Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4021,2,Mod(1,4021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4021.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1078466528\) |
Analytic rank: | \(0\) |
Dimension: | \(182\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4021.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57672 | −1.82201 | −0.911007 | − | 0.412390i | \(-0.864694\pi\) | ||||
−0.911007 | + | 0.412390i | \(0.864694\pi\) | |||||||
\(3\) | −1.91417 | −1.10515 | −0.552574 | − | 0.833464i | \(-0.686354\pi\) | ||||
−0.552574 | + | 0.833464i | \(0.686354\pi\) | |||||||
\(4\) | 4.63947 | 2.31974 | ||||||||
\(5\) | −2.65404 | −1.18692 | −0.593461 | − | 0.804863i | \(-0.702239\pi\) | ||||
−0.593461 | + | 0.804863i | \(0.702239\pi\) | |||||||
\(6\) | 4.93228 | 2.01360 | ||||||||
\(7\) | −2.26992 | −0.857947 | −0.428974 | − | 0.903317i | \(-0.641125\pi\) | ||||
−0.428974 | + | 0.903317i | \(0.641125\pi\) | |||||||
\(8\) | −6.80118 | −2.40458 | ||||||||
\(9\) | 0.664061 | 0.221354 | ||||||||
\(10\) | 6.83870 | 2.16259 | ||||||||
\(11\) | 4.73227 | 1.42683 | 0.713417 | − | 0.700740i | \(-0.247147\pi\) | ||||
0.713417 | + | 0.700740i | \(0.247147\pi\) | |||||||
\(12\) | −8.88076 | −2.56365 | ||||||||
\(13\) | −2.48260 | −0.688551 | −0.344275 | − | 0.938869i | \(-0.611875\pi\) | ||||
−0.344275 | + | 0.938869i | \(0.611875\pi\) | |||||||
\(14\) | 5.84893 | 1.56319 | ||||||||
\(15\) | 5.08029 | 1.31172 | ||||||||
\(16\) | 8.24577 | 2.06144 | ||||||||
\(17\) | 6.94871 | 1.68531 | 0.842655 | − | 0.538453i | \(-0.180991\pi\) | ||||
0.842655 | + | 0.538453i | \(0.180991\pi\) | |||||||
\(18\) | −1.71110 | −0.403309 | ||||||||
\(19\) | 6.99836 | 1.60553 | 0.802767 | − | 0.596293i | \(-0.203360\pi\) | ||||
0.802767 | + | 0.596293i | \(0.203360\pi\) | |||||||
\(20\) | −12.3133 | −2.75334 | ||||||||
\(21\) | 4.34501 | 0.948159 | ||||||||
\(22\) | −12.1937 | −2.59971 | ||||||||
\(23\) | −1.86740 | −0.389379 | −0.194690 | − | 0.980865i | \(-0.562370\pi\) | ||||
−0.194690 | + | 0.980865i | \(0.562370\pi\) | |||||||
\(24\) | 13.0186 | 2.65742 | ||||||||
\(25\) | 2.04391 | 0.408782 | ||||||||
\(26\) | 6.39697 | 1.25455 | ||||||||
\(27\) | 4.47139 | 0.860520 | ||||||||
\(28\) | −10.5312 | −1.99021 | ||||||||
\(29\) | 4.00495 | 0.743701 | 0.371851 | − | 0.928293i | \(-0.378723\pi\) | ||||
0.371851 | + | 0.928293i | \(0.378723\pi\) | |||||||
\(30\) | −13.0905 | −2.38998 | ||||||||
\(31\) | 7.17667 | 1.28897 | 0.644484 | − | 0.764618i | \(-0.277072\pi\) | ||||
0.644484 | + | 0.764618i | \(0.277072\pi\) | |||||||
\(32\) | −7.64466 | −1.35140 | ||||||||
\(33\) | −9.05839 | −1.57686 | ||||||||
\(34\) | −17.9049 | −3.07066 | ||||||||
\(35\) | 6.02444 | 1.01832 | ||||||||
\(36\) | 3.08089 | 0.513482 | ||||||||
\(37\) | 1.89761 | 0.311966 | 0.155983 | − | 0.987760i | \(-0.450146\pi\) | ||||
0.155983 | + | 0.987760i | \(0.450146\pi\) | |||||||
\(38\) | −18.0328 | −2.92531 | ||||||||
\(39\) | 4.75214 | 0.760951 | ||||||||
\(40\) | 18.0506 | 2.85405 | ||||||||
\(41\) | 11.5731 | 1.80741 | 0.903706 | − | 0.428153i | \(-0.140835\pi\) | ||||
0.903706 | + | 0.428153i | \(0.140835\pi\) | |||||||
\(42\) | −11.1959 | −1.72756 | ||||||||
\(43\) | 0.0405043 | 0.00617684 | 0.00308842 | − | 0.999995i | \(-0.499017\pi\) | ||||
0.00308842 | + | 0.999995i | \(0.499017\pi\) | |||||||
\(44\) | 21.9553 | 3.30988 | ||||||||
\(45\) | −1.76244 | −0.262729 | ||||||||
\(46\) | 4.81176 | 0.709455 | ||||||||
\(47\) | −5.73327 | −0.836284 | −0.418142 | − | 0.908382i | \(-0.637319\pi\) | ||||
−0.418142 | + | 0.908382i | \(0.637319\pi\) | |||||||
\(48\) | −15.7838 | −2.27820 | ||||||||
\(49\) | −1.84748 | −0.263926 | ||||||||
\(50\) | −5.26658 | −0.744807 | ||||||||
\(51\) | −13.3010 | −1.86252 | ||||||||
\(52\) | −11.5180 | −1.59726 | ||||||||
\(53\) | 0.0902283 | 0.0123938 | 0.00619690 | − | 0.999981i | \(-0.498027\pi\) | ||||
0.00619690 | + | 0.999981i | \(0.498027\pi\) | |||||||
\(54\) | −11.5215 | −1.56788 | ||||||||
\(55\) | −12.5596 | −1.69354 | ||||||||
\(56\) | 15.4381 | 2.06300 | ||||||||
\(57\) | −13.3961 | −1.77435 | ||||||||
\(58\) | −10.3196 | −1.35503 | ||||||||
\(59\) | −8.79942 | −1.14559 | −0.572794 | − | 0.819700i | \(-0.694140\pi\) | ||||
−0.572794 | + | 0.819700i | \(0.694140\pi\) | |||||||
\(60\) | 23.5699 | 3.04286 | ||||||||
\(61\) | 4.59972 | 0.588934 | 0.294467 | − | 0.955662i | \(-0.404858\pi\) | ||||
0.294467 | + | 0.955662i | \(0.404858\pi\) | |||||||
\(62\) | −18.4922 | −2.34852 | ||||||||
\(63\) | −1.50736 | −0.189910 | ||||||||
\(64\) | 3.20659 | 0.400824 | ||||||||
\(65\) | 6.58892 | 0.817255 | ||||||||
\(66\) | 23.3409 | 2.87307 | ||||||||
\(67\) | −3.60761 | −0.440739 | −0.220370 | − | 0.975416i | \(-0.570726\pi\) | ||||
−0.220370 | + | 0.975416i | \(0.570726\pi\) | |||||||
\(68\) | 32.2384 | 3.90948 | ||||||||
\(69\) | 3.57452 | 0.430322 | ||||||||
\(70\) | −15.5233 | −1.85539 | ||||||||
\(71\) | 1.18514 | 0.140650 | 0.0703250 | − | 0.997524i | \(-0.477596\pi\) | ||||
0.0703250 | + | 0.997524i | \(0.477596\pi\) | |||||||
\(72\) | −4.51640 | −0.532262 | ||||||||
\(73\) | 8.77763 | 1.02734 | 0.513672 | − | 0.857987i | \(-0.328285\pi\) | ||||
0.513672 | + | 0.857987i | \(0.328285\pi\) | |||||||
\(74\) | −4.88961 | −0.568406 | ||||||||
\(75\) | −3.91240 | −0.451765 | ||||||||
\(76\) | 32.4687 | 3.72442 | ||||||||
\(77\) | −10.7419 | −1.22415 | ||||||||
\(78\) | −12.2449 | −1.38646 | ||||||||
\(79\) | −3.43149 | −0.386073 | −0.193036 | − | 0.981192i | \(-0.561834\pi\) | ||||
−0.193036 | + | 0.981192i | \(0.561834\pi\) | |||||||
\(80\) | −21.8846 | −2.44677 | ||||||||
\(81\) | −10.5512 | −1.17236 | ||||||||
\(82\) | −29.8206 | −3.29313 | ||||||||
\(83\) | 9.53079 | 1.04614 | 0.523070 | − | 0.852290i | \(-0.324787\pi\) | ||||
0.523070 | + | 0.852290i | \(0.324787\pi\) | |||||||
\(84\) | 20.1586 | 2.19948 | ||||||||
\(85\) | −18.4421 | −2.00033 | ||||||||
\(86\) | −0.104368 | −0.0112543 | ||||||||
\(87\) | −7.66618 | −0.821900 | ||||||||
\(88\) | −32.1850 | −3.43094 | ||||||||
\(89\) | 13.7694 | 1.45955 | 0.729776 | − | 0.683687i | \(-0.239625\pi\) | ||||
0.729776 | + | 0.683687i | \(0.239625\pi\) | |||||||
\(90\) | 4.54131 | 0.478697 | ||||||||
\(91\) | 5.63530 | 0.590740 | ||||||||
\(92\) | −8.66374 | −0.903257 | ||||||||
\(93\) | −13.7374 | −1.42450 | ||||||||
\(94\) | 14.7730 | 1.52372 | ||||||||
\(95\) | −18.5739 | −1.90564 | ||||||||
\(96\) | 14.6332 | 1.49350 | ||||||||
\(97\) | −10.7704 | −1.09357 | −0.546785 | − | 0.837273i | \(-0.684149\pi\) | ||||
−0.546785 | + | 0.837273i | \(0.684149\pi\) | |||||||
\(98\) | 4.76045 | 0.480878 | ||||||||
\(99\) | 3.14252 | 0.315835 | ||||||||
\(100\) | 9.48267 | 0.948267 | ||||||||
\(101\) | −9.34439 | −0.929801 | −0.464901 | − | 0.885363i | \(-0.653910\pi\) | ||||
−0.464901 | + | 0.885363i | \(0.653910\pi\) | |||||||
\(102\) | 34.2730 | 3.39354 | ||||||||
\(103\) | 1.23116 | 0.121309 | 0.0606547 | − | 0.998159i | \(-0.480681\pi\) | ||||
0.0606547 | + | 0.998159i | \(0.480681\pi\) | |||||||
\(104\) | 16.8846 | 1.65567 | ||||||||
\(105\) | −11.5318 | −1.12539 | ||||||||
\(106\) | −0.232493 | −0.0225817 | ||||||||
\(107\) | 17.7459 | 1.71556 | 0.857781 | − | 0.514015i | \(-0.171843\pi\) | ||||
0.857781 | + | 0.514015i | \(0.171843\pi\) | |||||||
\(108\) | 20.7449 | 1.99618 | ||||||||
\(109\) | −4.36145 | −0.417751 | −0.208876 | − | 0.977942i | \(-0.566980\pi\) | ||||
−0.208876 | + | 0.977942i | \(0.566980\pi\) | |||||||
\(110\) | 32.3626 | 3.08565 | ||||||||
\(111\) | −3.63236 | −0.344768 | ||||||||
\(112\) | −18.7172 | −1.76861 | ||||||||
\(113\) | 19.3105 | 1.81658 | 0.908292 | − | 0.418338i | \(-0.137387\pi\) | ||||
0.908292 | + | 0.418338i | \(0.137387\pi\) | |||||||
\(114\) | 34.5179 | 3.23290 | ||||||||
\(115\) | 4.95614 | 0.462163 | ||||||||
\(116\) | 18.5809 | 1.72519 | ||||||||
\(117\) | −1.64860 | −0.152413 | ||||||||
\(118\) | 22.6736 | 2.08728 | ||||||||
\(119\) | −15.7730 | −1.44591 | ||||||||
\(120\) | −34.5519 | −3.15415 | ||||||||
\(121\) | 11.3944 | 1.03585 | ||||||||
\(122\) | −11.8522 | −1.07305 | ||||||||
\(123\) | −22.1529 | −1.99746 | ||||||||
\(124\) | 33.2960 | 2.99007 | ||||||||
\(125\) | 7.84557 | 0.701729 | ||||||||
\(126\) | 3.88405 | 0.346018 | ||||||||
\(127\) | −5.35836 | −0.475478 | −0.237739 | − | 0.971329i | \(-0.576406\pi\) | ||||
−0.237739 | + | 0.971329i | \(0.576406\pi\) | |||||||
\(128\) | 7.02683 | 0.621090 | ||||||||
\(129\) | −0.0775322 | −0.00682633 | ||||||||
\(130\) | −16.9778 | −1.48905 | ||||||||
\(131\) | 4.35598 | 0.380584 | 0.190292 | − | 0.981728i | \(-0.439057\pi\) | ||||
0.190292 | + | 0.981728i | \(0.439057\pi\) | |||||||
\(132\) | −42.0262 | −3.65791 | ||||||||
\(133\) | −15.8857 | −1.37746 | ||||||||
\(134\) | 9.29578 | 0.803033 | ||||||||
\(135\) | −11.8672 | −1.02137 | ||||||||
\(136\) | −47.2594 | −4.05246 | ||||||||
\(137\) | −10.7159 | −0.915520 | −0.457760 | − | 0.889076i | \(-0.651348\pi\) | ||||
−0.457760 | + | 0.889076i | \(0.651348\pi\) | |||||||
\(138\) | −9.21054 | −0.784053 | ||||||||
\(139\) | 7.91755 | 0.671558 | 0.335779 | − | 0.941941i | \(-0.391001\pi\) | ||||
0.335779 | + | 0.941941i | \(0.391001\pi\) | |||||||
\(140\) | 27.9502 | 2.36223 | ||||||||
\(141\) | 10.9745 | 0.924218 | ||||||||
\(142\) | −3.05377 | −0.256267 | ||||||||
\(143\) | −11.7484 | −0.982447 | ||||||||
\(144\) | 5.47569 | 0.456308 | ||||||||
\(145\) | −10.6293 | −0.882715 | ||||||||
\(146\) | −22.6175 | −1.87183 | ||||||||
\(147\) | 3.53641 | 0.291678 | ||||||||
\(148\) | 8.80392 | 0.723678 | ||||||||
\(149\) | 5.94316 | 0.486883 | 0.243441 | − | 0.969916i | \(-0.421724\pi\) | ||||
0.243441 | + | 0.969916i | \(0.421724\pi\) | |||||||
\(150\) | 10.0811 | 0.823122 | ||||||||
\(151\) | −10.1332 | −0.824629 | −0.412314 | − | 0.911042i | \(-0.635279\pi\) | ||||
−0.412314 | + | 0.911042i | \(0.635279\pi\) | |||||||
\(152\) | −47.5971 | −3.86063 | ||||||||
\(153\) | 4.61437 | 0.373050 | ||||||||
\(154\) | 27.6787 | 2.23042 | ||||||||
\(155\) | −19.0471 | −1.52990 | ||||||||
\(156\) | 22.0474 | 1.76521 | ||||||||
\(157\) | −22.6114 | −1.80459 | −0.902295 | − | 0.431119i | \(-0.858119\pi\) | ||||
−0.902295 | + | 0.431119i | \(0.858119\pi\) | |||||||
\(158\) | 8.84198 | 0.703430 | ||||||||
\(159\) | −0.172713 | −0.0136970 | ||||||||
\(160\) | 20.2892 | 1.60400 | ||||||||
\(161\) | 4.23883 | 0.334067 | ||||||||
\(162\) | 27.1875 | 2.13605 | ||||||||
\(163\) | 3.01022 | 0.235779 | 0.117889 | − | 0.993027i | \(-0.462387\pi\) | ||||
0.117889 | + | 0.993027i | \(0.462387\pi\) | |||||||
\(164\) | 53.6930 | 4.19272 | ||||||||
\(165\) | 24.0413 | 1.87161 | ||||||||
\(166\) | −24.5582 | −1.90608 | ||||||||
\(167\) | 12.7493 | 0.986570 | 0.493285 | − | 0.869868i | \(-0.335796\pi\) | ||||
0.493285 | + | 0.869868i | \(0.335796\pi\) | |||||||
\(168\) | −29.5512 | −2.27992 | ||||||||
\(169\) | −6.83667 | −0.525898 | ||||||||
\(170\) | 47.5202 | 3.64463 | ||||||||
\(171\) | 4.64734 | 0.355391 | ||||||||
\(172\) | 0.187919 | 0.0143287 | ||||||||
\(173\) | 15.5816 | 1.18465 | 0.592325 | − | 0.805699i | \(-0.298210\pi\) | ||||
0.592325 | + | 0.805699i | \(0.298210\pi\) | |||||||
\(174\) | 19.7536 | 1.49751 | ||||||||
\(175\) | −4.63950 | −0.350714 | ||||||||
\(176\) | 39.0212 | 2.94134 | ||||||||
\(177\) | 16.8436 | 1.26604 | ||||||||
\(178\) | −35.4798 | −2.65932 | ||||||||
\(179\) | −20.3759 | −1.52297 | −0.761484 | − | 0.648184i | \(-0.775529\pi\) | ||||
−0.761484 | + | 0.648184i | \(0.775529\pi\) | |||||||
\(180\) | −8.17680 | −0.609463 | ||||||||
\(181\) | −19.7765 | −1.46997 | −0.734987 | − | 0.678081i | \(-0.762812\pi\) | ||||
−0.734987 | + | 0.678081i | \(0.762812\pi\) | |||||||
\(182\) | −14.5206 | −1.07634 | ||||||||
\(183\) | −8.80467 | −0.650860 | ||||||||
\(184\) | 12.7005 | 0.936293 | ||||||||
\(185\) | −5.03633 | −0.370278 | ||||||||
\(186\) | 35.3974 | 2.59546 | ||||||||
\(187\) | 32.8832 | 2.40466 | ||||||||
\(188\) | −26.5994 | −1.93996 | ||||||||
\(189\) | −10.1497 | −0.738281 | ||||||||
\(190\) | 47.8597 | 3.47211 | ||||||||
\(191\) | −0.857870 | −0.0620733 | −0.0310367 | − | 0.999518i | \(-0.509881\pi\) | ||||
−0.0310367 | + | 0.999518i | \(0.509881\pi\) | |||||||
\(192\) | −6.13798 | −0.442970 | ||||||||
\(193\) | 19.4475 | 1.39986 | 0.699930 | − | 0.714211i | \(-0.253214\pi\) | ||||
0.699930 | + | 0.714211i | \(0.253214\pi\) | |||||||
\(194\) | 27.7523 | 1.99250 | ||||||||
\(195\) | −12.6123 | −0.903189 | ||||||||
\(196\) | −8.57136 | −0.612240 | ||||||||
\(197\) | −23.9929 | −1.70943 | −0.854713 | − | 0.519101i | \(-0.826267\pi\) | ||||
−0.854713 | + | 0.519101i | \(0.826267\pi\) | |||||||
\(198\) | −8.09738 | −0.575455 | ||||||||
\(199\) | −14.4351 | −1.02328 | −0.511639 | − | 0.859201i | \(-0.670961\pi\) | ||||
−0.511639 | + | 0.859201i | \(0.670961\pi\) | |||||||
\(200\) | −13.9010 | −0.982949 | ||||||||
\(201\) | 6.90559 | 0.487082 | ||||||||
\(202\) | 24.0778 | 1.69411 | ||||||||
\(203\) | −9.09091 | −0.638057 | ||||||||
\(204\) | −61.7098 | −4.32055 | ||||||||
\(205\) | −30.7154 | −2.14526 | ||||||||
\(206\) | −3.17234 | −0.221028 | ||||||||
\(207\) | −1.24007 | −0.0861905 | ||||||||
\(208\) | −20.4710 | −1.41941 | ||||||||
\(209\) | 33.1181 | 2.29083 | ||||||||
\(210\) | 29.7142 | 2.05048 | ||||||||
\(211\) | 2.01506 | 0.138722 | 0.0693611 | − | 0.997592i | \(-0.477904\pi\) | ||||
0.0693611 | + | 0.997592i | \(0.477904\pi\) | |||||||
\(212\) | 0.418612 | 0.0287504 | ||||||||
\(213\) | −2.26856 | −0.155439 | ||||||||
\(214\) | −45.7262 | −3.12578 | ||||||||
\(215\) | −0.107500 | −0.00733143 | ||||||||
\(216\) | −30.4107 | −2.06919 | ||||||||
\(217\) | −16.2904 | −1.10587 | ||||||||
\(218\) | 11.2382 | 0.761149 | ||||||||
\(219\) | −16.8019 | −1.13537 | ||||||||
\(220\) | −58.2700 | −3.92857 | ||||||||
\(221\) | −17.2509 | −1.16042 | ||||||||
\(222\) | 9.35956 | 0.628173 | ||||||||
\(223\) | −12.5923 | −0.843242 | −0.421621 | − | 0.906772i | \(-0.638539\pi\) | ||||
−0.421621 | + | 0.906772i | \(0.638539\pi\) | |||||||
\(224\) | 17.3527 | 1.15943 | ||||||||
\(225\) | 1.35728 | 0.0904854 | ||||||||
\(226\) | −49.7578 | −3.30984 | ||||||||
\(227\) | −15.6280 | −1.03727 | −0.518635 | − | 0.854996i | \(-0.673560\pi\) | ||||
−0.518635 | + | 0.854996i | \(0.673560\pi\) | |||||||
\(228\) | −62.1507 | −4.11603 | ||||||||
\(229\) | 15.0188 | 0.992470 | 0.496235 | − | 0.868188i | \(-0.334716\pi\) | ||||
0.496235 | + | 0.868188i | \(0.334716\pi\) | |||||||
\(230\) | −12.7706 | −0.842067 | ||||||||
\(231\) | 20.5618 | 1.35287 | ||||||||
\(232\) | −27.2384 | −1.78829 | ||||||||
\(233\) | 11.1846 | 0.732728 | 0.366364 | − | 0.930472i | \(-0.380602\pi\) | ||||
0.366364 | + | 0.930472i | \(0.380602\pi\) | |||||||
\(234\) | 4.24798 | 0.277699 | ||||||||
\(235\) | 15.2163 | 0.992603 | ||||||||
\(236\) | −40.8247 | −2.65746 | ||||||||
\(237\) | 6.56846 | 0.426668 | ||||||||
\(238\) | 40.6425 | 2.63446 | ||||||||
\(239\) | 24.5933 | 1.59081 | 0.795405 | − | 0.606079i | \(-0.207258\pi\) | ||||
0.795405 | + | 0.606079i | \(0.207258\pi\) | |||||||
\(240\) | 41.8909 | 2.70404 | ||||||||
\(241\) | −17.6948 | −1.13982 | −0.569911 | − | 0.821706i | \(-0.693022\pi\) | ||||
−0.569911 | + | 0.821706i | \(0.693022\pi\) | |||||||
\(242\) | −29.3601 | −1.88734 | ||||||||
\(243\) | 6.78266 | 0.435108 | ||||||||
\(244\) | 21.3403 | 1.36617 | ||||||||
\(245\) | 4.90329 | 0.313260 | ||||||||
\(246\) | 57.0818 | 3.63940 | ||||||||
\(247\) | −17.3742 | −1.10549 | ||||||||
\(248\) | −48.8098 | −3.09943 | ||||||||
\(249\) | −18.2436 | −1.15614 | ||||||||
\(250\) | −20.2158 | −1.27856 | ||||||||
\(251\) | 8.95633 | 0.565318 | 0.282659 | − | 0.959220i | \(-0.408783\pi\) | ||||
0.282659 | + | 0.959220i | \(0.408783\pi\) | |||||||
\(252\) | −6.99336 | −0.440541 | ||||||||
\(253\) | −8.83703 | −0.555579 | ||||||||
\(254\) | 13.8070 | 0.866328 | ||||||||
\(255\) | 35.3015 | 2.21066 | ||||||||
\(256\) | −24.5194 | −1.53246 | ||||||||
\(257\) | 4.93425 | 0.307790 | 0.153895 | − | 0.988087i | \(-0.450818\pi\) | ||||
0.153895 | + | 0.988087i | \(0.450818\pi\) | |||||||
\(258\) | 0.199779 | 0.0124377 | ||||||||
\(259\) | −4.30742 | −0.267650 | ||||||||
\(260\) | 30.5691 | 1.89582 | ||||||||
\(261\) | 2.65953 | 0.164621 | ||||||||
\(262\) | −11.2241 | −0.693429 | ||||||||
\(263\) | −25.4726 | −1.57071 | −0.785353 | − | 0.619048i | \(-0.787518\pi\) | ||||
−0.785353 | + | 0.619048i | \(0.787518\pi\) | |||||||
\(264\) | 61.6077 | 3.79169 | ||||||||
\(265\) | −0.239469 | −0.0147105 | ||||||||
\(266\) | 40.9329 | 2.50976 | ||||||||
\(267\) | −26.3570 | −1.61302 | ||||||||
\(268\) | −16.7374 | −1.02240 | ||||||||
\(269\) | 18.5852 | 1.13316 | 0.566579 | − | 0.824007i | \(-0.308267\pi\) | ||||
0.566579 | + | 0.824007i | \(0.308267\pi\) | |||||||
\(270\) | 30.5785 | 1.86095 | ||||||||
\(271\) | 21.3047 | 1.29417 | 0.647084 | − | 0.762419i | \(-0.275988\pi\) | ||||
0.647084 | + | 0.762419i | \(0.275988\pi\) | |||||||
\(272\) | 57.2975 | 3.47417 | ||||||||
\(273\) | −10.7869 | −0.652856 | ||||||||
\(274\) | 27.6118 | 1.66809 | ||||||||
\(275\) | 9.67234 | 0.583264 | ||||||||
\(276\) | 16.5839 | 0.998234 | ||||||||
\(277\) | 2.91881 | 0.175374 | 0.0876872 | − | 0.996148i | \(-0.472052\pi\) | ||||
0.0876872 | + | 0.996148i | \(0.472052\pi\) | |||||||
\(278\) | −20.4013 | −1.22359 | ||||||||
\(279\) | 4.76574 | 0.285318 | ||||||||
\(280\) | −40.9733 | −2.44862 | ||||||||
\(281\) | 4.11840 | 0.245683 | 0.122841 | − | 0.992426i | \(-0.460799\pi\) | ||||
0.122841 | + | 0.992426i | \(0.460799\pi\) | |||||||
\(282\) | −28.2781 | −1.68394 | ||||||||
\(283\) | 4.42704 | 0.263160 | 0.131580 | − | 0.991306i | \(-0.457995\pi\) | ||||
0.131580 | + | 0.991306i | \(0.457995\pi\) | |||||||
\(284\) | 5.49842 | 0.326271 | ||||||||
\(285\) | 35.5537 | 2.10602 | ||||||||
\(286\) | 30.2722 | 1.79003 | ||||||||
\(287\) | −26.2699 | −1.55067 | ||||||||
\(288\) | −5.07652 | −0.299137 | ||||||||
\(289\) | 31.2846 | 1.84027 | ||||||||
\(290\) | 27.3887 | 1.60832 | ||||||||
\(291\) | 20.6164 | 1.20856 | ||||||||
\(292\) | 40.7236 | 2.38317 | ||||||||
\(293\) | −3.27044 | −0.191061 | −0.0955307 | − | 0.995426i | \(-0.530455\pi\) | ||||
−0.0955307 | + | 0.995426i | \(0.530455\pi\) | |||||||
\(294\) | −9.11232 | −0.531441 | ||||||||
\(295\) | 23.3540 | 1.35972 | ||||||||
\(296\) | −12.9060 | −0.750146 | ||||||||
\(297\) | 21.1598 | 1.22782 | ||||||||
\(298\) | −15.3138 | −0.887107 | ||||||||
\(299\) | 4.63601 | 0.268107 | ||||||||
\(300\) | −18.1515 | −1.04798 | ||||||||
\(301\) | −0.0919413 | −0.00529941 | ||||||||
\(302\) | 26.1104 | 1.50249 | ||||||||
\(303\) | 17.8868 | 1.02757 | ||||||||
\(304\) | 57.7068 | 3.30971 | ||||||||
\(305\) | −12.2078 | −0.699019 | ||||||||
\(306\) | −11.8899 | −0.679702 | ||||||||
\(307\) | −17.6483 | −1.00724 | −0.503622 | − | 0.863924i | \(-0.667999\pi\) | ||||
−0.503622 | + | 0.863924i | \(0.667999\pi\) | |||||||
\(308\) | −49.8366 | −2.83970 | ||||||||
\(309\) | −2.35665 | −0.134065 | ||||||||
\(310\) | 49.0791 | 2.78751 | ||||||||
\(311\) | 18.9064 | 1.07208 | 0.536042 | − | 0.844191i | \(-0.319919\pi\) | ||||
0.536042 | + | 0.844191i | \(0.319919\pi\) | |||||||
\(312\) | −32.3201 | −1.82977 | ||||||||
\(313\) | −4.04392 | −0.228576 | −0.114288 | − | 0.993448i | \(-0.536459\pi\) | ||||
−0.114288 | + | 0.993448i | \(0.536459\pi\) | |||||||
\(314\) | 58.2633 | 3.28799 | ||||||||
\(315\) | 4.00059 | 0.225408 | ||||||||
\(316\) | −15.9203 | −0.895587 | ||||||||
\(317\) | 17.5345 | 0.984835 | 0.492417 | − | 0.870359i | \(-0.336113\pi\) | ||||
0.492417 | + | 0.870359i | \(0.336113\pi\) | |||||||
\(318\) | 0.445032 | 0.0249561 | ||||||||
\(319\) | 18.9525 | 1.06114 | ||||||||
\(320\) | −8.51042 | −0.475747 | ||||||||
\(321\) | −33.9688 | −1.89595 | ||||||||
\(322\) | −10.9223 | −0.608675 | ||||||||
\(323\) | 48.6296 | 2.70582 | ||||||||
\(324\) | −48.9520 | −2.71956 | ||||||||
\(325\) | −5.07422 | −0.281467 | ||||||||
\(326\) | −7.75648 | −0.429592 | ||||||||
\(327\) | 8.34857 | 0.461677 | ||||||||
\(328\) | −78.7106 | −4.34607 | ||||||||
\(329\) | 13.0140 | 0.717487 | ||||||||
\(330\) | −61.9476 | −3.41011 | ||||||||
\(331\) | −21.0337 | −1.15612 | −0.578058 | − | 0.815996i | \(-0.696189\pi\) | ||||
−0.578058 | + | 0.815996i | \(0.696189\pi\) | |||||||
\(332\) | 44.2178 | 2.42677 | ||||||||
\(333\) | 1.26013 | 0.0690547 | ||||||||
\(334\) | −32.8513 | −1.79754 | ||||||||
\(335\) | 9.57472 | 0.523123 | ||||||||
\(336\) | 35.8280 | 1.95458 | ||||||||
\(337\) | 31.8176 | 1.73322 | 0.866608 | − | 0.498990i | \(-0.166296\pi\) | ||||
0.866608 | + | 0.498990i | \(0.166296\pi\) | |||||||
\(338\) | 17.6162 | 0.958194 | ||||||||
\(339\) | −36.9637 | −2.00759 | ||||||||
\(340\) | −85.5618 | −4.64024 | ||||||||
\(341\) | 33.9619 | 1.83914 | ||||||||
\(342\) | −11.9749 | −0.647527 | ||||||||
\(343\) | 20.0830 | 1.08438 | ||||||||
\(344\) | −0.275477 | −0.0148527 | ||||||||
\(345\) | −9.48691 | −0.510758 | ||||||||
\(346\) | −40.1495 | −2.15845 | ||||||||
\(347\) | 25.5560 | 1.37192 | 0.685959 | − | 0.727640i | \(-0.259383\pi\) | ||||
0.685959 | + | 0.727640i | \(0.259383\pi\) | |||||||
\(348\) | −35.5670 | −1.90659 | ||||||||
\(349\) | −6.35171 | −0.339999 | −0.170000 | − | 0.985444i | \(-0.554377\pi\) | ||||
−0.170000 | + | 0.985444i | \(0.554377\pi\) | |||||||
\(350\) | 11.9547 | 0.639005 | ||||||||
\(351\) | −11.1007 | −0.592512 | ||||||||
\(352\) | −36.1766 | −1.92822 | ||||||||
\(353\) | 23.2340 | 1.23662 | 0.618310 | − | 0.785935i | \(-0.287818\pi\) | ||||
0.618310 | + | 0.785935i | \(0.287818\pi\) | |||||||
\(354\) | −43.4013 | −2.30675 | ||||||||
\(355\) | −3.14540 | −0.166941 | ||||||||
\(356\) | 63.8827 | 3.38577 | ||||||||
\(357\) | 30.1922 | 1.59794 | ||||||||
\(358\) | 52.5030 | 2.77487 | ||||||||
\(359\) | −5.78782 | −0.305470 | −0.152735 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152735 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(360\) | 11.9867 | 0.631753 | ||||||||
\(361\) | 29.9770 | 1.57774 | ||||||||
\(362\) | 50.9584 | 2.67832 | ||||||||
\(363\) | −21.8109 | −1.14477 | ||||||||
\(364\) | 26.1448 | 1.37036 | ||||||||
\(365\) | −23.2961 | −1.21938 | ||||||||
\(366\) | 22.6872 | 1.18588 | ||||||||
\(367\) | 4.71983 | 0.246373 | 0.123186 | − | 0.992384i | \(-0.460689\pi\) | ||||
0.123186 | + | 0.992384i | \(0.460689\pi\) | |||||||
\(368\) | −15.3981 | −0.802683 | ||||||||
\(369\) | 7.68523 | 0.400077 | ||||||||
\(370\) | 12.9772 | 0.674653 | ||||||||
\(371\) | −0.204811 | −0.0106332 | ||||||||
\(372\) | −63.7343 | −3.30447 | ||||||||
\(373\) | 34.1382 | 1.76761 | 0.883805 | − | 0.467856i | \(-0.154973\pi\) | ||||
0.883805 | + | 0.467856i | \(0.154973\pi\) | |||||||
\(374\) | −84.7307 | −4.38132 | ||||||||
\(375\) | −15.0178 | −0.775515 | ||||||||
\(376\) | 38.9930 | 2.01091 | ||||||||
\(377\) | −9.94272 | −0.512076 | ||||||||
\(378\) | 26.1529 | 1.34516 | ||||||||
\(379\) | −4.91206 | −0.252316 | −0.126158 | − | 0.992010i | \(-0.540265\pi\) | ||||
−0.126158 | + | 0.992010i | \(0.540265\pi\) | |||||||
\(380\) | −86.1731 | −4.42059 | ||||||||
\(381\) | 10.2568 | 0.525474 | ||||||||
\(382\) | 2.21049 | 0.113098 | ||||||||
\(383\) | −13.9987 | −0.715298 | −0.357649 | − | 0.933856i | \(-0.616422\pi\) | ||||
−0.357649 | + | 0.933856i | \(0.616422\pi\) | |||||||
\(384\) | −13.4506 | −0.686397 | ||||||||
\(385\) | 28.5093 | 1.45297 | ||||||||
\(386\) | −50.1107 | −2.55057 | ||||||||
\(387\) | 0.0268973 | 0.00136727 | ||||||||
\(388\) | −49.9691 | −2.53679 | ||||||||
\(389\) | −1.90056 | −0.0963621 | −0.0481810 | − | 0.998839i | \(-0.515342\pi\) | ||||
−0.0481810 | + | 0.998839i | \(0.515342\pi\) | |||||||
\(390\) | 32.4984 | 1.64562 | ||||||||
\(391\) | −12.9760 | −0.656225 | ||||||||
\(392\) | 12.5651 | 0.634632 | ||||||||
\(393\) | −8.33811 | −0.420602 | ||||||||
\(394\) | 61.8230 | 3.11460 | ||||||||
\(395\) | 9.10730 | 0.458238 | ||||||||
\(396\) | 14.5796 | 0.732653 | ||||||||
\(397\) | 10.8753 | 0.545814 | 0.272907 | − | 0.962040i | \(-0.412015\pi\) | ||||
0.272907 | + | 0.962040i | \(0.412015\pi\) | |||||||
\(398\) | 37.1952 | 1.86443 | ||||||||
\(399\) | 30.4080 | 1.52230 | ||||||||
\(400\) | 16.8536 | 0.842681 | ||||||||
\(401\) | −17.0903 | −0.853447 | −0.426724 | − | 0.904382i | \(-0.640332\pi\) | ||||
−0.426724 | + | 0.904382i | \(0.640332\pi\) | |||||||
\(402\) | −17.7937 | −0.887471 | ||||||||
\(403\) | −17.8168 | −0.887520 | ||||||||
\(404\) | −43.3530 | −2.15689 | ||||||||
\(405\) | 28.0033 | 1.39149 | ||||||||
\(406\) | 23.4247 | 1.16255 | ||||||||
\(407\) | 8.98002 | 0.445123 | ||||||||
\(408\) | 90.4628 | 4.47857 | ||||||||
\(409\) | −32.0950 | −1.58700 | −0.793499 | − | 0.608572i | \(-0.791743\pi\) | ||||
−0.793499 | + | 0.608572i | \(0.791743\pi\) | |||||||
\(410\) | 79.1449 | 3.90869 | ||||||||
\(411\) | 20.5121 | 1.01179 | ||||||||
\(412\) | 5.71192 | 0.281406 | ||||||||
\(413\) | 19.9739 | 0.982854 | ||||||||
\(414\) | 3.19530 | 0.157040 | ||||||||
\(415\) | −25.2951 | −1.24169 | ||||||||
\(416\) | 18.9787 | 0.930506 | ||||||||
\(417\) | −15.1556 | −0.742171 | ||||||||
\(418\) | −85.3361 | −4.17392 | ||||||||
\(419\) | −38.4446 | −1.87814 | −0.939072 | − | 0.343722i | \(-0.888312\pi\) | ||||
−0.939072 | + | 0.343722i | \(0.888312\pi\) | |||||||
\(420\) | −53.5016 | −2.61061 | ||||||||
\(421\) | −15.5038 | −0.755607 | −0.377804 | − | 0.925886i | \(-0.623321\pi\) | ||||
−0.377804 | + | 0.925886i | \(0.623321\pi\) | |||||||
\(422\) | −5.19223 | −0.252754 | ||||||||
\(423\) | −3.80724 | −0.185114 | ||||||||
\(424\) | −0.613659 | −0.0298019 | ||||||||
\(425\) | 14.2025 | 0.688925 | ||||||||
\(426\) | 5.84544 | 0.283213 | ||||||||
\(427\) | −10.4410 | −0.505275 | ||||||||
\(428\) | 82.3317 | 3.97965 | ||||||||
\(429\) | 22.4884 | 1.08575 | ||||||||
\(430\) | 0.276997 | 0.0133580 | ||||||||
\(431\) | 4.48230 | 0.215905 | 0.107952 | − | 0.994156i | \(-0.465571\pi\) | ||||
0.107952 | + | 0.994156i | \(0.465571\pi\) | |||||||
\(432\) | 36.8701 | 1.77391 | ||||||||
\(433\) | −24.2286 | −1.16435 | −0.582177 | − | 0.813062i | \(-0.697799\pi\) | ||||
−0.582177 | + | 0.813062i | \(0.697799\pi\) | |||||||
\(434\) | 41.9758 | 2.01490 | ||||||||
\(435\) | 20.3463 | 0.975531 | ||||||||
\(436\) | −20.2348 | −0.969073 | ||||||||
\(437\) | −13.0687 | −0.625161 | ||||||||
\(438\) | 43.2937 | 2.06866 | ||||||||
\(439\) | 34.8132 | 1.66154 | 0.830772 | − | 0.556614i | \(-0.187900\pi\) | ||||
0.830772 | + | 0.556614i | \(0.187900\pi\) | |||||||
\(440\) | 85.4202 | 4.07225 | ||||||||
\(441\) | −1.22684 | −0.0584210 | ||||||||
\(442\) | 44.4507 | 2.11431 | ||||||||
\(443\) | 14.7812 | 0.702276 | 0.351138 | − | 0.936324i | \(-0.385795\pi\) | ||||
0.351138 | + | 0.936324i | \(0.385795\pi\) | |||||||
\(444\) | −16.8522 | −0.799772 | ||||||||
\(445\) | −36.5444 | −1.73237 | ||||||||
\(446\) | 32.4468 | 1.53640 | ||||||||
\(447\) | −11.3762 | −0.538078 | ||||||||
\(448\) | −7.27870 | −0.343886 | ||||||||
\(449\) | −15.4273 | −0.728058 | −0.364029 | − | 0.931388i | \(-0.618599\pi\) | ||||
−0.364029 | + | 0.931388i | \(0.618599\pi\) | |||||||
\(450\) | −3.49733 | −0.164866 | ||||||||
\(451\) | 54.7670 | 2.57888 | ||||||||
\(452\) | 89.5908 | 4.21399 | ||||||||
\(453\) | 19.3967 | 0.911337 | ||||||||
\(454\) | 40.2691 | 1.88992 | ||||||||
\(455\) | −14.9563 | −0.701162 | ||||||||
\(456\) | 91.1091 | 4.26657 | ||||||||
\(457\) | −29.5467 | −1.38214 | −0.691068 | − | 0.722789i | \(-0.742860\pi\) | ||||
−0.691068 | + | 0.722789i | \(0.742860\pi\) | |||||||
\(458\) | −38.6992 | −1.80829 | ||||||||
\(459\) | 31.0704 | 1.45024 | ||||||||
\(460\) | 22.9939 | 1.07210 | ||||||||
\(461\) | 12.9564 | 0.603438 | 0.301719 | − | 0.953397i | \(-0.402440\pi\) | ||||
0.301719 | + | 0.953397i | \(0.402440\pi\) | |||||||
\(462\) | −52.9819 | −2.46494 | ||||||||
\(463\) | 11.9852 | 0.556998 | 0.278499 | − | 0.960437i | \(-0.410163\pi\) | ||||
0.278499 | + | 0.960437i | \(0.410163\pi\) | |||||||
\(464\) | 33.0239 | 1.53310 | ||||||||
\(465\) | 36.4595 | 1.69077 | ||||||||
\(466\) | −28.8196 | −1.33504 | ||||||||
\(467\) | −5.44812 | −0.252109 | −0.126055 | − | 0.992023i | \(-0.540231\pi\) | ||||
−0.126055 | + | 0.992023i | \(0.540231\pi\) | |||||||
\(468\) | −7.64864 | −0.353558 | ||||||||
\(469\) | 8.18896 | 0.378131 | ||||||||
\(470\) | −39.2081 | −1.80854 | ||||||||
\(471\) | 43.2822 | 1.99434 | ||||||||
\(472\) | 59.8464 | 2.75466 | ||||||||
\(473\) | 0.191677 | 0.00881333 | ||||||||
\(474\) | −16.9251 | −0.777395 | ||||||||
\(475\) | 14.3040 | 0.656313 | ||||||||
\(476\) | −73.1784 | −3.35413 | ||||||||
\(477\) | 0.0599171 | 0.00274341 | ||||||||
\(478\) | −63.3700 | −2.89848 | ||||||||
\(479\) | −1.06431 | −0.0486295 | −0.0243147 | − | 0.999704i | \(-0.507740\pi\) | ||||
−0.0243147 | + | 0.999704i | \(0.507740\pi\) | |||||||
\(480\) | −38.8371 | −1.77266 | ||||||||
\(481\) | −4.71102 | −0.214804 | ||||||||
\(482\) | 45.5945 | 2.07677 | ||||||||
\(483\) | −8.11386 | −0.369194 | ||||||||
\(484\) | 52.8640 | 2.40291 | ||||||||
\(485\) | 28.5851 | 1.29798 | ||||||||
\(486\) | −17.4770 | −0.792773 | ||||||||
\(487\) | 22.2238 | 1.00706 | 0.503529 | − | 0.863978i | \(-0.332035\pi\) | ||||
0.503529 | + | 0.863978i | \(0.332035\pi\) | |||||||
\(488\) | −31.2835 | −1.41614 | ||||||||
\(489\) | −5.76208 | −0.260570 | ||||||||
\(490\) | −12.6344 | −0.570764 | ||||||||
\(491\) | 25.0065 | 1.12853 | 0.564263 | − | 0.825595i | \(-0.309160\pi\) | ||||
0.564263 | + | 0.825595i | \(0.309160\pi\) | |||||||
\(492\) | −102.778 | −4.63358 | ||||||||
\(493\) | 27.8293 | 1.25337 | ||||||||
\(494\) | 44.7683 | 2.01422 | ||||||||
\(495\) | −8.34035 | −0.374871 | ||||||||
\(496\) | 59.1771 | 2.65713 | ||||||||
\(497\) | −2.69016 | −0.120670 | ||||||||
\(498\) | 47.0086 | 2.10650 | ||||||||
\(499\) | 16.8169 | 0.752829 | 0.376415 | − | 0.926451i | \(-0.377157\pi\) | ||||
0.376415 | + | 0.926451i | \(0.377157\pi\) | |||||||
\(500\) | 36.3993 | 1.62783 | ||||||||
\(501\) | −24.4044 | −1.09031 | ||||||||
\(502\) | −23.0779 | −1.03002 | ||||||||
\(503\) | 8.55031 | 0.381239 | 0.190620 | − | 0.981664i | \(-0.438950\pi\) | ||||
0.190620 | + | 0.981664i | \(0.438950\pi\) | |||||||
\(504\) | 10.2518 | 0.456653 | ||||||||
\(505\) | 24.8003 | 1.10360 | ||||||||
\(506\) | 22.7705 | 1.01227 | ||||||||
\(507\) | 13.0866 | 0.581196 | ||||||||
\(508\) | −24.8600 | −1.10298 | ||||||||
\(509\) | −15.4007 | −0.682624 | −0.341312 | − | 0.939950i | \(-0.610871\pi\) | ||||
−0.341312 | + | 0.939950i | \(0.610871\pi\) | |||||||
\(510\) | −90.9619 | −4.02786 | ||||||||
\(511\) | −19.9245 | −0.881407 | ||||||||
\(512\) | 49.1258 | 2.17107 | ||||||||
\(513\) | 31.2924 | 1.38159 | ||||||||
\(514\) | −12.7142 | −0.560798 | ||||||||
\(515\) | −3.26754 | −0.143985 | ||||||||
\(516\) | −0.359709 | −0.0158353 | ||||||||
\(517\) | −27.1314 | −1.19324 | ||||||||
\(518\) | 11.0990 | 0.487662 | ||||||||
\(519\) | −29.8260 | −1.30921 | ||||||||
\(520\) | −44.8124 | −1.96516 | ||||||||
\(521\) | −21.3467 | −0.935216 | −0.467608 | − | 0.883936i | \(-0.654884\pi\) | ||||
−0.467608 | + | 0.883936i | \(0.654884\pi\) | |||||||
\(522\) | −6.85286 | −0.299942 | ||||||||
\(523\) | 13.4031 | 0.586075 | 0.293037 | − | 0.956101i | \(-0.405334\pi\) | ||||
0.293037 | + | 0.956101i | \(0.405334\pi\) | |||||||
\(524\) | 20.2095 | 0.882854 | ||||||||
\(525\) | 8.88082 | 0.387591 | ||||||||
\(526\) | 65.6356 | 2.86185 | ||||||||
\(527\) | 49.8686 | 2.17231 | ||||||||
\(528\) | −74.6934 | −3.25061 | ||||||||
\(529\) | −19.5128 | −0.848384 | ||||||||
\(530\) | 0.617044 | 0.0268027 | ||||||||
\(531\) | −5.84335 | −0.253580 | ||||||||
\(532\) | −73.7012 | −3.19535 | ||||||||
\(533\) | −28.7314 | −1.24450 | ||||||||
\(534\) | 67.9145 | 2.93895 | ||||||||
\(535\) | −47.0983 | −2.03624 | ||||||||
\(536\) | 24.5360 | 1.05979 | ||||||||
\(537\) | 39.0030 | 1.68311 | ||||||||
\(538\) | −47.8888 | −2.06463 | ||||||||
\(539\) | −8.74280 | −0.376579 | ||||||||
\(540\) | −55.0578 | −2.36931 | ||||||||
\(541\) | 37.8026 | 1.62526 | 0.812631 | − | 0.582778i | \(-0.198034\pi\) | ||||
0.812631 | + | 0.582778i | \(0.198034\pi\) | |||||||
\(542\) | −54.8961 | −2.35799 | ||||||||
\(543\) | 37.8556 | 1.62454 | ||||||||
\(544\) | −53.1206 | −2.27753 | ||||||||
\(545\) | 11.5754 | 0.495838 | ||||||||
\(546\) | 27.7949 | 1.18951 | ||||||||
\(547\) | 31.9069 | 1.36424 | 0.682121 | − | 0.731240i | \(-0.261058\pi\) | ||||
0.682121 | + | 0.731240i | \(0.261058\pi\) | |||||||
\(548\) | −49.7161 | −2.12376 | ||||||||
\(549\) | 3.05450 | 0.130363 | ||||||||
\(550\) | −24.9229 | −1.06272 | ||||||||
\(551\) | 28.0281 | 1.19404 | ||||||||
\(552\) | −24.3110 | −1.03474 | ||||||||
\(553\) | 7.78919 | 0.331230 | ||||||||
\(554\) | −7.52096 | −0.319535 | ||||||||
\(555\) | 9.64041 | 0.409213 | ||||||||
\(556\) | 36.7333 | 1.55784 | ||||||||
\(557\) | −31.0592 | −1.31602 | −0.658010 | − | 0.753010i | \(-0.728601\pi\) | ||||
−0.658010 | + | 0.753010i | \(0.728601\pi\) | |||||||
\(558\) | −12.2800 | −0.519853 | ||||||||
\(559\) | −0.100556 | −0.00425307 | ||||||||
\(560\) | 49.6761 | 2.09920 | ||||||||
\(561\) | −62.9442 | −2.65750 | ||||||||
\(562\) | −10.6119 | −0.447638 | ||||||||
\(563\) | 7.01223 | 0.295530 | 0.147765 | − | 0.989022i | \(-0.452792\pi\) | ||||
0.147765 | + | 0.989022i | \(0.452792\pi\) | |||||||
\(564\) | 50.9158 | 2.14394 | ||||||||
\(565\) | −51.2509 | −2.15614 | ||||||||
\(566\) | −11.4072 | −0.479482 | ||||||||
\(567\) | 23.9503 | 1.00582 | ||||||||
\(568\) | −8.06034 | −0.338204 | ||||||||
\(569\) | 10.7364 | 0.450093 | 0.225047 | − | 0.974348i | \(-0.427747\pi\) | ||||
0.225047 | + | 0.974348i | \(0.427747\pi\) | |||||||
\(570\) | −91.6118 | −3.83719 | ||||||||
\(571\) | 37.3744 | 1.56407 | 0.782035 | − | 0.623235i | \(-0.214182\pi\) | ||||
0.782035 | + | 0.623235i | \(0.214182\pi\) | |||||||
\(572\) | −54.5062 | −2.27902 | ||||||||
\(573\) | 1.64211 | 0.0686002 | ||||||||
\(574\) | 67.6902 | 2.82533 | ||||||||
\(575\) | −3.81679 | −0.159171 | ||||||||
\(576\) | 2.12937 | 0.0887239 | ||||||||
\(577\) | −26.9211 | −1.12074 | −0.560370 | − | 0.828242i | \(-0.689341\pi\) | ||||
−0.560370 | + | 0.828242i | \(0.689341\pi\) | |||||||
\(578\) | −80.6116 | −3.35300 | ||||||||
\(579\) | −37.2259 | −1.54705 | ||||||||
\(580\) | −49.3143 | −2.04767 | ||||||||
\(581\) | −21.6341 | −0.897533 | ||||||||
\(582\) | −53.1228 | −2.20201 | ||||||||
\(583\) | 0.426985 | 0.0176839 | ||||||||
\(584\) | −59.6982 | −2.47033 | ||||||||
\(585\) | 4.37545 | 0.180902 | ||||||||
\(586\) | 8.42701 | 0.348117 | ||||||||
\(587\) | 6.38712 | 0.263625 | 0.131812 | − | 0.991275i | \(-0.457920\pi\) | ||||
0.131812 | + | 0.991275i | \(0.457920\pi\) | |||||||
\(588\) | 16.4071 | 0.676616 | ||||||||
\(589\) | 50.2249 | 2.06948 | ||||||||
\(590\) | −60.1766 | −2.47743 | ||||||||
\(591\) | 45.9266 | 1.88917 | ||||||||
\(592\) | 15.6473 | 0.643099 | ||||||||
\(593\) | −9.97703 | −0.409708 | −0.204854 | − | 0.978793i | \(-0.565672\pi\) | ||||
−0.204854 | + | 0.978793i | \(0.565672\pi\) | |||||||
\(594\) | −54.5230 | −2.23710 | ||||||||
\(595\) | 41.8621 | 1.71618 | ||||||||
\(596\) | 27.5731 | 1.12944 | ||||||||
\(597\) | 27.6313 | 1.13087 | ||||||||
\(598\) | −11.9457 | −0.488495 | ||||||||
\(599\) | 39.5902 | 1.61761 | 0.808806 | − | 0.588076i | \(-0.200114\pi\) | ||||
0.808806 | + | 0.588076i | \(0.200114\pi\) | |||||||
\(600\) | 26.6089 | 1.08630 | ||||||||
\(601\) | 20.9390 | 0.854122 | 0.427061 | − | 0.904223i | \(-0.359549\pi\) | ||||
0.427061 | + | 0.904223i | \(0.359549\pi\) | |||||||
\(602\) | 0.236907 | 0.00965560 | ||||||||
\(603\) | −2.39567 | −0.0975592 | ||||||||
\(604\) | −47.0128 | −1.91292 | ||||||||
\(605\) | −30.2411 | −1.22948 | ||||||||
\(606\) | −46.0892 | −1.87225 | ||||||||
\(607\) | −26.0358 | −1.05676 | −0.528381 | − | 0.849008i | \(-0.677201\pi\) | ||||
−0.528381 | + | 0.849008i | \(0.677201\pi\) | |||||||
\(608\) | −53.5001 | −2.16971 | ||||||||
\(609\) | 17.4016 | 0.705147 | ||||||||
\(610\) | 31.4561 | 1.27362 | ||||||||
\(611\) | 14.2334 | 0.575824 | ||||||||
\(612\) | 21.4082 | 0.865377 | ||||||||
\(613\) | 26.8998 | 1.08647 | 0.543236 | − | 0.839580i | \(-0.317199\pi\) | ||||
0.543236 | + | 0.839580i | \(0.317199\pi\) | |||||||
\(614\) | 45.4748 | 1.83521 | ||||||||
\(615\) | 58.7946 | 2.37083 | ||||||||
\(616\) | 73.0573 | 2.94356 | ||||||||
\(617\) | −20.9015 | −0.841464 | −0.420732 | − | 0.907185i | \(-0.638227\pi\) | ||||
−0.420732 | + | 0.907185i | \(0.638227\pi\) | |||||||
\(618\) | 6.07242 | 0.244268 | ||||||||
\(619\) | 8.34078 | 0.335244 | 0.167622 | − | 0.985851i | \(-0.446391\pi\) | ||||
0.167622 | + | 0.985851i | \(0.446391\pi\) | |||||||
\(620\) | −88.3687 | −3.54897 | ||||||||
\(621\) | −8.34987 | −0.335069 | ||||||||
\(622\) | −48.7165 | −1.95335 | ||||||||
\(623\) | −31.2553 | −1.25222 | ||||||||
\(624\) | 39.1850 | 1.56866 | ||||||||
\(625\) | −31.0420 | −1.24168 | ||||||||
\(626\) | 10.4200 | 0.416469 | ||||||||
\(627\) | −63.3939 | −2.53171 | ||||||||
\(628\) | −104.905 | −4.18617 | ||||||||
\(629\) | 13.1860 | 0.525759 | ||||||||
\(630\) | −10.3084 | −0.410696 | ||||||||
\(631\) | −23.9785 | −0.954569 | −0.477285 | − | 0.878749i | \(-0.658379\pi\) | ||||
−0.477285 | + | 0.878749i | \(0.658379\pi\) | |||||||
\(632\) | 23.3382 | 0.928342 | ||||||||
\(633\) | −3.85717 | −0.153309 | ||||||||
\(634\) | −45.1814 | −1.79438 | ||||||||
\(635\) | 14.2213 | 0.564355 | ||||||||
\(636\) | −0.801295 | −0.0317734 | ||||||||
\(637\) | 4.58657 | 0.181727 | ||||||||
\(638\) | −48.8353 | −1.93341 | ||||||||
\(639\) | 0.787004 | 0.0311334 | ||||||||
\(640\) | −18.6495 | −0.737185 | ||||||||
\(641\) | 6.25528 | 0.247069 | 0.123534 | − | 0.992340i | \(-0.460577\pi\) | ||||
0.123534 | + | 0.992340i | \(0.460577\pi\) | |||||||
\(642\) | 87.5279 | 3.45445 | ||||||||
\(643\) | 30.3958 | 1.19869 | 0.599346 | − | 0.800490i | \(-0.295427\pi\) | ||||
0.599346 | + | 0.800490i | \(0.295427\pi\) | |||||||
\(644\) | 19.6660 | 0.774947 | ||||||||
\(645\) | 0.205773 | 0.00810232 | ||||||||
\(646\) | −125.305 | −4.93005 | ||||||||
\(647\) | −26.4583 | −1.04018 | −0.520092 | − | 0.854110i | \(-0.674102\pi\) | ||||
−0.520092 | + | 0.854110i | \(0.674102\pi\) | |||||||
\(648\) | 71.7606 | 2.81902 | ||||||||
\(649\) | −41.6413 | −1.63456 | ||||||||
\(650\) | 13.0748 | 0.512837 | ||||||||
\(651\) | 31.1827 | 1.22215 | ||||||||
\(652\) | 13.9658 | 0.546944 | ||||||||
\(653\) | 24.8499 | 0.972452 | 0.486226 | − | 0.873833i | \(-0.338373\pi\) | ||||
0.486226 | + | 0.873833i | \(0.338373\pi\) | |||||||
\(654\) | −21.5119 | −0.841182 | ||||||||
\(655\) | −11.5609 | −0.451723 | ||||||||
\(656\) | 95.4290 | 3.72588 | ||||||||
\(657\) | 5.82888 | 0.227406 | ||||||||
\(658\) | −33.5335 | −1.30727 | ||||||||
\(659\) | −6.01352 | −0.234253 | −0.117127 | − | 0.993117i | \(-0.537368\pi\) | ||||
−0.117127 | + | 0.993117i | \(0.537368\pi\) | |||||||
\(660\) | 111.539 | 4.34165 | ||||||||
\(661\) | −26.6630 | −1.03707 | −0.518535 | − | 0.855057i | \(-0.673522\pi\) | ||||
−0.518535 | + | 0.855057i | \(0.673522\pi\) | |||||||
\(662\) | 54.1978 | 2.10646 | ||||||||
\(663\) | 33.0212 | 1.28244 | ||||||||
\(664\) | −64.8206 | −2.51553 | ||||||||
\(665\) | 42.1612 | 1.63494 | ||||||||
\(666\) | −3.24700 | −0.125819 | ||||||||
\(667\) | −7.47884 | −0.289582 | ||||||||
\(668\) | 59.1500 | 2.28858 | ||||||||
\(669\) | 24.1038 | 0.931908 | ||||||||
\(670\) | −24.6714 | −0.953138 | ||||||||
\(671\) | 21.7671 | 0.840311 | ||||||||
\(672\) | −33.2161 | −1.28134 | ||||||||
\(673\) | −30.7772 | −1.18637 | −0.593186 | − | 0.805065i | \(-0.702130\pi\) | ||||
−0.593186 | + | 0.805065i | \(0.702130\pi\) | |||||||
\(674\) | −81.9850 | −3.15794 | ||||||||
\(675\) | 9.13913 | 0.351765 | ||||||||
\(676\) | −31.7186 | −1.21995 | ||||||||
\(677\) | −31.3691 | −1.20561 | −0.602806 | − | 0.797887i | \(-0.705951\pi\) | ||||
−0.602806 | + | 0.797887i | \(0.705951\pi\) | |||||||
\(678\) | 95.2451 | 3.65787 | ||||||||
\(679\) | 24.4479 | 0.938226 | ||||||||
\(680\) | 125.428 | 4.80996 | ||||||||
\(681\) | 29.9148 | 1.14634 | ||||||||
\(682\) | −87.5103 | −3.35094 | ||||||||
\(683\) | 48.8406 | 1.86883 | 0.934416 | − | 0.356183i | \(-0.115922\pi\) | ||||
0.934416 | + | 0.356183i | \(0.115922\pi\) | |||||||
\(684\) | 21.5612 | 0.824413 | ||||||||
\(685\) | 28.4403 | 1.08665 | ||||||||
\(686\) | −51.7483 | −1.97576 | ||||||||
\(687\) | −28.7486 | −1.09683 | ||||||||
\(688\) | 0.333989 | 0.0127332 | ||||||||
\(689\) | −0.224001 | −0.00853376 | ||||||||
\(690\) | 24.4451 | 0.930609 | ||||||||
\(691\) | −15.7648 | −0.599721 | −0.299861 | − | 0.953983i | \(-0.596940\pi\) | ||||
−0.299861 | + | 0.953983i | \(0.596940\pi\) | |||||||
\(692\) | 72.2906 | 2.74808 | ||||||||
\(693\) | −7.13325 | −0.270970 | ||||||||
\(694\) | −65.8506 | −2.49966 | ||||||||
\(695\) | −21.0135 | −0.797086 | ||||||||
\(696\) | 52.1390 | 1.97633 | ||||||||
\(697\) | 80.4181 | 3.04605 | ||||||||
\(698\) | 16.3666 | 0.619483 | ||||||||
\(699\) | −21.4093 | −0.809774 | ||||||||
\(700\) | −21.5249 | −0.813563 | ||||||||
\(701\) | 11.1097 | 0.419607 | 0.209804 | − | 0.977744i | \(-0.432718\pi\) | ||||
0.209804 | + | 0.977744i | \(0.432718\pi\) | |||||||
\(702\) | 28.6034 | 1.07956 | ||||||||
\(703\) | 13.2802 | 0.500871 | ||||||||
\(704\) | 15.1745 | 0.571910 | ||||||||
\(705\) | −29.1267 | −1.09697 | ||||||||
\(706\) | −59.8674 | −2.25314 | ||||||||
\(707\) | 21.2110 | 0.797721 | ||||||||
\(708\) | 78.1455 | 2.93689 | ||||||||
\(709\) | −2.95242 | −0.110880 | −0.0554401 | − | 0.998462i | \(-0.517656\pi\) | ||||
−0.0554401 | + | 0.998462i | \(0.517656\pi\) | |||||||
\(710\) | 8.10481 | 0.304168 | ||||||||
\(711\) | −2.27872 | −0.0854585 | ||||||||
\(712\) | −93.6480 | −3.50961 | ||||||||
\(713\) | −13.4017 | −0.501897 | ||||||||
\(714\) | −77.7969 | −2.91148 | ||||||||
\(715\) | 31.1806 | 1.16609 | ||||||||
\(716\) | −94.5335 | −3.53288 | ||||||||
\(717\) | −47.0759 | −1.75808 | ||||||||
\(718\) | 14.9136 | 0.556570 | ||||||||
\(719\) | −3.71870 | −0.138684 | −0.0693421 | − | 0.997593i | \(-0.522090\pi\) | ||||
−0.0693421 | + | 0.997593i | \(0.522090\pi\) | |||||||
\(720\) | −14.5327 | −0.541601 | ||||||||
\(721\) | −2.79462 | −0.104077 | ||||||||
\(722\) | −77.2423 | −2.87466 | ||||||||
\(723\) | 33.8709 | 1.25967 | ||||||||
\(724\) | −91.7525 | −3.40995 | ||||||||
\(725\) | 8.18577 | 0.304012 | ||||||||
\(726\) | 56.2004 | 2.08579 | ||||||||
\(727\) | −17.1367 | −0.635564 | −0.317782 | − | 0.948164i | \(-0.602938\pi\) | ||||
−0.317782 | + | 0.948164i | \(0.602938\pi\) | |||||||
\(728\) | −38.3267 | −1.42048 | ||||||||
\(729\) | 18.6704 | 0.691497 | ||||||||
\(730\) | 60.0276 | 2.22172 | ||||||||
\(731\) | 0.281453 | 0.0104099 | ||||||||
\(732\) | −40.8490 | −1.50982 | ||||||||
\(733\) | 8.31045 | 0.306954 | 0.153477 | − | 0.988152i | \(-0.450953\pi\) | ||||
0.153477 | + | 0.988152i | \(0.450953\pi\) | |||||||
\(734\) | −12.1617 | −0.448895 | ||||||||
\(735\) | −9.38575 | −0.346199 | ||||||||
\(736\) | 14.2756 | 0.526206 | ||||||||
\(737\) | −17.0722 | −0.628862 | ||||||||
\(738\) | −19.8027 | −0.728947 | ||||||||
\(739\) | 35.7576 | 1.31537 | 0.657683 | − | 0.753295i | \(-0.271537\pi\) | ||||
0.657683 | + | 0.753295i | \(0.271537\pi\) | |||||||
\(740\) | −23.3659 | −0.858949 | ||||||||
\(741\) | 33.2572 | 1.22173 | ||||||||
\(742\) | 0.527739 | 0.0193739 | ||||||||
\(743\) | −37.9376 | −1.39180 | −0.695898 | − | 0.718140i | \(-0.744994\pi\) | ||||
−0.695898 | + | 0.718140i | \(0.744994\pi\) | |||||||
\(744\) | 93.4304 | 3.42533 | ||||||||
\(745\) | −15.7734 | −0.577891 | ||||||||
\(746\) | −87.9645 | −3.22061 | ||||||||
\(747\) | 6.32902 | 0.231567 | ||||||||
\(748\) | 152.561 | 5.57817 | ||||||||
\(749\) | −40.2817 | −1.47186 | ||||||||
\(750\) | 38.6966 | 1.41300 | ||||||||
\(751\) | 49.4956 | 1.80612 | 0.903060 | − | 0.429515i | \(-0.141316\pi\) | ||||
0.903060 | + | 0.429515i | \(0.141316\pi\) | |||||||
\(752\) | −47.2752 | −1.72395 | ||||||||
\(753\) | −17.1440 | −0.624761 | ||||||||
\(754\) | 25.6196 | 0.933010 | ||||||||
\(755\) | 26.8939 | 0.978769 | ||||||||
\(756\) | −47.0892 | −1.71262 | ||||||||
\(757\) | −22.8003 | −0.828690 | −0.414345 | − | 0.910120i | \(-0.635989\pi\) | ||||
−0.414345 | + | 0.910120i | \(0.635989\pi\) | |||||||
\(758\) | 12.6570 | 0.459723 | ||||||||
\(759\) | 16.9156 | 0.613998 | ||||||||
\(760\) | 126.324 | 4.58227 | ||||||||
\(761\) | −29.2756 | −1.06124 | −0.530619 | − | 0.847610i | \(-0.678041\pi\) | ||||
−0.530619 | + | 0.847610i | \(0.678041\pi\) | |||||||
\(762\) | −26.4290 | −0.957421 | ||||||||
\(763\) | 9.90012 | 0.358408 | ||||||||
\(764\) | −3.98007 | −0.143994 | ||||||||
\(765\) | −12.2467 | −0.442780 | ||||||||
\(766\) | 36.0706 | 1.30328 | ||||||||
\(767\) | 21.8455 | 0.788795 | ||||||||
\(768\) | 46.9343 | 1.69360 | ||||||||
\(769\) | 30.2704 | 1.09158 | 0.545790 | − | 0.837922i | \(-0.316230\pi\) | ||||
0.545790 | + | 0.837922i | \(0.316230\pi\) | |||||||
\(770\) | −73.4604 | −2.64733 | ||||||||
\(771\) | −9.44502 | −0.340154 | ||||||||
\(772\) | 90.2261 | 3.24731 | ||||||||
\(773\) | −1.52485 | −0.0548451 | −0.0274225 | − | 0.999624i | \(-0.508730\pi\) | ||||
−0.0274225 | + | 0.999624i | \(0.508730\pi\) | |||||||
\(774\) | −0.0693068 | −0.00249118 | ||||||||
\(775\) | 14.6685 | 0.526907 | ||||||||
\(776\) | 73.2515 | 2.62958 | ||||||||
\(777\) | 8.24515 | 0.295793 | ||||||||
\(778\) | 4.89720 | 0.175573 | ||||||||
\(779\) | 80.9926 | 2.90186 | ||||||||
\(780\) | −58.5146 | −2.09516 | ||||||||
\(781\) | 5.60840 | 0.200684 | ||||||||
\(782\) | 33.4355 | 1.19565 | ||||||||
\(783\) | 17.9077 | 0.639970 | ||||||||
\(784\) | −15.2339 | −0.544069 | ||||||||
\(785\) | 60.0116 | 2.14191 | ||||||||
\(786\) | 21.4849 | 0.766343 | ||||||||
\(787\) | −24.5821 | −0.876259 | −0.438129 | − | 0.898912i | \(-0.644359\pi\) | ||||
−0.438129 | + | 0.898912i | \(0.644359\pi\) | |||||||
\(788\) | −111.315 | −3.96542 | ||||||||
\(789\) | 48.7589 | 1.73586 | ||||||||
\(790\) | −23.4669 | −0.834916 | ||||||||
\(791\) | −43.8333 | −1.55853 | ||||||||
\(792\) | −21.3728 | −0.759450 | ||||||||
\(793\) | −11.4193 | −0.405511 | ||||||||
\(794\) | −28.0225 | −0.994481 | ||||||||
\(795\) | 0.458386 | 0.0162573 | ||||||||
\(796\) | −66.9713 | −2.37374 | ||||||||
\(797\) | −47.8717 | −1.69570 | −0.847851 | − | 0.530235i | \(-0.822104\pi\) | ||||
−0.847851 | + | 0.530235i | \(0.822104\pi\) | |||||||
\(798\) | −78.3527 | −2.77366 | ||||||||
\(799\) | −39.8389 | −1.40940 | ||||||||
\(800\) | −15.6250 | −0.552427 | ||||||||
\(801\) | 9.14370 | 0.323077 | ||||||||
\(802\) | 44.0368 | 1.55499 | ||||||||
\(803\) | 41.5381 | 1.46585 | ||||||||
\(804\) | 32.0383 | 1.12990 | ||||||||
\(805\) | −11.2500 | −0.396511 | ||||||||
\(806\) | 45.9089 | 1.61707 | ||||||||
\(807\) | −35.5753 | −1.25231 | ||||||||
\(808\) | 63.5528 | 2.23578 | ||||||||
\(809\) | −24.1519 | −0.849137 | −0.424569 | − | 0.905396i | \(-0.639574\pi\) | ||||
−0.424569 | + | 0.905396i | \(0.639574\pi\) | |||||||
\(810\) | −72.1566 | −2.53532 | ||||||||
\(811\) | −36.6966 | −1.28859 | −0.644296 | − | 0.764776i | \(-0.722849\pi\) | ||||
−0.644296 | + | 0.764776i | \(0.722849\pi\) | |||||||
\(812\) | −42.1770 | −1.48012 | ||||||||
\(813\) | −40.7809 | −1.43025 | ||||||||
\(814\) | −23.1390 | −0.811020 | ||||||||
\(815\) | −7.98923 | −0.279851 | ||||||||
\(816\) | −109.677 | −3.83947 | ||||||||
\(817\) | 0.283463 | 0.00991713 | ||||||||
\(818\) | 82.6998 | 2.89153 | ||||||||
\(819\) | 3.74218 | 0.130762 | ||||||||
\(820\) | −142.503 | −4.97643 | ||||||||
\(821\) | −40.0829 | −1.39890 | −0.699451 | − | 0.714680i | \(-0.746572\pi\) | ||||
−0.699451 | + | 0.714680i | \(0.746572\pi\) | |||||||
\(822\) | −52.8538 | −1.84349 | ||||||||
\(823\) | 26.2834 | 0.916180 | 0.458090 | − | 0.888906i | \(-0.348534\pi\) | ||||
0.458090 | + | 0.888906i | \(0.348534\pi\) | |||||||
\(824\) | −8.37332 | −0.291698 | ||||||||
\(825\) | −18.5145 | −0.644593 | ||||||||
\(826\) | −51.4672 | −1.79077 | ||||||||
\(827\) | −40.9458 | −1.42382 | −0.711912 | − | 0.702269i | \(-0.752170\pi\) | ||||
−0.711912 | + | 0.702269i | \(0.752170\pi\) | |||||||
\(828\) | −5.75325 | −0.199939 | ||||||||
\(829\) | −53.0947 | −1.84406 | −0.922028 | − | 0.387124i | \(-0.873469\pi\) | ||||
−0.922028 | + | 0.387124i | \(0.873469\pi\) | |||||||
\(830\) | 65.1782 | 2.26237 | ||||||||
\(831\) | −5.58712 | −0.193815 | ||||||||
\(832\) | −7.96071 | −0.275988 | ||||||||
\(833\) | −12.8376 | −0.444798 | ||||||||
\(834\) | 39.0516 | 1.35225 | ||||||||
\(835\) | −33.8371 | −1.17098 | ||||||||
\(836\) | 153.651 | 5.31412 | ||||||||
\(837\) | 32.0897 | 1.10918 | ||||||||
\(838\) | 99.0610 | 3.42200 | ||||||||
\(839\) | −30.9315 | −1.06788 | −0.533938 | − | 0.845524i | \(-0.679288\pi\) | ||||
−0.533938 | + | 0.845524i | \(0.679288\pi\) | |||||||
\(840\) | 78.4300 | 2.70609 | ||||||||
\(841\) | −12.9603 | −0.446908 | ||||||||
\(842\) | 39.9488 | 1.37673 | ||||||||
\(843\) | −7.88332 | −0.271516 | ||||||||
\(844\) | 9.34881 | 0.321799 | ||||||||
\(845\) | 18.1448 | 0.624200 | ||||||||
\(846\) | 9.81019 | 0.337281 | ||||||||
\(847\) | −25.8643 | −0.888708 | ||||||||
\(848\) | 0.744001 | 0.0255491 | ||||||||
\(849\) | −8.47413 | −0.290831 | ||||||||
\(850\) | −36.5960 | −1.25523 | ||||||||
\(851\) | −3.54360 | −0.121473 | ||||||||
\(852\) | −10.5249 | −0.360578 | ||||||||
\(853\) | 18.3165 | 0.627146 | 0.313573 | − | 0.949564i | \(-0.398474\pi\) | ||||
0.313573 | + | 0.949564i | \(0.398474\pi\) | |||||||
\(854\) | 26.9035 | 0.920618 | ||||||||
\(855\) | −12.3342 | −0.421821 | ||||||||
\(856\) | −120.693 | −4.12521 | ||||||||
\(857\) | −13.8660 | −0.473655 | −0.236827 | − | 0.971552i | \(-0.576108\pi\) | ||||
−0.236827 | + | 0.971552i | \(0.576108\pi\) | |||||||
\(858\) | −57.9463 | −1.97825 | ||||||||
\(859\) | 26.7169 | 0.911570 | 0.455785 | − | 0.890090i | \(-0.349359\pi\) | ||||
0.455785 | + | 0.890090i | \(0.349359\pi\) | |||||||
\(860\) | −0.498743 | −0.0170070 | ||||||||
\(861\) | 50.2852 | 1.71372 | ||||||||
\(862\) | −11.5496 | −0.393382 | ||||||||
\(863\) | −31.9618 | −1.08799 | −0.543997 | − | 0.839087i | \(-0.683090\pi\) | ||||
−0.543997 | + | 0.839087i | \(0.683090\pi\) | |||||||
\(864\) | −34.1823 | −1.16290 | ||||||||
\(865\) | −41.3543 | −1.40609 | ||||||||
\(866\) | 62.4304 | 2.12147 | ||||||||
\(867\) | −59.8842 | −2.03377 | ||||||||
\(868\) | −75.5790 | −2.56532 | ||||||||
\(869\) | −16.2387 | −0.550861 | ||||||||
\(870\) | −52.4267 | −1.77743 | ||||||||
\(871\) | 8.95626 | 0.303471 | ||||||||
\(872\) | 29.6630 | 1.00452 | ||||||||
\(873\) | −7.15221 | −0.242066 | ||||||||
\(874\) | 33.6744 | 1.13905 | ||||||||
\(875\) | −17.8088 | −0.602047 | ||||||||
\(876\) | −77.9520 | −2.63375 | ||||||||
\(877\) | 24.8319 | 0.838513 | 0.419256 | − | 0.907868i | \(-0.362291\pi\) | ||||
0.419256 | + | 0.907868i | \(0.362291\pi\) | |||||||
\(878\) | −89.7038 | −3.02736 | ||||||||
\(879\) | 6.26020 | 0.211151 | ||||||||
\(880\) | −103.564 | −3.49113 | ||||||||
\(881\) | −27.9991 | −0.943314 | −0.471657 | − | 0.881782i | \(-0.656344\pi\) | ||||
−0.471657 | + | 0.881782i | \(0.656344\pi\) | |||||||
\(882\) | 3.16123 | 0.106444 | ||||||||
\(883\) | 29.5070 | 0.992989 | 0.496495 | − | 0.868040i | \(-0.334620\pi\) | ||||
0.496495 | + | 0.868040i | \(0.334620\pi\) | |||||||
\(884\) | −80.0351 | −2.69187 | ||||||||
\(885\) | −44.7036 | −1.50269 | ||||||||
\(886\) | −38.0870 | −1.27956 | ||||||||
\(887\) | 10.9172 | 0.366563 | 0.183281 | − | 0.983061i | \(-0.441328\pi\) | ||||
0.183281 | + | 0.983061i | \(0.441328\pi\) | |||||||
\(888\) | 24.7043 | 0.829023 | ||||||||
\(889\) | 12.1630 | 0.407935 | ||||||||
\(890\) | 94.1647 | 3.15641 | ||||||||
\(891\) | −49.9312 | −1.67276 | ||||||||
\(892\) | −58.4216 | −1.95610 | ||||||||
\(893\) | −40.1235 | −1.34268 | ||||||||
\(894\) | 29.3134 | 0.980385 | ||||||||
\(895\) | 54.0784 | 1.80764 | ||||||||
\(896\) | −15.9503 | −0.532863 | ||||||||
\(897\) | −8.87413 | −0.296298 | ||||||||
\(898\) | 39.7517 | 1.32653 | ||||||||
\(899\) | 28.7422 | 0.958607 | ||||||||
\(900\) | 6.29707 | 0.209902 | ||||||||
\(901\) | 0.626970 | 0.0208874 | ||||||||
\(902\) | −141.119 | −4.69875 | ||||||||
\(903\) | 0.175992 | 0.00585663 | ||||||||
\(904\) | −131.334 | −4.36812 | ||||||||
\(905\) | 52.4875 | 1.74474 | ||||||||
\(906\) | −49.9799 | −1.66047 | ||||||||
\(907\) | −16.2988 | −0.541193 | −0.270597 | − | 0.962693i | \(-0.587221\pi\) | ||||
−0.270597 | + | 0.962693i | \(0.587221\pi\) | |||||||
\(908\) | −72.5059 | −2.40619 | ||||||||
\(909\) | −6.20524 | −0.205815 | ||||||||
\(910\) | 38.5382 | 1.27753 | ||||||||
\(911\) | 37.3926 | 1.23887 | 0.619436 | − | 0.785047i | \(-0.287361\pi\) | ||||
0.619436 | + | 0.785047i | \(0.287361\pi\) | |||||||
\(912\) | −110.461 | −3.65773 | ||||||||
\(913\) | 45.1023 | 1.49267 | ||||||||
\(914\) | 76.1335 | 2.51827 | ||||||||
\(915\) | 23.3679 | 0.772520 | ||||||||
\(916\) | 69.6793 | 2.30227 | ||||||||
\(917\) | −9.88771 | −0.326521 | ||||||||
\(918\) | −80.0597 | −2.64236 | ||||||||
\(919\) | −1.61261 | −0.0531950 | −0.0265975 | − | 0.999646i | \(-0.508467\pi\) | ||||
−0.0265975 | + | 0.999646i | \(0.508467\pi\) | |||||||
\(920\) | −33.7076 | −1.11131 | ||||||||
\(921\) | 33.7820 | 1.11315 | ||||||||
\(922\) | −33.3849 | −1.09947 | ||||||||
\(923\) | −2.94223 | −0.0968447 | ||||||||
\(924\) | 95.3958 | 3.13829 | ||||||||
\(925\) | 3.87855 | 0.127526 | ||||||||
\(926\) | −30.8824 | −1.01486 | ||||||||
\(927\) | 0.817563 | 0.0268523 | ||||||||
\(928\) | −30.6165 | −1.00504 | ||||||||
\(929\) | −2.23013 | −0.0731683 | −0.0365842 | − | 0.999331i | \(-0.511648\pi\) | ||||
−0.0365842 | + | 0.999331i | \(0.511648\pi\) | |||||||
\(930\) | −93.9459 | −3.08061 | ||||||||
\(931\) | −12.9294 | −0.423743 | ||||||||
\(932\) | 51.8907 | 1.69974 | ||||||||
\(933\) | −36.1901 | −1.18481 | ||||||||
\(934\) | 14.0383 | 0.459346 | ||||||||
\(935\) | −87.2732 | −2.85414 | ||||||||
\(936\) | 11.2124 | 0.366490 | ||||||||
\(937\) | 38.2604 | 1.24991 | 0.624957 | − | 0.780659i | \(-0.285117\pi\) | ||||
0.624957 | + | 0.780659i | \(0.285117\pi\) | |||||||
\(938\) | −21.1006 | −0.688960 | ||||||||
\(939\) | 7.74076 | 0.252610 | ||||||||
\(940\) | 70.5957 | 2.30258 | ||||||||
\(941\) | −3.58632 | −0.116911 | −0.0584554 | − | 0.998290i | \(-0.518618\pi\) | ||||
−0.0584554 | + | 0.998290i | \(0.518618\pi\) | |||||||
\(942\) | −111.526 | −3.63372 | ||||||||
\(943\) | −21.6116 | −0.703769 | ||||||||
\(944\) | −72.5580 | −2.36156 | ||||||||
\(945\) | 26.9376 | 0.876281 | ||||||||
\(946\) | −0.493898 | −0.0160580 | ||||||||
\(947\) | 19.1578 | 0.622546 | 0.311273 | − | 0.950321i | \(-0.399245\pi\) | ||||
0.311273 | + | 0.950321i | \(0.399245\pi\) | |||||||
\(948\) | 30.4742 | 0.989757 | ||||||||
\(949\) | −21.7914 | −0.707378 | ||||||||
\(950\) | −36.8574 | −1.19581 | ||||||||
\(951\) | −33.5640 | −1.08839 | ||||||||
\(952\) | 107.275 | 3.47680 | ||||||||
\(953\) | −18.7954 | −0.608841 | −0.304421 | − | 0.952538i | \(-0.598463\pi\) | ||||
−0.304421 | + | 0.952538i | \(0.598463\pi\) | |||||||
\(954\) | −0.154389 | −0.00499854 | ||||||||
\(955\) | 2.27682 | 0.0736761 | ||||||||
\(956\) | 114.100 | 3.69026 | ||||||||
\(957\) | −36.2784 | −1.17272 | ||||||||
\(958\) | 2.74242 | 0.0886036 | ||||||||
\(959\) | 24.3241 | 0.785468 | ||||||||
\(960\) | 16.2904 | 0.525771 | ||||||||
\(961\) | 20.5046 | 0.661438 | ||||||||
\(962\) | 12.1390 | 0.391376 | ||||||||
\(963\) | 11.7844 | 0.379746 | ||||||||
\(964\) | −82.0946 | −2.64409 | ||||||||
\(965\) | −51.6143 | −1.66152 | ||||||||
\(966\) | 20.9071 | 0.672676 | ||||||||
\(967\) | −53.6211 | −1.72434 | −0.862169 | − | 0.506620i | \(-0.830895\pi\) | ||||
−0.862169 | + | 0.506620i | \(0.830895\pi\) | |||||||
\(968\) | −77.4953 | −2.49079 | ||||||||
\(969\) | −93.0855 | −2.99034 | ||||||||
\(970\) | −73.6557 | −2.36494 | ||||||||
\(971\) | 60.4535 | 1.94005 | 0.970023 | − | 0.243015i | \(-0.0781364\pi\) | ||||
0.970023 | + | 0.243015i | \(0.0781364\pi\) | |||||||
\(972\) | 31.4680 | 1.00934 | ||||||||
\(973\) | −17.9722 | −0.576161 | ||||||||
\(974\) | −57.2645 | −1.83487 | ||||||||
\(975\) | 9.71294 | 0.311063 | ||||||||
\(976\) | 37.9283 | 1.21405 | ||||||||
\(977\) | −6.64655 | −0.212642 | −0.106321 | − | 0.994332i | \(-0.533907\pi\) | ||||
−0.106321 | + | 0.994332i | \(0.533907\pi\) | |||||||
\(978\) | 14.8473 | 0.474763 | ||||||||
\(979\) | 65.1604 | 2.08254 | ||||||||
\(980\) | 22.7487 | 0.726680 | ||||||||
\(981\) | −2.89627 | −0.0924707 | ||||||||
\(982\) | −64.4346 | −2.05619 | ||||||||
\(983\) | −41.0547 | −1.30944 | −0.654721 | − | 0.755871i | \(-0.727214\pi\) | ||||
−0.654721 | + | 0.755871i | \(0.727214\pi\) | |||||||
\(984\) | 150.666 | 4.80305 | ||||||||
\(985\) | 63.6781 | 2.02895 | ||||||||
\(986\) | −71.7082 | −2.28365 | ||||||||
\(987\) | −24.9111 | −0.792930 | ||||||||
\(988\) | −80.6069 | −2.56445 | ||||||||
\(989\) | −0.0756376 | −0.00240514 | ||||||||
\(990\) | 21.4907 | 0.683020 | ||||||||
\(991\) | −2.35477 | −0.0748016 | −0.0374008 | − | 0.999300i | \(-0.511908\pi\) | ||||
−0.0374008 | + | 0.999300i | \(0.511908\pi\) | |||||||
\(992\) | −54.8632 | −1.74191 | ||||||||
\(993\) | 40.2621 | 1.27768 | ||||||||
\(994\) | 6.93179 | 0.219863 | ||||||||
\(995\) | 38.3113 | 1.21455 | ||||||||
\(996\) | −84.6406 | −2.68194 | ||||||||
\(997\) | 42.8665 | 1.35760 | 0.678798 | − | 0.734325i | \(-0.262501\pi\) | ||||
0.678798 | + | 0.734325i | \(0.262501\pi\) | |||||||
\(998\) | −43.3325 | −1.37167 | ||||||||
\(999\) | 8.48497 | 0.268453 |
(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 | 4021.2.a.c.1.10 | ✓ | 182 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4021.2.a.c.1.10 | ✓ | 182 | 1.1 | even | 1 | trivial |