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 | 1.5 | ||
Root | \(-204.972\) 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 | ||||||||
\(5\) | 320.628 | 1.14711 | 0.573557 | − | 0.819166i | \(-0.305563\pi\) | ||||
0.573557 | + | 0.819166i | \(0.305563\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −2565.02 | −0.811132 | ||||||||
\(11\) | −1110.99 | −0.251672 | −0.125836 | − | 0.992051i | \(-0.540161\pi\) | ||||
−0.125836 | + | 0.992051i | \(0.540161\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | 2197.00 | 0.277350 | ||||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | 8656.96 | 0.662286 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 3826.09 | 0.188879 | 0.0944396 | − | 0.995531i | \(-0.469894\pi\) | ||||
0.0944396 | + | 0.995531i | \(0.469894\pi\) | |||||||
\(18\) | −5832.00 | −0.235702 | ||||||||
\(19\) | −45323.1 | −1.51594 | −0.757970 | − | 0.652289i | \(-0.773809\pi\) | ||||
−0.757970 | + | 0.652289i | \(0.773809\pi\) | |||||||
\(20\) | 20520.2 | 0.573557 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | 8887.91 | 0.177959 | ||||||||
\(23\) | −5254.10 | −0.0900432 | −0.0450216 | − | 0.998986i | \(-0.514336\pi\) | ||||
−0.0450216 | + | 0.998986i | \(0.514336\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 24677.3 | 0.315870 | ||||||||
\(26\) | −17576.0 | −0.196116 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | 25163.2 | 0.191590 | 0.0957951 | − | 0.995401i | \(-0.469461\pi\) | ||||
0.0957951 | + | 0.995401i | \(0.469461\pi\) | |||||||
\(30\) | −69255.7 | −0.468307 | ||||||||
\(31\) | −223416. | −1.34694 | −0.673471 | − | 0.739214i | \(-0.735197\pi\) | ||||
−0.673471 | + | 0.739214i | \(0.735197\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | −29996.7 | −0.145303 | ||||||||
\(34\) | −30608.7 | −0.133558 | ||||||||
\(35\) | 109975. | 0.433568 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 238713. | 0.774767 | 0.387383 | − | 0.921919i | \(-0.373379\pi\) | ||||
0.387383 | + | 0.921919i | \(0.373379\pi\) | |||||||
\(38\) | 362585. | 1.07193 | ||||||||
\(39\) | 59319.0 | 0.160128 | ||||||||
\(40\) | −164162. | −0.405566 | ||||||||
\(41\) | 42730.0 | 0.0968254 | 0.0484127 | − | 0.998827i | \(-0.484584\pi\) | ||||
0.0484127 | + | 0.998827i | \(0.484584\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | −819703. | −1.57223 | −0.786117 | − | 0.618078i | \(-0.787912\pi\) | ||||
−0.786117 | + | 0.618078i | \(0.787912\pi\) | |||||||
\(44\) | −71103.2 | −0.125836 | ||||||||
\(45\) | 233738. | 0.382371 | ||||||||
\(46\) | 42032.8 | 0.0636702 | ||||||||
\(47\) | −684959. | −0.962325 | −0.481163 | − | 0.876631i | \(-0.659785\pi\) | ||||
−0.481163 | + | 0.876631i | \(0.659785\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −197419. | −0.223354 | ||||||||
\(51\) | 103304. | 0.109049 | ||||||||
\(52\) | 140608. | 0.138675 | ||||||||
\(53\) | −1.18203e6 | −1.09059 | −0.545295 | − | 0.838244i | \(-0.683583\pi\) | ||||
−0.545295 | + | 0.838244i | \(0.683583\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −356214. | −0.288696 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | −1.22372e6 | −0.875229 | ||||||||
\(58\) | −201306. | −0.135475 | ||||||||
\(59\) | −2.74036e6 | −1.73710 | −0.868550 | − | 0.495601i | \(-0.834948\pi\) | ||||
−0.868550 | + | 0.495601i | \(0.834948\pi\) | |||||||
\(60\) | 554045. | 0.331143 | ||||||||
\(61\) | 1.94158e6 | 1.09522 | 0.547608 | − | 0.836735i | \(-0.315539\pi\) | ||||
0.547608 | + | 0.836735i | \(0.315539\pi\) | |||||||
\(62\) | 1.78733e6 | 0.952432 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 704420. | 0.318152 | ||||||||
\(66\) | 239973. | 0.102745 | ||||||||
\(67\) | −1.62868e6 | −0.661568 | −0.330784 | − | 0.943706i | \(-0.607313\pi\) | ||||
−0.330784 | + | 0.943706i | \(0.607313\pi\) | |||||||
\(68\) | 244870. | 0.0944396 | ||||||||
\(69\) | −141861. | −0.0519865 | ||||||||
\(70\) | −879803. | −0.306579 | ||||||||
\(71\) | −1.88558e6 | −0.625231 | −0.312615 | − | 0.949880i | \(-0.601205\pi\) | ||||
−0.312615 | + | 0.949880i | \(0.601205\pi\) | |||||||
\(72\) | −373248. | −0.117851 | ||||||||
\(73\) | −5.69023e6 | −1.71199 | −0.855993 | − | 0.516988i | \(-0.827053\pi\) | ||||
−0.855993 | + | 0.516988i | \(0.827053\pi\) | |||||||
\(74\) | −1.90971e6 | −0.547843 | ||||||||
\(75\) | 666288. | 0.182367 | ||||||||
\(76\) | −2.90068e6 | −0.757970 | ||||||||
\(77\) | −381069. | −0.0951231 | ||||||||
\(78\) | −474552. | −0.113228 | ||||||||
\(79\) | −4.76272e6 | −1.08683 | −0.543413 | − | 0.839465i | \(-0.682868\pi\) | ||||
−0.543413 | + | 0.839465i | \(0.682868\pi\) | |||||||
\(80\) | 1.31329e6 | 0.286778 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −341840. | −0.0684659 | ||||||||
\(83\) | 96910.3 | 0.0186036 | 0.00930179 | − | 0.999957i | \(-0.497039\pi\) | ||||
0.00930179 | + | 0.999957i | \(0.497039\pi\) | |||||||
\(84\) | 592704. | 0.109109 | ||||||||
\(85\) | 1.22675e6 | 0.216666 | ||||||||
\(86\) | 6.55763e6 | 1.11174 | ||||||||
\(87\) | 679407. | 0.110615 | ||||||||
\(88\) | 568826. | 0.0889795 | ||||||||
\(89\) | −485878. | −0.0730571 | −0.0365285 | − | 0.999333i | \(-0.511630\pi\) | ||||
−0.0365285 | + | 0.999333i | \(0.511630\pi\) | |||||||
\(90\) | −1.86990e6 | −0.270377 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −336262. | −0.0450216 | ||||||||
\(93\) | −6.03224e6 | −0.777657 | ||||||||
\(94\) | 5.47967e6 | 0.680467 | ||||||||
\(95\) | −1.45319e7 | −1.73896 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | 1.65671e7 | 1.84309 | 0.921544 | − | 0.388274i | \(-0.126928\pi\) | ||||
0.921544 | + | 0.388274i | \(0.126928\pi\) | |||||||
\(98\) | −941192. | −0.101015 | ||||||||
\(99\) | −809910. | −0.0838907 | ||||||||
\(100\) | 1.57935e6 | 0.157935 | ||||||||
\(101\) | 5.23826e6 | 0.505897 | 0.252948 | − | 0.967480i | \(-0.418600\pi\) | ||||
0.252948 | + | 0.967480i | \(0.418600\pi\) | |||||||
\(102\) | −826436. | −0.0771096 | ||||||||
\(103\) | 5.76806e6 | 0.520115 | 0.260058 | − | 0.965593i | \(-0.416258\pi\) | ||||
0.260058 | + | 0.965593i | \(0.416258\pi\) | |||||||
\(104\) | −1.12486e6 | −0.0980581 | ||||||||
\(105\) | 2.96934e6 | 0.250321 | ||||||||
\(106\) | 9.45622e6 | 0.771164 | ||||||||
\(107\) | 3.10359e6 | 0.244918 | 0.122459 | − | 0.992474i | \(-0.460922\pi\) | ||||
0.122459 | + | 0.992474i | \(0.460922\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −7.81668e6 | −0.578136 | −0.289068 | − | 0.957309i | \(-0.593345\pi\) | ||||
−0.289068 | + | 0.957309i | \(0.593345\pi\) | |||||||
\(110\) | 2.84971e6 | 0.204139 | ||||||||
\(111\) | 6.44526e6 | 0.447312 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | 1.46151e7 | 0.952857 | 0.476429 | − | 0.879213i | \(-0.341931\pi\) | ||||
0.476429 | + | 0.879213i | \(0.341931\pi\) | |||||||
\(114\) | 9.78980e6 | 0.618880 | ||||||||
\(115\) | −1.68461e6 | −0.103290 | ||||||||
\(116\) | 1.61045e6 | 0.0957951 | ||||||||
\(117\) | 1.60161e6 | 0.0924500 | ||||||||
\(118\) | 2.19228e7 | 1.22832 | ||||||||
\(119\) | 1.31235e6 | 0.0713896 | ||||||||
\(120\) | −4.43236e6 | −0.234154 | ||||||||
\(121\) | −1.82529e7 | −0.936661 | ||||||||
\(122\) | −1.55326e7 | −0.774435 | ||||||||
\(123\) | 1.15371e6 | 0.0559022 | ||||||||
\(124\) | −1.42986e7 | −0.673471 | ||||||||
\(125\) | −1.71368e7 | −0.784775 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | −5.89808e6 | −0.255504 | −0.127752 | − | 0.991806i | \(-0.540776\pi\) | ||||
−0.127752 | + | 0.991806i | \(0.540776\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | −2.21320e7 | −0.907730 | ||||||||
\(130\) | −5.63536e6 | −0.224967 | ||||||||
\(131\) | −2.33015e6 | −0.0905597 | −0.0452799 | − | 0.998974i | \(-0.514418\pi\) | ||||
−0.0452799 | + | 0.998974i | \(0.514418\pi\) | |||||||
\(132\) | −1.91979e6 | −0.0726515 | ||||||||
\(133\) | −1.55458e7 | −0.572972 | ||||||||
\(134\) | 1.30295e7 | 0.467799 | ||||||||
\(135\) | 6.31092e6 | 0.220762 | ||||||||
\(136\) | −1.95896e6 | −0.0667789 | ||||||||
\(137\) | 2.87952e7 | 0.956750 | 0.478375 | − | 0.878156i | \(-0.341226\pi\) | ||||
0.478375 | + | 0.878156i | \(0.341226\pi\) | |||||||
\(138\) | 1.13489e6 | 0.0367600 | ||||||||
\(139\) | −1.11937e7 | −0.353527 | −0.176764 | − | 0.984253i | \(-0.556563\pi\) | ||||
−0.176764 | + | 0.984253i | \(0.556563\pi\) | |||||||
\(140\) | 7.03843e6 | 0.216784 | ||||||||
\(141\) | −1.84939e7 | −0.555599 | ||||||||
\(142\) | 1.50846e7 | 0.442105 | ||||||||
\(143\) | −2.44084e6 | −0.0698013 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 8.06804e6 | 0.219776 | ||||||||
\(146\) | 4.55219e7 | 1.21056 | ||||||||
\(147\) | 3.17652e6 | 0.0824786 | ||||||||
\(148\) | 1.52777e7 | 0.387383 | ||||||||
\(149\) | 5.31071e7 | 1.31523 | 0.657614 | − | 0.753355i | \(-0.271566\pi\) | ||||
0.657614 | + | 0.753355i | \(0.271566\pi\) | |||||||
\(150\) | −5.33030e6 | −0.128953 | ||||||||
\(151\) | 5.15820e7 | 1.21921 | 0.609605 | − | 0.792705i | \(-0.291328\pi\) | ||||
0.609605 | + | 0.792705i | \(0.291328\pi\) | |||||||
\(152\) | 2.32054e7 | 0.535966 | ||||||||
\(153\) | 2.78922e6 | 0.0629597 | ||||||||
\(154\) | 3.04855e6 | 0.0672622 | ||||||||
\(155\) | −7.16335e7 | −1.54510 | ||||||||
\(156\) | 3.79642e6 | 0.0800641 | ||||||||
\(157\) | 5.18036e7 | 1.06834 | 0.534172 | − | 0.845376i | \(-0.320624\pi\) | ||||
0.534172 | + | 0.845376i | \(0.320624\pi\) | |||||||
\(158\) | 3.81017e7 | 0.768502 | ||||||||
\(159\) | −3.19147e7 | −0.629653 | ||||||||
\(160\) | −1.05063e7 | −0.202783 | ||||||||
\(161\) | −1.80216e6 | −0.0340331 | ||||||||
\(162\) | −4.25153e6 | −0.0785674 | ||||||||
\(163\) | −6.58655e7 | −1.19125 | −0.595623 | − | 0.803264i | \(-0.703095\pi\) | ||||
−0.595623 | + | 0.803264i | \(0.703095\pi\) | |||||||
\(164\) | 2.73472e6 | 0.0484127 | ||||||||
\(165\) | −9.61778e6 | −0.166679 | ||||||||
\(166\) | −775282. | −0.0131547 | ||||||||
\(167\) | 2.02037e6 | 0.0335678 | 0.0167839 | − | 0.999859i | \(-0.494657\pi\) | ||||
0.0167839 | + | 0.999859i | \(0.494657\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −9.81402e6 | −0.153206 | ||||||||
\(171\) | −3.30406e7 | −0.505314 | ||||||||
\(172\) | −5.24610e7 | −0.786117 | ||||||||
\(173\) | 4.20671e7 | 0.617705 | 0.308853 | − | 0.951110i | \(-0.400055\pi\) | ||||
0.308853 | + | 0.951110i | \(0.400055\pi\) | |||||||
\(174\) | −5.43526e6 | −0.0782164 | ||||||||
\(175\) | 8.46432e6 | 0.119388 | ||||||||
\(176\) | −4.55061e6 | −0.0629180 | ||||||||
\(177\) | −7.39896e7 | −1.00292 | ||||||||
\(178\) | 3.88702e6 | 0.0516591 | ||||||||
\(179\) | 4.98549e7 | 0.649713 | 0.324857 | − | 0.945763i | \(-0.394684\pi\) | ||||
0.324857 | + | 0.945763i | \(0.394684\pi\) | |||||||
\(180\) | 1.49592e7 | 0.191186 | ||||||||
\(181\) | −9.66132e6 | −0.121105 | −0.0605524 | − | 0.998165i | \(-0.519286\pi\) | ||||
−0.0605524 | + | 0.998165i | \(0.519286\pi\) | |||||||
\(182\) | −6.02857e6 | −0.0741249 | ||||||||
\(183\) | 5.24225e7 | 0.632323 | ||||||||
\(184\) | 2.69010e6 | 0.0318351 | ||||||||
\(185\) | 7.65382e7 | 0.888745 | ||||||||
\(186\) | 4.82579e7 | 0.549887 | ||||||||
\(187\) | −4.25074e6 | −0.0475356 | ||||||||
\(188\) | −4.38374e7 | −0.481163 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | 1.16255e8 | 1.22963 | ||||||||
\(191\) | −1.10454e7 | −0.114700 | −0.0573501 | − | 0.998354i | \(-0.518265\pi\) | ||||
−0.0573501 | + | 0.998354i | \(0.518265\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | −1.39943e8 | −1.40121 | −0.700603 | − | 0.713551i | \(-0.747086\pi\) | ||||
−0.700603 | + | 0.713551i | \(0.747086\pi\) | |||||||
\(194\) | −1.32537e8 | −1.30326 | ||||||||
\(195\) | 1.90193e7 | 0.183685 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | −1.77512e7 | −0.165423 | −0.0827117 | − | 0.996574i | \(-0.526358\pi\) | ||||
−0.0827117 | + | 0.996574i | \(0.526358\pi\) | |||||||
\(198\) | 6.47928e6 | 0.0593197 | ||||||||
\(199\) | 1.70775e8 | 1.53617 | 0.768083 | − | 0.640351i | \(-0.221211\pi\) | ||||
0.768083 | + | 0.640351i | \(0.221211\pi\) | |||||||
\(200\) | −1.26348e7 | −0.111677 | ||||||||
\(201\) | −4.39744e7 | −0.381957 | ||||||||
\(202\) | −4.19060e7 | −0.357723 | ||||||||
\(203\) | 8.63099e6 | 0.0724143 | ||||||||
\(204\) | 6.61149e6 | 0.0545247 | ||||||||
\(205\) | 1.37004e7 | 0.111070 | ||||||||
\(206\) | −4.61445e7 | −0.367777 | ||||||||
\(207\) | −3.83024e6 | −0.0300144 | ||||||||
\(208\) | 8.99891e6 | 0.0693375 | ||||||||
\(209\) | 5.03535e7 | 0.381520 | ||||||||
\(210\) | −2.37547e7 | −0.177003 | ||||||||
\(211\) | 7.64383e7 | 0.560173 | 0.280086 | − | 0.959975i | \(-0.409637\pi\) | ||||
0.280086 | + | 0.959975i | \(0.409637\pi\) | |||||||
\(212\) | −7.56497e7 | −0.545295 | ||||||||
\(213\) | −5.09106e7 | −0.360977 | ||||||||
\(214\) | −2.48287e7 | −0.173183 | ||||||||
\(215\) | −2.62820e8 | −1.80353 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −7.66318e7 | −0.509096 | ||||||||
\(218\) | 6.25335e7 | 0.408804 | ||||||||
\(219\) | −1.53636e8 | −0.988415 | ||||||||
\(220\) | −2.27977e7 | −0.144348 | ||||||||
\(221\) | 8.40592e6 | 0.0523857 | ||||||||
\(222\) | −5.15621e7 | −0.316297 | ||||||||
\(223\) | −4.83280e7 | −0.291831 | −0.145916 | − | 0.989297i | \(-0.546613\pi\) | ||||
−0.145916 | + | 0.989297i | \(0.546613\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | 1.79898e7 | 0.105290 | ||||||||
\(226\) | −1.16921e8 | −0.673772 | ||||||||
\(227\) | −2.37950e7 | −0.135019 | −0.0675094 | − | 0.997719i | \(-0.521505\pi\) | ||||
−0.0675094 | + | 0.997719i | \(0.521505\pi\) | |||||||
\(228\) | −7.83184e7 | −0.437614 | ||||||||
\(229\) | −3.44969e7 | −0.189826 | −0.0949132 | − | 0.995486i | \(-0.530257\pi\) | ||||
−0.0949132 | + | 0.995486i | \(0.530257\pi\) | |||||||
\(230\) | 1.34769e7 | 0.0730369 | ||||||||
\(231\) | −1.02889e7 | −0.0549193 | ||||||||
\(232\) | −1.28836e7 | −0.0677374 | ||||||||
\(233\) | −1.55458e8 | −0.805130 | −0.402565 | − | 0.915391i | \(-0.631881\pi\) | ||||
−0.402565 | + | 0.915391i | \(0.631881\pi\) | |||||||
\(234\) | −1.28129e7 | −0.0653720 | ||||||||
\(235\) | −2.19617e8 | −1.10390 | ||||||||
\(236\) | −1.75383e8 | −0.868550 | ||||||||
\(237\) | −1.28593e8 | −0.627479 | ||||||||
\(238\) | −1.04988e7 | −0.0504801 | ||||||||
\(239\) | 1.34685e8 | 0.638158 | 0.319079 | − | 0.947728i | \(-0.396626\pi\) | ||||
0.319079 | + | 0.947728i | \(0.396626\pi\) | |||||||
\(240\) | 3.54589e7 | 0.165572 | ||||||||
\(241\) | 1.98178e8 | 0.912004 | 0.456002 | − | 0.889979i | \(-0.349281\pi\) | ||||
0.456002 | + | 0.889979i | \(0.349281\pi\) | |||||||
\(242\) | 1.46023e8 | 0.662319 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 1.24261e8 | 0.547608 | ||||||||
\(245\) | 3.77216e7 | 0.163873 | ||||||||
\(246\) | −9.22968e6 | −0.0395288 | ||||||||
\(247\) | −9.95749e7 | −0.420446 | ||||||||
\(248\) | 1.14389e8 | 0.476216 | ||||||||
\(249\) | 2.61658e6 | 0.0107408 | ||||||||
\(250\) | 1.37095e8 | 0.554920 | ||||||||
\(251\) | −4.24782e8 | −1.69554 | −0.847770 | − | 0.530364i | \(-0.822055\pi\) | ||||
−0.847770 | + | 0.530364i | \(0.822055\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | 5.83724e6 | 0.0226614 | ||||||||
\(254\) | 4.71846e7 | 0.180669 | ||||||||
\(255\) | 3.31223e7 | 0.125092 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −4.34494e8 | −1.59668 | −0.798340 | − | 0.602207i | \(-0.794288\pi\) | ||||
−0.798340 | + | 0.602207i | \(0.794288\pi\) | |||||||
\(258\) | 1.77056e8 | 0.641862 | ||||||||
\(259\) | 8.18787e7 | 0.292834 | ||||||||
\(260\) | 4.50829e7 | 0.159076 | ||||||||
\(261\) | 1.83440e7 | 0.0638634 | ||||||||
\(262\) | 1.86412e7 | 0.0640354 | ||||||||
\(263\) | −5.57596e8 | −1.89006 | −0.945028 | − | 0.326989i | \(-0.893966\pi\) | ||||
−0.945028 | + | 0.326989i | \(0.893966\pi\) | |||||||
\(264\) | 1.53583e7 | 0.0513723 | ||||||||
\(265\) | −3.78991e8 | −1.25103 | ||||||||
\(266\) | 1.24367e8 | 0.405152 | ||||||||
\(267\) | −1.31187e7 | −0.0421795 | ||||||||
\(268\) | −1.04236e8 | −0.330784 | ||||||||
\(269\) | 1.32138e7 | 0.0413899 | 0.0206950 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206950 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(270\) | −5.04874e7 | −0.156102 | ||||||||
\(271\) | 2.73603e8 | 0.835080 | 0.417540 | − | 0.908659i | \(-0.362892\pi\) | ||||
0.417540 | + | 0.908659i | \(0.362892\pi\) | |||||||
\(272\) | 1.56717e7 | 0.0472198 | ||||||||
\(273\) | 2.03464e7 | 0.0605228 | ||||||||
\(274\) | −2.30362e8 | −0.676525 | ||||||||
\(275\) | −2.74162e7 | −0.0794956 | ||||||||
\(276\) | −9.07909e6 | −0.0259932 | ||||||||
\(277\) | 1.43058e8 | 0.404420 | 0.202210 | − | 0.979342i | \(-0.435188\pi\) | ||||
0.202210 | + | 0.979342i | \(0.435188\pi\) | |||||||
\(278\) | 8.95498e7 | 0.249982 | ||||||||
\(279\) | −1.62870e8 | −0.448981 | ||||||||
\(280\) | −5.63074e7 | −0.153290 | ||||||||
\(281\) | 3.10101e8 | 0.833740 | 0.416870 | − | 0.908966i | \(-0.363127\pi\) | ||||
0.416870 | + | 0.908966i | \(0.363127\pi\) | |||||||
\(282\) | 1.47951e8 | 0.392868 | ||||||||
\(283\) | 1.89157e8 | 0.496100 | 0.248050 | − | 0.968747i | \(-0.420210\pi\) | ||||
0.248050 | + | 0.968747i | \(0.420210\pi\) | |||||||
\(284\) | −1.20677e8 | −0.312615 | ||||||||
\(285\) | −3.92360e8 | −1.00399 | ||||||||
\(286\) | 1.95267e7 | 0.0493570 | ||||||||
\(287\) | 1.46564e7 | 0.0365966 | ||||||||
\(288\) | −2.38879e7 | −0.0589256 | ||||||||
\(289\) | −3.95700e8 | −0.964325 | ||||||||
\(290\) | −6.45443e7 | −0.155405 | ||||||||
\(291\) | 4.47312e8 | 1.06411 | ||||||||
\(292\) | −3.64175e8 | −0.855993 | ||||||||
\(293\) | −5.03406e8 | −1.16918 | −0.584591 | − | 0.811328i | \(-0.698745\pi\) | ||||
−0.584591 | + | 0.811328i | \(0.698745\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | −8.78635e8 | −1.99265 | ||||||||
\(296\) | −1.22221e8 | −0.273921 | ||||||||
\(297\) | −2.18676e7 | −0.0484343 | ||||||||
\(298\) | −4.24857e8 | −0.930007 | ||||||||
\(299\) | −1.15433e7 | −0.0249735 | ||||||||
\(300\) | 4.26424e7 | 0.0911837 | ||||||||
\(301\) | −2.81158e8 | −0.594248 | ||||||||
\(302\) | −4.12656e8 | −0.862112 | ||||||||
\(303\) | 1.41433e8 | 0.292080 | ||||||||
\(304\) | −1.85644e8 | −0.378985 | ||||||||
\(305\) | 6.22523e8 | 1.25634 | ||||||||
\(306\) | −2.23138e7 | −0.0445193 | ||||||||
\(307\) | −3.81400e7 | −0.0752309 | −0.0376155 | − | 0.999292i | \(-0.511976\pi\) | ||||
−0.0376155 | + | 0.999292i | \(0.511976\pi\) | |||||||
\(308\) | −2.43884e7 | −0.0475616 | ||||||||
\(309\) | 1.55738e8 | 0.300289 | ||||||||
\(310\) | 5.73068e8 | 1.09255 | ||||||||
\(311\) | −2.60068e8 | −0.490259 | −0.245129 | − | 0.969490i | \(-0.578830\pi\) | ||||
−0.245129 | + | 0.969490i | \(0.578830\pi\) | |||||||
\(312\) | −3.03713e7 | −0.0566139 | ||||||||
\(313\) | −8.66820e7 | −0.159780 | −0.0798902 | − | 0.996804i | \(-0.525457\pi\) | ||||
−0.0798902 | + | 0.996804i | \(0.525457\pi\) | |||||||
\(314\) | −4.14429e8 | −0.755433 | ||||||||
\(315\) | 8.01721e7 | 0.144523 | ||||||||
\(316\) | −3.04814e8 | −0.543413 | ||||||||
\(317\) | −5.94023e8 | −1.04736 | −0.523680 | − | 0.851915i | \(-0.675441\pi\) | ||||
−0.523680 | + | 0.851915i | \(0.675441\pi\) | |||||||
\(318\) | 2.55318e8 | 0.445232 | ||||||||
\(319\) | −2.79560e7 | −0.0482179 | ||||||||
\(320\) | 8.40507e7 | 0.143389 | ||||||||
\(321\) | 8.37968e7 | 0.141403 | ||||||||
\(322\) | 1.44173e7 | 0.0240651 | ||||||||
\(323\) | −1.73410e8 | −0.286330 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | 5.42161e7 | 0.0876065 | ||||||||
\(326\) | 5.26924e8 | 0.842339 | ||||||||
\(327\) | −2.11050e8 | −0.333787 | ||||||||
\(328\) | −2.18777e7 | −0.0342329 | ||||||||
\(329\) | −2.34941e8 | −0.363725 | ||||||||
\(330\) | 7.69422e7 | 0.117860 | ||||||||
\(331\) | 2.52756e8 | 0.383092 | 0.191546 | − | 0.981484i | \(-0.438650\pi\) | ||||
0.191546 | + | 0.981484i | \(0.438650\pi\) | |||||||
\(332\) | 6.20226e6 | 0.00930179 | ||||||||
\(333\) | 1.74022e8 | 0.258256 | ||||||||
\(334\) | −1.61630e7 | −0.0237360 | ||||||||
\(335\) | −5.22201e8 | −0.758894 | ||||||||
\(336\) | 3.79331e7 | 0.0545545 | ||||||||
\(337\) | 6.26185e8 | 0.891246 | 0.445623 | − | 0.895221i | \(-0.352982\pi\) | ||||
0.445623 | + | 0.895221i | \(0.352982\pi\) | |||||||
\(338\) | −3.86145e7 | −0.0543928 | ||||||||
\(339\) | 3.94608e8 | 0.550132 | ||||||||
\(340\) | 7.85121e7 | 0.108333 | ||||||||
\(341\) | 2.48213e8 | 0.338988 | ||||||||
\(342\) | 2.64324e8 | 0.357311 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 4.19688e8 | 0.555869 | ||||||||
\(345\) | −4.54845e7 | −0.0596344 | ||||||||
\(346\) | −3.36537e8 | −0.436783 | ||||||||
\(347\) | −1.39552e9 | −1.79301 | −0.896504 | − | 0.443036i | \(-0.853901\pi\) | ||||
−0.896504 | + | 0.443036i | \(0.853901\pi\) | |||||||
\(348\) | 4.34821e7 | 0.0553073 | ||||||||
\(349\) | −4.92681e8 | −0.620407 | −0.310204 | − | 0.950670i | \(-0.600397\pi\) | ||||
−0.310204 | + | 0.950670i | \(0.600397\pi\) | |||||||
\(350\) | −6.77146e7 | −0.0844197 | ||||||||
\(351\) | 4.32436e7 | 0.0533761 | ||||||||
\(352\) | 3.64049e7 | 0.0444898 | ||||||||
\(353\) | −1.01808e9 | −1.23189 | −0.615945 | − | 0.787789i | \(-0.711226\pi\) | ||||
−0.615945 | + | 0.787789i | \(0.711226\pi\) | |||||||
\(354\) | 5.91917e8 | 0.709168 | ||||||||
\(355\) | −6.04569e8 | −0.717211 | ||||||||
\(356\) | −3.10962e7 | −0.0365285 | ||||||||
\(357\) | 3.54334e7 | 0.0412168 | ||||||||
\(358\) | −3.98839e8 | −0.459417 | ||||||||
\(359\) | 3.21767e8 | 0.367038 | 0.183519 | − | 0.983016i | \(-0.441251\pi\) | ||||
0.183519 | + | 0.983016i | \(0.441251\pi\) | |||||||
\(360\) | −1.19674e8 | −0.135189 | ||||||||
\(361\) | 1.16031e9 | 1.29808 | ||||||||
\(362\) | 7.72906e7 | 0.0856341 | ||||||||
\(363\) | −4.92828e8 | −0.540782 | ||||||||
\(364\) | 4.82285e7 | 0.0524142 | ||||||||
\(365\) | −1.82445e9 | −1.96384 | ||||||||
\(366\) | −4.19380e8 | −0.447120 | ||||||||
\(367\) | 7.56662e8 | 0.799044 | 0.399522 | − | 0.916724i | \(-0.369176\pi\) | ||||
0.399522 | + | 0.916724i | \(0.369176\pi\) | |||||||
\(368\) | −2.15208e7 | −0.0225108 | ||||||||
\(369\) | 3.11502e7 | 0.0322751 | ||||||||
\(370\) | −6.12306e8 | −0.628438 | ||||||||
\(371\) | −4.05435e8 | −0.412205 | ||||||||
\(372\) | −3.86063e8 | −0.388829 | ||||||||
\(373\) | 5.74749e8 | 0.573452 | 0.286726 | − | 0.958013i | \(-0.407433\pi\) | ||||
0.286726 | + | 0.958013i | \(0.407433\pi\) | |||||||
\(374\) | 3.40059e7 | 0.0336128 | ||||||||
\(375\) | −4.62694e8 | −0.453090 | ||||||||
\(376\) | 3.50699e8 | 0.340233 | ||||||||
\(377\) | 5.52836e7 | 0.0531376 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | −7.64701e8 | −0.721530 | −0.360765 | − | 0.932657i | \(-0.617484\pi\) | ||||
−0.360765 | + | 0.932657i | \(0.617484\pi\) | |||||||
\(380\) | −9.30039e8 | −0.869478 | ||||||||
\(381\) | −1.59248e8 | −0.147515 | ||||||||
\(382\) | 8.83631e7 | 0.0811053 | ||||||||
\(383\) | −1.58252e9 | −1.43931 | −0.719654 | − | 0.694333i | \(-0.755699\pi\) | ||||
−0.719654 | + | 0.694333i | \(0.755699\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | −1.22181e8 | −0.109117 | ||||||||
\(386\) | 1.11955e9 | 0.990802 | ||||||||
\(387\) | −5.97564e8 | −0.524078 | ||||||||
\(388\) | 1.06030e9 | 0.921544 | ||||||||
\(389\) | −2.49156e8 | −0.214608 | −0.107304 | − | 0.994226i | \(-0.534222\pi\) | ||||
−0.107304 | + | 0.994226i | \(0.534222\pi\) | |||||||
\(390\) | −1.52155e8 | −0.129885 | ||||||||
\(391\) | −2.01027e7 | −0.0170073 | ||||||||
\(392\) | −6.02363e7 | −0.0505076 | ||||||||
\(393\) | −6.29142e7 | −0.0522847 | ||||||||
\(394\) | 1.42010e8 | 0.116972 | ||||||||
\(395\) | −1.52706e9 | −1.24671 | ||||||||
\(396\) | −5.18343e7 | −0.0419453 | ||||||||
\(397\) | 2.05599e9 | 1.64913 | 0.824564 | − | 0.565768i | \(-0.191420\pi\) | ||||
0.824564 | + | 0.565768i | \(0.191420\pi\) | |||||||
\(398\) | −1.36620e9 | −1.08623 | ||||||||
\(399\) | −4.19737e8 | −0.330805 | ||||||||
\(400\) | 1.01078e8 | 0.0789674 | ||||||||
\(401\) | −1.69943e9 | −1.31613 | −0.658063 | − | 0.752963i | \(-0.728624\pi\) | ||||
−0.658063 | + | 0.752963i | \(0.728624\pi\) | |||||||
\(402\) | 3.51795e8 | 0.270084 | ||||||||
\(403\) | −4.90845e8 | −0.373574 | ||||||||
\(404\) | 3.35248e8 | 0.252948 | ||||||||
\(405\) | 1.70395e8 | 0.127457 | ||||||||
\(406\) | −6.90479e7 | −0.0512046 | ||||||||
\(407\) | −2.65208e8 | −0.194987 | ||||||||
\(408\) | −5.28919e7 | −0.0385548 | ||||||||
\(409\) | −3.61692e8 | −0.261401 | −0.130701 | − | 0.991422i | \(-0.541723\pi\) | ||||
−0.130701 | + | 0.991422i | \(0.541723\pi\) | |||||||
\(410\) | −1.09603e8 | −0.0785381 | ||||||||
\(411\) | 7.77471e8 | 0.552380 | ||||||||
\(412\) | 3.69156e8 | 0.260058 | ||||||||
\(413\) | −9.39942e8 | −0.656562 | ||||||||
\(414\) | 3.06419e7 | 0.0212234 | ||||||||
\(415\) | 3.10721e7 | 0.0213404 | ||||||||
\(416\) | −7.19913e7 | −0.0490290 | ||||||||
\(417\) | −3.02231e8 | −0.204109 | ||||||||
\(418\) | −4.02828e8 | −0.269775 | ||||||||
\(419\) | −9.48233e8 | −0.629747 | −0.314874 | − | 0.949134i | \(-0.601962\pi\) | ||||
−0.314874 | + | 0.949134i | \(0.601962\pi\) | |||||||
\(420\) | 1.90038e8 | 0.125160 | ||||||||
\(421\) | 2.30131e9 | 1.50310 | 0.751550 | − | 0.659676i | \(-0.229307\pi\) | ||||
0.751550 | + | 0.659676i | \(0.229307\pi\) | |||||||
\(422\) | −6.11506e8 | −0.396102 | ||||||||
\(423\) | −4.99335e8 | −0.320775 | ||||||||
\(424\) | 6.05198e8 | 0.385582 | ||||||||
\(425\) | 9.44177e7 | 0.0596612 | ||||||||
\(426\) | 4.07285e8 | 0.255249 | ||||||||
\(427\) | 6.65960e8 | 0.413953 | ||||||||
\(428\) | 1.98630e8 | 0.122459 | ||||||||
\(429\) | −6.59027e7 | −0.0402998 | ||||||||
\(430\) | 2.10256e9 | 1.27529 | ||||||||
\(431\) | −1.26527e9 | −0.761223 | −0.380611 | − | 0.924735i | \(-0.624286\pi\) | ||||
−0.380611 | + | 0.924735i | \(0.624286\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | −2.32918e9 | −1.37878 | −0.689390 | − | 0.724390i | \(-0.742121\pi\) | ||||
−0.689390 | + | 0.724390i | \(0.742121\pi\) | |||||||
\(434\) | 6.13054e8 | 0.359985 | ||||||||
\(435\) | 2.17837e8 | 0.126888 | ||||||||
\(436\) | −5.00268e8 | −0.289068 | ||||||||
\(437\) | 2.38132e8 | 0.136500 | ||||||||
\(438\) | 1.22909e9 | 0.698915 | ||||||||
\(439\) | 2.40266e8 | 0.135539 | 0.0677697 | − | 0.997701i | \(-0.478412\pi\) | ||||
0.0677697 | + | 0.997701i | \(0.478412\pi\) | |||||||
\(440\) | 1.82382e8 | 0.102070 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −6.72474e7 | −0.0370423 | ||||||||
\(443\) | 9.37083e8 | 0.512112 | 0.256056 | − | 0.966662i | \(-0.417577\pi\) | ||||
0.256056 | + | 0.966662i | \(0.417577\pi\) | |||||||
\(444\) | 4.12497e8 | 0.223656 | ||||||||
\(445\) | −1.55786e8 | −0.0838047 | ||||||||
\(446\) | 3.86624e8 | 0.206356 | ||||||||
\(447\) | 1.43389e9 | 0.759347 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | 1.14102e9 | 0.594884 | 0.297442 | − | 0.954740i | \(-0.403867\pi\) | ||||
0.297442 | + | 0.954740i | \(0.403867\pi\) | |||||||
\(450\) | −1.43918e8 | −0.0744512 | ||||||||
\(451\) | −4.74725e7 | −0.0243682 | ||||||||
\(452\) | 9.35368e8 | 0.476429 | ||||||||
\(453\) | 1.39271e9 | 0.703911 | ||||||||
\(454\) | 1.90360e8 | 0.0954728 | ||||||||
\(455\) | 2.41616e8 | 0.120250 | ||||||||
\(456\) | 6.26547e8 | 0.309440 | ||||||||
\(457\) | 9.47498e8 | 0.464378 | 0.232189 | − | 0.972671i | \(-0.425411\pi\) | ||||
0.232189 | + | 0.972671i | \(0.425411\pi\) | |||||||
\(458\) | 2.75976e8 | 0.134227 | ||||||||
\(459\) | 7.53090e7 | 0.0363498 | ||||||||
\(460\) | −1.07815e8 | −0.0516449 | ||||||||
\(461\) | −6.50894e8 | −0.309426 | −0.154713 | − | 0.987959i | \(-0.549445\pi\) | ||||
−0.154713 | + | 0.987959i | \(0.549445\pi\) | |||||||
\(462\) | 8.23109e7 | 0.0388338 | ||||||||
\(463\) | 2.35034e9 | 1.10052 | 0.550258 | − | 0.834994i | \(-0.314529\pi\) | ||||
0.550258 | + | 0.834994i | \(0.314529\pi\) | |||||||
\(464\) | 1.03069e8 | 0.0478976 | ||||||||
\(465\) | −1.93410e9 | −0.892061 | ||||||||
\(466\) | 1.24366e9 | 0.569313 | ||||||||
\(467\) | 1.45048e9 | 0.659028 | 0.329514 | − | 0.944151i | \(-0.393115\pi\) | ||||
0.329514 | + | 0.944151i | \(0.393115\pi\) | |||||||
\(468\) | 1.02503e8 | 0.0462250 | ||||||||
\(469\) | −5.58638e8 | −0.250049 | ||||||||
\(470\) | 1.75694e9 | 0.780573 | ||||||||
\(471\) | 1.39870e9 | 0.616808 | ||||||||
\(472\) | 1.40306e9 | 0.614158 | ||||||||
\(473\) | 9.10681e8 | 0.395687 | ||||||||
\(474\) | 1.02875e9 | 0.443695 | ||||||||
\(475\) | −1.11845e9 | −0.478840 | ||||||||
\(476\) | 8.39904e7 | 0.0356948 | ||||||||
\(477\) | −8.61698e8 | −0.363530 | ||||||||
\(478\) | −1.07748e9 | −0.451246 | ||||||||
\(479\) | 4.18056e8 | 0.173804 | 0.0869022 | − | 0.996217i | \(-0.472303\pi\) | ||||
0.0869022 | + | 0.996217i | \(0.472303\pi\) | |||||||
\(480\) | −2.83671e8 | −0.117077 | ||||||||
\(481\) | 5.24454e8 | 0.214882 | ||||||||
\(482\) | −1.58543e9 | −0.644884 | ||||||||
\(483\) | −4.86582e7 | −0.0196490 | ||||||||
\(484\) | −1.16818e9 | −0.468331 | ||||||||
\(485\) | 5.31189e9 | 2.11423 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | 8.19072e8 | 0.321345 | 0.160672 | − | 0.987008i | \(-0.448634\pi\) | ||||
0.160672 | + | 0.987008i | \(0.448634\pi\) | |||||||
\(488\) | −9.94087e8 | −0.387217 | ||||||||
\(489\) | −1.77837e9 | −0.687767 | ||||||||
\(490\) | −3.01773e8 | −0.115876 | ||||||||
\(491\) | −7.02054e7 | −0.0267661 | −0.0133831 | − | 0.999910i | \(-0.504260\pi\) | ||||
−0.0133831 | + | 0.999910i | \(0.504260\pi\) | |||||||
\(492\) | 7.38374e7 | 0.0279511 | ||||||||
\(493\) | 9.62768e7 | 0.0361874 | ||||||||
\(494\) | 7.96599e8 | 0.297300 | ||||||||
\(495\) | −2.59680e8 | −0.0962322 | ||||||||
\(496\) | −9.15113e8 | −0.336735 | ||||||||
\(497\) | −6.46753e8 | −0.236315 | ||||||||
\(498\) | −2.09326e7 | −0.00759488 | ||||||||
\(499\) | 2.19043e8 | 0.0789184 | 0.0394592 | − | 0.999221i | \(-0.487436\pi\) | ||||
0.0394592 | + | 0.999221i | \(0.487436\pi\) | |||||||
\(500\) | −1.09676e9 | −0.392388 | ||||||||
\(501\) | 5.45500e7 | 0.0193804 | ||||||||
\(502\) | 3.39826e9 | 1.19893 | ||||||||
\(503\) | 1.81072e9 | 0.634400 | 0.317200 | − | 0.948359i | \(-0.397257\pi\) | ||||
0.317200 | + | 0.948359i | \(0.397257\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | 1.67953e9 | 0.580321 | ||||||||
\(506\) | −4.66980e7 | −0.0160240 | ||||||||
\(507\) | 1.30324e8 | 0.0444116 | ||||||||
\(508\) | −3.77477e8 | −0.127752 | ||||||||
\(509\) | −5.30736e9 | −1.78388 | −0.891941 | − | 0.452153i | \(-0.850656\pi\) | ||||
−0.891941 | + | 0.452153i | \(0.850656\pi\) | |||||||
\(510\) | −2.64978e8 | −0.0884535 | ||||||||
\(511\) | −1.95175e9 | −0.647070 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | −8.92095e8 | −0.291743 | ||||||||
\(514\) | 3.47595e9 | 1.12902 | ||||||||
\(515\) | 1.84940e9 | 0.596632 | ||||||||
\(516\) | −1.41645e9 | −0.453865 | ||||||||
\(517\) | 7.60981e8 | 0.242190 | ||||||||
\(518\) | −6.55030e8 | −0.207065 | ||||||||
\(519\) | 1.13581e9 | 0.356632 | ||||||||
\(520\) | −3.60663e8 | −0.112484 | ||||||||
\(521\) | 6.31200e9 | 1.95540 | 0.977699 | − | 0.210012i | \(-0.0673504\pi\) | ||||
0.977699 | + | 0.210012i | \(0.0673504\pi\) | |||||||
\(522\) | −1.46752e8 | −0.0451583 | ||||||||
\(523\) | 1.84810e9 | 0.564896 | 0.282448 | − | 0.959283i | \(-0.408853\pi\) | ||||
0.282448 | + | 0.959283i | \(0.408853\pi\) | |||||||
\(524\) | −1.49130e8 | −0.0452799 | ||||||||
\(525\) | 2.28537e8 | 0.0689284 | ||||||||
\(526\) | 4.46077e9 | 1.33647 | ||||||||
\(527\) | −8.54811e8 | −0.254409 | ||||||||
\(528\) | −1.22866e8 | −0.0363257 | ||||||||
\(529\) | −3.37722e9 | −0.991892 | ||||||||
\(530\) | 3.03193e9 | 0.884613 | ||||||||
\(531\) | −1.99772e9 | −0.579033 | ||||||||
\(532\) | −9.94933e8 | −0.286486 | ||||||||
\(533\) | 9.38778e7 | 0.0268545 | ||||||||
\(534\) | 1.04950e8 | 0.0298254 | ||||||||
\(535\) | 9.95097e8 | 0.280949 | ||||||||
\(536\) | 8.33885e8 | 0.233900 | ||||||||
\(537\) | 1.34608e9 | 0.375112 | ||||||||
\(538\) | −1.05710e8 | −0.0292671 | ||||||||
\(539\) | −1.30707e8 | −0.0359532 | ||||||||
\(540\) | 4.03899e8 | 0.110381 | ||||||||
\(541\) | 6.08437e9 | 1.65206 | 0.826029 | − | 0.563628i | \(-0.190595\pi\) | ||||
0.826029 | + | 0.563628i | \(0.190595\pi\) | |||||||
\(542\) | −2.18882e9 | −0.590491 | ||||||||
\(543\) | −2.60856e8 | −0.0699199 | ||||||||
\(544\) | −1.25373e8 | −0.0333894 | ||||||||
\(545\) | −2.50625e9 | −0.663187 | ||||||||
\(546\) | −1.62771e8 | −0.0427960 | ||||||||
\(547\) | 2.54355e9 | 0.664483 | 0.332242 | − | 0.943194i | \(-0.392195\pi\) | ||||
0.332242 | + | 0.943194i | \(0.392195\pi\) | |||||||
\(548\) | 1.84290e9 | 0.478375 | ||||||||
\(549\) | 1.41541e9 | 0.365072 | ||||||||
\(550\) | 2.19330e8 | 0.0562119 | ||||||||
\(551\) | −1.14048e9 | −0.290439 | ||||||||
\(552\) | 7.26327e7 | 0.0183800 | ||||||||
\(553\) | −1.63361e9 | −0.410782 | ||||||||
\(554\) | −1.14446e9 | −0.285968 | ||||||||
\(555\) | 2.06653e9 | 0.513117 | ||||||||
\(556\) | −7.16399e8 | −0.176764 | ||||||||
\(557\) | 7.37210e9 | 1.80758 | 0.903791 | − | 0.427974i | \(-0.140773\pi\) | ||||
0.903791 | + | 0.427974i | \(0.140773\pi\) | |||||||
\(558\) | 1.30296e9 | 0.317477 | ||||||||
\(559\) | −1.80089e9 | −0.436059 | ||||||||
\(560\) | 4.50459e8 | 0.108392 | ||||||||
\(561\) | −1.14770e8 | −0.0274447 | ||||||||
\(562\) | −2.48081e9 | −0.589544 | ||||||||
\(563\) | 4.40072e9 | 1.03931 | 0.519654 | − | 0.854377i | \(-0.326061\pi\) | ||||
0.519654 | + | 0.854377i | \(0.326061\pi\) | |||||||
\(564\) | −1.18361e9 | −0.277799 | ||||||||
\(565\) | 4.68602e9 | 1.09304 | ||||||||
\(566\) | −1.51325e9 | −0.350796 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | 9.65416e8 | 0.221052 | ||||||||
\(569\) | −8.50460e9 | −1.93536 | −0.967678 | − | 0.252189i | \(-0.918849\pi\) | ||||
−0.967678 | + | 0.252189i | \(0.918849\pi\) | |||||||
\(570\) | 3.13888e9 | 0.709926 | ||||||||
\(571\) | −1.25169e9 | −0.281365 | −0.140683 | − | 0.990055i | \(-0.544930\pi\) | ||||
−0.140683 | + | 0.990055i | \(0.544930\pi\) | |||||||
\(572\) | −1.56214e8 | −0.0349006 | ||||||||
\(573\) | −2.98226e8 | −0.0662222 | ||||||||
\(574\) | −1.17251e8 | −0.0258777 | ||||||||
\(575\) | −1.29657e8 | −0.0284419 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −3.77454e9 | −0.817991 | −0.408996 | − | 0.912536i | \(-0.634121\pi\) | ||||
−0.408996 | + | 0.912536i | \(0.634121\pi\) | |||||||
\(578\) | 3.16560e9 | 0.681881 | ||||||||
\(579\) | −3.77847e9 | −0.808987 | ||||||||
\(580\) | 5.16354e8 | 0.109888 | ||||||||
\(581\) | 3.32402e7 | 0.00703149 | ||||||||
\(582\) | −3.57850e9 | −0.752438 | ||||||||
\(583\) | 1.31322e9 | 0.274471 | ||||||||
\(584\) | 2.91340e9 | 0.605278 | ||||||||
\(585\) | 5.13522e8 | 0.106051 | ||||||||
\(586\) | 4.02725e9 | 0.826736 | ||||||||
\(587\) | −2.36405e9 | −0.482419 | −0.241209 | − | 0.970473i | \(-0.577544\pi\) | ||||
−0.241209 | + | 0.970473i | \(0.577544\pi\) | |||||||
\(588\) | 2.03297e8 | 0.0412393 | ||||||||
\(589\) | 1.01259e10 | 2.04188 | ||||||||
\(590\) | 7.02908e9 | 1.40902 | ||||||||
\(591\) | −4.79283e8 | −0.0955072 | ||||||||
\(592\) | 9.77770e8 | 0.193692 | ||||||||
\(593\) | 1.33822e9 | 0.263533 | 0.131767 | − | 0.991281i | \(-0.457935\pi\) | ||||
0.131767 | + | 0.991281i | \(0.457935\pi\) | |||||||
\(594\) | 1.74941e8 | 0.0342482 | ||||||||
\(595\) | 4.20776e8 | 0.0818920 | ||||||||
\(596\) | 3.39886e9 | 0.657614 | ||||||||
\(597\) | 4.61092e9 | 0.886906 | ||||||||
\(598\) | 9.23461e7 | 0.0176589 | ||||||||
\(599\) | 3.05277e9 | 0.580364 | 0.290182 | − | 0.956971i | \(-0.406284\pi\) | ||||
0.290182 | + | 0.956971i | \(0.406284\pi\) | |||||||
\(600\) | −3.41139e8 | −0.0644766 | ||||||||
\(601\) | −1.83491e9 | −0.344789 | −0.172394 | − | 0.985028i | \(-0.555150\pi\) | ||||
−0.172394 | + | 0.985028i | \(0.555150\pi\) | |||||||
\(602\) | 2.24927e9 | 0.420197 | ||||||||
\(603\) | −1.18731e9 | −0.220523 | ||||||||
\(604\) | 3.30125e9 | 0.609605 | ||||||||
\(605\) | −5.85238e9 | −1.07446 | ||||||||
\(606\) | −1.13146e9 | −0.206531 | ||||||||
\(607\) | −1.77447e9 | −0.322039 | −0.161019 | − | 0.986951i | \(-0.551478\pi\) | ||||
−0.161019 | + | 0.986951i | \(0.551478\pi\) | |||||||
\(608\) | 1.48515e9 | 0.267983 | ||||||||
\(609\) | 2.33037e8 | 0.0418084 | ||||||||
\(610\) | −4.98019e9 | −0.888365 | ||||||||
\(611\) | −1.50485e9 | −0.266901 | ||||||||
\(612\) | 1.78510e8 | 0.0314799 | ||||||||
\(613\) | −3.51920e9 | −0.617066 | −0.308533 | − | 0.951214i | \(-0.599838\pi\) | ||||
−0.308533 | + | 0.951214i | \(0.599838\pi\) | |||||||
\(614\) | 3.05120e8 | 0.0531963 | ||||||||
\(615\) | 3.69912e8 | 0.0641261 | ||||||||
\(616\) | 1.95107e8 | 0.0336311 | ||||||||
\(617\) | 1.64076e9 | 0.281220 | 0.140610 | − | 0.990065i | \(-0.455094\pi\) | ||||
0.140610 | + | 0.990065i | \(0.455094\pi\) | |||||||
\(618\) | −1.24590e9 | −0.212336 | ||||||||
\(619\) | −1.78142e9 | −0.301890 | −0.150945 | − | 0.988542i | \(-0.548232\pi\) | ||||
−0.150945 | + | 0.988542i | \(0.548232\pi\) | |||||||
\(620\) | −4.58454e9 | −0.772548 | ||||||||
\(621\) | −1.03416e8 | −0.0173288 | ||||||||
\(622\) | 2.08054e9 | 0.346665 | ||||||||
\(623\) | −1.66656e8 | −0.0276130 | ||||||||
\(624\) | 2.42971e8 | 0.0400320 | ||||||||
\(625\) | −7.42246e9 | −1.21610 | ||||||||
\(626\) | 6.93456e8 | 0.112982 | ||||||||
\(627\) | 1.35954e9 | 0.220271 | ||||||||
\(628\) | 3.31543e9 | 0.534172 | ||||||||
\(629\) | 9.13340e8 | 0.146337 | ||||||||
\(630\) | −6.41377e8 | −0.102193 | ||||||||
\(631\) | 1.15408e8 | 0.0182867 | 0.00914334 | − | 0.999958i | \(-0.497090\pi\) | ||||
0.00914334 | + | 0.999958i | \(0.497090\pi\) | |||||||
\(632\) | 2.43851e9 | 0.384251 | ||||||||
\(633\) | 2.06383e9 | 0.323416 | ||||||||
\(634\) | 4.75218e9 | 0.740595 | ||||||||
\(635\) | −1.89109e9 | −0.293092 | ||||||||
\(636\) | −2.04254e9 | −0.314826 | ||||||||
\(637\) | 2.58475e8 | 0.0396214 | ||||||||
\(638\) | 2.23648e8 | 0.0340952 | ||||||||
\(639\) | −1.37459e9 | −0.208410 | ||||||||
\(640\) | −6.72406e8 | −0.101391 | ||||||||
\(641\) | −4.00292e9 | −0.600308 | −0.300154 | − | 0.953891i | \(-0.597038\pi\) | ||||
−0.300154 | + | 0.953891i | \(0.597038\pi\) | |||||||
\(642\) | −6.70375e8 | −0.0999874 | ||||||||
\(643\) | 7.66717e9 | 1.13736 | 0.568679 | − | 0.822560i | \(-0.307455\pi\) | ||||
0.568679 | + | 0.822560i | \(0.307455\pi\) | |||||||
\(644\) | −1.15338e8 | −0.0170166 | ||||||||
\(645\) | −7.09614e9 | −1.04127 | ||||||||
\(646\) | 1.38728e9 | 0.202466 | ||||||||
\(647\) | −1.11982e10 | −1.62548 | −0.812741 | − | 0.582624i | \(-0.802026\pi\) | ||||
−0.812741 | + | 0.582624i | \(0.802026\pi\) | |||||||
\(648\) | −2.72098e8 | −0.0392837 | ||||||||
\(649\) | 3.04450e9 | 0.437180 | ||||||||
\(650\) | −4.33729e8 | −0.0619471 | ||||||||
\(651\) | −2.06906e9 | −0.293927 | ||||||||
\(652\) | −4.21540e9 | −0.595623 | ||||||||
\(653\) | 1.05903e10 | 1.48837 | 0.744185 | − | 0.667973i | \(-0.232838\pi\) | ||||
0.744185 | + | 0.667973i | \(0.232838\pi\) | |||||||
\(654\) | 1.68840e9 | 0.236023 | ||||||||
\(655\) | −7.47113e8 | −0.103882 | ||||||||
\(656\) | 1.75022e8 | 0.0242063 | ||||||||
\(657\) | −4.14818e9 | −0.570662 | ||||||||
\(658\) | 1.87953e9 | 0.257192 | ||||||||
\(659\) | 1.06277e10 | 1.44658 | 0.723288 | − | 0.690547i | \(-0.242630\pi\) | ||||
0.723288 | + | 0.690547i | \(0.242630\pi\) | |||||||
\(660\) | −6.15538e8 | −0.0833395 | ||||||||
\(661\) | −6.29528e9 | −0.847832 | −0.423916 | − | 0.905702i | \(-0.639345\pi\) | ||||
−0.423916 | + | 0.905702i | \(0.639345\pi\) | |||||||
\(662\) | −2.02205e9 | −0.270887 | ||||||||
\(663\) | 2.26960e8 | 0.0302449 | ||||||||
\(664\) | −4.96181e7 | −0.00657736 | ||||||||
\(665\) | −4.98443e9 | −0.657264 | ||||||||
\(666\) | −1.39218e9 | −0.182614 | ||||||||
\(667\) | −1.32210e8 | −0.0172514 | ||||||||
\(668\) | 1.29304e8 | 0.0167839 | ||||||||
\(669\) | −1.30486e9 | −0.168489 | ||||||||
\(670\) | 4.17761e9 | 0.536619 | ||||||||
\(671\) | −2.15707e9 | −0.275635 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | −5.77604e9 | −0.730428 | −0.365214 | − | 0.930924i | \(-0.619004\pi\) | ||||
−0.365214 | + | 0.930924i | \(0.619004\pi\) | |||||||
\(674\) | −5.00948e9 | −0.630206 | ||||||||
\(675\) | 4.85724e8 | 0.0607892 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | −9.02566e9 | −1.11794 | −0.558970 | − | 0.829188i | \(-0.688803\pi\) | ||||
−0.558970 | + | 0.829188i | \(0.688803\pi\) | |||||||
\(678\) | −3.15687e9 | −0.389002 | ||||||||
\(679\) | 5.68252e9 | 0.696622 | ||||||||
\(680\) | −6.28097e8 | −0.0766030 | ||||||||
\(681\) | −6.42464e8 | −0.0779532 | ||||||||
\(682\) | −1.98570e9 | −0.239700 | ||||||||
\(683\) | −7.49694e9 | −0.900351 | −0.450175 | − | 0.892940i | \(-0.648639\pi\) | ||||
−0.450175 | + | 0.892940i | \(0.648639\pi\) | |||||||
\(684\) | −2.11460e9 | −0.252657 | ||||||||
\(685\) | 9.23256e9 | 1.09750 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | −9.31418e8 | −0.109596 | ||||||||
\(688\) | −3.35750e9 | −0.393058 | ||||||||
\(689\) | −2.59691e9 | −0.302475 | ||||||||
\(690\) | 3.63876e8 | 0.0421679 | ||||||||
\(691\) | 7.10232e9 | 0.818893 | 0.409446 | − | 0.912334i | \(-0.365722\pi\) | ||||
0.409446 | + | 0.912334i | \(0.365722\pi\) | |||||||
\(692\) | 2.69229e9 | 0.308853 | ||||||||
\(693\) | −2.77799e8 | −0.0317077 | ||||||||
\(694\) | 1.11641e10 | 1.26785 | ||||||||
\(695\) | −3.58902e9 | −0.405536 | ||||||||
\(696\) | −3.47856e8 | −0.0391082 | ||||||||
\(697\) | 1.63489e8 | 0.0182883 | ||||||||
\(698\) | 3.94145e9 | 0.438694 | ||||||||
\(699\) | −4.19735e9 | −0.464842 | ||||||||
\(700\) | 5.41717e8 | 0.0596938 | ||||||||
\(701\) | −1.51925e10 | −1.66577 | −0.832886 | − | 0.553445i | \(-0.813313\pi\) | ||||
−0.832886 | + | 0.553445i | \(0.813313\pi\) | |||||||
\(702\) | −3.45948e8 | −0.0377426 | ||||||||
\(703\) | −1.08192e10 | −1.17450 | ||||||||
\(704\) | −2.91239e8 | −0.0314590 | ||||||||
\(705\) | −5.92966e9 | −0.637335 | ||||||||
\(706\) | 8.14467e9 | 0.871078 | ||||||||
\(707\) | 1.79672e9 | 0.191211 | ||||||||
\(708\) | −4.73533e9 | −0.501458 | ||||||||
\(709\) | 1.65464e9 | 0.174358 | 0.0871790 | − | 0.996193i | \(-0.472215\pi\) | ||||
0.0871790 | + | 0.996193i | \(0.472215\pi\) | |||||||
\(710\) | 4.83655e9 | 0.507144 | ||||||||
\(711\) | −3.47202e9 | −0.362275 | ||||||||
\(712\) | 2.48770e8 | 0.0258296 | ||||||||
\(713\) | 1.17385e9 | 0.121283 | ||||||||
\(714\) | −2.83467e8 | −0.0291447 | ||||||||
\(715\) | −7.82602e8 | −0.0800700 | ||||||||
\(716\) | 3.19071e9 | 0.324857 | ||||||||
\(717\) | 3.63651e9 | 0.368441 | ||||||||
\(718\) | −2.57414e9 | −0.259535 | ||||||||
\(719\) | 1.32039e10 | 1.32480 | 0.662399 | − | 0.749151i | \(-0.269538\pi\) | ||||
0.662399 | + | 0.749151i | \(0.269538\pi\) | |||||||
\(720\) | 9.57390e8 | 0.0955928 | ||||||||
\(721\) | 1.97845e9 | 0.196585 | ||||||||
\(722\) | −9.28251e9 | −0.917879 | ||||||||
\(723\) | 5.35082e9 | 0.526546 | ||||||||
\(724\) | −6.18325e8 | −0.0605524 | ||||||||
\(725\) | 6.20961e8 | 0.0605176 | ||||||||
\(726\) | 3.94262e9 | 0.382390 | ||||||||
\(727\) | −1.52218e10 | −1.46925 | −0.734626 | − | 0.678473i | \(-0.762642\pi\) | ||||
−0.734626 | + | 0.678473i | \(0.762642\pi\) | |||||||
\(728\) | −3.85828e8 | −0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.45956e10 | 1.38865 | ||||||||
\(731\) | −3.13626e9 | −0.296962 | ||||||||
\(732\) | 3.35504e9 | 0.316162 | ||||||||
\(733\) | 3.32757e9 | 0.312078 | 0.156039 | − | 0.987751i | \(-0.450127\pi\) | ||||
0.156039 | + | 0.987751i | \(0.450127\pi\) | |||||||
\(734\) | −6.05330e9 | −0.565009 | ||||||||
\(735\) | 1.01848e9 | 0.0946123 | ||||||||
\(736\) | 1.72166e8 | 0.0159175 | ||||||||
\(737\) | 1.80945e9 | 0.166498 | ||||||||
\(738\) | −2.49201e8 | −0.0228220 | ||||||||
\(739\) | −8.46389e9 | −0.771462 | −0.385731 | − | 0.922611i | \(-0.626051\pi\) | ||||
−0.385731 | + | 0.922611i | \(0.626051\pi\) | |||||||
\(740\) | 4.89845e9 | 0.444373 | ||||||||
\(741\) | −2.68852e9 | −0.242745 | ||||||||
\(742\) | 3.24348e9 | 0.291473 | ||||||||
\(743\) | 5.37695e9 | 0.480922 | 0.240461 | − | 0.970659i | \(-0.422701\pi\) | ||||
0.240461 | + | 0.970659i | \(0.422701\pi\) | |||||||
\(744\) | 3.08851e9 | 0.274943 | ||||||||
\(745\) | 1.70276e10 | 1.50872 | ||||||||
\(746\) | −4.59799e9 | −0.405492 | ||||||||
\(747\) | 7.06476e7 | 0.00620119 | ||||||||
\(748\) | −2.72047e8 | −0.0237678 | ||||||||
\(749\) | 1.06453e9 | 0.0925703 | ||||||||
\(750\) | 3.70155e9 | 0.320383 | ||||||||
\(751\) | 2.09510e10 | 1.80495 | 0.902473 | − | 0.430747i | \(-0.141750\pi\) | ||||
0.902473 | + | 0.430747i | \(0.141750\pi\) | |||||||
\(752\) | −2.80559e9 | −0.240581 | ||||||||
\(753\) | −1.14691e10 | −0.978921 | ||||||||
\(754\) | −4.42269e8 | −0.0375739 | ||||||||
\(755\) | 1.65386e10 | 1.39857 | ||||||||
\(756\) | 4.32081e8 | 0.0363696 | ||||||||
\(757\) | −1.41362e9 | −0.118439 | −0.0592197 | − | 0.998245i | \(-0.518861\pi\) | ||||
−0.0592197 | + | 0.998245i | \(0.518861\pi\) | |||||||
\(758\) | 6.11760e9 | 0.510199 | ||||||||
\(759\) | 1.57606e8 | 0.0130835 | ||||||||
\(760\) | 7.44031e9 | 0.614814 | ||||||||
\(761\) | −2.03319e10 | −1.67237 | −0.836184 | − | 0.548449i | \(-0.815219\pi\) | ||||
−0.836184 | + | 0.548449i | \(0.815219\pi\) | |||||||
\(762\) | 1.27399e9 | 0.104309 | ||||||||
\(763\) | −2.68112e9 | −0.218515 | ||||||||
\(764\) | −7.06905e8 | −0.0573501 | ||||||||
\(765\) | 8.94302e8 | 0.0722220 | ||||||||
\(766\) | 1.26602e10 | 1.01774 | ||||||||
\(767\) | −6.02056e9 | −0.481785 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | −5.34010e9 | −0.423455 | −0.211728 | − | 0.977329i | \(-0.567909\pi\) | ||||
−0.211728 | + | 0.977329i | \(0.567909\pi\) | |||||||
\(770\) | 9.77451e8 | 0.0771574 | ||||||||
\(771\) | −1.17313e10 | −0.921844 | ||||||||
\(772\) | −8.95638e9 | −0.700603 | ||||||||
\(773\) | 3.06137e7 | 0.00238389 | 0.00119195 | − | 0.999999i | \(-0.499621\pi\) | ||||
0.00119195 | + | 0.999999i | \(0.499621\pi\) | |||||||
\(774\) | 4.78051e9 | 0.370579 | ||||||||
\(775\) | −5.51331e9 | −0.425458 | ||||||||
\(776\) | −8.48237e9 | −0.651630 | ||||||||
\(777\) | 2.21073e9 | 0.169068 | ||||||||
\(778\) | 1.99324e9 | 0.151751 | ||||||||
\(779\) | −1.93666e9 | −0.146782 | ||||||||
\(780\) | 1.21724e9 | 0.0918426 | ||||||||
\(781\) | 2.09485e9 | 0.157353 | ||||||||
\(782\) | 1.60821e8 | 0.0120260 | ||||||||
\(783\) | 4.95288e8 | 0.0368716 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | 1.66097e10 | 1.22551 | ||||||||
\(786\) | 5.03313e8 | 0.0369709 | ||||||||
\(787\) | −2.31371e10 | −1.69199 | −0.845993 | − | 0.533194i | \(-0.820992\pi\) | ||||
−0.845993 | + | 0.533194i | \(0.820992\pi\) | |||||||
\(788\) | −1.13608e9 | −0.0827117 | ||||||||
\(789\) | −1.50551e10 | −1.09122 | ||||||||
\(790\) | 1.22165e10 | 0.881559 | ||||||||
\(791\) | 5.01299e9 | 0.360146 | ||||||||
\(792\) | 4.14674e8 | 0.0296598 | ||||||||
\(793\) | 4.26564e9 | 0.303758 | ||||||||
\(794\) | −1.64479e10 | −1.16611 | ||||||||
\(795\) | −1.02328e10 | −0.722283 | ||||||||
\(796\) | 1.09296e10 | 0.768083 | ||||||||
\(797\) | 1.30643e9 | 0.0914075 | 0.0457037 | − | 0.998955i | \(-0.485447\pi\) | ||||
0.0457037 | + | 0.998955i | \(0.485447\pi\) | |||||||
\(798\) | 3.35790e9 | 0.233915 | ||||||||
\(799\) | −2.62071e9 | −0.181763 | ||||||||
\(800\) | −8.08626e8 | −0.0558384 | ||||||||
\(801\) | −3.54205e8 | −0.0243524 | ||||||||
\(802\) | 1.35954e10 | 0.930642 | ||||||||
\(803\) | 6.32178e9 | 0.430859 | ||||||||
\(804\) | −2.81436e9 | −0.190978 | ||||||||
\(805\) | −5.77822e8 | −0.0390399 | ||||||||
\(806\) | 3.92676e9 | 0.264157 | ||||||||
\(807\) | 3.56772e8 | 0.0238965 | ||||||||
\(808\) | −2.68199e9 | −0.178862 | ||||||||
\(809\) | −3.52571e9 | −0.234114 | −0.117057 | − | 0.993125i | \(-0.537346\pi\) | ||||
−0.117057 | + | 0.993125i | \(0.537346\pi\) | |||||||
\(810\) | −1.36316e9 | −0.0901258 | ||||||||
\(811\) | −9.55800e9 | −0.629208 | −0.314604 | − | 0.949223i | \(-0.601872\pi\) | ||||
−0.314604 | + | 0.949223i | \(0.601872\pi\) | |||||||
\(812\) | 5.52383e8 | 0.0362072 | ||||||||
\(813\) | 7.38728e9 | 0.482134 | ||||||||
\(814\) | 2.12166e9 | 0.137877 | ||||||||
\(815\) | −2.11183e10 | −1.36650 | ||||||||
\(816\) | 4.23135e8 | 0.0272624 | ||||||||
\(817\) | 3.71515e10 | 2.38341 | ||||||||
\(818\) | 2.89354e9 | 0.184839 | ||||||||
\(819\) | 5.49353e8 | 0.0349428 | ||||||||
\(820\) | 8.76827e8 | 0.0555349 | ||||||||
\(821\) | 1.56683e10 | 0.988144 | 0.494072 | − | 0.869421i | \(-0.335508\pi\) | ||||
0.494072 | + | 0.869421i | \(0.335508\pi\) | |||||||
\(822\) | −6.21977e9 | −0.390592 | ||||||||
\(823\) | 3.18921e10 | 1.99427 | 0.997135 | − | 0.0756368i | \(-0.0240990\pi\) | ||||
0.997135 | + | 0.0756368i | \(0.0240990\pi\) | |||||||
\(824\) | −2.95325e9 | −0.183889 | ||||||||
\(825\) | −7.40238e8 | −0.0458968 | ||||||||
\(826\) | 7.51954e9 | 0.464260 | ||||||||
\(827\) | −2.60377e10 | −1.60079 | −0.800395 | − | 0.599473i | \(-0.795377\pi\) | ||||
−0.800395 | + | 0.599473i | \(0.795377\pi\) | |||||||
\(828\) | −2.45135e8 | −0.0150072 | ||||||||
\(829\) | 1.92272e10 | 1.17213 | 0.586064 | − | 0.810265i | \(-0.300677\pi\) | ||||
0.586064 | + | 0.810265i | \(0.300677\pi\) | |||||||
\(830\) | −2.48577e8 | −0.0150900 | ||||||||
\(831\) | 3.86256e9 | 0.233492 | ||||||||
\(832\) | 5.75930e8 | 0.0346688 | ||||||||
\(833\) | 4.50136e8 | 0.0269827 | ||||||||
\(834\) | 2.41785e9 | 0.144327 | ||||||||
\(835\) | 6.47787e8 | 0.0385061 | ||||||||
\(836\) | 3.22262e9 | 0.190760 | ||||||||
\(837\) | −4.39750e9 | −0.259219 | ||||||||
\(838\) | 7.58587e9 | 0.445298 | ||||||||
\(839\) | 1.73816e10 | 1.01607 | 0.508033 | − | 0.861337i | \(-0.330373\pi\) | ||||
0.508033 | + | 0.861337i | \(0.330373\pi\) | |||||||
\(840\) | −1.52030e9 | −0.0885017 | ||||||||
\(841\) | −1.66167e10 | −0.963293 | ||||||||
\(842\) | −1.84105e10 | −1.06285 | ||||||||
\(843\) | 8.37272e9 | 0.481360 | ||||||||
\(844\) | 4.89205e9 | 0.280086 | ||||||||
\(845\) | 1.54761e9 | 0.0882395 | ||||||||
\(846\) | 3.99468e9 | 0.226822 | ||||||||
\(847\) | −6.26074e9 | −0.354025 | ||||||||
\(848\) | −4.84158e9 | −0.272648 | ||||||||
\(849\) | 5.10723e9 | 0.286424 | ||||||||
\(850\) | −7.55341e8 | −0.0421869 | ||||||||
\(851\) | −1.25422e9 | −0.0697625 | ||||||||
\(852\) | −3.25828e9 | −0.180489 | ||||||||
\(853\) | 6.38256e9 | 0.352106 | 0.176053 | − | 0.984381i | \(-0.443667\pi\) | ||||
0.176053 | + | 0.984381i | \(0.443667\pi\) | |||||||
\(854\) | −5.32768e9 | −0.292709 | ||||||||
\(855\) | −1.05937e10 | −0.579652 | ||||||||
\(856\) | −1.58904e9 | −0.0865916 | ||||||||
\(857\) | −1.63505e9 | −0.0887355 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(858\) | 5.27222e8 | 0.0284963 | ||||||||
\(859\) | 2.60092e10 | 1.40008 | 0.700038 | − | 0.714106i | \(-0.253167\pi\) | ||||
0.700038 | + | 0.714106i | \(0.253167\pi\) | |||||||
\(860\) | −1.68205e10 | −0.901765 | ||||||||
\(861\) | 3.95722e8 | 0.0211290 | ||||||||
\(862\) | 1.01221e10 | 0.538266 | ||||||||
\(863\) | −1.30487e10 | −0.691084 | −0.345542 | − | 0.938403i | \(-0.612305\pi\) | ||||
−0.345542 | + | 0.938403i | \(0.612305\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 1.34879e10 | 0.708578 | ||||||||
\(866\) | 1.86334e10 | 0.974945 | ||||||||
\(867\) | −1.06839e10 | −0.556753 | ||||||||
\(868\) | −4.90443e9 | −0.254548 | ||||||||
\(869\) | 5.29132e9 | 0.273524 | ||||||||
\(870\) | −1.74270e9 | −0.0897231 | ||||||||
\(871\) | −3.57822e9 | −0.183486 | ||||||||
\(872\) | 4.00214e9 | 0.204402 | ||||||||
\(873\) | 1.20774e10 | 0.614363 | ||||||||
\(874\) | −1.90506e9 | −0.0965202 | ||||||||
\(875\) | −5.87793e9 | −0.296617 | ||||||||
\(876\) | −9.83272e9 | −0.494208 | ||||||||
\(877\) | −2.14559e10 | −1.07411 | −0.537055 | − | 0.843547i | \(-0.680463\pi\) | ||||
−0.537055 | + | 0.843547i | \(0.680463\pi\) | |||||||
\(878\) | −1.92212e9 | −0.0958409 | ||||||||
\(879\) | −1.35920e10 | −0.675028 | ||||||||
\(880\) | −1.45905e9 | −0.0721741 | ||||||||
\(881\) | −3.01082e10 | −1.48344 | −0.741720 | − | 0.670710i | \(-0.765989\pi\) | ||||
−0.741720 | + | 0.670710i | \(0.765989\pi\) | |||||||
\(882\) | −6.86129e8 | −0.0336718 | ||||||||
\(883\) | −1.58149e10 | −0.773043 | −0.386521 | − | 0.922280i | \(-0.626323\pi\) | ||||
−0.386521 | + | 0.922280i | \(0.626323\pi\) | |||||||
\(884\) | 5.37979e8 | 0.0261928 | ||||||||
\(885\) | −2.37231e10 | −1.15046 | ||||||||
\(886\) | −7.49667e9 | −0.362118 | ||||||||
\(887\) | 1.11270e10 | 0.535361 | 0.267681 | − | 0.963508i | \(-0.413743\pi\) | ||||
0.267681 | + | 0.963508i | \(0.413743\pi\) | |||||||
\(888\) | −3.29998e9 | −0.158149 | ||||||||
\(889\) | −2.02304e9 | −0.0965714 | ||||||||
\(890\) | 1.24629e9 | 0.0592589 | ||||||||
\(891\) | −5.90425e8 | −0.0279636 | ||||||||
\(892\) | −3.09299e9 | −0.145916 | ||||||||
\(893\) | 3.10445e10 | 1.45883 | ||||||||
\(894\) | −1.14711e10 | −0.536940 | ||||||||
\(895\) | 1.59849e10 | 0.745295 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | −3.11668e8 | −0.0144185 | ||||||||
\(898\) | −9.12818e9 | −0.420646 | ||||||||
\(899\) | −5.62187e9 | −0.258061 | ||||||||
\(900\) | 1.15135e9 | 0.0526450 | ||||||||
\(901\) | −4.52254e9 | −0.205990 | ||||||||
\(902\) | 3.79780e8 | 0.0172309 | ||||||||
\(903\) | −7.59127e9 | −0.343090 | ||||||||
\(904\) | −7.48294e9 | −0.336886 | ||||||||
\(905\) | −3.09769e9 | −0.138921 | ||||||||
\(906\) | −1.11417e10 | −0.497740 | ||||||||
\(907\) | −1.75118e10 | −0.779303 | −0.389652 | − | 0.920962i | \(-0.627405\pi\) | ||||
−0.389652 | + | 0.920962i | \(0.627405\pi\) | |||||||
\(908\) | −1.52288e9 | −0.0675094 | ||||||||
\(909\) | 3.81869e9 | 0.168632 | ||||||||
\(910\) | −1.93293e9 | −0.0850297 | ||||||||
\(911\) | 8.91656e9 | 0.390736 | 0.195368 | − | 0.980730i | \(-0.437410\pi\) | ||||
0.195368 | + | 0.980730i | \(0.437410\pi\) | |||||||
\(912\) | −5.01238e9 | −0.218807 | ||||||||
\(913\) | −1.07666e8 | −0.00468200 | ||||||||
\(914\) | −7.57998e9 | −0.328365 | ||||||||
\(915\) | 1.68081e10 | 0.725347 | ||||||||
\(916\) | −2.20780e9 | −0.0949132 | ||||||||
\(917\) | −7.99243e8 | −0.0342284 | ||||||||
\(918\) | −6.02472e8 | −0.0257032 | ||||||||
\(919\) | 3.42415e10 | 1.45529 | 0.727643 | − | 0.685956i | \(-0.240616\pi\) | ||||
0.727643 | + | 0.685956i | \(0.240616\pi\) | |||||||
\(920\) | 8.62521e8 | 0.0365185 | ||||||||
\(921\) | −1.02978e9 | −0.0434346 | ||||||||
\(922\) | 5.20715e9 | 0.218797 | ||||||||
\(923\) | −4.14261e9 | −0.173408 | ||||||||
\(924\) | −6.58487e8 | −0.0274597 | ||||||||
\(925\) | 5.89081e9 | 0.244725 | ||||||||
\(926\) | −1.88027e10 | −0.778183 | ||||||||
\(927\) | 4.20492e9 | 0.173372 | ||||||||
\(928\) | −8.24549e8 | −0.0338687 | ||||||||
\(929\) | −4.09072e10 | −1.67396 | −0.836980 | − | 0.547234i | \(-0.815681\pi\) | ||||
−0.836980 | + | 0.547234i | \(0.815681\pi\) | |||||||
\(930\) | 1.54728e10 | 0.630782 | ||||||||
\(931\) | −5.33222e9 | −0.216563 | ||||||||
\(932\) | −9.94928e9 | −0.402565 | ||||||||
\(933\) | −7.02183e9 | −0.283051 | ||||||||
\(934\) | −1.16039e10 | −0.466003 | ||||||||
\(935\) | −1.36291e9 | −0.0545288 | ||||||||
\(936\) | −8.20026e8 | −0.0326860 | ||||||||
\(937\) | −3.49842e10 | −1.38926 | −0.694629 | − | 0.719368i | \(-0.744432\pi\) | ||||
−0.694629 | + | 0.719368i | \(0.744432\pi\) | |||||||
\(938\) | 4.46910e9 | 0.176812 | ||||||||
\(939\) | −2.34041e9 | −0.0922493 | ||||||||
\(940\) | −1.40555e10 | −0.551948 | ||||||||
\(941\) | −4.53033e10 | −1.77242 | −0.886209 | − | 0.463286i | \(-0.846670\pi\) | ||||
−0.886209 | + | 0.463286i | \(0.846670\pi\) | |||||||
\(942\) | −1.11896e10 | −0.436149 | ||||||||
\(943\) | −2.24508e8 | −0.00871847 | ||||||||
\(944\) | −1.12245e10 | −0.434275 | ||||||||
\(945\) | 2.16465e9 | 0.0834402 | ||||||||
\(946\) | −7.28545e9 | −0.279793 | ||||||||
\(947\) | 1.56611e10 | 0.599234 | 0.299617 | − | 0.954059i | \(-0.403141\pi\) | ||||
0.299617 | + | 0.954059i | \(0.403141\pi\) | |||||||
\(948\) | −8.22998e9 | −0.313740 | ||||||||
\(949\) | −1.25014e10 | −0.474819 | ||||||||
\(950\) | 8.94763e9 | 0.338591 | ||||||||
\(951\) | −1.60386e10 | −0.604693 | ||||||||
\(952\) | −6.71923e8 | −0.0252400 | ||||||||
\(953\) | 8.65764e9 | 0.324022 | 0.162011 | − | 0.986789i | \(-0.448202\pi\) | ||||
0.162011 | + | 0.986789i | \(0.448202\pi\) | |||||||
\(954\) | 6.89358e9 | 0.257055 | ||||||||
\(955\) | −3.54146e9 | −0.131574 | ||||||||
\(956\) | 8.61987e9 | 0.319079 | ||||||||
\(957\) | −7.54813e8 | −0.0278386 | ||||||||
\(958\) | −3.34445e9 | −0.122898 | ||||||||
\(959\) | 9.87677e9 | 0.361618 | ||||||||
\(960\) | 2.26937e9 | 0.0827858 | ||||||||
\(961\) | 2.24022e10 | 0.814252 | ||||||||
\(962\) | −4.19563e9 | −0.151944 | ||||||||
\(963\) | 2.26251e9 | 0.0816393 | ||||||||
\(964\) | 1.26834e10 | 0.456002 | ||||||||
\(965\) | −4.48698e10 | −1.60734 | ||||||||
\(966\) | 3.89266e8 | 0.0138940 | ||||||||
\(967\) | 1.98037e10 | 0.704293 | 0.352146 | − | 0.935945i | \(-0.385452\pi\) | ||||
0.352146 | + | 0.935945i | \(0.385452\pi\) | |||||||
\(968\) | 9.34547e9 | 0.331160 | ||||||||
\(969\) | −4.68208e9 | −0.165313 | ||||||||
\(970\) | −4.24951e10 | −1.49499 | ||||||||
\(971\) | 2.81016e10 | 0.985061 | 0.492530 | − | 0.870295i | \(-0.336072\pi\) | ||||
0.492530 | + | 0.870295i | \(0.336072\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | −3.83945e9 | −0.133621 | ||||||||
\(974\) | −6.55258e9 | −0.227225 | ||||||||
\(975\) | 1.46383e9 | 0.0505796 | ||||||||
\(976\) | 7.95269e9 | 0.273804 | ||||||||
\(977\) | −2.41616e10 | −0.828885 | −0.414443 | − | 0.910075i | \(-0.636023\pi\) | ||||
−0.414443 | + | 0.910075i | \(0.636023\pi\) | |||||||
\(978\) | 1.42270e10 | 0.486324 | ||||||||
\(979\) | 5.39805e8 | 0.0183864 | ||||||||
\(980\) | 2.41418e9 | 0.0819367 | ||||||||
\(981\) | −5.69836e9 | −0.192712 | ||||||||
\(982\) | 5.61643e8 | 0.0189265 | ||||||||
\(983\) | −3.43109e9 | −0.115211 | −0.0576057 | − | 0.998339i | \(-0.518347\pi\) | ||||
−0.0576057 | + | 0.998339i | \(0.518347\pi\) | |||||||
\(984\) | −5.90699e8 | −0.0197644 | ||||||||
\(985\) | −5.69154e9 | −0.189759 | ||||||||
\(986\) | −7.70214e8 | −0.0255884 | ||||||||
\(987\) | −6.34340e9 | −0.209997 | ||||||||
\(988\) | −6.37279e9 | −0.210223 | ||||||||
\(989\) | 4.30680e9 | 0.141569 | ||||||||
\(990\) | 2.07744e9 | 0.0680464 | ||||||||
\(991\) | −2.49715e10 | −0.815054 | −0.407527 | − | 0.913193i | \(-0.633609\pi\) | ||||
−0.407527 | + | 0.913193i | \(0.633609\pi\) | |||||||
\(992\) | 7.32090e9 | 0.238108 | ||||||||
\(993\) | 6.82440e9 | 0.221178 | ||||||||
\(994\) | 5.17403e9 | 0.167100 | ||||||||
\(995\) | 5.47552e10 | 1.76216 | ||||||||
\(996\) | 1.67461e8 | 0.00537039 | ||||||||
\(997\) | 1.13671e10 | 0.363258 | 0.181629 | − | 0.983367i | \(-0.441863\pi\) | ||||
0.181629 | + | 0.983367i | \(0.441863\pi\) | |||||||
\(998\) | −1.75235e9 | −0.0558037 | ||||||||
\(999\) | 4.69860e9 | 0.149104 |
(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.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.i.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial |