Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.680303 | 0.481047 | 0.240523 | − | 0.970643i | \(-0.422681\pi\) | ||||
0.240523 | + | 0.970643i | \(0.422681\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.53719 | −0.768594 | ||||||||
\(5\) | −1.16933 | −0.522938 | −0.261469 | − | 0.965212i | \(-0.584207\pi\) | ||||
−0.261469 | + | 0.965212i | \(0.584207\pi\) | |||||||
\(6\) | 0.680303 | 0.277732 | ||||||||
\(7\) | −3.22223 | −1.21789 | −0.608944 | − | 0.793214i | \(-0.708406\pi\) | ||||
−0.608944 | + | 0.793214i | \(0.708406\pi\) | |||||||
\(8\) | −2.40636 | −0.850776 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.795496 | −0.251558 | ||||||||
\(11\) | −3.38790 | −1.02149 | −0.510745 | − | 0.859732i | \(-0.670631\pi\) | ||||
−0.510745 | + | 0.859732i | \(0.670631\pi\) | |||||||
\(12\) | −1.53719 | −0.443748 | ||||||||
\(13\) | −0.639664 | −0.177411 | −0.0887054 | − | 0.996058i | \(-0.528273\pi\) | ||||
−0.0887054 | + | 0.996058i | \(0.528273\pi\) | |||||||
\(14\) | −2.19209 | −0.585860 | ||||||||
\(15\) | −1.16933 | −0.301919 | ||||||||
\(16\) | 1.43732 | 0.359331 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0.680303 | 0.160349 | ||||||||
\(19\) | −1.61887 | −0.371395 | −0.185698 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185698 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(20\) | 1.79747 | 0.401927 | ||||||||
\(21\) | −3.22223 | −0.703147 | ||||||||
\(22\) | −2.30480 | −0.491385 | ||||||||
\(23\) | 2.39077 | 0.498510 | 0.249255 | − | 0.968438i | \(-0.419814\pi\) | ||||
0.249255 | + | 0.968438i | \(0.419814\pi\) | |||||||
\(24\) | −2.40636 | −0.491196 | ||||||||
\(25\) | −3.63268 | −0.726535 | ||||||||
\(26\) | −0.435165 | −0.0853429 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.95317 | 0.936061 | ||||||||
\(29\) | −7.67112 | −1.42449 | −0.712245 | − | 0.701931i | \(-0.752322\pi\) | ||||
−0.712245 | + | 0.701931i | \(0.752322\pi\) | |||||||
\(30\) | −0.795496 | −0.145237 | ||||||||
\(31\) | 0.963944 | 0.173129 | 0.0865647 | − | 0.996246i | \(-0.472411\pi\) | ||||
0.0865647 | + | 0.996246i | \(0.472411\pi\) | |||||||
\(32\) | 5.79053 | 1.02363 | ||||||||
\(33\) | −3.38790 | −0.589758 | ||||||||
\(34\) | 0.680303 | 0.116671 | ||||||||
\(35\) | 3.76783 | 0.636880 | ||||||||
\(36\) | −1.53719 | −0.256198 | ||||||||
\(37\) | −1.66517 | −0.273752 | −0.136876 | − | 0.990588i | \(-0.543706\pi\) | ||||
−0.136876 | + | 0.990588i | \(0.543706\pi\) | |||||||
\(38\) | −1.10132 | −0.178658 | ||||||||
\(39\) | −0.639664 | −0.102428 | ||||||||
\(40\) | 2.81382 | 0.444904 | ||||||||
\(41\) | 2.74542 | 0.428762 | 0.214381 | − | 0.976750i | \(-0.431227\pi\) | ||||
0.214381 | + | 0.976750i | \(0.431227\pi\) | |||||||
\(42\) | −2.19209 | −0.338247 | ||||||||
\(43\) | 9.66615 | 1.47407 | 0.737037 | − | 0.675852i | \(-0.236224\pi\) | ||||
0.737037 | + | 0.675852i | \(0.236224\pi\) | |||||||
\(44\) | 5.20784 | 0.785112 | ||||||||
\(45\) | −1.16933 | −0.174313 | ||||||||
\(46\) | 1.62645 | 0.239807 | ||||||||
\(47\) | 10.9547 | 1.59791 | 0.798955 | − | 0.601391i | \(-0.205387\pi\) | ||||
0.798955 | + | 0.601391i | \(0.205387\pi\) | |||||||
\(48\) | 1.43732 | 0.207460 | ||||||||
\(49\) | 3.38274 | 0.483249 | ||||||||
\(50\) | −2.47132 | −0.349497 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0.983284 | 0.136357 | ||||||||
\(53\) | −4.10641 | −0.564059 | −0.282029 | − | 0.959406i | \(-0.591008\pi\) | ||||
−0.282029 | + | 0.959406i | \(0.591008\pi\) | |||||||
\(54\) | 0.680303 | 0.0925775 | ||||||||
\(55\) | 3.96156 | 0.534177 | ||||||||
\(56\) | 7.75383 | 1.03615 | ||||||||
\(57\) | −1.61887 | −0.214425 | ||||||||
\(58\) | −5.21868 | −0.685246 | ||||||||
\(59\) | −4.30295 | −0.560197 | −0.280098 | − | 0.959971i | \(-0.590367\pi\) | ||||
−0.280098 | + | 0.959971i | \(0.590367\pi\) | |||||||
\(60\) | 1.79747 | 0.232053 | ||||||||
\(61\) | 13.9821 | 1.79022 | 0.895109 | − | 0.445847i | \(-0.147097\pi\) | ||||
0.895109 | + | 0.445847i | \(0.147097\pi\) | |||||||
\(62\) | 0.655773 | 0.0832833 | ||||||||
\(63\) | −3.22223 | −0.405962 | ||||||||
\(64\) | 1.06467 | 0.133083 | ||||||||
\(65\) | 0.747976 | 0.0927749 | ||||||||
\(66\) | −2.30480 | −0.283701 | ||||||||
\(67\) | −7.65075 | −0.934687 | −0.467344 | − | 0.884076i | \(-0.654789\pi\) | ||||
−0.467344 | + | 0.884076i | \(0.654789\pi\) | |||||||
\(68\) | −1.53719 | −0.186411 | ||||||||
\(69\) | 2.39077 | 0.287815 | ||||||||
\(70\) | 2.56327 | 0.306369 | ||||||||
\(71\) | 8.73752 | 1.03695 | 0.518476 | − | 0.855092i | \(-0.326499\pi\) | ||||
0.518476 | + | 0.855092i | \(0.326499\pi\) | |||||||
\(72\) | −2.40636 | −0.283592 | ||||||||
\(73\) | 0.0689540 | 0.00807045 | 0.00403523 | − | 0.999992i | \(-0.498716\pi\) | ||||
0.00403523 | + | 0.999992i | \(0.498716\pi\) | |||||||
\(74\) | −1.13282 | −0.131687 | ||||||||
\(75\) | −3.63268 | −0.419465 | ||||||||
\(76\) | 2.48851 | 0.285452 | ||||||||
\(77\) | 10.9166 | 1.24406 | ||||||||
\(78\) | −0.435165 | −0.0492727 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −1.68070 | −0.187908 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.86772 | 0.206255 | ||||||||
\(83\) | −16.0736 | −1.76430 | −0.882152 | − | 0.470964i | \(-0.843906\pi\) | ||||
−0.882152 | + | 0.470964i | \(0.843906\pi\) | |||||||
\(84\) | 4.95317 | 0.540435 | ||||||||
\(85\) | −1.16933 | −0.126831 | ||||||||
\(86\) | 6.57591 | 0.709099 | ||||||||
\(87\) | −7.67112 | −0.822430 | ||||||||
\(88\) | 8.15251 | 0.869060 | ||||||||
\(89\) | 13.8761 | 1.47086 | 0.735432 | − | 0.677598i | \(-0.236979\pi\) | ||||
0.735432 | + | 0.677598i | \(0.236979\pi\) | |||||||
\(90\) | −0.795496 | −0.0838526 | ||||||||
\(91\) | 2.06114 | 0.216066 | ||||||||
\(92\) | −3.67507 | −0.383152 | ||||||||
\(93\) | 0.963944 | 0.0999563 | ||||||||
\(94\) | 7.45252 | 0.768669 | ||||||||
\(95\) | 1.89299 | 0.194217 | ||||||||
\(96\) | 5.79053 | 0.590994 | ||||||||
\(97\) | 0.235021 | 0.0238627 | 0.0119314 | − | 0.999929i | \(-0.496202\pi\) | ||||
0.0119314 | + | 0.999929i | \(0.496202\pi\) | |||||||
\(98\) | 2.30129 | 0.232465 | ||||||||
\(99\) | −3.38790 | −0.340497 | ||||||||
\(100\) | 5.58411 | 0.558411 | ||||||||
\(101\) | 3.30839 | 0.329197 | 0.164598 | − | 0.986361i | \(-0.447367\pi\) | ||||
0.164598 | + | 0.986361i | \(0.447367\pi\) | |||||||
\(102\) | 0.680303 | 0.0673600 | ||||||||
\(103\) | −9.76268 | −0.961945 | −0.480973 | − | 0.876736i | \(-0.659716\pi\) | ||||
−0.480973 | + | 0.876736i | \(0.659716\pi\) | |||||||
\(104\) | 1.53926 | 0.150937 | ||||||||
\(105\) | 3.76783 | 0.367703 | ||||||||
\(106\) | −2.79360 | −0.271339 | ||||||||
\(107\) | 10.9916 | 1.06260 | 0.531301 | − | 0.847183i | \(-0.321703\pi\) | ||||
0.531301 | + | 0.847183i | \(0.321703\pi\) | |||||||
\(108\) | −1.53719 | −0.147916 | ||||||||
\(109\) | 8.50204 | 0.814348 | 0.407174 | − | 0.913351i | \(-0.366514\pi\) | ||||
0.407174 | + | 0.913351i | \(0.366514\pi\) | |||||||
\(110\) | 2.69506 | 0.256964 | ||||||||
\(111\) | −1.66517 | −0.158051 | ||||||||
\(112\) | −4.63139 | −0.437625 | ||||||||
\(113\) | −2.25201 | −0.211852 | −0.105926 | − | 0.994374i | \(-0.533781\pi\) | ||||
−0.105926 | + | 0.994374i | \(0.533781\pi\) | |||||||
\(114\) | −1.10132 | −0.103148 | ||||||||
\(115\) | −2.79559 | −0.260690 | ||||||||
\(116\) | 11.7920 | 1.09486 | ||||||||
\(117\) | −0.639664 | −0.0591369 | ||||||||
\(118\) | −2.92731 | −0.269481 | ||||||||
\(119\) | −3.22223 | −0.295381 | ||||||||
\(120\) | 2.81382 | 0.256865 | ||||||||
\(121\) | 0.477880 | 0.0434437 | ||||||||
\(122\) | 9.51203 | 0.861178 | ||||||||
\(123\) | 2.74542 | 0.247546 | ||||||||
\(124\) | −1.48176 | −0.133066 | ||||||||
\(125\) | 10.0944 | 0.902872 | ||||||||
\(126\) | −2.19209 | −0.195287 | ||||||||
\(127\) | 11.9982 | 1.06467 | 0.532334 | − | 0.846535i | \(-0.321315\pi\) | ||||
0.532334 | + | 0.846535i | \(0.321315\pi\) | |||||||
\(128\) | −10.8568 | −0.959612 | ||||||||
\(129\) | 9.66615 | 0.851057 | ||||||||
\(130\) | 0.508850 | 0.0446291 | ||||||||
\(131\) | 1.20920 | 0.105648 | 0.0528240 | − | 0.998604i | \(-0.483178\pi\) | ||||
0.0528240 | + | 0.998604i | \(0.483178\pi\) | |||||||
\(132\) | 5.20784 | 0.453285 | ||||||||
\(133\) | 5.21638 | 0.452317 | ||||||||
\(134\) | −5.20482 | −0.449628 | ||||||||
\(135\) | −1.16933 | −0.100640 | ||||||||
\(136\) | −2.40636 | −0.206344 | ||||||||
\(137\) | 17.4632 | 1.49198 | 0.745991 | − | 0.665956i | \(-0.231976\pi\) | ||||
0.745991 | + | 0.665956i | \(0.231976\pi\) | |||||||
\(138\) | 1.62645 | 0.138452 | ||||||||
\(139\) | 5.08696 | 0.431470 | 0.215735 | − | 0.976452i | \(-0.430785\pi\) | ||||
0.215735 | + | 0.976452i | \(0.430785\pi\) | |||||||
\(140\) | −5.79187 | −0.489502 | ||||||||
\(141\) | 10.9547 | 0.922554 | ||||||||
\(142\) | 5.94416 | 0.498823 | ||||||||
\(143\) | 2.16712 | 0.181224 | ||||||||
\(144\) | 1.43732 | 0.119777 | ||||||||
\(145\) | 8.97004 | 0.744921 | ||||||||
\(146\) | 0.0469096 | 0.00388226 | ||||||||
\(147\) | 3.38274 | 0.279004 | ||||||||
\(148\) | 2.55967 | 0.210404 | ||||||||
\(149\) | 7.60475 | 0.623005 | 0.311503 | − | 0.950245i | \(-0.399168\pi\) | ||||
0.311503 | + | 0.950245i | \(0.399168\pi\) | |||||||
\(150\) | −2.47132 | −0.201782 | ||||||||
\(151\) | −3.93261 | −0.320032 | −0.160016 | − | 0.987114i | \(-0.551155\pi\) | ||||
−0.160016 | + | 0.987114i | \(0.551155\pi\) | |||||||
\(152\) | 3.89559 | 0.315974 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 7.42658 | 0.598451 | ||||||||
\(155\) | −1.12716 | −0.0905360 | ||||||||
\(156\) | 0.983284 | 0.0787257 | ||||||||
\(157\) | 22.6629 | 1.80870 | 0.904348 | − | 0.426795i | \(-0.140357\pi\) | ||||
0.904348 | + | 0.426795i | \(0.140357\pi\) | |||||||
\(158\) | 0.680303 | 0.0541220 | ||||||||
\(159\) | −4.10641 | −0.325659 | ||||||||
\(160\) | −6.77102 | −0.535296 | ||||||||
\(161\) | −7.70361 | −0.607129 | ||||||||
\(162\) | 0.680303 | 0.0534496 | ||||||||
\(163\) | 8.52864 | 0.668014 | 0.334007 | − | 0.942571i | \(-0.391599\pi\) | ||||
0.334007 | + | 0.942571i | \(0.391599\pi\) | |||||||
\(164\) | −4.22023 | −0.329544 | ||||||||
\(165\) | 3.96156 | 0.308407 | ||||||||
\(166\) | −10.9349 | −0.848713 | ||||||||
\(167\) | −15.5085 | −1.20008 | −0.600040 | − | 0.799970i | \(-0.704849\pi\) | ||||
−0.600040 | + | 0.799970i | \(0.704849\pi\) | |||||||
\(168\) | 7.75383 | 0.598221 | ||||||||
\(169\) | −12.5908 | −0.968525 | ||||||||
\(170\) | −0.795496 | −0.0610117 | ||||||||
\(171\) | −1.61887 | −0.123798 | ||||||||
\(172\) | −14.8587 | −1.13297 | ||||||||
\(173\) | −7.19773 | −0.547233 | −0.273617 | − | 0.961839i | \(-0.588220\pi\) | ||||
−0.273617 | + | 0.961839i | \(0.588220\pi\) | |||||||
\(174\) | −5.21868 | −0.395627 | ||||||||
\(175\) | 11.7053 | 0.884838 | ||||||||
\(176\) | −4.86951 | −0.367053 | ||||||||
\(177\) | −4.30295 | −0.323430 | ||||||||
\(178\) | 9.43995 | 0.707554 | ||||||||
\(179\) | 3.71861 | 0.277942 | 0.138971 | − | 0.990296i | \(-0.455621\pi\) | ||||
0.138971 | + | 0.990296i | \(0.455621\pi\) | |||||||
\(180\) | 1.79747 | 0.133976 | ||||||||
\(181\) | −23.5768 | −1.75245 | −0.876223 | − | 0.481906i | \(-0.839945\pi\) | ||||
−0.876223 | + | 0.481906i | \(0.839945\pi\) | |||||||
\(182\) | 1.40220 | 0.103938 | ||||||||
\(183\) | 13.9821 | 1.03358 | ||||||||
\(184\) | −5.75305 | −0.424121 | ||||||||
\(185\) | 1.94712 | 0.143155 | ||||||||
\(186\) | 0.655773 | 0.0480836 | ||||||||
\(187\) | −3.38790 | −0.247748 | ||||||||
\(188\) | −16.8395 | −1.22814 | ||||||||
\(189\) | −3.22223 | −0.234382 | ||||||||
\(190\) | 1.28781 | 0.0934274 | ||||||||
\(191\) | −16.2749 | −1.17761 | −0.588805 | − | 0.808275i | \(-0.700402\pi\) | ||||
−0.588805 | + | 0.808275i | \(0.700402\pi\) | |||||||
\(192\) | 1.06467 | 0.0768356 | ||||||||
\(193\) | 2.68251 | 0.193091 | 0.0965457 | − | 0.995329i | \(-0.469221\pi\) | ||||
0.0965457 | + | 0.995329i | \(0.469221\pi\) | |||||||
\(194\) | 0.159885 | 0.0114791 | ||||||||
\(195\) | 0.747976 | 0.0535636 | ||||||||
\(196\) | −5.19991 | −0.371422 | ||||||||
\(197\) | 18.7273 | 1.33427 | 0.667134 | − | 0.744938i | \(-0.267521\pi\) | ||||
0.667134 | + | 0.744938i | \(0.267521\pi\) | |||||||
\(198\) | −2.30480 | −0.163795 | ||||||||
\(199\) | 16.1182 | 1.14259 | 0.571295 | − | 0.820745i | \(-0.306441\pi\) | ||||
0.571295 | + | 0.820745i | \(0.306441\pi\) | |||||||
\(200\) | 8.74152 | 0.618119 | ||||||||
\(201\) | −7.65075 | −0.539642 | ||||||||
\(202\) | 2.25070 | 0.158359 | ||||||||
\(203\) | 24.7181 | 1.73487 | ||||||||
\(204\) | −1.53719 | −0.107625 | ||||||||
\(205\) | −3.21029 | −0.224216 | ||||||||
\(206\) | −6.64158 | −0.462741 | ||||||||
\(207\) | 2.39077 | 0.166170 | ||||||||
\(208\) | −0.919405 | −0.0637492 | ||||||||
\(209\) | 5.48459 | 0.379377 | ||||||||
\(210\) | 2.56327 | 0.176882 | ||||||||
\(211\) | 22.2783 | 1.53370 | 0.766850 | − | 0.641826i | \(-0.221823\pi\) | ||||
0.766850 | + | 0.641826i | \(0.221823\pi\) | |||||||
\(212\) | 6.31232 | 0.433532 | ||||||||
\(213\) | 8.73752 | 0.598685 | ||||||||
\(214\) | 7.47764 | 0.511161 | ||||||||
\(215\) | −11.3029 | −0.770850 | ||||||||
\(216\) | −2.40636 | −0.163732 | ||||||||
\(217\) | −3.10604 | −0.210852 | ||||||||
\(218\) | 5.78396 | 0.391739 | ||||||||
\(219\) | 0.0689540 | 0.00465948 | ||||||||
\(220\) | −6.08967 | −0.410565 | ||||||||
\(221\) | −0.639664 | −0.0430284 | ||||||||
\(222\) | −1.13282 | −0.0760297 | ||||||||
\(223\) | −20.2701 | −1.35739 | −0.678694 | − | 0.734421i | \(-0.737454\pi\) | ||||
−0.678694 | + | 0.734421i | \(0.737454\pi\) | |||||||
\(224\) | −18.6584 | −1.24667 | ||||||||
\(225\) | −3.63268 | −0.242178 | ||||||||
\(226\) | −1.53205 | −0.101911 | ||||||||
\(227\) | 11.9417 | 0.792596 | 0.396298 | − | 0.918122i | \(-0.370295\pi\) | ||||
0.396298 | + | 0.918122i | \(0.370295\pi\) | |||||||
\(228\) | 2.48851 | 0.164806 | ||||||||
\(229\) | −3.75816 | −0.248346 | −0.124173 | − | 0.992261i | \(-0.539628\pi\) | ||||
−0.124173 | + | 0.992261i | \(0.539628\pi\) | |||||||
\(230\) | −1.90185 | −0.125404 | ||||||||
\(231\) | 10.9166 | 0.718259 | ||||||||
\(232\) | 18.4595 | 1.21192 | ||||||||
\(233\) | −16.5382 | −1.08346 | −0.541728 | − | 0.840554i | \(-0.682230\pi\) | ||||
−0.541728 | + | 0.840554i | \(0.682230\pi\) | |||||||
\(234\) | −0.435165 | −0.0284476 | ||||||||
\(235\) | −12.8096 | −0.835608 | ||||||||
\(236\) | 6.61445 | 0.430564 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | −2.19209 | −0.142092 | ||||||||
\(239\) | −18.7524 | −1.21299 | −0.606496 | − | 0.795086i | \(-0.707426\pi\) | ||||
−0.606496 | + | 0.795086i | \(0.707426\pi\) | |||||||
\(240\) | −1.68070 | −0.108489 | ||||||||
\(241\) | −0.484078 | −0.0311822 | −0.0155911 | − | 0.999878i | \(-0.504963\pi\) | ||||
−0.0155911 | + | 0.999878i | \(0.504963\pi\) | |||||||
\(242\) | 0.325103 | 0.0208984 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −21.4930 | −1.37595 | ||||||||
\(245\) | −3.95553 | −0.252709 | ||||||||
\(246\) | 1.86772 | 0.119081 | ||||||||
\(247\) | 1.03554 | 0.0658895 | ||||||||
\(248\) | −2.31959 | −0.147294 | ||||||||
\(249\) | −16.0736 | −1.01862 | ||||||||
\(250\) | 6.86726 | 0.434323 | ||||||||
\(251\) | −22.7890 | −1.43843 | −0.719215 | − | 0.694787i | \(-0.755498\pi\) | ||||
−0.719215 | + | 0.694787i | \(0.755498\pi\) | |||||||
\(252\) | 4.95317 | 0.312020 | ||||||||
\(253\) | −8.09970 | −0.509224 | ||||||||
\(254\) | 8.16240 | 0.512155 | ||||||||
\(255\) | −1.16933 | −0.0732260 | ||||||||
\(256\) | −9.51522 | −0.594701 | ||||||||
\(257\) | 10.5780 | 0.659839 | 0.329920 | − | 0.944009i | \(-0.392978\pi\) | ||||
0.329920 | + | 0.944009i | \(0.392978\pi\) | |||||||
\(258\) | 6.57591 | 0.409398 | ||||||||
\(259\) | 5.36554 | 0.333399 | ||||||||
\(260\) | −1.14978 | −0.0713063 | ||||||||
\(261\) | −7.67112 | −0.474830 | ||||||||
\(262\) | 0.822619 | 0.0508216 | ||||||||
\(263\) | 23.0197 | 1.41946 | 0.709728 | − | 0.704476i | \(-0.248818\pi\) | ||||
0.709728 | + | 0.704476i | \(0.248818\pi\) | |||||||
\(264\) | 8.15251 | 0.501752 | ||||||||
\(265\) | 4.80173 | 0.294968 | ||||||||
\(266\) | 3.54872 | 0.217586 | ||||||||
\(267\) | 13.8761 | 0.849204 | ||||||||
\(268\) | 11.7606 | 0.718395 | ||||||||
\(269\) | 22.7666 | 1.38811 | 0.694053 | − | 0.719924i | \(-0.255824\pi\) | ||||
0.694053 | + | 0.719924i | \(0.255824\pi\) | |||||||
\(270\) | −0.795496 | −0.0484123 | ||||||||
\(271\) | −2.26550 | −0.137620 | −0.0688098 | − | 0.997630i | \(-0.521920\pi\) | ||||
−0.0688098 | + | 0.997630i | \(0.521920\pi\) | |||||||
\(272\) | 1.43732 | 0.0871506 | ||||||||
\(273\) | 2.06114 | 0.124746 | ||||||||
\(274\) | 11.8803 | 0.717713 | ||||||||
\(275\) | 12.3072 | 0.742149 | ||||||||
\(276\) | −3.67507 | −0.221213 | ||||||||
\(277\) | −14.8072 | −0.889679 | −0.444839 | − | 0.895610i | \(-0.646739\pi\) | ||||
−0.444839 | + | 0.895610i | \(0.646739\pi\) | |||||||
\(278\) | 3.46067 | 0.207557 | ||||||||
\(279\) | 0.963944 | 0.0577098 | ||||||||
\(280\) | −9.06676 | −0.541842 | ||||||||
\(281\) | −18.7820 | −1.12044 | −0.560221 | − | 0.828343i | \(-0.689284\pi\) | ||||
−0.560221 | + | 0.828343i | \(0.689284\pi\) | |||||||
\(282\) | 7.45252 | 0.443791 | ||||||||
\(283\) | 27.0646 | 1.60883 | 0.804413 | − | 0.594071i | \(-0.202480\pi\) | ||||
0.804413 | + | 0.594071i | \(0.202480\pi\) | |||||||
\(284\) | −13.4312 | −0.796996 | ||||||||
\(285\) | 1.89299 | 0.112131 | ||||||||
\(286\) | 1.47430 | 0.0871770 | ||||||||
\(287\) | −8.84636 | −0.522184 | ||||||||
\(288\) | 5.79053 | 0.341210 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 6.10234 | 0.358342 | ||||||||
\(291\) | 0.235021 | 0.0137772 | ||||||||
\(292\) | −0.105995 | −0.00620290 | ||||||||
\(293\) | −23.5463 | −1.37559 | −0.687794 | − | 0.725906i | \(-0.741421\pi\) | ||||
−0.687794 | + | 0.725906i | \(0.741421\pi\) | |||||||
\(294\) | 2.30129 | 0.134214 | ||||||||
\(295\) | 5.03155 | 0.292948 | ||||||||
\(296\) | 4.00699 | 0.232901 | ||||||||
\(297\) | −3.38790 | −0.196586 | ||||||||
\(298\) | 5.17353 | 0.299694 | ||||||||
\(299\) | −1.52929 | −0.0884411 | ||||||||
\(300\) | 5.58411 | 0.322399 | ||||||||
\(301\) | −31.1465 | −1.79526 | ||||||||
\(302\) | −2.67537 | −0.153950 | ||||||||
\(303\) | 3.30839 | 0.190062 | ||||||||
\(304\) | −2.32685 | −0.133454 | ||||||||
\(305\) | −16.3496 | −0.936174 | ||||||||
\(306\) | 0.680303 | 0.0388903 | ||||||||
\(307\) | −19.6462 | −1.12127 | −0.560635 | − | 0.828063i | \(-0.689443\pi\) | ||||
−0.560635 | + | 0.828063i | \(0.689443\pi\) | |||||||
\(308\) | −16.7809 | −0.956178 | ||||||||
\(309\) | −9.76268 | −0.555379 | ||||||||
\(310\) | −0.766813 | −0.0435520 | ||||||||
\(311\) | −5.69179 | −0.322752 | −0.161376 | − | 0.986893i | \(-0.551593\pi\) | ||||
−0.161376 | + | 0.986893i | \(0.551593\pi\) | |||||||
\(312\) | 1.53926 | 0.0871435 | ||||||||
\(313\) | −5.20447 | −0.294174 | −0.147087 | − | 0.989124i | \(-0.546990\pi\) | ||||
−0.147087 | + | 0.989124i | \(0.546990\pi\) | |||||||
\(314\) | 15.4176 | 0.870068 | ||||||||
\(315\) | 3.76783 | 0.212293 | ||||||||
\(316\) | −1.53719 | −0.0864736 | ||||||||
\(317\) | 14.0120 | 0.786993 | 0.393496 | − | 0.919326i | \(-0.371265\pi\) | ||||
0.393496 | + | 0.919326i | \(0.371265\pi\) | |||||||
\(318\) | −2.79360 | −0.156657 | ||||||||
\(319\) | 25.9890 | 1.45510 | ||||||||
\(320\) | −1.24494 | −0.0695943 | ||||||||
\(321\) | 10.9916 | 0.613493 | ||||||||
\(322\) | −5.24078 | −0.292057 | ||||||||
\(323\) | −1.61887 | −0.0900766 | ||||||||
\(324\) | −1.53719 | −0.0853994 | ||||||||
\(325\) | 2.32369 | 0.128895 | ||||||||
\(326\) | 5.80205 | 0.321346 | ||||||||
\(327\) | 8.50204 | 0.470164 | ||||||||
\(328\) | −6.60646 | −0.364781 | ||||||||
\(329\) | −35.2986 | −1.94607 | ||||||||
\(330\) | 2.69506 | 0.148358 | ||||||||
\(331\) | 29.4898 | 1.62091 | 0.810453 | − | 0.585803i | \(-0.199221\pi\) | ||||
0.810453 | + | 0.585803i | \(0.199221\pi\) | |||||||
\(332\) | 24.7081 | 1.35603 | ||||||||
\(333\) | −1.66517 | −0.0912506 | ||||||||
\(334\) | −10.5504 | −0.577295 | ||||||||
\(335\) | 8.94622 | 0.488784 | ||||||||
\(336\) | −4.63139 | −0.252663 | ||||||||
\(337\) | 5.76733 | 0.314166 | 0.157083 | − | 0.987585i | \(-0.449791\pi\) | ||||
0.157083 | + | 0.987585i | \(0.449791\pi\) | |||||||
\(338\) | −8.56558 | −0.465906 | ||||||||
\(339\) | −2.25201 | −0.122313 | ||||||||
\(340\) | 1.79747 | 0.0974817 | ||||||||
\(341\) | −3.26575 | −0.176850 | ||||||||
\(342\) | −1.10132 | −0.0595528 | ||||||||
\(343\) | 11.6556 | 0.629344 | ||||||||
\(344\) | −23.2602 | −1.25411 | ||||||||
\(345\) | −2.79559 | −0.150510 | ||||||||
\(346\) | −4.89664 | −0.263245 | ||||||||
\(347\) | 16.4684 | 0.884071 | 0.442036 | − | 0.896997i | \(-0.354256\pi\) | ||||
0.442036 | + | 0.896997i | \(0.354256\pi\) | |||||||
\(348\) | 11.7920 | 0.632115 | ||||||||
\(349\) | 9.09941 | 0.487080 | 0.243540 | − | 0.969891i | \(-0.421691\pi\) | ||||
0.243540 | + | 0.969891i | \(0.421691\pi\) | |||||||
\(350\) | 7.96315 | 0.425648 | ||||||||
\(351\) | −0.639664 | −0.0341427 | ||||||||
\(352\) | −19.6178 | −1.04563 | ||||||||
\(353\) | 16.5448 | 0.880593 | 0.440296 | − | 0.897852i | \(-0.354873\pi\) | ||||
0.440296 | + | 0.897852i | \(0.354873\pi\) | |||||||
\(354\) | −2.92731 | −0.155585 | ||||||||
\(355\) | −10.2170 | −0.542263 | ||||||||
\(356\) | −21.3302 | −1.13050 | ||||||||
\(357\) | −3.22223 | −0.170538 | ||||||||
\(358\) | 2.52978 | 0.133703 | ||||||||
\(359\) | 7.29846 | 0.385198 | 0.192599 | − | 0.981278i | \(-0.438308\pi\) | ||||
0.192599 | + | 0.981278i | \(0.438308\pi\) | |||||||
\(360\) | 2.81382 | 0.148301 | ||||||||
\(361\) | −16.3792 | −0.862066 | ||||||||
\(362\) | −16.0393 | −0.843008 | ||||||||
\(363\) | 0.477880 | 0.0250822 | ||||||||
\(364\) | −3.16836 | −0.166067 | ||||||||
\(365\) | −0.0806297 | −0.00422035 | ||||||||
\(366\) | 9.51203 | 0.497202 | ||||||||
\(367\) | −20.4360 | −1.06675 | −0.533376 | − | 0.845878i | \(-0.679077\pi\) | ||||
−0.533376 | + | 0.845878i | \(0.679077\pi\) | |||||||
\(368\) | 3.43631 | 0.179130 | ||||||||
\(369\) | 2.74542 | 0.142921 | ||||||||
\(370\) | 1.32463 | 0.0688644 | ||||||||
\(371\) | 13.2318 | 0.686960 | ||||||||
\(372\) | −1.48176 | −0.0768258 | ||||||||
\(373\) | −12.2406 | −0.633797 | −0.316898 | − | 0.948460i | \(-0.602641\pi\) | ||||
−0.316898 | + | 0.948460i | \(0.602641\pi\) | |||||||
\(374\) | −2.30480 | −0.119178 | ||||||||
\(375\) | 10.0944 | 0.521273 | ||||||||
\(376\) | −26.3610 | −1.35946 | ||||||||
\(377\) | 4.90694 | 0.252720 | ||||||||
\(378\) | −2.19209 | −0.112749 | ||||||||
\(379\) | 10.7197 | 0.550634 | 0.275317 | − | 0.961353i | \(-0.411217\pi\) | ||||
0.275317 | + | 0.961353i | \(0.411217\pi\) | |||||||
\(380\) | −2.90988 | −0.149274 | ||||||||
\(381\) | 11.9982 | 0.614686 | ||||||||
\(382\) | −11.0719 | −0.566486 | ||||||||
\(383\) | −11.3689 | −0.580926 | −0.290463 | − | 0.956886i | \(-0.593809\pi\) | ||||
−0.290463 | + | 0.956886i | \(0.593809\pi\) | |||||||
\(384\) | −10.8568 | −0.554032 | ||||||||
\(385\) | −12.7650 | −0.650567 | ||||||||
\(386\) | 1.82492 | 0.0928860 | ||||||||
\(387\) | 9.66615 | 0.491358 | ||||||||
\(388\) | −0.361271 | −0.0183408 | ||||||||
\(389\) | 14.0806 | 0.713914 | 0.356957 | − | 0.934121i | \(-0.383814\pi\) | ||||
0.356957 | + | 0.934121i | \(0.383814\pi\) | |||||||
\(390\) | 0.508850 | 0.0257666 | ||||||||
\(391\) | 2.39077 | 0.120907 | ||||||||
\(392\) | −8.14009 | −0.411137 | ||||||||
\(393\) | 1.20920 | 0.0609959 | ||||||||
\(394\) | 12.7403 | 0.641845 | ||||||||
\(395\) | −1.16933 | −0.0588352 | ||||||||
\(396\) | 5.20784 | 0.261704 | ||||||||
\(397\) | 0.569760 | 0.0285954 | 0.0142977 | − | 0.999898i | \(-0.495449\pi\) | ||||
0.0142977 | + | 0.999898i | \(0.495449\pi\) | |||||||
\(398\) | 10.9653 | 0.549639 | ||||||||
\(399\) | 5.21638 | 0.261146 | ||||||||
\(400\) | −5.22134 | −0.261067 | ||||||||
\(401\) | −21.4758 | −1.07245 | −0.536226 | − | 0.844074i | \(-0.680151\pi\) | ||||
−0.536226 | + | 0.844074i | \(0.680151\pi\) | |||||||
\(402\) | −5.20482 | −0.259593 | ||||||||
\(403\) | −0.616600 | −0.0307150 | ||||||||
\(404\) | −5.08561 | −0.253019 | ||||||||
\(405\) | −1.16933 | −0.0581043 | ||||||||
\(406\) | 16.8158 | 0.834553 | ||||||||
\(407\) | 5.64142 | 0.279635 | ||||||||
\(408\) | −2.40636 | −0.119133 | ||||||||
\(409\) | −24.5365 | −1.21325 | −0.606626 | − | 0.794987i | \(-0.707478\pi\) | ||||
−0.606626 | + | 0.794987i | \(0.707478\pi\) | |||||||
\(410\) | −2.18397 | −0.107859 | ||||||||
\(411\) | 17.4632 | 0.861397 | ||||||||
\(412\) | 15.0071 | 0.739346 | ||||||||
\(413\) | 13.8651 | 0.682256 | ||||||||
\(414\) | 1.62645 | 0.0799356 | ||||||||
\(415\) | 18.7953 | 0.922623 | ||||||||
\(416\) | −3.70399 | −0.181603 | ||||||||
\(417\) | 5.08696 | 0.249109 | ||||||||
\(418\) | 3.73118 | 0.182498 | ||||||||
\(419\) | 13.3456 | 0.651974 | 0.325987 | − | 0.945374i | \(-0.394303\pi\) | ||||
0.325987 | + | 0.945374i | \(0.394303\pi\) | |||||||
\(420\) | −5.79187 | −0.282614 | ||||||||
\(421\) | −33.7493 | −1.64484 | −0.822419 | − | 0.568882i | \(-0.807376\pi\) | ||||
−0.822419 | + | 0.568882i | \(0.807376\pi\) | |||||||
\(422\) | 15.1560 | 0.737782 | ||||||||
\(423\) | 10.9547 | 0.532637 | ||||||||
\(424\) | 9.88149 | 0.479888 | ||||||||
\(425\) | −3.63268 | −0.176211 | ||||||||
\(426\) | 5.94416 | 0.287995 | ||||||||
\(427\) | −45.0533 | −2.18028 | ||||||||
\(428\) | −16.8962 | −0.816709 | ||||||||
\(429\) | 2.16712 | 0.104629 | ||||||||
\(430\) | −7.68938 | −0.370815 | ||||||||
\(431\) | 1.79289 | 0.0863606 | 0.0431803 | − | 0.999067i | \(-0.486251\pi\) | ||||
0.0431803 | + | 0.999067i | \(0.486251\pi\) | |||||||
\(432\) | 1.43732 | 0.0691533 | ||||||||
\(433\) | 6.24663 | 0.300194 | 0.150097 | − | 0.988671i | \(-0.452041\pi\) | ||||
0.150097 | + | 0.988671i | \(0.452041\pi\) | |||||||
\(434\) | −2.11305 | −0.101430 | ||||||||
\(435\) | 8.97004 | 0.430080 | ||||||||
\(436\) | −13.0692 | −0.625903 | ||||||||
\(437\) | −3.87036 | −0.185144 | ||||||||
\(438\) | 0.0469096 | 0.00224143 | ||||||||
\(439\) | −32.0645 | −1.53036 | −0.765178 | − | 0.643819i | \(-0.777349\pi\) | ||||
−0.765178 | + | 0.643819i | \(0.777349\pi\) | |||||||
\(440\) | −9.53294 | −0.454465 | ||||||||
\(441\) | 3.38274 | 0.161083 | ||||||||
\(442\) | −0.435165 | −0.0206987 | ||||||||
\(443\) | 37.4856 | 1.78099 | 0.890497 | − | 0.454989i | \(-0.150357\pi\) | ||||
0.890497 | + | 0.454989i | \(0.150357\pi\) | |||||||
\(444\) | 2.55967 | 0.121477 | ||||||||
\(445\) | −16.2257 | −0.769172 | ||||||||
\(446\) | −13.7898 | −0.652967 | ||||||||
\(447\) | 7.60475 | 0.359692 | ||||||||
\(448\) | −3.43059 | −0.162080 | ||||||||
\(449\) | 14.4890 | 0.683777 | 0.341888 | − | 0.939741i | \(-0.388934\pi\) | ||||
0.341888 | + | 0.939741i | \(0.388934\pi\) | |||||||
\(450\) | −2.47132 | −0.116499 | ||||||||
\(451\) | −9.30121 | −0.437977 | ||||||||
\(452\) | 3.46177 | 0.162828 | ||||||||
\(453\) | −3.93261 | −0.184770 | ||||||||
\(454\) | 8.12395 | 0.381276 | ||||||||
\(455\) | −2.41015 | −0.112989 | ||||||||
\(456\) | 3.89559 | 0.182428 | ||||||||
\(457\) | 7.59012 | 0.355051 | 0.177525 | − | 0.984116i | \(-0.443191\pi\) | ||||
0.177525 | + | 0.984116i | \(0.443191\pi\) | |||||||
\(458\) | −2.55668 | −0.119466 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 4.29735 | 0.200365 | ||||||||
\(461\) | 6.83207 | 0.318201 | 0.159101 | − | 0.987262i | \(-0.449141\pi\) | ||||
0.159101 | + | 0.987262i | \(0.449141\pi\) | |||||||
\(462\) | 7.42658 | 0.345516 | ||||||||
\(463\) | −10.6639 | −0.495595 | −0.247797 | − | 0.968812i | \(-0.579707\pi\) | ||||
−0.247797 | + | 0.968812i | \(0.579707\pi\) | |||||||
\(464\) | −11.0259 | −0.511864 | ||||||||
\(465\) | −1.12716 | −0.0522710 | ||||||||
\(466\) | −11.2510 | −0.521192 | ||||||||
\(467\) | 6.42530 | 0.297327 | 0.148664 | − | 0.988888i | \(-0.452503\pi\) | ||||
0.148664 | + | 0.988888i | \(0.452503\pi\) | |||||||
\(468\) | 0.983284 | 0.0454523 | ||||||||
\(469\) | 24.6524 | 1.13834 | ||||||||
\(470\) | −8.71443 | −0.401967 | ||||||||
\(471\) | 22.6629 | 1.04425 | ||||||||
\(472\) | 10.3544 | 0.476602 | ||||||||
\(473\) | −32.7480 | −1.50575 | ||||||||
\(474\) | 0.680303 | 0.0312473 | ||||||||
\(475\) | 5.88085 | 0.269832 | ||||||||
\(476\) | 4.95317 | 0.227028 | ||||||||
\(477\) | −4.10641 | −0.188020 | ||||||||
\(478\) | −12.7573 | −0.583506 | ||||||||
\(479\) | −16.7896 | −0.767135 | −0.383568 | − | 0.923513i | \(-0.625305\pi\) | ||||
−0.383568 | + | 0.923513i | \(0.625305\pi\) | |||||||
\(480\) | −6.77102 | −0.309053 | ||||||||
\(481\) | 1.06515 | 0.0485665 | ||||||||
\(482\) | −0.329319 | −0.0150001 | ||||||||
\(483\) | −7.70361 | −0.350526 | ||||||||
\(484\) | −0.734592 | −0.0333906 | ||||||||
\(485\) | −0.274816 | −0.0124787 | ||||||||
\(486\) | 0.680303 | 0.0308592 | ||||||||
\(487\) | 4.90747 | 0.222379 | 0.111189 | − | 0.993799i | \(-0.464534\pi\) | ||||
0.111189 | + | 0.993799i | \(0.464534\pi\) | |||||||
\(488\) | −33.6458 | −1.52308 | ||||||||
\(489\) | 8.52864 | 0.385678 | ||||||||
\(490\) | −2.69096 | −0.121565 | ||||||||
\(491\) | 36.2132 | 1.63428 | 0.817139 | − | 0.576440i | \(-0.195559\pi\) | ||||
0.817139 | + | 0.576440i | \(0.195559\pi\) | |||||||
\(492\) | −4.22023 | −0.190263 | ||||||||
\(493\) | −7.67112 | −0.345490 | ||||||||
\(494\) | 0.704477 | 0.0316959 | ||||||||
\(495\) | 3.96156 | 0.178059 | ||||||||
\(496\) | 1.38550 | 0.0622108 | ||||||||
\(497\) | −28.1543 | −1.26289 | ||||||||
\(498\) | −10.9349 | −0.490005 | ||||||||
\(499\) | 18.1662 | 0.813231 | 0.406616 | − | 0.913599i | \(-0.366709\pi\) | ||||
0.406616 | + | 0.913599i | \(0.366709\pi\) | |||||||
\(500\) | −15.5170 | −0.693942 | ||||||||
\(501\) | −15.5085 | −0.692867 | ||||||||
\(502\) | −15.5034 | −0.691952 | ||||||||
\(503\) | 15.8740 | 0.707786 | 0.353893 | − | 0.935286i | \(-0.384858\pi\) | ||||
0.353893 | + | 0.935286i | \(0.384858\pi\) | |||||||
\(504\) | 7.75383 | 0.345383 | ||||||||
\(505\) | −3.86858 | −0.172150 | ||||||||
\(506\) | −5.51025 | −0.244960 | ||||||||
\(507\) | −12.5908 | −0.559178 | ||||||||
\(508\) | −18.4435 | −0.818297 | ||||||||
\(509\) | −0.637468 | −0.0282553 | −0.0141276 | − | 0.999900i | \(-0.504497\pi\) | ||||
−0.0141276 | + | 0.999900i | \(0.504497\pi\) | |||||||
\(510\) | −0.795496 | −0.0352251 | ||||||||
\(511\) | −0.222185 | −0.00982890 | ||||||||
\(512\) | 15.2403 | 0.673533 | ||||||||
\(513\) | −1.61887 | −0.0714750 | ||||||||
\(514\) | 7.19626 | 0.317413 | ||||||||
\(515\) | 11.4158 | 0.503038 | ||||||||
\(516\) | −14.8587 | −0.654118 | ||||||||
\(517\) | −37.1135 | −1.63225 | ||||||||
\(518\) | 3.65019 | 0.160380 | ||||||||
\(519\) | −7.19773 | −0.315945 | ||||||||
\(520\) | −1.79990 | −0.0789307 | ||||||||
\(521\) | 15.6632 | 0.686219 | 0.343109 | − | 0.939295i | \(-0.388520\pi\) | ||||
0.343109 | + | 0.939295i | \(0.388520\pi\) | |||||||
\(522\) | −5.21868 | −0.228415 | ||||||||
\(523\) | −25.2970 | −1.10616 | −0.553081 | − | 0.833128i | \(-0.686548\pi\) | ||||
−0.553081 | + | 0.833128i | \(0.686548\pi\) | |||||||
\(524\) | −1.85876 | −0.0812004 | ||||||||
\(525\) | 11.7053 | 0.510861 | ||||||||
\(526\) | 15.6604 | 0.682825 | ||||||||
\(527\) | 0.963944 | 0.0419900 | ||||||||
\(528\) | −4.86951 | −0.211918 | ||||||||
\(529\) | −17.2842 | −0.751488 | ||||||||
\(530\) | 3.26663 | 0.141893 | ||||||||
\(531\) | −4.30295 | −0.186732 | ||||||||
\(532\) | −8.01856 | −0.347649 | ||||||||
\(533\) | −1.75615 | −0.0760671 | ||||||||
\(534\) | 9.43995 | 0.408507 | ||||||||
\(535\) | −12.8528 | −0.555675 | ||||||||
\(536\) | 18.4104 | 0.795210 | ||||||||
\(537\) | 3.71861 | 0.160470 | ||||||||
\(538\) | 15.4882 | 0.667743 | ||||||||
\(539\) | −11.4604 | −0.493634 | ||||||||
\(540\) | 1.79747 | 0.0773510 | ||||||||
\(541\) | −10.5568 | −0.453873 | −0.226937 | − | 0.973910i | \(-0.572871\pi\) | ||||
−0.226937 | + | 0.973910i | \(0.572871\pi\) | |||||||
\(542\) | −1.54123 | −0.0662014 | ||||||||
\(543\) | −23.5768 | −1.01178 | ||||||||
\(544\) | 5.79053 | 0.248267 | ||||||||
\(545\) | −9.94166 | −0.425854 | ||||||||
\(546\) | 1.40220 | 0.0600086 | ||||||||
\(547\) | −6.33274 | −0.270768 | −0.135384 | − | 0.990793i | \(-0.543227\pi\) | ||||
−0.135384 | + | 0.990793i | \(0.543227\pi\) | |||||||
\(548\) | −26.8442 | −1.14673 | ||||||||
\(549\) | 13.9821 | 0.596739 | ||||||||
\(550\) | 8.37259 | 0.357008 | ||||||||
\(551\) | 12.4186 | 0.529049 | ||||||||
\(552\) | −5.75305 | −0.244866 | ||||||||
\(553\) | −3.22223 | −0.137023 | ||||||||
\(554\) | −10.0734 | −0.427977 | ||||||||
\(555\) | 1.94712 | 0.0826507 | ||||||||
\(556\) | −7.81961 | −0.331625 | ||||||||
\(557\) | −29.2840 | −1.24080 | −0.620401 | − | 0.784284i | \(-0.713030\pi\) | ||||
−0.620401 | + | 0.784284i | \(0.713030\pi\) | |||||||
\(558\) | 0.655773 | 0.0277611 | ||||||||
\(559\) | −6.18309 | −0.261517 | ||||||||
\(560\) | 5.41560 | 0.228851 | ||||||||
\(561\) | −3.38790 | −0.143037 | ||||||||
\(562\) | −12.7775 | −0.538985 | ||||||||
\(563\) | 42.6336 | 1.79679 | 0.898395 | − | 0.439188i | \(-0.144734\pi\) | ||||
0.898395 | + | 0.439188i | \(0.144734\pi\) | |||||||
\(564\) | −16.8395 | −0.709069 | ||||||||
\(565\) | 2.63334 | 0.110785 | ||||||||
\(566\) | 18.4121 | 0.773920 | ||||||||
\(567\) | −3.22223 | −0.135321 | ||||||||
\(568\) | −21.0256 | −0.882215 | ||||||||
\(569\) | 13.0174 | 0.545716 | 0.272858 | − | 0.962054i | \(-0.412031\pi\) | ||||
0.272858 | + | 0.962054i | \(0.412031\pi\) | |||||||
\(570\) | 1.28781 | 0.0539403 | ||||||||
\(571\) | 15.1453 | 0.633813 | 0.316906 | − | 0.948457i | \(-0.397356\pi\) | ||||
0.316906 | + | 0.948457i | \(0.397356\pi\) | |||||||
\(572\) | −3.33127 | −0.139287 | ||||||||
\(573\) | −16.2749 | −0.679894 | ||||||||
\(574\) | −6.01820 | −0.251195 | ||||||||
\(575\) | −8.68490 | −0.362185 | ||||||||
\(576\) | 1.06467 | 0.0443611 | ||||||||
\(577\) | −11.9103 | −0.495831 | −0.247915 | − | 0.968782i | \(-0.579746\pi\) | ||||
−0.247915 | + | 0.968782i | \(0.579746\pi\) | |||||||
\(578\) | 0.680303 | 0.0282969 | ||||||||
\(579\) | 2.68251 | 0.111481 | ||||||||
\(580\) | −13.7886 | −0.572542 | ||||||||
\(581\) | 51.7927 | 2.14872 | ||||||||
\(582\) | 0.159885 | 0.00662746 | ||||||||
\(583\) | 13.9121 | 0.576181 | ||||||||
\(584\) | −0.165928 | −0.00686615 | ||||||||
\(585\) | 0.747976 | 0.0309250 | ||||||||
\(586\) | −16.0186 | −0.661722 | ||||||||
\(587\) | 26.1646 | 1.07993 | 0.539964 | − | 0.841688i | \(-0.318438\pi\) | ||||
0.539964 | + | 0.841688i | \(0.318438\pi\) | |||||||
\(588\) | −5.19991 | −0.214441 | ||||||||
\(589\) | −1.56050 | −0.0642994 | ||||||||
\(590\) | 3.42298 | 0.140922 | ||||||||
\(591\) | 18.7273 | 0.770340 | ||||||||
\(592\) | −2.39338 | −0.0983675 | ||||||||
\(593\) | 30.1410 | 1.23774 | 0.618870 | − | 0.785493i | \(-0.287591\pi\) | ||||
0.618870 | + | 0.785493i | \(0.287591\pi\) | |||||||
\(594\) | −2.30480 | −0.0945670 | ||||||||
\(595\) | 3.76783 | 0.154466 | ||||||||
\(596\) | −11.6899 | −0.478838 | ||||||||
\(597\) | 16.1182 | 0.659675 | ||||||||
\(598\) | −1.04038 | −0.0425443 | ||||||||
\(599\) | −33.3322 | −1.36192 | −0.680959 | − | 0.732321i | \(-0.738437\pi\) | ||||
−0.680959 | + | 0.732321i | \(0.738437\pi\) | |||||||
\(600\) | 8.74152 | 0.356871 | ||||||||
\(601\) | 45.7955 | 1.86804 | 0.934019 | − | 0.357224i | \(-0.116277\pi\) | ||||
0.934019 | + | 0.357224i | \(0.116277\pi\) | |||||||
\(602\) | −21.1891 | −0.863602 | ||||||||
\(603\) | −7.65075 | −0.311562 | ||||||||
\(604\) | 6.04517 | 0.245974 | ||||||||
\(605\) | −0.558798 | −0.0227184 | ||||||||
\(606\) | 2.25070 | 0.0914286 | ||||||||
\(607\) | −6.33341 | −0.257065 | −0.128533 | − | 0.991705i | \(-0.541027\pi\) | ||||
−0.128533 | + | 0.991705i | \(0.541027\pi\) | |||||||
\(608\) | −9.37414 | −0.380172 | ||||||||
\(609\) | 24.7181 | 1.00163 | ||||||||
\(610\) | −11.1227 | −0.450343 | ||||||||
\(611\) | −7.00734 | −0.283486 | ||||||||
\(612\) | −1.53719 | −0.0621372 | ||||||||
\(613\) | −41.3477 | −1.67002 | −0.835009 | − | 0.550237i | \(-0.814537\pi\) | ||||
−0.835009 | + | 0.550237i | \(0.814537\pi\) | |||||||
\(614\) | −13.3654 | −0.539383 | ||||||||
\(615\) | −3.21029 | −0.129451 | ||||||||
\(616\) | −26.2692 | −1.05842 | ||||||||
\(617\) | 42.4698 | 1.70977 | 0.854885 | − | 0.518818i | \(-0.173628\pi\) | ||||
0.854885 | + | 0.518818i | \(0.173628\pi\) | |||||||
\(618\) | −6.64158 | −0.267163 | ||||||||
\(619\) | 2.58275 | 0.103809 | 0.0519047 | − | 0.998652i | \(-0.483471\pi\) | ||||
0.0519047 | + | 0.998652i | \(0.483471\pi\) | |||||||
\(620\) | 1.73266 | 0.0695855 | ||||||||
\(621\) | 2.39077 | 0.0959383 | ||||||||
\(622\) | −3.87214 | −0.155259 | ||||||||
\(623\) | −44.7120 | −1.79135 | ||||||||
\(624\) | −0.919405 | −0.0368056 | ||||||||
\(625\) | 6.35973 | 0.254389 | ||||||||
\(626\) | −3.54062 | −0.141512 | ||||||||
\(627\) | 5.48459 | 0.219033 | ||||||||
\(628\) | −34.8372 | −1.39015 | ||||||||
\(629\) | −1.66517 | −0.0663945 | ||||||||
\(630\) | 2.56327 | 0.102123 | ||||||||
\(631\) | 9.38046 | 0.373430 | 0.186715 | − | 0.982414i | \(-0.440216\pi\) | ||||
0.186715 | + | 0.982414i | \(0.440216\pi\) | |||||||
\(632\) | −2.40636 | −0.0957198 | ||||||||
\(633\) | 22.2783 | 0.885483 | ||||||||
\(634\) | 9.53241 | 0.378580 | ||||||||
\(635\) | −14.0298 | −0.556756 | ||||||||
\(636\) | 6.31232 | 0.250300 | ||||||||
\(637\) | −2.16382 | −0.0857336 | ||||||||
\(638\) | 17.6804 | 0.699973 | ||||||||
\(639\) | 8.73752 | 0.345651 | ||||||||
\(640\) | 12.6951 | 0.501818 | ||||||||
\(641\) | 11.1827 | 0.441689 | 0.220845 | − | 0.975309i | \(-0.429119\pi\) | ||||
0.220845 | + | 0.975309i | \(0.429119\pi\) | |||||||
\(642\) | 7.47764 | 0.295119 | ||||||||
\(643\) | 12.3598 | 0.487425 | 0.243712 | − | 0.969848i | \(-0.421635\pi\) | ||||
0.243712 | + | 0.969848i | \(0.421635\pi\) | |||||||
\(644\) | 11.8419 | 0.466636 | ||||||||
\(645\) | −11.3029 | −0.445051 | ||||||||
\(646\) | −1.10132 | −0.0433310 | ||||||||
\(647\) | 30.7435 | 1.20865 | 0.604325 | − | 0.796738i | \(-0.293443\pi\) | ||||
0.604325 | + | 0.796738i | \(0.293443\pi\) | |||||||
\(648\) | −2.40636 | −0.0945307 | ||||||||
\(649\) | 14.5780 | 0.572236 | ||||||||
\(650\) | 1.58081 | 0.0620046 | ||||||||
\(651\) | −3.10604 | −0.121735 | ||||||||
\(652\) | −13.1101 | −0.513432 | ||||||||
\(653\) | 14.6447 | 0.573091 | 0.286545 | − | 0.958067i | \(-0.407493\pi\) | ||||
0.286545 | + | 0.958067i | \(0.407493\pi\) | |||||||
\(654\) | 5.78396 | 0.226171 | ||||||||
\(655\) | −1.41394 | −0.0552474 | ||||||||
\(656\) | 3.94606 | 0.154068 | ||||||||
\(657\) | 0.0689540 | 0.00269015 | ||||||||
\(658\) | −24.0137 | −0.936152 | ||||||||
\(659\) | 44.0204 | 1.71479 | 0.857395 | − | 0.514658i | \(-0.172081\pi\) | ||||
0.857395 | + | 0.514658i | \(0.172081\pi\) | |||||||
\(660\) | −6.08967 | −0.237040 | ||||||||
\(661\) | −22.4397 | −0.872804 | −0.436402 | − | 0.899752i | \(-0.643747\pi\) | ||||
−0.436402 | + | 0.899752i | \(0.643747\pi\) | |||||||
\(662\) | 20.0620 | 0.779732 | ||||||||
\(663\) | −0.639664 | −0.0248425 | ||||||||
\(664\) | 38.6788 | 1.50103 | ||||||||
\(665\) | −6.09965 | −0.236534 | ||||||||
\(666\) | −1.13282 | −0.0438958 | ||||||||
\(667\) | −18.3399 | −0.710123 | ||||||||
\(668\) | 23.8394 | 0.922375 | ||||||||
\(669\) | −20.2701 | −0.783688 | ||||||||
\(670\) | 6.08613 | 0.235128 | ||||||||
\(671\) | −47.3698 | −1.82869 | ||||||||
\(672\) | −18.6584 | −0.719764 | ||||||||
\(673\) | −20.5139 | −0.790752 | −0.395376 | − | 0.918519i | \(-0.629386\pi\) | ||||
−0.395376 | + | 0.918519i | \(0.629386\pi\) | |||||||
\(674\) | 3.92353 | 0.151129 | ||||||||
\(675\) | −3.63268 | −0.139822 | ||||||||
\(676\) | 19.3545 | 0.744403 | ||||||||
\(677\) | −2.56261 | −0.0984890 | −0.0492445 | − | 0.998787i | \(-0.515681\pi\) | ||||
−0.0492445 | + | 0.998787i | \(0.515681\pi\) | |||||||
\(678\) | −1.53205 | −0.0588381 | ||||||||
\(679\) | −0.757290 | −0.0290621 | ||||||||
\(680\) | 2.81382 | 0.107905 | ||||||||
\(681\) | 11.9417 | 0.457606 | ||||||||
\(682\) | −2.22170 | −0.0850731 | ||||||||
\(683\) | 12.7959 | 0.489620 | 0.244810 | − | 0.969571i | \(-0.421274\pi\) | ||||
0.244810 | + | 0.969571i | \(0.421274\pi\) | |||||||
\(684\) | 2.48851 | 0.0951507 | ||||||||
\(685\) | −20.4202 | −0.780215 | ||||||||
\(686\) | 7.92935 | 0.302744 | ||||||||
\(687\) | −3.75816 | −0.143383 | ||||||||
\(688\) | 13.8934 | 0.529681 | ||||||||
\(689\) | 2.62672 | 0.100070 | ||||||||
\(690\) | −1.90185 | −0.0724021 | ||||||||
\(691\) | −6.05582 | −0.230374 | −0.115187 | − | 0.993344i | \(-0.536747\pi\) | ||||
−0.115187 | + | 0.993344i | \(0.536747\pi\) | |||||||
\(692\) | 11.0643 | 0.420600 | ||||||||
\(693\) | 10.9166 | 0.414687 | ||||||||
\(694\) | 11.2035 | 0.425280 | ||||||||
\(695\) | −5.94831 | −0.225632 | ||||||||
\(696\) | 18.4595 | 0.699704 | ||||||||
\(697\) | 2.74542 | 0.103990 | ||||||||
\(698\) | 6.19035 | 0.234308 | ||||||||
\(699\) | −16.5382 | −0.625533 | ||||||||
\(700\) | −17.9933 | −0.680081 | ||||||||
\(701\) | 12.0305 | 0.454384 | 0.227192 | − | 0.973850i | \(-0.427045\pi\) | ||||
0.227192 | + | 0.973850i | \(0.427045\pi\) | |||||||
\(702\) | −0.435165 | −0.0164242 | ||||||||
\(703\) | 2.69570 | 0.101670 | ||||||||
\(704\) | −3.60698 | −0.135943 | ||||||||
\(705\) | −12.8096 | −0.482439 | ||||||||
\(706\) | 11.2555 | 0.423606 | ||||||||
\(707\) | −10.6604 | −0.400925 | ||||||||
\(708\) | 6.61445 | 0.248586 | ||||||||
\(709\) | −27.8892 | −1.04740 | −0.523701 | − | 0.851902i | \(-0.675449\pi\) | ||||
−0.523701 | + | 0.851902i | \(0.675449\pi\) | |||||||
\(710\) | −6.95066 | −0.260854 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −33.3909 | −1.25138 | ||||||||
\(713\) | 2.30457 | 0.0863068 | ||||||||
\(714\) | −2.19209 | −0.0820369 | ||||||||
\(715\) | −2.53407 | −0.0947688 | ||||||||
\(716\) | −5.71620 | −0.213624 | ||||||||
\(717\) | −18.7524 | −0.700322 | ||||||||
\(718\) | 4.96516 | 0.185298 | ||||||||
\(719\) | 37.8614 | 1.41199 | 0.705997 | − | 0.708215i | \(-0.250499\pi\) | ||||
0.705997 | + | 0.708215i | \(0.250499\pi\) | |||||||
\(720\) | −1.68070 | −0.0626360 | ||||||||
\(721\) | 31.4576 | 1.17154 | ||||||||
\(722\) | −11.1428 | −0.414694 | ||||||||
\(723\) | −0.484078 | −0.0180030 | ||||||||
\(724\) | 36.2419 | 1.34692 | ||||||||
\(725\) | 27.8667 | 1.03494 | ||||||||
\(726\) | 0.325103 | 0.0120657 | ||||||||
\(727\) | 2.72586 | 0.101096 | 0.0505482 | − | 0.998722i | \(-0.483903\pi\) | ||||
0.0505482 | + | 0.998722i | \(0.483903\pi\) | |||||||
\(728\) | −4.95985 | −0.183824 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.0548526 | −0.00203018 | ||||||||
\(731\) | 9.66615 | 0.357516 | ||||||||
\(732\) | −21.4930 | −0.794406 | ||||||||
\(733\) | 1.84593 | 0.0681811 | 0.0340906 | − | 0.999419i | \(-0.489147\pi\) | ||||
0.0340906 | + | 0.999419i | \(0.489147\pi\) | |||||||
\(734\) | −13.9027 | −0.513158 | ||||||||
\(735\) | −3.95553 | −0.145902 | ||||||||
\(736\) | 13.8438 | 0.510291 | ||||||||
\(737\) | 25.9200 | 0.954775 | ||||||||
\(738\) | 1.86772 | 0.0687516 | ||||||||
\(739\) | −1.52241 | −0.0560027 | −0.0280013 | − | 0.999608i | \(-0.508914\pi\) | ||||
−0.0280013 | + | 0.999608i | \(0.508914\pi\) | |||||||
\(740\) | −2.99309 | −0.110028 | ||||||||
\(741\) | 1.03554 | 0.0380413 | ||||||||
\(742\) | 9.00162 | 0.330460 | ||||||||
\(743\) | −14.2263 | −0.521913 | −0.260957 | − | 0.965351i | \(-0.584038\pi\) | ||||
−0.260957 | + | 0.965351i | \(0.584038\pi\) | |||||||
\(744\) | −2.31959 | −0.0850405 | ||||||||
\(745\) | −8.89243 | −0.325793 | ||||||||
\(746\) | −8.32734 | −0.304886 | ||||||||
\(747\) | −16.0736 | −0.588102 | ||||||||
\(748\) | 5.20784 | 0.190418 | ||||||||
\(749\) | −35.4175 | −1.29413 | ||||||||
\(750\) | 6.86726 | 0.250757 | ||||||||
\(751\) | −6.73917 | −0.245916 | −0.122958 | − | 0.992412i | \(-0.539238\pi\) | ||||
−0.122958 | + | 0.992412i | \(0.539238\pi\) | |||||||
\(752\) | 15.7455 | 0.574179 | ||||||||
\(753\) | −22.7890 | −0.830478 | ||||||||
\(754\) | 3.33820 | 0.121570 | ||||||||
\(755\) | 4.59851 | 0.167357 | ||||||||
\(756\) | 4.95317 | 0.180145 | ||||||||
\(757\) | 47.4866 | 1.72593 | 0.862964 | − | 0.505265i | \(-0.168605\pi\) | ||||
0.862964 | + | 0.505265i | \(0.168605\pi\) | |||||||
\(758\) | 7.29264 | 0.264881 | ||||||||
\(759\) | −8.09970 | −0.294000 | ||||||||
\(760\) | −4.55522 | −0.165235 | ||||||||
\(761\) | −20.2771 | −0.735045 | −0.367522 | − | 0.930015i | \(-0.619794\pi\) | ||||
−0.367522 | + | 0.930015i | \(0.619794\pi\) | |||||||
\(762\) | 8.16240 | 0.295693 | ||||||||
\(763\) | −27.3955 | −0.991784 | ||||||||
\(764\) | 25.0176 | 0.905105 | ||||||||
\(765\) | −1.16933 | −0.0422771 | ||||||||
\(766\) | −7.73432 | −0.279452 | ||||||||
\(767\) | 2.75244 | 0.0993850 | ||||||||
\(768\) | −9.51522 | −0.343351 | ||||||||
\(769\) | 14.3996 | 0.519261 | 0.259631 | − | 0.965708i | \(-0.416399\pi\) | ||||
0.259631 | + | 0.965708i | \(0.416399\pi\) | |||||||
\(770\) | −8.68410 | −0.312953 | ||||||||
\(771\) | 10.5780 | 0.380958 | ||||||||
\(772\) | −4.12353 | −0.148409 | ||||||||
\(773\) | 10.7101 | 0.385215 | 0.192607 | − | 0.981276i | \(-0.438306\pi\) | ||||
0.192607 | + | 0.981276i | \(0.438306\pi\) | |||||||
\(774\) | 6.57591 | 0.236366 | ||||||||
\(775\) | −3.50170 | −0.125785 | ||||||||
\(776\) | −0.565544 | −0.0203019 | ||||||||
\(777\) | 5.36554 | 0.192488 | ||||||||
\(778\) | 9.57905 | 0.343426 | ||||||||
\(779\) | −4.44449 | −0.159240 | ||||||||
\(780\) | −1.14978 | −0.0411687 | ||||||||
\(781\) | −29.6019 | −1.05924 | ||||||||
\(782\) | 1.62645 | 0.0581617 | ||||||||
\(783\) | −7.67112 | −0.274143 | ||||||||
\(784\) | 4.86210 | 0.173646 | ||||||||
\(785\) | −26.5003 | −0.945837 | ||||||||
\(786\) | 0.822619 | 0.0293418 | ||||||||
\(787\) | 33.7288 | 1.20230 | 0.601150 | − | 0.799136i | \(-0.294709\pi\) | ||||
0.601150 | + | 0.799136i | \(0.294709\pi\) | |||||||
\(788\) | −28.7874 | −1.02551 | ||||||||
\(789\) | 23.0197 | 0.819524 | ||||||||
\(790\) | −0.795496 | −0.0283025 | ||||||||
\(791\) | 7.25650 | 0.258011 | ||||||||
\(792\) | 8.15251 | 0.289687 | ||||||||
\(793\) | −8.94381 | −0.317604 | ||||||||
\(794\) | 0.387609 | 0.0137557 | ||||||||
\(795\) | 4.80173 | 0.170300 | ||||||||
\(796\) | −24.7767 | −0.878188 | ||||||||
\(797\) | −15.7768 | −0.558845 | −0.279422 | − | 0.960168i | \(-0.590143\pi\) | ||||
−0.279422 | + | 0.960168i | \(0.590143\pi\) | |||||||
\(798\) | 3.54872 | 0.125623 | ||||||||
\(799\) | 10.9547 | 0.387550 | ||||||||
\(800\) | −21.0351 | −0.743704 | ||||||||
\(801\) | 13.8761 | 0.490288 | ||||||||
\(802\) | −14.6101 | −0.515900 | ||||||||
\(803\) | −0.233609 | −0.00824389 | ||||||||
\(804\) | 11.7606 | 0.414766 | ||||||||
\(805\) | 9.00803 | 0.317491 | ||||||||
\(806\) | −0.419475 | −0.0147754 | ||||||||
\(807\) | 22.7666 | 0.801423 | ||||||||
\(808\) | −7.96116 | −0.280073 | ||||||||
\(809\) | −35.0687 | −1.23295 | −0.616475 | − | 0.787374i | \(-0.711440\pi\) | ||||
−0.616475 | + | 0.787374i | \(0.711440\pi\) | |||||||
\(810\) | −0.795496 | −0.0279509 | ||||||||
\(811\) | −24.1664 | −0.848597 | −0.424298 | − | 0.905522i | \(-0.639479\pi\) | ||||
−0.424298 | + | 0.905522i | \(0.639479\pi\) | |||||||
\(812\) | −37.9963 | −1.33341 | ||||||||
\(813\) | −2.26550 | −0.0794547 | ||||||||
\(814\) | 3.83787 | 0.134517 | ||||||||
\(815\) | −9.97275 | −0.349330 | ||||||||
\(816\) | 1.43732 | 0.0503164 | ||||||||
\(817\) | −15.6483 | −0.547464 | ||||||||
\(818\) | −16.6923 | −0.583631 | ||||||||
\(819\) | 2.06114 | 0.0720221 | ||||||||
\(820\) | 4.93482 | 0.172331 | ||||||||
\(821\) | −2.32220 | −0.0810452 | −0.0405226 | − | 0.999179i | \(-0.512902\pi\) | ||||
−0.0405226 | + | 0.999179i | \(0.512902\pi\) | |||||||
\(822\) | 11.8803 | 0.414372 | ||||||||
\(823\) | −56.3300 | −1.96354 | −0.981771 | − | 0.190069i | \(-0.939129\pi\) | ||||
−0.981771 | + | 0.190069i | \(0.939129\pi\) | |||||||
\(824\) | 23.4925 | 0.818400 | ||||||||
\(825\) | 12.3072 | 0.428480 | ||||||||
\(826\) | 9.43246 | 0.328197 | ||||||||
\(827\) | 7.78244 | 0.270622 | 0.135311 | − | 0.990803i | \(-0.456797\pi\) | ||||
0.135311 | + | 0.990803i | \(0.456797\pi\) | |||||||
\(828\) | −3.67507 | −0.127717 | ||||||||
\(829\) | −25.0005 | −0.868304 | −0.434152 | − | 0.900840i | \(-0.642952\pi\) | ||||
−0.434152 | + | 0.900840i | \(0.642952\pi\) | |||||||
\(830\) | 12.7865 | 0.443825 | ||||||||
\(831\) | −14.8072 | −0.513656 | ||||||||
\(832\) | −0.681028 | −0.0236104 | ||||||||
\(833\) | 3.38274 | 0.117205 | ||||||||
\(834\) | 3.46067 | 0.119833 | ||||||||
\(835\) | 18.1344 | 0.627568 | ||||||||
\(836\) | −8.43084 | −0.291587 | ||||||||
\(837\) | 0.963944 | 0.0333188 | ||||||||
\(838\) | 9.07904 | 0.313630 | ||||||||
\(839\) | −16.2981 | −0.562674 | −0.281337 | − | 0.959609i | \(-0.590778\pi\) | ||||
−0.281337 | + | 0.959609i | \(0.590778\pi\) | |||||||
\(840\) | −9.06676 | −0.312833 | ||||||||
\(841\) | 29.8460 | 1.02917 | ||||||||
\(842\) | −22.9597 | −0.791244 | ||||||||
\(843\) | −18.7820 | −0.646887 | ||||||||
\(844\) | −34.2459 | −1.17879 | ||||||||
\(845\) | 14.7228 | 0.506479 | ||||||||
\(846\) | 7.45252 | 0.256223 | ||||||||
\(847\) | −1.53984 | −0.0529095 | ||||||||
\(848\) | −5.90224 | −0.202684 | ||||||||
\(849\) | 27.0646 | 0.928856 | ||||||||
\(850\) | −2.47132 | −0.0847656 | ||||||||
\(851\) | −3.98103 | −0.136468 | ||||||||
\(852\) | −13.4312 | −0.460146 | ||||||||
\(853\) | 11.9132 | 0.407902 | 0.203951 | − | 0.978981i | \(-0.434622\pi\) | ||||
0.203951 | + | 0.978981i | \(0.434622\pi\) | |||||||
\(854\) | −30.6499 | −1.04882 | ||||||||
\(855\) | 1.89299 | 0.0647389 | ||||||||
\(856\) | −26.4498 | −0.904036 | ||||||||
\(857\) | −19.8048 | −0.676518 | −0.338259 | − | 0.941053i | \(-0.609838\pi\) | ||||
−0.338259 | + | 0.941053i | \(0.609838\pi\) | |||||||
\(858\) | 1.47430 | 0.0503316 | ||||||||
\(859\) | 38.4594 | 1.31222 | 0.656109 | − | 0.754666i | \(-0.272201\pi\) | ||||
0.656109 | + | 0.754666i | \(0.272201\pi\) | |||||||
\(860\) | 17.3747 | 0.592471 | ||||||||
\(861\) | −8.84636 | −0.301483 | ||||||||
\(862\) | 1.21971 | 0.0415435 | ||||||||
\(863\) | 23.0904 | 0.786005 | 0.393003 | − | 0.919537i | \(-0.371436\pi\) | ||||
0.393003 | + | 0.919537i | \(0.371436\pi\) | |||||||
\(864\) | 5.79053 | 0.196998 | ||||||||
\(865\) | 8.41649 | 0.286169 | ||||||||
\(866\) | 4.24960 | 0.144407 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 4.77458 | 0.162060 | ||||||||
\(869\) | −3.38790 | −0.114927 | ||||||||
\(870\) | 6.10234 | 0.206889 | ||||||||
\(871\) | 4.89391 | 0.165824 | ||||||||
\(872\) | −20.4590 | −0.692828 | ||||||||
\(873\) | 0.235021 | 0.00795425 | ||||||||
\(874\) | −2.63301 | −0.0890631 | ||||||||
\(875\) | −32.5265 | −1.09960 | ||||||||
\(876\) | −0.105995 | −0.00358125 | ||||||||
\(877\) | 30.8283 | 1.04100 | 0.520499 | − | 0.853863i | \(-0.325746\pi\) | ||||
0.520499 | + | 0.853863i | \(0.325746\pi\) | |||||||
\(878\) | −21.8136 | −0.736172 | ||||||||
\(879\) | −23.5463 | −0.794196 | ||||||||
\(880\) | 5.69405 | 0.191946 | ||||||||
\(881\) | 33.4394 | 1.12660 | 0.563302 | − | 0.826251i | \(-0.309531\pi\) | ||||
0.563302 | + | 0.826251i | \(0.309531\pi\) | |||||||
\(882\) | 2.30129 | 0.0774884 | ||||||||
\(883\) | −29.0856 | −0.978809 | −0.489404 | − | 0.872057i | \(-0.662786\pi\) | ||||
−0.489404 | + | 0.872057i | \(0.662786\pi\) | |||||||
\(884\) | 0.983284 | 0.0330714 | ||||||||
\(885\) | 5.03155 | 0.169134 | ||||||||
\(886\) | 25.5015 | 0.856741 | ||||||||
\(887\) | 4.97834 | 0.167156 | 0.0835782 | − | 0.996501i | \(-0.473365\pi\) | ||||
0.0835782 | + | 0.996501i | \(0.473365\pi\) | |||||||
\(888\) | 4.00699 | 0.134466 | ||||||||
\(889\) | −38.6609 | −1.29664 | ||||||||
\(890\) | −11.0384 | −0.370007 | ||||||||
\(891\) | −3.38790 | −0.113499 | ||||||||
\(892\) | 31.1590 | 1.04328 | ||||||||
\(893\) | −17.7343 | −0.593456 | ||||||||
\(894\) | 5.17353 | 0.173029 | ||||||||
\(895\) | −4.34826 | −0.145346 | ||||||||
\(896\) | 34.9830 | 1.16870 | ||||||||
\(897\) | −1.52929 | −0.0510615 | ||||||||
\(898\) | 9.85688 | 0.328928 | ||||||||
\(899\) | −7.39453 | −0.246621 | ||||||||
\(900\) | 5.58411 | 0.186137 | ||||||||
\(901\) | −4.10641 | −0.136804 | ||||||||
\(902\) | −6.32764 | −0.210687 | ||||||||
\(903\) | −31.1465 | −1.03649 | ||||||||
\(904\) | 5.41915 | 0.180238 | ||||||||
\(905\) | 27.5689 | 0.916421 | ||||||||
\(906\) | −2.67537 | −0.0888831 | ||||||||
\(907\) | −6.39323 | −0.212284 | −0.106142 | − | 0.994351i | \(-0.533850\pi\) | ||||
−0.106142 | + | 0.994351i | \(0.533850\pi\) | |||||||
\(908\) | −18.3566 | −0.609185 | ||||||||
\(909\) | 3.30839 | 0.109732 | ||||||||
\(910\) | −1.63963 | −0.0543532 | ||||||||
\(911\) | −5.54669 | −0.183770 | −0.0918849 | − | 0.995770i | \(-0.529289\pi\) | ||||
−0.0918849 | + | 0.995770i | \(0.529289\pi\) | |||||||
\(912\) | −2.32685 | −0.0770496 | ||||||||
\(913\) | 54.4557 | 1.80222 | ||||||||
\(914\) | 5.16358 | 0.170796 | ||||||||
\(915\) | −16.3496 | −0.540500 | ||||||||
\(916\) | 5.77699 | 0.190877 | ||||||||
\(917\) | −3.89630 | −0.128667 | ||||||||
\(918\) | 0.680303 | 0.0224533 | ||||||||
\(919\) | 36.6534 | 1.20908 | 0.604542 | − | 0.796573i | \(-0.293356\pi\) | ||||
0.604542 | + | 0.796573i | \(0.293356\pi\) | |||||||
\(920\) | 6.72719 | 0.221789 | ||||||||
\(921\) | −19.6462 | −0.647365 | ||||||||
\(922\) | 4.64787 | 0.153070 | ||||||||
\(923\) | −5.58908 | −0.183967 | ||||||||
\(924\) | −16.7809 | −0.552049 | ||||||||
\(925\) | 6.04901 | 0.198890 | ||||||||
\(926\) | −7.25470 | −0.238404 | ||||||||
\(927\) | −9.76268 | −0.320648 | ||||||||
\(928\) | −44.4199 | −1.45815 | ||||||||
\(929\) | 36.4348 | 1.19539 | 0.597693 | − | 0.801725i | \(-0.296084\pi\) | ||||
0.597693 | + | 0.801725i | \(0.296084\pi\) | |||||||
\(930\) | −0.766813 | −0.0251448 | ||||||||
\(931\) | −5.47623 | −0.179476 | ||||||||
\(932\) | 25.4224 | 0.832737 | ||||||||
\(933\) | −5.69179 | −0.186341 | ||||||||
\(934\) | 4.37115 | 0.143028 | ||||||||
\(935\) | 3.96156 | 0.129557 | ||||||||
\(936\) | 1.53926 | 0.0503123 | ||||||||
\(937\) | 6.50428 | 0.212485 | 0.106243 | − | 0.994340i | \(-0.466118\pi\) | ||||
0.106243 | + | 0.994340i | \(0.466118\pi\) | |||||||
\(938\) | 16.7711 | 0.547596 | ||||||||
\(939\) | −5.20447 | −0.169842 | ||||||||
\(940\) | 19.6908 | 0.642244 | ||||||||
\(941\) | −19.8395 | −0.646749 | −0.323374 | − | 0.946271i | \(-0.604817\pi\) | ||||
−0.323374 | + | 0.946271i | \(0.604817\pi\) | |||||||
\(942\) | 15.4176 | 0.502334 | ||||||||
\(943\) | 6.56367 | 0.213742 | ||||||||
\(944\) | −6.18474 | −0.201296 | ||||||||
\(945\) | 3.76783 | 0.122568 | ||||||||
\(946\) | −22.2785 | −0.724338 | ||||||||
\(947\) | −18.3063 | −0.594874 | −0.297437 | − | 0.954741i | \(-0.596132\pi\) | ||||
−0.297437 | + | 0.954741i | \(0.596132\pi\) | |||||||
\(948\) | −1.53719 | −0.0499256 | ||||||||
\(949\) | −0.0441074 | −0.00143179 | ||||||||
\(950\) | 4.00076 | 0.129802 | ||||||||
\(951\) | 14.0120 | 0.454371 | ||||||||
\(952\) | 7.75383 | 0.251303 | ||||||||
\(953\) | −3.89728 | −0.126245 | −0.0631226 | − | 0.998006i | \(-0.520106\pi\) | ||||
−0.0631226 | + | 0.998006i | \(0.520106\pi\) | |||||||
\(954\) | −2.79360 | −0.0904462 | ||||||||
\(955\) | 19.0307 | 0.615818 | ||||||||
\(956\) | 28.8260 | 0.932299 | ||||||||
\(957\) | 25.9890 | 0.840105 | ||||||||
\(958\) | −11.4220 | −0.369028 | ||||||||
\(959\) | −56.2704 | −1.81707 | ||||||||
\(960\) | −1.24494 | −0.0401803 | ||||||||
\(961\) | −30.0708 | −0.970026 | ||||||||
\(962\) | 0.724622 | 0.0233628 | ||||||||
\(963\) | 10.9916 | 0.354200 | ||||||||
\(964\) | 0.744119 | 0.0239664 | ||||||||
\(965\) | −3.13673 | −0.100975 | ||||||||
\(966\) | −5.24078 | −0.168619 | ||||||||
\(967\) | −57.8586 | −1.86061 | −0.930304 | − | 0.366790i | \(-0.880457\pi\) | ||||
−0.930304 | + | 0.366790i | \(0.880457\pi\) | |||||||
\(968\) | −1.14995 | −0.0369608 | ||||||||
\(969\) | −1.61887 | −0.0520057 | ||||||||
\(970\) | −0.186958 | −0.00600286 | ||||||||
\(971\) | 1.86291 | 0.0597837 | 0.0298919 | − | 0.999553i | \(-0.490484\pi\) | ||||
0.0298919 | + | 0.999553i | \(0.490484\pi\) | |||||||
\(972\) | −1.53719 | −0.0493053 | ||||||||
\(973\) | −16.3913 | −0.525482 | ||||||||
\(974\) | 3.33856 | 0.106974 | ||||||||
\(975\) | 2.32369 | 0.0744177 | ||||||||
\(976\) | 20.0967 | 0.643281 | ||||||||
\(977\) | 17.7417 | 0.567608 | 0.283804 | − | 0.958882i | \(-0.408403\pi\) | ||||
0.283804 | + | 0.958882i | \(0.408403\pi\) | |||||||
\(978\) | 5.80205 | 0.185529 | ||||||||
\(979\) | −47.0109 | −1.50247 | ||||||||
\(980\) | 6.08039 | 0.194231 | ||||||||
\(981\) | 8.50204 | 0.271449 | ||||||||
\(982\) | 24.6359 | 0.786164 | ||||||||
\(983\) | 2.31533 | 0.0738476 | 0.0369238 | − | 0.999318i | \(-0.488244\pi\) | ||||
0.0369238 | + | 0.999318i | \(0.488244\pi\) | |||||||
\(984\) | −6.60646 | −0.210606 | ||||||||
\(985\) | −21.8984 | −0.697740 | ||||||||
\(986\) | −5.21868 | −0.166197 | ||||||||
\(987\) | −35.2986 | −1.12357 | ||||||||
\(988\) | −1.59181 | −0.0506423 | ||||||||
\(989\) | 23.1096 | 0.734841 | ||||||||
\(990\) | 2.69506 | 0.0856547 | ||||||||
\(991\) | 11.1529 | 0.354285 | 0.177142 | − | 0.984185i | \(-0.443315\pi\) | ||||
0.177142 | + | 0.984185i | \(0.443315\pi\) | |||||||
\(992\) | 5.58175 | 0.177221 | ||||||||
\(993\) | 29.4898 | 0.935831 | ||||||||
\(994\) | −19.1534 | −0.607510 | ||||||||
\(995\) | −18.8474 | −0.597504 | ||||||||
\(996\) | 24.7081 | 0.782907 | ||||||||
\(997\) | −23.6499 | −0.749000 | −0.374500 | − | 0.927227i | \(-0.622186\pi\) | ||||
−0.374500 | + | 0.927227i | \(0.622186\pi\) | |||||||
\(998\) | 12.3585 | 0.391202 | ||||||||
\(999\) | −1.66517 | −0.0526835 |
(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 | 4029.2.a.k.1.19 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.19 | ✓ | 31 | 1.1 | even | 1 | trivial |