Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6162,2,Mod(1,6162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6162, 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("6162.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6162 = 2 \cdot 3 \cdot 13 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6162.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: | \(49.2038177255\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 22x^{8} + 84x^{7} + 149x^{6} - 596x^{5} - 300x^{4} + 1684x^{3} - 228x^{2} - 1520x + 688 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.30197\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6162.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.30197 | 1.02947 | 0.514737 | − | 0.857348i | \(-0.327890\pi\) | ||||
0.514737 | + | 0.857348i | \(0.327890\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.48369 | −0.560780 | −0.280390 | − | 0.959886i | \(-0.590464\pi\) | ||||
−0.280390 | + | 0.959886i | \(0.590464\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.30197 | 0.727947 | ||||||||
\(11\) | 1.45470 | 0.438608 | 0.219304 | − | 0.975657i | \(-0.429621\pi\) | ||||
0.219304 | + | 0.975657i | \(0.429621\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.48369 | −0.396532 | ||||||||
\(15\) | −2.30197 | −0.594367 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.05980 | −1.22718 | −0.613591 | − | 0.789624i | \(-0.710276\pi\) | ||||
−0.613591 | + | 0.789624i | \(0.710276\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.16141 | 0.266446 | 0.133223 | − | 0.991086i | \(-0.457467\pi\) | ||||
0.133223 | + | 0.991086i | \(0.457467\pi\) | |||||||
\(20\) | 2.30197 | 0.514737 | ||||||||
\(21\) | 1.48369 | 0.323767 | ||||||||
\(22\) | 1.45470 | 0.310143 | ||||||||
\(23\) | 1.42055 | 0.296206 | 0.148103 | − | 0.988972i | \(-0.452683\pi\) | ||||
0.148103 | + | 0.988972i | \(0.452683\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0.299075 | 0.0598150 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.48369 | −0.280390 | ||||||||
\(29\) | −0.645096 | −0.119791 | −0.0598957 | − | 0.998205i | \(-0.519077\pi\) | ||||
−0.0598957 | + | 0.998205i | \(0.519077\pi\) | |||||||
\(30\) | −2.30197 | −0.420281 | ||||||||
\(31\) | 5.49508 | 0.986945 | 0.493473 | − | 0.869761i | \(-0.335727\pi\) | ||||
0.493473 | + | 0.869761i | \(0.335727\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.45470 | −0.253231 | ||||||||
\(34\) | −5.05980 | −0.867749 | ||||||||
\(35\) | −3.41540 | −0.577308 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.13743 | 1.50218 | 0.751092 | − | 0.660198i | \(-0.229527\pi\) | ||||
0.751092 | + | 0.660198i | \(0.229527\pi\) | |||||||
\(38\) | 1.16141 | 0.188406 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 2.30197 | 0.363974 | ||||||||
\(41\) | −3.13816 | −0.490099 | −0.245049 | − | 0.969511i | \(-0.578804\pi\) | ||||
−0.245049 | + | 0.969511i | \(0.578804\pi\) | |||||||
\(42\) | 1.48369 | 0.228938 | ||||||||
\(43\) | 9.55158 | 1.45660 | 0.728301 | − | 0.685257i | \(-0.240310\pi\) | ||||
0.728301 | + | 0.685257i | \(0.240310\pi\) | |||||||
\(44\) | 1.45470 | 0.219304 | ||||||||
\(45\) | 2.30197 | 0.343158 | ||||||||
\(46\) | 1.42055 | 0.209449 | ||||||||
\(47\) | −0.649167 | −0.0946908 | −0.0473454 | − | 0.998879i | \(-0.515076\pi\) | ||||
−0.0473454 | + | 0.998879i | \(0.515076\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.79868 | −0.685525 | ||||||||
\(50\) | 0.299075 | 0.0422956 | ||||||||
\(51\) | 5.05980 | 0.708514 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 12.3104 | 1.69096 | 0.845482 | − | 0.534004i | \(-0.179313\pi\) | ||||
0.845482 | + | 0.534004i | \(0.179313\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 3.34868 | 0.451535 | ||||||||
\(56\) | −1.48369 | −0.198266 | ||||||||
\(57\) | −1.16141 | −0.153833 | ||||||||
\(58\) | −0.645096 | −0.0847052 | ||||||||
\(59\) | −4.11934 | −0.536292 | −0.268146 | − | 0.963378i | \(-0.586411\pi\) | ||||
−0.268146 | + | 0.963378i | \(0.586411\pi\) | |||||||
\(60\) | −2.30197 | −0.297183 | ||||||||
\(61\) | 6.41227 | 0.821007 | 0.410504 | − | 0.911859i | \(-0.365353\pi\) | ||||
0.410504 | + | 0.911859i | \(0.365353\pi\) | |||||||
\(62\) | 5.49508 | 0.697876 | ||||||||
\(63\) | −1.48369 | −0.186927 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.30197 | −0.285524 | ||||||||
\(66\) | −1.45470 | −0.179061 | ||||||||
\(67\) | −8.73905 | −1.06764 | −0.533822 | − | 0.845597i | \(-0.679245\pi\) | ||||
−0.533822 | + | 0.845597i | \(0.679245\pi\) | |||||||
\(68\) | −5.05980 | −0.613591 | ||||||||
\(69\) | −1.42055 | −0.171014 | ||||||||
\(70\) | −3.41540 | −0.408219 | ||||||||
\(71\) | 5.64506 | 0.669945 | 0.334973 | − | 0.942228i | \(-0.391273\pi\) | ||||
0.334973 | + | 0.942228i | \(0.391273\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 13.3593 | 1.56359 | 0.781795 | − | 0.623535i | \(-0.214304\pi\) | ||||
0.781795 | + | 0.623535i | \(0.214304\pi\) | |||||||
\(74\) | 9.13743 | 1.06220 | ||||||||
\(75\) | −0.299075 | −0.0345342 | ||||||||
\(76\) | 1.16141 | 0.133223 | ||||||||
\(77\) | −2.15832 | −0.245963 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 2.30197 | 0.257368 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.13816 | −0.346552 | ||||||||
\(83\) | 9.50219 | 1.04300 | 0.521500 | − | 0.853251i | \(-0.325372\pi\) | ||||
0.521500 | + | 0.853251i | \(0.325372\pi\) | |||||||
\(84\) | 1.48369 | 0.161883 | ||||||||
\(85\) | −11.6475 | −1.26335 | ||||||||
\(86\) | 9.55158 | 1.02997 | ||||||||
\(87\) | 0.645096 | 0.0691615 | ||||||||
\(88\) | 1.45470 | 0.155071 | ||||||||
\(89\) | 2.12365 | 0.225107 | 0.112553 | − | 0.993646i | \(-0.464097\pi\) | ||||
0.112553 | + | 0.993646i | \(0.464097\pi\) | |||||||
\(90\) | 2.30197 | 0.242649 | ||||||||
\(91\) | 1.48369 | 0.155533 | ||||||||
\(92\) | 1.42055 | 0.148103 | ||||||||
\(93\) | −5.49508 | −0.569813 | ||||||||
\(94\) | −0.649167 | −0.0669565 | ||||||||
\(95\) | 2.67353 | 0.274299 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 12.4889 | 1.26805 | 0.634026 | − | 0.773312i | \(-0.281401\pi\) | ||||
0.634026 | + | 0.773312i | \(0.281401\pi\) | |||||||
\(98\) | −4.79868 | −0.484740 | ||||||||
\(99\) | 1.45470 | 0.146203 | ||||||||
\(100\) | 0.299075 | 0.0299075 | ||||||||
\(101\) | 18.7245 | 1.86316 | 0.931580 | − | 0.363537i | \(-0.118431\pi\) | ||||
0.931580 | + | 0.363537i | \(0.118431\pi\) | |||||||
\(102\) | 5.05980 | 0.500995 | ||||||||
\(103\) | −2.93346 | −0.289043 | −0.144521 | − | 0.989502i | \(-0.546164\pi\) | ||||
−0.144521 | + | 0.989502i | \(0.546164\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 3.41540 | 0.333309 | ||||||||
\(106\) | 12.3104 | 1.19569 | ||||||||
\(107\) | −4.87580 | −0.471362 | −0.235681 | − | 0.971831i | \(-0.575732\pi\) | ||||
−0.235681 | + | 0.971831i | \(0.575732\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −4.36952 | −0.418524 | −0.209262 | − | 0.977860i | \(-0.567106\pi\) | ||||
−0.209262 | + | 0.977860i | \(0.567106\pi\) | |||||||
\(110\) | 3.34868 | 0.319284 | ||||||||
\(111\) | −9.13743 | −0.867286 | ||||||||
\(112\) | −1.48369 | −0.140195 | ||||||||
\(113\) | 10.1291 | 0.952867 | 0.476434 | − | 0.879210i | \(-0.341929\pi\) | ||||
0.476434 | + | 0.879210i | \(0.341929\pi\) | |||||||
\(114\) | −1.16141 | −0.108776 | ||||||||
\(115\) | 3.27007 | 0.304936 | ||||||||
\(116\) | −0.645096 | −0.0598957 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −4.11934 | −0.379216 | ||||||||
\(119\) | 7.50715 | 0.688180 | ||||||||
\(120\) | −2.30197 | −0.210140 | ||||||||
\(121\) | −8.88385 | −0.807623 | ||||||||
\(122\) | 6.41227 | 0.580540 | ||||||||
\(123\) | 3.13816 | 0.282959 | ||||||||
\(124\) | 5.49508 | 0.493473 | ||||||||
\(125\) | −10.8214 | −0.967895 | ||||||||
\(126\) | −1.48369 | −0.132177 | ||||||||
\(127\) | −11.2206 | −0.995667 | −0.497834 | − | 0.867273i | \(-0.665871\pi\) | ||||
−0.497834 | + | 0.867273i | \(0.665871\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.55158 | −0.840970 | ||||||||
\(130\) | −2.30197 | −0.201896 | ||||||||
\(131\) | −1.89704 | −0.165745 | −0.0828726 | − | 0.996560i | \(-0.526409\pi\) | ||||
−0.0828726 | + | 0.996560i | \(0.526409\pi\) | |||||||
\(132\) | −1.45470 | −0.126615 | ||||||||
\(133\) | −1.72317 | −0.149418 | ||||||||
\(134\) | −8.73905 | −0.754939 | ||||||||
\(135\) | −2.30197 | −0.198122 | ||||||||
\(136\) | −5.05980 | −0.433874 | ||||||||
\(137\) | 8.45406 | 0.722279 | 0.361139 | − | 0.932512i | \(-0.382388\pi\) | ||||
0.361139 | + | 0.932512i | \(0.382388\pi\) | |||||||
\(138\) | −1.42055 | −0.120925 | ||||||||
\(139\) | −6.96044 | −0.590377 | −0.295188 | − | 0.955439i | \(-0.595382\pi\) | ||||
−0.295188 | + | 0.955439i | \(0.595382\pi\) | |||||||
\(140\) | −3.41540 | −0.288654 | ||||||||
\(141\) | 0.649167 | 0.0546698 | ||||||||
\(142\) | 5.64506 | 0.473723 | ||||||||
\(143\) | −1.45470 | −0.121648 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.48499 | −0.123322 | ||||||||
\(146\) | 13.3593 | 1.10563 | ||||||||
\(147\) | 4.79868 | 0.395788 | ||||||||
\(148\) | 9.13743 | 0.751092 | ||||||||
\(149\) | −6.81810 | −0.558560 | −0.279280 | − | 0.960210i | \(-0.590096\pi\) | ||||
−0.279280 | + | 0.960210i | \(0.590096\pi\) | |||||||
\(150\) | −0.299075 | −0.0244194 | ||||||||
\(151\) | 18.2202 | 1.48274 | 0.741371 | − | 0.671096i | \(-0.234176\pi\) | ||||
0.741371 | + | 0.671096i | \(0.234176\pi\) | |||||||
\(152\) | 1.16141 | 0.0942028 | ||||||||
\(153\) | −5.05980 | −0.409061 | ||||||||
\(154\) | −2.15832 | −0.173922 | ||||||||
\(155\) | 12.6495 | 1.01603 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 0.757630 | 0.0604654 | 0.0302327 | − | 0.999543i | \(-0.490375\pi\) | ||||
0.0302327 | + | 0.999543i | \(0.490375\pi\) | |||||||
\(158\) | −1.00000 | −0.0795557 | ||||||||
\(159\) | −12.3104 | −0.976278 | ||||||||
\(160\) | 2.30197 | 0.181987 | ||||||||
\(161\) | −2.10765 | −0.166106 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −24.6698 | −1.93229 | −0.966144 | − | 0.258003i | \(-0.916936\pi\) | ||||
−0.966144 | + | 0.258003i | \(0.916936\pi\) | |||||||
\(164\) | −3.13816 | −0.245049 | ||||||||
\(165\) | −3.34868 | −0.260694 | ||||||||
\(166\) | 9.50219 | 0.737513 | ||||||||
\(167\) | 20.8856 | 1.61618 | 0.808090 | − | 0.589059i | \(-0.200502\pi\) | ||||
0.808090 | + | 0.589059i | \(0.200502\pi\) | |||||||
\(168\) | 1.48369 | 0.114469 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −11.6475 | −0.893324 | ||||||||
\(171\) | 1.16141 | 0.0888153 | ||||||||
\(172\) | 9.55158 | 0.728301 | ||||||||
\(173\) | −5.10263 | −0.387946 | −0.193973 | − | 0.981007i | \(-0.562137\pi\) | ||||
−0.193973 | + | 0.981007i | \(0.562137\pi\) | |||||||
\(174\) | 0.645096 | 0.0489046 | ||||||||
\(175\) | −0.443733 | −0.0335431 | ||||||||
\(176\) | 1.45470 | 0.109652 | ||||||||
\(177\) | 4.11934 | 0.309629 | ||||||||
\(178\) | 2.12365 | 0.159175 | ||||||||
\(179\) | −7.54212 | −0.563725 | −0.281862 | − | 0.959455i | \(-0.590952\pi\) | ||||
−0.281862 | + | 0.959455i | \(0.590952\pi\) | |||||||
\(180\) | 2.30197 | 0.171579 | ||||||||
\(181\) | 6.99392 | 0.519854 | 0.259927 | − | 0.965628i | \(-0.416301\pi\) | ||||
0.259927 | + | 0.965628i | \(0.416301\pi\) | |||||||
\(182\) | 1.48369 | 0.109978 | ||||||||
\(183\) | −6.41227 | −0.474009 | ||||||||
\(184\) | 1.42055 | 0.104725 | ||||||||
\(185\) | 21.0341 | 1.54646 | ||||||||
\(186\) | −5.49508 | −0.402919 | ||||||||
\(187\) | −7.36049 | −0.538252 | ||||||||
\(188\) | −0.649167 | −0.0473454 | ||||||||
\(189\) | 1.48369 | 0.107922 | ||||||||
\(190\) | 2.67353 | 0.193959 | ||||||||
\(191\) | 4.09683 | 0.296436 | 0.148218 | − | 0.988955i | \(-0.452646\pi\) | ||||
0.148218 | + | 0.988955i | \(0.452646\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −13.1156 | −0.944078 | −0.472039 | − | 0.881578i | \(-0.656482\pi\) | ||||
−0.472039 | + | 0.881578i | \(0.656482\pi\) | |||||||
\(194\) | 12.4889 | 0.896648 | ||||||||
\(195\) | 2.30197 | 0.164848 | ||||||||
\(196\) | −4.79868 | −0.342763 | ||||||||
\(197\) | −9.84786 | −0.701631 | −0.350816 | − | 0.936445i | \(-0.614096\pi\) | ||||
−0.350816 | + | 0.936445i | \(0.614096\pi\) | |||||||
\(198\) | 1.45470 | 0.103381 | ||||||||
\(199\) | 27.3916 | 1.94174 | 0.970869 | − | 0.239610i | \(-0.0770196\pi\) | ||||
0.970869 | + | 0.239610i | \(0.0770196\pi\) | |||||||
\(200\) | 0.299075 | 0.0211478 | ||||||||
\(201\) | 8.73905 | 0.616405 | ||||||||
\(202\) | 18.7245 | 1.31745 | ||||||||
\(203\) | 0.957120 | 0.0671766 | ||||||||
\(204\) | 5.05980 | 0.354257 | ||||||||
\(205\) | −7.22396 | −0.504543 | ||||||||
\(206\) | −2.93346 | −0.204384 | ||||||||
\(207\) | 1.42055 | 0.0987352 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 1.68950 | 0.116865 | ||||||||
\(210\) | 3.41540 | 0.235685 | ||||||||
\(211\) | −11.7715 | −0.810385 | −0.405193 | − | 0.914231i | \(-0.632796\pi\) | ||||
−0.405193 | + | 0.914231i | \(0.632796\pi\) | |||||||
\(212\) | 12.3104 | 0.845482 | ||||||||
\(213\) | −5.64506 | −0.386793 | ||||||||
\(214\) | −4.87580 | −0.333303 | ||||||||
\(215\) | 21.9875 | 1.49953 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −8.15297 | −0.553460 | ||||||||
\(218\) | −4.36952 | −0.295941 | ||||||||
\(219\) | −13.3593 | −0.902739 | ||||||||
\(220\) | 3.34868 | 0.225768 | ||||||||
\(221\) | 5.05980 | 0.340359 | ||||||||
\(222\) | −9.13743 | −0.613264 | ||||||||
\(223\) | 12.6013 | 0.843844 | 0.421922 | − | 0.906632i | \(-0.361356\pi\) | ||||
0.421922 | + | 0.906632i | \(0.361356\pi\) | |||||||
\(224\) | −1.48369 | −0.0991329 | ||||||||
\(225\) | 0.299075 | 0.0199383 | ||||||||
\(226\) | 10.1291 | 0.673779 | ||||||||
\(227\) | −27.0019 | −1.79218 | −0.896088 | − | 0.443876i | \(-0.853603\pi\) | ||||
−0.896088 | + | 0.443876i | \(0.853603\pi\) | |||||||
\(228\) | −1.16141 | −0.0769163 | ||||||||
\(229\) | 19.2273 | 1.27057 | 0.635287 | − | 0.772276i | \(-0.280882\pi\) | ||||
0.635287 | + | 0.772276i | \(0.280882\pi\) | |||||||
\(230\) | 3.27007 | 0.215622 | ||||||||
\(231\) | 2.15832 | 0.142007 | ||||||||
\(232\) | −0.645096 | −0.0423526 | ||||||||
\(233\) | 21.2824 | 1.39426 | 0.697129 | − | 0.716946i | \(-0.254461\pi\) | ||||
0.697129 | + | 0.716946i | \(0.254461\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −1.49437 | −0.0974816 | ||||||||
\(236\) | −4.11934 | −0.268146 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 7.50715 | 0.486617 | ||||||||
\(239\) | −21.0272 | −1.36013 | −0.680067 | − | 0.733150i | \(-0.738049\pi\) | ||||
−0.680067 | + | 0.733150i | \(0.738049\pi\) | |||||||
\(240\) | −2.30197 | −0.148592 | ||||||||
\(241\) | 2.57137 | 0.165636 | 0.0828182 | − | 0.996565i | \(-0.473608\pi\) | ||||
0.0828182 | + | 0.996565i | \(0.473608\pi\) | |||||||
\(242\) | −8.88385 | −0.571076 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.41227 | 0.410504 | ||||||||
\(245\) | −11.0464 | −0.705730 | ||||||||
\(246\) | 3.13816 | 0.200082 | ||||||||
\(247\) | −1.16141 | −0.0738988 | ||||||||
\(248\) | 5.49508 | 0.348938 | ||||||||
\(249\) | −9.50219 | −0.602177 | ||||||||
\(250\) | −10.8214 | −0.684405 | ||||||||
\(251\) | −11.4065 | −0.719969 | −0.359985 | − | 0.932958i | \(-0.617218\pi\) | ||||
−0.359985 | + | 0.932958i | \(0.617218\pi\) | |||||||
\(252\) | −1.48369 | −0.0934634 | ||||||||
\(253\) | 2.06648 | 0.129918 | ||||||||
\(254\) | −11.2206 | −0.704043 | ||||||||
\(255\) | 11.6475 | 0.729396 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.25709 | 0.452685 | 0.226342 | − | 0.974048i | \(-0.427323\pi\) | ||||
0.226342 | + | 0.974048i | \(0.427323\pi\) | |||||||
\(258\) | −9.55158 | −0.594655 | ||||||||
\(259\) | −13.5571 | −0.842395 | ||||||||
\(260\) | −2.30197 | −0.142762 | ||||||||
\(261\) | −0.645096 | −0.0399304 | ||||||||
\(262\) | −1.89704 | −0.117200 | ||||||||
\(263\) | −0.363767 | −0.0224309 | −0.0112154 | − | 0.999937i | \(-0.503570\pi\) | ||||
−0.0112154 | + | 0.999937i | \(0.503570\pi\) | |||||||
\(264\) | −1.45470 | −0.0895305 | ||||||||
\(265\) | 28.3382 | 1.74080 | ||||||||
\(266\) | −1.72317 | −0.105654 | ||||||||
\(267\) | −2.12365 | −0.129966 | ||||||||
\(268\) | −8.73905 | −0.533822 | ||||||||
\(269\) | 24.2421 | 1.47807 | 0.739033 | − | 0.673669i | \(-0.235283\pi\) | ||||
0.739033 | + | 0.673669i | \(0.235283\pi\) | |||||||
\(270\) | −2.30197 | −0.140094 | ||||||||
\(271\) | −22.4435 | −1.36335 | −0.681673 | − | 0.731657i | \(-0.738747\pi\) | ||||
−0.681673 | + | 0.731657i | \(0.738747\pi\) | |||||||
\(272\) | −5.05980 | −0.306796 | ||||||||
\(273\) | −1.48369 | −0.0897967 | ||||||||
\(274\) | 8.45406 | 0.510728 | ||||||||
\(275\) | 0.435064 | 0.0262353 | ||||||||
\(276\) | −1.42055 | −0.0855072 | ||||||||
\(277\) | 0.0354150 | 0.00212788 | 0.00106394 | − | 0.999999i | \(-0.499661\pi\) | ||||
0.00106394 | + | 0.999999i | \(0.499661\pi\) | |||||||
\(278\) | −6.96044 | −0.417459 | ||||||||
\(279\) | 5.49508 | 0.328982 | ||||||||
\(280\) | −3.41540 | −0.204109 | ||||||||
\(281\) | 13.4969 | 0.805158 | 0.402579 | − | 0.915385i | \(-0.368114\pi\) | ||||
0.402579 | + | 0.915385i | \(0.368114\pi\) | |||||||
\(282\) | 0.649167 | 0.0386574 | ||||||||
\(283\) | 10.8497 | 0.644950 | 0.322475 | − | 0.946578i | \(-0.395485\pi\) | ||||
0.322475 | + | 0.946578i | \(0.395485\pi\) | |||||||
\(284\) | 5.64506 | 0.334973 | ||||||||
\(285\) | −2.67353 | −0.158366 | ||||||||
\(286\) | −1.45470 | −0.0860181 | ||||||||
\(287\) | 4.65605 | 0.274838 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 8.60159 | 0.505976 | ||||||||
\(290\) | −1.48499 | −0.0872018 | ||||||||
\(291\) | −12.4889 | −0.732110 | ||||||||
\(292\) | 13.3593 | 0.781795 | ||||||||
\(293\) | −8.99683 | −0.525601 | −0.262800 | − | 0.964850i | \(-0.584646\pi\) | ||||
−0.262800 | + | 0.964850i | \(0.584646\pi\) | |||||||
\(294\) | 4.79868 | 0.279865 | ||||||||
\(295\) | −9.48261 | −0.552099 | ||||||||
\(296\) | 9.13743 | 0.531102 | ||||||||
\(297\) | −1.45470 | −0.0844102 | ||||||||
\(298\) | −6.81810 | −0.394962 | ||||||||
\(299\) | −1.42055 | −0.0821527 | ||||||||
\(300\) | −0.299075 | −0.0172671 | ||||||||
\(301\) | −14.1715 | −0.816834 | ||||||||
\(302\) | 18.2202 | 1.04846 | ||||||||
\(303\) | −18.7245 | −1.07570 | ||||||||
\(304\) | 1.16141 | 0.0666114 | ||||||||
\(305\) | 14.7609 | 0.845205 | ||||||||
\(306\) | −5.05980 | −0.289250 | ||||||||
\(307\) | −12.7618 | −0.728356 | −0.364178 | − | 0.931329i | \(-0.618650\pi\) | ||||
−0.364178 | + | 0.931329i | \(0.618650\pi\) | |||||||
\(308\) | −2.15832 | −0.122981 | ||||||||
\(309\) | 2.93346 | 0.166879 | ||||||||
\(310\) | 12.6495 | 0.718444 | ||||||||
\(311\) | 26.1546 | 1.48309 | 0.741547 | − | 0.670901i | \(-0.234092\pi\) | ||||
0.741547 | + | 0.670901i | \(0.234092\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 21.7717 | 1.23061 | 0.615304 | − | 0.788290i | \(-0.289033\pi\) | ||||
0.615304 | + | 0.788290i | \(0.289033\pi\) | |||||||
\(314\) | 0.757630 | 0.0427555 | ||||||||
\(315\) | −3.41540 | −0.192436 | ||||||||
\(316\) | −1.00000 | −0.0562544 | ||||||||
\(317\) | 12.7294 | 0.714953 | 0.357477 | − | 0.933922i | \(-0.383637\pi\) | ||||
0.357477 | + | 0.933922i | \(0.383637\pi\) | |||||||
\(318\) | −12.3104 | −0.690333 | ||||||||
\(319\) | −0.938420 | −0.0525414 | ||||||||
\(320\) | 2.30197 | 0.128684 | ||||||||
\(321\) | 4.87580 | 0.272141 | ||||||||
\(322\) | −2.10765 | −0.117455 | ||||||||
\(323\) | −5.87651 | −0.326977 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.299075 | −0.0165897 | ||||||||
\(326\) | −24.6698 | −1.36633 | ||||||||
\(327\) | 4.36952 | 0.241635 | ||||||||
\(328\) | −3.13816 | −0.173276 | ||||||||
\(329\) | 0.963160 | 0.0531007 | ||||||||
\(330\) | −3.34868 | −0.184339 | ||||||||
\(331\) | 5.60613 | 0.308141 | 0.154070 | − | 0.988060i | \(-0.450762\pi\) | ||||
0.154070 | + | 0.988060i | \(0.450762\pi\) | |||||||
\(332\) | 9.50219 | 0.521500 | ||||||||
\(333\) | 9.13743 | 0.500728 | ||||||||
\(334\) | 20.8856 | 1.14281 | ||||||||
\(335\) | −20.1170 | −1.09911 | ||||||||
\(336\) | 1.48369 | 0.0809417 | ||||||||
\(337\) | −16.3236 | −0.889203 | −0.444602 | − | 0.895728i | \(-0.646655\pi\) | ||||
−0.444602 | + | 0.895728i | \(0.646655\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −10.1291 | −0.550138 | ||||||||
\(340\) | −11.6475 | −0.631675 | ||||||||
\(341\) | 7.99368 | 0.432882 | ||||||||
\(342\) | 1.16141 | 0.0628019 | ||||||||
\(343\) | 17.5055 | 0.945210 | ||||||||
\(344\) | 9.55158 | 0.514987 | ||||||||
\(345\) | −3.27007 | −0.176055 | ||||||||
\(346\) | −5.10263 | −0.274319 | ||||||||
\(347\) | 7.64170 | 0.410228 | 0.205114 | − | 0.978738i | \(-0.434244\pi\) | ||||
0.205114 | + | 0.978738i | \(0.434244\pi\) | |||||||
\(348\) | 0.645096 | 0.0345808 | ||||||||
\(349\) | 16.5198 | 0.884286 | 0.442143 | − | 0.896945i | \(-0.354218\pi\) | ||||
0.442143 | + | 0.896945i | \(0.354218\pi\) | |||||||
\(350\) | −0.443733 | −0.0237185 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 1.45470 | 0.0775357 | ||||||||
\(353\) | −24.3507 | −1.29606 | −0.648029 | − | 0.761616i | \(-0.724407\pi\) | ||||
−0.648029 | + | 0.761616i | \(0.724407\pi\) | |||||||
\(354\) | 4.11934 | 0.218940 | ||||||||
\(355\) | 12.9948 | 0.689691 | ||||||||
\(356\) | 2.12365 | 0.112553 | ||||||||
\(357\) | −7.50715 | −0.397321 | ||||||||
\(358\) | −7.54212 | −0.398613 | ||||||||
\(359\) | −31.0362 | −1.63803 | −0.819014 | − | 0.573774i | \(-0.805479\pi\) | ||||
−0.819014 | + | 0.573774i | \(0.805479\pi\) | |||||||
\(360\) | 2.30197 | 0.121325 | ||||||||
\(361\) | −17.6511 | −0.929007 | ||||||||
\(362\) | 6.99392 | 0.367592 | ||||||||
\(363\) | 8.88385 | 0.466281 | ||||||||
\(364\) | 1.48369 | 0.0777663 | ||||||||
\(365\) | 30.7528 | 1.60967 | ||||||||
\(366\) | −6.41227 | −0.335175 | ||||||||
\(367\) | 18.2454 | 0.952400 | 0.476200 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476200 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(368\) | 1.42055 | 0.0740514 | ||||||||
\(369\) | −3.13816 | −0.163366 | ||||||||
\(370\) | 21.0341 | 1.09351 | ||||||||
\(371\) | −18.2648 | −0.948260 | ||||||||
\(372\) | −5.49508 | −0.284907 | ||||||||
\(373\) | 15.2593 | 0.790098 | 0.395049 | − | 0.918660i | \(-0.370728\pi\) | ||||
0.395049 | + | 0.918660i | \(0.370728\pi\) | |||||||
\(374\) | −7.36049 | −0.380602 | ||||||||
\(375\) | 10.8214 | 0.558815 | ||||||||
\(376\) | −0.649167 | −0.0334783 | ||||||||
\(377\) | 0.645096 | 0.0332241 | ||||||||
\(378\) | 1.48369 | 0.0763126 | ||||||||
\(379\) | −36.2255 | −1.86078 | −0.930389 | − | 0.366574i | \(-0.880531\pi\) | ||||
−0.930389 | + | 0.366574i | \(0.880531\pi\) | |||||||
\(380\) | 2.67353 | 0.137149 | ||||||||
\(381\) | 11.2206 | 0.574849 | ||||||||
\(382\) | 4.09683 | 0.209612 | ||||||||
\(383\) | 19.1781 | 0.979957 | 0.489978 | − | 0.871735i | \(-0.337005\pi\) | ||||
0.489978 | + | 0.871735i | \(0.337005\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −4.96838 | −0.253212 | ||||||||
\(386\) | −13.1156 | −0.667564 | ||||||||
\(387\) | 9.55158 | 0.485534 | ||||||||
\(388\) | 12.4889 | 0.634026 | ||||||||
\(389\) | −26.8310 | −1.36039 | −0.680193 | − | 0.733033i | \(-0.738104\pi\) | ||||
−0.680193 | + | 0.733033i | \(0.738104\pi\) | |||||||
\(390\) | 2.30197 | 0.116565 | ||||||||
\(391\) | −7.18771 | −0.363498 | ||||||||
\(392\) | −4.79868 | −0.242370 | ||||||||
\(393\) | 1.89704 | 0.0956930 | ||||||||
\(394\) | −9.84786 | −0.496128 | ||||||||
\(395\) | −2.30197 | −0.115825 | ||||||||
\(396\) | 1.45470 | 0.0731014 | ||||||||
\(397\) | 30.5548 | 1.53350 | 0.766752 | − | 0.641944i | \(-0.221872\pi\) | ||||
0.766752 | + | 0.641944i | \(0.221872\pi\) | |||||||
\(398\) | 27.3916 | 1.37302 | ||||||||
\(399\) | 1.72317 | 0.0862663 | ||||||||
\(400\) | 0.299075 | 0.0149537 | ||||||||
\(401\) | 2.46636 | 0.123164 | 0.0615821 | − | 0.998102i | \(-0.480385\pi\) | ||||
0.0615821 | + | 0.998102i | \(0.480385\pi\) | |||||||
\(402\) | 8.73905 | 0.435864 | ||||||||
\(403\) | −5.49508 | −0.273729 | ||||||||
\(404\) | 18.7245 | 0.931580 | ||||||||
\(405\) | 2.30197 | 0.114386 | ||||||||
\(406\) | 0.957120 | 0.0475010 | ||||||||
\(407\) | 13.2922 | 0.658870 | ||||||||
\(408\) | 5.05980 | 0.250497 | ||||||||
\(409\) | −0.815979 | −0.0403476 | −0.0201738 | − | 0.999796i | \(-0.506422\pi\) | ||||
−0.0201738 | + | 0.999796i | \(0.506422\pi\) | |||||||
\(410\) | −7.22396 | −0.356766 | ||||||||
\(411\) | −8.45406 | −0.417008 | ||||||||
\(412\) | −2.93346 | −0.144521 | ||||||||
\(413\) | 6.11181 | 0.300742 | ||||||||
\(414\) | 1.42055 | 0.0698164 | ||||||||
\(415\) | 21.8738 | 1.07374 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 6.96044 | 0.340854 | ||||||||
\(418\) | 1.68950 | 0.0826362 | ||||||||
\(419\) | 34.3996 | 1.68053 | 0.840264 | − | 0.542177i | \(-0.182400\pi\) | ||||
0.840264 | + | 0.542177i | \(0.182400\pi\) | |||||||
\(420\) | 3.41540 | 0.166655 | ||||||||
\(421\) | 14.9486 | 0.728550 | 0.364275 | − | 0.931291i | \(-0.381317\pi\) | ||||
0.364275 | + | 0.931291i | \(0.381317\pi\) | |||||||
\(422\) | −11.7715 | −0.573029 | ||||||||
\(423\) | −0.649167 | −0.0315636 | ||||||||
\(424\) | 12.3104 | 0.597846 | ||||||||
\(425\) | −1.51326 | −0.0734039 | ||||||||
\(426\) | −5.64506 | −0.273504 | ||||||||
\(427\) | −9.51379 | −0.460405 | ||||||||
\(428\) | −4.87580 | −0.235681 | ||||||||
\(429\) | 1.45470 | 0.0702335 | ||||||||
\(430\) | 21.9875 | 1.06033 | ||||||||
\(431\) | 13.0932 | 0.630678 | 0.315339 | − | 0.948979i | \(-0.397882\pi\) | ||||
0.315339 | + | 0.948979i | \(0.397882\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 32.1195 | 1.54356 | 0.771782 | − | 0.635888i | \(-0.219366\pi\) | ||||
0.771782 | + | 0.635888i | \(0.219366\pi\) | |||||||
\(434\) | −8.15297 | −0.391355 | ||||||||
\(435\) | 1.48499 | 0.0711999 | ||||||||
\(436\) | −4.36952 | −0.209262 | ||||||||
\(437\) | 1.64984 | 0.0789228 | ||||||||
\(438\) | −13.3593 | −0.638333 | ||||||||
\(439\) | −19.2393 | −0.918240 | −0.459120 | − | 0.888374i | \(-0.651835\pi\) | ||||
−0.459120 | + | 0.888374i | \(0.651835\pi\) | |||||||
\(440\) | 3.34868 | 0.159642 | ||||||||
\(441\) | −4.79868 | −0.228508 | ||||||||
\(442\) | 5.05980 | 0.240670 | ||||||||
\(443\) | −12.7622 | −0.606349 | −0.303174 | − | 0.952935i | \(-0.598046\pi\) | ||||
−0.303174 | + | 0.952935i | \(0.598046\pi\) | |||||||
\(444\) | −9.13743 | −0.433643 | ||||||||
\(445\) | 4.88859 | 0.231742 | ||||||||
\(446\) | 12.6013 | 0.596688 | ||||||||
\(447\) | 6.81810 | 0.322485 | ||||||||
\(448\) | −1.48369 | −0.0700976 | ||||||||
\(449\) | −2.42272 | −0.114335 | −0.0571676 | − | 0.998365i | \(-0.518207\pi\) | ||||
−0.0571676 | + | 0.998365i | \(0.518207\pi\) | |||||||
\(450\) | 0.299075 | 0.0140985 | ||||||||
\(451\) | −4.56508 | −0.214961 | ||||||||
\(452\) | 10.1291 | 0.476434 | ||||||||
\(453\) | −18.2202 | −0.856061 | ||||||||
\(454\) | −27.0019 | −1.26726 | ||||||||
\(455\) | 3.41540 | 0.160117 | ||||||||
\(456\) | −1.16141 | −0.0543880 | ||||||||
\(457\) | −20.8164 | −0.973751 | −0.486875 | − | 0.873471i | \(-0.661863\pi\) | ||||
−0.486875 | + | 0.873471i | \(0.661863\pi\) | |||||||
\(458\) | 19.2273 | 0.898431 | ||||||||
\(459\) | 5.05980 | 0.236171 | ||||||||
\(460\) | 3.27007 | 0.152468 | ||||||||
\(461\) | 1.56625 | 0.0729475 | 0.0364738 | − | 0.999335i | \(-0.488387\pi\) | ||||
0.0364738 | + | 0.999335i | \(0.488387\pi\) | |||||||
\(462\) | 2.15832 | 0.100414 | ||||||||
\(463\) | 27.5241 | 1.27915 | 0.639577 | − | 0.768727i | \(-0.279109\pi\) | ||||
0.639577 | + | 0.768727i | \(0.279109\pi\) | |||||||
\(464\) | −0.645096 | −0.0299478 | ||||||||
\(465\) | −12.6495 | −0.586607 | ||||||||
\(466\) | 21.2824 | 0.985889 | ||||||||
\(467\) | −16.8995 | −0.782017 | −0.391008 | − | 0.920387i | \(-0.627874\pi\) | ||||
−0.391008 | + | 0.920387i | \(0.627874\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 12.9660 | 0.598714 | ||||||||
\(470\) | −1.49437 | −0.0689299 | ||||||||
\(471\) | −0.757630 | −0.0349097 | ||||||||
\(472\) | −4.11934 | −0.189608 | ||||||||
\(473\) | 13.8947 | 0.638877 | ||||||||
\(474\) | 1.00000 | 0.0459315 | ||||||||
\(475\) | 0.347349 | 0.0159374 | ||||||||
\(476\) | 7.50715 | 0.344090 | ||||||||
\(477\) | 12.3104 | 0.563655 | ||||||||
\(478\) | −21.0272 | −0.961760 | ||||||||
\(479\) | −27.9916 | −1.27897 | −0.639483 | − | 0.768805i | \(-0.720852\pi\) | ||||
−0.639483 | + | 0.768805i | \(0.720852\pi\) | |||||||
\(480\) | −2.30197 | −0.105070 | ||||||||
\(481\) | −9.13743 | −0.416631 | ||||||||
\(482\) | 2.57137 | 0.117123 | ||||||||
\(483\) | 2.10765 | 0.0959016 | ||||||||
\(484\) | −8.88385 | −0.403811 | ||||||||
\(485\) | 28.7490 | 1.30542 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −35.0710 | −1.58922 | −0.794610 | − | 0.607121i | \(-0.792324\pi\) | ||||
−0.794610 | + | 0.607121i | \(0.792324\pi\) | |||||||
\(488\) | 6.41227 | 0.290270 | ||||||||
\(489\) | 24.6698 | 1.11561 | ||||||||
\(490\) | −11.0464 | −0.499026 | ||||||||
\(491\) | 12.2653 | 0.553527 | 0.276764 | − | 0.960938i | \(-0.410738\pi\) | ||||
0.276764 | + | 0.960938i | \(0.410738\pi\) | |||||||
\(492\) | 3.13816 | 0.141479 | ||||||||
\(493\) | 3.26406 | 0.147006 | ||||||||
\(494\) | −1.16141 | −0.0522543 | ||||||||
\(495\) | 3.34868 | 0.150512 | ||||||||
\(496\) | 5.49508 | 0.246736 | ||||||||
\(497\) | −8.37549 | −0.375692 | ||||||||
\(498\) | −9.50219 | −0.425803 | ||||||||
\(499\) | 11.7808 | 0.527379 | 0.263689 | − | 0.964608i | \(-0.415061\pi\) | ||||
0.263689 | + | 0.964608i | \(0.415061\pi\) | |||||||
\(500\) | −10.8214 | −0.483948 | ||||||||
\(501\) | −20.8856 | −0.933102 | ||||||||
\(502\) | −11.4065 | −0.509095 | ||||||||
\(503\) | −42.4425 | −1.89242 | −0.946208 | − | 0.323559i | \(-0.895121\pi\) | ||||
−0.946208 | + | 0.323559i | \(0.895121\pi\) | |||||||
\(504\) | −1.48369 | −0.0660886 | ||||||||
\(505\) | 43.1033 | 1.91807 | ||||||||
\(506\) | 2.06648 | 0.0918661 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −11.2206 | −0.497834 | ||||||||
\(509\) | −23.2304 | −1.02967 | −0.514835 | − | 0.857290i | \(-0.672147\pi\) | ||||
−0.514835 | + | 0.857290i | \(0.672147\pi\) | |||||||
\(510\) | 11.6475 | 0.515761 | ||||||||
\(511\) | −19.8210 | −0.876831 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.16141 | −0.0512775 | ||||||||
\(514\) | 7.25709 | 0.320096 | ||||||||
\(515\) | −6.75275 | −0.297562 | ||||||||
\(516\) | −9.55158 | −0.420485 | ||||||||
\(517\) | −0.944343 | −0.0415322 | ||||||||
\(518\) | −13.5571 | −0.595663 | ||||||||
\(519\) | 5.10263 | 0.223981 | ||||||||
\(520\) | −2.30197 | −0.100948 | ||||||||
\(521\) | −17.5034 | −0.766839 | −0.383419 | − | 0.923574i | \(-0.625254\pi\) | ||||
−0.383419 | + | 0.923574i | \(0.625254\pi\) | |||||||
\(522\) | −0.645096 | −0.0282351 | ||||||||
\(523\) | 24.7944 | 1.08418 | 0.542091 | − | 0.840320i | \(-0.317633\pi\) | ||||
0.542091 | + | 0.840320i | \(0.317633\pi\) | |||||||
\(524\) | −1.89704 | −0.0828726 | ||||||||
\(525\) | 0.443733 | 0.0193661 | ||||||||
\(526\) | −0.363767 | −0.0158610 | ||||||||
\(527\) | −27.8040 | −1.21116 | ||||||||
\(528\) | −1.45470 | −0.0633076 | ||||||||
\(529\) | −20.9820 | −0.912262 | ||||||||
\(530\) | 28.3382 | 1.23093 | ||||||||
\(531\) | −4.11934 | −0.178764 | ||||||||
\(532\) | −1.72317 | −0.0747088 | ||||||||
\(533\) | 3.13816 | 0.135929 | ||||||||
\(534\) | −2.12365 | −0.0918995 | ||||||||
\(535\) | −11.2240 | −0.485254 | ||||||||
\(536\) | −8.73905 | −0.377469 | ||||||||
\(537\) | 7.54212 | 0.325467 | ||||||||
\(538\) | 24.2421 | 1.04515 | ||||||||
\(539\) | −6.98063 | −0.300677 | ||||||||
\(540\) | −2.30197 | −0.0990611 | ||||||||
\(541\) | 35.3754 | 1.52091 | 0.760454 | − | 0.649392i | \(-0.224977\pi\) | ||||
0.760454 | + | 0.649392i | \(0.224977\pi\) | |||||||
\(542\) | −22.4435 | −0.964031 | ||||||||
\(543\) | −6.99392 | −0.300138 | ||||||||
\(544\) | −5.05980 | −0.216937 | ||||||||
\(545\) | −10.0585 | −0.430860 | ||||||||
\(546\) | −1.48369 | −0.0634959 | ||||||||
\(547\) | −0.647125 | −0.0276691 | −0.0138345 | − | 0.999904i | \(-0.504404\pi\) | ||||
−0.0138345 | + | 0.999904i | \(0.504404\pi\) | |||||||
\(548\) | 8.45406 | 0.361139 | ||||||||
\(549\) | 6.41227 | 0.273669 | ||||||||
\(550\) | 0.435064 | 0.0185512 | ||||||||
\(551\) | −0.749221 | −0.0319179 | ||||||||
\(552\) | −1.42055 | −0.0604627 | ||||||||
\(553\) | 1.48369 | 0.0630927 | ||||||||
\(554\) | 0.0354150 | 0.00150464 | ||||||||
\(555\) | −21.0341 | −0.892848 | ||||||||
\(556\) | −6.96044 | −0.295188 | ||||||||
\(557\) | −18.6489 | −0.790181 | −0.395090 | − | 0.918642i | \(-0.629287\pi\) | ||||
−0.395090 | + | 0.918642i | \(0.629287\pi\) | |||||||
\(558\) | 5.49508 | 0.232625 | ||||||||
\(559\) | −9.55158 | −0.403989 | ||||||||
\(560\) | −3.41540 | −0.144327 | ||||||||
\(561\) | 7.36049 | 0.310760 | ||||||||
\(562\) | 13.4969 | 0.569333 | ||||||||
\(563\) | −31.0815 | −1.30993 | −0.654964 | − | 0.755660i | \(-0.727316\pi\) | ||||
−0.654964 | + | 0.755660i | \(0.727316\pi\) | |||||||
\(564\) | 0.649167 | 0.0273349 | ||||||||
\(565\) | 23.3169 | 0.980951 | ||||||||
\(566\) | 10.8497 | 0.456049 | ||||||||
\(567\) | −1.48369 | −0.0623089 | ||||||||
\(568\) | 5.64506 | 0.236861 | ||||||||
\(569\) | 31.1041 | 1.30395 | 0.651977 | − | 0.758239i | \(-0.273940\pi\) | ||||
0.651977 | + | 0.758239i | \(0.273940\pi\) | |||||||
\(570\) | −2.67353 | −0.111982 | ||||||||
\(571\) | −20.2921 | −0.849197 | −0.424598 | − | 0.905382i | \(-0.639585\pi\) | ||||
−0.424598 | + | 0.905382i | \(0.639585\pi\) | |||||||
\(572\) | −1.45470 | −0.0608240 | ||||||||
\(573\) | −4.09683 | −0.171147 | ||||||||
\(574\) | 4.65605 | 0.194340 | ||||||||
\(575\) | 0.424852 | 0.0177175 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −11.0741 | −0.461019 | −0.230510 | − | 0.973070i | \(-0.574039\pi\) | ||||
−0.230510 | + | 0.973070i | \(0.574039\pi\) | |||||||
\(578\) | 8.60159 | 0.357779 | ||||||||
\(579\) | 13.1156 | 0.545064 | ||||||||
\(580\) | −1.48499 | −0.0616610 | ||||||||
\(581\) | −14.0983 | −0.584894 | ||||||||
\(582\) | −12.4889 | −0.517680 | ||||||||
\(583\) | 17.9079 | 0.741671 | ||||||||
\(584\) | 13.3593 | 0.552813 | ||||||||
\(585\) | −2.30197 | −0.0951748 | ||||||||
\(586\) | −8.99683 | −0.371656 | ||||||||
\(587\) | 20.3364 | 0.839373 | 0.419686 | − | 0.907669i | \(-0.362140\pi\) | ||||
0.419686 | + | 0.907669i | \(0.362140\pi\) | |||||||
\(588\) | 4.79868 | 0.197894 | ||||||||
\(589\) | 6.38204 | 0.262967 | ||||||||
\(590\) | −9.48261 | −0.390393 | ||||||||
\(591\) | 9.84786 | 0.405087 | ||||||||
\(592\) | 9.13743 | 0.375546 | ||||||||
\(593\) | 6.87519 | 0.282330 | 0.141165 | − | 0.989986i | \(-0.454915\pi\) | ||||
0.141165 | + | 0.989986i | \(0.454915\pi\) | |||||||
\(594\) | −1.45470 | −0.0596870 | ||||||||
\(595\) | 17.2813 | 0.708463 | ||||||||
\(596\) | −6.81810 | −0.279280 | ||||||||
\(597\) | −27.3916 | −1.12106 | ||||||||
\(598\) | −1.42055 | −0.0580907 | ||||||||
\(599\) | −3.40322 | −0.139052 | −0.0695258 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695258 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(600\) | −0.299075 | −0.0122097 | ||||||||
\(601\) | −3.76888 | −0.153736 | −0.0768679 | − | 0.997041i | \(-0.524492\pi\) | ||||
−0.0768679 | + | 0.997041i | \(0.524492\pi\) | |||||||
\(602\) | −14.1715 | −0.577589 | ||||||||
\(603\) | −8.73905 | −0.355882 | ||||||||
\(604\) | 18.2202 | 0.741371 | ||||||||
\(605\) | −20.4504 | −0.831426 | ||||||||
\(606\) | −18.7245 | −0.760632 | ||||||||
\(607\) | −45.5526 | −1.84892 | −0.924461 | − | 0.381276i | \(-0.875485\pi\) | ||||
−0.924461 | + | 0.381276i | \(0.875485\pi\) | |||||||
\(608\) | 1.16141 | 0.0471014 | ||||||||
\(609\) | −0.957120 | −0.0387844 | ||||||||
\(610\) | 14.7609 | 0.597650 | ||||||||
\(611\) | 0.649167 | 0.0262625 | ||||||||
\(612\) | −5.05980 | −0.204530 | ||||||||
\(613\) | 28.4843 | 1.15047 | 0.575236 | − | 0.817988i | \(-0.304910\pi\) | ||||
0.575236 | + | 0.817988i | \(0.304910\pi\) | |||||||
\(614\) | −12.7618 | −0.515025 | ||||||||
\(615\) | 7.22396 | 0.291298 | ||||||||
\(616\) | −2.15832 | −0.0869610 | ||||||||
\(617\) | 22.7000 | 0.913868 | 0.456934 | − | 0.889501i | \(-0.348948\pi\) | ||||
0.456934 | + | 0.889501i | \(0.348948\pi\) | |||||||
\(618\) | 2.93346 | 0.118001 | ||||||||
\(619\) | −1.37535 | −0.0552800 | −0.0276400 | − | 0.999618i | \(-0.508799\pi\) | ||||
−0.0276400 | + | 0.999618i | \(0.508799\pi\) | |||||||
\(620\) | 12.6495 | 0.508017 | ||||||||
\(621\) | −1.42055 | −0.0570048 | ||||||||
\(622\) | 26.1546 | 1.04871 | ||||||||
\(623\) | −3.15084 | −0.126236 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −26.4059 | −1.05624 | ||||||||
\(626\) | 21.7717 | 0.870171 | ||||||||
\(627\) | −1.68950 | −0.0674722 | ||||||||
\(628\) | 0.757630 | 0.0302327 | ||||||||
\(629\) | −46.2336 | −1.84345 | ||||||||
\(630\) | −3.41540 | −0.136073 | ||||||||
\(631\) | 30.1305 | 1.19948 | 0.599738 | − | 0.800196i | \(-0.295271\pi\) | ||||
0.599738 | + | 0.800196i | \(0.295271\pi\) | |||||||
\(632\) | −1.00000 | −0.0397779 | ||||||||
\(633\) | 11.7715 | 0.467876 | ||||||||
\(634\) | 12.7294 | 0.505548 | ||||||||
\(635\) | −25.8295 | −1.02501 | ||||||||
\(636\) | −12.3104 | −0.488139 | ||||||||
\(637\) | 4.79868 | 0.190131 | ||||||||
\(638\) | −0.938420 | −0.0371524 | ||||||||
\(639\) | 5.64506 | 0.223315 | ||||||||
\(640\) | 2.30197 | 0.0909934 | ||||||||
\(641\) | −45.0137 | −1.77794 | −0.888968 | − | 0.457970i | \(-0.848577\pi\) | ||||
−0.888968 | + | 0.457970i | \(0.848577\pi\) | |||||||
\(642\) | 4.87580 | 0.192433 | ||||||||
\(643\) | −44.7871 | −1.76623 | −0.883115 | − | 0.469157i | \(-0.844558\pi\) | ||||
−0.883115 | + | 0.469157i | \(0.844558\pi\) | |||||||
\(644\) | −2.10765 | −0.0830532 | ||||||||
\(645\) | −21.9875 | −0.865756 | ||||||||
\(646\) | −5.87651 | −0.231208 | ||||||||
\(647\) | −19.4056 | −0.762913 | −0.381456 | − | 0.924387i | \(-0.624577\pi\) | ||||
−0.381456 | + | 0.924387i | \(0.624577\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.99240 | −0.235222 | ||||||||
\(650\) | −0.299075 | −0.0117307 | ||||||||
\(651\) | 8.15297 | 0.319540 | ||||||||
\(652\) | −24.6698 | −0.966144 | ||||||||
\(653\) | −3.92665 | −0.153662 | −0.0768309 | − | 0.997044i | \(-0.524480\pi\) | ||||
−0.0768309 | + | 0.997044i | \(0.524480\pi\) | |||||||
\(654\) | 4.36952 | 0.170862 | ||||||||
\(655\) | −4.36693 | −0.170630 | ||||||||
\(656\) | −3.13816 | −0.122525 | ||||||||
\(657\) | 13.3593 | 0.521197 | ||||||||
\(658\) | 0.963160 | 0.0375479 | ||||||||
\(659\) | −22.2076 | −0.865085 | −0.432543 | − | 0.901613i | \(-0.642384\pi\) | ||||
−0.432543 | + | 0.901613i | \(0.642384\pi\) | |||||||
\(660\) | −3.34868 | −0.130347 | ||||||||
\(661\) | −10.0502 | −0.390906 | −0.195453 | − | 0.980713i | \(-0.562618\pi\) | ||||
−0.195453 | + | 0.980713i | \(0.562618\pi\) | |||||||
\(662\) | 5.60613 | 0.217888 | ||||||||
\(663\) | −5.05980 | −0.196506 | ||||||||
\(664\) | 9.50219 | 0.368756 | ||||||||
\(665\) | −3.96668 | −0.153821 | ||||||||
\(666\) | 9.13743 | 0.354068 | ||||||||
\(667\) | −0.916393 | −0.0354829 | ||||||||
\(668\) | 20.8856 | 0.808090 | ||||||||
\(669\) | −12.6013 | −0.487194 | ||||||||
\(670\) | −20.1170 | −0.777189 | ||||||||
\(671\) | 9.32792 | 0.360100 | ||||||||
\(672\) | 1.48369 | 0.0572344 | ||||||||
\(673\) | 14.7754 | 0.569550 | 0.284775 | − | 0.958594i | \(-0.408081\pi\) | ||||
0.284775 | + | 0.958594i | \(0.408081\pi\) | |||||||
\(674\) | −16.3236 | −0.628762 | ||||||||
\(675\) | −0.299075 | −0.0115114 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 39.6311 | 1.52315 | 0.761574 | − | 0.648078i | \(-0.224427\pi\) | ||||
0.761574 | + | 0.648078i | \(0.224427\pi\) | |||||||
\(678\) | −10.1291 | −0.389006 | ||||||||
\(679\) | −18.5295 | −0.711098 | ||||||||
\(680\) | −11.6475 | −0.446662 | ||||||||
\(681\) | 27.0019 | 1.03471 | ||||||||
\(682\) | 7.99368 | 0.306094 | ||||||||
\(683\) | 22.6411 | 0.866339 | 0.433170 | − | 0.901312i | \(-0.357395\pi\) | ||||
0.433170 | + | 0.901312i | \(0.357395\pi\) | |||||||
\(684\) | 1.16141 | 0.0444076 | ||||||||
\(685\) | 19.4610 | 0.743567 | ||||||||
\(686\) | 17.5055 | 0.668364 | ||||||||
\(687\) | −19.2273 | −0.733566 | ||||||||
\(688\) | 9.55158 | 0.364150 | ||||||||
\(689\) | −12.3104 | −0.468989 | ||||||||
\(690\) | −3.27007 | −0.124490 | ||||||||
\(691\) | −40.7768 | −1.55122 | −0.775610 | − | 0.631212i | \(-0.782558\pi\) | ||||
−0.775610 | + | 0.631212i | \(0.782558\pi\) | |||||||
\(692\) | −5.10263 | −0.193973 | ||||||||
\(693\) | −2.15832 | −0.0819876 | ||||||||
\(694\) | 7.64170 | 0.290075 | ||||||||
\(695\) | −16.0227 | −0.607777 | ||||||||
\(696\) | 0.645096 | 0.0244523 | ||||||||
\(697\) | 15.8785 | 0.601440 | ||||||||
\(698\) | 16.5198 | 0.625285 | ||||||||
\(699\) | −21.2824 | −0.804975 | ||||||||
\(700\) | −0.443733 | −0.0167715 | ||||||||
\(701\) | −39.3364 | −1.48571 | −0.742857 | − | 0.669450i | \(-0.766530\pi\) | ||||
−0.742857 | + | 0.669450i | \(0.766530\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 10.6123 | 0.400251 | ||||||||
\(704\) | 1.45470 | 0.0548260 | ||||||||
\(705\) | 1.49437 | 0.0562810 | ||||||||
\(706\) | −24.3507 | −0.916452 | ||||||||
\(707\) | −27.7813 | −1.04482 | ||||||||
\(708\) | 4.11934 | 0.154814 | ||||||||
\(709\) | −14.3109 | −0.537458 | −0.268729 | − | 0.963216i | \(-0.586604\pi\) | ||||
−0.268729 | + | 0.963216i | \(0.586604\pi\) | |||||||
\(710\) | 12.9948 | 0.487685 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | 2.12365 | 0.0795873 | ||||||||
\(713\) | 7.80605 | 0.292339 | ||||||||
\(714\) | −7.50715 | −0.280948 | ||||||||
\(715\) | −3.34868 | −0.125233 | ||||||||
\(716\) | −7.54212 | −0.281862 | ||||||||
\(717\) | 21.0272 | 0.785274 | ||||||||
\(718\) | −31.0362 | −1.15826 | ||||||||
\(719\) | 32.2993 | 1.20456 | 0.602280 | − | 0.798285i | \(-0.294259\pi\) | ||||
0.602280 | + | 0.798285i | \(0.294259\pi\) | |||||||
\(720\) | 2.30197 | 0.0857894 | ||||||||
\(721\) | 4.35233 | 0.162089 | ||||||||
\(722\) | −17.6511 | −0.656907 | ||||||||
\(723\) | −2.57137 | −0.0956302 | ||||||||
\(724\) | 6.99392 | 0.259927 | ||||||||
\(725\) | −0.192932 | −0.00716531 | ||||||||
\(726\) | 8.88385 | 0.329711 | ||||||||
\(727\) | 23.5937 | 0.875041 | 0.437521 | − | 0.899208i | \(-0.355857\pi\) | ||||
0.437521 | + | 0.899208i | \(0.355857\pi\) | |||||||
\(728\) | 1.48369 | 0.0549890 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 30.7528 | 1.13821 | ||||||||
\(731\) | −48.3291 | −1.78752 | ||||||||
\(732\) | −6.41227 | −0.237004 | ||||||||
\(733\) | 3.95608 | 0.146121 | 0.0730606 | − | 0.997328i | \(-0.476723\pi\) | ||||
0.0730606 | + | 0.997328i | \(0.476723\pi\) | |||||||
\(734\) | 18.2454 | 0.673449 | ||||||||
\(735\) | 11.0464 | 0.407453 | ||||||||
\(736\) | 1.42055 | 0.0523623 | ||||||||
\(737\) | −12.7127 | −0.468278 | ||||||||
\(738\) | −3.13816 | −0.115517 | ||||||||
\(739\) | 13.0338 | 0.479456 | 0.239728 | − | 0.970840i | \(-0.422942\pi\) | ||||
0.239728 | + | 0.970840i | \(0.422942\pi\) | |||||||
\(740\) | 21.0341 | 0.773229 | ||||||||
\(741\) | 1.16141 | 0.0426655 | ||||||||
\(742\) | −18.2648 | −0.670521 | ||||||||
\(743\) | −40.1994 | −1.47477 | −0.737387 | − | 0.675470i | \(-0.763941\pi\) | ||||
−0.737387 | + | 0.675470i | \(0.763941\pi\) | |||||||
\(744\) | −5.49508 | −0.201459 | ||||||||
\(745\) | −15.6951 | −0.575023 | ||||||||
\(746\) | 15.2593 | 0.558684 | ||||||||
\(747\) | 9.50219 | 0.347667 | ||||||||
\(748\) | −7.36049 | −0.269126 | ||||||||
\(749\) | 7.23416 | 0.264330 | ||||||||
\(750\) | 10.8214 | 0.395142 | ||||||||
\(751\) | 19.3427 | 0.705825 | 0.352912 | − | 0.935656i | \(-0.385191\pi\) | ||||
0.352912 | + | 0.935656i | \(0.385191\pi\) | |||||||
\(752\) | −0.649167 | −0.0236727 | ||||||||
\(753\) | 11.4065 | 0.415675 | ||||||||
\(754\) | 0.645096 | 0.0234930 | ||||||||
\(755\) | 41.9425 | 1.52644 | ||||||||
\(756\) | 1.48369 | 0.0539611 | ||||||||
\(757\) | 42.1224 | 1.53097 | 0.765483 | − | 0.643456i | \(-0.222500\pi\) | ||||
0.765483 | + | 0.643456i | \(0.222500\pi\) | |||||||
\(758\) | −36.2255 | −1.31577 | ||||||||
\(759\) | −2.06648 | −0.0750083 | ||||||||
\(760\) | 2.67353 | 0.0969793 | ||||||||
\(761\) | −26.1817 | −0.949086 | −0.474543 | − | 0.880232i | \(-0.657387\pi\) | ||||
−0.474543 | + | 0.880232i | \(0.657387\pi\) | |||||||
\(762\) | 11.2206 | 0.406479 | ||||||||
\(763\) | 6.48300 | 0.234700 | ||||||||
\(764\) | 4.09683 | 0.148218 | ||||||||
\(765\) | −11.6475 | −0.421117 | ||||||||
\(766\) | 19.1781 | 0.692934 | ||||||||
\(767\) | 4.11934 | 0.148741 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 41.5183 | 1.49719 | 0.748593 | − | 0.663029i | \(-0.230730\pi\) | ||||
0.748593 | + | 0.663029i | \(0.230730\pi\) | |||||||
\(770\) | −4.96838 | −0.179048 | ||||||||
\(771\) | −7.25709 | −0.261358 | ||||||||
\(772\) | −13.1156 | −0.472039 | ||||||||
\(773\) | −0.652280 | −0.0234609 | −0.0117304 | − | 0.999931i | \(-0.503734\pi\) | ||||
−0.0117304 | + | 0.999931i | \(0.503734\pi\) | |||||||
\(774\) | 9.55158 | 0.343324 | ||||||||
\(775\) | 1.64344 | 0.0590341 | ||||||||
\(776\) | 12.4889 | 0.448324 | ||||||||
\(777\) | 13.5571 | 0.486357 | ||||||||
\(778\) | −26.8310 | −0.961939 | ||||||||
\(779\) | −3.64469 | −0.130585 | ||||||||
\(780\) | 2.30197 | 0.0824238 | ||||||||
\(781\) | 8.21186 | 0.293843 | ||||||||
\(782\) | −7.18771 | −0.257032 | ||||||||
\(783\) | 0.645096 | 0.0230538 | ||||||||
\(784\) | −4.79868 | −0.171381 | ||||||||
\(785\) | 1.74404 | 0.0622475 | ||||||||
\(786\) | 1.89704 | 0.0676652 | ||||||||
\(787\) | 55.4068 | 1.97504 | 0.987520 | − | 0.157492i | \(-0.0503409\pi\) | ||||
0.987520 | + | 0.157492i | \(0.0503409\pi\) | |||||||
\(788\) | −9.84786 | −0.350816 | ||||||||
\(789\) | 0.363767 | 0.0129505 | ||||||||
\(790\) | −2.30197 | −0.0819005 | ||||||||
\(791\) | −15.0284 | −0.534349 | ||||||||
\(792\) | 1.45470 | 0.0516905 | ||||||||
\(793\) | −6.41227 | −0.227706 | ||||||||
\(794\) | 30.5548 | 1.08435 | ||||||||
\(795\) | −28.3382 | −1.00505 | ||||||||
\(796\) | 27.3916 | 0.970869 | ||||||||
\(797\) | −6.42604 | −0.227622 | −0.113811 | − | 0.993502i | \(-0.536306\pi\) | ||||
−0.113811 | + | 0.993502i | \(0.536306\pi\) | |||||||
\(798\) | 1.72317 | 0.0609995 | ||||||||
\(799\) | 3.28466 | 0.116203 | ||||||||
\(800\) | 0.299075 | 0.0105739 | ||||||||
\(801\) | 2.12365 | 0.0750357 | ||||||||
\(802\) | 2.46636 | 0.0870902 | ||||||||
\(803\) | 19.4338 | 0.685803 | ||||||||
\(804\) | 8.73905 | 0.308203 | ||||||||
\(805\) | −4.85176 | −0.171002 | ||||||||
\(806\) | −5.49508 | −0.193556 | ||||||||
\(807\) | −24.2421 | −0.853362 | ||||||||
\(808\) | 18.7245 | 0.658726 | ||||||||
\(809\) | −26.0313 | −0.915213 | −0.457607 | − | 0.889155i | \(-0.651293\pi\) | ||||
−0.457607 | + | 0.889155i | \(0.651293\pi\) | |||||||
\(810\) | 2.30197 | 0.0808830 | ||||||||
\(811\) | −9.63357 | −0.338280 | −0.169140 | − | 0.985592i | \(-0.554099\pi\) | ||||
−0.169140 | + | 0.985592i | \(0.554099\pi\) | |||||||
\(812\) | 0.957120 | 0.0335883 | ||||||||
\(813\) | 22.4435 | 0.787128 | ||||||||
\(814\) | 13.2922 | 0.465891 | ||||||||
\(815\) | −56.7892 | −1.98924 | ||||||||
\(816\) | 5.05980 | 0.177128 | ||||||||
\(817\) | 11.0933 | 0.388105 | ||||||||
\(818\) | −0.815979 | −0.0285301 | ||||||||
\(819\) | 1.48369 | 0.0518442 | ||||||||
\(820\) | −7.22396 | −0.252272 | ||||||||
\(821\) | −30.8580 | −1.07695 | −0.538475 | − | 0.842641i | \(-0.681000\pi\) | ||||
−0.538475 | + | 0.842641i | \(0.681000\pi\) | |||||||
\(822\) | −8.45406 | −0.294869 | ||||||||
\(823\) | −8.38167 | −0.292167 | −0.146083 | − | 0.989272i | \(-0.546667\pi\) | ||||
−0.146083 | + | 0.989272i | \(0.546667\pi\) | |||||||
\(824\) | −2.93346 | −0.102192 | ||||||||
\(825\) | −0.435064 | −0.0151470 | ||||||||
\(826\) | 6.11181 | 0.212657 | ||||||||
\(827\) | 14.1204 | 0.491014 | 0.245507 | − | 0.969395i | \(-0.421046\pi\) | ||||
0.245507 | + | 0.969395i | \(0.421046\pi\) | |||||||
\(828\) | 1.42055 | 0.0493676 | ||||||||
\(829\) | −57.4619 | −1.99574 | −0.997868 | − | 0.0652707i | \(-0.979209\pi\) | ||||
−0.997868 | + | 0.0652707i | \(0.979209\pi\) | |||||||
\(830\) | 21.8738 | 0.759250 | ||||||||
\(831\) | −0.0354150 | −0.00122853 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 24.2804 | 0.841264 | ||||||||
\(834\) | 6.96044 | 0.241020 | ||||||||
\(835\) | 48.0782 | 1.66381 | ||||||||
\(836\) | 1.68950 | 0.0584326 | ||||||||
\(837\) | −5.49508 | −0.189938 | ||||||||
\(838\) | 34.3996 | 1.18831 | ||||||||
\(839\) | −31.1607 | −1.07579 | −0.537893 | − | 0.843013i | \(-0.680780\pi\) | ||||
−0.537893 | + | 0.843013i | \(0.680780\pi\) | |||||||
\(840\) | 3.41540 | 0.117843 | ||||||||
\(841\) | −28.5839 | −0.985650 | ||||||||
\(842\) | 14.9486 | 0.515163 | ||||||||
\(843\) | −13.4969 | −0.464858 | ||||||||
\(844\) | −11.7715 | −0.405193 | ||||||||
\(845\) | 2.30197 | 0.0791902 | ||||||||
\(846\) | −0.649167 | −0.0223188 | ||||||||
\(847\) | 13.1808 | 0.452899 | ||||||||
\(848\) | 12.3104 | 0.422741 | ||||||||
\(849\) | −10.8497 | −0.372362 | ||||||||
\(850\) | −1.51326 | −0.0519044 | ||||||||
\(851\) | 12.9802 | 0.444955 | ||||||||
\(852\) | −5.64506 | −0.193397 | ||||||||
\(853\) | 44.6981 | 1.53043 | 0.765217 | − | 0.643773i | \(-0.222632\pi\) | ||||
0.765217 | + | 0.643773i | \(0.222632\pi\) | |||||||
\(854\) | −9.51379 | −0.325555 | ||||||||
\(855\) | 2.67353 | 0.0914329 | ||||||||
\(856\) | −4.87580 | −0.166652 | ||||||||
\(857\) | 47.0832 | 1.60833 | 0.804166 | − | 0.594405i | \(-0.202613\pi\) | ||||
0.804166 | + | 0.594405i | \(0.202613\pi\) | |||||||
\(858\) | 1.45470 | 0.0496626 | ||||||||
\(859\) | 1.01030 | 0.0344710 | 0.0172355 | − | 0.999851i | \(-0.494513\pi\) | ||||
0.0172355 | + | 0.999851i | \(0.494513\pi\) | |||||||
\(860\) | 21.9875 | 0.749766 | ||||||||
\(861\) | −4.65605 | −0.158678 | ||||||||
\(862\) | 13.0932 | 0.445957 | ||||||||
\(863\) | −14.9703 | −0.509595 | −0.254797 | − | 0.966994i | \(-0.582009\pi\) | ||||
−0.254797 | + | 0.966994i | \(0.582009\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −11.7461 | −0.399380 | ||||||||
\(866\) | 32.1195 | 1.09146 | ||||||||
\(867\) | −8.60159 | −0.292125 | ||||||||
\(868\) | −8.15297 | −0.276730 | ||||||||
\(869\) | −1.45470 | −0.0493473 | ||||||||
\(870\) | 1.48499 | 0.0503460 | ||||||||
\(871\) | 8.73905 | 0.296111 | ||||||||
\(872\) | −4.36952 | −0.147971 | ||||||||
\(873\) | 12.4889 | 0.422684 | ||||||||
\(874\) | 1.64984 | 0.0558068 | ||||||||
\(875\) | 16.0556 | 0.542777 | ||||||||
\(876\) | −13.3593 | −0.451370 | ||||||||
\(877\) | 41.9923 | 1.41798 | 0.708989 | − | 0.705219i | \(-0.249152\pi\) | ||||
0.708989 | + | 0.705219i | \(0.249152\pi\) | |||||||
\(878\) | −19.2393 | −0.649294 | ||||||||
\(879\) | 8.99683 | 0.303456 | ||||||||
\(880\) | 3.34868 | 0.112884 | ||||||||
\(881\) | −25.4477 | −0.857354 | −0.428677 | − | 0.903458i | \(-0.641020\pi\) | ||||
−0.428677 | + | 0.903458i | \(0.641020\pi\) | |||||||
\(882\) | −4.79868 | −0.161580 | ||||||||
\(883\) | −23.7953 | −0.800777 | −0.400388 | − | 0.916346i | \(-0.631125\pi\) | ||||
−0.400388 | + | 0.916346i | \(0.631125\pi\) | |||||||
\(884\) | 5.05980 | 0.170180 | ||||||||
\(885\) | 9.48261 | 0.318754 | ||||||||
\(886\) | −12.7622 | −0.428753 | ||||||||
\(887\) | 45.2655 | 1.51987 | 0.759934 | − | 0.650001i | \(-0.225231\pi\) | ||||
0.759934 | + | 0.650001i | \(0.225231\pi\) | |||||||
\(888\) | −9.13743 | −0.306632 | ||||||||
\(889\) | 16.6478 | 0.558351 | ||||||||
\(890\) | 4.88859 | 0.163866 | ||||||||
\(891\) | 1.45470 | 0.0487342 | ||||||||
\(892\) | 12.6013 | 0.421922 | ||||||||
\(893\) | −0.753950 | −0.0252300 | ||||||||
\(894\) | 6.81810 | 0.228031 | ||||||||
\(895\) | −17.3618 | −0.580339 | ||||||||
\(896\) | −1.48369 | −0.0495665 | ||||||||
\(897\) | 1.42055 | 0.0474309 | ||||||||
\(898\) | −2.42272 | −0.0808472 | ||||||||
\(899\) | −3.54485 | −0.118227 | ||||||||
\(900\) | 0.299075 | 0.00996916 | ||||||||
\(901\) | −62.2882 | −2.07512 | ||||||||
\(902\) | −4.56508 | −0.152001 | ||||||||
\(903\) | 14.1715 | 0.471599 | ||||||||
\(904\) | 10.1291 | 0.336889 | ||||||||
\(905\) | 16.0998 | 0.535176 | ||||||||
\(906\) | −18.2202 | −0.605327 | ||||||||
\(907\) | 11.2355 | 0.373067 | 0.186534 | − | 0.982449i | \(-0.440275\pi\) | ||||
0.186534 | + | 0.982449i | \(0.440275\pi\) | |||||||
\(908\) | −27.0019 | −0.896088 | ||||||||
\(909\) | 18.7245 | 0.621053 | ||||||||
\(910\) | 3.41540 | 0.113219 | ||||||||
\(911\) | 23.9390 | 0.793133 | 0.396567 | − | 0.918006i | \(-0.370202\pi\) | ||||
0.396567 | + | 0.918006i | \(0.370202\pi\) | |||||||
\(912\) | −1.16141 | −0.0384581 | ||||||||
\(913\) | 13.8228 | 0.457469 | ||||||||
\(914\) | −20.8164 | −0.688546 | ||||||||
\(915\) | −14.7609 | −0.487979 | ||||||||
\(916\) | 19.2273 | 0.635287 | ||||||||
\(917\) | 2.81461 | 0.0929467 | ||||||||
\(918\) | 5.05980 | 0.166998 | ||||||||
\(919\) | −11.2065 | −0.369669 | −0.184835 | − | 0.982770i | \(-0.559175\pi\) | ||||
−0.184835 | + | 0.982770i | \(0.559175\pi\) | |||||||
\(920\) | 3.27007 | 0.107811 | ||||||||
\(921\) | 12.7618 | 0.420516 | ||||||||
\(922\) | 1.56625 | 0.0515817 | ||||||||
\(923\) | −5.64506 | −0.185809 | ||||||||
\(924\) | 2.15832 | 0.0710034 | ||||||||
\(925\) | 2.73277 | 0.0898531 | ||||||||
\(926\) | 27.5241 | 0.904499 | ||||||||
\(927\) | −2.93346 | −0.0963475 | ||||||||
\(928\) | −0.645096 | −0.0211763 | ||||||||
\(929\) | −27.9760 | −0.917862 | −0.458931 | − | 0.888472i | \(-0.651768\pi\) | ||||
−0.458931 | + | 0.888472i | \(0.651768\pi\) | |||||||
\(930\) | −12.6495 | −0.414794 | ||||||||
\(931\) | −5.57323 | −0.182655 | ||||||||
\(932\) | 21.2824 | 0.697129 | ||||||||
\(933\) | −26.1546 | −0.856265 | ||||||||
\(934\) | −16.8995 | −0.552969 | ||||||||
\(935\) | −16.9436 | −0.554116 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 58.0040 | 1.89491 | 0.947454 | − | 0.319891i | \(-0.103646\pi\) | ||||
0.947454 | + | 0.319891i | \(0.103646\pi\) | |||||||
\(938\) | 12.9660 | 0.423355 | ||||||||
\(939\) | −21.7717 | −0.710492 | ||||||||
\(940\) | −1.49437 | −0.0487408 | ||||||||
\(941\) | −37.5826 | −1.22516 | −0.612580 | − | 0.790409i | \(-0.709868\pi\) | ||||
−0.612580 | + | 0.790409i | \(0.709868\pi\) | |||||||
\(942\) | −0.757630 | −0.0246849 | ||||||||
\(943\) | −4.45793 | −0.145170 | ||||||||
\(944\) | −4.11934 | −0.134073 | ||||||||
\(945\) | 3.41540 | 0.111103 | ||||||||
\(946\) | 13.8947 | 0.451755 | ||||||||
\(947\) | −12.0068 | −0.390167 | −0.195083 | − | 0.980787i | \(-0.562498\pi\) | ||||
−0.195083 | + | 0.980787i | \(0.562498\pi\) | |||||||
\(948\) | 1.00000 | 0.0324785 | ||||||||
\(949\) | −13.3593 | −0.433662 | ||||||||
\(950\) | 0.347349 | 0.0112695 | ||||||||
\(951\) | −12.7294 | −0.412778 | ||||||||
\(952\) | 7.50715 | 0.243308 | ||||||||
\(953\) | 25.6971 | 0.832410 | 0.416205 | − | 0.909271i | \(-0.363360\pi\) | ||||
0.416205 | + | 0.909271i | \(0.363360\pi\) | |||||||
\(954\) | 12.3104 | 0.398564 | ||||||||
\(955\) | 9.43078 | 0.305173 | ||||||||
\(956\) | −21.0272 | −0.680067 | ||||||||
\(957\) | 0.938420 | 0.0303348 | ||||||||
\(958\) | −27.9916 | −0.904366 | ||||||||
\(959\) | −12.5432 | −0.405040 | ||||||||
\(960\) | −2.30197 | −0.0742958 | ||||||||
\(961\) | −0.804122 | −0.0259394 | ||||||||
\(962\) | −9.13743 | −0.294602 | ||||||||
\(963\) | −4.87580 | −0.157121 | ||||||||
\(964\) | 2.57137 | 0.0828182 | ||||||||
\(965\) | −30.1916 | −0.971903 | ||||||||
\(966\) | 2.10765 | 0.0678126 | ||||||||
\(967\) | −58.1085 | −1.86864 | −0.934322 | − | 0.356430i | \(-0.883994\pi\) | ||||
−0.934322 | + | 0.356430i | \(0.883994\pi\) | |||||||
\(968\) | −8.88385 | −0.285538 | ||||||||
\(969\) | 5.87651 | 0.188781 | ||||||||
\(970\) | 28.7490 | 0.923075 | ||||||||
\(971\) | −17.1974 | −0.551892 | −0.275946 | − | 0.961173i | \(-0.588991\pi\) | ||||
−0.275946 | + | 0.961173i | \(0.588991\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 10.3271 | 0.331072 | ||||||||
\(974\) | −35.0710 | −1.12375 | ||||||||
\(975\) | 0.299075 | 0.00957806 | ||||||||
\(976\) | 6.41227 | 0.205252 | ||||||||
\(977\) | 45.3160 | 1.44979 | 0.724894 | − | 0.688861i | \(-0.241889\pi\) | ||||
0.724894 | + | 0.688861i | \(0.241889\pi\) | |||||||
\(978\) | 24.6698 | 0.788853 | ||||||||
\(979\) | 3.08928 | 0.0987337 | ||||||||
\(980\) | −11.0464 | −0.352865 | ||||||||
\(981\) | −4.36952 | −0.139508 | ||||||||
\(982\) | 12.2653 | 0.391403 | ||||||||
\(983\) | −22.9205 | −0.731049 | −0.365524 | − | 0.930802i | \(-0.619110\pi\) | ||||
−0.365524 | + | 0.930802i | \(0.619110\pi\) | |||||||
\(984\) | 3.13816 | 0.100041 | ||||||||
\(985\) | −22.6695 | −0.722310 | ||||||||
\(986\) | 3.26406 | 0.103949 | ||||||||
\(987\) | −0.963160 | −0.0306577 | ||||||||
\(988\) | −1.16141 | −0.0369494 | ||||||||
\(989\) | 13.5685 | 0.431454 | ||||||||
\(990\) | 3.34868 | 0.106428 | ||||||||
\(991\) | −42.0829 | −1.33681 | −0.668404 | − | 0.743798i | \(-0.733022\pi\) | ||||
−0.668404 | + | 0.743798i | \(0.733022\pi\) | |||||||
\(992\) | 5.49508 | 0.174469 | ||||||||
\(993\) | −5.60613 | −0.177905 | ||||||||
\(994\) | −8.37549 | −0.265654 | ||||||||
\(995\) | 63.0547 | 1.99897 | ||||||||
\(996\) | −9.50219 | −0.301088 | ||||||||
\(997\) | −19.1999 | −0.608068 | −0.304034 | − | 0.952661i | \(-0.598334\pi\) | ||||
−0.304034 | + | 0.952661i | \(0.598334\pi\) | |||||||
\(998\) | 11.7808 | 0.372913 | ||||||||
\(999\) | −9.13743 | −0.289095 |
(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 | 6162.2.a.bj.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6162.2.a.bj.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial |