Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.45 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.67602 | 1.89223 | 0.946116 | − | 0.323828i | \(-0.104970\pi\) | ||||
0.946116 | + | 0.323828i | \(0.104970\pi\) | |||||||
\(3\) | 0.199289 | 0.115060 | 0.0575298 | − | 0.998344i | \(-0.481678\pi\) | ||||
0.0575298 | + | 0.998344i | \(0.481678\pi\) | |||||||
\(4\) | 5.16108 | 2.58054 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.533301 | 0.217719 | ||||||||
\(7\) | −2.87374 | −1.08617 | −0.543085 | − | 0.839678i | \(-0.682744\pi\) | ||||
−0.543085 | + | 0.839678i | \(0.682744\pi\) | |||||||
\(8\) | 8.45912 | 2.99075 | ||||||||
\(9\) | −2.96028 | −0.986761 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.806904 | −0.243291 | −0.121645 | − | 0.992574i | \(-0.538817\pi\) | ||||
−0.121645 | + | 0.992574i | \(0.538817\pi\) | |||||||
\(12\) | 1.02855 | 0.296916 | ||||||||
\(13\) | −5.09752 | −1.41380 | −0.706899 | − | 0.707315i | \(-0.749906\pi\) | ||||
−0.706899 | + | 0.707315i | \(0.749906\pi\) | |||||||
\(14\) | −7.69018 | −2.05529 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.3146 | 3.07865 | ||||||||
\(17\) | −0.390647 | −0.0947457 | −0.0473729 | − | 0.998877i | \(-0.515085\pi\) | ||||
−0.0473729 | + | 0.998877i | \(0.515085\pi\) | |||||||
\(18\) | −7.92178 | −1.86718 | ||||||||
\(19\) | 0.489734 | 0.112353 | 0.0561763 | − | 0.998421i | \(-0.482109\pi\) | ||||
0.0561763 | + | 0.998421i | \(0.482109\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.572704 | −0.124974 | ||||||||
\(22\) | −2.15929 | −0.460362 | ||||||||
\(23\) | −1.83958 | −0.383579 | −0.191789 | − | 0.981436i | \(-0.561429\pi\) | ||||
−0.191789 | + | 0.981436i | \(0.561429\pi\) | |||||||
\(24\) | 1.68581 | 0.344114 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −13.6411 | −2.67523 | ||||||||
\(27\) | −1.18782 | −0.228596 | ||||||||
\(28\) | −14.8316 | −2.80291 | ||||||||
\(29\) | −8.05368 | −1.49553 | −0.747765 | − | 0.663963i | \(-0.768873\pi\) | ||||
−0.747765 | + | 0.663963i | \(0.768873\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.55127 | −0.997038 | −0.498519 | − | 0.866879i | \(-0.666123\pi\) | ||||
−0.498519 | + | 0.866879i | \(0.666123\pi\) | |||||||
\(32\) | 16.0359 | 2.83477 | ||||||||
\(33\) | −0.160807 | −0.0279929 | ||||||||
\(34\) | −1.04538 | −0.179281 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −15.2783 | −2.54638 | ||||||||
\(37\) | −2.20153 | −0.361930 | −0.180965 | − | 0.983490i | \(-0.557922\pi\) | ||||
−0.180965 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(38\) | 1.31054 | 0.212597 | ||||||||
\(39\) | −1.01588 | −0.162671 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.59719 | −0.561787 | −0.280893 | − | 0.959739i | \(-0.590631\pi\) | ||||
−0.280893 | + | 0.959739i | \(0.590631\pi\) | |||||||
\(42\) | −1.53257 | −0.236480 | ||||||||
\(43\) | −9.27459 | −1.41436 | −0.707181 | − | 0.707033i | \(-0.750033\pi\) | ||||
−0.707181 | + | 0.707033i | \(0.750033\pi\) | |||||||
\(44\) | −4.16450 | −0.627821 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.92275 | −0.725820 | ||||||||
\(47\) | 10.9779 | 1.60130 | 0.800649 | − | 0.599134i | \(-0.204488\pi\) | ||||
0.800649 | + | 0.599134i | \(0.204488\pi\) | |||||||
\(48\) | 2.45416 | 0.354228 | ||||||||
\(49\) | 1.25837 | 0.179767 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0778515 | −0.0109014 | ||||||||
\(52\) | −26.3087 | −3.64836 | ||||||||
\(53\) | −1.68955 | −0.232077 | −0.116039 | − | 0.993245i | \(-0.537020\pi\) | ||||
−0.116039 | + | 0.993245i | \(0.537020\pi\) | |||||||
\(54\) | −3.17863 | −0.432556 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −24.3093 | −3.24847 | ||||||||
\(57\) | 0.0975985 | 0.0129272 | ||||||||
\(58\) | −21.5518 | −2.82989 | ||||||||
\(59\) | −5.02546 | −0.654259 | −0.327130 | − | 0.944979i | \(-0.606081\pi\) | ||||
−0.327130 | + | 0.944979i | \(0.606081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.39923 | 0.435227 | 0.217613 | − | 0.976035i | \(-0.430173\pi\) | ||||
0.217613 | + | 0.976035i | \(0.430173\pi\) | |||||||
\(62\) | −14.8553 | −1.88663 | ||||||||
\(63\) | 8.50708 | 1.07179 | ||||||||
\(64\) | 18.2832 | 2.28539 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.430323 | −0.0529690 | ||||||||
\(67\) | 12.9814 | 1.58594 | 0.792968 | − | 0.609263i | \(-0.208535\pi\) | ||||
0.792968 | + | 0.609263i | \(0.208535\pi\) | |||||||
\(68\) | −2.01616 | −0.244495 | ||||||||
\(69\) | −0.366608 | −0.0441344 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48671 | 1.00719 | 0.503594 | − | 0.863941i | \(-0.332011\pi\) | ||||
0.503594 | + | 0.863941i | \(0.332011\pi\) | |||||||
\(72\) | −25.0414 | −2.95116 | ||||||||
\(73\) | 13.1818 | 1.54281 | 0.771404 | − | 0.636346i | \(-0.219555\pi\) | ||||
0.771404 | + | 0.636346i | \(0.219555\pi\) | |||||||
\(74\) | −5.89135 | −0.684855 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.52756 | 0.289931 | ||||||||
\(77\) | 2.31883 | 0.264255 | ||||||||
\(78\) | −2.71851 | −0.307811 | ||||||||
\(79\) | 8.08502 | 0.909636 | 0.454818 | − | 0.890584i | \(-0.349704\pi\) | ||||
0.454818 | + | 0.890584i | \(0.349704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.64413 | 0.960459 | ||||||||
\(82\) | −9.62615 | −1.06303 | ||||||||
\(83\) | 0.366678 | 0.0402481 | 0.0201240 | − | 0.999797i | \(-0.493594\pi\) | ||||
0.0201240 | + | 0.999797i | \(0.493594\pi\) | |||||||
\(84\) | −2.95577 | −0.322501 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −24.8190 | −2.67630 | ||||||||
\(87\) | −1.60501 | −0.172075 | ||||||||
\(88\) | −6.82569 | −0.727621 | ||||||||
\(89\) | −2.24259 | −0.237715 | −0.118857 | − | 0.992911i | \(-0.537923\pi\) | ||||
−0.118857 | + | 0.992911i | \(0.537923\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.6489 | 1.53563 | ||||||||
\(92\) | −9.49422 | −0.989841 | ||||||||
\(93\) | −1.10631 | −0.114719 | ||||||||
\(94\) | 29.3772 | 3.03003 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.19578 | 0.326168 | ||||||||
\(97\) | 7.32434 | 0.743674 | 0.371837 | − | 0.928298i | \(-0.378728\pi\) | ||||
0.371837 | + | 0.928298i | \(0.378728\pi\) | |||||||
\(98\) | 3.36741 | 0.340160 | ||||||||
\(99\) | 2.38866 | 0.240070 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.65598 | 0.363783 | 0.181892 | − | 0.983319i | \(-0.441778\pi\) | ||||
0.181892 | + | 0.983319i | \(0.441778\pi\) | |||||||
\(102\) | −0.208332 | −0.0206280 | ||||||||
\(103\) | −19.1218 | −1.88413 | −0.942064 | − | 0.335434i | \(-0.891117\pi\) | ||||
−0.942064 | + | 0.335434i | \(0.891117\pi\) | |||||||
\(104\) | −43.1205 | −4.22832 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.52127 | −0.439144 | ||||||||
\(107\) | 6.56240 | 0.634411 | 0.317205 | − | 0.948357i | \(-0.397256\pi\) | ||||
0.317205 | + | 0.948357i | \(0.397256\pi\) | |||||||
\(108\) | −6.13043 | −0.589901 | ||||||||
\(109\) | −15.2722 | −1.46282 | −0.731408 | − | 0.681940i | \(-0.761136\pi\) | ||||
−0.731408 | + | 0.681940i | \(0.761136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.438741 | −0.0416435 | ||||||||
\(112\) | −35.3889 | −3.34394 | ||||||||
\(113\) | 0.183036 | 0.0172186 | 0.00860929 | − | 0.999963i | \(-0.497260\pi\) | ||||
0.00860929 | + | 0.999963i | \(0.497260\pi\) | |||||||
\(114\) | 0.261176 | 0.0244613 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −41.5657 | −3.85928 | ||||||||
\(117\) | 15.0901 | 1.39508 | ||||||||
\(118\) | −13.4482 | −1.23801 | ||||||||
\(119\) | 1.12262 | 0.102910 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3489 | −0.940810 | ||||||||
\(122\) | 9.09640 | 0.823550 | ||||||||
\(123\) | −0.716880 | −0.0646389 | ||||||||
\(124\) | −28.6506 | −2.57290 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 22.7651 | 2.02808 | ||||||||
\(127\) | 15.1585 | 1.34510 | 0.672551 | − | 0.740051i | \(-0.265199\pi\) | ||||
0.672551 | + | 0.740051i | \(0.265199\pi\) | |||||||
\(128\) | 16.8543 | 1.48972 | ||||||||
\(129\) | −1.84832 | −0.162736 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.10114 | 0.620430 | 0.310215 | − | 0.950667i | \(-0.399599\pi\) | ||||
0.310215 | + | 0.950667i | \(0.399599\pi\) | |||||||
\(132\) | −0.829938 | −0.0722368 | ||||||||
\(133\) | −1.40737 | −0.122034 | ||||||||
\(134\) | 34.7386 | 3.00096 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.30453 | −0.283361 | ||||||||
\(137\) | −7.60403 | −0.649656 | −0.324828 | − | 0.945773i | \(-0.605306\pi\) | ||||
−0.324828 | + | 0.945773i | \(0.605306\pi\) | |||||||
\(138\) | −0.981050 | −0.0835125 | ||||||||
\(139\) | −21.2414 | −1.80167 | −0.900835 | − | 0.434161i | \(-0.857045\pi\) | ||||
−0.900835 | + | 0.434161i | \(0.857045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.18778 | 0.184245 | ||||||||
\(142\) | 22.7106 | 1.90583 | ||||||||
\(143\) | 4.11321 | 0.343964 | ||||||||
\(144\) | −36.4547 | −3.03789 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 35.2746 | 2.91935 | ||||||||
\(147\) | 0.250778 | 0.0206839 | ||||||||
\(148\) | −11.3623 | −0.933975 | ||||||||
\(149\) | −16.0916 | −1.31827 | −0.659137 | − | 0.752023i | \(-0.729078\pi\) | ||||
−0.659137 | + | 0.752023i | \(0.729078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5518 | −0.858695 | −0.429348 | − | 0.903139i | \(-0.641256\pi\) | ||||
−0.429348 | + | 0.903139i | \(0.641256\pi\) | |||||||
\(152\) | 4.14272 | 0.336019 | ||||||||
\(153\) | 1.15642 | 0.0934914 | ||||||||
\(154\) | 6.20523 | 0.500032 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.24304 | −0.419779 | ||||||||
\(157\) | 0.254366 | 0.0203006 | 0.0101503 | − | 0.999948i | \(-0.496769\pi\) | ||||
0.0101503 | + | 0.999948i | \(0.496769\pi\) | |||||||
\(158\) | 21.6357 | 1.72124 | ||||||||
\(159\) | −0.336708 | −0.0267027 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.28647 | 0.416632 | ||||||||
\(162\) | 23.1319 | 1.81741 | ||||||||
\(163\) | 8.82845 | 0.691497 | 0.345749 | − | 0.938327i | \(-0.387625\pi\) | ||||
0.345749 | + | 0.938327i | \(0.387625\pi\) | |||||||
\(164\) | −18.5654 | −1.44971 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.981236 | 0.0761587 | ||||||||
\(167\) | −3.04162 | −0.235367 | −0.117684 | − | 0.993051i | \(-0.537547\pi\) | ||||
−0.117684 | + | 0.993051i | \(0.537547\pi\) | |||||||
\(168\) | −4.84457 | −0.373767 | ||||||||
\(169\) | 12.9847 | 0.998824 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.44975 | −0.110865 | ||||||||
\(172\) | −47.8669 | −3.64982 | ||||||||
\(173\) | 6.02560 | 0.458118 | 0.229059 | − | 0.973413i | \(-0.426435\pi\) | ||||
0.229059 | + | 0.973413i | \(0.426435\pi\) | |||||||
\(174\) | −4.29504 | −0.325606 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.93670 | −0.749007 | ||||||||
\(177\) | −1.00152 | −0.0752787 | ||||||||
\(178\) | −6.00123 | −0.449811 | ||||||||
\(179\) | 7.72419 | 0.577333 | 0.288667 | − | 0.957430i | \(-0.406788\pi\) | ||||
0.288667 | + | 0.957430i | \(0.406788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3144 | −0.766662 | −0.383331 | − | 0.923611i | \(-0.625223\pi\) | ||||
−0.383331 | + | 0.923611i | \(0.625223\pi\) | |||||||
\(182\) | 39.2008 | 2.90576 | ||||||||
\(183\) | 0.677429 | 0.0500770 | ||||||||
\(184\) | −15.5612 | −1.14719 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.96050 | −0.217074 | ||||||||
\(187\) | 0.315214 | 0.0230507 | ||||||||
\(188\) | 56.6581 | 4.13221 | ||||||||
\(189\) | 3.41348 | 0.248294 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6263 | −1.20304 | −0.601519 | − | 0.798858i | \(-0.705438\pi\) | ||||
−0.601519 | + | 0.798858i | \(0.705438\pi\) | |||||||
\(192\) | 3.64363 | 0.262956 | ||||||||
\(193\) | −26.5699 | −1.91254 | −0.956271 | − | 0.292481i | \(-0.905519\pi\) | ||||
−0.956271 | + | 0.292481i | \(0.905519\pi\) | |||||||
\(194\) | 19.6001 | 1.40720 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.49453 | 0.463895 | ||||||||
\(197\) | −4.42875 | −0.315536 | −0.157768 | − | 0.987476i | \(-0.550430\pi\) | ||||
−0.157768 | + | 0.987476i | \(0.550430\pi\) | |||||||
\(198\) | 6.39211 | 0.454268 | ||||||||
\(199\) | 3.44630 | 0.244302 | 0.122151 | − | 0.992512i | \(-0.461021\pi\) | ||||
0.122151 | + | 0.992512i | \(0.461021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.58706 | 0.182477 | ||||||||
\(202\) | 9.78347 | 0.688362 | ||||||||
\(203\) | 23.1442 | 1.62440 | ||||||||
\(204\) | −0.401798 | −0.0281315 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −51.1703 | −3.56521 | ||||||||
\(207\) | 5.44568 | 0.378501 | ||||||||
\(208\) | −62.7740 | −4.35259 | ||||||||
\(209\) | −0.395168 | −0.0273343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.758471 | −0.0522153 | −0.0261076 | − | 0.999659i | \(-0.508311\pi\) | ||||
−0.0261076 | + | 0.999659i | \(0.508311\pi\) | |||||||
\(212\) | −8.71990 | −0.598885 | ||||||||
\(213\) | 1.69131 | 0.115886 | ||||||||
\(214\) | 17.5611 | 1.20045 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.0479 | −0.683673 | ||||||||
\(217\) | 15.9529 | 1.08295 | ||||||||
\(218\) | −40.8688 | −2.76799 | ||||||||
\(219\) | 2.62698 | 0.177515 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.99133 | 0.133951 | ||||||||
\(222\) | −1.17408 | −0.0787991 | ||||||||
\(223\) | −0.994567 | −0.0666011 | −0.0333006 | − | 0.999445i | \(-0.510602\pi\) | ||||
−0.0333006 | + | 0.999445i | \(0.510602\pi\) | |||||||
\(224\) | −46.0830 | −3.07905 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.489808 | 0.0325815 | ||||||||
\(227\) | −9.15012 | −0.607315 | −0.303657 | − | 0.952781i | \(-0.598208\pi\) | ||||
−0.303657 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(228\) | 0.503714 | 0.0333593 | ||||||||
\(229\) | 24.8061 | 1.63924 | 0.819618 | − | 0.572910i | \(-0.194186\pi\) | ||||
0.819618 | + | 0.572910i | \(0.194186\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.462117 | 0.0304051 | ||||||||
\(232\) | −68.1270 | −4.47276 | ||||||||
\(233\) | 20.8307 | 1.36466 | 0.682332 | − | 0.731042i | \(-0.260966\pi\) | ||||
0.682332 | + | 0.731042i | \(0.260966\pi\) | |||||||
\(234\) | 40.3814 | 2.63982 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −25.9368 | −1.68834 | ||||||||
\(237\) | 1.61126 | 0.104662 | ||||||||
\(238\) | 3.00414 | 0.194730 | ||||||||
\(239\) | −27.2186 | −1.76062 | −0.880311 | − | 0.474397i | \(-0.842666\pi\) | ||||
−0.880311 | + | 0.474397i | \(0.842666\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −27.6939 | −1.78023 | ||||||||
\(243\) | 5.28614 | 0.339106 | ||||||||
\(244\) | 17.5437 | 1.12312 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.91839 | −0.122312 | ||||||||
\(247\) | −2.49643 | −0.158844 | ||||||||
\(248\) | −46.9589 | −2.98189 | ||||||||
\(249\) | 0.0730748 | 0.00463093 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.6839 | 1.11620 | 0.558100 | − | 0.829774i | \(-0.311531\pi\) | ||||
0.558100 | + | 0.829774i | \(0.311531\pi\) | |||||||
\(252\) | 43.9057 | 2.76580 | ||||||||
\(253\) | 1.48436 | 0.0933211 | ||||||||
\(254\) | 40.5645 | 2.54524 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.53615 | 0.533509 | ||||||||
\(257\) | −24.6433 | −1.53721 | −0.768604 | − | 0.639725i | \(-0.779048\pi\) | ||||
−0.768604 | + | 0.639725i | \(0.779048\pi\) | |||||||
\(258\) | −4.94615 | −0.307934 | ||||||||
\(259\) | 6.32663 | 0.393118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.8412 | 1.47573 | ||||||||
\(262\) | 19.0028 | 1.17400 | ||||||||
\(263\) | −21.3217 | −1.31475 | −0.657376 | − | 0.753563i | \(-0.728334\pi\) | ||||
−0.657376 | + | 0.753563i | \(0.728334\pi\) | |||||||
\(264\) | −1.36029 | −0.0837198 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.76614 | −0.230917 | ||||||||
\(267\) | −0.446924 | −0.0273513 | ||||||||
\(268\) | 66.9983 | 4.09257 | ||||||||
\(269\) | 21.8448 | 1.33190 | 0.665951 | − | 0.745996i | \(-0.268026\pi\) | ||||
0.665951 | + | 0.745996i | \(0.268026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.65986 | 0.100830 | 0.0504148 | − | 0.998728i | \(-0.483946\pi\) | ||||
0.0504148 | + | 0.998728i | \(0.483946\pi\) | |||||||
\(272\) | −4.81066 | −0.291689 | ||||||||
\(273\) | 2.91937 | 0.176688 | ||||||||
\(274\) | −20.3485 | −1.22930 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.89209 | −0.113891 | ||||||||
\(277\) | 17.1120 | 1.02816 | 0.514080 | − | 0.857742i | \(-0.328134\pi\) | ||||
0.514080 | + | 0.857742i | \(0.328134\pi\) | |||||||
\(278\) | −56.8424 | −3.40918 | ||||||||
\(279\) | 16.4333 | 0.983839 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.8613 | 1.60241 | 0.801205 | − | 0.598390i | \(-0.204193\pi\) | ||||
0.801205 | + | 0.598390i | \(0.204193\pi\) | |||||||
\(282\) | 5.85455 | 0.348633 | ||||||||
\(283\) | −4.41536 | −0.262466 | −0.131233 | − | 0.991352i | \(-0.541894\pi\) | ||||
−0.131233 | + | 0.991352i | \(0.541894\pi\) | |||||||
\(284\) | 43.8006 | 2.59909 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.0070 | 0.650859 | ||||||||
\(287\) | 10.3374 | 0.610196 | ||||||||
\(288\) | −47.4708 | −2.79724 | ||||||||
\(289\) | −16.8474 | −0.991023 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.45966 | 0.0855668 | ||||||||
\(292\) | 68.0321 | 3.98128 | ||||||||
\(293\) | 27.4208 | 1.60194 | 0.800971 | − | 0.598703i | \(-0.204317\pi\) | ||||
0.800971 | + | 0.598703i | \(0.204317\pi\) | |||||||
\(294\) | 0.671088 | 0.0391387 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −18.6230 | −1.08244 | ||||||||
\(297\) | 0.958455 | 0.0556152 | ||||||||
\(298\) | −43.0614 | −2.49448 | ||||||||
\(299\) | 9.37730 | 0.542303 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.6527 | 1.53624 | ||||||||
\(302\) | −28.2369 | −1.62485 | ||||||||
\(303\) | 0.728596 | 0.0418567 | ||||||||
\(304\) | 6.03088 | 0.345895 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.09462 | 0.176907 | ||||||||
\(307\) | 22.4558 | 1.28162 | 0.640809 | − | 0.767700i | \(-0.278599\pi\) | ||||
0.640809 | + | 0.767700i | \(0.278599\pi\) | |||||||
\(308\) | 11.9677 | 0.681921 | ||||||||
\(309\) | −3.81076 | −0.216787 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.0158 | −0.964880 | −0.482440 | − | 0.875929i | \(-0.660249\pi\) | ||||
−0.482440 | + | 0.875929i | \(0.660249\pi\) | |||||||
\(312\) | −8.59344 | −0.486508 | ||||||||
\(313\) | −30.6076 | −1.73004 | −0.865022 | − | 0.501734i | \(-0.832696\pi\) | ||||
−0.865022 | + | 0.501734i | \(0.832696\pi\) | |||||||
\(314\) | 0.680689 | 0.0384135 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 41.7275 | 2.34735 | ||||||||
\(317\) | −13.1196 | −0.736869 | −0.368434 | − | 0.929654i | \(-0.620106\pi\) | ||||
−0.368434 | + | 0.929654i | \(0.620106\pi\) | |||||||
\(318\) | −0.901039 | −0.0505277 | ||||||||
\(319\) | 6.49854 | 0.363848 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.30781 | 0.0729950 | ||||||||
\(322\) | 14.1467 | 0.788365 | ||||||||
\(323\) | −0.191313 | −0.0106449 | ||||||||
\(324\) | 44.6131 | 2.47850 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.6251 | 1.30847 | ||||||||
\(327\) | −3.04359 | −0.168311 | ||||||||
\(328\) | −30.4291 | −1.68016 | ||||||||
\(329\) | −31.5477 | −1.73928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.2977 | 1.11566 | 0.557832 | − | 0.829954i | \(-0.311633\pi\) | ||||
0.557832 | + | 0.829954i | \(0.311633\pi\) | |||||||
\(332\) | 1.89245 | 0.103862 | ||||||||
\(333\) | 6.51716 | 0.357138 | ||||||||
\(334\) | −8.13942 | −0.445369 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.05262 | −0.384752 | ||||||||
\(337\) | −10.6212 | −0.578575 | −0.289287 | − | 0.957242i | \(-0.593418\pi\) | ||||
−0.289287 | + | 0.957242i | \(0.593418\pi\) | |||||||
\(338\) | 34.7473 | 1.89001 | ||||||||
\(339\) | 0.0364771 | 0.00198116 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.47934 | 0.242570 | ||||||||
\(342\) | −3.87956 | −0.209783 | ||||||||
\(343\) | 16.4999 | 0.890913 | ||||||||
\(344\) | −78.4549 | −4.23000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.1246 | 0.866865 | ||||||||
\(347\) | 1.73240 | 0.0930001 | 0.0465001 | − | 0.998918i | \(-0.485193\pi\) | ||||
0.0465001 | + | 0.998918i | \(0.485193\pi\) | |||||||
\(348\) | −8.28358 | −0.444047 | ||||||||
\(349\) | −31.0836 | −1.66387 | −0.831933 | − | 0.554876i | \(-0.812766\pi\) | ||||
−0.831933 | + | 0.554876i | \(0.812766\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.05493 | 0.323188 | ||||||||
\(352\) | −12.9394 | −0.689673 | ||||||||
\(353\) | 33.0003 | 1.75643 | 0.878214 | − | 0.478268i | \(-0.158735\pi\) | ||||
0.878214 | + | 0.478268i | \(0.158735\pi\) | |||||||
\(354\) | −2.68008 | −0.142445 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.5742 | −0.613432 | ||||||||
\(357\) | 0.223725 | 0.0118408 | ||||||||
\(358\) | 20.6701 | 1.09245 | ||||||||
\(359\) | 32.1190 | 1.69518 | 0.847589 | − | 0.530654i | \(-0.178054\pi\) | ||||
0.847589 | + | 0.530654i | \(0.178054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7602 | −0.987377 | ||||||||
\(362\) | −27.6015 | −1.45070 | ||||||||
\(363\) | −2.06242 | −0.108249 | ||||||||
\(364\) | 75.6044 | 3.96275 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.81281 | 0.0947572 | ||||||||
\(367\) | 1.93764 | 0.101144 | 0.0505719 | − | 0.998720i | \(-0.483896\pi\) | ||||
0.0505719 | + | 0.998720i | \(0.483896\pi\) | |||||||
\(368\) | −22.6537 | −1.18091 | ||||||||
\(369\) | 10.6487 | 0.554349 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.85532 | 0.252076 | ||||||||
\(372\) | −5.70974 | −0.296036 | ||||||||
\(373\) | −8.78738 | −0.454993 | −0.227497 | − | 0.973779i | \(-0.573054\pi\) | ||||
−0.227497 | + | 0.973779i | \(0.573054\pi\) | |||||||
\(374\) | 0.843519 | 0.0436173 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 92.8637 | 4.78908 | ||||||||
\(377\) | 41.0538 | 2.11438 | ||||||||
\(378\) | 9.13454 | 0.469830 | ||||||||
\(379\) | 15.6012 | 0.801378 | 0.400689 | − | 0.916214i | \(-0.368771\pi\) | ||||
0.400689 | + | 0.916214i | \(0.368771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.02093 | 0.154767 | ||||||||
\(382\) | −44.4924 | −2.27643 | ||||||||
\(383\) | −3.43332 | −0.175435 | −0.0877173 | − | 0.996145i | \(-0.527957\pi\) | ||||
−0.0877173 | + | 0.996145i | \(0.527957\pi\) | |||||||
\(384\) | 3.35888 | 0.171407 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −71.1016 | −3.61897 | ||||||||
\(387\) | 27.4554 | 1.39564 | ||||||||
\(388\) | 37.8015 | 1.91908 | ||||||||
\(389\) | −16.1302 | −0.817836 | −0.408918 | − | 0.912571i | \(-0.634094\pi\) | ||||
−0.408918 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.718626 | 0.0363425 | ||||||||
\(392\) | 10.6447 | 0.537637 | ||||||||
\(393\) | 1.41518 | 0.0713863 | ||||||||
\(394\) | −11.8514 | −0.597067 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.3281 | 0.619510 | ||||||||
\(397\) | −4.27325 | −0.214468 | −0.107234 | − | 0.994234i | \(-0.534199\pi\) | ||||
−0.107234 | + | 0.994234i | \(0.534199\pi\) | |||||||
\(398\) | 9.22236 | 0.462275 | ||||||||
\(399\) | −0.280472 | −0.0140412 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.0337541 | −0.00168560 | −0.000842800 | − | 1.00000i | \(-0.500268\pi\) | ||||
−0.000842800 | 1.00000i | \(0.500268\pi\) | ||||||||
\(402\) | 6.92302 | 0.345289 | ||||||||
\(403\) | 28.2977 | 1.40961 | ||||||||
\(404\) | 18.8688 | 0.938758 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 61.9342 | 3.07374 | ||||||||
\(407\) | 1.77642 | 0.0880541 | ||||||||
\(408\) | −0.658555 | −0.0326034 | ||||||||
\(409\) | 12.7748 | 0.631672 | 0.315836 | − | 0.948814i | \(-0.397715\pi\) | ||||
0.315836 | + | 0.948814i | \(0.397715\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.51540 | −0.0747491 | ||||||||
\(412\) | −98.6892 | −4.86207 | ||||||||
\(413\) | 14.4419 | 0.710637 | ||||||||
\(414\) | 14.5727 | 0.716211 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −81.7433 | −4.00780 | ||||||||
\(417\) | −4.23317 | −0.207299 | ||||||||
\(418\) | −1.05748 | −0.0517229 | ||||||||
\(419\) | −37.5266 | −1.83329 | −0.916646 | − | 0.399699i | \(-0.869115\pi\) | ||||
−0.916646 | + | 0.399699i | \(0.869115\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.23835 | −0.450250 | −0.225125 | − | 0.974330i | \(-0.572279\pi\) | ||||
−0.225125 | + | 0.974330i | \(0.572279\pi\) | |||||||
\(422\) | −2.02968 | −0.0988034 | ||||||||
\(423\) | −32.4978 | −1.58010 | ||||||||
\(424\) | −14.2921 | −0.694086 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.52597 | 0.219284 | ||||||||
\(427\) | −9.76849 | −0.472730 | ||||||||
\(428\) | 33.8691 | 1.63712 | ||||||||
\(429\) | 0.819717 | 0.0395763 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.2694 | −1.36169 | −0.680845 | − | 0.732427i | \(-0.738387\pi\) | ||||
−0.680845 | + | 0.732427i | \(0.738387\pi\) | |||||||
\(432\) | −14.6275 | −0.703767 | ||||||||
\(433\) | −2.19007 | −0.105248 | −0.0526239 | − | 0.998614i | \(-0.516758\pi\) | ||||
−0.0526239 | + | 0.998614i | \(0.516758\pi\) | |||||||
\(434\) | 42.6903 | 2.04920 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −78.8213 | −3.77486 | ||||||||
\(437\) | −0.900904 | −0.0430961 | ||||||||
\(438\) | 7.02984 | 0.335899 | ||||||||
\(439\) | 16.6956 | 0.796839 | 0.398419 | − | 0.917203i | \(-0.369559\pi\) | ||||
0.398419 | + | 0.917203i | \(0.369559\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.72512 | −0.177387 | ||||||||
\(442\) | 5.32884 | 0.253467 | ||||||||
\(443\) | −10.7664 | −0.511529 | −0.255764 | − | 0.966739i | \(-0.582327\pi\) | ||||
−0.255764 | + | 0.966739i | \(0.582327\pi\) | |||||||
\(444\) | −2.26438 | −0.107463 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.66148 | −0.126025 | ||||||||
\(447\) | −3.20688 | −0.151680 | ||||||||
\(448\) | −52.5410 | −2.48233 | ||||||||
\(449\) | −32.2748 | −1.52314 | −0.761571 | − | 0.648082i | \(-0.775571\pi\) | ||||
−0.761571 | + | 0.648082i | \(0.775571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.90259 | 0.136677 | ||||||||
\(452\) | 0.944664 | 0.0444333 | ||||||||
\(453\) | −2.10286 | −0.0988011 | ||||||||
\(454\) | −24.4859 | −1.14918 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.825597 | 0.0386621 | ||||||||
\(457\) | 19.5040 | 0.912358 | 0.456179 | − | 0.889888i | \(-0.349218\pi\) | ||||
0.456179 | + | 0.889888i | \(0.349218\pi\) | |||||||
\(458\) | 66.3817 | 3.10181 | ||||||||
\(459\) | 0.464017 | 0.0216585 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.59585 | −0.353774 | −0.176887 | − | 0.984231i | \(-0.556603\pi\) | ||||
−0.176887 | + | 0.984231i | \(0.556603\pi\) | |||||||
\(462\) | 1.23663 | 0.0575334 | ||||||||
\(463\) | 12.5155 | 0.581644 | 0.290822 | − | 0.956777i | \(-0.406071\pi\) | ||||
0.290822 | + | 0.956777i | \(0.406071\pi\) | |||||||
\(464\) | −99.1779 | −4.60422 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 55.7433 | 2.58226 | ||||||||
\(467\) | 11.4282 | 0.528833 | 0.264416 | − | 0.964409i | \(-0.414821\pi\) | ||||
0.264416 | + | 0.964409i | \(0.414821\pi\) | |||||||
\(468\) | 77.8813 | 3.60006 | ||||||||
\(469\) | −37.3053 | −1.72260 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0506924 | 0.00233578 | ||||||||
\(472\) | −42.5110 | −1.95673 | ||||||||
\(473\) | 7.48370 | 0.344101 | ||||||||
\(474\) | 4.31175 | 0.198045 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.79391 | 0.265564 | ||||||||
\(477\) | 5.00155 | 0.229005 | ||||||||
\(478\) | −72.8374 | −3.33150 | ||||||||
\(479\) | 24.3966 | 1.11471 | 0.557354 | − | 0.830275i | \(-0.311817\pi\) | ||||
0.557354 | + | 0.830275i | \(0.311817\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2224 | 0.511696 | ||||||||
\(482\) | 2.67602 | 0.121889 | ||||||||
\(483\) | 1.05353 | 0.0479375 | ||||||||
\(484\) | −53.4116 | −2.42780 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.1458 | 0.641667 | ||||||||
\(487\) | −32.5012 | −1.47277 | −0.736385 | − | 0.676563i | \(-0.763469\pi\) | ||||
−0.736385 | + | 0.676563i | \(0.763469\pi\) | |||||||
\(488\) | 28.7545 | 1.30165 | ||||||||
\(489\) | 1.75941 | 0.0795633 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.3890 | 0.694498 | 0.347249 | − | 0.937773i | \(-0.387116\pi\) | ||||
0.347249 | + | 0.937773i | \(0.387116\pi\) | |||||||
\(492\) | −3.69988 | −0.166803 | ||||||||
\(493\) | 3.14614 | 0.141695 | ||||||||
\(494\) | −6.68049 | −0.300569 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.3618 | −3.06953 | ||||||||
\(497\) | −24.3886 | −1.09398 | ||||||||
\(498\) | 0.195550 | 0.00876278 | ||||||||
\(499\) | −33.4862 | −1.49905 | −0.749525 | − | 0.661976i | \(-0.769718\pi\) | ||||
−0.749525 | + | 0.661976i | \(0.769718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.606160 | −0.0270812 | ||||||||
\(502\) | 47.3225 | 2.11211 | ||||||||
\(503\) | −38.0060 | −1.69460 | −0.847302 | − | 0.531111i | \(-0.821775\pi\) | ||||
−0.847302 | + | 0.531111i | \(0.821775\pi\) | |||||||
\(504\) | 71.9624 | 3.20546 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.97219 | 0.176585 | ||||||||
\(507\) | 2.58771 | 0.114924 | ||||||||
\(508\) | 78.2344 | 3.47109 | ||||||||
\(509\) | 28.9990 | 1.28536 | 0.642679 | − | 0.766136i | \(-0.277823\pi\) | ||||
0.642679 | + | 0.766136i | \(0.277823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.8809 | −1.67575 | ||||||||
\(512\) | −10.8657 | −0.480202 | ||||||||
\(513\) | −0.581715 | −0.0256833 | ||||||||
\(514\) | −65.9460 | −2.90875 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.53935 | −0.419946 | ||||||||
\(517\) | −8.85814 | −0.389581 | ||||||||
\(518\) | 16.9302 | 0.743870 | ||||||||
\(519\) | 1.20083 | 0.0527108 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.52198 | −0.373355 | −0.186677 | − | 0.982421i | \(-0.559772\pi\) | ||||
−0.186677 | + | 0.982421i | \(0.559772\pi\) | |||||||
\(522\) | 63.7995 | 2.79243 | ||||||||
\(523\) | −6.18981 | −0.270662 | −0.135331 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135331 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(524\) | 36.6496 | 1.60104 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −57.0573 | −2.48782 | ||||||||
\(527\) | 2.16859 | 0.0944651 | ||||||||
\(528\) | −1.98027 | −0.0861804 | ||||||||
\(529\) | −19.6159 | −0.852867 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.8768 | 0.645598 | ||||||||
\(532\) | −7.26353 | −0.314914 | ||||||||
\(533\) | 18.3367 | 0.794253 | ||||||||
\(534\) | −1.19598 | −0.0517550 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 109.812 | 4.74314 | ||||||||
\(537\) | 1.53935 | 0.0664277 | ||||||||
\(538\) | 58.4572 | 2.52027 | ||||||||
\(539\) | −1.01538 | −0.0437355 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0092 | 0.989244 | 0.494622 | − | 0.869108i | \(-0.335306\pi\) | ||||
0.494622 | + | 0.869108i | \(0.335306\pi\) | |||||||
\(542\) | 4.44183 | 0.190793 | ||||||||
\(543\) | −2.05554 | −0.0882117 | ||||||||
\(544\) | −6.26437 | −0.268583 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.81229 | 0.334335 | ||||||||
\(547\) | −34.2241 | −1.46332 | −0.731658 | − | 0.681672i | \(-0.761253\pi\) | ||||
−0.731658 | + | 0.681672i | \(0.761253\pi\) | |||||||
\(548\) | −39.2450 | −1.67646 | ||||||||
\(549\) | −10.0627 | −0.429465 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.94416 | −0.168027 | ||||||||
\(552\) | −3.10118 | −0.131995 | ||||||||
\(553\) | −23.2342 | −0.988020 | ||||||||
\(554\) | 45.7920 | 1.94552 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −109.629 | −4.64929 | ||||||||
\(557\) | 8.34480 | 0.353580 | 0.176790 | − | 0.984249i | \(-0.443429\pi\) | ||||
0.176790 | + | 0.984249i | \(0.443429\pi\) | |||||||
\(558\) | 43.9760 | 1.86165 | ||||||||
\(559\) | 47.2774 | 1.99962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0628187 | 0.00265221 | ||||||||
\(562\) | 71.8813 | 3.03213 | ||||||||
\(563\) | 21.1210 | 0.890146 | 0.445073 | − | 0.895494i | \(-0.353178\pi\) | ||||
0.445073 | + | 0.895494i | \(0.353178\pi\) | |||||||
\(564\) | 11.2913 | 0.475451 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.8156 | −0.496647 | ||||||||
\(567\) | −24.8410 | −1.04322 | ||||||||
\(568\) | 71.7901 | 3.01225 | ||||||||
\(569\) | 38.2880 | 1.60512 | 0.802559 | − | 0.596573i | \(-0.203471\pi\) | ||||
0.802559 | + | 0.596573i | \(0.203471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.36826 | 0.182806 | 0.0914031 | − | 0.995814i | \(-0.470865\pi\) | ||||
0.0914031 | + | 0.995814i | \(0.470865\pi\) | |||||||
\(572\) | 21.2286 | 0.887612 | ||||||||
\(573\) | −3.31344 | −0.138421 | ||||||||
\(574\) | 27.6630 | 1.15463 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −54.1233 | −2.25514 | ||||||||
\(577\) | −9.27981 | −0.386324 | −0.193162 | − | 0.981167i | \(-0.561874\pi\) | ||||
−0.193162 | + | 0.981167i | \(0.561874\pi\) | |||||||
\(578\) | −45.0840 | −1.87525 | ||||||||
\(579\) | −5.29508 | −0.220056 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.05373 | −0.0437163 | ||||||||
\(582\) | 3.90608 | 0.161912 | ||||||||
\(583\) | 1.36330 | 0.0564623 | ||||||||
\(584\) | 111.506 | 4.61415 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 73.3787 | 3.03125 | ||||||||
\(587\) | 12.4373 | 0.513342 | 0.256671 | − | 0.966499i | \(-0.417374\pi\) | ||||
0.256671 | + | 0.966499i | \(0.417374\pi\) | |||||||
\(588\) | 1.29429 | 0.0533755 | ||||||||
\(589\) | −2.71865 | −0.112020 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.882602 | −0.0363054 | ||||||||
\(592\) | −27.1110 | −1.11426 | ||||||||
\(593\) | 37.5611 | 1.54245 | 0.771225 | − | 0.636563i | \(-0.219644\pi\) | ||||
0.771225 | + | 0.636563i | \(0.219644\pi\) | |||||||
\(594\) | 2.56484 | 0.105237 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −83.0500 | −3.40186 | ||||||||
\(597\) | 0.686809 | 0.0281092 | ||||||||
\(598\) | 25.0938 | 1.02616 | ||||||||
\(599\) | −22.2278 | −0.908204 | −0.454102 | − | 0.890950i | \(-0.650040\pi\) | ||||
−0.454102 | + | 0.890950i | \(0.650040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.9863 | −1.91661 | −0.958305 | − | 0.285747i | \(-0.907758\pi\) | ||||
−0.958305 | + | 0.285747i | \(0.907758\pi\) | |||||||
\(602\) | 71.3233 | 2.90692 | ||||||||
\(603\) | −38.4288 | −1.56494 | ||||||||
\(604\) | −54.4588 | −2.21590 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.94974 | 0.0792026 | ||||||||
\(607\) | −0.527341 | −0.0214041 | −0.0107021 | − | 0.999943i | \(-0.503407\pi\) | ||||
−0.0107021 | + | 0.999943i | \(0.503407\pi\) | |||||||
\(608\) | 7.85332 | 0.318494 | ||||||||
\(609\) | 4.61237 | 0.186903 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −55.9603 | −2.26391 | ||||||||
\(612\) | 5.96840 | 0.241258 | ||||||||
\(613\) | −9.71818 | −0.392514 | −0.196257 | − | 0.980553i | \(-0.562879\pi\) | ||||
−0.196257 | + | 0.980553i | \(0.562879\pi\) | |||||||
\(614\) | 60.0921 | 2.42512 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.6153 | 0.790321 | ||||||||
\(617\) | 2.81867 | 0.113476 | 0.0567378 | − | 0.998389i | \(-0.481930\pi\) | ||||
0.0567378 | + | 0.998389i | \(0.481930\pi\) | |||||||
\(618\) | −10.1977 | −0.410211 | ||||||||
\(619\) | −2.75560 | −0.110757 | −0.0553785 | − | 0.998465i | \(-0.517637\pi\) | ||||
−0.0553785 | + | 0.998465i | \(0.517637\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.18509 | 0.0876845 | ||||||||
\(622\) | −45.5347 | −1.82578 | ||||||||
\(623\) | 6.44463 | 0.258199 | ||||||||
\(624\) | −12.5102 | −0.500807 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −81.9065 | −3.27364 | ||||||||
\(627\) | −0.0787526 | −0.00314507 | ||||||||
\(628\) | 1.31281 | 0.0523866 | ||||||||
\(629\) | 0.860022 | 0.0342913 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.5819 | −0.859161 | −0.429580 | − | 0.903029i | \(-0.641338\pi\) | ||||
−0.429580 | + | 0.903029i | \(0.641338\pi\) | |||||||
\(632\) | 68.3922 | 2.72050 | ||||||||
\(633\) | −0.151155 | −0.00600787 | ||||||||
\(634\) | −35.1083 | −1.39433 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.73778 | −0.0689075 | ||||||||
\(637\) | −6.41455 | −0.254154 | ||||||||
\(638\) | 17.3902 | 0.688486 | ||||||||
\(639\) | −25.1231 | −0.993853 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.4224 | −0.846135 | −0.423068 | − | 0.906098i | \(-0.639047\pi\) | ||||
−0.423068 | + | 0.906098i | \(0.639047\pi\) | |||||||
\(642\) | 3.49973 | 0.138123 | ||||||||
\(643\) | 29.1001 | 1.14760 | 0.573798 | − | 0.818997i | \(-0.305469\pi\) | ||||
0.573798 | + | 0.818997i | \(0.305469\pi\) | |||||||
\(644\) | 27.2839 | 1.07514 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.511957 | −0.0201427 | ||||||||
\(647\) | −8.60753 | −0.338397 | −0.169198 | − | 0.985582i | \(-0.554118\pi\) | ||||
−0.169198 | + | 0.985582i | \(0.554118\pi\) | |||||||
\(648\) | 73.1218 | 2.87249 | ||||||||
\(649\) | 4.05506 | 0.159175 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.17924 | 0.124604 | ||||||||
\(652\) | 45.5643 | 1.78444 | ||||||||
\(653\) | −10.3765 | −0.406062 | −0.203031 | − | 0.979172i | \(-0.565079\pi\) | ||||
−0.203031 | + | 0.979172i | \(0.565079\pi\) | |||||||
\(654\) | −8.14470 | −0.318483 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −44.2980 | −1.72955 | ||||||||
\(657\) | −39.0217 | −1.52238 | ||||||||
\(658\) | −84.4223 | −3.29113 | ||||||||
\(659\) | −39.6868 | −1.54598 | −0.772990 | − | 0.634418i | \(-0.781240\pi\) | ||||
−0.772990 | + | 0.634418i | \(0.781240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.6874 | −1.46587 | −0.732934 | − | 0.680300i | \(-0.761850\pi\) | ||||
−0.732934 | + | 0.680300i | \(0.761850\pi\) | |||||||
\(662\) | 54.3171 | 2.11109 | ||||||||
\(663\) | 0.396850 | 0.0154124 | ||||||||
\(664\) | 3.10177 | 0.120372 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.4401 | 0.675789 | ||||||||
\(667\) | 14.8154 | 0.573654 | ||||||||
\(668\) | −15.6980 | −0.607375 | ||||||||
\(669\) | −0.198206 | −0.00766309 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.74285 | −0.105887 | ||||||||
\(672\) | −9.18382 | −0.354274 | ||||||||
\(673\) | 31.7217 | 1.22278 | 0.611390 | − | 0.791329i | \(-0.290610\pi\) | ||||
0.611390 | + | 0.791329i | \(0.290610\pi\) | |||||||
\(674\) | −28.4226 | −1.09480 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 67.0152 | 2.57751 | ||||||||
\(677\) | 45.3409 | 1.74259 | 0.871297 | − | 0.490757i | \(-0.163280\pi\) | ||||
0.871297 | + | 0.490757i | \(0.163280\pi\) | |||||||
\(678\) | 0.0976133 | 0.00374882 | ||||||||
\(679\) | −21.0482 | −0.807757 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.82352 | −0.0698773 | ||||||||
\(682\) | 11.9868 | 0.458999 | ||||||||
\(683\) | 7.82593 | 0.299451 | 0.149726 | − | 0.988728i | \(-0.452161\pi\) | ||||
0.149726 | + | 0.988728i | \(0.452161\pi\) | |||||||
\(684\) | −7.48228 | −0.286092 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 44.1542 | 1.68581 | ||||||||
\(687\) | 4.94359 | 0.188610 | ||||||||
\(688\) | −114.213 | −4.35433 | ||||||||
\(689\) | 8.61251 | 0.328111 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.0023 | −1.33155 | −0.665775 | − | 0.746152i | \(-0.731899\pi\) | ||||
−0.665775 | + | 0.746152i | \(0.731899\pi\) | |||||||
\(692\) | 31.0986 | 1.18219 | ||||||||
\(693\) | −6.86439 | −0.260757 | ||||||||
\(694\) | 4.63594 | 0.175978 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.5770 | −0.514633 | ||||||||
\(697\) | 1.40523 | 0.0532269 | ||||||||
\(698\) | −83.1803 | −3.14842 | ||||||||
\(699\) | 4.15133 | 0.157018 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.28122 | −0.312778 | −0.156389 | − | 0.987696i | \(-0.549985\pi\) | ||||
−0.156389 | + | 0.987696i | \(0.549985\pi\) | |||||||
\(702\) | 16.2031 | 0.611547 | ||||||||
\(703\) | −1.07816 | −0.0406638 | ||||||||
\(704\) | −14.7527 | −0.556015 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 88.3094 | 3.32357 | ||||||||
\(707\) | −10.5063 | −0.395131 | ||||||||
\(708\) | −5.16892 | −0.194260 | ||||||||
\(709\) | −23.7901 | −0.893458 | −0.446729 | − | 0.894669i | \(-0.647411\pi\) | ||||
−0.446729 | + | 0.894669i | \(0.647411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.9340 | −0.897594 | ||||||||
\(712\) | −18.9704 | −0.710945 | ||||||||
\(713\) | 10.2120 | 0.382443 | ||||||||
\(714\) | 0.598692 | 0.0224055 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 39.8652 | 1.48983 | ||||||||
\(717\) | −5.42436 | −0.202576 | ||||||||
\(718\) | 85.9512 | 3.20767 | ||||||||
\(719\) | 33.8950 | 1.26407 | 0.632035 | − | 0.774940i | \(-0.282220\pi\) | ||||
0.632035 | + | 0.774940i | \(0.282220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 54.9510 | 2.04648 | ||||||||
\(722\) | −50.2026 | −1.86835 | ||||||||
\(723\) | 0.199289 | 0.00741163 | ||||||||
\(724\) | −53.2334 | −1.97840 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.51908 | −0.204832 | ||||||||
\(727\) | 26.5707 | 0.985451 | 0.492725 | − | 0.870185i | \(-0.336001\pi\) | ||||
0.492725 | + | 0.870185i | \(0.336001\pi\) | |||||||
\(728\) | 123.917 | 4.59267 | ||||||||
\(729\) | −24.8789 | −0.921442 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.62309 | 0.134005 | ||||||||
\(732\) | 3.49627 | 0.129226 | ||||||||
\(733\) | 50.9266 | 1.88102 | 0.940509 | − | 0.339768i | \(-0.110349\pi\) | ||||
0.940509 | + | 0.339768i | \(0.110349\pi\) | |||||||
\(734\) | 5.18516 | 0.191388 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.4993 | −1.08736 | ||||||||
\(737\) | −10.4748 | −0.385843 | ||||||||
\(738\) | 28.4961 | 1.04896 | ||||||||
\(739\) | 37.8448 | 1.39214 | 0.696071 | − | 0.717973i | \(-0.254930\pi\) | ||||
0.696071 | + | 0.717973i | \(0.254930\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.497510 | −0.0182765 | ||||||||
\(742\) | 12.9929 | 0.476986 | ||||||||
\(743\) | 18.8351 | 0.690992 | 0.345496 | − | 0.938420i | \(-0.387711\pi\) | ||||
0.345496 | + | 0.938420i | \(0.387711\pi\) | |||||||
\(744\) | −9.35839 | −0.343095 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.5152 | −0.860953 | ||||||||
\(747\) | −1.08547 | −0.0397153 | ||||||||
\(748\) | 1.62685 | 0.0594834 | ||||||||
\(749\) | −18.8586 | −0.689079 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.1498 | 1.46509 | 0.732544 | − | 0.680720i | \(-0.238333\pi\) | ||||
0.732544 | + | 0.680720i | \(0.238333\pi\) | |||||||
\(752\) | 135.189 | 4.92984 | ||||||||
\(753\) | 3.52421 | 0.128429 | ||||||||
\(754\) | 109.861 | 4.00089 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 17.6172 | 0.640733 | ||||||||
\(757\) | 11.3231 | 0.411546 | 0.205773 | − | 0.978600i | \(-0.434029\pi\) | ||||
0.205773 | + | 0.978600i | \(0.434029\pi\) | |||||||
\(758\) | 41.7490 | 1.51639 | ||||||||
\(759\) | 0.295817 | 0.0107375 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.9931 | 1.01475 | 0.507374 | − | 0.861726i | \(-0.330616\pi\) | ||||
0.507374 | + | 0.861726i | \(0.330616\pi\) | |||||||
\(762\) | 8.08406 | 0.292855 | ||||||||
\(763\) | 43.8884 | 1.58887 | ||||||||
\(764\) | −85.8098 | −3.10449 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.18764 | −0.331963 | ||||||||
\(767\) | 25.6174 | 0.924990 | ||||||||
\(768\) | 1.70116 | 0.0613853 | ||||||||
\(769\) | −8.32041 | −0.300042 | −0.150021 | − | 0.988683i | \(-0.547934\pi\) | ||||
−0.150021 | + | 0.988683i | \(0.547934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.91114 | −0.176870 | ||||||||
\(772\) | −137.129 | −4.93539 | ||||||||
\(773\) | −11.4321 | −0.411183 | −0.205591 | − | 0.978638i | \(-0.565912\pi\) | ||||
−0.205591 | + | 0.978638i | \(0.565912\pi\) | |||||||
\(774\) | 73.4713 | 2.64087 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 61.9575 | 2.22414 | ||||||||
\(777\) | 1.26083 | 0.0452319 | ||||||||
\(778\) | −43.1649 | −1.54754 | ||||||||
\(779\) | −1.76167 | −0.0631182 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.84796 | −0.245039 | ||||||||
\(782\) | 1.92306 | 0.0687684 | ||||||||
\(783\) | 9.56631 | 0.341872 | ||||||||
\(784\) | 15.4963 | 0.553439 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.78705 | 0.135079 | ||||||||
\(787\) | 11.5127 | 0.410384 | 0.205192 | − | 0.978722i | \(-0.434218\pi\) | ||||
0.205192 | + | 0.978722i | \(0.434218\pi\) | |||||||
\(788\) | −22.8572 | −0.814253 | ||||||||
\(789\) | −4.24918 | −0.151275 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.525997 | −0.0187023 | ||||||||
\(792\) | 20.2060 | 0.717989 | ||||||||
\(793\) | −17.3276 | −0.615323 | ||||||||
\(794\) | −11.4353 | −0.405824 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.7866 | 0.630430 | ||||||||
\(797\) | 8.19431 | 0.290257 | 0.145129 | − | 0.989413i | \(-0.453640\pi\) | ||||
0.145129 | + | 0.989413i | \(0.453640\pi\) | |||||||
\(798\) | −0.750550 | −0.0265692 | ||||||||
\(799\) | −4.28850 | −0.151716 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.63872 | 0.234568 | ||||||||
\(802\) | −0.0903266 | −0.00318954 | ||||||||
\(803\) | −10.6364 | −0.375351 | ||||||||
\(804\) | 13.3520 | 0.470889 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 75.7253 | 2.66731 | ||||||||
\(807\) | 4.35343 | 0.153248 | ||||||||
\(808\) | 30.9263 | 1.08799 | ||||||||
\(809\) | 9.19094 | 0.323136 | 0.161568 | − | 0.986862i | \(-0.448345\pi\) | ||||
0.161568 | + | 0.986862i | \(0.448345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.9711 | −0.841740 | −0.420870 | − | 0.907121i | \(-0.638275\pi\) | ||||
−0.420870 | + | 0.907121i | \(0.638275\pi\) | |||||||
\(812\) | 119.449 | 4.19183 | ||||||||
\(813\) | 0.330793 | 0.0116014 | ||||||||
\(814\) | 4.75375 | 0.166619 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.958711 | −0.0335616 | ||||||||
\(817\) | −4.54208 | −0.158907 | ||||||||
\(818\) | 34.1856 | 1.19527 | ||||||||
\(819\) | −43.3650 | −1.51530 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.58377 | −0.194875 | −0.0974375 | − | 0.995242i | \(-0.531065\pi\) | ||||
−0.0974375 | + | 0.995242i | \(0.531065\pi\) | |||||||
\(822\) | −4.05524 | −0.141443 | ||||||||
\(823\) | 2.02001 | 0.0704131 | 0.0352066 | − | 0.999380i | \(-0.488791\pi\) | ||||
0.0352066 | + | 0.999380i | \(0.488791\pi\) | |||||||
\(824\) | −161.754 | −5.63495 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 38.6467 | 1.34469 | ||||||||
\(827\) | 24.2638 | 0.843735 | 0.421867 | − | 0.906658i | \(-0.361375\pi\) | ||||
0.421867 | + | 0.906658i | \(0.361375\pi\) | |||||||
\(828\) | 28.1056 | 0.976737 | ||||||||
\(829\) | 0.464596 | 0.0161361 | 0.00806805 | − | 0.999967i | \(-0.497432\pi\) | ||||
0.00806805 | + | 0.999967i | \(0.497432\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.41023 | 0.118299 | ||||||||
\(832\) | −93.1988 | −3.23109 | ||||||||
\(833\) | −0.491577 | −0.0170321 | ||||||||
\(834\) | −11.3281 | −0.392258 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.03949 | −0.0705374 | ||||||||
\(837\) | 6.59391 | 0.227919 | ||||||||
\(838\) | −100.422 | −3.46901 | ||||||||
\(839\) | 11.0915 | 0.382921 | 0.191461 | − | 0.981500i | \(-0.438678\pi\) | ||||
0.191461 | + | 0.981500i | \(0.438678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.8617 | 1.23661 | ||||||||
\(842\) | −24.7220 | −0.851977 | ||||||||
\(843\) | 5.35316 | 0.184372 | ||||||||
\(844\) | −3.91453 | −0.134744 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −86.9648 | −2.98991 | ||||||||
\(847\) | 29.7400 | 1.02188 | ||||||||
\(848\) | −20.8061 | −0.714486 | ||||||||
\(849\) | −0.879933 | −0.0301992 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.04990 | 0.138829 | ||||||||
\(852\) | 8.72897 | 0.299050 | ||||||||
\(853\) | −38.1172 | −1.30511 | −0.652553 | − | 0.757743i | \(-0.726302\pi\) | ||||
−0.652553 | + | 0.757743i | \(0.726302\pi\) | |||||||
\(854\) | −26.1407 | −0.894516 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 55.5121 | 1.89736 | ||||||||
\(857\) | −17.6418 | −0.602634 | −0.301317 | − | 0.953524i | \(-0.597426\pi\) | ||||
−0.301317 | + | 0.953524i | \(0.597426\pi\) | |||||||
\(858\) | 2.19358 | 0.0748875 | ||||||||
\(859\) | −27.4875 | −0.937862 | −0.468931 | − | 0.883235i | \(-0.655361\pi\) | ||||
−0.468931 | + | 0.883235i | \(0.655361\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.06013 | 0.0702089 | ||||||||
\(862\) | −75.6495 | −2.57663 | ||||||||
\(863\) | −19.2496 | −0.655263 | −0.327632 | − | 0.944806i | \(-0.606250\pi\) | ||||
−0.327632 | + | 0.944806i | \(0.606250\pi\) | |||||||
\(864\) | −19.0477 | −0.648017 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.86066 | −0.199153 | ||||||||
\(867\) | −3.35750 | −0.114027 | ||||||||
\(868\) | 82.3342 | 2.79461 | ||||||||
\(869\) | −6.52383 | −0.221306 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −66.1732 | −2.24219 | ||||||||
\(872\) | −129.190 | −4.37492 | ||||||||
\(873\) | −21.6821 | −0.733829 | ||||||||
\(874\) | −2.41084 | −0.0815478 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.5580 | 0.458084 | ||||||||
\(877\) | −41.2611 | −1.39329 | −0.696644 | − | 0.717417i | \(-0.745324\pi\) | ||||
−0.696644 | + | 0.717417i | \(0.745324\pi\) | |||||||
\(878\) | 44.6778 | 1.50780 | ||||||||
\(879\) | 5.46467 | 0.184319 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.1377 | 1.08275 | 0.541373 | − | 0.840783i | \(-0.317905\pi\) | ||||
0.541373 | + | 0.840783i | \(0.317905\pi\) | |||||||
\(882\) | −9.96850 | −0.335657 | ||||||||
\(883\) | 9.13498 | 0.307416 | 0.153708 | − | 0.988116i | \(-0.450878\pi\) | ||||
0.153708 | + | 0.988116i | \(0.450878\pi\) | |||||||
\(884\) | 10.2774 | 0.345667 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.8112 | −0.967931 | ||||||||
\(887\) | 13.8765 | 0.465928 | 0.232964 | − | 0.972485i | \(-0.425158\pi\) | ||||
0.232964 | + | 0.972485i | \(0.425158\pi\) | |||||||
\(888\) | −3.71136 | −0.124545 | ||||||||
\(889\) | −43.5616 | −1.46101 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.97498 | −0.233671 | ||||||||
\(892\) | −5.13304 | −0.171867 | ||||||||
\(893\) | 5.37627 | 0.179910 | ||||||||
\(894\) | −8.58167 | −0.287014 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −48.4349 | −1.61809 | ||||||||
\(897\) | 1.86879 | 0.0623971 | ||||||||
\(898\) | −86.3680 | −2.88214 | ||||||||
\(899\) | 44.7082 | 1.49110 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.660017 | 0.0219883 | ||||||||
\(902\) | 7.76738 | 0.258625 | ||||||||
\(903\) | 5.31160 | 0.176759 | ||||||||
\(904\) | 1.54832 | 0.0514965 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.62730 | −0.186954 | ||||||||
\(907\) | −20.5930 | −0.683778 | −0.341889 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341889 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(908\) | −47.2245 | −1.56720 | ||||||||
\(909\) | −10.8227 | −0.358967 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.8513 | −0.989018 | −0.494509 | − | 0.869173i | \(-0.664652\pi\) | ||||
−0.494509 | + | 0.869173i | \(0.664652\pi\) | |||||||
\(912\) | 1.20189 | 0.0397985 | ||||||||
\(913\) | −0.295873 | −0.00979198 | ||||||||
\(914\) | 52.1931 | 1.72639 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 128.027 | 4.23012 | ||||||||
\(917\) | −20.4068 | −0.673892 | ||||||||
\(918\) | 1.24172 | 0.0409828 | ||||||||
\(919\) | −44.8288 | −1.47877 | −0.739383 | − | 0.673285i | \(-0.764883\pi\) | ||||
−0.739383 | + | 0.673285i | \(0.764883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.47519 | 0.147462 | ||||||||
\(922\) | −20.3266 | −0.669422 | ||||||||
\(923\) | −43.2612 | −1.42396 | ||||||||
\(924\) | 2.38502 | 0.0784615 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 33.4917 | 1.10061 | ||||||||
\(927\) | 56.6060 | 1.85918 | ||||||||
\(928\) | −129.148 | −4.23949 | ||||||||
\(929\) | −53.9902 | −1.77136 | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||||
−0.885681 | + | 0.464294i | \(0.846308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.616264 | 0.0201972 | ||||||||
\(932\) | 107.509 | 3.52157 | ||||||||
\(933\) | −3.39107 | −0.111019 | ||||||||
\(934\) | 30.5820 | 1.00067 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 127.649 | 4.17234 | ||||||||
\(937\) | 41.8090 | 1.36584 | 0.682920 | − | 0.730493i | \(-0.260710\pi\) | ||||
0.682920 | + | 0.730493i | \(0.260710\pi\) | |||||||
\(938\) | −99.8296 | −3.25955 | ||||||||
\(939\) | −6.09975 | −0.199058 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.5326 | 0.571548 | 0.285774 | − | 0.958297i | \(-0.407749\pi\) | ||||
0.285774 | + | 0.958297i | \(0.407749\pi\) | |||||||
\(942\) | 0.135654 | 0.00441984 | ||||||||
\(943\) | 6.61732 | 0.215490 | ||||||||
\(944\) | −61.8866 | −2.01424 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.0265 | 0.651119 | ||||||||
\(947\) | 60.8556 | 1.97754 | 0.988770 | − | 0.149444i | \(-0.0477483\pi\) | ||||
0.988770 | + | 0.149444i | \(0.0477483\pi\) | |||||||
\(948\) | 8.31582 | 0.270085 | ||||||||
\(949\) | −67.1943 | −2.18122 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.61459 | −0.0847838 | ||||||||
\(952\) | 9.49634 | 0.307778 | ||||||||
\(953\) | 47.7538 | 1.54690 | 0.773449 | − | 0.633859i | \(-0.218530\pi\) | ||||
0.773449 | + | 0.633859i | \(0.218530\pi\) | |||||||
\(954\) | 13.3842 | 0.433331 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −140.477 | −4.54336 | ||||||||
\(957\) | 1.29509 | 0.0418642 | ||||||||
\(958\) | 65.2857 | 2.10928 | ||||||||
\(959\) | 21.8520 | 0.705637 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.183358 | −0.00591476 | ||||||||
\(962\) | 30.0313 | 0.968247 | ||||||||
\(963\) | −19.4266 | −0.626012 | ||||||||
\(964\) | 5.16108 | 0.166227 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.81928 | 0.0907088 | ||||||||
\(967\) | 10.5625 | 0.339666 | 0.169833 | − | 0.985473i | \(-0.445677\pi\) | ||||
0.169833 | + | 0.985473i | \(0.445677\pi\) | |||||||
\(968\) | −87.5426 | −2.81373 | ||||||||
\(969\) | −0.0381265 | −0.00122480 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.2601 | −1.35619 | −0.678096 | − | 0.734973i | \(-0.737195\pi\) | ||||
−0.678096 | + | 0.734973i | \(0.737195\pi\) | |||||||
\(972\) | 27.2822 | 0.875076 | ||||||||
\(973\) | 61.0422 | 1.95692 | ||||||||
\(974\) | −86.9739 | −2.78682 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41.8602 | 1.33991 | ||||||||
\(977\) | −0.878630 | −0.0281099 | −0.0140549 | − | 0.999901i | \(-0.504474\pi\) | ||||
−0.0140549 | + | 0.999901i | \(0.504474\pi\) | |||||||
\(978\) | 4.70822 | 0.150552 | ||||||||
\(979\) | 1.80956 | 0.0578337 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.2102 | 1.44345 | ||||||||
\(982\) | 41.1814 | 1.31415 | ||||||||
\(983\) | −20.9666 | −0.668731 | −0.334365 | − | 0.942444i | \(-0.608522\pi\) | ||||
−0.334365 | + | 0.942444i | \(0.608522\pi\) | |||||||
\(984\) | −6.06417 | −0.193319 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.41914 | 0.268120 | ||||||||
\(987\) | −6.28711 | −0.200121 | ||||||||
\(988\) | −12.8843 | −0.409903 | ||||||||
\(989\) | 17.0614 | 0.542519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.56254 | 0.113168 | 0.0565840 | − | 0.998398i | \(-0.481979\pi\) | ||||
0.0565840 | + | 0.998398i | \(0.481979\pi\) | |||||||
\(992\) | −89.0196 | −2.82638 | ||||||||
\(993\) | 4.04511 | 0.128368 | ||||||||
\(994\) | −65.2643 | −2.07006 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.377145 | 0.0119503 | ||||||||
\(997\) | −5.26746 | −0.166822 | −0.0834111 | − | 0.996515i | \(-0.526581\pi\) | ||||
−0.0834111 | + | 0.996515i | \(0.526581\pi\) | |||||||
\(998\) | −89.6098 | −2.83655 | ||||||||
\(999\) | 2.61502 | 0.0827356 |
(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 | 6025.2.a.p.1.45 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.45 | yes | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.2 | ✓ | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.2 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.2 | ✓ | 46 | 5.3 | odd | 4 | ||
1205.2.b.c.724.45 | yes | 46 | 5.2 | odd | 4 | ||
6025.2.a.p.1.2 | 46 | 5.4 | even | 2 | inner | ||
6025.2.a.p.1.45 | 46 | 1.1 | even | 1 | trivial |