Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,7,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(40.7195728007\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.19 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.7.c.a.58.42 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.02990i | − | 0.878737i | −0.898307 | − | 0.439369i | \(-0.855202\pi\) | ||
0.898307 | − | 0.439369i | \(-0.144798\pi\) | |||||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | 14.5805 | 0.227821 | ||||||||
\(5\) | 242.375 | 1.93900 | 0.969501 | − | 0.245086i | \(-0.0788163\pi\) | ||||
0.969501 | + | 0.245086i | \(0.0788163\pi\) | |||||||
\(6\) | 109.585i | 0.507339i | ||||||||
\(7\) | 243.138 | 0.708856 | 0.354428 | − | 0.935083i | \(-0.384676\pi\) | ||||
0.354428 | + | 0.935083i | \(0.384676\pi\) | |||||||
\(8\) | − | 552.413i | − | 1.07893i | ||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 1703.87i | − | 1.70387i | ||||||
\(11\) | − | 1556.52i | − | 1.16944i | −0.811235 | − | 0.584720i | \(-0.801204\pi\) | ||
0.811235 | − | 0.584720i | \(-0.198796\pi\) | |||||||
\(12\) | −227.288 | −0.131532 | ||||||||
\(13\) | 1415.05i | 0.644084i | 0.946725 | + | 0.322042i | \(0.104369\pi\) | ||||
−0.946725 | + | 0.322042i | \(0.895631\pi\) | |||||||
\(14\) | − | 1709.23i | − | 0.622898i | ||||||
\(15\) | −3778.26 | −1.11948 | ||||||||
\(16\) | −2950.26 | −0.720277 | ||||||||
\(17\) | 3197.13 | 0.650749 | 0.325374 | − | 0.945585i | \(-0.394510\pi\) | ||||
0.325374 | + | 0.945585i | \(0.394510\pi\) | |||||||
\(18\) | − | 1708.27i | − | 0.292912i | ||||||
\(19\) | −454.920 | −0.0663245 | −0.0331623 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331623 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(20\) | 3533.96 | 0.441745 | ||||||||
\(21\) | −3790.14 | −0.409258 | ||||||||
\(22\) | −10942.2 | −1.02763 | ||||||||
\(23\) | 1158.71i | 0.0952340i | 0.998866 | + | 0.0476170i | \(0.0151627\pi\) | ||||
−0.998866 | + | 0.0476170i | \(0.984837\pi\) | |||||||
\(24\) | 8611.27i | 0.622922i | ||||||||
\(25\) | 43120.8 | 2.75973 | ||||||||
\(26\) | 9947.68 | 0.565981 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | 3545.07 | 0.161492 | ||||||||
\(29\) | 21964.5 | 0.900590 | 0.450295 | − | 0.892880i | \(-0.351319\pi\) | ||||
0.450295 | + | 0.892880i | \(0.351319\pi\) | |||||||
\(30\) | 26560.8i | 0.983732i | ||||||||
\(31\) | 4418.81i | 0.148327i | 0.997246 | + | 0.0741636i | \(0.0236287\pi\) | ||||
−0.997246 | + | 0.0741636i | \(0.976371\pi\) | |||||||
\(32\) | − | 14614.4i | − | 0.445997i | ||||||
\(33\) | 24263.8i | 0.675176i | ||||||||
\(34\) | − | 22475.5i | − | 0.571837i | ||||||
\(35\) | 58930.6 | 1.37447 | ||||||||
\(36\) | 3543.06 | 0.0759402 | ||||||||
\(37\) | 46436.0i | 0.916748i | 0.888760 | + | 0.458374i | \(0.151568\pi\) | ||||
−0.888760 | + | 0.458374i | \(0.848432\pi\) | |||||||
\(38\) | 3198.04i | 0.0582818i | ||||||||
\(39\) | − | 22058.5i | − | 0.371862i | ||||||
\(40\) | − | 133891.i | − | 2.09205i | ||||||
\(41\) | −132979. | −1.92945 | −0.964724 | − | 0.263264i | \(-0.915201\pi\) | ||||
−0.964724 | + | 0.263264i | \(0.915201\pi\) | |||||||
\(42\) | 26644.3i | 0.359631i | ||||||||
\(43\) | 157011.i | 1.97481i | 0.158219 | + | 0.987404i | \(0.449425\pi\) | ||||
−0.158219 | + | 0.987404i | \(0.550575\pi\) | |||||||
\(44\) | − | 22694.9i | − | 0.266422i | ||||||
\(45\) | 58897.2 | 0.646334 | ||||||||
\(46\) | 8145.63 | 0.0836857 | ||||||||
\(47\) | − | 163691.i | − | 1.57663i | −0.615271 | − | 0.788316i | \(-0.710953\pi\) | ||
0.615271 | − | 0.788316i | \(-0.289047\pi\) | |||||||
\(48\) | 45989.9 | 0.415852 | ||||||||
\(49\) | −58533.1 | −0.497523 | ||||||||
\(50\) | − | 303135.i | − | 2.42508i | ||||||
\(51\) | −49838.3 | −0.375710 | ||||||||
\(52\) | 20632.2i | 0.146736i | ||||||||
\(53\) | 192890. | 1.29563 | 0.647816 | − | 0.761797i | \(-0.275683\pi\) | ||||
0.647816 | + | 0.761797i | \(0.275683\pi\) | |||||||
\(54\) | 26629.2i | 0.169113i | ||||||||
\(55\) | − | 377263.i | − | 2.26755i | ||||||
\(56\) | − | 134312.i | − | 0.764807i | ||||||
\(57\) | 7091.50 | 0.0382925 | ||||||||
\(58\) | − | 154408.i | − | 0.791382i | ||||||
\(59\) | 14748.1 | − | 204849.i | 0.0718094 | − | 0.997418i | ||||
\(60\) | −55088.9 | −0.255041 | ||||||||
\(61\) | 340178.i | 1.49871i | 0.662170 | + | 0.749354i | \(0.269636\pi\) | ||||
−0.662170 | + | 0.749354i | \(0.730364\pi\) | |||||||
\(62\) | 31063.8 | 0.130341 | ||||||||
\(63\) | 59082.4 | 0.236285 | ||||||||
\(64\) | −291554. | −1.11219 | ||||||||
\(65\) | 342974.i | 1.24888i | ||||||||
\(66\) | 170572. | 0.593303 | ||||||||
\(67\) | − | 237657.i | − | 0.790180i | −0.918643 | − | 0.395090i | \(-0.870713\pi\) | ||
0.918643 | − | 0.395090i | \(-0.129287\pi\) | |||||||
\(68\) | 46615.8 | 0.148254 | ||||||||
\(69\) | − | 18062.5i | − | 0.0549834i | ||||||
\(70\) | − | 414276.i | − | 1.20780i | ||||||
\(71\) | −352597. | −0.985151 | −0.492576 | − | 0.870270i | \(-0.663945\pi\) | ||||
−0.492576 | + | 0.870270i | \(0.663945\pi\) | |||||||
\(72\) | − | 134236.i | − | 0.359644i | ||||||
\(73\) | − | 456696.i | − | 1.17398i | −0.809596 | − | 0.586988i | \(-0.800314\pi\) | ||
0.809596 | − | 0.586988i | \(-0.199686\pi\) | |||||||
\(74\) | 326441. | 0.805580 | ||||||||
\(75\) | −672187. | −1.59333 | ||||||||
\(76\) | −6632.97 | −0.0151101 | ||||||||
\(77\) | − | 378450.i | − | 0.828964i | ||||||
\(78\) | −155069. | −0.326769 | ||||||||
\(79\) | 33053.2 | 0.0670398 | 0.0335199 | − | 0.999438i | \(-0.489328\pi\) | ||||
0.0335199 | + | 0.999438i | \(0.489328\pi\) | |||||||
\(80\) | −715069. | −1.39662 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 934832.i | 1.69548i | ||||||||
\(83\) | 40540.7i | 0.0709018i | 0.999371 | + | 0.0354509i | \(0.0112867\pi\) | ||||
−0.999371 | + | 0.0354509i | \(0.988713\pi\) | |||||||
\(84\) | −55262.2 | −0.0932374 | ||||||||
\(85\) | 774905. | 1.26180 | ||||||||
\(86\) | 1.10377e6 | 1.73534 | ||||||||
\(87\) | −342393. | −0.519956 | ||||||||
\(88\) | −859844. | −1.26175 | ||||||||
\(89\) | 1.07456e6i | 1.52427i | 0.647420 | + | 0.762133i | \(0.275848\pi\) | ||||
−0.647420 | + | 0.762133i | \(0.724152\pi\) | |||||||
\(90\) | − | 414041.i | − | 0.567958i | ||||||
\(91\) | 344053.i | 0.456563i | ||||||||
\(92\) | 16894.6i | 0.0216963i | ||||||||
\(93\) | − | 68882.5i | − | 0.0856367i | ||||||
\(94\) | −1.15073e6 | −1.38545 | ||||||||
\(95\) | −110261. | −0.128603 | ||||||||
\(96\) | 227817.i | 0.257497i | ||||||||
\(97\) | − | 1.45966e6i | − | 1.59932i | −0.600454 | − | 0.799660i | \(-0.705013\pi\) | ||
0.600454 | − | 0.799660i | \(-0.294987\pi\) | |||||||
\(98\) | 411482.i | 0.437192i | ||||||||
\(99\) | − | 378235.i | − | 0.389813i | ||||||
\(100\) | 628723. | 0.628723 | ||||||||
\(101\) | 264109.i | 0.256341i | 0.991752 | + | 0.128171i | \(0.0409105\pi\) | ||||
−0.991752 | + | 0.128171i | \(0.959089\pi\) | |||||||
\(102\) | 350358.i | 0.330150i | ||||||||
\(103\) | − | 410416.i | − | 0.375589i | −0.982208 | − | 0.187795i | \(-0.939866\pi\) | ||
0.982208 | − | 0.187795i | \(-0.0601339\pi\) | |||||||
\(104\) | 781694. | 0.694923 | ||||||||
\(105\) | −918636. | −0.793553 | ||||||||
\(106\) | − | 1.35600e6i | − | 1.13852i | ||||||
\(107\) | 1.11097e6 | 0.906879 | 0.453439 | − | 0.891287i | \(-0.350197\pi\) | ||||
0.453439 | + | 0.891287i | \(0.350197\pi\) | |||||||
\(108\) | −55230.9 | −0.0438441 | ||||||||
\(109\) | − | 2.09796e6i | − | 1.62001i | −0.586422 | − | 0.810006i | \(-0.699464\pi\) | ||
0.586422 | − | 0.810006i | \(-0.300536\pi\) | |||||||
\(110\) | −2.65212e6 | −1.99258 | ||||||||
\(111\) | − | 723866.i | − | 0.529284i | ||||||
\(112\) | −717318. | −0.510573 | ||||||||
\(113\) | 266601.i | 0.184768i | 0.995723 | + | 0.0923839i | \(0.0294487\pi\) | ||||
−0.995723 | + | 0.0923839i | \(0.970551\pi\) | |||||||
\(114\) | − | 49852.5i | − | 0.0336490i | ||||||
\(115\) | 280843.i | 0.184659i | ||||||||
\(116\) | 320254. | 0.205173 | ||||||||
\(117\) | 343858.i | 0.214695i | ||||||||
\(118\) | −1.44007e6 | − | 103678.i | −0.876469 | − | 0.0631016i | ||||
\(119\) | 777342. | 0.461287 | ||||||||
\(120\) | 2.08716e6i | 1.20785i | ||||||||
\(121\) | −651206. | −0.367589 | ||||||||
\(122\) | 2.39142e6 | 1.31697 | ||||||||
\(123\) | 2.07294e6 | 1.11397 | ||||||||
\(124\) | 64428.6i | 0.0337920i | ||||||||
\(125\) | 6.66430e6 | 3.41212 | ||||||||
\(126\) | − | 415344.i | − | 0.207633i | ||||||
\(127\) | −1.74962e6 | −0.854148 | −0.427074 | − | 0.904217i | \(-0.640456\pi\) | ||||
−0.427074 | + | 0.904217i | \(0.640456\pi\) | |||||||
\(128\) | 1.11427e6i | 0.531327i | ||||||||
\(129\) | − | 2.44756e6i | − | 1.14016i | ||||||
\(130\) | 2.41107e6 | 1.09744 | ||||||||
\(131\) | − | 187240.i | − | 0.0832886i | −0.999132 | − | 0.0416443i | \(-0.986740\pi\) | ||
0.999132 | − | 0.0416443i | \(-0.0132596\pi\) | |||||||
\(132\) | 353779.i | 0.153819i | ||||||||
\(133\) | −110608. | −0.0470145 | ||||||||
\(134\) | −1.67070e6 | −0.694360 | ||||||||
\(135\) | −918116. | −0.373161 | ||||||||
\(136\) | − | 1.76614e6i | − | 0.702114i | ||||||
\(137\) | −2.02527e6 | −0.787628 | −0.393814 | − | 0.919190i | \(-0.628845\pi\) | ||||
−0.393814 | + | 0.919190i | \(0.628845\pi\) | |||||||
\(138\) | −126978. | −0.0483159 | ||||||||
\(139\) | −448349. | −0.166944 | −0.0834722 | − | 0.996510i | \(-0.526601\pi\) | ||||
−0.0834722 | + | 0.996510i | \(0.526601\pi\) | |||||||
\(140\) | 859238. | 0.313133 | ||||||||
\(141\) | 2.55168e6i | 0.910269i | ||||||||
\(142\) | 2.47872e6i | 0.865689i | ||||||||
\(143\) | 2.20256e6 | 0.753218 | ||||||||
\(144\) | −716912. | −0.240092 | ||||||||
\(145\) | 5.32365e6 | 1.74625 | ||||||||
\(146\) | −3.21053e6 | −1.03162 | ||||||||
\(147\) | 912441. | 0.287245 | ||||||||
\(148\) | 677061.i | 0.208854i | ||||||||
\(149\) | 1.99524e6i | 0.603166i | 0.953440 | + | 0.301583i | \(0.0975150\pi\) | ||||
−0.953440 | + | 0.301583i | \(0.902485\pi\) | |||||||
\(150\) | 4.72540e6i | 1.40012i | ||||||||
\(151\) | 2.13822e6i | 0.621042i | 0.950567 | + | 0.310521i | \(0.100503\pi\) | ||||
−0.950567 | + | 0.310521i | \(0.899497\pi\) | |||||||
\(152\) | 251304.i | 0.0715596i | ||||||||
\(153\) | 776902. | 0.216916 | ||||||||
\(154\) | −2.66046e6 | −0.728442 | ||||||||
\(155\) | 1.07101e6i | 0.287607i | ||||||||
\(156\) | − | 321624.i | − | 0.0847178i | ||||||
\(157\) | 4.26617e6i | 1.10240i | 0.834373 | + | 0.551200i | \(0.185830\pi\) | ||||
−0.834373 | + | 0.551200i | \(0.814170\pi\) | |||||||
\(158\) | − | 232361.i | − | 0.0589104i | ||||||
\(159\) | −3.00685e6 | −0.748033 | ||||||||
\(160\) | − | 3.54218e6i | − | 0.864790i | ||||||
\(161\) | 281726.i | 0.0675072i | ||||||||
\(162\) | − | 415109.i | − | 0.0976375i | ||||||
\(163\) | −5.52187e6 | −1.27504 | −0.637519 | − | 0.770434i | \(-0.720039\pi\) | ||||
−0.637519 | + | 0.770434i | \(0.720039\pi\) | |||||||
\(164\) | −1.93891e6 | −0.439568 | ||||||||
\(165\) | 5.88095e6i | 1.30917i | ||||||||
\(166\) | 284997. | 0.0623041 | ||||||||
\(167\) | −1.59986e6 | −0.343505 | −0.171753 | − | 0.985140i | \(-0.554943\pi\) | ||||
−0.171753 | + | 0.985140i | \(0.554943\pi\) | |||||||
\(168\) | 2.09372e6i | 0.441562i | ||||||||
\(169\) | 2.82443e6 | 0.585155 | ||||||||
\(170\) | − | 5.44750e6i | − | 1.10879i | ||||||
\(171\) | −110546. | −0.0221082 | ||||||||
\(172\) | 2.28930e6i | 0.449902i | ||||||||
\(173\) | 4.65918e6i | 0.899852i | 0.893066 | + | 0.449926i | \(0.148550\pi\) | ||||
−0.893066 | + | 0.449926i | \(0.851450\pi\) | |||||||
\(174\) | 2.40699e6i | 0.456905i | ||||||||
\(175\) | 1.04843e7 | 1.95625 | ||||||||
\(176\) | 4.59214e6i | 0.842321i | ||||||||
\(177\) | −229901. | + | 3.19328e6i | −0.0414592 | + | 0.575860i | ||||
\(178\) | 7.55405e6 | 1.33943 | ||||||||
\(179\) | − | 8.35387e6i | − | 1.45656i | −0.685280 | − | 0.728280i | \(-0.740320\pi\) | ||
0.685280 | − | 0.728280i | \(-0.259680\pi\) | |||||||
\(180\) | 858751. | 0.147248 | ||||||||
\(181\) | −2.85135e6 | −0.480855 | −0.240427 | − | 0.970667i | \(-0.577288\pi\) | ||||
−0.240427 | + | 0.970667i | \(0.577288\pi\) | |||||||
\(182\) | 2.41866e6 | 0.401199 | ||||||||
\(183\) | − | 5.30285e6i | − | 0.865279i | ||||||
\(184\) | 640088. | 0.102751 | ||||||||
\(185\) | 1.12549e7i | 1.77758i | ||||||||
\(186\) | −484237. | −0.0752522 | ||||||||
\(187\) | − | 4.97641e6i | − | 0.761011i | ||||||
\(188\) | − | 2.38669e6i | − | 0.359189i | ||||||
\(189\) | −921004. | −0.136419 | ||||||||
\(190\) | 775126.i | 0.113009i | ||||||||
\(191\) | 9.07270e6i | 1.30208i | 0.759045 | + | 0.651038i | \(0.225666\pi\) | ||||
−0.759045 | + | 0.651038i | \(0.774334\pi\) | |||||||
\(192\) | 4.54488e6 | 0.642124 | ||||||||
\(193\) | −7.29522e6 | −1.01477 | −0.507384 | − | 0.861720i | \(-0.669387\pi\) | ||||
−0.507384 | + | 0.861720i | \(0.669387\pi\) | |||||||
\(194\) | −1.02612e7 | −1.40538 | ||||||||
\(195\) | − | 5.34643e6i | − | 0.721042i | ||||||
\(196\) | −853443. | −0.113346 | ||||||||
\(197\) | 777089. | 0.101642 | 0.0508209 | − | 0.998708i | \(-0.483816\pi\) | ||||
0.0508209 | + | 0.998708i | \(0.483816\pi\) | |||||||
\(198\) | −2.65896e6 | −0.342543 | ||||||||
\(199\) | 7.75894e6 | 0.984562 | 0.492281 | − | 0.870436i | \(-0.336163\pi\) | ||||
0.492281 | + | 0.870436i | \(0.336163\pi\) | |||||||
\(200\) | − | 2.38205e7i | − | 2.97756i | ||||||
\(201\) | 3.70470e6i | 0.456210i | ||||||||
\(202\) | 1.85666e6 | 0.225257 | ||||||||
\(203\) | 5.34040e6 | 0.638389 | ||||||||
\(204\) | −726668. | −0.0855944 | ||||||||
\(205\) | −3.22309e7 | −3.74120 | ||||||||
\(206\) | −2.88519e6 | −0.330044 | ||||||||
\(207\) | 281567.i | 0.0317447i | ||||||||
\(208\) | − | 4.17477e6i | − | 0.463919i | ||||||
\(209\) | 708094.i | 0.0775625i | ||||||||
\(210\) | 6.45792e6i | 0.697324i | ||||||||
\(211\) | − | 7.35347e6i | − | 0.782789i | −0.920223 | − | 0.391395i | \(-0.871993\pi\) | ||
0.920223 | − | 0.391395i | \(-0.128007\pi\) | |||||||
\(212\) | 2.81243e6 | 0.295171 | ||||||||
\(213\) | 5.49644e6 | 0.568777 | ||||||||
\(214\) | − | 7.80997e6i | − | 0.796908i | ||||||
\(215\) | 3.80556e7i | 3.82916i | ||||||||
\(216\) | 2.09254e6i | 0.207641i | ||||||||
\(217\) | 1.07438e6i | 0.105143i | ||||||||
\(218\) | −1.47485e7 | −1.42356 | ||||||||
\(219\) | 7.11919e6i | 0.677795i | ||||||||
\(220\) | − | 5.50069e6i | − | 0.516594i | ||||||
\(221\) | 4.52411e6i | 0.419137i | ||||||||
\(222\) | −5.08870e6 | −0.465102 | ||||||||
\(223\) | −1.21133e7 | −1.09232 | −0.546159 | − | 0.837682i | \(-0.683911\pi\) | ||||
−0.546159 | + | 0.837682i | \(0.683911\pi\) | |||||||
\(224\) | − | 3.55332e6i | − | 0.316148i | ||||||
\(225\) | 1.04784e7 | 0.919910 | ||||||||
\(226\) | 1.87418e6 | 0.162362 | ||||||||
\(227\) | 1.74805e7i | 1.49443i | 0.664580 | + | 0.747217i | \(0.268610\pi\) | ||||
−0.664580 | + | 0.747217i | \(0.731390\pi\) | |||||||
\(228\) | 103398. | 0.00872381 | ||||||||
\(229\) | 1.33528e7i | 1.11190i | 0.831215 | + | 0.555952i | \(0.187646\pi\) | ||||
−0.831215 | + | 0.555952i | \(0.812354\pi\) | |||||||
\(230\) | 1.97430e6 | 0.162267 | ||||||||
\(231\) | 5.89944e6i | 0.478603i | ||||||||
\(232\) | − | 1.21335e7i | − | 0.971676i | ||||||
\(233\) | 2.01747e6i | 0.159492i | 0.996815 | + | 0.0797462i | \(0.0254110\pi\) | ||||
−0.996815 | + | 0.0797462i | \(0.974589\pi\) | |||||||
\(234\) | 2.41729e6 | 0.188660 | ||||||||
\(235\) | − | 3.96746e7i | − | 3.05709i | ||||||
\(236\) | 215035. | − | 2.98680e6i | 0.0163597 | − | 0.227232i | ||||
\(237\) | −515249. | −0.0387054 | ||||||||
\(238\) | − | 5.46464e6i | − | 0.405350i | ||||||
\(239\) | 1.26466e7 | 0.926361 | 0.463180 | − | 0.886264i | \(-0.346708\pi\) | ||||
0.463180 | + | 0.886264i | \(0.346708\pi\) | |||||||
\(240\) | 1.11468e7 | 0.806339 | ||||||||
\(241\) | 2.18434e7 | 1.56052 | 0.780261 | − | 0.625454i | \(-0.215086\pi\) | ||||
0.780261 | + | 0.625454i | \(0.215086\pi\) | |||||||
\(242\) | 4.57791e6i | 0.323014i | ||||||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | 4.95997e6i | 0.341436i | ||||||||
\(245\) | −1.41870e7 | −0.964699 | ||||||||
\(246\) | − | 1.45726e7i | − | 0.978885i | ||||||
\(247\) | − | 643736.i | − | 0.0427186i | ||||||
\(248\) | 2.44101e6 | 0.160035 | ||||||||
\(249\) | − | 631968.i | − | 0.0409352i | ||||||
\(250\) | − | 4.68494e7i | − | 2.99836i | ||||||
\(251\) | 1.43275e7 | 0.906042 | 0.453021 | − | 0.891500i | \(-0.350346\pi\) | ||||
0.453021 | + | 0.891500i | \(0.350346\pi\) | |||||||
\(252\) | 861452. | 0.0538307 | ||||||||
\(253\) | 1.80356e6 | 0.111370 | ||||||||
\(254\) | 1.22997e7i | 0.750571i | ||||||||
\(255\) | −1.20796e7 | −0.728503 | ||||||||
\(256\) | −1.08262e7 | −0.645295 | ||||||||
\(257\) | −8.65834e6 | −0.510076 | −0.255038 | − | 0.966931i | \(-0.582088\pi\) | ||||
−0.255038 | + | 0.966931i | \(0.582088\pi\) | |||||||
\(258\) | −1.72061e7 | −1.00190 | ||||||||
\(259\) | 1.12903e7i | 0.649842i | ||||||||
\(260\) | 5.00074e6i | 0.284521i | ||||||||
\(261\) | 5.33737e6 | 0.300197 | ||||||||
\(262\) | −1.31628e6 | −0.0731888 | ||||||||
\(263\) | −1.37885e7 | −0.757965 | −0.378982 | − | 0.925404i | \(-0.623726\pi\) | ||||
−0.378982 | + | 0.925404i | \(0.623726\pi\) | |||||||
\(264\) | 1.34036e7 | 0.728469 | ||||||||
\(265\) | 4.67517e7 | 2.51223 | ||||||||
\(266\) | 777564.i | 0.0413134i | ||||||||
\(267\) | − | 1.67507e7i | − | 0.880036i | ||||||
\(268\) | − | 3.46516e6i | − | 0.180019i | ||||||
\(269\) | − | 5.67928e6i | − | 0.291767i | −0.989302 | − | 0.145884i | \(-0.953398\pi\) | ||
0.989302 | − | 0.145884i | \(-0.0466025\pi\) | |||||||
\(270\) | 6.45427e6i | 0.327911i | ||||||||
\(271\) | 1.92958e7 | 0.969515 | 0.484757 | − | 0.874649i | \(-0.338908\pi\) | ||||
0.484757 | + | 0.874649i | \(0.338908\pi\) | |||||||
\(272\) | −9.43235e6 | −0.468720 | ||||||||
\(273\) | − | 5.36325e6i | − | 0.263597i | ||||||
\(274\) | 1.42374e7i | 0.692118i | ||||||||
\(275\) | − | 6.71185e7i | − | 3.22734i | ||||||
\(276\) | − | 263361.i | − | 0.0125263i | ||||||
\(277\) | −2.29460e6 | −0.107961 | −0.0539805 | − | 0.998542i | \(-0.517191\pi\) | ||||
−0.0539805 | + | 0.998542i | \(0.517191\pi\) | |||||||
\(278\) | 3.15185e6i | 0.146700i | ||||||||
\(279\) | 1.07377e6i | 0.0494424i | ||||||||
\(280\) | − | 3.25540e7i | − | 1.48296i | ||||||
\(281\) | −5.95760e6 | −0.268505 | −0.134252 | − | 0.990947i | \(-0.542863\pi\) | ||||
−0.134252 | + | 0.990947i | \(0.542863\pi\) | |||||||
\(282\) | 1.79381e7 | 0.799887 | ||||||||
\(283\) | − | 4.14139e6i | − | 0.182720i | −0.995818 | − | 0.0913602i | \(-0.970879\pi\) | ||
0.995818 | − | 0.0913602i | \(-0.0291214\pi\) | |||||||
\(284\) | −5.14104e6 | −0.224438 | ||||||||
\(285\) | 1.71880e6 | 0.0742492 | ||||||||
\(286\) | − | 1.54838e7i | − | 0.661880i | ||||||
\(287\) | −3.23323e7 | −1.36770 | ||||||||
\(288\) | − | 3.55131e6i | − | 0.148666i | ||||||
\(289\) | −1.39159e7 | −0.576526 | ||||||||
\(290\) | − | 3.74247e7i | − | 1.53449i | ||||||
\(291\) | 2.27538e7i | 0.923367i | ||||||||
\(292\) | − | 6.65887e6i | − | 0.267456i | ||||||
\(293\) | −1.53783e7 | −0.611372 | −0.305686 | − | 0.952132i | \(-0.598886\pi\) | ||||
−0.305686 | + | 0.952132i | \(0.598886\pi\) | |||||||
\(294\) | − | 6.41437e6i | − | 0.252413i | ||||||
\(295\) | 3.57459e6 | − | 4.96503e7i | 0.139239 | − | 1.93400i | ||||
\(296\) | 2.56519e7 | 0.989108 | ||||||||
\(297\) | 5.89611e6i | 0.225059i | ||||||||
\(298\) | 1.40264e7 | 0.530025 | ||||||||
\(299\) | −1.63964e6 | −0.0613387 | ||||||||
\(300\) | −9.80083e6 | −0.362994 | ||||||||
\(301\) | 3.81753e7i | 1.39985i | ||||||||
\(302\) | 1.50314e7 | 0.545733 | ||||||||
\(303\) | − | 4.11705e6i | − | 0.147999i | ||||||
\(304\) | 1.34213e6 | 0.0477721 | ||||||||
\(305\) | 8.24508e7i | 2.90600i | ||||||||
\(306\) | − | 5.46154e6i | − | 0.190612i | ||||||
\(307\) | 1.16956e7 | 0.404210 | 0.202105 | − | 0.979364i | \(-0.435222\pi\) | ||||
0.202105 | + | 0.979364i | \(0.435222\pi\) | |||||||
\(308\) | − | 5.51799e6i | − | 0.188855i | ||||||
\(309\) | 6.39776e6i | 0.216846i | ||||||||
\(310\) | 7.52910e6 | 0.252731 | ||||||||
\(311\) | 4.23584e7 | 1.40818 | 0.704090 | − | 0.710110i | \(-0.251355\pi\) | ||||
0.704090 | + | 0.710110i | \(0.251355\pi\) | |||||||
\(312\) | −1.21854e7 | −0.401214 | ||||||||
\(313\) | − | 1.68961e7i | − | 0.551002i | −0.961301 | − | 0.275501i | \(-0.911156\pi\) | ||
0.961301 | − | 0.275501i | \(-0.0888437\pi\) | |||||||
\(314\) | 2.99908e7 | 0.968721 | ||||||||
\(315\) | 1.43201e7 | 0.458158 | ||||||||
\(316\) | 481933. | 0.0152730 | ||||||||
\(317\) | −1.41974e7 | −0.445688 | −0.222844 | − | 0.974854i | \(-0.571534\pi\) | ||||
−0.222844 | + | 0.974854i | \(0.571534\pi\) | |||||||
\(318\) | 2.11379e7i | 0.657325i | ||||||||
\(319\) | − | 3.41883e7i | − | 1.05319i | ||||||
\(320\) | −7.06656e7 | −2.15654 | ||||||||
\(321\) | −1.73182e7 | −0.523587 | ||||||||
\(322\) | 1.98051e6 | 0.0593211 | ||||||||
\(323\) | −1.45444e6 | −0.0431606 | ||||||||
\(324\) | 860965. | 0.0253134 | ||||||||
\(325\) | 6.10182e7i | 1.77750i | ||||||||
\(326\) | 3.88182e7i | 1.12042i | ||||||||
\(327\) | 3.27040e7i | 0.935314i | ||||||||
\(328\) | 7.34596e7i | 2.08174i | ||||||||
\(329\) | − | 3.97993e7i | − | 1.11760i | ||||||
\(330\) | 4.13425e7 | 1.15042 | ||||||||
\(331\) | −5.51311e7 | −1.52024 | −0.760121 | − | 0.649781i | \(-0.774860\pi\) | ||||
−0.760121 | + | 0.649781i | \(0.774860\pi\) | |||||||
\(332\) | 591105.i | 0.0161529i | ||||||||
\(333\) | 1.12840e7i | 0.305583i | ||||||||
\(334\) | 1.12469e7i | 0.301851i | ||||||||
\(335\) | − | 5.76021e7i | − | 1.53216i | ||||||
\(336\) | 1.11819e7 | 0.294779 | ||||||||
\(337\) | 6.03833e7i | 1.57771i | 0.614580 | + | 0.788855i | \(0.289326\pi\) | ||||
−0.614580 | + | 0.788855i | \(0.710674\pi\) | |||||||
\(338\) | − | 1.98555e7i | − | 0.514198i | ||||||
\(339\) | − | 4.15589e6i | − | 0.106676i | ||||||
\(340\) | 1.12985e7 | 0.287465 | ||||||||
\(341\) | 6.87799e6 | 0.173460 | ||||||||
\(342\) | 777124.i | 0.0194273i | ||||||||
\(343\) | −4.28365e7 | −1.06153 | ||||||||
\(344\) | 8.67350e7 | 2.13068 | ||||||||
\(345\) | − | 4.37791e6i | − | 0.106613i | ||||||
\(346\) | 3.27536e7 | 0.790734 | ||||||||
\(347\) | 8.76068e6i | 0.209676i | 0.994489 | + | 0.104838i | \(0.0334325\pi\) | ||||
−0.994489 | + | 0.104838i | \(0.966568\pi\) | |||||||
\(348\) | −4.99226e6 | −0.118457 | ||||||||
\(349\) | 4.14009e7i | 0.973943i | 0.873418 | + | 0.486971i | \(0.161898\pi\) | ||||
−0.873418 | + | 0.486971i | \(0.838102\pi\) | |||||||
\(350\) | − | 7.37035e7i | − | 1.71903i | ||||||
\(351\) | − | 5.36021e6i | − | 0.123954i | ||||||
\(352\) | −2.27477e7 | −0.521567 | ||||||||
\(353\) | 3.12584e7i | 0.710629i | 0.934747 | + | 0.355315i | \(0.115626\pi\) | ||||
−0.934747 | + | 0.355315i | \(0.884374\pi\) | |||||||
\(354\) | 2.24484e7 | + | 1.61618e6i | 0.506030 | + | 0.0364317i | ||||
\(355\) | −8.54607e7 | −1.91021 | ||||||||
\(356\) | 1.56676e7i | 0.347259i | ||||||||
\(357\) | −1.21176e7 | −0.266324 | ||||||||
\(358\) | −5.87268e7 | −1.27993 | ||||||||
\(359\) | −2.79538e7 | −0.604168 | −0.302084 | − | 0.953281i | \(-0.597682\pi\) | ||||
−0.302084 | + | 0.953281i | \(0.597682\pi\) | |||||||
\(360\) | − | 3.25356e7i | − | 0.697351i | ||||||
\(361\) | −4.68389e7 | −0.995601 | ||||||||
\(362\) | 2.00447e7i | 0.422545i | ||||||||
\(363\) | 1.01513e7 | 0.212227 | ||||||||
\(364\) | 5.01646e6i | 0.104014i | ||||||||
\(365\) | − | 1.10692e8i | − | 2.27634i | ||||||
\(366\) | −3.72785e7 | −0.760353 | ||||||||
\(367\) | − | 1.31779e7i | − | 0.266592i | −0.991076 | − | 0.133296i | \(-0.957444\pi\) | ||
0.991076 | − | 0.133296i | \(-0.0425562\pi\) | |||||||
\(368\) | − | 3.41850e6i | − | 0.0685949i | ||||||
\(369\) | −3.23140e7 | −0.643149 | ||||||||
\(370\) | 7.91211e7 | 1.56202 | ||||||||
\(371\) | 4.68987e7 | 0.918416 | ||||||||
\(372\) | − | 1.00434e6i | − | 0.0195098i | ||||||
\(373\) | 4.74124e7 | 0.913619 | 0.456810 | − | 0.889564i | \(-0.348992\pi\) | ||||
0.456810 | + | 0.889564i | \(0.348992\pi\) | |||||||
\(374\) | −3.49836e7 | −0.668729 | ||||||||
\(375\) | −1.03886e8 | −1.96999 | ||||||||
\(376\) | −9.04248e7 | −1.70108 | ||||||||
\(377\) | 3.10809e7i | 0.580056i | ||||||||
\(378\) | 6.47457e6i | 0.119877i | ||||||||
\(379\) | 8.30070e7 | 1.52475 | 0.762373 | − | 0.647138i | \(-0.224034\pi\) | ||||
0.762373 | + | 0.647138i | \(0.224034\pi\) | |||||||
\(380\) | −1.60767e6 | −0.0292985 | ||||||||
\(381\) | 2.72739e7 | 0.493142 | ||||||||
\(382\) | 6.37801e7 | 1.14418 | ||||||||
\(383\) | −5.00229e7 | −0.890375 | −0.445187 | − | 0.895437i | \(-0.646863\pi\) | ||||
−0.445187 | + | 0.895437i | \(0.646863\pi\) | |||||||
\(384\) | − | 1.73698e7i | − | 0.306762i | ||||||
\(385\) | − | 9.17268e7i | − | 1.60736i | ||||||
\(386\) | 5.12847e7i | 0.891715i | ||||||||
\(387\) | 3.81537e7i | 0.658269i | ||||||||
\(388\) | − | 2.12825e7i | − | 0.364358i | ||||||
\(389\) | 5.23965e7 | 0.890131 | 0.445065 | − | 0.895498i | \(-0.353180\pi\) | ||||
0.445065 | + | 0.895498i | \(0.353180\pi\) | |||||||
\(390\) | −3.75849e7 | −0.633606 | ||||||||
\(391\) | 3.70455e6i | 0.0619734i | ||||||||
\(392\) | 3.23344e7i | 0.536794i | ||||||||
\(393\) | 2.91879e6i | 0.0480867i | ||||||||
\(394\) | − | 5.46286e6i | − | 0.0893164i | ||||||
\(395\) | 8.01129e6 | 0.129990 | ||||||||
\(396\) | − | 5.51487e6i | − | 0.0888074i | ||||||
\(397\) | 3.41681e6i | 0.0546072i | 0.999627 | + | 0.0273036i | \(0.00869209\pi\) | ||||
−0.999627 | + | 0.0273036i | \(0.991308\pi\) | |||||||
\(398\) | − | 5.45446e7i | − | 0.865172i | ||||||
\(399\) | 1.72421e6 | 0.0271439 | ||||||||
\(400\) | −1.27217e8 | −1.98777 | ||||||||
\(401\) | 1.60966e7i | 0.249633i | 0.992180 | + | 0.124817i | \(0.0398342\pi\) | ||||
−0.992180 | + | 0.124817i | \(0.960166\pi\) | |||||||
\(402\) | 2.60437e7 | 0.400889 | ||||||||
\(403\) | −6.25286e6 | −0.0955352 | ||||||||
\(404\) | 3.85084e6i | 0.0583998i | ||||||||
\(405\) | 1.43120e7 | 0.215445 | ||||||||
\(406\) | − | 3.75424e7i | − | 0.560976i | ||||||
\(407\) | 7.22788e7 | 1.07208 | ||||||||
\(408\) | 2.75313e7i | 0.405365i | ||||||||
\(409\) | 6.15574e7i | 0.899726i | 0.893097 | + | 0.449863i | \(0.148527\pi\) | ||||
−0.893097 | + | 0.449863i | \(0.851473\pi\) | |||||||
\(410\) | 2.26580e8i | 3.28754i | ||||||||
\(411\) | 3.15708e7 | 0.454737 | ||||||||
\(412\) | − | 5.98408e6i | − | 0.0855669i | ||||||
\(413\) | 3.58583e6 | − | 4.98064e7i | 0.0509025 | − | 0.707026i | ||||
\(414\) | 1.97939e6 | 0.0278952 | ||||||||
\(415\) | 9.82607e6i | 0.137479i | ||||||||
\(416\) | 2.06802e7 | 0.287260 | ||||||||
\(417\) | 6.98907e6 | 0.0963854 | ||||||||
\(418\) | 4.97783e6 | 0.0681571 | ||||||||
\(419\) | 8.43328e7i | 1.14645i | 0.819399 | + | 0.573224i | \(0.194308\pi\) | ||||
−0.819399 | + | 0.573224i | \(0.805692\pi\) | |||||||
\(420\) | −1.33942e7 | −0.180788 | ||||||||
\(421\) | 1.10031e8i | 1.47458i | 0.675578 | + | 0.737288i | \(0.263894\pi\) | ||||
−0.675578 | + | 0.737288i | \(0.736106\pi\) | |||||||
\(422\) | −5.16941e7 | −0.687866 | ||||||||
\(423\) | − | 3.97768e7i | − | 0.525544i | ||||||
\(424\) | − | 1.06555e8i | − | 1.39790i | ||||||
\(425\) | 1.37863e8 | 1.79589 | ||||||||
\(426\) | − | 3.86394e7i | − | 0.499806i | ||||||
\(427\) | 8.27101e7i | 1.06237i | ||||||||
\(428\) | 1.61984e7 | 0.206606 | ||||||||
\(429\) | −3.43346e7 | −0.434870 | ||||||||
\(430\) | 2.67527e8 | 3.36482 | ||||||||
\(431\) | − | 7.18805e7i | − | 0.897799i | −0.893582 | − | 0.448900i | \(-0.851816\pi\) | ||
0.893582 | − | 0.448900i | \(-0.148184\pi\) | |||||||
\(432\) | 1.11756e7 | 0.138617 | ||||||||
\(433\) | −7.25464e7 | −0.893618 | −0.446809 | − | 0.894629i | \(-0.647440\pi\) | ||||
−0.446809 | + | 0.894629i | \(0.647440\pi\) | |||||||
\(434\) | 7.55278e6 | 0.0923927 | ||||||||
\(435\) | −8.29875e7 | −1.00820 | ||||||||
\(436\) | − | 3.05894e7i | − | 0.369072i | ||||||
\(437\) | − | 527121.i | − | 0.00631635i | ||||||
\(438\) | 5.00472e7 | 0.595604 | ||||||||
\(439\) | 1.41616e7 | 0.167386 | 0.0836930 | − | 0.996492i | \(-0.473328\pi\) | ||||
0.0836930 | + | 0.996492i | \(0.473328\pi\) | |||||||
\(440\) | −2.08405e8 | −2.44653 | ||||||||
\(441\) | −1.42235e7 | −0.165841 | ||||||||
\(442\) | 3.18040e7 | 0.368311 | ||||||||
\(443\) | 1.02675e8i | 1.18101i | 0.807034 | + | 0.590504i | \(0.201071\pi\) | ||||
−0.807034 | + | 0.590504i | \(0.798929\pi\) | |||||||
\(444\) | − | 1.05543e7i | − | 0.120582i | ||||||
\(445\) | 2.60447e8i | 2.95556i | ||||||||
\(446\) | 8.51555e7i | 0.959861i | ||||||||
\(447\) | − | 3.11028e7i | − | 0.348238i | ||||||
\(448\) | −7.08878e7 | −0.788384 | ||||||||
\(449\) | 2.43759e7 | 0.269290 | 0.134645 | − | 0.990894i | \(-0.457011\pi\) | ||||
0.134645 | + | 0.990894i | \(0.457011\pi\) | |||||||
\(450\) | − | 7.36618e7i | − | 0.808360i | ||||||
\(451\) | 2.06986e8i | 2.25637i | ||||||||
\(452\) | 3.88718e6i | 0.0420939i | ||||||||
\(453\) | − | 3.33315e7i | − | 0.358559i | ||||||
\(454\) | 1.22886e8 | 1.31322 | ||||||||
\(455\) | 8.33899e7i | 0.885277i | ||||||||
\(456\) | − | 3.91744e6i | − | 0.0413150i | ||||||
\(457\) | − | 5.10616e7i | − | 0.534990i | −0.963559 | − | 0.267495i | \(-0.913804\pi\) | ||
0.963559 | − | 0.267495i | \(-0.0861959\pi\) | |||||||
\(458\) | 9.38691e7 | 0.977071 | ||||||||
\(459\) | −1.21107e7 | −0.125237 | ||||||||
\(460\) | 4.09484e6i | 0.0420691i | ||||||||
\(461\) | −1.05217e8 | −1.07395 | −0.536976 | − | 0.843598i | \(-0.680433\pi\) | ||||
−0.536976 | + | 0.843598i | \(0.680433\pi\) | |||||||
\(462\) | 4.14725e7 | 0.420566 | ||||||||
\(463\) | 9.27594e7i | 0.934577i | 0.884105 | + | 0.467288i | \(0.154769\pi\) | ||||
−0.884105 | + | 0.467288i | \(0.845231\pi\) | |||||||
\(464\) | −6.48009e7 | −0.648675 | ||||||||
\(465\) | − | 1.66954e7i | − | 0.166050i | ||||||
\(466\) | 1.41826e7 | 0.140152 | ||||||||
\(467\) | 9.12870e7i | 0.896310i | 0.893956 | + | 0.448155i | \(0.147919\pi\) | ||||
−0.893956 | + | 0.448155i | \(0.852081\pi\) | |||||||
\(468\) | 5.01362e6i | 0.0489119i | ||||||||
\(469\) | − | 5.77833e7i | − | 0.560124i | ||||||
\(470\) | −2.78908e8 | −2.68638 | ||||||||
\(471\) | − | 6.65031e7i | − | 0.636471i | ||||||
\(472\) | −1.13161e8 | − | 8.14707e6i | −1.07615 | − | 0.0774774i | ||||
\(473\) | 2.44391e8 | 2.30942 | ||||||||
\(474\) | 3.62215e6i | 0.0340119i | ||||||||
\(475\) | −1.96165e7 | −0.183038 | ||||||||
\(476\) | 1.13340e7 | 0.105091 | ||||||||
\(477\) | 4.68722e7 | 0.431877 | ||||||||
\(478\) | − | 8.89044e7i | − | 0.814028i | ||||||
\(479\) | 1.64950e8 | 1.50088 | 0.750441 | − | 0.660938i | \(-0.229841\pi\) | ||||
0.750441 | + | 0.660938i | \(0.229841\pi\) | |||||||
\(480\) | 5.52171e7i | 0.499287i | ||||||||
\(481\) | −6.57094e7 | −0.590463 | ||||||||
\(482\) | − | 1.53557e8i | − | 1.37129i | ||||||
\(483\) | − | 4.39168e6i | − | 0.0389753i | ||||||
\(484\) | −9.49492e6 | −0.0837443 | ||||||||
\(485\) | − | 3.53784e8i | − | 3.10108i | ||||||
\(486\) | 6.47090e6i | 0.0563710i | ||||||||
\(487\) | −1.45605e8 | −1.26063 | −0.630315 | − | 0.776339i | \(-0.717074\pi\) | ||||
−0.630315 | + | 0.776339i | \(0.717074\pi\) | |||||||
\(488\) | 1.87919e8 | 1.61700 | ||||||||
\(489\) | 8.60775e7 | 0.736144 | ||||||||
\(490\) | 9.97330e7i | 0.847717i | ||||||||
\(491\) | 1.50309e8 | 1.26981 | 0.634907 | − | 0.772589i | \(-0.281038\pi\) | ||||
0.634907 | + | 0.772589i | \(0.281038\pi\) | |||||||
\(492\) | 3.02246e7 | 0.253785 | ||||||||
\(493\) | 7.02233e7 | 0.586058 | ||||||||
\(494\) | −4.52540e6 | −0.0375384 | ||||||||
\(495\) | − | 9.16749e7i | − | 0.755849i | ||||||
\(496\) | − | 1.30366e7i | − | 0.106837i | ||||||
\(497\) | −8.57295e7 | −0.698331 | ||||||||
\(498\) | −4.44267e6 | −0.0359713 | ||||||||
\(499\) | 7.21471e7 | 0.580654 | 0.290327 | − | 0.956927i | \(-0.406236\pi\) | ||||
0.290327 | + | 0.956927i | \(0.406236\pi\) | |||||||
\(500\) | 9.71689e7 | 0.777351 | ||||||||
\(501\) | 2.49394e7 | 0.198323 | ||||||||
\(502\) | − | 1.00721e8i | − | 0.796173i | ||||||
\(503\) | − | 1.37613e8i | − | 1.08132i | −0.841240 | − | 0.540662i | \(-0.818174\pi\) | ||
0.841240 | − | 0.540662i | \(-0.181826\pi\) | |||||||
\(504\) | − | 3.26379e7i | − | 0.254936i | ||||||
\(505\) | 6.40134e7i | 0.497046i | ||||||||
\(506\) | − | 1.26789e7i | − | 0.0978653i | ||||||
\(507\) | −4.40286e7 | −0.337840 | ||||||||
\(508\) | −2.55104e7 | −0.194592 | ||||||||
\(509\) | 9.86537e7i | 0.748101i | 0.927408 | + | 0.374050i | \(0.122031\pi\) | ||||
−0.927408 | + | 0.374050i | \(0.877969\pi\) | |||||||
\(510\) | 8.49182e7i | 0.640162i | ||||||||
\(511\) | − | 1.11040e8i | − | 0.832180i | ||||||
\(512\) | 1.47421e8i | 1.09837i | ||||||||
\(513\) | 1.72323e6 | 0.0127642 | ||||||||
\(514\) | 6.08672e7i | 0.448223i | ||||||||
\(515\) | − | 9.94748e7i | − | 0.728268i | ||||||
\(516\) | − | 3.56867e7i | − | 0.259751i | ||||||
\(517\) | −2.54788e8 | −1.84378 | ||||||||
\(518\) | 7.93700e7 | 0.571041 | ||||||||
\(519\) | − | 7.26294e7i | − | 0.519530i | ||||||
\(520\) | 1.89463e8 | 1.34746 | ||||||||
\(521\) | −1.22686e8 | −0.867524 | −0.433762 | − | 0.901028i | \(-0.642814\pi\) | ||||
−0.433762 | + | 0.901028i | \(0.642814\pi\) | |||||||
\(522\) | − | 3.75212e7i | − | 0.263794i | ||||||
\(523\) | 1.06812e8 | 0.746645 | 0.373323 | − | 0.927702i | \(-0.378218\pi\) | ||||
0.373323 | + | 0.927702i | \(0.378218\pi\) | |||||||
\(524\) | − | 2.73006e6i | − | 0.0189749i | ||||||
\(525\) | −1.63434e8 | −1.12944 | ||||||||
\(526\) | 9.69316e7i | 0.666052i | ||||||||
\(527\) | 1.41275e7i | 0.0965237i | ||||||||
\(528\) | − | 7.15844e7i | − | 0.486314i | ||||||
\(529\) | 1.46693e8 | 0.990930 | ||||||||
\(530\) | − | 3.28660e8i | − | 2.20759i | ||||||
\(531\) | 3.58380e6 | − | 4.97783e7i | 0.0239365 | − | 0.332473i | ||||
\(532\) | −1.61272e6 | −0.0107109 | ||||||||
\(533\) | − | 1.88173e8i | − | 1.24273i | ||||||
\(534\) | −1.17756e8 | −0.773320 | ||||||||
\(535\) | 2.69271e8 | 1.75844 | ||||||||
\(536\) | −1.31285e8 | −0.852550 | ||||||||
\(537\) | 1.30224e8i | 0.840945i | ||||||||
\(538\) | −3.99248e7 | −0.256387 | ||||||||
\(539\) | 9.11082e7i | 0.581823i | ||||||||
\(540\) | −1.33866e7 | −0.0850138 | ||||||||
\(541\) | 8.06570e7i | 0.509390i | 0.967021 | + | 0.254695i | \(0.0819750\pi\) | ||||
−0.967021 | + | 0.254695i | \(0.918025\pi\) | |||||||
\(542\) | − | 1.35647e8i | − | 0.851949i | ||||||
\(543\) | 4.44481e7 | 0.277622 | ||||||||
\(544\) | − | 4.67242e7i | − | 0.290232i | ||||||
\(545\) | − | 5.08494e8i | − | 3.14121i | ||||||
\(546\) | −3.77031e7 | −0.231632 | ||||||||
\(547\) | −8.28546e7 | −0.506238 | −0.253119 | − | 0.967435i | \(-0.581456\pi\) | ||||
−0.253119 | + | 0.967435i | \(0.581456\pi\) | |||||||
\(548\) | −2.95295e7 | −0.179438 | ||||||||
\(549\) | 8.26633e7i | 0.499569i | ||||||||
\(550\) | −4.71837e8 | −2.83598 | ||||||||
\(551\) | −9.99209e6 | −0.0597312 | ||||||||
\(552\) | −9.97798e6 | −0.0593233 | ||||||||
\(553\) | 8.03648e6 | 0.0475216 | ||||||||
\(554\) | 1.61308e7i | 0.0948694i | ||||||||
\(555\) | − | 1.75447e8i | − | 1.02628i | ||||||
\(556\) | −6.53716e6 | −0.0380334 | ||||||||
\(557\) | −1.37517e8 | −0.795774 | −0.397887 | − | 0.917434i | \(-0.630256\pi\) | ||||
−0.397887 | + | 0.917434i | \(0.630256\pi\) | |||||||
\(558\) | 7.54851e6 | 0.0434469 | ||||||||
\(559\) | −2.22179e8 | −1.27194 | ||||||||
\(560\) | −1.73860e8 | −0.990002 | ||||||||
\(561\) | 7.75745e7i | 0.439370i | ||||||||
\(562\) | 4.18813e7i | 0.235945i | ||||||||
\(563\) | 6.42052e6i | 0.0359786i | 0.999838 | + | 0.0179893i | \(0.00572649\pi\) | ||||
−0.999838 | + | 0.0179893i | \(0.994274\pi\) | |||||||
\(564\) | 3.72049e7i | 0.207378i | ||||||||
\(565\) | 6.46174e7i | 0.358265i | ||||||||
\(566\) | −2.91136e7 | −0.160563 | ||||||||
\(567\) | 1.43570e7 | 0.0787618 | ||||||||
\(568\) | 1.94779e8i | 1.06291i | ||||||||
\(569\) | 9.06946e7i | 0.492317i | 0.969230 | + | 0.246158i | \(0.0791684\pi\) | ||||
−0.969230 | + | 0.246158i | \(0.920832\pi\) | |||||||
\(570\) | − | 1.20830e7i | − | 0.0652456i | ||||||
\(571\) | − | 5.56109e7i | − | 0.298711i | −0.988784 | − | 0.149356i | \(-0.952280\pi\) | ||
0.988784 | − | 0.149356i | \(-0.0477199\pi\) | |||||||
\(572\) | 3.21145e7 | 0.171598 | ||||||||
\(573\) | − | 1.41429e8i | − | 0.751754i | ||||||
\(574\) | 2.27293e8i | 1.20185i | ||||||||
\(575\) | 4.99646e7i | 0.262820i | ||||||||
\(576\) | −7.08477e7 | −0.370731 | ||||||||
\(577\) | 1.05665e8 | 0.550050 | 0.275025 | − | 0.961437i | \(-0.411314\pi\) | ||||
0.275025 | + | 0.961437i | \(0.411314\pi\) | |||||||
\(578\) | 9.78277e7i | 0.506615i | ||||||||
\(579\) | 1.13721e8 | 0.585877 | ||||||||
\(580\) | 7.76216e7 | 0.397831 | ||||||||
\(581\) | 9.85698e6i | 0.0502592i | ||||||||
\(582\) | 1.59957e8 | 0.811397 | ||||||||
\(583\) | − | 3.00237e8i | − | 1.51516i | ||||||
\(584\) | −2.52285e8 | −1.26664 | ||||||||
\(585\) | 8.33427e7i | 0.416294i | ||||||||
\(586\) | 1.08108e8i | 0.537236i | ||||||||
\(587\) | − | 3.43340e8i | − | 1.69750i | −0.528792 | − | 0.848752i | \(-0.677355\pi\) | ||
0.528792 | − | 0.848752i | \(-0.322645\pi\) | |||||||
\(588\) | 1.33039e7 | 0.0654403 | ||||||||
\(589\) | − | 2.01021e6i | − | 0.00983773i | ||||||
\(590\) | −3.49037e8 | − | 2.51290e7i | −1.69948 | − | 0.122354i | ||||
\(591\) | −1.21136e7 | −0.0586829 | ||||||||
\(592\) | − | 1.36998e8i | − | 0.660312i | ||||||
\(593\) | 2.14834e8 | 1.03024 | 0.515121 | − | 0.857118i | \(-0.327747\pi\) | ||||
0.515121 | + | 0.857118i | \(0.327747\pi\) | |||||||
\(594\) | 4.14490e7 | 0.197768 | ||||||||
\(595\) | 1.88409e8 | 0.894437 | ||||||||
\(596\) | 2.90917e7i | 0.137414i | ||||||||
\(597\) | −1.20950e8 | −0.568437 | ||||||||
\(598\) | 1.15265e7i | 0.0539006i | ||||||||
\(599\) | −3.49377e8 | −1.62560 | −0.812800 | − | 0.582543i | \(-0.802058\pi\) | ||||
−0.812800 | + | 0.582543i | \(0.802058\pi\) | |||||||
\(600\) | 3.71325e8i | 1.71910i | ||||||||
\(601\) | 1.07047e8i | 0.493117i | 0.969128 | + | 0.246558i | \(0.0792997\pi\) | ||||
−0.969128 | + | 0.246558i | \(0.920700\pi\) | |||||||
\(602\) | 2.68369e8 | 1.23010 | ||||||||
\(603\) | − | 5.77506e7i | − | 0.263393i | ||||||
\(604\) | 3.11763e7i | 0.141486i | ||||||||
\(605\) | −1.57836e8 | −0.712755 | ||||||||
\(606\) | −2.89424e7 | −0.130052 | ||||||||
\(607\) | 1.14105e8 | 0.510197 | 0.255098 | − | 0.966915i | \(-0.417892\pi\) | ||||
0.255098 | + | 0.966915i | \(0.417892\pi\) | |||||||
\(608\) | 6.64840e6i | 0.0295806i | ||||||||
\(609\) | −8.32485e7 | −0.368574 | ||||||||
\(610\) | 5.79621e8 | 2.55361 | ||||||||
\(611\) | 2.31631e8 | 1.01548 | ||||||||
\(612\) | 1.13276e7 | 0.0494180 | ||||||||
\(613\) | − | 2.88932e8i | − | 1.25434i | −0.778884 | − | 0.627169i | \(-0.784214\pi\) | ||
0.778884 | − | 0.627169i | \(-0.215786\pi\) | |||||||
\(614\) | − | 8.22189e7i | − | 0.355195i | ||||||
\(615\) | 5.02431e8 | 2.15998 | ||||||||
\(616\) | −2.09060e8 | −0.894396 | ||||||||
\(617\) | −2.75011e8 | −1.17083 | −0.585415 | − | 0.810734i | \(-0.699068\pi\) | ||||
−0.585415 | + | 0.810734i | \(0.699068\pi\) | |||||||
\(618\) | 4.49756e7 | 0.190551 | ||||||||
\(619\) | −3.55949e8 | −1.50078 | −0.750388 | − | 0.660998i | \(-0.770133\pi\) | ||||
−0.750388 | + | 0.660998i | \(0.770133\pi\) | |||||||
\(620\) | 1.56159e7i | 0.0655227i | ||||||||
\(621\) | − | 4.38919e6i | − | 0.0183278i | ||||||
\(622\) | − | 2.97775e8i | − | 1.23742i | ||||||
\(623\) | 2.61266e8i | 1.08049i | ||||||||
\(624\) | 6.50782e7i | 0.267844i | ||||||||
\(625\) | 9.41500e8 | 3.85638 | ||||||||
\(626\) | −1.18778e8 | −0.484186 | ||||||||
\(627\) | − | 1.10381e7i | − | 0.0447807i | ||||||
\(628\) | 6.22030e7i | 0.251150i | ||||||||
\(629\) | 1.48462e8i | 0.596572i | ||||||||
\(630\) | − | 1.00669e8i | − | 0.402600i | ||||||
\(631\) | −1.67383e8 | −0.666228 | −0.333114 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333114 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(632\) | − | 1.82590e7i | − | 0.0723314i | ||||||
\(633\) | 1.14629e8i | 0.451944i | ||||||||
\(634\) | 9.98063e7i | 0.391643i | ||||||||
\(635\) | −4.24065e8 | −1.65619 | ||||||||
\(636\) | −4.38415e7 | −0.170417 | ||||||||
\(637\) | − | 8.28274e7i | − | 0.320447i | ||||||
\(638\) | −2.40340e8 | −0.925474 | ||||||||
\(639\) | −8.56810e7 | −0.328384 | ||||||||
\(640\) | 2.70073e8i | 1.03024i | ||||||||
\(641\) | −2.37255e8 | −0.900826 | −0.450413 | − | 0.892820i | \(-0.648723\pi\) | ||||
−0.450413 | + | 0.892820i | \(0.648723\pi\) | |||||||
\(642\) | 1.21745e8i | 0.460095i | ||||||||
\(643\) | 6.55653e7 | 0.246627 | 0.123314 | − | 0.992368i | \(-0.460648\pi\) | ||||
0.123314 | + | 0.992368i | \(0.460648\pi\) | |||||||
\(644\) | 4.10772e6i | 0.0153795i | ||||||||
\(645\) | − | 5.93228e8i | − | 2.21077i | ||||||
\(646\) | 1.02245e7i | 0.0379268i | ||||||||
\(647\) | −3.23977e8 | −1.19619 | −0.598096 | − | 0.801425i | \(-0.704076\pi\) | ||||
−0.598096 | + | 0.801425i | \(0.704076\pi\) | |||||||
\(648\) | − | 3.26194e7i | − | 0.119881i | ||||||
\(649\) | −3.18852e8 | − | 2.29558e7i | −1.16642 | − | 0.0839767i | ||||
\(650\) | 4.28952e8 | 1.56195 | ||||||||
\(651\) | − | 1.67479e7i | − | 0.0607041i | ||||||
\(652\) | −8.05117e7 | −0.290480 | ||||||||
\(653\) | 3.44498e8 | 1.23722 | 0.618611 | − | 0.785697i | \(-0.287696\pi\) | ||||
0.618611 | + | 0.785697i | \(0.287696\pi\) | |||||||
\(654\) | 2.29906e8 | 0.821896 | ||||||||
\(655\) | − | 4.53824e7i | − | 0.161497i | ||||||
\(656\) | 3.92323e8 | 1.38974 | ||||||||
\(657\) | − | 1.10977e8i | − | 0.391325i | ||||||
\(658\) | −2.79785e8 | −0.982081 | ||||||||
\(659\) | 9.99031e7i | 0.349078i | 0.984650 | + | 0.174539i | \(0.0558436\pi\) | ||||
−0.984650 | + | 0.174539i | \(0.944156\pi\) | |||||||
\(660\) | 8.57472e7i | 0.298255i | ||||||||
\(661\) | 2.49357e8 | 0.863409 | 0.431705 | − | 0.902015i | \(-0.357912\pi\) | ||||
0.431705 | + | 0.902015i | \(0.357912\pi\) | |||||||
\(662\) | 3.87566e8i | 1.33589i | ||||||||
\(663\) | − | 7.05238e7i | − | 0.241989i | ||||||
\(664\) | 2.23952e7 | 0.0764982 | ||||||||
\(665\) | −2.68087e7 | −0.0911613 | ||||||||
\(666\) | 7.93250e7 | 0.268527 | ||||||||
\(667\) | 2.54505e7i | 0.0857668i | ||||||||
\(668\) | −2.33268e7 | −0.0782575 | ||||||||
\(669\) | 1.88828e8 | 0.630650 | ||||||||
\(670\) | −4.04937e8 | −1.34637 | ||||||||
\(671\) | 5.29495e8 | 1.75265 | ||||||||
\(672\) | 5.53908e7i | 0.182528i | ||||||||
\(673\) | 9.58193e6i | 0.0314346i | 0.999876 | + | 0.0157173i | \(0.00500317\pi\) | ||||
−0.999876 | + | 0.0157173i | \(0.994997\pi\) | |||||||
\(674\) | 4.24488e8 | 1.38639 | ||||||||
\(675\) | −1.63341e8 | −0.531110 | ||||||||
\(676\) | 4.11817e7 | 0.133310 | ||||||||
\(677\) | −4.60108e8 | −1.48284 | −0.741420 | − | 0.671042i | \(-0.765847\pi\) | ||||
−0.741420 | + | 0.671042i | \(0.765847\pi\) | |||||||
\(678\) | −2.92155e7 | −0.0937399 | ||||||||
\(679\) | − | 3.54897e8i | − | 1.13369i | ||||||
\(680\) | − | 4.28068e8i | − | 1.36140i | ||||||
\(681\) | − | 2.72494e8i | − | 0.862812i | ||||||
\(682\) | − | 4.83516e7i | − | 0.152425i | ||||||
\(683\) | 3.83112e8i | 1.20244i | 0.799083 | + | 0.601221i | \(0.205319\pi\) | ||||
−0.799083 | + | 0.601221i | \(0.794681\pi\) | |||||||
\(684\) | −1.61181e6 | −0.00503670 | ||||||||
\(685\) | −4.90875e8 | −1.52721 | ||||||||
\(686\) | 3.01136e8i | 0.932805i | ||||||||
\(687\) | − | 2.08150e8i | − | 0.641958i | ||||||
\(688\) | − | 4.63223e8i | − | 1.42241i | ||||||
\(689\) | 2.72949e8i | 0.834496i | ||||||||
\(690\) | −3.07763e7 | −0.0936847 | ||||||||
\(691\) | 3.91705e8i | 1.18720i | 0.804759 | + | 0.593602i | \(0.202294\pi\) | ||||
−0.804759 | + | 0.593602i | \(0.797706\pi\) | |||||||
\(692\) | 6.79332e7i | 0.205005i | ||||||||
\(693\) | − | 9.19632e7i | − | 0.276321i | ||||||
\(694\) | 6.15867e7 | 0.184250 | ||||||||
\(695\) | −1.08669e8 | −0.323706 | ||||||||
\(696\) | 1.89142e8i | 0.560997i | ||||||||
\(697\) | −4.25152e8 | −1.25559 | ||||||||
\(698\) | 2.91044e8 | 0.855840 | ||||||||
\(699\) | − | 3.14493e7i | − | 0.0920829i | ||||||
\(700\) | 1.52866e8 | 0.445674 | ||||||||
\(701\) | − | 5.84516e8i | − | 1.69685i | −0.529318 | − | 0.848423i | \(-0.677552\pi\) | ||
0.529318 | − | 0.848423i | \(-0.322448\pi\) | |||||||
\(702\) | −3.76818e7 | −0.108923 | ||||||||
\(703\) | − | 2.11247e7i | − | 0.0608029i | ||||||
\(704\) | 4.53811e8i | 1.30064i | ||||||||
\(705\) | 6.18465e8i | 1.76501i | ||||||||
\(706\) | 2.19744e8 | 0.624456 | ||||||||
\(707\) | 6.42148e7i | 0.181709i | ||||||||
\(708\) | −3.35207e6 | + | 4.65596e7i | −0.00944525 | + | 0.131193i | ||||
\(709\) | 1.79681e8 | 0.504154 | 0.252077 | − | 0.967707i | \(-0.418886\pi\) | ||||
0.252077 | + | 0.967707i | \(0.418886\pi\) | |||||||
\(710\) | 6.00780e8i | 1.67857i | ||||||||
\(711\) | 8.03193e6 | 0.0223466 | ||||||||
\(712\) | 5.93601e8 | 1.64458 | ||||||||
\(713\) | −5.12013e6 | −0.0141258 | ||||||||
\(714\) | 8.51853e7i | 0.234029i | ||||||||
\(715\) | 5.33847e8 | 1.46049 | ||||||||
\(716\) | − | 1.21804e8i | − | 0.331834i | ||||||
\(717\) | −1.97141e8 | −0.534835 | ||||||||
\(718\) | 1.96512e8i | 0.530905i | ||||||||
\(719\) | 4.43984e7i | 0.119448i | 0.998215 | + | 0.0597242i | \(0.0190221\pi\) | ||||
−0.998215 | + | 0.0597242i | \(0.980978\pi\) | |||||||
\(720\) | −1.73762e8 | −0.465540 | ||||||||
\(721\) | − | 9.97877e7i | − | 0.266239i | ||||||
\(722\) | 3.29273e8i | 0.874872i | ||||||||
\(723\) | −3.40505e8 | −0.900968 | ||||||||
\(724\) | −4.15741e7 | −0.109549 | ||||||||
\(725\) | 9.47127e8 | 2.48539 | ||||||||
\(726\) | − | 7.13626e7i | − | 0.186492i | ||||||
\(727\) | −1.40640e8 | −0.366021 | −0.183011 | − | 0.983111i | \(-0.558584\pi\) | ||||
−0.183011 | + | 0.983111i | \(0.558584\pi\) | |||||||
\(728\) | 1.90059e8 | 0.492600 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −7.78153e8 | −2.00031 | ||||||||
\(731\) | 5.01985e8i | 1.28510i | ||||||||
\(732\) | − | 7.73183e7i | − | 0.197128i | ||||||
\(733\) | 3.63182e8 | 0.922173 | 0.461087 | − | 0.887355i | \(-0.347460\pi\) | ||||
0.461087 | + | 0.887355i | \(0.347460\pi\) | |||||||
\(734\) | −9.26393e7 | −0.234265 | ||||||||
\(735\) | 2.21153e8 | 0.556969 | ||||||||
\(736\) | 1.69339e7 | 0.0424741 | ||||||||
\(737\) | −3.69918e8 | −0.924067 | ||||||||
\(738\) | 2.27164e8i | 0.565159i | ||||||||
\(739\) | − | 5.57713e6i | − | 0.0138190i | −0.999976 | − | 0.00690951i | \(-0.997801\pi\) | ||
0.999976 | − | 0.00690951i | \(-0.00219938\pi\) | |||||||
\(740\) | 1.64103e8i | 0.404968i | ||||||||
\(741\) | 1.00348e7i | 0.0246636i | ||||||||
\(742\) | − | 3.29693e8i | − | 0.807047i | ||||||
\(743\) | 3.32916e8 | 0.811648 | 0.405824 | − | 0.913951i | \(-0.366985\pi\) | ||||
0.405824 | + | 0.913951i | \(0.366985\pi\) | |||||||
\(744\) | −3.80516e7 | −0.0923962 | ||||||||
\(745\) | 4.83597e8i | 1.16954i | ||||||||
\(746\) | − | 3.33304e8i | − | 0.802832i | ||||||
\(747\) | 9.85140e6i | 0.0236339i | ||||||||
\(748\) | − | 7.25586e7i | − | 0.173374i | ||||||
\(749\) | 2.70117e8 | 0.642846 | ||||||||
\(750\) | 7.30309e8i | 1.73110i | ||||||||
\(751\) | − | 3.17334e8i | − | 0.749199i | −0.927187 | − | 0.374599i | \(-0.877780\pi\) | ||
0.927187 | − | 0.374599i | \(-0.122220\pi\) | |||||||
\(752\) | 4.82929e8i | 1.13561i | ||||||||
\(753\) | −2.23343e8 | −0.523104 | ||||||||
\(754\) | 2.18496e8 | 0.509717 | ||||||||
\(755\) | 5.18251e8i | 1.20420i | ||||||||
\(756\) | −1.34287e7 | −0.0310791 | ||||||||
\(757\) | −4.60544e8 | −1.06165 | −0.530827 | − | 0.847480i | \(-0.678119\pi\) | ||||
−0.530827 | + | 0.847480i | \(0.678119\pi\) | |||||||
\(758\) | − | 5.83531e8i | − | 1.33985i | ||||||
\(759\) | −2.81148e7 | −0.0642997 | ||||||||
\(760\) | 6.09098e7i | 0.138754i | ||||||||
\(761\) | 6.75942e8 | 1.53375 | 0.766877 | − | 0.641795i | \(-0.221810\pi\) | ||||
0.766877 | + | 0.641795i | \(0.221810\pi\) | |||||||
\(762\) | − | 1.91733e8i | − | 0.433343i | ||||||
\(763\) | − | 5.10094e8i | − | 1.14836i | ||||||
\(764\) | 1.32285e8i | 0.296640i | ||||||||
\(765\) | 1.88302e8 | 0.420601 | ||||||||
\(766\) | 3.51656e8i | 0.782405i | ||||||||
\(767\) | 2.89872e8 | + | 2.08694e7i | 0.642421 | + | 0.0462513i | ||||
\(768\) | 1.68764e8 | 0.372561 | ||||||||
\(769\) | 6.34399e8i | 1.39503i | 0.716571 | + | 0.697514i | \(0.245711\pi\) | ||||
−0.716571 | + | 0.697514i | \(0.754289\pi\) | |||||||
\(770\) | −6.44830e8 | −1.41245 | ||||||||
\(771\) | 1.34970e8 | 0.294493 | ||||||||
\(772\) | −1.06368e8 | −0.231185 | ||||||||
\(773\) | − | 8.78120e8i | − | 1.90115i | −0.310501 | − | 0.950573i | \(-0.600497\pi\) | ||
0.310501 | − | 0.950573i | \(-0.399503\pi\) | |||||||
\(774\) | 2.68217e8 | 0.578446 | ||||||||
\(775\) | 1.90543e8i | 0.409343i | ||||||||
\(776\) | −8.06333e8 | −1.72556 | ||||||||
\(777\) | − | 1.75999e8i | − | 0.375186i | ||||||
\(778\) | − | 3.68342e8i | − | 0.782191i | ||||||
\(779\) | 6.04950e7 | 0.127970 | ||||||||
\(780\) | − | 7.79538e7i | − | 0.164268i | ||||||
\(781\) | 5.48825e8i | 1.15207i | ||||||||
\(782\) | 2.60426e7 | 0.0544583 | ||||||||
\(783\) | −8.32014e7 | −0.173319 | ||||||||
\(784\) | 1.72688e8 | 0.358355 | ||||||||
\(785\) | 1.03402e9i | 2.13756i | ||||||||
\(786\) | 2.05188e7 | 0.0422556 | ||||||||
\(787\) | 4.50279e8 | 0.923757 | 0.461878 | − | 0.886943i | \(-0.347176\pi\) | ||||
0.461878 | + | 0.886943i | \(0.347176\pi\) | |||||||
\(788\) | 1.13304e7 | 0.0231561 | ||||||||
\(789\) | 2.14941e8 | 0.437611 | ||||||||
\(790\) | − | 5.63185e7i | − | 0.114227i | ||||||
\(791\) | 6.48207e7i | 0.130974i | ||||||||
\(792\) | −2.08942e8 | −0.420582 | ||||||||
\(793\) | −4.81370e8 | −0.965294 | ||||||||
\(794\) | 2.40199e7 | 0.0479854 | ||||||||
\(795\) | −7.28787e8 | −1.45044 | ||||||||
\(796\) | 1.13129e8 | 0.224303 | ||||||||
\(797\) | 7.09594e8i | 1.40164i | 0.713340 | + | 0.700818i | \(0.247181\pi\) | ||||
−0.713340 | + | 0.700818i | \(0.752819\pi\) | |||||||
\(798\) | − | 1.21210e7i | − | 0.0238523i | ||||||
\(799\) | − | 5.23340e8i | − | 1.02599i | ||||||
\(800\) | − | 6.30186e8i | − | 1.23083i | ||||||
\(801\) | 2.61118e8i | 0.508089i | ||||||||
\(802\) | 1.13158e8 | 0.219362 | ||||||||
\(803\) | −7.10859e8 | −1.37289 | ||||||||
\(804\) | 5.40165e7i | 0.103934i | ||||||||
\(805\) | 6.82835e7i | 0.130897i | ||||||||
\(806\) | 4.39570e7i | 0.0839503i | ||||||||
\(807\) | 8.85312e7i | 0.168452i | ||||||||
\(808\) | 1.45897e8 | 0.276575 | ||||||||
\(809\) | − | 9.28962e8i | − | 1.75450i | −0.480038 | − | 0.877248i | \(-0.659377\pi\) | ||
0.480038 | − | 0.877248i | \(-0.340623\pi\) | |||||||
\(810\) | − | 1.00612e8i | − | 0.189319i | ||||||
\(811\) | − | 5.31263e8i | − | 0.995972i | −0.867185 | − | 0.497986i | \(-0.834073\pi\) | ||
0.867185 | − | 0.497986i | \(-0.165927\pi\) | |||||||
\(812\) | 7.78657e7 | 0.145438 | ||||||||
\(813\) | −3.00791e8 | −0.559750 | ||||||||
\(814\) | − | 5.08112e8i | − | 0.942078i | ||||||
\(815\) | −1.33837e9 | −2.47230 | ||||||||
\(816\) | 1.47036e8 | 0.270615 | ||||||||
\(817\) | − | 7.14275e7i | − | 0.130978i | ||||||
\(818\) | 4.32742e8 | 0.790623 | ||||||||
\(819\) | 8.36048e7i | 0.152188i | ||||||||
\(820\) | −4.69944e8 | −0.852323 | ||||||||
\(821\) | − | 5.91335e8i | − | 1.06857i | −0.845303 | − | 0.534287i | \(-0.820580\pi\) | ||
0.845303 | − | 0.534287i | \(-0.179420\pi\) | |||||||
\(822\) | − | 2.21940e8i | − | 0.399595i | ||||||
\(823\) | 3.62827e8i | 0.650879i | 0.945563 | + | 0.325439i | \(0.105512\pi\) | ||||
−0.945563 | + | 0.325439i | \(0.894488\pi\) | |||||||
\(824\) | −2.26719e8 | −0.405235 | ||||||||
\(825\) | 1.04627e9i | 1.86330i | ||||||||
\(826\) | −3.50134e8 | − | 2.52080e7i | −0.621290 | − | 0.0447300i | ||||
\(827\) | −4.48415e8 | −0.792799 | −0.396400 | − | 0.918078i | \(-0.629741\pi\) | ||||
−0.396400 | + | 0.918078i | \(0.629741\pi\) | |||||||
\(828\) | 4.10539e6i | 0.00723208i | ||||||||
\(829\) | 2.31653e8 | 0.406606 | 0.203303 | − | 0.979116i | \(-0.434832\pi\) | ||||
0.203303 | + | 0.979116i | \(0.434832\pi\) | |||||||
\(830\) | 6.90763e7 | 0.120808 | ||||||||
\(831\) | 3.57692e7 | 0.0623313 | ||||||||
\(832\) | − | 4.12565e8i | − | 0.716345i | ||||||
\(833\) | −1.87138e8 | −0.323763 | ||||||||
\(834\) | − | 4.91325e7i | − | 0.0846975i | ||||||
\(835\) | −3.87767e8 | −0.666057 | ||||||||
\(836\) | 1.03244e7i | 0.0176703i | ||||||||
\(837\) | − | 1.67384e7i | − | 0.0285456i | ||||||
\(838\) | 5.92851e8 | 1.00743 | ||||||||
\(839\) | − | 1.10355e9i | − | 1.86856i | −0.356543 | − | 0.934279i | \(-0.616045\pi\) | ||
0.356543 | − | 0.934279i | \(-0.383955\pi\) | |||||||
\(840\) | 5.07467e8i | 0.856189i | ||||||||
\(841\) | −1.12384e8 | −0.188937 | ||||||||
\(842\) | 7.73504e8 | 1.29577 | ||||||||
\(843\) | 9.28697e7 | 0.155021 | ||||||||
\(844\) | − | 1.07217e8i | − | 0.178335i | ||||||
\(845\) | 6.84573e8 | 1.13462 | ||||||||
\(846\) | −2.79627e8 | −0.461815 | ||||||||
\(847\) | −1.58333e8 | −0.260568 | ||||||||
\(848\) | −5.69074e8 | −0.933214 | ||||||||
\(849\) | 6.45579e7i | 0.105494i | ||||||||
\(850\) | − | 9.69161e8i | − | 1.57812i | ||||||
\(851\) | −5.38060e7 | −0.0873055 | ||||||||
\(852\) | 8.01409e7 | 0.129579 | ||||||||
\(853\) | −5.49608e8 | −0.885535 | −0.442768 | − | 0.896636i | \(-0.646003\pi\) | ||||
−0.442768 | + | 0.896636i | \(0.646003\pi\) | |||||||
\(854\) | 5.81444e8 | 0.933543 | ||||||||
\(855\) | −2.67935e7 | −0.0428678 | ||||||||
\(856\) | − | 6.13712e8i | − | 0.978460i | ||||||
\(857\) | − | 1.68235e8i | − | 0.267285i | −0.991030 | − | 0.133642i | \(-0.957333\pi\) | ||
0.991030 | − | 0.133642i | \(-0.0426673\pi\) | |||||||
\(858\) | 2.41369e8i | 0.382137i | ||||||||
\(859\) | − | 1.19293e9i | − | 1.88207i | −0.338304 | − | 0.941037i | \(-0.609853\pi\) | ||
0.338304 | − | 0.941037i | \(-0.390147\pi\) | |||||||
\(860\) | 5.54870e8i | 0.872361i | ||||||||
\(861\) | 5.04011e8 | 0.789642 | ||||||||
\(862\) | −5.05313e8 | −0.788930 | ||||||||
\(863\) | − | 1.86737e8i | − | 0.290535i | −0.989392 | − | 0.145267i | \(-0.953596\pi\) | ||
0.989392 | − | 0.145267i | \(-0.0464043\pi\) | |||||||
\(864\) | 5.53594e7i | 0.0858322i | ||||||||
\(865\) | 1.12927e9i | 1.74482i | ||||||||
\(866\) | 5.09994e8i | 0.785256i | ||||||||
\(867\) | 2.16928e8 | 0.332858 | ||||||||
\(868\) | 1.56650e7i | 0.0239536i | ||||||||
\(869\) | − | 5.14481e7i | − | 0.0783990i | ||||||
\(870\) | 5.83394e8i | 0.885940i | ||||||||
\(871\) | 3.36297e8 | 0.508942 | ||||||||
\(872\) | −1.15894e9 | −1.74788 | ||||||||
\(873\) | − | 3.54696e8i | − | 0.533106i | ||||||
\(874\) | −3.70561e6 | −0.00555041 | ||||||||
\(875\) | 1.62034e9 | 2.41870 | ||||||||
\(876\) | 1.03801e8i | 0.154416i | ||||||||
\(877\) | −6.25541e8 | −0.927379 | −0.463689 | − | 0.885998i | \(-0.653475\pi\) | ||||
−0.463689 | + | 0.885998i | \(0.653475\pi\) | |||||||
\(878\) | − | 9.95547e7i | − | 0.147088i | ||||||
\(879\) | 2.39724e8 | 0.352976 | ||||||||
\(880\) | 1.11302e9i | 1.63326i | ||||||||
\(881\) | 2.10650e6i | 0.00308059i | 0.999999 | + | 0.00154029i | \(0.000490291\pi\) | ||||
−0.999999 | + | 0.00154029i | \(0.999510\pi\) | |||||||
\(882\) | 9.99901e7i | 0.145731i | ||||||||
\(883\) | −1.36927e9 | −1.98888 | −0.994438 | − | 0.105325i | \(-0.966412\pi\) | ||||
−0.994438 | + | 0.105325i | \(0.966412\pi\) | |||||||
\(884\) | 6.59638e7i | 0.0954880i | ||||||||
\(885\) | −5.57223e7 | + | 7.73971e8i | −0.0803894 | + | 1.11659i | ||||
\(886\) | 7.21794e8 | 1.03780 | ||||||||
\(887\) | − | 3.56428e8i | − | 0.510742i | −0.966843 | − | 0.255371i | \(-0.917802\pi\) | ||
0.966843 | − | 0.255371i | \(-0.0821976\pi\) | |||||||
\(888\) | −3.99873e8 | −0.571062 | ||||||||
\(889\) | −4.25399e8 | −0.605468 | ||||||||
\(890\) | 1.83092e9 | 2.59716 | ||||||||
\(891\) | − | 9.19112e7i | − | 0.129938i | ||||||
\(892\) | −1.76619e8 | −0.248852 | ||||||||
\(893\) | 7.44661e7i | 0.104569i | ||||||||
\(894\) | −2.18649e8 | −0.306010 | ||||||||
\(895\) | − | 2.02477e9i | − | 2.82427i | ||||||
\(896\) | 2.70922e8i | 0.376635i | ||||||||
\(897\) | 2.55594e7 | 0.0354139 | ||||||||
\(898\) | − | 1.71360e8i | − | 0.236636i | ||||||
\(899\) | 9.70570e7i | 0.133582i | ||||||||
\(900\) | 1.52780e8 | 0.209574 | ||||||||
\(901\) | 6.16693e8 | 0.843130 | ||||||||
\(902\) | 1.45509e9 | 1.98276 | ||||||||
\(903\) | − | 5.95094e8i | − | 0.808206i | ||||||
\(904\) | 1.47274e8 | 0.199352 | ||||||||
\(905\) | −6.91096e8 | −0.932379 | ||||||||
\(906\) | −2.34317e8 | −0.315079 | ||||||||
\(907\) | −1.00962e9 | −1.35312 | −0.676559 | − | 0.736389i | \(-0.736529\pi\) | ||||
−0.676559 | + | 0.736389i | \(0.736529\pi\) | |||||||
\(908\) | 2.54875e8i | 0.340463i | ||||||||
\(909\) | 6.41784e7i | 0.0854471i | ||||||||
\(910\) | 5.86222e8 | 0.777926 | ||||||||
\(911\) | −9.28756e8 | −1.22842 | −0.614210 | − | 0.789143i | \(-0.710525\pi\) | ||||
−0.614210 | + | 0.789143i | \(0.710525\pi\) | |||||||
\(912\) | −2.09217e7 | −0.0275812 | ||||||||
\(913\) | 6.31026e7 | 0.0829154 | ||||||||
\(914\) | −3.58958e8 | −0.470116 | ||||||||
\(915\) | − | 1.28528e9i | − | 1.67778i | ||||||
\(916\) | 1.94691e8i | 0.253314i | ||||||||
\(917\) | − | 4.55252e7i | − | 0.0590396i | ||||||
\(918\) | 8.51371e7i | 0.110050i | ||||||||
\(919\) | − | 1.05932e8i | − | 0.136483i | −0.997669 | − | 0.0682416i | \(-0.978261\pi\) | ||
0.997669 | − | 0.0682416i | \(-0.0217389\pi\) | |||||||
\(920\) | 1.55141e8 | 0.199234 | ||||||||
\(921\) | −1.82316e8 | −0.233371 | ||||||||
\(922\) | 7.39668e8i | 0.943722i | ||||||||
\(923\) | − | 4.98943e8i | − | 0.634521i | ||||||
\(924\) | 8.60169e7i | 0.109036i | ||||||||
\(925\) | 2.00236e9i | 2.52998i | ||||||||
\(926\) | 6.52089e8 | 0.821248 | ||||||||
\(927\) | − | 9.97312e7i | − | 0.125196i | ||||||
\(928\) | − | 3.20999e8i | − | 0.401661i | ||||||
\(929\) | 1.07899e9i | 1.34577i | 0.739746 | + | 0.672887i | \(0.234946\pi\) | ||||
−0.739746 | + | 0.672887i | \(0.765054\pi\) | |||||||
\(930\) | −1.17367e8 | −0.145914 | ||||||||
\(931\) | 2.66279e7 | 0.0329980 | ||||||||
\(932\) | 2.94158e7i | 0.0363356i | ||||||||
\(933\) | −6.60302e8 | −0.813014 | ||||||||
\(934\) | 6.41738e8 | 0.787621 | ||||||||
\(935\) | − | 1.20616e9i | − | 1.47560i | ||||||
\(936\) | 1.89952e8 | 0.231641 | ||||||||
\(937\) | 1.20021e9i | 1.45894i | 0.684010 | + | 0.729472i | \(0.260234\pi\) | ||||
−0.684010 | + | 0.729472i | \(0.739766\pi\) | |||||||
\(938\) | −4.06211e8 | −0.492202 | ||||||||
\(939\) | 2.63384e8i | 0.318121i | ||||||||
\(940\) | − | 5.78476e8i | − | 0.696468i | ||||||
\(941\) | − | 8.64892e8i | − | 1.03799i | −0.854777 | − | 0.518995i | \(-0.826306\pi\) | ||
0.854777 | − | 0.518995i | \(-0.173694\pi\) | |||||||
\(942\) | −4.67510e8 | −0.559291 | ||||||||
\(943\) | − | 1.54085e8i | − | 0.183749i | ||||||
\(944\) | −4.35108e7 | + | 6.04356e8i | −0.0517227 | + | 0.718418i | ||||
\(945\) | −2.23229e8 | −0.264518 | ||||||||
\(946\) | − | 1.71805e9i | − | 2.02937i | ||||||
\(947\) | 1.20025e9 | 1.41325 | 0.706627 | − | 0.707586i | \(-0.250216\pi\) | ||||
0.706627 | + | 0.707586i | \(0.250216\pi\) | |||||||
\(948\) | −7.51259e6 | −0.00881789 | ||||||||
\(949\) | 6.46250e8 | 0.756139 | ||||||||
\(950\) | 1.37902e8i | 0.160842i | ||||||||
\(951\) | 2.21315e8 | 0.257318 | ||||||||
\(952\) | − | 4.29414e8i | − | 0.497697i | ||||||
\(953\) | 1.39575e9 | 1.61261 | 0.806303 | − | 0.591502i | \(-0.201465\pi\) | ||||
0.806303 | + | 0.591502i | \(0.201465\pi\) | |||||||
\(954\) | − | 3.29507e8i | − | 0.379507i | ||||||
\(955\) | 2.19900e9i | 2.52473i | ||||||||
\(956\) | 1.84394e8 | 0.211044 | ||||||||
\(957\) | 5.32942e8i | 0.608057i | ||||||||
\(958\) | − | 1.15958e9i | − | 1.31888i | ||||||
\(959\) | −4.92419e8 | −0.558315 | ||||||||
\(960\) | 1.10157e9 | 1.24508 | ||||||||
\(961\) | 8.67978e8 | 0.977999 | ||||||||
\(962\) | 4.61931e8i | 0.518862i | ||||||||
\(963\) | 2.69965e8 | 0.302293 | ||||||||
\(964\) | 3.18488e8 | 0.355519 | ||||||||
\(965\) | −1.76818e9 | −1.96764 | ||||||||
\(966\) | −3.08731e7 | −0.0342490 | ||||||||
\(967\) | − | 8.11424e8i | − | 0.897363i | −0.893692 | − | 0.448682i | \(-0.851894\pi\) | ||
0.893692 | − | 0.448682i | \(-0.148106\pi\) | |||||||
\(968\) | 3.59735e8i | 0.396603i | ||||||||
\(969\) | 2.26724e7 | 0.0249188 | ||||||||
\(970\) | −2.48707e9 | −2.72504 | ||||||||
\(971\) | −8.07317e8 | −0.881834 | −0.440917 | − | 0.897548i | \(-0.645347\pi\) | ||||
−0.440917 | + | 0.897548i | \(0.645347\pi\) | |||||||
\(972\) | −1.34211e7 | −0.0146147 | ||||||||
\(973\) | −1.09011e8 | −0.118340 | ||||||||
\(974\) | 1.02359e9i | 1.10776i | ||||||||
\(975\) | − | 9.51180e8i | − | 1.02624i | ||||||
\(976\) | − | 1.00361e9i | − | 1.07949i | ||||||
\(977\) | − | 1.60834e9i | − | 1.72462i | −0.506377 | − | 0.862312i | \(-0.669016\pi\) | ||
0.506377 | − | 0.862312i | \(-0.330984\pi\) | |||||||
\(978\) | − | 6.05116e8i | − | 0.646877i | ||||||
\(979\) | 1.67258e9 | 1.78254 | ||||||||
\(980\) | −2.06853e8 | −0.219778 | ||||||||
\(981\) | − | 5.09805e8i | − | 0.540004i | ||||||
\(982\) | − | 1.05666e9i | − | 1.11583i | ||||||
\(983\) | − | 1.90194e8i | − | 0.200234i | −0.994976 | − | 0.100117i | \(-0.968078\pi\) | ||
0.994976 | − | 0.100117i | \(-0.0319217\pi\) | |||||||
\(984\) | − | 1.14512e9i | − | 1.20189i | ||||||
\(985\) | 1.88347e8 | 0.197084 | ||||||||
\(986\) | − | 4.93663e8i | − | 0.514991i | ||||||
\(987\) | 6.20410e8i | 0.645249i | ||||||||
\(988\) | − | 9.38600e6i | − | 0.00973217i | ||||||
\(989\) | −1.81931e8 | −0.188069 | ||||||||
\(990\) | −6.44465e8 | −0.664193 | ||||||||
\(991\) | − | 5.02109e8i | − | 0.515914i | −0.966156 | − | 0.257957i | \(-0.916951\pi\) | ||
0.966156 | − | 0.257957i | \(-0.0830493\pi\) | |||||||
\(992\) | 6.45785e7 | 0.0661535 | ||||||||
\(993\) | 8.59409e8 | 0.877712 | ||||||||
\(994\) | 6.02670e8i | 0.613649i | ||||||||
\(995\) | 1.88058e9 | 1.90907 | ||||||||
\(996\) | − | 9.21441e6i | − | 0.00932587i | ||||||
\(997\) | 9.76161e8 | 0.985000 | 0.492500 | − | 0.870313i | \(-0.336083\pi\) | ||||
0.492500 | + | 0.870313i | \(0.336083\pi\) | |||||||
\(998\) | − | 5.07187e8i | − | 0.510242i | ||||||
\(999\) | − | 1.75899e8i | − | 0.176428i |
(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 | 177.7.c.a.58.19 | ✓ | 60 | |
59.58 | odd | 2 | inner | 177.7.c.a.58.42 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.7.c.a.58.19 | ✓ | 60 | 1.1 | even | 1 | trivial | |
177.7.c.a.58.42 | yes | 60 | 59.58 | odd | 2 | inner |