Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), 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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 553.20 | ||
Character | \(\chi\) | \(=\) | 690.553 |
Dual form | 690.3.k.a.277.20 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 1.06006 | − | 4.88634i | 0.212011 | − | 0.977267i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 6.77823 | − | 6.77823i | 0.968319 | − | 0.968319i | −0.0311941 | − | 0.999513i | \(-0.509931\pi\) |
0.999513 | + | 0.0311941i | \(0.00993100\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | −3.82628 | − | 5.94639i | −0.382628 | − | 0.594639i | ||||
\(11\) | 6.48073 | 0.589157 | 0.294579 | − | 0.955627i | \(-0.404821\pi\) | ||||
0.294579 | + | 0.955627i | \(0.404821\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.204124 | − | 0.204124i | ||||
\(13\) | 7.70435 | + | 7.70435i | 0.592642 | + | 0.592642i | 0.938344 | − | 0.345702i | \(-0.112359\pi\) |
−0.345702 | + | 0.938344i | \(0.612359\pi\) | |||||||
\(14\) | − | 13.5565i | − | 0.968319i | ||||||
\(15\) | 7.28281 | − | 4.68622i | 0.485521 | − | 0.312414i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 0.781759 | − | 0.781759i | 0.0459858 | − | 0.0459858i | −0.683740 | − | 0.729726i | \(-0.739648\pi\) |
0.729726 | + | 0.683740i | \(0.239648\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | 0.529087i | 0.0278467i | 0.999903 | + | 0.0139233i | \(0.00443208\pi\) | ||||
−0.999903 | + | 0.0139233i | \(0.995568\pi\) | |||||||
\(20\) | −9.77267 | − | 2.12011i | −0.488634 | − | 0.106006i | ||||
\(21\) | 16.6032 | 0.790629 | ||||||||
\(22\) | 6.48073 | − | 6.48073i | 0.294579 | − | 0.294579i | ||||
\(23\) | −3.39116 | − | 3.39116i | −0.147442 | − | 0.147442i | ||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | −22.7526 | − | 10.3596i | −0.910102 | − | 0.414383i | ||||
\(26\) | 15.4087 | 0.592642 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | −13.5565 | − | 13.5565i | −0.484160 | − | 0.484160i | ||||
\(29\) | − | 22.8105i | − | 0.786570i | −0.919417 | − | 0.393285i | \(-0.871338\pi\) | ||
0.919417 | − | 0.393285i | \(-0.128662\pi\) | |||||||
\(30\) | 2.59660 | − | 11.9690i | 0.0865532 | − | 0.398968i | ||||
\(31\) | −24.3355 | −0.785017 | −0.392508 | − | 0.919748i | \(-0.628393\pi\) | ||||
−0.392508 | + | 0.919748i | \(0.628393\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 7.93724 | + | 7.93724i | 0.240522 | + | 0.240522i | ||||
\(34\) | − | 1.56352i | − | 0.0459858i | ||||||
\(35\) | −25.9354 | − | 40.3060i | −0.741012 | − | 1.15160i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 6.38099 | − | 6.38099i | 0.172459 | − | 0.172459i | −0.615600 | − | 0.788059i | \(-0.711086\pi\) |
0.788059 | + | 0.615600i | \(0.211086\pi\) | |||||||
\(38\) | 0.529087 | + | 0.529087i | 0.0139233 | + | 0.0139233i | ||||
\(39\) | 18.8717i | 0.483890i | ||||||||
\(40\) | −11.8928 | + | 7.65256i | −0.297320 | + | 0.191314i | ||||
\(41\) | 16.5189 | 0.402899 | 0.201450 | − | 0.979499i | \(-0.435435\pi\) | ||||
0.201450 | + | 0.979499i | \(0.435435\pi\) | |||||||
\(42\) | 16.6032 | − | 16.6032i | 0.395315 | − | 0.395315i | ||||
\(43\) | 11.3582 | + | 11.3582i | 0.264144 | + | 0.264144i | 0.826735 | − | 0.562591i | \(-0.190195\pi\) |
−0.562591 | + | 0.826735i | \(0.690195\pi\) | |||||||
\(44\) | − | 12.9615i | − | 0.294579i | ||||||
\(45\) | 14.6590 | + | 3.18017i | 0.325756 | + | 0.0706704i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | −19.1854 | + | 19.1854i | −0.408199 | + | 0.408199i | −0.881110 | − | 0.472911i | \(-0.843203\pi\) |
0.472911 | + | 0.881110i | \(0.343203\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 42.8889i | − | 0.875284i | ||||||
\(50\) | −33.1121 | + | 12.3930i | −0.662243 | + | 0.247860i | ||||
\(51\) | 1.91491 | 0.0375473 | ||||||||
\(52\) | 15.4087 | − | 15.4087i | 0.296321 | − | 0.296321i | ||||
\(53\) | −7.76688 | − | 7.76688i | −0.146545 | − | 0.146545i | 0.630028 | − | 0.776573i | \(-0.283043\pi\) |
−0.776573 | + | 0.630028i | \(0.783043\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 6.86994 | − | 31.6670i | 0.124908 | − | 0.575764i | ||||
\(56\) | −27.1129 | −0.484160 | ||||||||
\(57\) | −0.647996 | + | 0.647996i | −0.0113684 | + | 0.0113684i | ||||
\(58\) | −22.8105 | − | 22.8105i | −0.393285 | − | 0.393285i | ||||
\(59\) | − | 62.7613i | − | 1.06375i | −0.846822 | − | 0.531876i | \(-0.821487\pi\) | ||
0.846822 | − | 0.531876i | \(-0.178513\pi\) | |||||||
\(60\) | −9.37243 | − | 14.5656i | −0.156207 | − | 0.242760i | ||||
\(61\) | 37.8465 | 0.620435 | 0.310218 | − | 0.950666i | \(-0.399598\pi\) | ||||
0.310218 | + | 0.950666i | \(0.399598\pi\) | |||||||
\(62\) | −24.3355 | + | 24.3355i | −0.392508 | + | 0.392508i | ||||
\(63\) | 20.3347 | + | 20.3347i | 0.322773 | + | 0.322773i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 45.8131 | − | 29.4790i | 0.704817 | − | 0.453523i | ||||
\(66\) | 15.8745 | 0.240522 | ||||||||
\(67\) | −23.8308 | + | 23.8308i | −0.355683 | + | 0.355683i | −0.862219 | − | 0.506536i | \(-0.830926\pi\) |
0.506536 | + | 0.862219i | \(0.330926\pi\) | |||||||
\(68\) | −1.56352 | − | 1.56352i | −0.0229929 | − | 0.0229929i | ||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | −66.2415 | − | 14.3706i | −0.946307 | − | 0.205295i | ||||
\(71\) | 82.9169 | 1.16784 | 0.583922 | − | 0.811810i | \(-0.301517\pi\) | ||||
0.583922 | + | 0.811810i | \(0.301517\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 32.9265 | + | 32.9265i | 0.451048 | + | 0.451048i | 0.895702 | − | 0.444654i | \(-0.146674\pi\) |
−0.444654 | + | 0.895702i | \(0.646674\pi\) | |||||||
\(74\) | − | 12.7620i | − | 0.172459i | ||||||
\(75\) | −15.1782 | − | 40.5539i | −0.202377 | − | 0.540719i | ||||
\(76\) | 1.05817 | 0.0139233 | ||||||||
\(77\) | 43.9279 | − | 43.9279i | 0.570492 | − | 0.570492i | ||||
\(78\) | 18.8717 | + | 18.8717i | 0.241945 | + | 0.241945i | ||||
\(79\) | 55.5424i | 0.703069i | 0.936175 | + | 0.351534i | \(0.114340\pi\) | ||||
−0.936175 | + | 0.351534i | \(0.885660\pi\) | |||||||
\(80\) | −4.24022 | + | 19.5453i | −0.0530028 | + | 0.244317i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 16.5189 | − | 16.5189i | 0.201450 | − | 0.201450i | ||||
\(83\) | −53.8067 | − | 53.8067i | −0.648274 | − | 0.648274i | 0.304302 | − | 0.952576i | \(-0.401577\pi\) |
−0.952576 | + | 0.304302i | \(0.901577\pi\) | |||||||
\(84\) | − | 33.2064i | − | 0.395315i | ||||||
\(85\) | −2.99123 | − | 4.64864i | −0.0351909 | − | 0.0546899i | ||||
\(86\) | 22.7164 | 0.264144 | ||||||||
\(87\) | 27.9371 | − | 27.9371i | 0.321116 | − | 0.321116i | ||||
\(88\) | −12.9615 | − | 12.9615i | −0.147289 | − | 0.147289i | ||||
\(89\) | − | 9.20780i | − | 0.103458i | −0.998661 | − | 0.0517292i | \(-0.983527\pi\) | ||
0.998661 | − | 0.0517292i | \(-0.0164733\pi\) | |||||||
\(90\) | 17.8392 | − | 11.4788i | 0.198213 | − | 0.127543i | ||||
\(91\) | 104.444 | 1.14773 | ||||||||
\(92\) | −6.78233 | + | 6.78233i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | −29.8048 | − | 29.8048i | −0.320482 | − | 0.320482i | ||||
\(94\) | 38.3707i | 0.408199i | ||||||||
\(95\) | 2.58529 | + | 0.560862i | 0.0272136 | + | 0.00590381i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 79.6850 | − | 79.6850i | 0.821495 | − | 0.821495i | −0.164828 | − | 0.986322i | \(-0.552707\pi\) |
0.986322 | + | 0.164828i | \(0.0527068\pi\) | |||||||
\(98\) | −42.8889 | − | 42.8889i | −0.437642 | − | 0.437642i | ||||
\(99\) | 19.4422i | 0.196386i | ||||||||
\(100\) | −20.7192 | + | 45.5051i | −0.207192 | + | 0.455051i | ||||
\(101\) | −139.733 | −1.38350 | −0.691749 | − | 0.722138i | \(-0.743160\pi\) | ||||
−0.691749 | + | 0.722138i | \(0.743160\pi\) | |||||||
\(102\) | 1.91491 | − | 1.91491i | 0.0187736 | − | 0.0187736i | ||||
\(103\) | 98.3312 | + | 98.3312i | 0.954672 | + | 0.954672i | 0.999016 | − | 0.0443444i | \(-0.0141199\pi\) |
−0.0443444 | + | 0.999016i | \(0.514120\pi\) | |||||||
\(104\) | − | 30.8174i | − | 0.296321i | ||||||
\(105\) | 17.6003 | − | 81.1289i | 0.167622 | − | 0.772656i | ||||
\(106\) | −15.5338 | −0.146545 | ||||||||
\(107\) | −11.4279 | + | 11.4279i | −0.106803 | + | 0.106803i | −0.758489 | − | 0.651686i | \(-0.774062\pi\) |
0.651686 | + | 0.758489i | \(0.274062\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 79.8261i | 0.732350i | 0.930546 | + | 0.366175i | \(0.119333\pi\) | ||||
−0.930546 | + | 0.366175i | \(0.880667\pi\) | |||||||
\(110\) | −24.7971 | − | 38.5370i | −0.225428 | − | 0.350336i | ||||
\(111\) | 15.6302 | 0.140812 | ||||||||
\(112\) | −27.1129 | + | 27.1129i | −0.242080 | + | 0.242080i | ||||
\(113\) | 80.7359 | + | 80.7359i | 0.714477 | + | 0.714477i | 0.967468 | − | 0.252992i | \(-0.0814145\pi\) |
−0.252992 | + | 0.967468i | \(0.581415\pi\) | |||||||
\(114\) | 1.29599i | 0.0113684i | ||||||||
\(115\) | −20.1652 | + | 12.9755i | −0.175350 | + | 0.112831i | ||||
\(116\) | −45.6211 | −0.393285 | ||||||||
\(117\) | −23.1130 | + | 23.1130i | −0.197547 | + | 0.197547i | ||||
\(118\) | −62.7613 | − | 62.7613i | −0.531876 | − | 0.531876i | ||||
\(119\) | − | 10.5979i | − | 0.0890579i | ||||||
\(120\) | −23.9381 | − | 5.19319i | −0.199484 | − | 0.0432766i | ||||
\(121\) | −79.0002 | −0.652894 | ||||||||
\(122\) | 37.8465 | − | 37.8465i | 0.310218 | − | 0.310218i | ||||
\(123\) | 20.2314 | + | 20.2314i | 0.164483 | + | 0.164483i | ||||
\(124\) | 48.6710i | 0.392508i | ||||||||
\(125\) | −74.7394 | + | 100.195i | −0.597915 | + | 0.801559i | ||||
\(126\) | 40.6694 | 0.322773 | ||||||||
\(127\) | −130.755 | + | 130.755i | −1.02957 | + | 1.02957i | −0.0300209 | + | 0.999549i | \(0.509557\pi\) |
−0.999549 | + | 0.0300209i | \(0.990443\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 27.8218i | 0.215673i | ||||||||
\(130\) | 16.3341 | − | 75.2921i | 0.125647 | − | 0.579170i | ||||
\(131\) | 38.3122 | 0.292459 | 0.146230 | − | 0.989251i | \(-0.453286\pi\) | ||||
0.146230 | + | 0.989251i | \(0.453286\pi\) | |||||||
\(132\) | 15.8745 | − | 15.8745i | 0.120261 | − | 0.120261i | ||||
\(133\) | 3.58627 | + | 3.58627i | 0.0269645 | + | 0.0269645i | ||||
\(134\) | 47.6616i | 0.355683i | ||||||||
\(135\) | 14.0587 | + | 21.8484i | 0.104138 | + | 0.161840i | ||||
\(136\) | −3.12703 | −0.0229929 | ||||||||
\(137\) | −43.2358 | + | 43.2358i | −0.315589 | + | 0.315589i | −0.847070 | − | 0.531481i | \(-0.821636\pi\) |
0.531481 | + | 0.847070i | \(0.321636\pi\) | |||||||
\(138\) | −8.30662 | − | 8.30662i | −0.0601929 | − | 0.0601929i | ||||
\(139\) | 113.502i | 0.816562i | 0.912856 | + | 0.408281i | \(0.133872\pi\) | ||||
−0.912856 | + | 0.408281i | \(0.866128\pi\) | |||||||
\(140\) | −80.6121 | + | 51.8708i | −0.575801 | + | 0.370506i | ||||
\(141\) | −46.9944 | −0.333293 | ||||||||
\(142\) | 82.9169 | − | 82.9169i | 0.583922 | − | 0.583922i | ||||
\(143\) | 49.9298 | + | 49.9298i | 0.349159 | + | 0.349159i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | −111.460 | − | 24.1805i | −0.768690 | − | 0.166762i | ||||
\(146\) | 65.8530 | 0.451048 | ||||||||
\(147\) | 52.5280 | − | 52.5280i | 0.357333 | − | 0.357333i | ||||
\(148\) | −12.7620 | − | 12.7620i | −0.0862295 | − | 0.0862295i | ||||
\(149\) | 80.8820i | 0.542832i | 0.962462 | + | 0.271416i | \(0.0874920\pi\) | ||||
−0.962462 | + | 0.271416i | \(0.912508\pi\) | |||||||
\(150\) | −55.7322 | − | 25.3757i | −0.371548 | − | 0.169171i | ||||
\(151\) | −54.8655 | −0.363348 | −0.181674 | − | 0.983359i | \(-0.558152\pi\) | ||||
−0.181674 | + | 0.983359i | \(0.558152\pi\) | |||||||
\(152\) | 1.05817 | − | 1.05817i | 0.00696167 | − | 0.00696167i | ||||
\(153\) | 2.34528 | + | 2.34528i | 0.0153286 | + | 0.0153286i | ||||
\(154\) | − | 87.8558i | − | 0.570492i | ||||||
\(155\) | −25.7970 | + | 118.912i | −0.166432 | + | 0.767171i | ||||
\(156\) | 37.7434 | 0.241945 | ||||||||
\(157\) | −143.794 | + | 143.794i | −0.915885 | + | 0.915885i | −0.996727 | − | 0.0808422i | \(-0.974239\pi\) |
0.0808422 | + | 0.996727i | \(0.474239\pi\) | |||||||
\(158\) | 55.5424 | + | 55.5424i | 0.351534 | + | 0.351534i | ||||
\(159\) | − | 19.0249i | − | 0.119653i | ||||||
\(160\) | 15.3051 | + | 23.7856i | 0.0956570 | + | 0.148660i | ||||
\(161\) | −45.9722 | −0.285542 | ||||||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 108.194 | + | 108.194i | 0.663769 | + | 0.663769i | 0.956266 | − | 0.292497i | \(-0.0944862\pi\) |
−0.292497 | + | 0.956266i | \(0.594486\pi\) | |||||||
\(164\) | − | 33.0377i | − | 0.201450i | ||||||
\(165\) | 47.1979 | − | 30.3701i | 0.286048 | − | 0.184061i | ||||
\(166\) | −107.613 | −0.648274 | ||||||||
\(167\) | 178.168 | − | 178.168i | 1.06688 | − | 1.06688i | 0.0692787 | − | 0.997597i | \(-0.477930\pi\) |
0.997597 | − | 0.0692787i | \(-0.0220698\pi\) | |||||||
\(168\) | −33.2064 | − | 33.2064i | −0.197657 | − | 0.197657i | ||||
\(169\) | − | 50.2860i | − | 0.297550i | ||||||
\(170\) | −7.63987 | − | 1.65742i | −0.0449404 | − | 0.00974951i | ||||
\(171\) | −1.58726 | −0.00928222 | ||||||||
\(172\) | 22.7164 | − | 22.7164i | 0.132072 | − | 0.132072i | ||||
\(173\) | −12.0550 | − | 12.0550i | −0.0696822 | − | 0.0696822i | 0.671407 | − | 0.741089i | \(-0.265690\pi\) |
−0.741089 | + | 0.671407i | \(0.765690\pi\) | |||||||
\(174\) | − | 55.8742i | − | 0.321116i | ||||||
\(175\) | −224.442 | + | 84.0025i | −1.28253 | + | 0.480014i | ||||
\(176\) | −25.9229 | −0.147289 | ||||||||
\(177\) | 76.8666 | − | 76.8666i | 0.434275 | − | 0.434275i | ||||
\(178\) | −9.20780 | − | 9.20780i | −0.0517292 | − | 0.0517292i | ||||
\(179\) | − | 47.2728i | − | 0.264094i | −0.991243 | − | 0.132047i | \(-0.957845\pi\) | ||
0.991243 | − | 0.132047i | \(-0.0421550\pi\) | |||||||
\(180\) | 6.36034 | − | 29.3180i | 0.0353352 | − | 0.162878i | ||||
\(181\) | −47.4383 | −0.262090 | −0.131045 | − | 0.991376i | \(-0.541833\pi\) | ||||
−0.131045 | + | 0.991376i | \(0.541833\pi\) | |||||||
\(182\) | 104.444 | − | 104.444i | 0.573867 | − | 0.573867i | ||||
\(183\) | 46.3524 | + | 46.3524i | 0.253292 | + | 0.253292i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −24.4154 | − | 37.9438i | −0.131975 | − | 0.205102i | ||||
\(186\) | −59.6096 | −0.320482 | ||||||||
\(187\) | 5.06637 | − | 5.06637i | 0.0270929 | − | 0.0270929i | ||||
\(188\) | 38.3707 | + | 38.3707i | 0.204100 | + | 0.204100i | ||||
\(189\) | 49.8097i | 0.263543i | ||||||||
\(190\) | 3.14616 | − | 2.02443i | 0.0165587 | − | 0.0106549i | ||||
\(191\) | 126.903 | 0.664416 | 0.332208 | − | 0.943206i | \(-0.392206\pi\) | ||||
0.332208 | + | 0.943206i | \(0.392206\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −148.959 | − | 148.959i | −0.771811 | − | 0.771811i | 0.206612 | − | 0.978423i | \(-0.433756\pi\) |
−0.978423 | + | 0.206612i | \(0.933756\pi\) | |||||||
\(194\) | − | 159.370i | − | 0.821495i | ||||||
\(195\) | 92.2136 | + | 20.0051i | 0.472890 | + | 0.102590i | ||||
\(196\) | −85.7779 | −0.437642 | ||||||||
\(197\) | 10.2081 | − | 10.2081i | 0.0518175 | − | 0.0518175i | −0.680723 | − | 0.732541i | \(-0.738334\pi\) |
0.732541 | + | 0.680723i | \(0.238334\pi\) | |||||||
\(198\) | 19.4422 | + | 19.4422i | 0.0981929 | + | 0.0981929i | ||||
\(199\) | 365.840i | 1.83839i | 0.393803 | + | 0.919195i | \(0.371159\pi\) | ||||
−0.393803 | + | 0.919195i | \(0.628841\pi\) | |||||||
\(200\) | 24.7860 | + | 66.2243i | 0.123930 | + | 0.331121i | ||||
\(201\) | −58.3732 | −0.290414 | ||||||||
\(202\) | −139.733 | + | 139.733i | −0.691749 | + | 0.691749i | ||||
\(203\) | −154.615 | − | 154.615i | −0.761651 | − | 0.761651i | ||||
\(204\) | − | 3.82982i | − | 0.0187736i | ||||||
\(205\) | 17.5109 | − | 80.7167i | 0.0854192 | − | 0.393740i | ||||
\(206\) | 196.662 | 0.954672 | ||||||||
\(207\) | 10.1735 | − | 10.1735i | 0.0491473 | − | 0.0491473i | ||||
\(208\) | −30.8174 | − | 30.8174i | −0.148161 | − | 0.148161i | ||||
\(209\) | 3.42887i | 0.0164061i | ||||||||
\(210\) | −63.5286 | − | 98.7292i | −0.302517 | − | 0.470139i | ||||
\(211\) | 52.5021 | 0.248825 | 0.124413 | − | 0.992231i | \(-0.460295\pi\) | ||||
0.124413 | + | 0.992231i | \(0.460295\pi\) | |||||||
\(212\) | −15.5338 | + | 15.5338i | −0.0732724 | + | 0.0732724i | ||||
\(213\) | 101.552 | + | 101.552i | 0.476770 | + | 0.476770i | ||||
\(214\) | 22.8558i | 0.106803i | ||||||||
\(215\) | 67.5403 | − | 43.4596i | 0.314141 | − | 0.202138i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −164.952 | + | 164.952i | −0.760147 | + | 0.760147i | ||||
\(218\) | 79.8261 | + | 79.8261i | 0.366175 | + | 0.366175i | ||||
\(219\) | 80.6531i | 0.368279i | ||||||||
\(220\) | −63.3340 | − | 13.7399i | −0.287882 | − | 0.0624540i | ||||
\(221\) | 12.0459 | 0.0545063 | ||||||||
\(222\) | 15.6302 | − | 15.6302i | 0.0704061 | − | 0.0704061i | ||||
\(223\) | −20.5666 | − | 20.5666i | −0.0922271 | − | 0.0922271i | 0.659488 | − | 0.751715i | \(-0.270773\pi\) |
−0.751715 | + | 0.659488i | \(0.770773\pi\) | |||||||
\(224\) | 54.2259i | 0.242080i | ||||||||
\(225\) | 31.0787 | − | 68.2577i | 0.138128 | − | 0.303367i | ||||
\(226\) | 161.472 | 0.714477 | ||||||||
\(227\) | 233.250 | − | 233.250i | 1.02753 | − | 1.02753i | 0.0279229 | − | 0.999610i | \(-0.491111\pi\) |
0.999610 | − | 0.0279229i | \(-0.00888930\pi\) | |||||||
\(228\) | 1.29599 | + | 1.29599i | 0.00568418 | + | 0.00568418i | ||||
\(229\) | 407.228i | 1.77829i | 0.457629 | + | 0.889143i | \(0.348699\pi\) | ||||
−0.457629 | + | 0.889143i | \(0.651301\pi\) | |||||||
\(230\) | −7.18965 | + | 33.1407i | −0.0312594 | + | 0.144090i | ||||
\(231\) | 107.601 | 0.465805 | ||||||||
\(232\) | −45.6211 | + | 45.6211i | −0.196643 | + | 0.196643i | ||||
\(233\) | 67.8138 | + | 67.8138i | 0.291046 | + | 0.291046i | 0.837494 | − | 0.546447i | \(-0.184020\pi\) |
−0.546447 | + | 0.837494i | \(0.684020\pi\) | |||||||
\(234\) | 46.2261i | 0.197547i | ||||||||
\(235\) | 73.4086 | + | 114.084i | 0.312377 | + | 0.485463i | ||||
\(236\) | −125.523 | −0.531876 | ||||||||
\(237\) | −68.0253 | + | 68.0253i | −0.287027 | + | 0.287027i | ||||
\(238\) | −10.5979 | − | 10.5979i | −0.0445289 | − | 0.0445289i | ||||
\(239\) | 126.104i | 0.527630i | 0.964573 | + | 0.263815i | \(0.0849808\pi\) | ||||
−0.964573 | + | 0.263815i | \(0.915019\pi\) | |||||||
\(240\) | −29.1313 | + | 18.7449i | −0.121380 | + | 0.0781036i | ||||
\(241\) | 169.295 | 0.702467 | 0.351234 | − | 0.936288i | \(-0.385762\pi\) | ||||
0.351234 | + | 0.936288i | \(0.385762\pi\) | |||||||
\(242\) | −79.0002 | + | 79.0002i | −0.326447 | + | 0.326447i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 75.6931i | − | 0.310218i | ||||||
\(245\) | −209.570 | − | 45.4647i | −0.855387 | − | 0.185570i | ||||
\(246\) | 40.4628 | 0.164483 | ||||||||
\(247\) | −4.07627 | + | 4.07627i | −0.0165031 | + | 0.0165031i | ||||
\(248\) | 48.6710 | + | 48.6710i | 0.196254 | + | 0.196254i | ||||
\(249\) | − | 131.799i | − | 0.529313i | ||||||
\(250\) | 25.4555 | + | 174.934i | 0.101822 | + | 0.699737i | ||||
\(251\) | 352.257 | 1.40341 | 0.701707 | − | 0.712466i | \(-0.252422\pi\) | ||||
0.701707 | + | 0.712466i | \(0.252422\pi\) | |||||||
\(252\) | 40.6694 | − | 40.6694i | 0.161387 | − | 0.161387i | ||||
\(253\) | −21.9772 | − | 21.9772i | −0.0868665 | − | 0.0868665i | ||||
\(254\) | 261.511i | 1.02957i | ||||||||
\(255\) | 2.02991 | − | 9.35689i | 0.00796044 | − | 0.0366937i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 36.1183 | − | 36.1183i | 0.140538 | − | 0.140538i | −0.633338 | − | 0.773876i | \(-0.718316\pi\) |
0.773876 | + | 0.633338i | \(0.218316\pi\) | |||||||
\(258\) | 27.8218 | + | 27.8218i | 0.107836 | + | 0.107836i | ||||
\(259\) | − | 86.5037i | − | 0.333991i | ||||||
\(260\) | −58.9580 | − | 91.6262i | −0.226762 | − | 0.352408i | ||||
\(261\) | 68.4316 | 0.262190 | ||||||||
\(262\) | 38.3122 | − | 38.3122i | 0.146230 | − | 0.146230i | ||||
\(263\) | −217.636 | − | 217.636i | −0.827513 | − | 0.827513i | 0.159660 | − | 0.987172i | \(-0.448960\pi\) |
−0.987172 | + | 0.159660i | \(0.948960\pi\) | |||||||
\(264\) | − | 31.7490i | − | 0.120261i | ||||||
\(265\) | −46.1849 | + | 29.7182i | −0.174283 | + | 0.112144i | ||||
\(266\) | 7.17255 | 0.0269645 | ||||||||
\(267\) | 11.2772 | − | 11.2772i | 0.0422367 | − | 0.0422367i | ||||
\(268\) | 47.6616 | + | 47.6616i | 0.177842 | + | 0.177842i | ||||
\(269\) | 525.831i | 1.95476i | 0.211488 | + | 0.977381i | \(0.432169\pi\) | ||||
−0.211488 | + | 0.977381i | \(0.567831\pi\) | |||||||
\(270\) | 35.9071 | + | 7.78979i | 0.132989 | + | 0.0288511i | ||||
\(271\) | 518.661 | 1.91388 | 0.956939 | − | 0.290289i | \(-0.0937514\pi\) | ||||
0.956939 | + | 0.290289i | \(0.0937514\pi\) | |||||||
\(272\) | −3.12703 | + | 3.12703i | −0.0114965 | + | 0.0114965i | ||||
\(273\) | 127.917 | + | 127.917i | 0.468560 | + | 0.468560i | ||||
\(274\) | 86.4715i | 0.315589i | ||||||||
\(275\) | −147.453 | − | 67.1376i | −0.536193 | − | 0.244137i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | −223.617 | + | 223.617i | −0.807281 | + | 0.807281i | −0.984222 | − | 0.176940i | \(-0.943380\pi\) |
0.176940 | + | 0.984222i | \(0.443380\pi\) | |||||||
\(278\) | 113.502 | + | 113.502i | 0.408281 | + | 0.408281i | ||||
\(279\) | − | 73.0066i | − | 0.261672i | ||||||
\(280\) | −28.7412 | + | 132.483i | −0.102647 | + | 0.473153i | ||||
\(281\) | 425.954 | 1.51585 | 0.757926 | − | 0.652341i | \(-0.226213\pi\) | ||||
0.757926 | + | 0.652341i | \(0.226213\pi\) | |||||||
\(282\) | −46.9944 | + | 46.9944i | −0.166647 | + | 0.166647i | ||||
\(283\) | 30.5658 | + | 30.5658i | 0.108006 | + | 0.108006i | 0.759045 | − | 0.651038i | \(-0.225666\pi\) |
−0.651038 | + | 0.759045i | \(0.725666\pi\) | |||||||
\(284\) | − | 165.834i | − | 0.583922i | ||||||
\(285\) | 2.47941 | + | 3.85324i | 0.00869970 | + | 0.0135201i | ||||
\(286\) | 99.8596 | 0.349159 | ||||||||
\(287\) | 111.969 | − | 111.969i | 0.390135 | − | 0.390135i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 287.778i | 0.995771i | ||||||||
\(290\) | −135.640 | + | 87.2795i | −0.467726 | + | 0.300964i | ||||
\(291\) | 195.188 | 0.670748 | ||||||||
\(292\) | 65.8530 | − | 65.8530i | 0.225524 | − | 0.225524i | ||||
\(293\) | −237.549 | − | 237.549i | −0.810749 | − | 0.810749i | 0.173997 | − | 0.984746i | \(-0.444332\pi\) |
−0.984746 | + | 0.173997i | \(0.944332\pi\) | |||||||
\(294\) | − | 105.056i | − | 0.357333i | ||||||
\(295\) | −306.673 | − | 66.5305i | −1.03957 | − | 0.225527i | ||||
\(296\) | −25.5239 | −0.0862295 | ||||||||
\(297\) | −23.8117 | + | 23.8117i | −0.0801741 | + | 0.0801741i | ||||
\(298\) | 80.8820 | + | 80.8820i | 0.271416 | + | 0.271416i | ||||
\(299\) | − | 52.2534i | − | 0.174761i | ||||||
\(300\) | −81.1079 | + | 30.3565i | −0.270360 | + | 0.101188i | ||||
\(301\) | 153.977 | 0.511552 | ||||||||
\(302\) | −54.8655 | + | 54.8655i | −0.181674 | + | 0.181674i | ||||
\(303\) | −171.138 | − | 171.138i | −0.564811 | − | 0.564811i | ||||
\(304\) | − | 2.11635i | − | 0.00696167i | ||||||
\(305\) | 40.1195 | − | 184.931i | 0.131539 | − | 0.606331i | ||||
\(306\) | 4.69055 | 0.0153286 | ||||||||
\(307\) | −237.912 | + | 237.912i | −0.774959 | + | 0.774959i | −0.978969 | − | 0.204010i | \(-0.934602\pi\) |
0.204010 | + | 0.978969i | \(0.434602\pi\) | |||||||
\(308\) | −87.8558 | − | 87.8558i | −0.285246 | − | 0.285246i | ||||
\(309\) | 240.861i | 0.779486i | ||||||||
\(310\) | 93.1145 | + | 144.709i | 0.300369 | + | 0.466802i | ||||
\(311\) | −81.3114 | −0.261452 | −0.130726 | − | 0.991419i | \(-0.541731\pi\) | ||||
−0.130726 | + | 0.991419i | \(0.541731\pi\) | |||||||
\(312\) | 37.7434 | − | 37.7434i | 0.120973 | − | 0.120973i | ||||
\(313\) | −327.200 | − | 327.200i | −1.04537 | − | 1.04537i | −0.998921 | − | 0.0464467i | \(-0.985210\pi\) |
−0.0464467 | − | 0.998921i | \(-0.514790\pi\) | |||||||
\(314\) | 287.588i | 0.915885i | ||||||||
\(315\) | 120.918 | − | 77.8063i | 0.383867 | − | 0.247004i | ||||
\(316\) | 111.085 | 0.351534 | ||||||||
\(317\) | 274.470 | − | 274.470i | 0.865837 | − | 0.865837i | −0.126171 | − | 0.992008i | \(-0.540269\pi\) |
0.992008 | + | 0.126171i | \(0.0402690\pi\) | |||||||
\(318\) | −19.0249 | − | 19.0249i | −0.0598267 | − | 0.0598267i | ||||
\(319\) | − | 147.829i | − | 0.463414i | ||||||
\(320\) | 39.0907 | + | 8.48045i | 0.122158 | + | 0.0265014i | ||||
\(321\) | −27.9925 | −0.0872040 | ||||||||
\(322\) | −45.9722 | + | 45.9722i | −0.142771 | + | 0.142771i | ||||
\(323\) | 0.413618 | + | 0.413618i | 0.00128055 | + | 0.00128055i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | −95.4798 | − | 255.108i | −0.293784 | − | 0.784946i | ||||
\(326\) | 216.389 | 0.663769 | ||||||||
\(327\) | −97.7666 | + | 97.7666i | −0.298981 | + | 0.298981i | ||||
\(328\) | −33.0377 | − | 33.0377i | −0.100725 | − | 0.100725i | ||||
\(329\) | 260.086i | 0.790535i | ||||||||
\(330\) | 16.8278 | − | 77.5680i | 0.0509934 | − | 0.235055i | ||||
\(331\) | 209.454 | 0.632791 | 0.316396 | − | 0.948627i | \(-0.397527\pi\) | ||||
0.316396 | + | 0.948627i | \(0.397527\pi\) | |||||||
\(332\) | −107.613 | + | 107.613i | −0.324137 | + | 0.324137i | ||||
\(333\) | 19.1430 | + | 19.1430i | 0.0574864 | + | 0.0574864i | ||||
\(334\) | − | 356.337i | − | 1.06688i | ||||||
\(335\) | 91.1832 | + | 141.707i | 0.272189 | + | 0.423006i | ||||
\(336\) | −66.4129 | −0.197657 | ||||||||
\(337\) | −267.075 | + | 267.075i | −0.792506 | + | 0.792506i | −0.981901 | − | 0.189395i | \(-0.939347\pi\) |
0.189395 | + | 0.981901i | \(0.439347\pi\) | |||||||
\(338\) | −50.2860 | − | 50.2860i | −0.148775 | − | 0.148775i | ||||
\(339\) | 197.762i | 0.583368i | ||||||||
\(340\) | −9.29729 | + | 5.98246i | −0.0273450 | + | 0.0175955i | ||||
\(341\) | −157.712 | −0.462498 | ||||||||
\(342\) | −1.58726 | + | 1.58726i | −0.00464111 | + | 0.00464111i | ||||
\(343\) | 41.4222 | + | 41.4222i | 0.120765 | + | 0.120765i | ||||
\(344\) | − | 45.4328i | − | 0.132072i | ||||||
\(345\) | −40.5890 | − | 8.80549i | −0.117649 | − | 0.0255232i | ||||
\(346\) | −24.1100 | −0.0696822 | ||||||||
\(347\) | 302.377 | − | 302.377i | 0.871403 | − | 0.871403i | −0.121222 | − | 0.992625i | \(-0.538681\pi\) |
0.992625 | + | 0.121222i | \(0.0386813\pi\) | |||||||
\(348\) | −55.8742 | − | 55.8742i | −0.160558 | − | 0.160558i | ||||
\(349\) | 38.7883i | 0.111141i | 0.998455 | + | 0.0555706i | \(0.0176978\pi\) | ||||
−0.998455 | + | 0.0555706i | \(0.982302\pi\) | |||||||
\(350\) | −140.439 | + | 308.444i | −0.401255 | + | 0.881270i | ||||
\(351\) | −56.6152 | −0.161297 | ||||||||
\(352\) | −25.9229 | + | 25.9229i | −0.0736446 | + | 0.0736446i | ||||
\(353\) | 228.425 | + | 228.425i | 0.647096 | + | 0.647096i | 0.952290 | − | 0.305194i | \(-0.0987213\pi\) |
−0.305194 | + | 0.952290i | \(0.598721\pi\) | |||||||
\(354\) | − | 153.733i | − | 0.434275i | ||||||
\(355\) | 87.8966 | − | 405.160i | 0.247596 | − | 1.14130i | ||||
\(356\) | −18.4156 | −0.0517292 | ||||||||
\(357\) | 12.9797 | − | 12.9797i | 0.0363577 | − | 0.0363577i | ||||
\(358\) | −47.2728 | − | 47.2728i | −0.132047 | − | 0.132047i | ||||
\(359\) | − | 572.493i | − | 1.59469i | −0.603525 | − | 0.797344i | \(-0.706238\pi\) | ||
0.603525 | − | 0.797344i | \(-0.293762\pi\) | |||||||
\(360\) | −22.9577 | − | 35.6784i | −0.0637713 | − | 0.0991065i | ||||
\(361\) | 360.720 | 0.999225 | ||||||||
\(362\) | −47.4383 | + | 47.4383i | −0.131045 | + | 0.131045i | ||||
\(363\) | −96.7550 | − | 96.7550i | −0.266543 | − | 0.266543i | ||||
\(364\) | − | 208.888i | − | 0.573867i | ||||||
\(365\) | 195.794 | − | 125.986i | 0.536421 | − | 0.345167i | ||||
\(366\) | 92.7047 | 0.253292 | ||||||||
\(367\) | −156.250 | + | 156.250i | −0.425750 | + | 0.425750i | −0.887178 | − | 0.461428i | \(-0.847337\pi\) |
0.461428 | + | 0.887178i | \(0.347337\pi\) | |||||||
\(368\) | 13.5647 | + | 13.5647i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 49.5566i | 0.134300i | ||||||||
\(370\) | −62.3593 | − | 13.5284i | −0.168539 | − | 0.0365633i | ||||
\(371\) | −105.291 | −0.283804 | ||||||||
\(372\) | −59.6096 | + | 59.6096i | −0.160241 | + | 0.160241i | ||||
\(373\) | 14.7884 | + | 14.7884i | 0.0396472 | + | 0.0396472i | 0.726652 | − | 0.687005i | \(-0.241075\pi\) |
−0.687005 | + | 0.726652i | \(0.741075\pi\) | |||||||
\(374\) | − | 10.1327i | − | 0.0270929i | ||||||
\(375\) | −214.250 | + | 31.1765i | −0.571333 | + | 0.0831374i | ||||
\(376\) | 76.7415 | 0.204100 | ||||||||
\(377\) | 175.740 | − | 175.740i | 0.466155 | − | 0.466155i | ||||
\(378\) | 49.8097 | + | 49.8097i | 0.131772 | + | 0.131772i | ||||
\(379\) | − | 39.4302i | − | 0.104038i | −0.998646 | − | 0.0520188i | \(-0.983434\pi\) | ||
0.998646 | − | 0.0520188i | \(-0.0165656\pi\) | |||||||
\(380\) | 1.12172 | − | 5.17059i | 0.00295190 | − | 0.0136068i | ||||
\(381\) | −320.284 | −0.840640 | ||||||||
\(382\) | 126.903 | − | 126.903i | 0.332208 | − | 0.332208i | ||||
\(383\) | −262.977 | − | 262.977i | −0.686624 | − | 0.686624i | 0.274860 | − | 0.961484i | \(-0.411368\pi\) |
−0.961484 | + | 0.274860i | \(0.911368\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −168.080 | − | 261.213i | −0.436573 | − | 0.678474i | ||||
\(386\) | −297.919 | −0.771811 | ||||||||
\(387\) | −34.0746 | + | 34.0746i | −0.0880480 | + | 0.0880480i | ||||
\(388\) | −159.370 | − | 159.370i | −0.410747 | − | 0.410747i | ||||
\(389\) | 412.312i | 1.05993i | 0.848021 | + | 0.529963i | \(0.177794\pi\) | ||||
−0.848021 | + | 0.529963i | \(0.822206\pi\) | |||||||
\(390\) | 112.219 | − | 72.2085i | 0.287740 | − | 0.185150i | ||||
\(391\) | −5.30215 | −0.0135605 | ||||||||
\(392\) | −85.7779 | + | 85.7779i | −0.218821 | + | 0.218821i | ||||
\(393\) | 46.9226 | + | 46.9226i | 0.119396 | + | 0.119396i | ||||
\(394\) | − | 20.4161i | − | 0.0518175i | ||||||
\(395\) | 271.399 | + | 58.8781i | 0.687086 | + | 0.149058i | ||||
\(396\) | 38.8844 | 0.0981929 | ||||||||
\(397\) | 79.4123 | − | 79.4123i | 0.200031 | − | 0.200031i | −0.599982 | − | 0.800013i | \(-0.704826\pi\) |
0.800013 | + | 0.599982i | \(0.204826\pi\) | |||||||
\(398\) | 365.840 | + | 365.840i | 0.919195 | + | 0.919195i | ||||
\(399\) | 8.78454i | 0.0220164i | ||||||||
\(400\) | 91.0102 | + | 41.4383i | 0.227526 | + | 0.103596i | ||||
\(401\) | −604.333 | −1.50706 | −0.753532 | − | 0.657411i | \(-0.771651\pi\) | ||||
−0.753532 | + | 0.657411i | \(0.771651\pi\) | |||||||
\(402\) | −58.3732 | + | 58.3732i | −0.145207 | + | 0.145207i | ||||
\(403\) | −187.489 | − | 187.489i | −0.465234 | − | 0.465234i | ||||
\(404\) | 279.467i | 0.691749i | ||||||||
\(405\) | −9.54051 | + | 43.9770i | −0.0235568 | + | 0.108585i | ||||
\(406\) | −309.230 | −0.761651 | ||||||||
\(407\) | 41.3534 | − | 41.3534i | 0.101606 | − | 0.101606i | ||||
\(408\) | −3.82982 | − | 3.82982i | −0.00938681 | − | 0.00938681i | ||||
\(409\) | 31.8712i | 0.0779247i | 0.999241 | + | 0.0389624i | \(0.0124052\pi\) | ||||
−0.999241 | + | 0.0389624i | \(0.987595\pi\) | |||||||
\(410\) | −63.2058 | − | 98.2277i | −0.154161 | − | 0.239580i | ||||
\(411\) | −105.906 | −0.257678 | ||||||||
\(412\) | 196.662 | − | 196.662i | 0.477336 | − | 0.477336i | ||||
\(413\) | −425.411 | − | 425.411i | −1.03005 | − | 1.03005i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | −319.956 | + | 205.880i | −0.770978 | + | 0.496095i | ||||
\(416\) | −61.6348 | −0.148161 | ||||||||
\(417\) | −139.011 | + | 139.011i | −0.333360 | + | 0.333360i | ||||
\(418\) | 3.42887 | + | 3.42887i | 0.00820303 | + | 0.00820303i | ||||
\(419\) | 542.434i | 1.29459i | 0.762239 | + | 0.647296i | \(0.224100\pi\) | ||||
−0.762239 | + | 0.647296i | \(0.775900\pi\) | |||||||
\(420\) | −162.258 | − | 35.2007i | −0.386328 | − | 0.0838112i | ||||
\(421\) | −377.783 | −0.897347 | −0.448673 | − | 0.893696i | \(-0.648103\pi\) | ||||
−0.448673 | + | 0.893696i | \(0.648103\pi\) | |||||||
\(422\) | 52.5021 | − | 52.5021i | 0.124413 | − | 0.124413i | ||||
\(423\) | −57.5561 | − | 57.5561i | −0.136066 | − | 0.136066i | ||||
\(424\) | 31.0675i | 0.0732724i | ||||||||
\(425\) | −25.8857 | + | 9.68832i | −0.0609075 | + | 0.0227960i | ||||
\(426\) | 203.104 | 0.476770 | ||||||||
\(427\) | 256.533 | − | 256.533i | 0.600779 | − | 0.600779i | ||||
\(428\) | 22.8558 | + | 22.8558i | 0.0534013 | + | 0.0534013i | ||||
\(429\) | 122.303i | 0.285087i | ||||||||
\(430\) | 24.0807 | − | 111.000i | 0.0560015 | − | 0.258139i | ||||
\(431\) | −380.401 | −0.882600 | −0.441300 | − | 0.897360i | \(-0.645483\pi\) | ||||
−0.441300 | + | 0.897360i | \(0.645483\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −520.972 | − | 520.972i | −1.20317 | − | 1.20317i | −0.973197 | − | 0.229972i | \(-0.926137\pi\) |
−0.229972 | − | 0.973197i | \(-0.573863\pi\) | |||||||
\(434\) | 329.904i | 0.760147i | ||||||||
\(435\) | −106.895 | − | 166.125i | −0.245736 | − | 0.381896i | ||||
\(436\) | 159.652 | 0.366175 | ||||||||
\(437\) | 1.79422 | − | 1.79422i | 0.00410577 | − | 0.00410577i | ||||
\(438\) | 80.6531 | + | 80.6531i | 0.184139 | + | 0.184139i | ||||
\(439\) | 62.4039i | 0.142150i | 0.997471 | + | 0.0710750i | \(0.0226430\pi\) | ||||
−0.997471 | + | 0.0710750i | \(0.977357\pi\) | |||||||
\(440\) | −77.0739 | + | 49.5942i | −0.175168 | + | 0.112714i | ||||
\(441\) | 128.667 | 0.291761 | ||||||||
\(442\) | 12.0459 | − | 12.0459i | 0.0272531 | − | 0.0272531i | ||||
\(443\) | 3.05050 | + | 3.05050i | 0.00688601 | + | 0.00688601i | 0.710541 | − | 0.703655i | \(-0.248450\pi\) |
−0.703655 | + | 0.710541i | \(0.748450\pi\) | |||||||
\(444\) | − | 31.2603i | − | 0.0704061i | ||||||
\(445\) | −44.9924 | − | 9.76079i | −0.101107 | − | 0.0219344i | ||||
\(446\) | −41.1333 | −0.0922271 | ||||||||
\(447\) | −99.0598 | + | 99.0598i | −0.221610 | + | 0.221610i | ||||
\(448\) | 54.2259 | + | 54.2259i | 0.121040 | + | 0.121040i | ||||
\(449\) | − | 122.374i | − | 0.272547i | −0.990671 | − | 0.136274i | \(-0.956487\pi\) | ||
0.990671 | − | 0.136274i | \(-0.0435127\pi\) | |||||||
\(450\) | −37.1789 | − | 99.3364i | −0.0826199 | − | 0.220748i | ||||
\(451\) | 107.054 | 0.237371 | ||||||||
\(452\) | 161.472 | − | 161.472i | 0.357238 | − | 0.357238i | ||||
\(453\) | −67.1963 | − | 67.1963i | −0.148336 | − | 0.148336i | ||||
\(454\) | − | 466.500i | − | 1.02753i | ||||||
\(455\) | 110.716 | − | 510.347i | 0.243332 | − | 1.12164i | ||||
\(456\) | 2.59198 | 0.00568418 | ||||||||
\(457\) | 191.581 | − | 191.581i | 0.419213 | − | 0.419213i | −0.465719 | − | 0.884933i | \(-0.654204\pi\) |
0.884933 | + | 0.465719i | \(0.154204\pi\) | |||||||
\(458\) | 407.228 | + | 407.228i | 0.889143 | + | 0.889143i | ||||
\(459\) | 5.74473i | 0.0125158i | ||||||||
\(460\) | 25.9511 | + | 40.3304i | 0.0564154 | + | 0.0876748i | ||||
\(461\) | −69.9790 | −0.151798 | −0.0758992 | − | 0.997115i | \(-0.524183\pi\) | ||||
−0.0758992 | + | 0.997115i | \(0.524183\pi\) | |||||||
\(462\) | 107.601 | − | 107.601i | 0.232902 | − | 0.232902i | ||||
\(463\) | −506.603 | − | 506.603i | −1.09417 | − | 1.09417i | −0.995078 | − | 0.0990971i | \(-0.968405\pi\) |
−0.0990971 | − | 0.995078i | \(-0.531595\pi\) | |||||||
\(464\) | 91.2422i | 0.196643i | ||||||||
\(465\) | −177.231 | + | 114.042i | −0.381142 | + | 0.245251i | ||||
\(466\) | 135.628 | 0.291046 | ||||||||
\(467\) | 361.691 | − | 361.691i | 0.774498 | − | 0.774498i | −0.204391 | − | 0.978889i | \(-0.565521\pi\) |
0.978889 | + | 0.204391i | \(0.0655215\pi\) | |||||||
\(468\) | 46.2261 | + | 46.2261i | 0.0987737 | + | 0.0987737i | ||||
\(469\) | 323.061i | 0.688830i | ||||||||
\(470\) | 187.492 | + | 40.6751i | 0.398920 | + | 0.0865429i | ||||
\(471\) | −352.222 | −0.747817 | ||||||||
\(472\) | −125.523 | + | 125.523i | −0.265938 | + | 0.265938i | ||||
\(473\) | 73.6094 | + | 73.6094i | 0.155622 | + | 0.155622i | ||||
\(474\) | 136.051i | 0.287027i | ||||||||
\(475\) | 5.48112 | − | 12.0381i | 0.0115392 | − | 0.0253433i | ||||
\(476\) | −21.1958 | −0.0445289 | ||||||||
\(477\) | 23.3006 | − | 23.3006i | 0.0488483 | − | 0.0488483i | ||||
\(478\) | 126.104 | + | 126.104i | 0.263815 | + | 0.263815i | ||||
\(479\) | − | 472.746i | − | 0.986945i | −0.869762 | − | 0.493472i | \(-0.835727\pi\) | ||
0.869762 | − | 0.493472i | \(-0.164273\pi\) | |||||||
\(480\) | −10.3864 | + | 47.8761i | −0.0216383 | + | 0.0997419i | ||||
\(481\) | 98.3227 | 0.204413 | ||||||||
\(482\) | 169.295 | − | 169.295i | 0.351234 | − | 0.351234i | ||||
\(483\) | −56.3042 | − | 56.3042i | −0.116572 | − | 0.116572i | ||||
\(484\) | 158.000i | 0.326447i | ||||||||
\(485\) | −304.897 | − | 473.838i | −0.628654 | − | 0.976986i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −245.070 | + | 245.070i | −0.503224 | + | 0.503224i | −0.912438 | − | 0.409214i | \(-0.865803\pi\) |
0.409214 | + | 0.912438i | \(0.365803\pi\) | |||||||
\(488\) | −75.6931 | − | 75.6931i | −0.155109 | − | 0.155109i | ||||
\(489\) | 265.021i | 0.541965i | ||||||||
\(490\) | −255.034 | + | 164.105i | −0.520478 | + | 0.334908i | ||||
\(491\) | −89.9842 | −0.183267 | −0.0916336 | − | 0.995793i | \(-0.529209\pi\) | ||||
−0.0916336 | + | 0.995793i | \(0.529209\pi\) | |||||||
\(492\) | 40.4628 | − | 40.4628i | 0.0822415 | − | 0.0822415i | ||||
\(493\) | −17.8323 | − | 17.8323i | −0.0361711 | − | 0.0361711i | ||||
\(494\) | 8.15254i | 0.0165031i | ||||||||
\(495\) | 95.0011 | + | 20.6098i | 0.191921 | + | 0.0416360i | ||||
\(496\) | 97.3421 | 0.196254 | ||||||||
\(497\) | 562.030 | − | 562.030i | 1.13085 | − | 1.13085i | ||||
\(498\) | −131.799 | − | 131.799i | −0.264657 | − | 0.264657i | ||||
\(499\) | − | 823.542i | − | 1.65038i | −0.564852 | − | 0.825192i | \(-0.691067\pi\) | ||
0.564852 | − | 0.825192i | \(-0.308933\pi\) | |||||||
\(500\) | 200.390 | + | 149.479i | 0.400780 | + | 0.298958i | ||||
\(501\) | 436.421 | 0.871101 | ||||||||
\(502\) | 352.257 | − | 352.257i | 0.701707 | − | 0.701707i | ||||
\(503\) | −141.332 | − | 141.332i | −0.280978 | − | 0.280978i | 0.552521 | − | 0.833499i | \(-0.313666\pi\) |
−0.833499 | + | 0.552521i | \(0.813666\pi\) | |||||||
\(504\) | − | 81.3388i | − | 0.161387i | ||||||
\(505\) | −148.125 | + | 682.784i | −0.293317 | + | 1.35205i | ||||
\(506\) | −43.9544 | −0.0868665 | ||||||||
\(507\) | 61.5875 | − | 61.5875i | 0.121474 | − | 0.121474i | ||||
\(508\) | 261.511 | + | 261.511i | 0.514785 | + | 0.514785i | ||||
\(509\) | 565.134i | 1.11028i | 0.831756 | + | 0.555141i | \(0.187336\pi\) | ||||
−0.831756 | + | 0.555141i | \(0.812664\pi\) | |||||||
\(510\) | −7.32698 | − | 11.3868i | −0.0143666 | − | 0.0223271i | ||||
\(511\) | 446.367 | 0.873517 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.94399 | − | 1.94399i | −0.00378945 | − | 0.00378945i | ||||
\(514\) | − | 72.2366i | − | 0.140538i | ||||||
\(515\) | 584.716 | − | 376.243i | 1.13537 | − | 0.730568i | ||||
\(516\) | 55.6436 | 0.107836 | ||||||||
\(517\) | −124.335 | + | 124.335i | −0.240494 | + | 0.240494i | ||||
\(518\) | −86.5037 | − | 86.5037i | −0.166995 | − | 0.166995i | ||||
\(519\) | − | 29.5286i | − | 0.0568953i | ||||||
\(520\) | −150.584 | − | 32.6682i | −0.289585 | − | 0.0628234i | ||||
\(521\) | −355.537 | −0.682413 | −0.341206 | − | 0.939988i | \(-0.610835\pi\) | ||||
−0.341206 | + | 0.939988i | \(0.610835\pi\) | |||||||
\(522\) | 68.4316 | − | 68.4316i | 0.131095 | − | 0.131095i | ||||
\(523\) | −325.412 | − | 325.412i | −0.622204 | − | 0.622204i | 0.323891 | − | 0.946094i | \(-0.395009\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(524\) | − | 76.6244i | − | 0.146230i | ||||||
\(525\) | −377.766 | − | 172.002i | −0.719554 | − | 0.327624i | ||||
\(526\) | −435.272 | −0.827513 | ||||||||
\(527\) | −19.0245 | + | 19.0245i | −0.0360996 | + | 0.0360996i | ||||
\(528\) | −31.7490 | − | 31.7490i | −0.0601306 | − | 0.0601306i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | −16.4666 | + | 75.9031i | −0.0310691 | + | 0.143213i | ||||
\(531\) | 188.284 | 0.354584 | ||||||||
\(532\) | 7.17255 | − | 7.17255i | 0.0134822 | − | 0.0134822i | ||||
\(533\) | 127.267 | + | 127.267i | 0.238775 | + | 0.238775i | ||||
\(534\) | − | 22.5544i | − | 0.0422367i | ||||||
\(535\) | 43.7263 | + | 67.9546i | 0.0817313 | + | 0.127018i | ||||
\(536\) | 95.3231 | 0.177842 | ||||||||
\(537\) | 57.8971 | − | 57.8971i | 0.107816 | − | 0.107816i | ||||
\(538\) | 525.831 | + | 525.831i | 0.977381 | + | 0.977381i | ||||
\(539\) | − | 277.952i | − | 0.515680i | ||||||
\(540\) | 43.6969 | − | 28.1173i | 0.0809202 | − | 0.0520691i | ||||
\(541\) | 862.324 | 1.59394 | 0.796972 | − | 0.604016i | \(-0.206434\pi\) | ||||
0.796972 | + | 0.604016i | \(0.206434\pi\) | |||||||
\(542\) | 518.661 | − | 518.661i | 0.956939 | − | 0.956939i | ||||
\(543\) | −58.0998 | − | 58.0998i | −0.106998 | − | 0.106998i | ||||
\(544\) | 6.25407i | 0.0114965i | ||||||||
\(545\) | 390.057 | + | 84.6202i | 0.715701 | + | 0.155266i | ||||
\(546\) | 255.834 | 0.468560 | ||||||||
\(547\) | 530.824 | − | 530.824i | 0.970429 | − | 0.970429i | −0.0291465 | − | 0.999575i | \(-0.509279\pi\) |
0.999575 | + | 0.0291465i | \(0.00927895\pi\) | |||||||
\(548\) | 86.4715 | + | 86.4715i | 0.157795 | + | 0.157795i | ||||
\(549\) | 113.540i | 0.206812i | ||||||||
\(550\) | −214.591 | + | 80.3155i | −0.390165 | + | 0.146028i | ||||
\(551\) | 12.0688 | 0.0219034 | ||||||||
\(552\) | −16.6132 | + | 16.6132i | −0.0300965 | + | 0.0300965i | ||||
\(553\) | 376.480 | + | 376.480i | 0.680795 | + | 0.680795i | ||||
\(554\) | 447.234i | 0.807281i | ||||||||
\(555\) | 16.5688 | − | 76.3742i | 0.0298538 | − | 0.137611i | ||||
\(556\) | 227.004 | 0.408281 | ||||||||
\(557\) | 82.0074 | − | 82.0074i | 0.147230 | − | 0.147230i | −0.629649 | − | 0.776880i | \(-0.716801\pi\) |
0.776880 | + | 0.629649i | \(0.216801\pi\) | |||||||
\(558\) | −73.0066 | − | 73.0066i | −0.130836 | − | 0.130836i | ||||
\(559\) | 175.015i | 0.313086i | ||||||||
\(560\) | 103.742 | + | 161.224i | 0.185253 | + | 0.287900i | ||||
\(561\) | 12.4100 | 0.0221212 | ||||||||
\(562\) | 425.954 | − | 425.954i | 0.757926 | − | 0.757926i | ||||
\(563\) | −467.229 | − | 467.229i | −0.829892 | − | 0.829892i | 0.157610 | − | 0.987501i | \(-0.449621\pi\) |
−0.987501 | + | 0.157610i | \(0.949621\pi\) | |||||||
\(564\) | 93.9887i | 0.166647i | ||||||||
\(565\) | 480.087 | − | 308.918i | 0.849712 | − | 0.546758i | ||||
\(566\) | 61.1315 | 0.108006 | ||||||||
\(567\) | −61.0041 | + | 61.0041i | −0.107591 | + | 0.107591i | ||||
\(568\) | −165.834 | − | 165.834i | −0.291961 | − | 0.291961i | ||||
\(569\) | 571.773i | 1.00487i | 0.864614 | + | 0.502437i | \(0.167563\pi\) | ||||
−0.864614 | + | 0.502437i | \(0.832437\pi\) | |||||||
\(570\) | 6.33265 | + | 1.37382i | 0.0111099 | + | 0.00241022i | ||||
\(571\) | 303.885 | 0.532197 | 0.266099 | − | 0.963946i | \(-0.414265\pi\) | ||||
0.266099 | + | 0.963946i | \(0.414265\pi\) | |||||||
\(572\) | 99.8596 | − | 99.8596i | 0.174580 | − | 0.174580i | ||||
\(573\) | 155.424 | + | 155.424i | 0.271247 | + | 0.271247i | ||||
\(574\) | − | 223.938i | − | 0.390135i | ||||||
\(575\) | 42.0266 | + | 112.289i | 0.0730898 | + | 0.195285i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 334.483 | − | 334.483i | 0.579693 | − | 0.579693i | −0.355126 | − | 0.934819i | \(-0.615562\pi\) |
0.934819 | + | 0.355126i | \(0.115562\pi\) | |||||||
\(578\) | 287.778 | + | 287.778i | 0.497885 | + | 0.497885i | ||||
\(579\) | − | 364.875i | − | 0.630181i | ||||||
\(580\) | −48.3609 | + | 222.920i | −0.0833809 | + | 0.384345i | ||||
\(581\) | −729.429 | −1.25547 | ||||||||
\(582\) | 195.188 | − | 195.188i | 0.335374 | − | 0.335374i | ||||
\(583\) | −50.3350 | − | 50.3350i | −0.0863379 | − | 0.0863379i | ||||
\(584\) | − | 131.706i | − | 0.225524i | ||||||
\(585\) | 88.4370 | + | 137.439i | 0.151174 | + | 0.234939i | ||||
\(586\) | −475.099 | −0.810749 | ||||||||
\(587\) | 102.989 | − | 102.989i | 0.175450 | − | 0.175450i | −0.613919 | − | 0.789369i | \(-0.710408\pi\) |
0.789369 | + | 0.613919i | \(0.210408\pi\) | |||||||
\(588\) | −105.056 | − | 105.056i | −0.178667 | − | 0.178667i | ||||
\(589\) | − | 12.8756i | − | 0.0218601i | ||||||
\(590\) | −373.204 | + | 240.142i | −0.632548 | + | 0.407021i | ||||
\(591\) | 25.0045 | 0.0423088 | ||||||||
\(592\) | −25.5239 | + | 25.5239i | −0.0431148 | + | 0.0431148i | ||||
\(593\) | −798.294 | − | 798.294i | −1.34620 | − | 1.34620i | −0.889752 | − | 0.456444i | \(-0.849123\pi\) |
−0.456444 | − | 0.889752i | \(-0.650877\pi\) | |||||||
\(594\) | 47.6234i | 0.0801741i | ||||||||
\(595\) | −51.7848 | − | 11.2344i | −0.0870333 | − | 0.0188813i | ||||
\(596\) | 161.764 | 0.271416 | ||||||||
\(597\) | −448.060 | + | 448.060i | −0.750520 | + | 0.750520i | ||||
\(598\) | −52.2534 | − | 52.2534i | −0.0873803 | − | 0.0873803i | ||||
\(599\) | − | 176.987i | − | 0.295471i | −0.989027 | − | 0.147736i | \(-0.952802\pi\) | ||
0.989027 | − | 0.147736i | \(-0.0471984\pi\) | |||||||
\(600\) | −50.7514 | + | 111.464i | −0.0845856 | + | 0.185774i | ||||
\(601\) | −879.913 | −1.46408 | −0.732041 | − | 0.681261i | \(-0.761432\pi\) | ||||
−0.732041 | + | 0.681261i | \(0.761432\pi\) | |||||||
\(602\) | 153.977 | − | 153.977i | 0.255776 | − | 0.255776i | ||||
\(603\) | −71.4923 | − | 71.4923i | −0.118561 | − | 0.118561i | ||||
\(604\) | 109.731i | 0.181674i | ||||||||
\(605\) | −83.7446 | + | 386.021i | −0.138421 | + | 0.638052i | ||||
\(606\) | −342.275 | −0.564811 | ||||||||
\(607\) | 80.2035 | − | 80.2035i | 0.132131 | − | 0.132131i | −0.637948 | − | 0.770079i | \(-0.720217\pi\) |
0.770079 | + | 0.637948i | \(0.220217\pi\) | |||||||
\(608\) | −2.11635 | − | 2.11635i | −0.00348083 | − | 0.00348083i | ||||
\(609\) | − | 378.728i | − | 0.621886i | ||||||
\(610\) | −144.811 | − | 225.050i | −0.237396 | − | 0.368935i | ||||
\(611\) | −295.622 | −0.483832 | ||||||||
\(612\) | 4.69055 | − | 4.69055i | 0.00766430 | − | 0.00766430i | ||||
\(613\) | −619.641 | − | 619.641i | −1.01083 | − | 1.01083i | −0.999941 | − | 0.0108925i | \(-0.996533\pi\) |
−0.0108925 | − | 0.999941i | \(-0.503467\pi\) | |||||||
\(614\) | 475.825i | 0.774959i | ||||||||
\(615\) | 120.304 | − | 77.4110i | 0.195616 | − | 0.125872i | ||||
\(616\) | −175.712 | −0.285246 | ||||||||
\(617\) | −29.7434 | + | 29.7434i | −0.0482065 | + | 0.0482065i | −0.730799 | − | 0.682593i | \(-0.760852\pi\) |
0.682593 | + | 0.730799i | \(0.260852\pi\) | |||||||
\(618\) | 240.861 | + | 240.861i | 0.389743 | + | 0.389743i | ||||
\(619\) | − | 220.508i | − | 0.356233i | −0.984009 | − | 0.178116i | \(-0.943000\pi\) | ||
0.984009 | − | 0.178116i | \(-0.0570004\pi\) | |||||||
\(620\) | 237.823 | + | 51.5940i | 0.383586 | + | 0.0832162i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | −81.3114 | + | 81.3114i | −0.130726 | + | 0.130726i | ||||
\(623\) | −62.4127 | − | 62.4127i | −0.100181 | − | 0.100181i | ||||
\(624\) | − | 75.4869i | − | 0.120973i | ||||||
\(625\) | 410.358 | + | 471.414i | 0.656573 | + | 0.754262i | ||||
\(626\) | −654.400 | −1.04537 | ||||||||
\(627\) | −4.19949 | + | 4.19949i | −0.00669775 | + | 0.00669775i | ||||
\(628\) | 287.588 | + | 287.588i | 0.457942 | + | 0.457942i | ||||
\(629\) | − | 9.97678i | − | 0.0158613i | ||||||
\(630\) | 43.1119 | − | 198.724i | 0.0684315 | − | 0.315436i | ||||
\(631\) | 716.316 | 1.13521 | 0.567604 | − | 0.823302i | \(-0.307871\pi\) | ||||
0.567604 | + | 0.823302i | \(0.307871\pi\) | |||||||
\(632\) | 111.085 | − | 111.085i | 0.175767 | − | 0.175767i | ||||
\(633\) | 64.3017 | + | 64.3017i | 0.101582 | + | 0.101582i | ||||
\(634\) | − | 548.941i | − | 0.865837i | ||||||
\(635\) | 500.307 | + | 777.523i | 0.787885 | + | 1.22445i | ||||
\(636\) | −38.0498 | −0.0598267 | ||||||||
\(637\) | 330.431 | − | 330.431i | 0.518730 | − | 0.518730i | ||||
\(638\) | −147.829 | − | 147.829i | −0.231707 | − | 0.231707i | ||||
\(639\) | 248.751i | 0.389281i | ||||||||
\(640\) | 47.5711 | − | 30.6102i | 0.0743299 | − | 0.0478285i | ||||
\(641\) | −969.601 | −1.51264 | −0.756319 | − | 0.654203i | \(-0.773004\pi\) | ||||
−0.756319 | + | 0.654203i | \(0.773004\pi\) | |||||||
\(642\) | −27.9925 | + | 27.9925i | −0.0436020 | + | 0.0436020i | ||||
\(643\) | 373.341 | + | 373.341i | 0.580623 | + | 0.580623i | 0.935075 | − | 0.354451i | \(-0.115332\pi\) |
−0.354451 | + | 0.935075i | \(0.615332\pi\) | |||||||
\(644\) | 91.9445i | 0.142771i | ||||||||
\(645\) | 135.947 | + | 29.4927i | 0.210770 | + | 0.0457250i | ||||
\(646\) | 0.827236 | 0.00128055 | ||||||||
\(647\) | −695.075 | + | 695.075i | −1.07430 | + | 1.07430i | −0.0772961 | + | 0.997008i | \(0.524629\pi\) |
−0.997008 | + | 0.0772961i | \(0.975371\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | − | 406.739i | − | 0.626717i | ||||||
\(650\) | −350.587 | − | 159.628i | −0.539365 | − | 0.245581i | ||||
\(651\) | −404.048 | −0.620657 | ||||||||
\(652\) | 216.389 | − | 216.389i | 0.331885 | − | 0.331885i | ||||
\(653\) | 42.2499 | + | 42.2499i | 0.0647012 | + | 0.0647012i | 0.738717 | − | 0.674016i | \(-0.235432\pi\) |
−0.674016 | + | 0.738717i | \(0.735432\pi\) | |||||||
\(654\) | 195.533i | 0.298981i | ||||||||
\(655\) | 40.6131 | − | 187.206i | 0.0620047 | − | 0.285811i | ||||
\(656\) | −66.0755 | −0.100725 | ||||||||
\(657\) | −98.7795 | + | 98.7795i | −0.150349 | + | 0.150349i | ||||
\(658\) | 260.086 | + | 260.086i | 0.395267 | + | 0.395267i | ||||
\(659\) | 961.226i | 1.45861i | 0.684187 | + | 0.729307i | \(0.260157\pi\) | ||||
−0.684187 | + | 0.729307i | \(0.739843\pi\) | |||||||
\(660\) | −60.7402 | − | 94.3959i | −0.0920306 | − | 0.143024i | ||||
\(661\) | 163.994 | 0.248100 | 0.124050 | − | 0.992276i | \(-0.460412\pi\) | ||||
0.124050 | + | 0.992276i | \(0.460412\pi\) | |||||||
\(662\) | 209.454 | − | 209.454i | 0.316396 | − | 0.316396i | ||||
\(663\) | 14.7531 | + | 14.7531i | 0.0222521 | + | 0.0222521i | ||||
\(664\) | 215.227i | 0.324137i | ||||||||
\(665\) | 21.3254 | − | 13.7221i | 0.0320683 | − | 0.0206347i | ||||
\(666\) | 38.2859 | 0.0574864 | ||||||||
\(667\) | −77.3543 | + | 77.3543i | −0.115973 | + | 0.115973i | ||||
\(668\) | −356.337 | − | 356.337i | −0.533438 | − | 0.533438i | ||||
\(669\) | − | 50.3778i | − | 0.0753031i | ||||||
\(670\) | 232.890 | + | 50.5239i | 0.347598 | + | 0.0754088i | ||||
\(671\) | 245.273 | 0.365534 | ||||||||
\(672\) | −66.4129 | + | 66.4129i | −0.0988287 | + | 0.0988287i | ||||
\(673\) | 171.550 | + | 171.550i | 0.254904 | + | 0.254904i | 0.822978 | − | 0.568074i | \(-0.192311\pi\) |
−0.568074 | + | 0.822978i | \(0.692311\pi\) | |||||||
\(674\) | 534.149i | 0.792506i | ||||||||
\(675\) | 121.662 | − | 45.5347i | 0.180240 | − | 0.0674588i | ||||
\(676\) | −100.572 | −0.148775 | ||||||||
\(677\) | −164.860 | + | 164.860i | −0.243516 | + | 0.243516i | −0.818303 | − | 0.574787i | \(-0.805085\pi\) |
0.574787 | + | 0.818303i | \(0.305085\pi\) | |||||||
\(678\) | 197.762 | + | 197.762i | 0.291684 | + | 0.291684i | ||||
\(679\) | − | 1080.25i | − | 1.59094i | ||||||
\(680\) | −3.31483 | + | 15.2797i | −0.00487475 | + | 0.0224702i | ||||
\(681\) | 571.343 | 0.838977 | ||||||||
\(682\) | −157.712 | + | 157.712i | −0.231249 | + | 0.231249i | ||||
\(683\) | 16.9389 | + | 16.9389i | 0.0248007 | + | 0.0248007i | 0.719398 | − | 0.694598i | \(-0.244418\pi\) |
−0.694598 | + | 0.719398i | \(0.744418\pi\) | |||||||
\(684\) | 3.17452i | 0.00464111i | ||||||||
\(685\) | 165.432 | + | 257.097i | 0.241507 | + | 0.375324i | ||||
\(686\) | 82.8445 | 0.120765 | ||||||||
\(687\) | −498.750 | + | 498.750i | −0.725982 | + | 0.725982i | ||||
\(688\) | −45.4328 | − | 45.4328i | −0.0660360 | − | 0.0660360i | ||||
\(689\) | − | 119.677i | − | 0.173697i | ||||||
\(690\) | −49.3944 | + | 31.7835i | −0.0715862 | + | 0.0460630i | ||||
\(691\) | 1270.25 | 1.83828 | 0.919141 | − | 0.393928i | \(-0.128884\pi\) | ||||
0.919141 | + | 0.393928i | \(0.128884\pi\) | |||||||
\(692\) | −24.1100 | + | 24.1100i | −0.0348411 | + | 0.0348411i | ||||
\(693\) | 131.784 | + | 131.784i | 0.190164 | + | 0.190164i | ||||
\(694\) | − | 604.754i | − | 0.871403i | ||||||
\(695\) | 554.609 | + | 120.319i | 0.797999 | + | 0.173120i | ||||
\(696\) | −111.748 | −0.160558 | ||||||||
\(697\) | 12.9138 | − | 12.9138i | 0.0185276 | − | 0.0185276i | ||||
\(698\) | 38.7883 | + | 38.7883i | 0.0555706 | + | 0.0555706i | ||||
\(699\) | 166.109i | 0.237638i | ||||||||
\(700\) | 168.005 | + | 448.884i | 0.240007 | + | 0.641263i | ||||
\(701\) | −1394.68 | −1.98956 | −0.994781 | − | 0.102031i | \(-0.967466\pi\) | ||||
−0.994781 | + | 0.102031i | \(0.967466\pi\) | |||||||
\(702\) | −56.6152 | + | 56.6152i | −0.0806484 | + | 0.0806484i | ||||
\(703\) | 3.37609 | + | 3.37609i | 0.00480241 | + | 0.00480241i | ||||
\(704\) | 51.8458i | 0.0736446i | ||||||||
\(705\) | −49.8167 | + | 229.630i | −0.0706620 | + | 0.325717i | ||||
\(706\) | 456.850 | 0.647096 | ||||||||
\(707\) | −947.145 | + | 947.145i | −1.33967 | + | 1.33967i | ||||
\(708\) | −153.733 | − | 153.733i | −0.217137 | − | 0.217137i | ||||
\(709\) | 842.555i | 1.18837i | 0.804328 | + | 0.594185i | \(0.202525\pi\) | ||||
−0.804328 | + | 0.594185i | \(0.797475\pi\) | |||||||
\(710\) | −317.263 | − | 493.057i | −0.446850 | − | 0.694446i | ||||
\(711\) | −166.627 | −0.234356 | ||||||||
\(712\) | −18.4156 | + | 18.4156i | −0.0258646 | + | 0.0258646i | ||||
\(713\) | 82.5258 | + | 82.5258i | 0.115744 | + | 0.115744i | ||||
\(714\) | − | 25.9594i | − | 0.0363577i | ||||||
\(715\) | 296.902 | − | 191.045i | 0.415248 | − | 0.267196i | ||||
\(716\) | −94.5456 | −0.132047 | ||||||||
\(717\) | −154.445 | + | 154.445i | −0.215404 | + | 0.215404i | ||||
\(718\) | −572.493 | − | 572.493i | −0.797344 | − | 0.797344i | ||||
\(719\) | − | 685.162i | − | 0.952937i | −0.879191 | − | 0.476469i | \(-0.841917\pi\) | ||
0.879191 | − | 0.476469i | \(-0.158083\pi\) | |||||||
\(720\) | −58.6360 | − | 12.7207i | −0.0814389 | − | 0.0176676i | ||||
\(721\) | 1333.02 | 1.84885 | ||||||||
\(722\) | 360.720 | − | 360.720i | 0.499612 | − | 0.499612i | ||||
\(723\) | 207.343 | + | 207.343i | 0.286781 | + | 0.286781i | ||||
\(724\) | 94.8765i | 0.131045i | ||||||||
\(725\) | −236.308 | + | 518.998i | −0.325942 | + | 0.715860i | ||||
\(726\) | −193.510 | −0.266543 | ||||||||
\(727\) | 752.841 | − | 752.841i | 1.03554 | − | 1.03554i | 0.0361997 | − | 0.999345i | \(-0.488475\pi\) |
0.999345 | − | 0.0361997i | \(-0.0115252\pi\) | |||||||
\(728\) | −208.888 | − | 208.888i | −0.286933 | − | 0.286933i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 69.8079 | − | 321.780i | 0.0956272 | − | 0.440794i | ||||
\(731\) | 17.7587 | 0.0242938 | ||||||||
\(732\) | 92.7047 | − | 92.7047i | 0.126646 | − | 0.126646i | ||||
\(733\) | −232.917 | − | 232.917i | −0.317758 | − | 0.317758i | 0.530148 | − | 0.847905i | \(-0.322137\pi\) |
−0.847905 | + | 0.530148i | \(0.822137\pi\) | |||||||
\(734\) | 312.501i | 0.425750i | ||||||||
\(735\) | −200.987 | − | 312.352i | −0.273451 | − | 0.424969i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −154.441 | + | 154.441i | −0.209553 | + | 0.209553i | ||||
\(738\) | 49.5566 | + | 49.5566i | 0.0671499 | + | 0.0671499i | ||||
\(739\) | 135.488i | 0.183339i | 0.995789 | + | 0.0916696i | \(0.0292204\pi\) | ||||
−0.995789 | + | 0.0916696i | \(0.970780\pi\) | |||||||
\(740\) | −75.8877 | + | 48.8309i | −0.102551 | + | 0.0659877i | ||||
\(741\) | −9.98478 | −0.0134747 | ||||||||
\(742\) | −105.291 | + | 105.291i | −0.141902 | + | 0.141902i | ||||
\(743\) | 726.590 | + | 726.590i | 0.977914 | + | 0.977914i | 0.999761 | − | 0.0218472i | \(-0.00695474\pi\) |
−0.0218472 | + | 0.999761i | \(0.506955\pi\) | |||||||
\(744\) | 119.219i | 0.160241i | ||||||||
\(745\) | 395.217 | + | 85.7395i | 0.530492 | + | 0.115087i | ||||
\(746\) | 29.5768 | 0.0396472 | ||||||||
\(747\) | 161.420 | − | 161.420i | 0.216091 | − | 0.216091i | ||||
\(748\) | −10.1327 | − | 10.1327i | −0.0135464 | − | 0.0135464i | ||||
\(749\) | 154.922i | 0.206838i | ||||||||
\(750\) | −183.073 | + | 245.426i | −0.244098 | + | 0.327235i | ||||
\(751\) | −1008.88 | −1.34339 | −0.671694 | − | 0.740829i | \(-0.734433\pi\) | ||||
−0.671694 | + | 0.740829i | \(0.734433\pi\) | |||||||
\(752\) | 76.7415 | − | 76.7415i | 0.102050 | − | 0.102050i | ||||
\(753\) | 431.425 | + | 431.425i | 0.572941 | + | 0.572941i | ||||
\(754\) | − | 351.481i | − | 0.466155i | ||||||
\(755\) | −58.1605 | + | 268.091i | −0.0770338 | + | 0.355088i | ||||
\(756\) | 99.6193 | 0.131772 | ||||||||
\(757\) | 570.746 | − | 570.746i | 0.753958 | − | 0.753958i | −0.221257 | − | 0.975215i | \(-0.571016\pi\) |
0.975215 | + | 0.221257i | \(0.0710161\pi\) | |||||||
\(758\) | −39.4302 | − | 39.4302i | −0.0520188 | − | 0.0520188i | ||||
\(759\) | − | 53.8330i | − | 0.0709262i | ||||||
\(760\) | −4.04887 | − | 6.29231i | −0.00532746 | − | 0.00827936i | ||||
\(761\) | −1183.62 | −1.55535 | −0.777675 | − | 0.628667i | \(-0.783601\pi\) | ||||
−0.777675 | + | 0.628667i | \(0.783601\pi\) | |||||||
\(762\) | −320.284 | + | 320.284i | −0.420320 | + | 0.420320i | ||||
\(763\) | 541.080 | + | 541.080i | 0.709148 | + | 0.709148i | ||||
\(764\) | − | 253.807i | − | 0.332208i | ||||||
\(765\) | 13.9459 | − | 8.97368i | 0.0182300 | − | 0.0117303i | ||||
\(766\) | −525.954 | −0.686624 | ||||||||
\(767\) | 483.535 | − | 483.535i | 0.630424 | − | 0.630424i | ||||
\(768\) | 19.5959 | + | 19.5959i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | 363.068i | 0.472130i | 0.971737 | + | 0.236065i | \(0.0758578\pi\) | ||||
−0.971737 | + | 0.236065i | \(0.924142\pi\) | |||||||
\(770\) | −429.293 | − | 93.1321i | −0.557523 | − | 0.120951i | ||||
\(771\) | 88.4714 | 0.114749 | ||||||||
\(772\) | −297.919 | + | 297.919i | −0.385905 | + | 0.385905i | ||||
\(773\) | −1014.90 | − | 1014.90i | −1.31293 | − | 1.31293i | −0.919242 | − | 0.393693i | \(-0.871197\pi\) |
−0.393693 | − | 0.919242i | \(-0.628803\pi\) | |||||||
\(774\) | 68.1492i | 0.0880480i | ||||||||
\(775\) | 553.695 | + | 252.106i | 0.714446 | + | 0.325298i | ||||
\(776\) | −318.740 | −0.410747 | ||||||||
\(777\) | 105.945 | − | 105.945i | 0.136351 | − | 0.136351i | ||||
\(778\) | 412.312 | + | 412.312i | 0.529963 | + | 0.529963i | ||||
\(779\) | 8.73991i | 0.0112194i | ||||||||
\(780\) | 40.0102 | − | 184.427i | 0.0512951 | − | 0.236445i | ||||
\(781\) | 537.362 | 0.688044 | ||||||||
\(782\) | −5.30215 | + | 5.30215i | −0.00678024 | + | 0.00678024i | ||||
\(783\) | 83.8113 | + | 83.8113i | 0.107039 | + | 0.107039i | ||||
\(784\) | 171.556i | 0.218821i | ||||||||
\(785\) | 550.196 | + | 855.055i | 0.700886 | + | 1.08924i | ||||
\(786\) | 93.8453 | 0.119396 | ||||||||
\(787\) | −225.596 | + | 225.596i | −0.286653 | + | 0.286653i | −0.835755 | − | 0.549102i | \(-0.814970\pi\) |
0.549102 | + | 0.835755i | \(0.314970\pi\) | |||||||
\(788\) | −20.4161 | − | 20.4161i | −0.0259088 | − | 0.0259088i | ||||
\(789\) | − | 533.097i | − | 0.675661i | ||||||
\(790\) | 330.277 | − | 212.521i | 0.418072 | − | 0.269014i | ||||
\(791\) | 1094.49 | 1.38368 | ||||||||
\(792\) | 38.8844 | − | 38.8844i | 0.0490964 | − | 0.0490964i | ||||
\(793\) | 291.583 | + | 291.583i | 0.367696 | + | 0.367696i | ||||
\(794\) | − | 158.825i | − | 0.200031i | ||||||
\(795\) | −92.9620 | − | 20.1674i | −0.116933 | − | 0.0253679i | ||||
\(796\) | 731.679 | 0.919195 | ||||||||
\(797\) | −991.681 | + | 991.681i | −1.24427 | + | 1.24427i | −0.286054 | + | 0.958213i | \(0.592344\pi\) |
−0.958213 | + | 0.286054i | \(0.907656\pi\) | |||||||
\(798\) | 8.78454 | + | 8.78454i | 0.0110082 | + | 0.0110082i | ||||
\(799\) | 29.9967i | 0.0375428i | ||||||||
\(800\) | 132.449 | − | 49.5719i | 0.165561 | − | 0.0619649i | ||||
\(801\) | 27.6234 | 0.0344862 | ||||||||
\(802\) | −604.333 | + | 604.333i | −0.753532 | + | 0.753532i | ||||
\(803\) | 213.388 | + | 213.388i | 0.265738 | + | 0.265738i | ||||
\(804\) | 116.746i | 0.145207i | ||||||||
\(805\) | −48.7331 | + | 224.636i | −0.0605381 | + | 0.279051i | ||||
\(806\) | −374.979 | −0.465234 | ||||||||
\(807\) | −644.009 | + | 644.009i | −0.798028 | + | 0.798028i | ||||
\(808\) | 279.467 | + | 279.467i | 0.345875 | + | 0.345875i | ||||
\(809\) | − | 846.880i | − | 1.04682i | −0.852080 | − | 0.523412i | \(-0.824659\pi\) | ||
0.852080 | − | 0.523412i | \(-0.175341\pi\) | |||||||
\(810\) | 34.4365 | + | 53.5175i | 0.0425142 | + | 0.0660710i | ||||
\(811\) | −703.466 | −0.867405 | −0.433703 | − | 0.901056i | \(-0.642793\pi\) | ||||
−0.433703 | + | 0.901056i | \(0.642793\pi\) | |||||||
\(812\) | −309.230 | + | 309.230i | −0.380826 | + | 0.380826i | ||||
\(813\) | 635.227 | + | 635.227i | 0.781337 | + | 0.781337i | ||||
\(814\) | − | 82.7069i | − | 0.101606i | ||||||
\(815\) | 643.366 | − | 413.982i | 0.789406 | − | 0.507953i | ||||
\(816\) | −7.65964 | −0.00938681 | ||||||||
\(817\) | −6.00947 | + | 6.00947i | −0.00735553 | + | 0.00735553i | ||||
\(818\) | 31.8712 | + | 31.8712i | 0.0389624 | + | 0.0389624i | ||||
\(819\) | 313.331i | 0.382578i | ||||||||
\(820\) | −161.433 | − | 35.0219i | −0.196870 | − | 0.0427096i | ||||
\(821\) | −252.059 | −0.307015 | −0.153507 | − | 0.988147i | \(-0.549057\pi\) | ||||
−0.153507 | + | 0.988147i | \(0.549057\pi\) | |||||||
\(822\) | −105.906 | + | 105.906i | −0.128839 | + | 0.128839i | ||||
\(823\) | 511.780 | + | 511.780i | 0.621847 | + | 0.621847i | 0.946003 | − | 0.324156i | \(-0.105080\pi\) |
−0.324156 | + | 0.946003i | \(0.605080\pi\) | |||||||
\(824\) | − | 393.325i | − | 0.477336i | ||||||
\(825\) | −98.3660 | − | 262.819i | −0.119232 | − | 0.318568i | ||||
\(826\) | −850.822 | −1.03005 | ||||||||
\(827\) | 169.581 | − | 169.581i | 0.205055 | − | 0.205055i | −0.597107 | − | 0.802162i | \(-0.703683\pi\) |
0.802162 | + | 0.597107i | \(0.203683\pi\) | |||||||
\(828\) | −20.3470 | − | 20.3470i | −0.0245737 | − | 0.0245737i | ||||
\(829\) | 772.576i | 0.931938i | 0.884801 | + | 0.465969i | \(0.154294\pi\) | ||||
−0.884801 | + | 0.465969i | \(0.845706\pi\) | |||||||
\(830\) | −114.076 | + | 525.835i | −0.137441 | + | 0.633537i | ||||
\(831\) | −547.747 | −0.659142 | ||||||||
\(832\) | −61.6348 | + | 61.6348i | −0.0740803 | + | 0.0740803i | ||||
\(833\) | −33.5288 | − | 33.5288i | −0.0402507 | − | 0.0402507i | ||||
\(834\) | 278.022i | 0.333360i | ||||||||
\(835\) | −681.722 | − | 1059.46i | −0.816433 | − | 1.26881i | ||||
\(836\) | 6.85773 | 0.00820303 | ||||||||
\(837\) | 89.4144 | − | 89.4144i | 0.106827 | − | 0.106827i | ||||
\(838\) | 542.434 | + | 542.434i | 0.647296 | + | 0.647296i | ||||
\(839\) | − | 252.116i | − | 0.300496i | −0.988648 | − | 0.150248i | \(-0.951993\pi\) | ||
0.988648 | − | 0.150248i | \(-0.0480072\pi\) | |||||||
\(840\) | −197.458 | + | 127.057i | −0.235070 | + | 0.151258i | ||||
\(841\) | 320.679 | 0.381307 | ||||||||
\(842\) | −377.783 | + | 377.783i | −0.448673 | + | 0.448673i | ||||
\(843\) | 521.685 | + | 521.685i | 0.618844 | + | 0.618844i | ||||
\(844\) | − | 105.004i | − | 0.124413i | ||||||
\(845\) | −245.714 | − | 53.3060i | −0.290786 | − | 0.0630840i | ||||
\(846\) | −115.112 | −0.136066 | ||||||||
\(847\) | −535.482 | + | 535.482i | −0.632210 | + | 0.632210i | ||||
\(848\) | 31.0675 | + | 31.0675i | 0.0366362 | + | 0.0366362i | ||||
\(849\) | 74.8705i | 0.0881867i | ||||||||
\(850\) | −16.1974 | + | 35.5740i | −0.0190557 | + | 0.0418518i | ||||
\(851\) | −43.2780 | −0.0508554 | ||||||||
\(852\) | 203.104 | − | 203.104i | 0.238385 | − | 0.238385i | ||||
\(853\) | −758.628 | − | 758.628i | −0.889365 | − | 0.889365i | 0.105097 | − | 0.994462i | \(-0.466485\pi\) |
−0.994462 | + | 0.105097i | \(0.966485\pi\) | |||||||
\(854\) | − | 513.066i | − | 0.600779i | ||||||
\(855\) | −1.68258 | + | 7.75588i | −0.00196794 | + | 0.00907121i | ||||
\(856\) | 45.7115 | 0.0534013 | ||||||||
\(857\) | −303.385 | + | 303.385i | −0.354008 | + | 0.354008i | −0.861598 | − | 0.507591i | \(-0.830536\pi\) |
0.507591 | + | 0.861598i | \(0.330536\pi\) | |||||||
\(858\) | 122.303 | + | 122.303i | 0.142544 | + | 0.142544i | ||||
\(859\) | − | 1629.59i | − | 1.89707i | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||
0.316668 | − | 0.948536i | \(-0.397436\pi\) | |||||||
\(860\) | −86.9193 | − | 135.081i | −0.101069 | − | 0.157070i | ||||
\(861\) | 274.266 | 0.318544 | ||||||||
\(862\) | −380.401 | + | 380.401i | −0.441300 | + | 0.441300i | ||||
\(863\) | −545.327 | − | 545.327i | −0.631896 | − | 0.631896i | 0.316647 | − | 0.948543i | \(-0.397443\pi\) |
−0.948543 | + | 0.316647i | \(0.897443\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | −71.6839 | + | 46.1259i | −0.0828715 | + | 0.0533247i | ||||
\(866\) | −1041.94 | −1.20317 | ||||||||
\(867\) | −352.454 | + | 352.454i | −0.406522 | + | 0.406522i | ||||
\(868\) | 329.904 | + | 329.904i | 0.380073 | + | 0.380073i | ||||
\(869\) | 359.955i | 0.414218i | ||||||||
\(870\) | −273.020 | − | 59.2298i | −0.313816 | − | 0.0680802i | ||||
\(871\) | −367.201 | −0.421586 | ||||||||
\(872\) | 159.652 | − | 159.652i | 0.183087 | − | 0.183087i | ||||
\(873\) | 239.055 | + | 239.055i | 0.273832 | + | 0.273832i | ||||
\(874\) | − | 3.58844i | − | 0.00410577i | ||||||
\(875\) | 172.544 | + | 1185.75i | 0.197193 | + | 1.35514i | ||||
\(876\) | 161.306 | 0.184139 | ||||||||
\(877\) | −229.151 | + | 229.151i | −0.261290 | + | 0.261290i | −0.825578 | − | 0.564288i | \(-0.809151\pi\) |
0.564288 | + | 0.825578i | \(0.309151\pi\) | |||||||
\(878\) | 62.4039 | + | 62.4039i | 0.0710750 | + | 0.0710750i | ||||
\(879\) | − | 581.875i | − | 0.661974i | ||||||
\(880\) | −27.4797 | + | 126.668i | −0.0312270 | + | 0.143941i | ||||
\(881\) | −1029.46 | −1.16851 | −0.584254 | − | 0.811571i | \(-0.698613\pi\) | ||||
−0.584254 | + | 0.811571i | \(0.698613\pi\) | |||||||
\(882\) | 128.667 | − | 128.667i | 0.145881 | − | 0.145881i | ||||
\(883\) | 1211.81 | + | 1211.81i | 1.37238 | + | 1.37238i | 0.856906 | + | 0.515473i | \(0.172384\pi\) |
0.515473 | + | 0.856906i | \(0.327616\pi\) | |||||||
\(884\) | − | 24.0918i | − | 0.0272531i | ||||||
\(885\) | −294.113 | − | 457.079i | −0.332331 | − | 0.516474i | ||||
\(886\) | 6.10101 | 0.00688601 | ||||||||
\(887\) | 653.892 | − | 653.892i | 0.737196 | − | 0.737196i | −0.234839 | − | 0.972034i | \(-0.575456\pi\) |
0.972034 | + | 0.234839i | \(0.0754562\pi\) | |||||||
\(888\) | −31.2603 | − | 31.2603i | −0.0352031 | − | 0.0352031i | ||||
\(889\) | 1772.58i | 1.99391i | ||||||||
\(890\) | −54.7532 | + | 35.2316i | −0.0615205 | + | 0.0395861i | ||||
\(891\) | −58.3266 | −0.0654619 | ||||||||
\(892\) | −41.1333 | + | 41.1333i | −0.0461136 | + | 0.0461136i | ||||
\(893\) | −10.1507 | − | 10.1507i | −0.0113670 | − | 0.0113670i | ||||
\(894\) | 198.120i | 0.221610i | ||||||||
\(895\) | −230.991 | − | 50.1118i | −0.258090 | − | 0.0559909i | ||||
\(896\) | 108.452 | 0.121040 | ||||||||
\(897\) | 63.9971 | − | 63.9971i | 0.0713457 | − | 0.0713457i | ||||
\(898\) | −122.374 | − | 122.374i | −0.136274 | − | 0.136274i | ||||
\(899\) | 555.106i | 0.617471i | ||||||||
\(900\) | −136.515 | − | 62.1575i | −0.151684 | − | 0.0690639i | ||||
\(901\) | −12.1436 | −0.0134780 | ||||||||
\(902\) | 107.054 | − | 107.054i | 0.118685 | − | 0.118685i | ||||
\(903\) | 188.583 | + | 188.583i | 0.208840 | + | 0.208840i | ||||
\(904\) | − | 322.943i | − | 0.357238i | ||||||
\(905\) | −50.2872 | + | 231.799i | −0.0555660 | + | 0.256132i | ||||
\(906\) | −134.393 | −0.148336 | ||||||||
\(907\) | −494.427 | + | 494.427i | −0.545123 | + | 0.545123i | −0.925026 | − | 0.379903i | \(-0.875957\pi\) |
0.379903 | + | 0.925026i | \(0.375957\pi\) | |||||||
\(908\) | −466.500 | − | 466.500i | −0.513767 | − | 0.513767i | ||||
\(909\) | − | 419.200i | − | 0.461166i | ||||||
\(910\) | −399.631 | − | 621.064i | −0.439155 | − | 0.682488i | ||||
\(911\) | 1357.22 | 1.48982 | 0.744909 | − | 0.667167i | \(-0.232493\pi\) | ||||
0.744909 | + | 0.667167i | \(0.232493\pi\) | |||||||
\(912\) | 2.59198 | − | 2.59198i | 0.00284209 | − | 0.00284209i | ||||
\(913\) | −348.707 | − | 348.707i | −0.381935 | − | 0.381935i | ||||
\(914\) | − | 383.161i | − | 0.419213i | ||||||
\(915\) | 275.629 | − | 177.357i | 0.301234 | − | 0.193833i | ||||
\(916\) | 814.455 | 0.889143 | ||||||||
\(917\) | 259.689 | − | 259.689i | 0.283194 | − | 0.283194i | ||||
\(918\) | 5.74473 | + | 5.74473i | 0.00625788 | + | 0.00625788i | ||||
\(919\) | 34.5757i | 0.0376232i | 0.999823 | + | 0.0188116i | \(0.00598828\pi\) | ||||
−0.999823 | + | 0.0188116i | \(0.994012\pi\) | |||||||
\(920\) | 66.2815 | + | 14.3793i | 0.0720451 | + | 0.0156297i | ||||
\(921\) | −582.764 | −0.632751 | ||||||||
\(922\) | −69.9790 | + | 69.9790i | −0.0758992 | + | 0.0758992i | ||||
\(923\) | 638.821 | + | 638.821i | 0.692114 | + | 0.692114i | ||||
\(924\) | − | 215.202i | − | 0.232902i | ||||||
\(925\) | −211.288 | + | 79.0794i | −0.228420 | + | 0.0854913i | ||||
\(926\) | −1013.21 | −1.09417 | ||||||||
\(927\) | −294.994 | + | 294.994i | −0.318224 | + | 0.318224i | ||||
\(928\) | 91.2422 | + | 91.2422i | 0.0983213 | + | 0.0983213i | ||||
\(929\) | 317.252i | 0.341499i | 0.985314 | + | 0.170749i | \(0.0546189\pi\) | ||||
−0.985314 | + | 0.170749i | \(0.945381\pi\) | |||||||
\(930\) | −63.1895 | + | 291.273i | −0.0679457 | + | 0.313196i | ||||
\(931\) | 22.6920 | 0.0243737 | ||||||||
\(932\) | 135.628 | − | 135.628i | 0.145523 | − | 0.145523i | ||||
\(933\) | −99.5858 | − | 99.5858i | −0.106737 | − | 0.106737i | ||||
\(934\) | − | 723.381i | − | 0.774498i | ||||||
\(935\) | −19.3853 | − | 30.1266i | −0.0207330 | − | 0.0322210i | ||||
\(936\) | 92.4522 | 0.0987737 | ||||||||
\(937\) | −1061.58 | + | 1061.58i | −1.13296 | + | 1.13296i | −0.143279 | + | 0.989682i | \(0.545765\pi\) |
−0.989682 | + | 0.143279i | \(0.954235\pi\) | |||||||
\(938\) | 323.061 | + | 323.061i | 0.344415 | + | 0.344415i | ||||
\(939\) | − | 801.473i | − | 0.853539i | ||||||
\(940\) | 228.168 | − | 146.817i | 0.242731 | − | 0.156189i | ||||
\(941\) | 615.031 | 0.653593 | 0.326797 | − | 0.945095i | \(-0.394031\pi\) | ||||
0.326797 | + | 0.945095i | \(0.394031\pi\) | |||||||
\(942\) | −352.222 | + | 352.222i | −0.373908 | + | 0.373908i | ||||
\(943\) | −56.0182 | − | 56.0182i | −0.0594042 | − | 0.0594042i | ||||
\(944\) | 251.045i | 0.265938i | ||||||||
\(945\) | 243.387 | + | 52.8010i | 0.257552 | + | 0.0558741i | ||||
\(946\) | 147.219 | 0.155622 | ||||||||
\(947\) | −560.762 | + | 560.762i | −0.592146 | + | 0.592146i | −0.938211 | − | 0.346065i | \(-0.887518\pi\) |
0.346065 | + | 0.938211i | \(0.387518\pi\) | |||||||
\(948\) | 136.051 | + | 136.051i | 0.143513 | + | 0.143513i | ||||
\(949\) | 507.354i | 0.534620i | ||||||||
\(950\) | −6.55696 | − | 17.5192i | −0.00690206 | − | 0.0184413i | ||||
\(951\) | 672.312 | 0.706953 | ||||||||
\(952\) | −21.1958 | + | 21.1958i | −0.0222645 | + | 0.0222645i | ||||
\(953\) | 576.041 | + | 576.041i | 0.604450 | + | 0.604450i | 0.941490 | − | 0.337040i | \(-0.109426\pi\) |
−0.337040 | + | 0.941490i | \(0.609426\pi\) | |||||||
\(954\) | − | 46.6013i | − | 0.0488483i | ||||||
\(955\) | 134.525 | − | 620.093i | 0.140864 | − | 0.649312i | ||||
\(956\) | 252.207 | 0.263815 | ||||||||
\(957\) | 181.053 | − | 181.053i | 0.189188 | − | 0.189188i | ||||
\(958\) | −472.746 | − | 472.746i | −0.493472 | − | 0.493472i | ||||
\(959\) | 586.124i | 0.611183i | ||||||||
\(960\) | 37.4897 | + | 58.2625i | 0.0390518 | + | 0.0606901i | ||||
\(961\) | −368.782 | −0.383749 | ||||||||
\(962\) | 98.3227 | − | 98.3227i | 0.102207 | − | 0.102207i | ||||
\(963\) | −34.2836 | − | 34.2836i | −0.0356009 | − | 0.0356009i | ||||
\(964\) | − | 338.589i | − | 0.351234i | ||||||
\(965\) | −885.772 | + | 569.961i | −0.917898 | + | 0.590633i | ||||
\(966\) | −112.608 | −0.116572 | ||||||||
\(967\) | −1250.23 | + | 1250.23i | −1.29290 | + | 1.29290i | −0.359910 | + | 0.932987i | \(0.617193\pi\) |
−0.932987 | + | 0.359910i | \(0.882807\pi\) | |||||||
\(968\) | 158.000 | + | 158.000i | 0.163223 | + | 0.163223i | ||||
\(969\) | 1.01315i | 0.00104557i | ||||||||
\(970\) | −778.735 | − | 168.941i | −0.802820 | − | 0.174166i | ||||
\(971\) | 1207.50 | 1.24357 | 0.621784 | − | 0.783189i | \(-0.286408\pi\) | ||||
0.621784 | + | 0.783189i | \(0.286408\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 769.344 | + | 769.344i | 0.790692 | + | 0.790692i | ||||
\(974\) | 490.141i | 0.503224i | ||||||||
\(975\) | 195.503 | − | 429.380i | 0.200516 | − | 0.440390i | ||||
\(976\) | −151.386 | −0.155109 | ||||||||
\(977\) | −873.381 | + | 873.381i | −0.893942 | + | 0.893942i | −0.994892 | − | 0.100950i | \(-0.967812\pi\) |
0.100950 | + | 0.994892i | \(0.467812\pi\) | |||||||
\(978\) | 265.021 | + | 265.021i | 0.270983 | + | 0.270983i | ||||
\(979\) | − | 59.6733i | − | 0.0609533i | ||||||
\(980\) | −90.9294 | + | 419.140i | −0.0927851 | + | 0.427693i | ||||
\(981\) | −239.478 | −0.244117 | ||||||||
\(982\) | −89.9842 | + | 89.9842i | −0.0916336 | + | 0.0916336i | ||||
\(983\) | 1034.87 | + | 1034.87i | 1.05277 | + | 1.05277i | 0.998528 | + | 0.0542382i | \(0.0172730\pi\) |
0.0542382 | + | 0.998528i | \(0.482727\pi\) | |||||||
\(984\) | − | 80.9256i | − | 0.0822415i | ||||||
\(985\) | −39.0589 | − | 60.7011i | −0.0396537 | − | 0.0616255i | ||||
\(986\) | −35.6647 | −0.0361711 | ||||||||
\(987\) | −318.539 | + | 318.539i | −0.322734 | + | 0.322734i | ||||
\(988\) | 8.15254 | + | 8.15254i | 0.00825155 | + | 0.00825155i | ||||
\(989\) | − | 77.0350i | − | 0.0778918i | ||||||
\(990\) | 115.611 | − | 74.3912i | 0.116779 | − | 0.0751427i | ||||
\(991\) | −665.229 | −0.671270 | −0.335635 | − | 0.941992i | \(-0.608951\pi\) | ||||
−0.335635 | + | 0.941992i | \(0.608951\pi\) | |||||||
\(992\) | 97.3421 | − | 97.3421i | 0.0981271 | − | 0.0981271i | ||||
\(993\) | 256.528 | + | 256.528i | 0.258336 | + | 0.258336i | ||||
\(994\) | − | 1124.06i | − | 1.13085i | ||||||
\(995\) | 1787.62 | + | 387.811i | 1.79660 | + | 0.389759i | ||||
\(996\) | −263.598 | −0.264657 | ||||||||
\(997\) | 802.959 | − | 802.959i | 0.805375 | − | 0.805375i | −0.178555 | − | 0.983930i | \(-0.557142\pi\) |
0.983930 | + | 0.178555i | \(0.0571423\pi\) | |||||||
\(998\) | −823.542 | − | 823.542i | −0.825192 | − | 0.825192i | ||||
\(999\) | 46.8905i | 0.0469374i |
(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 | 690.3.k.a.553.20 | yes | 40 | |
5.2 | odd | 4 | inner | 690.3.k.a.277.20 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.20 | ✓ | 40 | 5.2 | odd | 4 | inner | |
690.3.k.a.553.20 | yes | 40 | 1.1 | even | 1 | trivial |