0.565525\pi\) | |||||||
\(198\) | −1.37120e7 | −0.125537 | ||||||||
\(199\) | 4.42403e6 | 0.0397953 | 0.0198977 | − | 0.999802i | \(-0.493666\pi\) | ||||
0.0198977 | + | 0.999802i | \(0.493666\pi\) | |||||||
\(200\) | 3.99244e7 | 0.352885 | ||||||||
\(201\) | 7.93890e7 | 0.689563 | ||||||||
\(202\) | 1.00350e8 | 0.856622 | ||||||||
\(203\) | −5.00057e7 | −0.419550 | ||||||||
\(204\) | −4.10461e7 | −0.338506 | ||||||||
\(205\) | −7.19724e6 | −0.0583482 | ||||||||
\(206\) | −277662. | −0.00221300 | ||||||||
\(207\) | −2.67740e7 | −0.209805 | ||||||||
\(208\) | 8.99891e6 | 0.0693375 | ||||||||
\(209\) | 9.63005e7 | 0.729653 | ||||||||
\(210\) | 900203. | 0.00670769 | ||||||||
\(211\) | −1.40630e8 | −1.03060 | −0.515298 | − | 0.857011i | \(-0.672319\pi\) | ||||
−0.515298 | + | 0.857011i | \(0.672319\pi\) | |||||||
\(212\) | −1.02134e8 | −0.736201 | ||||||||
\(213\) | 7.54717e7 | 0.535126 | ||||||||
\(214\) | −1.14088e8 | −0.795777 | ||||||||
\(215\) | 4.96051e6 | 0.0340402 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −3.12432e7 | −0.207561 | ||||||||
\(218\) | 7.27305e7 | 0.475465 | ||||||||
\(219\) | 9.72134e7 | 0.625420 | ||||||||
\(220\) | −1.82833e6 | −0.0115765 | ||||||||
\(221\) | −5.21866e7 | −0.325226 | ||||||||
\(222\) | −8.41814e7 | −0.516394 | ||||||||
\(223\) | −1.68816e8 | −1.01940 | −0.509701 | − | 0.860352i | \(-0.670244\pi\) | ||||
−0.509701 | + | 0.860352i | \(0.670244\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | −5.68455e7 | −0.332703 | ||||||||
\(226\) | −4.89446e7 | −0.282049 | ||||||||
\(227\) | 1.76137e8 | 0.999445 | 0.499723 | − | 0.866185i | \(-0.333435\pi\) | ||||
0.499723 | + | 0.866185i | \(0.333435\pi\) | |||||||
\(228\) | 7.07765e7 | 0.395473 | ||||||||
\(229\) | −3.15877e8 | −1.73818 | −0.869089 | − | 0.494655i | \(-0.835294\pi\) | ||||
−0.869089 | + | 0.494655i | \(0.835294\pi\) | |||||||
\(230\) | −3.56999e6 | −0.0193473 | ||||||||
\(231\) | 2.17741e7 | 0.116225 | ||||||||
\(232\) | 7.46441e7 | 0.392453 | ||||||||
\(233\) | −1.57810e8 | −0.817311 | −0.408656 | − | 0.912689i | \(-0.634002\pi\) | ||||
−0.408656 | + | 0.912689i | \(0.634002\pi\) | |||||||
\(234\) | −1.28129e7 | −0.0653720 | ||||||||
\(235\) | 1.45208e7 | 0.0729880 | ||||||||
\(236\) | 4.46144e7 | 0.220944 | ||||||||
\(237\) | −1.41370e8 | −0.689823 | ||||||||
\(238\) | 6.51798e7 | 0.313396 | ||||||||
\(239\) | −3.00642e8 | −1.42448 | −0.712240 | − | 0.701936i | \(-0.752319\pi\) | ||||
−0.712240 | + | 0.701936i | \(0.752319\pi\) | |||||||
\(240\) | −1.34374e6 | −0.00627447 | ||||||||
\(241\) | −3.91798e8 | −1.80303 | −0.901514 | − | 0.432750i | \(-0.857543\pi\) | ||||
−0.901514 | + | 0.432750i | \(0.857543\pi\) | |||||||
\(242\) | 1.11674e8 | 0.506520 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −1.68738e8 | −0.743615 | ||||||||
\(245\) | −1.42949e6 | −0.00621011 | ||||||||
\(246\) | −1.27946e8 | −0.547967 | ||||||||
\(247\) | 8.99861e7 | 0.379958 | ||||||||
\(248\) | 4.66370e7 | 0.194156 | ||||||||
\(249\) | −8.25153e7 | −0.338717 | ||||||||
\(250\) | −1.51737e7 | −0.0614189 | ||||||||
\(251\) | −3.11086e8 | −1.24172 | −0.620858 | − | 0.783923i | \(-0.713215\pi\) | ||||
−0.620858 | + | 0.783923i | \(0.713215\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | −8.63512e7 | −0.335233 | ||||||||
\(254\) | −2.09640e8 | −0.802704 | ||||||||
\(255\) | 7.79264e6 | 0.0294303 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 2.78740e8 | 1.02431 | 0.512157 | − | 0.858892i | \(-0.328846\pi\) | ||||
0.512157 | + | 0.858892i | \(0.328846\pi\) | |||||||
\(258\) | 8.81836e7 | 0.319683 | ||||||||
\(259\) | 1.33677e8 | 0.478088 | ||||||||
\(260\) | −1.70845e6 | −0.00602831 | ||||||||
\(261\) | −1.06280e8 | −0.370008 | ||||||||
\(262\) | −2.58161e8 | −0.886821 | ||||||||
\(263\) | 2.01753e8 | 0.683871 | 0.341936 | − | 0.939723i | \(-0.388918\pi\) | ||||
0.341936 | + | 0.939723i | \(0.388918\pi\) | |||||||
\(264\) | −3.25025e7 | −0.108718 | ||||||||
\(265\) | 1.93903e7 | 0.0640064 | ||||||||
\(266\) | −1.12390e8 | −0.366137 | ||||||||
\(267\) | −5.94276e7 | −0.191073 | ||||||||
\(268\) | 1.88181e8 | 0.597179 | ||||||||
\(269\) | −4.48126e8 | −1.40368 | −0.701838 | − | 0.712337i | \(-0.747637\pi\) | ||||
−0.701838 | + | 0.712337i | \(0.747637\pi\) | |||||||
\(270\) | 1.91326e6 | 0.00591562 | ||||||||
\(271\) | 2.78349e8 | 0.849566 | 0.424783 | − | 0.905295i | \(-0.360350\pi\) | ||||
0.424783 | + | 0.905295i | \(0.360350\pi\) | |||||||
\(272\) | −9.72946e7 | −0.293155 | ||||||||
\(273\) | 2.03464e7 | 0.0605228 | ||||||||
\(274\) | −3.95821e7 | −0.116244 | ||||||||
\(275\) | −1.83338e8 | −0.531603 | ||||||||
\(276\) | −6.34642e7 | −0.181697 | ||||||||
\(277\) | −1.41961e7 | −0.0401320 | −0.0200660 | − | 0.999799i | \(-0.506388\pi\) | ||||
−0.0200660 | + | 0.999799i | \(0.506388\pi\) | |||||||
\(278\) | −3.78623e8 | −1.05694 | ||||||||
\(279\) | −6.64031e7 | −0.183052 | ||||||||
\(280\) | 2.13381e6 | 0.00580903 | ||||||||
\(281\) | −3.72754e8 | −1.00219 | −0.501095 | − | 0.865392i | \(-0.667069\pi\) | ||||
−0.501095 | + | 0.865392i | \(0.667069\pi\) | |||||||
\(282\) | 2.58137e8 | 0.685454 | ||||||||
\(283\) | −1.77407e8 | −0.465284 | −0.232642 | − | 0.972562i | \(-0.574737\pi\) | ||||
−0.232642 | + | 0.972562i | \(0.574737\pi\) | |||||||
\(284\) | 1.78896e8 | 0.463432 | ||||||||
\(285\) | −1.34370e7 | −0.0343831 | ||||||||
\(286\) | −4.13241e7 | −0.104453 | ||||||||
\(287\) | 2.03174e8 | 0.507319 | ||||||||
\(288\) | −2.38879e7 | −0.0589256 | ||||||||
\(289\) | 1.53893e8 | 0.375039 | ||||||||
\(290\) | −1.41712e7 | −0.0341205 | ||||||||
\(291\) | −4.63469e8 | −1.10254 | ||||||||
\(292\) | 2.30432e8 | 0.541630 | ||||||||
\(293\) | −4.77202e8 | −1.10832 | −0.554160 | − | 0.832410i | \(-0.686961\pi\) | ||||
−0.554160 | + | 0.832410i | \(0.686961\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | −8.47007e6 | −0.0192092 | ||||||||
\(296\) | −1.99541e8 | −0.447210 | ||||||||
\(297\) | 4.62780e7 | 0.102501 | ||||||||
\(298\) | 6.88915e7 | 0.150803 | ||||||||
\(299\) | −8.06892e7 | −0.174569 | ||||||||
\(300\) | −1.34745e8 | −0.288130 | ||||||||
\(301\) | −1.40032e8 | −0.295968 | ||||||||
\(302\) | 3.20667e8 | 0.669930 | ||||||||
\(303\) | −3.38682e8 | −0.699429 | ||||||||
\(304\) | 1.67767e8 | 0.342490 | ||||||||
\(305\) | 3.20350e7 | 0.0646510 | ||||||||
\(306\) | 1.38531e8 | 0.276389 | ||||||||
\(307\) | −8.98202e8 | −1.77170 | −0.885849 | − | 0.463973i | \(-0.846423\pi\) | ||||
−0.885849 | + | 0.463973i | \(0.846423\pi\) | |||||||
\(308\) | 5.16128e7 | 0.100654 | ||||||||
\(309\) | 937108. | 0.00180690 | ||||||||
\(310\) | −8.85407e6 | −0.0168802 | ||||||||
\(311\) | −2.44076e8 | −0.460112 | −0.230056 | − | 0.973177i | \(-0.573891\pi\) | ||||
−0.230056 | + | 0.973177i | \(0.573891\pi\) | |||||||
\(312\) | −3.03713e7 | −0.0566139 | ||||||||
\(313\) | −6.87239e8 | −1.26678 | −0.633392 | − | 0.773831i | \(-0.718338\pi\) | ||||
−0.633392 | + | 0.773831i | \(0.718338\pi\) | |||||||
\(314\) | −2.29771e7 | −0.0418834 | ||||||||
\(315\) | −3.03818e6 | −0.00547680 | ||||||||
\(316\) | −3.35099e8 | −0.597404 | ||||||||
\(317\) | −1.13427e8 | −0.199991 | −0.0999954 | − | 0.994988i | \(-0.531883\pi\) | ||||
−0.0999954 | + | 0.994988i | \(0.531883\pi\) | |||||||
\(318\) | 3.44703e8 | 0.601105 | ||||||||
\(319\) | −3.42775e8 | −0.591209 | ||||||||
\(320\) | −3.18517e6 | −0.00543385 | ||||||||
\(321\) | 3.85047e8 | 0.649749 | ||||||||
\(322\) | 1.00779e8 | 0.168218 | ||||||||
\(323\) | −9.72913e8 | −1.60644 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −1.71316e8 | −0.276826 | ||||||||
\(326\) | −7.38344e8 | −1.18031 | ||||||||
\(327\) | −2.45466e8 | −0.388216 | ||||||||
\(328\) | −3.03280e8 | −0.474554 | ||||||||
\(329\) | −4.09912e8 | −0.634607 | ||||||||
\(330\) | 6.17063e6 | 0.00945215 | ||||||||
\(331\) | −2.73163e8 | −0.414022 | −0.207011 | − | 0.978339i | \(-0.566374\pi\) | ||||
−0.207011 | + | 0.978339i | \(0.566374\pi\) | |||||||
\(332\) | −1.95592e8 | −0.293337 | ||||||||
\(333\) | 2.84112e8 | 0.421634 | ||||||||
\(334\) | 3.30789e8 | 0.485779 | ||||||||
\(335\) | −3.57264e7 | −0.0519197 | ||||||||
\(336\) | 3.79331e7 | 0.0545545 | ||||||||
\(337\) | −4.38234e8 | −0.623736 | −0.311868 | − | 0.950125i | \(-0.600955\pi\) | ||||
−0.311868 | + | 0.950125i | \(0.600955\pi\) | |||||||
\(338\) | −3.86145e7 | −0.0543928 | ||||||||
\(339\) | 1.65188e8 | 0.230292 | ||||||||
\(340\) | 1.84715e7 | 0.0254874 | ||||||||
\(341\) | −2.14163e8 | −0.292485 | ||||||||
\(342\) | −2.38871e8 | −0.322903 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 2.09028e8 | 0.276853 | ||||||||
\(345\) | 1.20487e7 | 0.0157970 | ||||||||
\(346\) | 6.05006e8 | 0.785224 | ||||||||
\(347\) | 1.99731e8 | 0.256622 | 0.128311 | − | 0.991734i | \(-0.459044\pi\) | ||||
0.128311 | + | 0.991734i | \(0.459044\pi\) | |||||||
\(348\) | −2.51924e8 | −0.320436 | ||||||||
\(349\) | 8.27137e8 | 1.04157 | 0.520785 | − | 0.853688i | \(-0.325639\pi\) | ||||
0.520785 | + | 0.853688i | \(0.325639\pi\) | |||||||
\(350\) | 2.13970e8 | 0.266756 | ||||||||
\(351\) | 4.32436e7 | 0.0533761 | ||||||||
\(352\) | −7.70430e7 | −0.0941529 | ||||||||
\(353\) | 6.66700e7 | 0.0806713 | 0.0403356 | − | 0.999186i | \(-0.487157\pi\) | ||||
0.0403356 | + | 0.999186i | \(0.487157\pi\) | |||||||
\(354\) | −1.50573e8 | −0.180400 | ||||||||
\(355\) | −3.39635e7 | −0.0402915 | ||||||||
\(356\) | −1.40865e8 | −0.165474 | ||||||||
\(357\) | −2.19982e8 | −0.255887 | ||||||||
\(358\) | 1.09853e9 | 1.26538 | ||||||||
\(359\) | −3.63566e8 | −0.414718 | −0.207359 | − | 0.978265i | \(-0.566487\pi\) | ||||
−0.207359 | + | 0.978265i | \(0.566487\pi\) | |||||||
\(360\) | 4.53513e6 | 0.00512308 | ||||||||
\(361\) | 7.83737e8 | 0.876789 | ||||||||
\(362\) | −1.08536e9 | −1.20253 | ||||||||
\(363\) | −3.76898e8 | −0.413572 | ||||||||
\(364\) | 4.82285e7 | 0.0524142 | ||||||||
\(365\) | −4.37477e7 | −0.0470901 | ||||||||
\(366\) | 5.69490e8 | 0.607159 | ||||||||
\(367\) | 1.04729e9 | 1.10595 | 0.552973 | − | 0.833199i | \(-0.313493\pi\) | ||||
0.552973 | + | 0.833199i | \(0.313493\pi\) | |||||||
\(368\) | −1.50434e8 | −0.157354 | ||||||||
\(369\) | 4.31819e8 | 0.447413 | ||||||||
\(370\) | 3.78831e7 | 0.0388811 | ||||||||
\(371\) | −5.47376e8 | −0.556515 | ||||||||
\(372\) | −1.57400e8 | −0.158527 | ||||||||
\(373\) | −1.49314e9 | −1.48977 | −0.744884 | − | 0.667194i | \(-0.767495\pi\) | ||||
−0.744884 | + | 0.667194i | \(0.767495\pi\) | |||||||
\(374\) | 4.46788e8 | 0.441623 | ||||||||
\(375\) | 5.12113e7 | 0.0501483 | ||||||||
\(376\) | 6.11881e8 | 0.593621 | ||||||||
\(377\) | −3.20299e8 | −0.307865 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | 4.44467e8 | 0.419375 | 0.209688 | − | 0.977768i | \(-0.432755\pi\) | ||||
0.209688 | + | 0.977768i | \(0.432755\pi\) | |||||||
\(380\) | −3.18506e7 | −0.0297766 | ||||||||
\(381\) | 7.07534e8 | 0.655405 | ||||||||
\(382\) | 1.22156e7 | 0.0112122 | ||||||||
\(383\) | 1.71656e9 | 1.56122 | 0.780609 | − | 0.625020i | \(-0.214909\pi\) | ||||
0.780609 | + | 0.625020i | \(0.214909\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | −9.79873e6 | −0.00875099 | ||||||||
\(386\) | −1.30408e9 | −1.15411 | ||||||||
\(387\) | −2.97620e8 | −0.261020 | ||||||||
\(388\) | −1.09859e9 | −0.954830 | ||||||||
\(389\) | −1.89671e9 | −1.63372 | −0.816861 | − | 0.576834i | \(-0.804288\pi\) | ||||
−0.816861 | + | 0.576834i | \(0.804288\pi\) | |||||||
\(390\) | 5.76602e6 | 0.00492210 | ||||||||
\(391\) | 8.72396e8 | 0.738066 | ||||||||
\(392\) | −6.02363e7 | −0.0505076 | ||||||||
\(393\) | 8.71293e8 | 0.724086 | ||||||||
\(394\) | 3.50945e8 | 0.289069 | ||||||||
\(395\) | 6.36188e7 | 0.0519392 | ||||||||
\(396\) | 1.09696e8 | 0.0887682 | ||||||||
\(397\) | −2.05358e9 | −1.64720 | −0.823599 | − | 0.567173i | \(-0.808037\pi\) | ||||
−0.823599 | + | 0.567173i | \(0.808037\pi\) | |||||||
\(398\) | −3.53922e7 | −0.0281395 | ||||||||
\(399\) | 3.79318e8 | 0.298950 | ||||||||
\(400\) | −3.19395e8 | −0.249528 | ||||||||
\(401\) | −1.61799e9 | −1.25306 | −0.626530 | − | 0.779398i | \(-0.715525\pi\) | ||||
−0.626530 | + | 0.779398i | \(0.715525\pi\) | |||||||
\(402\) | −6.35112e8 | −0.487595 | ||||||||
\(403\) | −2.00120e8 | −0.152308 | ||||||||
\(404\) | −8.02803e8 | −0.605723 | ||||||||
\(405\) | −6.45725e6 | −0.00483009 | ||||||||
\(406\) | 4.00046e8 | 0.296666 | ||||||||
\(407\) | 9.16317e8 | 0.673698 | ||||||||
\(408\) | 3.28369e8 | 0.239360 | ||||||||
\(409\) | −8.98794e8 | −0.649574 | −0.324787 | − | 0.945787i | \(-0.605293\pi\) | ||||
−0.324787 | + | 0.945787i | \(0.605293\pi\) | |||||||
\(410\) | 5.75780e7 | 0.0412584 | ||||||||
\(411\) | 1.33590e8 | 0.0949132 | ||||||||
\(412\) | 2.22129e6 | 0.00156482 | ||||||||
\(413\) | 2.39105e8 | 0.167018 | ||||||||
\(414\) | 2.14192e8 | 0.148355 | ||||||||
\(415\) | 3.71333e7 | 0.0255032 | ||||||||
\(416\) | −7.19913e7 | −0.0490290 | ||||||||
\(417\) | 1.27785e9 | 0.862987 | ||||||||
\(418\) | −7.70404e8 | −0.515943 | ||||||||
\(419\) | −8.08723e8 | −0.537095 | −0.268547 | − | 0.963266i | \(-0.586544\pi\) | ||||
−0.268547 | + | 0.963266i | \(0.586544\pi\) | |||||||
\(420\) | −7.20162e6 | −0.00474305 | ||||||||
\(421\) | 1.27096e9 | 0.830129 | 0.415064 | − | 0.909792i | \(-0.363759\pi\) | ||||
0.415064 | + | 0.909792i | \(0.363759\pi\) | |||||||
\(422\) | 1.12504e9 | 0.728741 | ||||||||
\(423\) | −8.71213e8 | −0.559671 | ||||||||
\(424\) | 8.17075e8 | 0.520572 | ||||||||
\(425\) | 1.85224e9 | 1.17040 | ||||||||
\(426\) | −6.03774e8 | −0.378391 | ||||||||
\(427\) | −9.04329e8 | −0.562120 | ||||||||
\(428\) | 9.12704e8 | 0.562700 | ||||||||
\(429\) | 1.39469e8 | 0.0852857 | ||||||||
\(430\) | −3.96841e7 | −0.0240700 | ||||||||
\(431\) | −1.09537e9 | −0.659008 | −0.329504 | − | 0.944154i | \(-0.606882\pi\) | ||||
−0.329504 | + | 0.944154i | \(0.606882\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | 2.16541e9 | 1.28183 | 0.640917 | − | 0.767610i | \(-0.278554\pi\) | ||||
0.640917 | + | 0.767610i | \(0.278554\pi\) | |||||||
\(434\) | 2.49945e8 | 0.146768 | ||||||||
\(435\) | 4.78279e7 | 0.0278592 | ||||||||
\(436\) | −5.81844e8 | −0.336205 | ||||||||
\(437\) | −1.50429e9 | −0.862274 | ||||||||
\(438\) | −7.77707e8 | −0.442239 | ||||||||
\(439\) | 7.97498e8 | 0.449887 | 0.224944 | − | 0.974372i | \(-0.427780\pi\) | ||||
0.224944 | + | 0.974372i | \(0.427780\pi\) | |||||||
\(440\) | 1.46267e7 | 0.00818580 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | 4.17493e8 | 0.229970 | ||||||||
\(443\) | −1.06435e8 | −0.0581665 | −0.0290832 | − | 0.999577i | \(-0.509259\pi\) | ||||
−0.0290832 | + | 0.999577i | \(0.509259\pi\) | |||||||
\(444\) | 6.73452e8 | 0.365145 | ||||||||
\(445\) | 2.67434e7 | 0.0143866 | ||||||||
\(446\) | 1.35052e9 | 0.720826 | ||||||||
\(447\) | −2.32509e8 | −0.123130 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | −9.25513e8 | −0.482526 | −0.241263 | − | 0.970460i | \(-0.577562\pi\) | ||||
−0.241263 | + | 0.970460i | \(0.577562\pi\) | |||||||
\(450\) | 4.54764e8 | 0.235257 | ||||||||
\(451\) | 1.39270e9 | 0.714890 | ||||||||
\(452\) | 3.91557e8 | 0.199439 | ||||||||
\(453\) | −1.08225e9 | −0.546995 | ||||||||
\(454\) | −1.40909e9 | −0.706715 | ||||||||
\(455\) | −9.15623e6 | −0.00455698 | ||||||||
\(456\) | −5.66212e8 | −0.279642 | ||||||||
\(457\) | −2.23261e8 | −0.109423 | −0.0547113 | − | 0.998502i | \(-0.517424\pi\) | ||||
−0.0547113 | + | 0.998502i | \(0.517424\pi\) | |||||||
\(458\) | 2.52702e9 | 1.22908 | ||||||||
\(459\) | −4.67541e8 | −0.225671 | ||||||||
\(460\) | 2.85600e7 | 0.0136806 | ||||||||
\(461\) | −3.98913e9 | −1.89638 | −0.948190 | − | 0.317705i | \(-0.897088\pi\) | ||||
−0.948190 | + | 0.317705i | \(0.897088\pi\) | |||||||
\(462\) | −1.74193e8 | −0.0821834 | ||||||||
\(463\) | −4.66671e8 | −0.218513 | −0.109256 | − | 0.994014i | \(-0.534847\pi\) | ||||
−0.109256 | + | 0.994014i | \(0.534847\pi\) | |||||||
\(464\) | −5.97153e8 | −0.277506 | ||||||||
\(465\) | 2.98825e7 | 0.0137826 | ||||||||
\(466\) | 1.26248e9 | 0.577926 | ||||||||
\(467\) | 1.70197e9 | 0.773291 | 0.386645 | − | 0.922228i | \(-0.373634\pi\) | ||||
0.386645 | + | 0.922228i | \(0.373634\pi\) | |||||||
\(468\) | 1.02503e8 | 0.0462250 | ||||||||
\(469\) | 1.00853e9 | 0.451425 | ||||||||
\(470\) | −1.16166e8 | −0.0516103 | ||||||||
\(471\) | 7.75477e7 | 0.0341976 | ||||||||
\(472\) | −3.56915e8 | −0.156231 | ||||||||
\(473\) | −9.59881e8 | −0.417065 | ||||||||
\(474\) | 1.13096e9 | 0.487778 | ||||||||
\(475\) | −3.19385e9 | −1.36737 | ||||||||
\(476\) | −5.21438e8 | −0.221604 | ||||||||
\(477\) | −1.16337e9 | −0.490800 | ||||||||
\(478\) | 2.40513e9 | 1.00726 | ||||||||
\(479\) | 1.31402e9 | 0.546297 | 0.273149 | − | 0.961972i | \(-0.411935\pi\) | ||||
0.273149 | + | 0.961972i | \(0.411935\pi\) | |||||||
\(480\) | 1.07499e7 | 0.00443672 | ||||||||
\(481\) | 8.56234e8 | 0.350820 | ||||||||
\(482\) | 3.13438e9 | 1.27493 | ||||||||
\(483\) | −3.40129e8 | −0.137350 | ||||||||
\(484\) | −8.93388e8 | −0.358164 | ||||||||
\(485\) | 2.08569e8 | 0.0830144 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | 2.58937e9 | 1.01588 | 0.507941 | − | 0.861392i | \(-0.330407\pi\) | ||||
0.507941 | + | 0.861392i | \(0.330407\pi\) | |||||||
\(488\) | 1.34990e9 | 0.525815 | ||||||||
\(489\) | 2.49191e9 | 0.963721 | ||||||||
\(490\) | 1.14359e7 | 0.00439121 | ||||||||
\(491\) | −2.73335e9 | −1.04210 | −0.521051 | − | 0.853525i | \(-0.674460\pi\) | ||||
−0.521051 | + | 0.853525i | \(0.674460\pi\) | |||||||
\(492\) | 1.02357e9 | 0.387471 | ||||||||
\(493\) | 3.46301e9 | 1.30164 | ||||||||
\(494\) | −7.19889e8 | −0.268671 | ||||||||
\(495\) | −2.08259e7 | −0.00771765 | ||||||||
\(496\) | −3.73096e8 | −0.137289 | ||||||||
\(497\) | 9.58771e8 | 0.350322 | ||||||||
\(498\) | 6.60122e8 | 0.239509 | ||||||||
\(499\) | 4.97895e9 | 1.79385 | 0.896925 | − | 0.442182i | \(-0.145796\pi\) | ||||
0.896925 | + | 0.442182i | \(0.145796\pi\) | |||||||
\(500\) | 1.21390e8 | 0.0434297 | ||||||||
\(501\) | −1.11641e9 | −0.396637 | ||||||||
\(502\) | 2.48869e9 | 0.878025 | ||||||||
\(503\) | 4.03599e8 | 0.141404 | 0.0707020 | − | 0.997497i | \(-0.477476\pi\) | ||||
0.0707020 | + | 0.997497i | \(0.477476\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | 1.52413e8 | 0.0526625 | ||||||||
\(506\) | 6.90810e8 | 0.237045 | ||||||||
\(507\) | 1.30324e8 | 0.0444116 | ||||||||
\(508\) | 1.67712e9 | 0.567598 | ||||||||
\(509\) | 1.42963e9 | 0.480521 | 0.240261 | − | 0.970708i | \(-0.422767\pi\) | ||||
0.240261 | + | 0.970708i | \(0.422767\pi\) | |||||||
\(510\) | −6.23412e7 | −0.0208103 | ||||||||
\(511\) | 1.23497e9 | 0.409434 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 8.06189e8 | 0.263649 | ||||||||
\(514\) | −2.22992e9 | −0.724300 | ||||||||
\(515\) | −421714. | −0.000136048 0 | ||||||||
\(516\) | −7.05469e8 | −0.226050 | ||||||||
\(517\) | −2.80983e9 | −0.894258 | ||||||||
\(518\) | −1.06942e9 | −0.338059 | ||||||||
\(519\) | −2.04190e9 | −0.641132 | ||||||||
\(520\) | 1.36676e7 | 0.00426266 | ||||||||
\(521\) | −3.69792e9 | −1.14558 | −0.572791 | − | 0.819702i | \(-0.694139\pi\) | ||||
−0.572791 | + | 0.819702i | \(0.694139\pi\) | |||||||
\(522\) | 8.50243e8 | 0.261635 | ||||||||
\(523\) | 4.45878e9 | 1.36289 | 0.681444 | − | 0.731870i | \(-0.261352\pi\) | ||||
0.681444 | + | 0.731870i | \(0.261352\pi\) | |||||||
\(524\) | 2.06529e9 | 0.627077 | ||||||||
\(525\) | −7.22148e8 | −0.217806 | ||||||||
\(526\) | −1.61402e9 | −0.483570 | ||||||||
\(527\) | 2.16366e9 | 0.643950 | ||||||||
\(528\) | 2.60020e8 | 0.0768755 | ||||||||
\(529\) | −2.05595e9 | −0.603836 | ||||||||
\(530\) | −1.55122e8 | −0.0452594 | ||||||||
\(531\) | 5.08185e8 | 0.147296 | ||||||||
\(532\) | 8.99124e8 | 0.258898 | ||||||||
\(533\) | 1.30138e9 | 0.372271 | ||||||||
\(534\) | 4.75421e8 | 0.135109 | ||||||||
\(535\) | −1.73277e8 | −0.0489220 | ||||||||
\(536\) | −1.50545e9 | −0.422269 | ||||||||
\(537\) | −3.70754e9 | −1.03318 | ||||||||
\(538\) | 3.58501e9 | 0.992549 | ||||||||
\(539\) | 2.76612e8 | 0.0760870 | ||||||||
\(540\) | −1.53061e7 | −0.00418298 | ||||||||
\(541\) | 2.07517e9 | 0.563459 | 0.281730 | − | 0.959494i | \(-0.409092\pi\) | ||||
0.281730 | + | 0.959494i | \(0.409092\pi\) | |||||||
\(542\) | −2.22679e9 | −0.600734 | ||||||||
\(543\) | 3.66309e9 | 0.981858 | ||||||||
\(544\) | 7.78357e8 | 0.207292 | ||||||||
\(545\) | 1.10464e8 | 0.0292302 | ||||||||
\(546\) | −1.62771e8 | −0.0427960 | ||||||||
\(547\) | 5.81898e9 | 1.52017 | 0.760084 | − | 0.649825i | \(-0.225158\pi\) | ||||
0.760084 | + | 0.649825i | \(0.225158\pi\) | |||||||
\(548\) | 3.16657e8 | 0.0821972 | ||||||||
\(549\) | −1.92203e9 | −0.495743 | ||||||||
\(550\) | 1.46670e9 | 0.375900 | ||||||||
\(551\) | −5.97133e9 | −1.52069 | ||||||||
\(552\) | 5.07714e8 | 0.128479 | ||||||||
\(553\) | −1.79592e9 | −0.451595 | ||||||||
\(554\) | 1.13569e8 | 0.0283776 | ||||||||
\(555\) | −1.27855e8 | −0.0317463 | ||||||||
\(556\) | 3.02898e9 | 0.747368 | ||||||||
\(557\) | 5.32423e9 | 1.30546 | 0.652730 | − | 0.757591i | \(-0.273624\pi\) | ||||
0.652730 | + | 0.757591i | \(0.273624\pi\) | |||||||
\(558\) | 5.31225e8 | 0.129437 | ||||||||
\(559\) | −8.96942e8 | −0.217181 | ||||||||
\(560\) | −1.70705e7 | −0.00410760 | ||||||||
\(561\) | −1.50791e9 | −0.360583 | ||||||||
\(562\) | 2.98203e9 | 0.708655 | ||||||||
\(563\) | 1.91319e9 | 0.451834 | 0.225917 | − | 0.974147i | \(-0.427462\pi\) | ||||
0.225917 | + | 0.974147i | \(0.427462\pi\) | |||||||
\(564\) | −2.06510e9 | −0.484689 | ||||||||
\(565\) | −7.43373e7 | −0.0173395 | ||||||||
\(566\) | 1.41926e9 | 0.329006 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | −1.43117e9 | −0.327696 | ||||||||
\(569\) | 2.81457e9 | 0.640499 | 0.320250 | − | 0.947333i | \(-0.396233\pi\) | ||||
0.320250 | + | 0.947333i | \(0.396233\pi\) | |||||||
\(570\) | 1.07496e8 | 0.0243125 | ||||||||
\(571\) | −4.87197e9 | −1.09516 | −0.547581 | − | 0.836753i | \(-0.684451\pi\) | ||||
−0.547581 | + | 0.836753i | \(0.684451\pi\) | |||||||
\(572\) | 3.30593e8 | 0.0738596 | ||||||||
\(573\) | −4.12276e7 | −0.00915476 | ||||||||
\(574\) | −1.62539e9 | −0.358729 | ||||||||
\(575\) | 2.86387e9 | 0.628227 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 5.36429e9 | 1.16251 | 0.581255 | − | 0.813722i | \(-0.302562\pi\) | ||||
0.581255 | + | 0.813722i | \(0.302562\pi\) | |||||||
\(578\) | −1.23114e9 | −0.265192 | ||||||||
\(579\) | 4.40126e9 | 0.942328 | ||||||||
\(580\) | 1.13370e8 | 0.0241268 | ||||||||
\(581\) | −1.04825e9 | −0.221742 | ||||||||
\(582\) | 3.70775e9 | 0.779615 | ||||||||
\(583\) | −3.75210e9 | −0.784215 | ||||||||
\(584\) | −1.84345e9 | −0.382990 | ||||||||
\(585\) | −1.94603e7 | −0.00401887 | ||||||||
\(586\) | 3.81762e9 | 0.783701 | ||||||||
\(587\) | −6.31539e9 | −1.28874 | −0.644372 | − | 0.764712i | \(-0.722881\pi\) | ||||
−0.644372 | + | 0.764712i | \(0.722881\pi\) | |||||||
\(588\) | 2.03297e8 | 0.0412393 | ||||||||
\(589\) | −3.73084e9 | −0.752320 | ||||||||
\(590\) | 6.77606e7 | 0.0135830 | ||||||||
\(591\) | −1.18444e9 | −0.236024 | ||||||||
\(592\) | 1.59633e9 | 0.316225 | ||||||||
\(593\) | 7.01786e9 | 1.38202 | 0.691008 | − | 0.722847i | \(-0.257167\pi\) | ||||
0.691008 | + | 0.722847i | \(0.257167\pi\) | |||||||
\(594\) | −3.70224e8 | −0.0724789 | ||||||||
\(595\) | 9.89954e7 | 0.0192666 | ||||||||
\(596\) | −5.51132e8 | −0.106634 | ||||||||
\(597\) | 1.19449e8 | 0.0229758 | ||||||||
\(598\) | 6.45513e8 | 0.123439 | ||||||||
\(599\) | 9.45941e8 | 0.179833 | 0.0899166 | − | 0.995949i | \(-0.471340\pi\) | ||||
0.0899166 | + | 0.995949i | \(0.471340\pi\) | |||||||
\(600\) | 1.07796e9 | 0.203738 | ||||||||
\(601\) | −1.51203e9 | −0.284119 | −0.142060 | − | 0.989858i | \(-0.545372\pi\) | ||||
−0.142060 | + | 0.989858i | \(0.545372\pi\) | |||||||
\(602\) | 1.12026e9 | 0.209281 | ||||||||
\(603\) | 2.14350e9 | 0.398119 | ||||||||
\(604\) | −2.56533e9 | −0.473712 | ||||||||
\(605\) | 1.69610e8 | 0.0311393 | ||||||||
\(606\) | 2.70946e9 | 0.494571 | ||||||||
\(607\) | 6.06641e9 | 1.10096 | 0.550479 | − | 0.834849i | \(-0.314445\pi\) | ||||
0.550479 | + | 0.834849i | \(0.314445\pi\) | |||||||
\(608\) | −1.34213e9 | −0.242177 | ||||||||
\(609\) | −1.35015e9 | −0.242227 | ||||||||
\(610\) | −2.56280e8 | −0.0457152 | ||||||||
\(611\) | −2.62559e9 | −0.465675 | ||||||||
\(612\) | −1.10825e9 | −0.195437 | ||||||||
\(613\) | −1.53297e8 | −0.0268796 | −0.0134398 | − | 0.999910i | \(-0.504278\pi\) | ||||
−0.0134398 | + | 0.999910i | \(0.504278\pi\) | |||||||
\(614\) | 7.18562e9 | 1.25278 | ||||||||
\(615\) | −1.94326e8 | −0.0336874 | ||||||||
\(616\) | −4.12902e8 | −0.0711729 | ||||||||
\(617\) | 5.78295e9 | 0.991177 | 0.495589 | − | 0.868557i | \(-0.334952\pi\) | ||||
0.495589 | + | 0.868557i | \(0.334952\pi\) | |||||||
\(618\) | −7.49687e6 | −0.00127767 | ||||||||
\(619\) | −1.12405e10 | −1.90488 | −0.952442 | − | 0.304720i | \(-0.901437\pi\) | ||||
−0.952442 | + | 0.304720i | \(0.901437\pi\) | |||||||
\(620\) | 7.08326e7 | 0.0119361 | ||||||||
\(621\) | −7.22897e8 | −0.121131 | ||||||||
\(622\) | 1.95261e9 | 0.325348 | ||||||||
\(623\) | −7.54951e8 | −0.125086 | ||||||||
\(624\) | 2.42971e8 | 0.0400320 | ||||||||
\(625\) | 6.06894e9 | 0.994334 | ||||||||
\(626\) | 5.49791e9 | 0.895751 | ||||||||
\(627\) | 2.60011e9 | 0.421265 | ||||||||
\(628\) | 1.83817e8 | 0.0296160 | ||||||||
\(629\) | −9.25745e9 | −1.48325 | ||||||||
\(630\) | 2.43055e7 | 0.00387268 | ||||||||
\(631\) | 8.68673e9 | 1.37643 | 0.688214 | − | 0.725508i | \(-0.258395\pi\) | ||||
0.688214 | + | 0.725508i | \(0.258395\pi\) | |||||||
\(632\) | 2.68079e9 | 0.422429 | ||||||||
\(633\) | −3.79700e9 | −0.595015 | ||||||||
\(634\) | 9.07418e8 | 0.141415 | ||||||||
\(635\) | −3.18402e8 | −0.0493478 | ||||||||
\(636\) | −2.75763e9 | −0.425046 | ||||||||
\(637\) | 2.58475e8 | 0.0396214 | ||||||||
\(638\) | 2.74220e9 | 0.418048 | ||||||||
\(639\) | 2.03774e9 | 0.308955 | ||||||||
\(640\) | 2.54813e7 | 0.00384231 | ||||||||
\(641\) | 7.98647e9 | 1.19771 | 0.598855 | − | 0.800857i | \(-0.295623\pi\) | ||||
0.598855 | + | 0.800857i | \(0.295623\pi\) | |||||||
\(642\) | −3.08037e9 | −0.459442 | ||||||||
\(643\) | −5.00901e9 | −0.743043 | −0.371521 | − | 0.928424i | \(-0.621164\pi\) | ||||
−0.371521 | + | 0.928424i | \(0.621164\pi\) | |||||||
\(644\) | −8.06231e8 | −0.118948 | ||||||||
\(645\) | 1.33934e8 | 0.0196531 | ||||||||
\(646\) | 7.78330e9 | 1.13593 | ||||||||
\(647\) | −3.56209e9 | −0.517059 | −0.258530 | − | 0.966003i | \(-0.583238\pi\) | ||||
−0.258530 | + | 0.966003i | \(0.583238\pi\) | |||||||
\(648\) | −2.72098e8 | −0.0392837 | ||||||||
\(649\) | 1.63900e9 | 0.235354 | ||||||||
\(650\) | 1.37053e9 | 0.195746 | ||||||||
\(651\) | −8.43565e8 | −0.119835 | ||||||||
\(652\) | 5.90675e9 | 0.834607 | ||||||||
\(653\) | −1.25486e10 | −1.76360 | −0.881799 | − | 0.471625i | \(-0.843667\pi\) | ||||
−0.881799 | + | 0.471625i | \(0.843667\pi\) | |||||||
\(654\) | 1.96372e9 | 0.274510 | ||||||||
\(655\) | −3.92096e8 | −0.0545191 | ||||||||
\(656\) | 2.42624e9 | 0.335560 | ||||||||
\(657\) | 2.62476e9 | 0.361086 | ||||||||
\(658\) | 3.27930e9 | 0.448735 | ||||||||
\(659\) | −1.66119e9 | −0.226110 | −0.113055 | − | 0.993589i | \(-0.536064\pi\) | ||||
−0.113055 | + | 0.993589i | \(0.536064\pi\) | |||||||
\(660\) | −4.93650e7 | −0.00668368 | ||||||||
\(661\) | 1.05642e10 | 1.42276 | 0.711380 | − | 0.702807i | \(-0.248070\pi\) | ||||
0.711380 | + | 0.702807i | \(0.248070\pi\) | |||||||
\(662\) | 2.18530e9 | 0.292758 | ||||||||
\(663\) | −1.40904e9 | −0.187770 | ||||||||
\(664\) | 1.56473e9 | 0.207421 | ||||||||
\(665\) | −1.70699e8 | −0.0225090 | ||||||||
\(666\) | −2.27290e9 | −0.298140 | ||||||||
\(667\) | 5.35440e9 | 0.698667 | ||||||||
\(668\) | −2.64631e9 | −0.343498 | ||||||||
\(669\) | −4.55802e9 | −0.588552 | ||||||||
\(670\) | 2.85811e8 | 0.0367128 | ||||||||
\(671\) | −6.19891e9 | −0.792112 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | −1.47467e10 | −1.86484 | −0.932421 | − | 0.361374i | \(-0.882308\pi\) | ||||
−0.932421 | + | 0.361374i | \(0.882308\pi\) | |||||||
\(674\) | 3.50587e9 | 0.441048 | ||||||||
\(675\) | −1.53483e9 | −0.192086 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | −1.14704e10 | −1.42076 | −0.710378 | − | 0.703820i | \(-0.751476\pi\) | ||||
−0.710378 | + | 0.703820i | \(0.751476\pi\) | |||||||
\(678\) | −1.32150e9 | −0.162841 | ||||||||
\(679\) | −5.88777e9 | −0.721783 | ||||||||
\(680\) | −1.47772e8 | −0.0180223 | ||||||||
\(681\) | 4.75569e9 | 0.577030 | ||||||||
\(682\) | 1.71330e9 | 0.206818 | ||||||||
\(683\) | −1.28166e10 | −1.53922 | −0.769610 | − | 0.638514i | \(-0.779549\pi\) | ||||
−0.769610 | + | 0.638514i | \(0.779549\pi\) | |||||||
\(684\) | 1.91097e9 | 0.228327 | ||||||||
\(685\) | −6.01176e7 | −0.00714636 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | −8.52869e9 | −1.00354 | ||||||||
\(688\) | −1.67222e9 | −0.195765 | ||||||||
\(689\) | −3.50608e9 | −0.408371 | ||||||||
\(690\) | −9.63899e7 | −0.0111702 | ||||||||
\(691\) | 9.69675e9 | 1.11803 | 0.559015 | − | 0.829158i | \(-0.311180\pi\) | ||||
0.559015 | + | 0.829158i | \(0.311180\pi\) | |||||||
\(692\) | −4.84005e9 | −0.555237 | ||||||||
\(693\) | 5.87902e8 | 0.0671025 | ||||||||
\(694\) | −1.59785e9 | −0.181459 | ||||||||
\(695\) | −5.75054e8 | −0.0649774 | ||||||||
\(696\) | 2.01539e9 | 0.226583 | ||||||||
\(697\) | −1.40703e10 | −1.57394 | ||||||||
\(698\) | −6.61710e9 | −0.736502 | ||||||||
\(699\) | −4.26086e9 | −0.471875 | ||||||||
\(700\) | −1.71176e9 | −0.188625 | ||||||||
\(701\) | 6.43479e9 | 0.705539 | 0.352770 | − | 0.935710i | \(-0.385240\pi\) | ||||
0.352770 | + | 0.935710i | \(0.385240\pi\) | |||||||
\(702\) | −3.45948e8 | −0.0377426 | ||||||||
\(703\) | 1.59628e10 | 1.73286 | ||||||||
\(704\) | 6.16344e8 | 0.0665762 | ||||||||
\(705\) | 3.92060e8 | 0.0421397 | ||||||||
\(706\) | −5.33360e8 | −0.0570432 | ||||||||
\(707\) | −4.30252e9 | −0.457884 | ||||||||
\(708\) | 1.20459e9 | 0.127562 | ||||||||
\(709\) | 1.04957e10 | 1.10598 | 0.552992 | − | 0.833187i | \(-0.313486\pi\) | ||||
0.552992 | + | 0.833187i | \(0.313486\pi\) | |||||||
\(710\) | 2.71708e8 | 0.0284904 | ||||||||
\(711\) | −3.81699e9 | −0.398269 | ||||||||
\(712\) | 1.12692e9 | 0.117008 | ||||||||
\(713\) | 3.34538e9 | 0.345647 | ||||||||
\(714\) | 1.75985e9 | 0.180939 | ||||||||
\(715\) | −6.27633e7 | −0.00642147 | ||||||||
\(716\) | −8.78823e9 | −0.894759 | ||||||||
\(717\) | −8.11732e9 | −0.822424 | ||||||||
\(718\) | 2.90853e9 | 0.293250 | ||||||||
\(719\) | −1.67170e10 | −1.67728 | −0.838641 | − | 0.544685i | \(-0.816649\pi\) | ||||
−0.838641 | + | 0.544685i | \(0.816649\pi\) | |||||||
\(720\) | −3.62811e7 | −0.00362256 | ||||||||
\(721\) | 1.19047e7 | 0.00118290 | ||||||||
\(722\) | −6.26990e9 | −0.619983 | ||||||||
\(723\) | −1.05785e10 | −1.04098 | ||||||||
\(724\) | 8.68289e9 | 0.850314 | ||||||||
\(725\) | 1.13683e10 | 1.10793 | ||||||||
\(726\) | 3.01519e9 | 0.292439 | ||||||||
\(727\) | 3.00200e9 | 0.289762 | 0.144881 | − | 0.989449i | \(-0.453720\pi\) | ||||
0.144881 | + | 0.989449i | \(0.453720\pi\) | |||||||
\(728\) | −3.85828e8 | −0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 3.49981e8 | 0.0332977 | ||||||||
\(731\) | 9.69757e9 | 0.918231 | ||||||||
\(732\) | −4.55592e9 | −0.429326 | ||||||||
\(733\) | 1.68142e10 | 1.57693 | 0.788465 | − | 0.615080i | \(-0.210876\pi\) | ||||
0.788465 | + | 0.615080i | \(0.210876\pi\) | |||||||
\(734\) | −8.37829e9 | −0.782022 | ||||||||
\(735\) | −3.85962e7 | −0.00358541 | ||||||||
\(736\) | 1.20347e9 | 0.111266 | ||||||||
\(737\) | 6.91321e9 | 0.636126 | ||||||||
\(738\) | −3.45455e9 | −0.316369 | ||||||||
\(739\) | −1.78287e9 | −0.162504 | −0.0812518 | − | 0.996694i | \(-0.525892\pi\) | ||||
−0.0812518 | + | 0.996694i | \(0.525892\pi\) | |||||||
\(740\) | −3.03064e8 | −0.0274931 | ||||||||
\(741\) | 2.42962e9 | 0.219369 | ||||||||
\(742\) | 4.37901e9 | 0.393516 | ||||||||
\(743\) | 6.48101e9 | 0.579671 | 0.289836 | − | 0.957076i | \(-0.406399\pi\) | ||||
0.289836 | + | 0.957076i | \(0.406399\pi\) | |||||||
\(744\) | 1.25920e9 | 0.112096 | ||||||||
\(745\) | 1.04633e8 | 0.00927089 | ||||||||
\(746\) | 1.19451e10 | 1.05343 | ||||||||
\(747\) | −2.22791e9 | −0.195558 | ||||||||
\(748\) | −3.57431e9 | −0.312274 | ||||||||
\(749\) | 4.89152e9 | 0.425361 | ||||||||
\(750\) | −4.09690e8 | −0.0354602 | ||||||||
\(751\) | 7.54558e9 | 0.650059 | 0.325030 | − | 0.945704i | \(-0.394626\pi\) | ||||
0.325030 | + | 0.945704i | \(0.394626\pi\) | |||||||
\(752\) | −4.89504e9 | −0.419753 | ||||||||
\(753\) | −8.39931e9 | −0.716905 | ||||||||
\(754\) | 2.56239e9 | 0.217694 | ||||||||
\(755\) | 4.87030e8 | 0.0411853 | ||||||||
\(756\) | 4.32081e8 | 0.0363696 | ||||||||
\(757\) | −2.12009e10 | −1.77631 | −0.888156 | − | 0.459542i | \(-0.848013\pi\) | ||||
−0.888156 | + | 0.459542i | \(0.848013\pi\) | |||||||
\(758\) | −3.55574e9 | −0.296543 | ||||||||
\(759\) | −2.33148e9 | −0.193547 | ||||||||
\(760\) | 2.54805e8 | 0.0210552 | ||||||||
\(761\) | −1.43518e10 | −1.18048 | −0.590241 | − | 0.807227i | \(-0.700967\pi\) | ||||
−0.590241 | + | 0.807227i | \(0.700967\pi\) | |||||||
\(762\) | −5.66027e9 | −0.463442 | ||||||||
\(763\) | −3.11832e9 | −0.254147 | ||||||||
\(764\) | −9.77247e7 | −0.00792825 | ||||||||
\(765\) | 2.10401e8 | 0.0169916 | ||||||||
\(766\) | −1.37325e10 | −1.10395 | ||||||||
\(767\) | 1.53153e9 | 0.122558 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | 4.75972e9 | 0.377433 | 0.188716 | − | 0.982032i | \(-0.439567\pi\) | ||||
0.188716 | + | 0.982032i | \(0.439567\pi\) | |||||||
\(770\) | 7.83898e7 | 0.00618788 | ||||||||
\(771\) | 7.52598e9 | 0.591388 | ||||||||
\(772\) | 1.04326e10 | 0.816080 | ||||||||
\(773\) | −3.10511e9 | −0.241796 | −0.120898 | − | 0.992665i | \(-0.538577\pi\) | ||||
−0.120898 | + | 0.992665i | \(0.538577\pi\) | |||||||
\(774\) | 2.38096e9 | 0.184569 | ||||||||
\(775\) | 7.10280e9 | 0.548117 | ||||||||
\(776\) | 8.78875e9 | 0.675167 | ||||||||
\(777\) | 3.60928e9 | 0.276024 | ||||||||
\(778\) | 1.51737e10 | 1.15522 | ||||||||
\(779\) | 2.42616e10 | 1.83882 | ||||||||
\(780\) | −4.61282e7 | −0.00348045 | ||||||||
\(781\) | 6.57209e9 | 0.493657 | ||||||||
\(782\) | −6.97917e9 | −0.521891 | ||||||||
\(783\) | −2.86957e9 | −0.213624 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −3.48978e7 | −0.00257486 | ||||||||
\(786\) | −6.97035e9 | −0.512006 | ||||||||
\(787\) | −1.45473e10 | −1.06382 | −0.531912 | − | 0.846800i | \(-0.678526\pi\) | ||||
−0.531912 | + | 0.846800i | \(0.678526\pi\) | |||||||
\(788\) | −2.80756e9 | −0.204403 | ||||||||
\(789\) | 5.44732e9 | 0.394833 | ||||||||
\(790\) | −5.08950e8 | −0.0367266 | ||||||||
\(791\) | 2.09850e9 | 0.150762 | ||||||||
\(792\) | −8.77568e8 | −0.0627686 | ||||||||
\(793\) | −5.79245e9 | −0.412483 | ||||||||
\(794\) | 1.64287e10 | 1.16474 | ||||||||
\(795\) | 5.23538e8 | 0.0369541 | ||||||||
\(796\) | 2.83138e8 | 0.0198977 | ||||||||
\(797\) | −1.42033e10 | −0.993766 | −0.496883 | − | 0.867818i | \(-0.665522\pi\) | ||||
−0.496883 | + | 0.867818i | \(0.665522\pi\) | |||||||
\(798\) | −3.03454e9 | −0.211389 | ||||||||
\(799\) | 2.83874e10 | 1.96885 | ||||||||
\(800\) | 2.55516e9 | 0.176443 | ||||||||
\(801\) | −1.60454e9 | −0.110316 | ||||||||
\(802\) | 1.29439e10 | 0.886047 | ||||||||
\(803\) | 8.46536e9 | 0.576954 | ||||||||
\(804\) | 5.08089e9 | 0.344782 | ||||||||
\(805\) | 1.53064e8 | 0.0103416 | ||||||||
\(806\) | 1.60096e9 | 0.107698 | ||||||||
\(807\) | −1.20994e10 | −0.810413 | ||||||||
\(808\) | 6.42242e9 | 0.428311 | ||||||||
\(809\) | 1.14889e10 | 0.762883 | 0.381442 | − | 0.924393i | \(-0.375428\pi\) | ||||
0.381442 | + | 0.924393i | \(0.375428\pi\) | |||||||
\(810\) | 5.16580e7 | 0.00341539 | ||||||||
\(811\) | −1.27152e10 | −0.837048 | −0.418524 | − | 0.908206i | \(-0.637452\pi\) | ||||
−0.418524 | + | 0.908206i | \(0.637452\pi\) | |||||||
\(812\) | −3.20037e9 | −0.209775 | ||||||||
\(813\) | 7.51542e9 | 0.490497 | ||||||||
\(814\) | −7.33054e9 | −0.476376 | ||||||||
\(815\) | −1.12140e9 | −0.0725620 | ||||||||
\(816\) | −2.62695e9 | −0.169253 | ||||||||
\(817\) | −1.67217e10 | −1.07276 | ||||||||
\(818\) | 7.19035e9 | 0.459318 | ||||||||
\(819\) | 5.49353e8 | 0.0349428 | ||||||||
\(820\) | −4.60624e8 | −0.0291741 | ||||||||
\(821\) | 2.47879e9 | 0.156329 | 0.0781644 | − | 0.996940i | \(-0.475094\pi\) | ||||
0.0781644 | + | 0.996940i | \(0.475094\pi\) | |||||||
\(822\) | −1.06872e9 | −0.0671138 | ||||||||
\(823\) | 1.25365e10 | 0.783927 | 0.391964 | − | 0.919981i | \(-0.371796\pi\) | ||||
0.391964 | + | 0.919981i | \(0.371796\pi\) | |||||||
\(824\) | −1.77703e7 | −0.00110650 | ||||||||
\(825\) | −4.95012e9 | −0.306921 | ||||||||
\(826\) | −1.91284e9 | −0.118100 | ||||||||
\(827\) | −1.01541e10 | −0.624269 | −0.312135 | − | 0.950038i | \(-0.601044\pi\) | ||||
−0.312135 | + | 0.950038i | \(0.601044\pi\) | |||||||
\(828\) | −1.71353e9 | −0.104903 | ||||||||
\(829\) | −1.14635e10 | −0.698837 | −0.349419 | − | 0.936967i | \(-0.613621\pi\) | ||||
−0.349419 | + | 0.936967i | \(0.613621\pi\) | |||||||
\(830\) | −2.97066e8 | −0.0180335 | ||||||||
\(831\) | −3.83295e8 | −0.0231702 | ||||||||
\(832\) | 5.75930e8 | 0.0346688 | ||||||||
\(833\) | −2.79458e9 | −0.167517 | ||||||||
\(834\) | −1.02228e10 | −0.610224 | ||||||||
\(835\) | 5.02405e8 | 0.0298642 | ||||||||
\(836\) | 6.16323e9 | 0.364827 | ||||||||
\(837\) | −1.79288e9 | −0.105685 | ||||||||
\(838\) | 6.46979e9 | 0.379783 | ||||||||
\(839\) | −1.33243e10 | −0.778892 | −0.389446 | − | 0.921049i | \(-0.627333\pi\) | ||||
−0.389446 | + | 0.921049i | \(0.627333\pi\) | |||||||
\(840\) | 5.76130e7 | 0.00335384 | ||||||||
\(841\) | 4.00462e9 | 0.232154 | ||||||||
\(842\) | −1.01677e10 | −0.586990 | ||||||||
\(843\) | −1.00644e10 | −0.578614 | ||||||||
\(844\) | −9.00030e9 | −0.515298 | ||||||||
\(845\) | −5.86479e7 | −0.00334391 | ||||||||
\(846\) | 6.96970e9 | 0.395747 | ||||||||
\(847\) | −4.78800e9 | −0.270746 | ||||||||
\(848\) | −6.53660e9 | −0.368100 | ||||||||
\(849\) | −4.78999e9 | −0.268632 | ||||||||
\(850\) | −1.48179e10 | −0.827601 | ||||||||
\(851\) | −1.43136e10 | −0.796149 | ||||||||
\(852\) | 4.83019e9 | 0.267563 | ||||||||
\(853\) | 3.41609e10 | 1.88455 | 0.942274 | − | 0.334843i | \(-0.108683\pi\) | ||||
0.942274 | + | 0.334843i | \(0.108683\pi\) | |||||||
\(854\) | 7.23463e9 | 0.397479 | ||||||||
\(855\) | −3.62798e8 | −0.0198511 | ||||||||
\(856\) | −7.30163e9 | −0.397889 | ||||||||
\(857\) | −3.06420e10 | −1.66297 | −0.831485 | − | 0.555548i | \(-0.812509\pi\) | ||||
−0.831485 | + | 0.555548i | \(0.812509\pi\) | |||||||
\(858\) | −1.11575e9 | −0.0603061 | ||||||||
\(859\) | −8.93738e9 | −0.481099 | −0.240549 | − | 0.970637i | \(-0.577328\pi\) | ||||
−0.240549 | + | 0.970637i | \(0.577328\pi\) | |||||||
\(860\) | 3.17473e8 | 0.0170201 | ||||||||
\(861\) | 5.48570e9 | 0.292901 | ||||||||
\(862\) | 8.76296e9 | 0.465989 | ||||||||
\(863\) | −9.35681e9 | −0.495553 | −0.247777 | − | 0.968817i | \(-0.579700\pi\) | ||||
−0.247777 | + | 0.968817i | \(0.579700\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 9.18887e8 | 0.0482732 | ||||||||
\(866\) | −1.73233e10 | −0.906394 | ||||||||
\(867\) | 4.15511e9 | 0.216529 | ||||||||
\(868\) | −1.99956e9 | −0.103781 | ||||||||
\(869\) | −1.23105e10 | −0.636366 | ||||||||
\(870\) | −3.82623e8 | −0.0196995 | ||||||||
\(871\) | 6.45991e9 | 0.331255 | ||||||||
\(872\) | 4.65475e9 | 0.237733 | ||||||||
\(873\) | −1.25137e10 | −0.636553 | ||||||||
\(874\) | 1.20343e10 | 0.609720 | ||||||||
\(875\) | 6.50573e8 | 0.0328298 | ||||||||
\(876\) | 6.22166e9 | 0.312710 | ||||||||
\(877\) | −4.31179e9 | −0.215853 | −0.107927 | − | 0.994159i | \(-0.534421\pi\) | ||||
−0.107927 | + | 0.994159i | \(0.534421\pi\) | |||||||
\(878\) | −6.37998e9 | −0.318118 | ||||||||
\(879\) | −1.28845e10 | −0.639889 | ||||||||
\(880\) | −1.17013e8 | −0.00578824 | ||||||||
\(881\) | 2.17775e10 | 1.07298 | 0.536491 | − | 0.843906i | \(-0.319750\pi\) | ||||
0.536491 | + | 0.843906i | \(0.319750\pi\) | |||||||
\(882\) | −6.86129e8 | −0.0336718 | ||||||||
\(883\) | 3.20221e10 | 1.56526 | 0.782631 | − | 0.622486i | \(-0.213877\pi\) | ||||
0.782631 | + | 0.622486i | \(0.213877\pi\) | |||||||
\(884\) | −3.33994e9 | −0.162613 | ||||||||
\(885\) | −2.28692e8 | −0.0110905 | ||||||||
\(886\) | 8.51483e8 | 0.0411299 | ||||||||
\(887\) | 1.71630e10 | 0.825774 | 0.412887 | − | 0.910782i | \(-0.364520\pi\) | ||||
0.412887 | + | 0.910782i | \(0.364520\pi\) | |||||||
\(888\) | −5.38761e9 | −0.258197 | ||||||||
\(889\) | 8.98831e9 | 0.429064 | ||||||||
\(890\) | −2.13947e8 | −0.0101728 | ||||||||
\(891\) | 1.24951e9 | 0.0591788 | ||||||||
\(892\) | −1.08042e10 | −0.509701 | ||||||||
\(893\) | −4.89488e10 | −2.30018 | ||||||||
\(894\) | 1.86007e9 | 0.0870660 | ||||||||
\(895\) | 1.66845e9 | 0.0777917 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | −2.17861e9 | −0.100787 | ||||||||
\(898\) | 7.40411e9 | 0.341197 | ||||||||
\(899\) | 1.32796e10 | 0.609575 | ||||||||
\(900\) | −3.63811e9 | −0.166352 | ||||||||
\(901\) | 3.79071e10 | 1.72657 | ||||||||
\(902\) | −1.11416e10 | −0.505503 | ||||||||
\(903\) | −3.78087e9 | −0.170877 | ||||||||
\(904\) | −3.13245e9 | −0.141025 | ||||||||
\(905\) | −1.64845e9 | −0.0739276 | ||||||||
\(906\) | 8.65800e9 | 0.386784 | ||||||||
\(907\) | 1.20055e10 | 0.534263 | 0.267132 | − | 0.963660i | \(-0.413924\pi\) | ||||
0.267132 | + | 0.963660i | \(0.413924\pi\) | |||||||
\(908\) | 1.12727e10 | 0.499723 | ||||||||
\(909\) | −9.14443e9 | −0.403815 | ||||||||
\(910\) | 7.32498e7 | 0.00322227 | ||||||||
\(911\) | 1.59171e10 | 0.697509 | 0.348755 | − | 0.937214i | \(-0.386605\pi\) | ||||
0.348755 | + | 0.937214i | \(0.386605\pi\) | |||||||
\(912\) | 4.52970e9 | 0.197737 | ||||||||
\(913\) | −7.18545e9 | −0.312468 | ||||||||
\(914\) | 1.78609e9 | 0.0773735 | ||||||||
\(915\) | 8.64945e8 | 0.0373263 | ||||||||
\(916\) | −2.02162e10 | −0.869089 | ||||||||
\(917\) | 1.10687e10 | 0.474026 | ||||||||
\(918\) | 3.74033e9 | 0.159573 | ||||||||
\(919\) | −5.58329e9 | −0.237293 | −0.118647 | − | 0.992937i | \(-0.537856\pi\) | ||||
−0.118647 | + | 0.992937i | \(0.537856\pi\) | |||||||
\(920\) | −2.28480e8 | −0.00967365 | ||||||||
\(921\) | −2.42515e10 | −1.02289 | ||||||||
\(922\) | 3.19131e10 | 1.34094 | ||||||||
\(923\) | 6.14116e9 | 0.257066 | ||||||||
\(924\) | 1.39355e9 | 0.0581124 | ||||||||
\(925\) | −3.03900e10 | −1.26251 | ||||||||
\(926\) | 3.73337e9 | 0.154512 | ||||||||
\(927\) | 2.53019e7 | 0.00104322 | ||||||||
\(928\) | 4.77722e9 | 0.196226 | ||||||||
\(929\) | 3.96979e10 | 1.62447 | 0.812237 | − | 0.583328i | \(-0.198250\pi\) | ||||
0.812237 | + | 0.583328i | \(0.198250\pi\) | |||||||
\(930\) | −2.39060e8 | −0.00974578 | ||||||||
\(931\) | 4.81874e9 | 0.195708 | ||||||||
\(932\) | −1.00998e10 | −0.408656 | ||||||||
\(933\) | −6.59004e9 | −0.265646 | ||||||||
\(934\) | −1.36158e10 | −0.546799 | ||||||||
\(935\) | 6.78585e8 | 0.0271496 | ||||||||
\(936\) | −8.20026e8 | −0.0326860 | ||||||||
\(937\) | −3.87603e10 | −1.53921 | −0.769606 | − | 0.638519i | \(-0.779547\pi\) | ||||
−0.769606 | + | 0.638519i | \(0.779547\pi\) | |||||||
\(938\) | −8.06827e9 | −0.319206 | ||||||||
\(939\) | −1.85554e10 | −0.731378 | ||||||||
\(940\) | 9.29328e8 | 0.0364940 | ||||||||
\(941\) | −9.23500e9 | −0.361304 | −0.180652 | − | 0.983547i | \(-0.557821\pi\) | ||||
−0.180652 | + | 0.983547i | \(0.557821\pi\) | |||||||
\(942\) | −6.20382e8 | −0.0241814 | ||||||||
\(943\) | −2.17550e10 | −0.844828 | ||||||||
\(944\) | 2.85532e9 | 0.110472 | ||||||||
\(945\) | −8.20310e7 | −0.00316203 | ||||||||
\(946\) | 7.67905e9 | 0.294909 | ||||||||
\(947\) | 3.97440e10 | 1.52071 | 0.760355 | − | 0.649508i | \(-0.225025\pi\) | ||||
0.760355 | + | 0.649508i | \(0.225025\pi\) | |||||||
\(948\) | −9.04767e9 | −0.344911 | ||||||||
\(949\) | 7.91029e9 | 0.300442 | ||||||||
\(950\) | 2.55508e10 | 0.966877 | ||||||||
\(951\) | −3.06254e9 | −0.115465 | ||||||||
\(952\) | 4.17150e9 | 0.156698 | ||||||||
\(953\) | 2.76232e10 | 1.03383 | 0.516914 | − | 0.856037i | \(-0.327081\pi\) | ||||
0.516914 | + | 0.856037i | \(0.327081\pi\) | |||||||
\(954\) | 9.30699e9 | 0.347048 | ||||||||
\(955\) | 1.85531e7 | 0.000689295 0 | ||||||||
\(956\) | −1.92411e10 | −0.712240 | ||||||||
\(957\) | −9.25491e9 | −0.341335 | ||||||||
\(958\) | −1.05122e10 | −0.386291 | ||||||||
\(959\) | 1.69708e9 | 0.0621353 | ||||||||
\(960\) | −8.59995e7 | −0.00313723 | ||||||||
\(961\) | −1.92156e10 | −0.698429 | ||||||||
\(962\) | −6.84987e9 | −0.248068 | ||||||||
\(963\) | 1.03963e10 | 0.375133 | ||||||||
\(964\) | −2.50751e10 | −0.901514 | ||||||||
\(965\) | −1.98064e9 | −0.0709512 | ||||||||
\(966\) | 2.72103e9 | 0.0971210 | ||||||||
\(967\) | −4.48219e10 | −1.59403 | −0.797017 | − | 0.603957i | \(-0.793590\pi\) | ||||
−0.797017 | + | 0.603957i | \(0.793590\pi\) | |||||||
\(968\) | 7.14711e9 | 0.253260 | ||||||||
\(969\) | −2.62687e10 | −0.927480 | ||||||||
\(970\) | −1.66855e9 | −0.0587000 | ||||||||
\(971\) | 3.63237e10 | 1.27328 | 0.636638 | − | 0.771163i | \(-0.280325\pi\) | ||||
0.636638 | + | 0.771163i | \(0.280325\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | 1.62334e10 | 0.564957 | ||||||||
\(974\) | −2.07150e10 | −0.718336 | ||||||||
\(975\) | −4.62554e9 | −0.159826 | ||||||||
\(976\) | −1.07992e10 | −0.371807 | ||||||||
\(977\) | 3.98690e10 | 1.36774 | 0.683871 | − | 0.729603i | \(-0.260295\pi\) | ||||
0.683871 | + | 0.729603i | \(0.260295\pi\) | |||||||
\(978\) | −1.99353e10 | −0.681454 | ||||||||
\(979\) | −5.17497e9 | −0.176266 | ||||||||
\(980\) | −9.14873e7 | −0.00310506 | ||||||||
\(981\) | −6.62757e9 | −0.224137 | ||||||||
\(982\) | 2.18668e10 | 0.736878 | ||||||||
\(983\) | 6.50063e9 | 0.218282 | 0.109141 | − | 0.994026i | \(-0.465190\pi\) | ||||
0.109141 | + | 0.994026i | \(0.465190\pi\) | |||||||
\(984\) | −8.18856e9 | −0.273984 | ||||||||
\(985\) | 5.33017e8 | 0.0177711 | ||||||||
\(986\) | −2.77041e10 | −0.920396 | ||||||||
\(987\) | −1.10676e10 | −0.366391 | ||||||||
\(988\) | 5.75911e9 | 0.189979 | ||||||||
\(989\) | 1.49941e10 | 0.492870 | ||||||||
\(990\) | 1.66607e8 | 0.00545720 | ||||||||
\(991\) | 2.84761e10 | 0.929443 | 0.464721 | − | 0.885457i | \(-0.346154\pi\) | ||||
0.464721 | + | 0.885457i | \(0.346154\pi\) | |||||||
\(992\) | 2.98477e9 | 0.0970778 | ||||||||
\(993\) | −7.37539e9 | −0.239036 | ||||||||
\(994\) | −7.67017e9 | −0.247715 | ||||||||
\(995\) | −5.37539e7 | −0.00172993 | ||||||||
\(996\) | −5.28098e9 | −0.169358 | ||||||||
\(997\) | 1.31123e10 | 0.419030 | 0.209515 | − | 0.977805i | \(-0.432811\pi\) | ||||
0.209515 | + | 0.977805i | \(0.432811\pi\) | |||||||
\(998\) | −3.98316e10 | −1.26844 | ||||||||
\(999\) | 7.67103e9 | 0.243430 |
(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 | 546.8.a.i.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.i.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial |