Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(160,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.160");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 14x^{10} + 67x^{8} + 141x^{6} + 129x^{4} + 39x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 160.3 | ||
Root | \(-1.64421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.160 |
Dual form | 483.2.h.b.160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11491 | −1.49547 | −0.747733 | − | 0.664000i | \(-0.768858\pi\) | ||||
−0.747733 | + | 0.664000i | \(0.768858\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 2.47283 | 1.23642 | ||||||||
\(5\) | −1.98969 | −0.889817 | −0.444909 | − | 0.895576i | \(-0.646764\pi\) | ||||
−0.444909 | + | 0.895576i | \(0.646764\pi\) | |||||||
\(6\) | − | 2.11491i | − | 0.863407i | ||||||
\(7\) | 2.62846 | + | 0.302029i | 0.993463 | + | 0.114156i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 4.20801 | 1.33069 | ||||||||
\(11\) | 2.93048i | 0.883574i | 0.897120 | + | 0.441787i | \(0.145655\pi\) | ||||
−0.897120 | + | 0.441787i | \(0.854345\pi\) | |||||||
\(12\) | 2.47283i | 0.713846i | ||||||||
\(13\) | − | 4.75698i | − | 1.31935i | −0.751551 | − | 0.659675i | \(-0.770694\pi\) | ||
0.751551 | − | 0.659675i | \(-0.229306\pi\) | |||||||
\(14\) | −5.55894 | − | 0.638764i | −1.48569 | − | 0.170717i | ||||
\(15\) | − | 1.98969i | − | 0.513736i | ||||||
\(16\) | −2.83076 | −0.707690 | ||||||||
\(17\) | 0.444839 | 0.107889 | 0.0539447 | − | 0.998544i | \(-0.482821\pi\) | ||||
0.0539447 | + | 0.998544i | \(0.482821\pi\) | |||||||
\(18\) | 2.11491 | 0.498488 | ||||||||
\(19\) | 6.30581 | 1.44665 | 0.723326 | − | 0.690507i | \(-0.242612\pi\) | ||||
0.723326 | + | 0.690507i | \(0.242612\pi\) | |||||||
\(20\) | −4.92018 | −1.10018 | ||||||||
\(21\) | −0.302029 | + | 2.62846i | −0.0659082 | + | 0.573576i | ||||
\(22\) | − | 6.19770i | − | 1.32136i | ||||||
\(23\) | 4.70265 | + | 0.940794i | 0.980570 | + | 0.196169i | ||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −1.04113 | −0.208226 | ||||||||
\(26\) | 10.0606i | 1.97304i | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 6.49973 | + | 0.746868i | 1.22833 | + | 0.141145i | ||||
\(29\) | −2.58774 | −0.480532 | −0.240266 | − | 0.970707i | \(-0.577235\pi\) | ||||
−0.240266 | + | 0.970707i | \(0.577235\pi\) | |||||||
\(30\) | 4.20801i | 0.768275i | ||||||||
\(31\) | 6.35793i | 1.14192i | 0.820979 | + | 0.570959i | \(0.193428\pi\) | ||||
−0.820979 | + | 0.570959i | \(0.806572\pi\) | |||||||
\(32\) | 7.98680 | 1.41188 | ||||||||
\(33\) | −2.93048 | −0.510132 | ||||||||
\(34\) | −0.940794 | −0.161345 | ||||||||
\(35\) | −5.22982 | − | 0.600945i | −0.884000 | − | 0.101578i | ||||
\(36\) | −2.47283 | −0.412139 | ||||||||
\(37\) | 6.69366i | 1.10043i | 0.835023 | + | 0.550215i | \(0.185454\pi\) | ||||
−0.835023 | + | 0.550215i | \(0.814546\pi\) | |||||||
\(38\) | −13.3362 | −2.16342 | ||||||||
\(39\) | 4.75698 | 0.761727 | ||||||||
\(40\) | 1.98969 | 0.314598 | ||||||||
\(41\) | − | 10.5877i | − | 1.65353i | −0.562549 | − | 0.826764i | \(-0.690179\pi\) | ||
0.562549 | − | 0.826764i | \(-0.309821\pi\) | |||||||
\(42\) | 0.638764 | − | 5.55894i | 0.0985635 | − | 0.857763i | ||||
\(43\) | 12.6627i | 1.93105i | 0.260313 | + | 0.965524i | \(0.416174\pi\) | ||||
−0.260313 | + | 0.965524i | \(0.583826\pi\) | |||||||
\(44\) | 7.24660i | 1.09247i | ||||||||
\(45\) | 1.98969 | 0.296606 | ||||||||
\(46\) | −9.94567 | − | 1.98969i | −1.46641 | − | 0.293364i | ||||
\(47\) | 5.66152i | 0.825818i | 0.910772 | + | 0.412909i | \(0.135487\pi\) | ||||
−0.910772 | + | 0.412909i | \(0.864513\pi\) | |||||||
\(48\) | − | 2.83076i | − | 0.408585i | ||||||
\(49\) | 6.81756 | + | 1.58774i | 0.973937 | + | 0.226820i | ||||
\(50\) | 2.20189 | 0.311394 | ||||||||
\(51\) | 0.444839i | 0.0622899i | ||||||||
\(52\) | − | 11.7632i | − | 1.63127i | ||||||
\(53\) | 10.6219i | 1.45903i | 0.683963 | + | 0.729517i | \(0.260255\pi\) | ||||
−0.683963 | + | 0.729517i | \(0.739745\pi\) | |||||||
\(54\) | 2.11491i | 0.287802i | ||||||||
\(55\) | − | 5.83076i | − | 0.786220i | ||||||
\(56\) | −2.62846 | − | 0.302029i | −0.351242 | − | 0.0403604i | ||||
\(57\) | 6.30581i | 0.835225i | ||||||||
\(58\) | 5.47283 | 0.718618 | ||||||||
\(59\) | 6.39905i | 0.833086i | 0.909116 | + | 0.416543i | \(0.136758\pi\) | ||||
−0.909116 | + | 0.416543i | \(0.863242\pi\) | |||||||
\(60\) | − | 4.92018i | − | 0.635192i | ||||||
\(61\) | 3.42644 | 0.438711 | 0.219355 | − | 0.975645i | \(-0.429605\pi\) | ||||
0.219355 | + | 0.975645i | \(0.429605\pi\) | |||||||
\(62\) | − | 13.4464i | − | 1.70770i | ||||||
\(63\) | −2.62846 | − | 0.302029i | −0.331154 | − | 0.0380521i | ||||
\(64\) | −11.2298 | −1.40373 | ||||||||
\(65\) | 9.46492i | 1.17398i | ||||||||
\(66\) | 6.19770 | 0.762885 | ||||||||
\(67\) | 9.73225i | 1.18898i | 0.804102 | + | 0.594492i | \(0.202647\pi\) | ||||
−0.804102 | + | 0.594492i | \(0.797353\pi\) | |||||||
\(68\) | 1.10001 | 0.133396 | ||||||||
\(69\) | −0.940794 | + | 4.70265i | −0.113258 | + | 0.566132i | ||||
\(70\) | 11.0606 | + | 1.27094i | 1.32199 | + | 0.151907i | ||||
\(71\) | 8.75698 | 1.03926 | 0.519631 | − | 0.854391i | \(-0.326069\pi\) | ||||
0.519631 | + | 0.854391i | \(0.326069\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.926221i | 0.108406i | 0.998530 | + | 0.0542030i | \(0.0172618\pi\) | ||||
−0.998530 | + | 0.0542030i | \(0.982738\pi\) | |||||||
\(74\) | − | 14.1565i | − | 1.64566i | ||||||
\(75\) | − | 1.04113i | − | 0.120219i | ||||||
\(76\) | 15.5932 | 1.78866 | ||||||||
\(77\) | −0.885092 | + | 7.70265i | −0.100866 | + | 0.877798i | ||||
\(78\) | −10.0606 | −1.13914 | ||||||||
\(79\) | − | 8.86087i | − | 0.996925i | −0.866911 | − | 0.498463i | \(-0.833898\pi\) | ||
0.866911 | − | 0.498463i | \(-0.166102\pi\) | |||||||
\(80\) | 5.63234 | 0.629715 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 22.3921i | 2.47279i | ||||||||
\(83\) | 4.81207 | 0.528194 | 0.264097 | − | 0.964496i | \(-0.414926\pi\) | ||||
0.264097 | + | 0.964496i | \(0.414926\pi\) | |||||||
\(84\) | −0.746868 | + | 6.49973i | −0.0814900 | + | 0.709179i | ||||
\(85\) | −0.885092 | −0.0960018 | ||||||||
\(86\) | − | 26.7805i | − | 2.88782i | ||||||
\(87\) | − | 2.58774i | − | 0.277435i | ||||||
\(88\) | − | 2.93048i | − | 0.312391i | ||||||
\(89\) | −0.0511154 | −0.00541822 | −0.00270911 | − | 0.999996i | \(-0.500862\pi\) | ||||
−0.00270911 | + | 0.999996i | \(0.500862\pi\) | |||||||
\(90\) | −4.20801 | −0.443564 | ||||||||
\(91\) | 1.43675 | − | 12.5035i | 0.150612 | − | 1.31072i | ||||
\(92\) | 11.6289 | + | 2.32643i | 1.21239 | + | 0.242547i | ||||
\(93\) | −6.35793 | −0.659286 | ||||||||
\(94\) | − | 11.9736i | − | 1.23498i | ||||||
\(95\) | −12.5466 | −1.28726 | ||||||||
\(96\) | 7.98680i | 0.815149i | ||||||||
\(97\) | −17.4237 | −1.76911 | −0.884554 | − | 0.466438i | \(-0.845537\pi\) | ||||
−0.884554 | + | 0.466438i | \(0.845537\pi\) | |||||||
\(98\) | −14.4185 | − | 3.35793i | −1.45649 | − | 0.339202i | ||||
\(99\) | − | 2.93048i | − | 0.294525i | ||||||
\(100\) | −2.57454 | −0.257454 | ||||||||
\(101\) | − | 12.7500i | − | 1.26867i | −0.773056 | − | 0.634337i | \(-0.781273\pi\) | ||
0.773056 | − | 0.634337i | \(-0.218727\pi\) | |||||||
\(102\) | − | 0.940794i | − | 0.0931524i | ||||||
\(103\) | 6.46503 | 0.637018 | 0.318509 | − | 0.947920i | \(-0.396818\pi\) | ||||
0.318509 | + | 0.947920i | \(0.396818\pi\) | |||||||
\(104\) | 4.75698i | 0.466460i | ||||||||
\(105\) | 0.600945 | − | 5.22982i | 0.0586462 | − | 0.510378i | ||||
\(106\) | − | 22.4644i | − | 2.18193i | ||||||
\(107\) | − | 13.0506i | − | 1.26165i | −0.775926 | − | 0.630824i | \(-0.782717\pi\) | ||
0.775926 | − | 0.630824i | \(-0.217283\pi\) | |||||||
\(108\) | − | 2.47283i | − | 0.237949i | ||||||
\(109\) | − | 9.80166i | − | 0.938829i | −0.882978 | − | 0.469414i | \(-0.844465\pi\) | ||
0.882978 | − | 0.469414i | \(-0.155535\pi\) | |||||||
\(110\) | 12.3315i | 1.17576i | ||||||||
\(111\) | −6.69366 | −0.635334 | ||||||||
\(112\) | −7.44053 | − | 0.854973i | −0.703064 | − | 0.0807873i | ||||
\(113\) | 12.2873i | 1.15589i | 0.816075 | + | 0.577946i | \(0.196146\pi\) | ||||
−0.816075 | + | 0.577946i | \(0.803854\pi\) | |||||||
\(114\) | − | 13.3362i | − | 1.24905i | ||||||
\(115\) | −9.35682 | − | 1.87189i | −0.872528 | − | 0.174555i | ||||
\(116\) | −6.39905 | −0.594137 | ||||||||
\(117\) | 4.75698i | 0.439783i | ||||||||
\(118\) | − | 13.5334i | − | 1.24585i | ||||||
\(119\) | 1.16924 | + | 0.134354i | 0.107184 | + | 0.0123163i | ||||
\(120\) | 1.98969i | 0.181633i | ||||||||
\(121\) | 2.41226 | 0.219296 | ||||||||
\(122\) | −7.24660 | −0.656077 | ||||||||
\(123\) | 10.5877 | 0.954664 | ||||||||
\(124\) | 15.7221i | 1.41189i | ||||||||
\(125\) | 12.0200 | 1.07510 | ||||||||
\(126\) | 5.55894 | + | 0.638764i | 0.495230 | + | 0.0569056i | ||||
\(127\) | −3.81131 | −0.338199 | −0.169100 | − | 0.985599i | \(-0.554086\pi\) | ||||
−0.169100 | + | 0.985599i | \(0.554086\pi\) | |||||||
\(128\) | 7.77643 | 0.687346 | ||||||||
\(129\) | −12.6627 | −1.11489 | ||||||||
\(130\) | − | 20.0174i | − | 1.75565i | ||||||
\(131\) | 7.87189i | 0.687770i | 0.939012 | + | 0.343885i | \(0.111743\pi\) | ||||
−0.939012 | + | 0.343885i | \(0.888257\pi\) | |||||||
\(132\) | −7.24660 | −0.630736 | ||||||||
\(133\) | 16.5745 | + | 1.90454i | 1.43719 | + | 0.165145i | ||||
\(134\) | − | 20.5828i | − | 1.77808i | ||||||
\(135\) | 1.98969i | 0.171245i | ||||||||
\(136\) | −0.444839 | −0.0381446 | ||||||||
\(137\) | − | 17.8115i | − | 1.52174i | −0.648903 | − | 0.760871i | \(-0.724772\pi\) | ||
0.648903 | − | 0.760871i | \(-0.275228\pi\) | |||||||
\(138\) | 1.98969 | − | 9.94567i | 0.169374 | − | 0.846631i | ||||
\(139\) | − | 1.49228i | − | 0.126574i | −0.997995 | − | 0.0632868i | \(-0.979842\pi\) | ||
0.997995 | − | 0.0632868i | \(-0.0201583\pi\) | |||||||
\(140\) | −12.9325 | − | 1.48604i | −1.09299 | − | 0.125593i | ||||
\(141\) | −5.66152 | −0.476786 | ||||||||
\(142\) | −18.5202 | −1.55418 | ||||||||
\(143\) | 13.9403 | 1.16574 | ||||||||
\(144\) | 2.83076 | 0.235897 | ||||||||
\(145\) | 5.14881 | 0.427585 | ||||||||
\(146\) | − | 1.95887i | − | 0.162117i | ||||||
\(147\) | −1.58774 | + | 6.81756i | −0.130955 | + | 0.562303i | ||||
\(148\) | 16.5523i | 1.36059i | ||||||||
\(149\) | 4.15102i | 0.340065i | 0.985438 | + | 0.170033i | \(0.0543873\pi\) | ||||
−0.985438 | + | 0.170033i | \(0.945613\pi\) | |||||||
\(150\) | 2.20189i | 0.179784i | ||||||||
\(151\) | −4.08226 | −0.332209 | −0.166105 | − | 0.986108i | \(-0.553119\pi\) | ||||
−0.166105 | + | 0.986108i | \(0.553119\pi\) | |||||||
\(152\) | −6.30581 | −0.511469 | ||||||||
\(153\) | −0.444839 | −0.0359631 | ||||||||
\(154\) | 1.87189 | − | 16.2904i | 0.150841 | − | 1.31272i | ||||
\(155\) | − | 12.6503i | − | 1.01610i | ||||||
\(156\) | 11.7632 | 0.941812 | ||||||||
\(157\) | 1.56315 | 0.124753 | 0.0623764 | − | 0.998053i | \(-0.480132\pi\) | ||||
0.0623764 | + | 0.998053i | \(0.480132\pi\) | |||||||
\(158\) | 18.7399i | 1.49087i | ||||||||
\(159\) | −10.6219 | −0.842374 | ||||||||
\(160\) | −15.8913 | −1.25631 | ||||||||
\(161\) | 12.0766 | + | 3.89317i | 0.951766 | + | 0.306825i | ||||
\(162\) | −2.11491 | −0.166163 | ||||||||
\(163\) | −2.54661 | −0.199466 | −0.0997331 | − | 0.995014i | \(-0.531799\pi\) | ||||
−0.0997331 | + | 0.995014i | \(0.531799\pi\) | |||||||
\(164\) | − | 26.1817i | − | 2.04445i | ||||||
\(165\) | 5.83076 | 0.453924 | ||||||||
\(166\) | −10.1771 | −0.789895 | ||||||||
\(167\) | − | 3.07378i | − | 0.237856i | −0.992903 | − | 0.118928i | \(-0.962054\pi\) | ||
0.992903 | − | 0.118928i | \(-0.0379458\pi\) | |||||||
\(168\) | 0.302029 | − | 2.62846i | 0.0233021 | − | 0.202790i | ||||
\(169\) | −9.62887 | −0.740682 | ||||||||
\(170\) | 1.87189 | 0.143567 | ||||||||
\(171\) | −6.30581 | −0.482217 | ||||||||
\(172\) | 31.3128i | 2.38758i | ||||||||
\(173\) | 6.24926i | 0.475123i | 0.971373 | + | 0.237561i | \(0.0763481\pi\) | ||||
−0.971373 | + | 0.237561i | \(0.923652\pi\) | |||||||
\(174\) | 5.47283i | 0.414894i | ||||||||
\(175\) | −2.73656 | − | 0.314451i | −0.206864 | − | 0.0237703i | ||||
\(176\) | − | 8.29550i | − | 0.625297i | ||||||
\(177\) | −6.39905 | −0.480982 | ||||||||
\(178\) | 0.108104 | 0.00810276 | ||||||||
\(179\) | −18.6678 | −1.39529 | −0.697647 | − | 0.716442i | \(-0.745770\pi\) | ||||
−0.697647 | + | 0.716442i | \(0.745770\pi\) | |||||||
\(180\) | 4.92018 | 0.366728 | ||||||||
\(181\) | 16.8890 | 1.25535 | 0.627676 | − | 0.778474i | \(-0.284006\pi\) | ||||
0.627676 | + | 0.778474i | \(0.284006\pi\) | |||||||
\(182\) | −3.03859 | + | 26.4438i | −0.225235 | + | 1.96014i | ||||
\(183\) | 3.42644i | 0.253290i | ||||||||
\(184\) | −4.70265 | − | 0.940794i | −0.346684 | − | 0.0693562i | ||||
\(185\) | − | 13.3183i | − | 0.979182i | ||||||
\(186\) | 13.4464 | 0.985940 | ||||||||
\(187\) | 1.30359i | 0.0953282i | ||||||||
\(188\) | 14.0000i | 1.02105i | ||||||||
\(189\) | 0.302029 | − | 2.62846i | 0.0219694 | − | 0.191192i | ||||
\(190\) | 26.5349 | 1.92505 | ||||||||
\(191\) | 5.54253i | 0.401043i | 0.979689 | + | 0.200522i | \(0.0642637\pi\) | ||||
−0.979689 | + | 0.200522i | \(0.935736\pi\) | |||||||
\(192\) | − | 11.2298i | − | 0.810442i | ||||||
\(193\) | −8.91926 | −0.642022 | −0.321011 | − | 0.947075i | \(-0.604023\pi\) | ||||
−0.321011 | + | 0.947075i | \(0.604023\pi\) | |||||||
\(194\) | 36.8495 | 2.64564 | ||||||||
\(195\) | −9.46492 | −0.677797 | ||||||||
\(196\) | 16.8587 | + | 3.92622i | 1.20419 | + | 0.280444i | ||||
\(197\) | 24.1623 | 1.72149 | 0.860746 | − | 0.509035i | \(-0.169998\pi\) | ||||
0.860746 | + | 0.509035i | \(0.169998\pi\) | |||||||
\(198\) | 6.19770i | 0.440452i | ||||||||
\(199\) | 23.5520 | 1.66956 | 0.834778 | − | 0.550587i | \(-0.185596\pi\) | ||||
0.834778 | + | 0.550587i | \(0.185596\pi\) | |||||||
\(200\) | 1.04113 | 0.0736189 | ||||||||
\(201\) | −9.73225 | −0.686460 | ||||||||
\(202\) | 26.9651i | 1.89726i | ||||||||
\(203\) | −6.80176 | − | 0.781574i | −0.477390 | − | 0.0548557i | ||||
\(204\) | 1.10001i | 0.0770163i | ||||||||
\(205\) | 21.0663i | 1.47134i | ||||||||
\(206\) | −13.6729 | −0.952639 | ||||||||
\(207\) | −4.70265 | − | 0.940794i | −0.326857 | − | 0.0653897i | ||||
\(208\) | 13.4659i | 0.933690i | ||||||||
\(209\) | 18.4791i | 1.27822i | ||||||||
\(210\) | −1.27094 | + | 11.0606i | −0.0877034 | + | 0.763252i | ||||
\(211\) | −1.89830 | −0.130684 | −0.0653420 | − | 0.997863i | \(-0.520814\pi\) | ||||
−0.0653420 | + | 0.997863i | \(0.520814\pi\) | |||||||
\(212\) | 26.2663i | 1.80397i | ||||||||
\(213\) | 8.75698i | 0.600018i | ||||||||
\(214\) | 27.6008i | 1.88675i | ||||||||
\(215\) | − | 25.1949i | − | 1.71828i | ||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −1.92028 | + | 16.7115i | −0.130357 | + | 1.13445i | ||||
\(218\) | 20.7296i | 1.40399i | ||||||||
\(219\) | −0.926221 | −0.0625882 | ||||||||
\(220\) | − | 14.4185i | − | 0.972095i | ||||||
\(221\) | − | 2.11609i | − | 0.142344i | ||||||
\(222\) | 14.1565 | 0.950120 | ||||||||
\(223\) | 5.19716i | 0.348028i | 0.984743 | + | 0.174014i | \(0.0556738\pi\) | ||||
−0.984743 | + | 0.174014i | \(0.944326\pi\) | |||||||
\(224\) | 20.9929 | + | 2.41225i | 1.40265 | + | 0.161175i | ||||
\(225\) | 1.04113 | 0.0694086 | ||||||||
\(226\) | − | 25.9865i | − | 1.72860i | ||||||
\(227\) | −1.03060 | −0.0684035 | −0.0342017 | − | 0.999415i | \(-0.510889\pi\) | ||||
−0.0342017 | + | 0.999415i | \(0.510889\pi\) | |||||||
\(228\) | 15.5932i | 1.03269i | ||||||||
\(229\) | −12.8914 | −0.851885 | −0.425943 | − | 0.904750i | \(-0.640057\pi\) | ||||
−0.425943 | + | 0.904750i | \(0.640057\pi\) | |||||||
\(230\) | 19.7888 | + | 3.95887i | 1.30484 | + | 0.261040i | ||||
\(231\) | −7.70265 | − | 0.885092i | −0.506797 | − | 0.0582348i | ||||
\(232\) | 2.58774 | 0.169894 | ||||||||
\(233\) | 22.1817 | 1.45317 | 0.726587 | − | 0.687075i | \(-0.241106\pi\) | ||||
0.726587 | + | 0.687075i | \(0.241106\pi\) | |||||||
\(234\) | − | 10.0606i | − | 0.657680i | ||||||
\(235\) | − | 11.2647i | − | 0.734827i | ||||||
\(236\) | 15.8238i | 1.03004i | ||||||||
\(237\) | 8.86087 | 0.575575 | ||||||||
\(238\) | −2.47283 | − | 0.284147i | −0.160290 | − | 0.0184185i | ||||
\(239\) | 14.0995 | 0.912019 | 0.456009 | − | 0.889975i | \(-0.349278\pi\) | ||||
0.456009 | + | 0.889975i | \(0.349278\pi\) | |||||||
\(240\) | 5.63234i | 0.363566i | ||||||||
\(241\) | −15.9994 | −1.03061 | −0.515305 | − | 0.857007i | \(-0.672321\pi\) | ||||
−0.515305 | + | 0.857007i | \(0.672321\pi\) | |||||||
\(242\) | −5.10170 | −0.327950 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 8.47302 | 0.542429 | ||||||||
\(245\) | −13.5648 | − | 3.15912i | −0.866625 | − | 0.201828i | ||||
\(246\) | −22.3921 | −1.42767 | ||||||||
\(247\) | − | 29.9966i | − | 1.90864i | ||||||
\(248\) | − | 6.35793i | − | 0.403729i | ||||||
\(249\) | 4.81207i | 0.304953i | ||||||||
\(250\) | −25.4211 | −1.60777 | ||||||||
\(251\) | −15.3829 | −0.970959 | −0.485479 | − | 0.874248i | \(-0.661355\pi\) | ||||
−0.485479 | + | 0.874248i | \(0.661355\pi\) | |||||||
\(252\) | −6.49973 | − | 0.746868i | −0.409445 | − | 0.0470483i | ||||
\(253\) | −2.75698 | + | 13.7810i | −0.173330 | + | 0.866407i | ||||
\(254\) | 8.06058 | 0.505765 | ||||||||
\(255\) | − | 0.885092i | − | 0.0554266i | ||||||
\(256\) | 6.01320 | 0.375825 | ||||||||
\(257\) | − | 9.74378i | − | 0.607800i | −0.952704 | − | 0.303900i | \(-0.901711\pi\) | ||
0.952704 | − | 0.303900i | \(-0.0982889\pi\) | |||||||
\(258\) | 26.7805 | 1.66728 | ||||||||
\(259\) | −2.02168 | + | 17.5940i | −0.125621 | + | 1.09324i | ||||
\(260\) | 23.4052i | 1.45153i | ||||||||
\(261\) | 2.58774 | 0.160177 | ||||||||
\(262\) | − | 16.6483i | − | 1.02854i | ||||||
\(263\) | 11.3465i | 0.699656i | 0.936814 | + | 0.349828i | \(0.113760\pi\) | ||||
−0.936814 | + | 0.349828i | \(0.886240\pi\) | |||||||
\(264\) | 2.93048 | 0.180359 | ||||||||
\(265\) | − | 21.1344i | − | 1.29827i | ||||||
\(266\) | −35.0536 | − | 4.02792i | −2.14928 | − | 0.246968i | ||||
\(267\) | − | 0.0511154i | − | 0.00312821i | ||||||
\(268\) | 24.0662i | 1.47008i | ||||||||
\(269\) | 8.79588i | 0.536294i | 0.963378 | + | 0.268147i | \(0.0864113\pi\) | ||||
−0.963378 | + | 0.268147i | \(0.913589\pi\) | |||||||
\(270\) | − | 4.20801i | − | 0.256092i | ||||||
\(271\) | − | 32.1142i | − | 1.95080i | −0.220447 | − | 0.975399i | \(-0.570751\pi\) | ||
0.220447 | − | 0.975399i | \(-0.429249\pi\) | |||||||
\(272\) | −1.25923 | −0.0763522 | ||||||||
\(273\) | 12.5035 | + | 1.43675i | 0.756747 | + | 0.0869559i | ||||
\(274\) | 37.6698i | 2.27571i | ||||||||
\(275\) | − | 3.05101i | − | 0.183983i | ||||||
\(276\) | −2.32643 | + | 11.6289i | −0.140034 | + | 0.699976i | ||||
\(277\) | −1.39058 | −0.0835517 | −0.0417758 | − | 0.999127i | \(-0.513302\pi\) | ||||
−0.0417758 | + | 0.999127i | \(0.513302\pi\) | |||||||
\(278\) | 3.15604i | 0.189286i | ||||||||
\(279\) | − | 6.35793i | − | 0.380639i | ||||||
\(280\) | 5.22982 | + | 0.600945i | 0.312541 | + | 0.0359133i | ||||
\(281\) | − | 17.4361i | − | 1.04015i | −0.854120 | − | 0.520076i | \(-0.825904\pi\) | ||
0.854120 | − | 0.520076i | \(-0.174096\pi\) | |||||||
\(282\) | 11.9736 | 0.713017 | ||||||||
\(283\) | 18.3645 | 1.09166 | 0.545828 | − | 0.837898i | \(-0.316215\pi\) | ||||
0.545828 | + | 0.837898i | \(0.316215\pi\) | |||||||
\(284\) | 21.6546 | 1.28496 | ||||||||
\(285\) | − | 12.5466i | − | 0.743197i | ||||||
\(286\) | −29.4824 | −1.74333 | ||||||||
\(287\) | 3.19781 | − | 27.8294i | 0.188761 | − | 1.64272i | ||||
\(288\) | −7.98680 | −0.470626 | ||||||||
\(289\) | −16.8021 | −0.988360 | ||||||||
\(290\) | −10.8893 | −0.639439 | ||||||||
\(291\) | − | 17.4237i | − | 1.02139i | ||||||
\(292\) | 2.29039i | 0.134035i | ||||||||
\(293\) | 1.70995 | 0.0998961 | 0.0499480 | − | 0.998752i | \(-0.484094\pi\) | ||||
0.0499480 | + | 0.998752i | \(0.484094\pi\) | |||||||
\(294\) | 3.35793 | − | 14.4185i | 0.195838 | − | 0.840904i | ||||
\(295\) | − | 12.7321i | − | 0.741294i | ||||||
\(296\) | − | 6.69366i | − | 0.389061i | ||||||
\(297\) | 2.93048 | 0.170044 | ||||||||
\(298\) | − | 8.77903i | − | 0.508556i | ||||||
\(299\) | 4.47534 | − | 22.3704i | 0.258815 | − | 1.29371i | ||||
\(300\) | − | 2.57454i | − | 0.148641i | ||||||
\(301\) | −3.82452 | + | 33.2834i | −0.220442 | + | 1.91843i | ||||
\(302\) | 8.63360 | 0.496808 | ||||||||
\(303\) | 12.7500 | 0.732470 | ||||||||
\(304\) | −17.8502 | −1.02378 | ||||||||
\(305\) | −6.81756 | −0.390372 | ||||||||
\(306\) | 0.940794 | 0.0537816 | ||||||||
\(307\) | − | 5.34696i | − | 0.305167i | −0.988291 | − | 0.152583i | \(-0.951241\pi\) | ||
0.988291 | − | 0.152583i | \(-0.0487593\pi\) | |||||||
\(308\) | −2.18869 | + | 19.0474i | −0.124712 | + | 1.08532i | ||||
\(309\) | 6.46503i | 0.367783i | ||||||||
\(310\) | 26.7542i | 1.51954i | ||||||||
\(311\) | 1.72906i | 0.0980458i | 0.998798 | + | 0.0490229i | \(0.0156107\pi\) | ||||
−0.998798 | + | 0.0490229i | \(0.984389\pi\) | |||||||
\(312\) | −4.75698 | −0.269311 | ||||||||
\(313\) | 5.54253 | 0.313282 | 0.156641 | − | 0.987656i | \(-0.449933\pi\) | ||||
0.156641 | + | 0.987656i | \(0.449933\pi\) | |||||||
\(314\) | −3.30591 | −0.186563 | ||||||||
\(315\) | 5.22982 | + | 0.600945i | 0.294667 | + | 0.0338594i | ||||
\(316\) | − | 21.9114i | − | 1.23262i | ||||||
\(317\) | −8.88509 | −0.499037 | −0.249518 | − | 0.968370i | \(-0.580272\pi\) | ||||
−0.249518 | + | 0.968370i | \(0.580272\pi\) | |||||||
\(318\) | 22.4644 | 1.25974 | ||||||||
\(319\) | − | 7.58334i | − | 0.424585i | ||||||
\(320\) | 22.3439 | 1.24906 | ||||||||
\(321\) | 13.0506 | 0.728413 | ||||||||
\(322\) | −25.5408 | − | 8.23370i | −1.42333 | − | 0.458846i | ||||
\(323\) | 2.80507 | 0.156078 | ||||||||
\(324\) | 2.47283 | 0.137380 | ||||||||
\(325\) | 4.95263i | 0.274722i | ||||||||
\(326\) | 5.38585 | 0.298295 | ||||||||
\(327\) | 9.80166 | 0.542033 | ||||||||
\(328\) | 10.5877i | 0.584610i | ||||||||
\(329\) | −1.70995 | + | 14.8811i | −0.0942723 | + | 0.820419i | ||||
\(330\) | −12.3315 | −0.678828 | ||||||||
\(331\) | −15.1491 | −0.832668 | −0.416334 | − | 0.909212i | \(-0.636685\pi\) | ||||
−0.416334 | + | 0.909212i | \(0.636685\pi\) | |||||||
\(332\) | 11.8995 | 0.653067 | ||||||||
\(333\) | − | 6.69366i | − | 0.366810i | ||||||
\(334\) | 6.50076i | 0.355706i | ||||||||
\(335\) | − | 19.3642i | − | 1.05798i | ||||||
\(336\) | 0.854973 | − | 7.44053i | 0.0466426 | − | 0.405914i | ||||
\(337\) | − | 14.8299i | − | 0.807838i | −0.914795 | − | 0.403919i | \(-0.867648\pi\) | ||
0.914795 | − | 0.403919i | \(-0.132352\pi\) | |||||||
\(338\) | 20.3642 | 1.10766 | ||||||||
\(339\) | −12.2873 | −0.667355 | ||||||||
\(340\) | −2.18869 | −0.118698 | ||||||||
\(341\) | −18.6318 | −1.00897 | ||||||||
\(342\) | 13.3362 | 0.721139 | ||||||||
\(343\) | 17.4401 | + | 6.23241i | 0.941677 | + | 0.336519i | ||||
\(344\) | − | 12.6627i | − | 0.682729i | ||||||
\(345\) | 1.87189 | − | 9.35682i | 0.100779 | − | 0.503754i | ||||
\(346\) | − | 13.2166i | − | 0.710529i | ||||||
\(347\) | −18.1017 | −0.971750 | −0.485875 | − | 0.874028i | \(-0.661499\pi\) | ||||
−0.485875 | + | 0.874028i | \(0.661499\pi\) | |||||||
\(348\) | − | 6.39905i | − | 0.343025i | ||||||
\(349\) | 21.0062i | 1.12444i | 0.826988 | + | 0.562219i | \(0.190052\pi\) | ||||
−0.826988 | + | 0.562219i | \(0.809948\pi\) | |||||||
\(350\) | 5.78757 | + | 0.665036i | 0.309359 | + | 0.0355476i | ||||
\(351\) | −4.75698 | −0.253909 | ||||||||
\(352\) | 23.4052i | 1.24750i | ||||||||
\(353\) | 21.4945i | 1.14404i | 0.820241 | + | 0.572019i | \(0.193840\pi\) | ||||
−0.820241 | + | 0.572019i | \(0.806160\pi\) | |||||||
\(354\) | 13.5334 | 0.719293 | ||||||||
\(355\) | −17.4237 | −0.924753 | ||||||||
\(356\) | −0.126400 | −0.00669918 | ||||||||
\(357\) | −0.134354 | + | 1.16924i | −0.00711079 | + | 0.0618827i | ||||
\(358\) | 39.4806 | 2.08661 | ||||||||
\(359\) | 2.16133i | 0.114071i | 0.998372 | + | 0.0570354i | \(0.0181648\pi\) | ||||
−0.998372 | + | 0.0570354i | \(0.981835\pi\) | |||||||
\(360\) | −1.98969 | −0.104866 | ||||||||
\(361\) | 20.7632 | 1.09280 | ||||||||
\(362\) | −35.7188 | −1.87734 | ||||||||
\(363\) | 2.41226i | 0.126611i | ||||||||
\(364\) | 3.55284 | − | 30.9191i | 0.186219 | − | 1.62060i | ||||
\(365\) | − | 1.84289i | − | 0.0964615i | ||||||
\(366\) | − | 7.24660i | − | 0.378786i | ||||||
\(367\) | −16.5399 | −0.863375 | −0.431687 | − | 0.902023i | \(-0.642082\pi\) | ||||
−0.431687 | + | 0.902023i | \(0.642082\pi\) | |||||||
\(368\) | −13.3121 | − | 2.66316i | −0.693940 | − | 0.138827i | ||||
\(369\) | 10.5877i | 0.551176i | ||||||||
\(370\) | 28.1670i | 1.46433i | ||||||||
\(371\) | −3.20813 | + | 27.9193i | −0.166558 | + | 1.44950i | ||||
\(372\) | −15.7221 | −0.815153 | ||||||||
\(373\) | 31.1660i | 1.61372i | 0.590745 | + | 0.806858i | \(0.298834\pi\) | ||||
−0.590745 | + | 0.806858i | \(0.701166\pi\) | |||||||
\(374\) | − | 2.75698i | − | 0.142560i | ||||||
\(375\) | 12.0200i | 0.620709i | ||||||||
\(376\) | − | 5.66152i | − | 0.291971i | ||||||
\(377\) | 12.3098i | 0.633989i | ||||||||
\(378\) | −0.638764 | + | 5.55894i | −0.0328545 | + | 0.285921i | ||||
\(379\) | − | 27.5949i | − | 1.41745i | −0.705482 | − | 0.708727i | \(-0.749270\pi\) | ||
0.705482 | − | 0.708727i | \(-0.250730\pi\) | |||||||
\(380\) | −31.0257 | −1.59158 | ||||||||
\(381\) | − | 3.81131i | − | 0.195259i | ||||||
\(382\) | − | 11.7219i | − | 0.599747i | ||||||
\(383\) | −12.9097 | −0.659653 | −0.329826 | − | 0.944042i | \(-0.606990\pi\) | ||||
−0.329826 | + | 0.944042i | \(0.606990\pi\) | |||||||
\(384\) | 7.77643i | 0.396839i | ||||||||
\(385\) | 1.76106 | − | 15.3259i | 0.0897520 | − | 0.781080i | ||||
\(386\) | 18.8634 | 0.960122 | ||||||||
\(387\) | − | 12.6627i | − | 0.643683i | ||||||
\(388\) | −43.0859 | −2.18735 | ||||||||
\(389\) | 15.8277i | 0.802497i | 0.915969 | + | 0.401249i | \(0.131424\pi\) | ||||
−0.915969 | + | 0.401249i | \(0.868576\pi\) | |||||||
\(390\) | 20.0174 | 1.01362 | ||||||||
\(391\) | 2.09192 | + | 0.418502i | 0.105793 | + | 0.0211645i | ||||
\(392\) | −6.81756 | − | 1.58774i | −0.344339 | − | 0.0801931i | ||||
\(393\) | −7.87189 | −0.397084 | ||||||||
\(394\) | −51.1010 | −2.57443 | ||||||||
\(395\) | 17.6304i | 0.887081i | ||||||||
\(396\) | − | 7.24660i | − | 0.364155i | ||||||
\(397\) | − | 12.7159i | − | 0.638190i | −0.947723 | − | 0.319095i | \(-0.896621\pi\) | ||
0.947723 | − | 0.319095i | \(-0.103379\pi\) | |||||||
\(398\) | −49.8103 | −2.49676 | ||||||||
\(399\) | −1.90454 | + | 16.5745i | −0.0953462 | + | 0.829765i | ||||
\(400\) | 2.94719 | 0.147359 | ||||||||
\(401\) | − | 9.53434i | − | 0.476122i | −0.971250 | − | 0.238061i | \(-0.923488\pi\) | ||
0.971250 | − | 0.238061i | \(-0.0765118\pi\) | |||||||
\(402\) | 20.5828 | 1.02658 | ||||||||
\(403\) | 30.2445 | 1.50659 | ||||||||
\(404\) | − | 31.5287i | − | 1.56861i | ||||||
\(405\) | −1.98969 | −0.0988686 | ||||||||
\(406\) | 14.3851 | + | 1.65296i | 0.713921 | + | 0.0820349i | ||||
\(407\) | −19.6157 | −0.972312 | ||||||||
\(408\) | − | 0.444839i | − | 0.0220228i | ||||||
\(409\) | − | 5.78963i | − | 0.286279i | −0.989703 | − | 0.143139i | \(-0.954280\pi\) | ||
0.989703 | − | 0.143139i | \(-0.0457197\pi\) | |||||||
\(410\) | − | 44.5534i | − | 2.20033i | ||||||
\(411\) | 17.8115 | 0.878578 | ||||||||
\(412\) | 15.9869 | 0.787620 | ||||||||
\(413\) | −1.93270 | + | 16.8196i | −0.0951021 | + | 0.827640i | ||||
\(414\) | 9.94567 | + | 1.98969i | 0.488803 | + | 0.0977880i | ||||
\(415\) | −9.57454 | −0.469996 | ||||||||
\(416\) | − | 37.9930i | − | 1.86276i | ||||||
\(417\) | 1.49228 | 0.0730773 | ||||||||
\(418\) | − | 39.0815i | − | 1.91154i | ||||||
\(419\) | 4.01808 | 0.196296 | 0.0981479 | − | 0.995172i | \(-0.468708\pi\) | ||||
0.0981479 | + | 0.995172i | \(0.468708\pi\) | |||||||
\(420\) | 1.48604 | − | 12.9325i | 0.0725112 | − | 0.631040i | ||||
\(421\) | − | 11.8425i | − | 0.577166i | −0.957455 | − | 0.288583i | \(-0.906816\pi\) | ||
0.957455 | − | 0.288583i | \(-0.0931842\pi\) | |||||||
\(422\) | 4.01472 | 0.195434 | ||||||||
\(423\) | − | 5.66152i | − | 0.275273i | ||||||
\(424\) | − | 10.6219i | − | 0.515846i | ||||||
\(425\) | −0.463135 | −0.0224653 | ||||||||
\(426\) | − | 18.5202i | − | 0.897307i | ||||||
\(427\) | 9.00624 | + | 1.03489i | 0.435843 | + | 0.0500816i | ||||
\(428\) | − | 32.2719i | − | 1.55992i | ||||||
\(429\) | 13.9403i | 0.673042i | ||||||||
\(430\) | 53.2849i | 2.56963i | ||||||||
\(431\) | − | 26.8703i | − | 1.29430i | −0.762364 | − | 0.647149i | \(-0.775961\pi\) | ||
0.762364 | − | 0.647149i | \(-0.224039\pi\) | |||||||
\(432\) | 2.83076i | 0.136195i | ||||||||
\(433\) | 3.76317 | 0.180847 | 0.0904233 | − | 0.995903i | \(-0.471178\pi\) | ||||
0.0904233 | + | 0.995903i | \(0.471178\pi\) | |||||||
\(434\) | 4.06122 | − | 35.3433i | 0.194945 | − | 1.69653i | ||||
\(435\) | 5.14881i | 0.246866i | ||||||||
\(436\) | − | 24.2379i | − | 1.16078i | ||||||
\(437\) | 29.6540 | + | 5.93246i | 1.41854 | + | 0.283788i | ||||
\(438\) | 1.95887 | 0.0935985 | ||||||||
\(439\) | − | 40.1531i | − | 1.91640i | −0.286096 | − | 0.958201i | \(-0.592358\pi\) | ||
0.286096 | − | 0.958201i | \(-0.407642\pi\) | |||||||
\(440\) | 5.83076i | 0.277971i | ||||||||
\(441\) | −6.81756 | − | 1.58774i | −0.324646 | − | 0.0756067i | ||||
\(442\) | 4.47534i | 0.212870i | ||||||||
\(443\) | 22.4985 | 1.06894 | 0.534469 | − | 0.845188i | \(-0.320512\pi\) | ||||
0.534469 | + | 0.845188i | \(0.320512\pi\) | |||||||
\(444\) | −16.5523 | −0.785538 | ||||||||
\(445\) | 0.101704 | 0.00482122 | ||||||||
\(446\) | − | 10.9915i | − | 0.520464i | ||||||
\(447\) | −4.15102 | −0.196337 | ||||||||
\(448\) | −29.5171 | − | 3.39173i | −1.39455 | − | 0.160244i | ||||
\(449\) | 13.0885 | 0.617685 | 0.308842 | − | 0.951113i | \(-0.400058\pi\) | ||||
0.308842 | + | 0.951113i | \(0.400058\pi\) | |||||||
\(450\) | −2.20189 | −0.103798 | ||||||||
\(451\) | 31.0272 | 1.46101 | ||||||||
\(452\) | 30.3845i | 1.42916i | ||||||||
\(453\) | − | 4.08226i | − | 0.191801i | ||||||
\(454\) | 2.17963 | 0.102295 | ||||||||
\(455\) | −2.85868 | + | 24.8781i | −0.134017 | + | 1.16630i | ||||
\(456\) | − | 6.30581i | − | 0.295297i | ||||||
\(457\) | − | 25.9354i | − | 1.21321i | −0.795005 | − | 0.606603i | \(-0.792532\pi\) | ||
0.795005 | − | 0.606603i | \(-0.207468\pi\) | |||||||
\(458\) | 27.2640 | 1.27397 | ||||||||
\(459\) | − | 0.444839i | − | 0.0207633i | ||||||
\(460\) | −23.1379 | − | 4.62887i | −1.07881 | − | 0.215822i | ||||
\(461\) | − | 19.2361i | − | 0.895913i | −0.894055 | − | 0.447956i | \(-0.852152\pi\) | ||
0.894055 | − | 0.447956i | \(-0.147848\pi\) | |||||||
\(462\) | 16.2904 | + | 1.87189i | 0.757898 | + | 0.0870881i | ||||
\(463\) | −23.6546 | −1.09932 | −0.549660 | − | 0.835388i | \(-0.685243\pi\) | ||||
−0.549660 | + | 0.835388i | \(0.685243\pi\) | |||||||
\(464\) | 7.32528 | 0.340067 | ||||||||
\(465\) | 12.6503 | 0.586644 | ||||||||
\(466\) | −46.9123 | −2.17317 | ||||||||
\(467\) | −37.3454 | −1.72814 | −0.864071 | − | 0.503371i | \(-0.832093\pi\) | ||||
−0.864071 | + | 0.503371i | \(0.832093\pi\) | |||||||
\(468\) | 11.7632i | 0.543755i | ||||||||
\(469\) | −2.93942 | + | 25.5808i | −0.135730 | + | 1.18121i | ||||
\(470\) | 23.8238i | 1.09891i | ||||||||
\(471\) | 1.56315i | 0.0720260i | ||||||||
\(472\) | − | 6.39905i | − | 0.294540i | ||||||
\(473\) | −37.1079 | −1.70623 | ||||||||
\(474\) | −18.7399 | −0.860753 | ||||||||
\(475\) | −6.56516 | −0.301230 | ||||||||
\(476\) | 2.89134 | + | 0.332236i | 0.132524 | + | 0.0152280i | ||||
\(477\) | − | 10.6219i | − | 0.486345i | ||||||
\(478\) | −29.8191 | −1.36389 | ||||||||
\(479\) | −23.7419 | −1.08480 | −0.542398 | − | 0.840122i | \(-0.682484\pi\) | ||||
−0.542398 | + | 0.840122i | \(0.682484\pi\) | |||||||
\(480\) | − | 15.8913i | − | 0.725333i | ||||||
\(481\) | 31.8416 | 1.45185 | ||||||||
\(482\) | 33.8372 | 1.54124 | ||||||||
\(483\) | −3.89317 | + | 12.0766i | −0.177145 | + | 0.549502i | ||||
\(484\) | 5.96511 | 0.271142 | ||||||||
\(485\) | 34.6678 | 1.57418 | ||||||||
\(486\) | − | 2.11491i | − | 0.0959342i | ||||||
\(487\) | 34.2229 | 1.55079 | 0.775393 | − | 0.631479i | \(-0.217552\pi\) | ||||
0.775393 | + | 0.631479i | \(0.217552\pi\) | |||||||
\(488\) | −3.42644 | −0.155108 | ||||||||
\(489\) | − | 2.54661i | − | 0.115162i | ||||||
\(490\) | 28.6884 | + | 6.68124i | 1.29601 | + | 0.301828i | ||||
\(491\) | −4.30984 | −0.194500 | −0.0972501 | − | 0.995260i | \(-0.531005\pi\) | ||||
−0.0972501 | + | 0.995260i | \(0.531005\pi\) | |||||||
\(492\) | 26.1817 | 1.18036 | ||||||||
\(493\) | −1.15113 | −0.0518442 | ||||||||
\(494\) | 63.4401i | 2.85430i | ||||||||
\(495\) | 5.83076i | 0.262073i | ||||||||
\(496\) | − | 17.9978i | − | 0.808124i | ||||||
\(497\) | 23.0173 | + | 2.64487i | 1.03247 | + | 0.118638i | ||||
\(498\) | − | 10.1771i | − | 0.456046i | ||||||
\(499\) | 30.5466 | 1.36745 | 0.683727 | − | 0.729738i | \(-0.260358\pi\) | ||||
0.683727 | + | 0.729738i | \(0.260358\pi\) | |||||||
\(500\) | 29.7234 | 1.32927 | ||||||||
\(501\) | 3.07378 | 0.137326 | ||||||||
\(502\) | 32.5334 | 1.45204 | ||||||||
\(503\) | −35.3433 | −1.57588 | −0.787941 | − | 0.615751i | \(-0.788853\pi\) | ||||
−0.787941 | + | 0.615751i | \(0.788853\pi\) | |||||||
\(504\) | 2.62846 | + | 0.302029i | 0.117081 | + | 0.0134535i | ||||
\(505\) | 25.3686i | 1.12889i | ||||||||
\(506\) | 5.83076 | − | 29.1456i | 0.259209 | − | 1.29568i | ||||
\(507\) | − | 9.62887i | − | 0.427633i | ||||||
\(508\) | −9.42474 | −0.418155 | ||||||||
\(509\) | − | 14.1212i | − | 0.625909i | −0.949768 | − | 0.312955i | \(-0.898681\pi\) | ||
0.949768 | − | 0.312955i | \(-0.101319\pi\) | |||||||
\(510\) | 1.87189i | 0.0828886i | ||||||||
\(511\) | −0.279746 | + | 2.43453i | −0.0123752 | + | 0.107697i | ||||
\(512\) | −28.2702 | −1.24938 | ||||||||
\(513\) | − | 6.30581i | − | 0.278408i | ||||||
\(514\) | 20.6072i | 0.908944i | ||||||||
\(515\) | −12.8634 | −0.566830 | ||||||||
\(516\) | −31.3128 | −1.37847 | ||||||||
\(517\) | −16.5910 | −0.729671 | ||||||||
\(518\) | 4.27567 | − | 37.2097i | 0.187862 | − | 1.63490i | ||||
\(519\) | −6.24926 | −0.274312 | ||||||||
\(520\) | − | 9.46492i | − | 0.415064i | ||||||
\(521\) | −13.3545 | −0.585071 | −0.292536 | − | 0.956255i | \(-0.594499\pi\) | ||||
−0.292536 | + | 0.956255i | \(0.594499\pi\) | |||||||
\(522\) | −5.47283 | −0.239539 | ||||||||
\(523\) | 26.7170 | 1.16825 | 0.584126 | − | 0.811663i | \(-0.301437\pi\) | ||||
0.584126 | + | 0.811663i | \(0.301437\pi\) | |||||||
\(524\) | 19.4659i | 0.850371i | ||||||||
\(525\) | 0.314451 | − | 2.73656i | 0.0137238 | − | 0.119433i | ||||
\(526\) | − | 23.9968i | − | 1.04631i | ||||||
\(527\) | 2.82825i | 0.123201i | ||||||||
\(528\) | 8.29550 | 0.361015 | ||||||||
\(529\) | 21.2298 | + | 8.84844i | 0.923035 | + | 0.384715i | ||||
\(530\) | 44.6972i | 1.94152i | ||||||||
\(531\) | − | 6.39905i | − | 0.277695i | ||||||
\(532\) | 40.9861 | + | 4.70961i | 1.77697 | + | 0.204187i | ||||
\(533\) | −50.3657 | −2.18158 | ||||||||
\(534\) | 0.108104i | 0.00467813i | ||||||||
\(535\) | 25.9666i | 1.12264i | ||||||||
\(536\) | − | 9.73225i | − | 0.420369i | ||||||
\(537\) | − | 18.6678i | − | 0.805573i | ||||||
\(538\) | − | 18.6025i | − | 0.802009i | ||||||
\(539\) | −4.65285 | + | 19.9787i | −0.200413 | + | 0.860546i | ||||
\(540\) | 4.92018i | 0.211731i | ||||||||
\(541\) | −16.7159 | −0.718671 | −0.359335 | − | 0.933209i | \(-0.616997\pi\) | ||||
−0.359335 | + | 0.933209i | \(0.616997\pi\) | |||||||
\(542\) | 67.9185i | 2.91735i | ||||||||
\(543\) | 16.8890i | 0.724778i | ||||||||
\(544\) | 3.55284 | 0.152327 | ||||||||
\(545\) | 19.5023i | 0.835386i | ||||||||
\(546\) | −26.4438 | − | 3.03859i | −1.13169 | − | 0.130040i | ||||
\(547\) | 8.31680 | 0.355601 | 0.177800 | − | 0.984067i | \(-0.443102\pi\) | ||||
0.177800 | + | 0.984067i | \(0.443102\pi\) | |||||||
\(548\) | − | 44.0450i | − | 1.88151i | ||||||
\(549\) | −3.42644 | −0.146237 | ||||||||
\(550\) | 6.45261i | 0.275140i | ||||||||
\(551\) | −16.3178 | −0.695162 | ||||||||
\(552\) | 0.940794 | − | 4.70265i | 0.0400428 | − | 0.200158i | ||||
\(553\) | 2.67624 | − | 23.2904i | 0.113805 | − | 0.990408i | ||||
\(554\) | 2.94094 | 0.124949 | ||||||||
\(555\) | 13.3183 | 0.565331 | ||||||||
\(556\) | − | 3.69016i | − | 0.156498i | ||||||
\(557\) | 39.9903i | 1.69444i | 0.531239 | + | 0.847222i | \(0.321727\pi\) | ||||
−0.531239 | + | 0.847222i | \(0.678273\pi\) | |||||||
\(558\) | 13.4464i | 0.569233i | ||||||||
\(559\) | 60.2364 | 2.54773 | ||||||||
\(560\) | 14.8044 | + | 1.70113i | 0.625598 | + | 0.0718859i | ||||
\(561\) | −1.30359 | −0.0550378 | ||||||||
\(562\) | 36.8758i | 1.55551i | ||||||||
\(563\) | −16.6093 | −0.699998 | −0.349999 | − | 0.936750i | \(-0.613818\pi\) | ||||
−0.349999 | + | 0.936750i | \(0.613818\pi\) | |||||||
\(564\) | −14.0000 | −0.589506 | ||||||||
\(565\) | − | 24.4479i | − | 1.02853i | ||||||
\(566\) | −38.8392 | −1.63253 | ||||||||
\(567\) | 2.62846 | + | 0.302029i | 0.110385 | + | 0.0126840i | ||||
\(568\) | −8.75698 | −0.367435 | ||||||||
\(569\) | − | 17.2973i | − | 0.725140i | −0.931957 | − | 0.362570i | \(-0.881899\pi\) | ||
0.931957 | − | 0.362570i | \(-0.118101\pi\) | |||||||
\(570\) | 26.5349i | 1.11143i | ||||||||
\(571\) | 13.3749i | 0.559722i | 0.960041 | + | 0.279861i | \(0.0902884\pi\) | ||||
−0.960041 | + | 0.279861i | \(0.909712\pi\) | |||||||
\(572\) | 34.4720 | 1.44134 | ||||||||
\(573\) | −5.54253 | −0.231543 | ||||||||
\(574\) | −6.76307 | + | 58.8566i | −0.282285 | + | 2.45663i | ||||
\(575\) | −4.89606 | − | 0.979487i | −0.204180 | − | 0.0408474i | ||||
\(576\) | 11.2298 | 0.467909 | ||||||||
\(577\) | − | 38.9193i | − | 1.62023i | −0.586271 | − | 0.810115i | \(-0.699405\pi\) | ||
0.586271 | − | 0.810115i | \(-0.300595\pi\) | |||||||
\(578\) | 35.5349 | 1.47806 | ||||||||
\(579\) | − | 8.91926i | − | 0.370672i | ||||||
\(580\) | 12.7321 | 0.528673 | ||||||||
\(581\) | 12.6483 | + | 1.45339i | 0.524741 | + | 0.0602967i | ||||
\(582\) | 36.8495i | 1.52746i | ||||||||
\(583\) | −31.1274 | −1.28916 | ||||||||
\(584\) | − | 0.926221i | − | 0.0383273i | ||||||
\(585\) | − | 9.46492i | − | 0.391326i | ||||||
\(586\) | −3.61638 | −0.149391 | ||||||||
\(587\) | − | 19.7974i | − | 0.817126i | −0.912730 | − | 0.408563i | \(-0.866030\pi\) | ||
0.912730 | − | 0.408563i | \(-0.133970\pi\) | |||||||
\(588\) | −3.92622 | + | 16.8587i | −0.161915 | + | 0.695240i | ||||
\(589\) | 40.0919i | 1.65196i | ||||||||
\(590\) | 26.9273i | 1.10858i | ||||||||
\(591\) | 24.1623i | 0.993903i | ||||||||
\(592\) | − | 18.9481i | − | 0.778764i | ||||||
\(593\) | − | 40.3370i | − | 1.65644i | −0.560400 | − | 0.828222i | \(-0.689353\pi\) | ||
0.560400 | − | 0.828222i | \(-0.310647\pi\) | |||||||
\(594\) | −6.19770 | −0.254295 | ||||||||
\(595\) | −2.32643 | − | 0.267324i | −0.0953742 | − | 0.0109592i | ||||
\(596\) | 10.2648i | 0.420462i | ||||||||
\(597\) | 23.5520i | 0.963918i | ||||||||
\(598\) | −9.46492 | + | 47.3114i | −0.387050 | + | 1.93471i | ||||
\(599\) | 16.2012 | 0.661962 | 0.330981 | − | 0.943637i | \(-0.392620\pi\) | ||||
0.330981 | + | 0.943637i | \(0.392620\pi\) | |||||||
\(600\) | 1.04113i | 0.0425039i | ||||||||
\(601\) | 0.750021i | 0.0305940i | 0.999883 | + | 0.0152970i | \(0.00486937\pi\) | ||||
−0.999883 | + | 0.0152970i | \(0.995131\pi\) | |||||||
\(602\) | 8.08850 | − | 70.3914i | 0.329663 | − | 2.86894i | ||||
\(603\) | − | 9.73225i | − | 0.396328i | ||||||
\(604\) | −10.0947 | −0.410749 | ||||||||
\(605\) | −4.79965 | −0.195134 | ||||||||
\(606\) | −26.9651 | −1.09538 | ||||||||
\(607\) | 21.0691i | 0.855166i | 0.903976 | + | 0.427583i | \(0.140635\pi\) | ||||
−0.903976 | + | 0.427583i | \(0.859365\pi\) | |||||||
\(608\) | 50.3632 | 2.04250 | ||||||||
\(609\) | 0.781574 | − | 6.80176i | 0.0316710 | − | 0.275621i | ||||
\(610\) | 14.4185 | 0.583788 | ||||||||
\(611\) | 26.9317 | 1.08954 | ||||||||
\(612\) | −1.10001 | −0.0444654 | ||||||||
\(613\) | − | 2.93048i | − | 0.118361i | −0.998247 | − | 0.0591806i | \(-0.981151\pi\) | ||
0.998247 | − | 0.0591806i | \(-0.0188488\pi\) | |||||||
\(614\) | 11.3083i | 0.456367i | ||||||||
\(615\) | −21.0663 | −0.849477 | ||||||||
\(616\) | 0.885092 | − | 7.70265i | 0.0356614 | − | 0.310349i | ||||
\(617\) | 7.33641i | 0.295353i | 0.989036 | + | 0.147676i | \(0.0471794\pi\) | ||||
−0.989036 | + | 0.147676i | \(0.952821\pi\) | |||||||
\(618\) | − | 13.6729i | − | 0.550006i | ||||||
\(619\) | −23.2905 | −0.936126 | −0.468063 | − | 0.883695i | \(-0.655048\pi\) | ||||
−0.468063 | + | 0.883695i | \(0.655048\pi\) | |||||||
\(620\) | − | 31.2821i | − | 1.25632i | ||||||
\(621\) | 0.940794 | − | 4.70265i | 0.0377527 | − | 0.188711i | ||||
\(622\) | − | 3.65679i | − | 0.146624i | ||||||
\(623\) | −0.134354 | − | 0.0154383i | −0.00538280 | − | 0.000618524i | ||||
\(624\) | −13.4659 | −0.539066 | ||||||||
\(625\) | −18.7104 | −0.748416 | ||||||||
\(626\) | −11.7219 | −0.468503 | ||||||||
\(627\) | −18.4791 | −0.737983 | ||||||||
\(628\) | 3.86540 | 0.154246 | ||||||||
\(629\) | 2.97760i | 0.118725i | ||||||||
\(630\) | −11.0606 | − | 1.27094i | −0.440664 | − | 0.0506356i | ||||
\(631\) | − | 21.1540i | − | 0.842129i | −0.907031 | − | 0.421065i | \(-0.861657\pi\) | ||
0.907031 | − | 0.421065i | \(-0.138343\pi\) | |||||||
\(632\) | 8.86087i | 0.352466i | ||||||||
\(633\) | − | 1.89830i | − | 0.0754505i | ||||||
\(634\) | 18.7911 | 0.746292 | ||||||||
\(635\) | 7.58334 | 0.300936 | ||||||||
\(636\) | −26.2663 | −1.04152 | ||||||||
\(637\) | 7.55286 | − | 32.4310i | 0.299255 | − | 1.28496i | ||||
\(638\) | 16.0381i | 0.634953i | ||||||||
\(639\) | −8.75698 | −0.346421 | ||||||||
\(640\) | −15.4727 | −0.611612 | ||||||||
\(641\) | − | 10.3487i | − | 0.408750i | −0.978893 | − | 0.204375i | \(-0.934484\pi\) | ||
0.978893 | − | 0.204375i | \(-0.0655162\pi\) | |||||||
\(642\) | −27.6008 | −1.08932 | ||||||||
\(643\) | −21.9318 | −0.864908 | −0.432454 | − | 0.901656i | \(-0.642352\pi\) | ||||
−0.432454 | + | 0.901656i | \(0.642352\pi\) | |||||||
\(644\) | 29.8633 | + | 9.62717i | 1.17678 | + | 0.379364i | ||||
\(645\) | 25.1949 | 0.992049 | ||||||||
\(646\) | −5.93246 | −0.233410 | ||||||||
\(647\) | − | 11.5356i | − | 0.453513i | −0.973951 | − | 0.226756i | \(-0.927188\pi\) | ||
0.973951 | − | 0.226756i | \(-0.0728121\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −18.7523 | −0.736093 | ||||||||
\(650\) | − | 10.4744i | − | 0.410838i | ||||||
\(651\) | −16.7115 | − | 1.92028i | −0.654976 | − | 0.0752617i | ||||
\(652\) | −6.29735 | −0.246623 | ||||||||
\(653\) | 40.3726 | 1.57990 | 0.789952 | − | 0.613169i | \(-0.210105\pi\) | ||||
0.789952 | + | 0.613169i | \(0.210105\pi\) | |||||||
\(654\) | −20.7296 | −0.810592 | ||||||||
\(655\) | − | 15.6626i | − | 0.611990i | ||||||
\(656\) | 29.9714i | 1.17018i | ||||||||
\(657\) | − | 0.926221i | − | 0.0361353i | ||||||
\(658\) | 3.61638 | − | 31.4721i | 0.140981 | − | 1.22691i | ||||
\(659\) | 40.0145i | 1.55874i | 0.626562 | + | 0.779371i | \(0.284461\pi\) | ||||
−0.626562 | + | 0.779371i | \(0.715539\pi\) | |||||||
\(660\) | 14.4185 | 0.561239 | ||||||||
\(661\) | −0.159220 | −0.00619293 | −0.00309646 | − | 0.999995i | \(-0.500986\pi\) | ||||
−0.00309646 | + | 0.999995i | \(0.500986\pi\) | |||||||
\(662\) | 32.0389 | 1.24523 | ||||||||
\(663\) | 2.11609 | 0.0821822 | ||||||||
\(664\) | −4.81207 | −0.186745 | ||||||||
\(665\) | −32.9782 | − | 3.78945i | −1.27884 | − | 0.146948i | ||||
\(666\) | 14.1565i | 0.548552i | ||||||||
\(667\) | −12.1692 | − | 2.43453i | −0.471195 | − | 0.0942654i | ||||
\(668\) | − | 7.60095i | − | 0.294089i | ||||||
\(669\) | −5.19716 | −0.200934 | ||||||||
\(670\) | 40.9534i | 1.58217i | ||||||||
\(671\) | 10.0411i | 0.387633i | ||||||||
\(672\) | −2.41225 | + | 20.9929i | −0.0930544 | + | 0.809820i | ||||
\(673\) | 37.5459 | 1.44729 | 0.723644 | − | 0.690173i | \(-0.242466\pi\) | ||||
0.723644 | + | 0.690173i | \(0.242466\pi\) | |||||||
\(674\) | 31.3640i | 1.20809i | ||||||||
\(675\) | 1.04113i | 0.0400731i | ||||||||
\(676\) | −23.8106 | −0.915792 | ||||||||
\(677\) | 37.0329 | 1.42329 | 0.711645 | − | 0.702540i | \(-0.247951\pi\) | ||||
0.711645 | + | 0.702540i | \(0.247951\pi\) | |||||||
\(678\) | 25.9865 | 0.998006 | ||||||||
\(679\) | −45.7974 | − | 5.26247i | −1.75754 | − | 0.201955i | ||||
\(680\) | 0.885092 | 0.0339417 | ||||||||
\(681\) | − | 1.03060i | − | 0.0394928i | ||||||
\(682\) | 39.4045 | 1.50888 | ||||||||
\(683\) | −45.1421 | −1.72732 | −0.863658 | − | 0.504079i | \(-0.831832\pi\) | ||||
−0.863658 | + | 0.504079i | \(0.831832\pi\) | |||||||
\(684\) | −15.5932 | −0.596222 | ||||||||
\(685\) | 35.4395i | 1.35407i | ||||||||
\(686\) | −36.8842 | − | 13.1810i | −1.40825 | − | 0.503252i | ||||
\(687\) | − | 12.8914i | − | 0.491836i | ||||||
\(688\) | − | 35.8452i | − | 1.36658i | ||||||
\(689\) | 50.5283 | 1.92498 | ||||||||
\(690\) | −3.95887 | + | 19.7888i | −0.150712 | + | 0.753347i | ||||
\(691\) | 29.1902i | 1.11045i | 0.831701 | + | 0.555224i | \(0.187367\pi\) | ||||
−0.831701 | + | 0.555224i | \(0.812633\pi\) | |||||||
\(692\) | 15.4534i | 0.587450i | ||||||||
\(693\) | 0.885092 | − | 7.70265i | 0.0336219 | − | 0.292599i | ||||
\(694\) | 38.2834 | 1.45322 | ||||||||
\(695\) | 2.96918i | 0.112627i | ||||||||
\(696\) | 2.58774i | 0.0980881i | ||||||||
\(697\) | − | 4.70984i | − | 0.178398i | ||||||
\(698\) | − | 44.4263i | − | 1.68156i | ||||||
\(699\) | 22.1817i | 0.838990i | ||||||||
\(700\) | −6.76706 | − | 0.777586i | −0.255771 | − | 0.0293900i | ||||
\(701\) | − | 22.0254i | − | 0.831889i | −0.909390 | − | 0.415944i | \(-0.863451\pi\) | ||
0.909390 | − | 0.415944i | \(-0.136549\pi\) | |||||||
\(702\) | 10.0606 | 0.379712 | ||||||||
\(703\) | 42.2089i | 1.59194i | ||||||||
\(704\) | − | 32.9088i | − | 1.24030i | ||||||
\(705\) | 11.2647 | 0.424252 | ||||||||
\(706\) | − | 45.4589i | − | 1.71087i | ||||||
\(707\) | 3.85088 | − | 33.5129i | 0.144827 | − | 1.26038i | ||||
\(708\) | −15.8238 | −0.594695 | ||||||||
\(709\) | 14.9322i | 0.560789i | 0.959885 | + | 0.280395i | \(0.0904654\pi\) | ||||
−0.959885 | + | 0.280395i | \(0.909535\pi\) | |||||||
\(710\) | 36.8495 | 1.38294 | ||||||||
\(711\) | 8.86087i | 0.332308i | ||||||||
\(712\) | 0.0511154 | 0.00191563 | ||||||||
\(713\) | −5.98150 | + | 29.8991i | −0.224009 | + | 1.11973i | ||||
\(714\) | 0.284147 | − | 2.47283i | 0.0106339 | − | 0.0925435i | ||||
\(715\) | −27.7368 | −1.03730 | ||||||||
\(716\) | −46.1623 | −1.72517 | ||||||||
\(717\) | 14.0995i | 0.526554i | ||||||||
\(718\) | − | 4.57102i | − | 0.170589i | ||||||
\(719\) | 18.0070i | 0.671546i | 0.941943 | + | 0.335773i | \(0.108998\pi\) | ||||
−0.941943 | + | 0.335773i | \(0.891002\pi\) | |||||||
\(720\) | −5.63234 | −0.209905 | ||||||||
\(721\) | 16.9930 | + | 1.95263i | 0.632854 | + | 0.0727197i | ||||
\(722\) | −43.9123 | −1.63425 | ||||||||
\(723\) | − | 15.9994i | − | 0.595023i | ||||||
\(724\) | 41.7638 | 1.55214 | ||||||||
\(725\) | 2.69417 | 0.100059 | ||||||||
\(726\) | − | 5.10170i | − | 0.189342i | ||||||
\(727\) | 24.9172 | 0.924128 | 0.462064 | − | 0.886846i | \(-0.347109\pi\) | ||||
0.462064 | + | 0.886846i | \(0.347109\pi\) | |||||||
\(728\) | −1.43675 | + | 12.5035i | −0.0532494 | + | 0.463411i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 3.89755i | 0.144255i | ||||||||
\(731\) | 5.63288i | 0.208340i | ||||||||
\(732\) | 8.47302i | 0.313172i | ||||||||
\(733\) | −37.5821 | −1.38812 | −0.694062 | − | 0.719915i | \(-0.744181\pi\) | ||||
−0.694062 | + | 0.719915i | \(0.744181\pi\) | |||||||
\(734\) | 34.9803 | 1.29115 | ||||||||
\(735\) | 3.15912 | − | 13.5648i | 0.116526 | − | 0.500346i | ||||
\(736\) | 37.5591 | + | 7.51393i | 1.38445 | + | 0.276967i | ||||
\(737\) | −28.5202 | −1.05056 | ||||||||
\(738\) | − | 22.3921i | − | 0.824264i | ||||||
\(739\) | 23.3983 | 0.860722 | 0.430361 | − | 0.902657i | \(-0.358386\pi\) | ||||
0.430361 | + | 0.902657i | \(0.358386\pi\) | |||||||
\(740\) | − | 32.9340i | − | 1.21068i | ||||||
\(741\) | 29.9966 | 1.10195 | ||||||||
\(742\) | 6.78491 | − | 59.0467i | 0.249082 | − | 2.16767i | ||||
\(743\) | 0.254902i | 0.00935144i | 0.999989 | + | 0.00467572i | \(0.00148833\pi\) | ||||
−0.999989 | + | 0.00467572i | \(0.998512\pi\) | |||||||
\(744\) | 6.35793 | 0.233093 | ||||||||
\(745\) | − | 8.25926i | − | 0.302596i | ||||||
\(746\) | − | 65.9133i | − | 2.41326i | ||||||
\(747\) | −4.81207 | −0.176065 | ||||||||
\(748\) | 3.22357i | 0.117865i | ||||||||
\(749\) | 3.94166 | − | 34.3029i | 0.144025 | − | 1.25340i | ||||
\(750\) | − | 25.4211i | − | 0.928249i | ||||||
\(751\) | 1.20224i | 0.0438705i | 0.999759 | + | 0.0219353i | \(0.00698277\pi\) | ||||
−0.999759 | + | 0.0219353i | \(0.993017\pi\) | |||||||
\(752\) | − | 16.0264i | − | 0.584423i | ||||||
\(753\) | − | 15.3829i | − | 0.560583i | ||||||
\(754\) | − | 26.0342i | − | 0.948108i | ||||||
\(755\) | 8.12243 | 0.295606 | ||||||||
\(756\) | 0.746868 | − | 6.49973i | 0.0271633 | − | 0.236393i | ||||
\(757\) | − | 3.06931i | − | 0.111556i | −0.998443 | − | 0.0557779i | \(-0.982236\pi\) | ||
0.998443 | − | 0.0557779i | \(-0.0177639\pi\) | |||||||
\(758\) | 58.3607i | 2.11975i | ||||||||
\(759\) | −13.7810 | − | 2.75698i | −0.500220 | − | 0.100072i | ||||
\(760\) | 12.5466 | 0.455113 | ||||||||
\(761\) | − | 0.186452i | − | 0.00675888i | −0.999994 | − | 0.00337944i | \(-0.998924\pi\) | ||
0.999994 | − | 0.00337944i | \(-0.00107571\pi\) | |||||||
\(762\) | 8.06058i | 0.292004i | ||||||||
\(763\) | 2.96039 | − | 25.7632i | 0.107173 | − | 0.932691i | ||||
\(764\) | 13.7058i | 0.495857i | ||||||||
\(765\) | 0.885092 | 0.0320006 | ||||||||
\(766\) | 27.3027 | 0.986488 | ||||||||
\(767\) | 30.4402 | 1.09913 | ||||||||
\(768\) | 6.01320i | 0.216983i | ||||||||
\(769\) | −45.8185 | −1.65226 | −0.826128 | − | 0.563483i | \(-0.809461\pi\) | ||||
−0.826128 | + | 0.563483i | \(0.809461\pi\) | |||||||
\(770\) | −3.72448 | + | 32.4128i | −0.134221 | + | 1.16808i | ||||
\(771\) | 9.74378 | 0.350914 | ||||||||
\(772\) | −22.0558 | −0.793807 | ||||||||
\(773\) | −40.5819 | −1.45963 | −0.729816 | − | 0.683644i | \(-0.760394\pi\) | ||||
−0.729816 | + | 0.683644i | \(0.760394\pi\) | |||||||
\(774\) | 26.7805i | 0.962606i | ||||||||
\(775\) | − | 6.61942i | − | 0.237777i | ||||||
\(776\) | 17.4237 | 0.625474 | ||||||||
\(777\) | −17.5940 | − | 2.02168i | −0.631181 | − | 0.0725274i | ||||
\(778\) | − | 33.4742i | − | 1.20011i | ||||||
\(779\) | − | 66.7643i | − | 2.39208i | ||||||
\(780\) | −23.4052 | −0.838040 | ||||||||
\(781\) | 25.6622i | 0.918266i | ||||||||
\(782\) | −4.42422 | − | 0.885092i | −0.158210 | − | 0.0316508i | ||||
\(783\) | 2.58774i | 0.0924783i | ||||||||
\(784\) | −19.2989 | − | 4.49452i | −0.689245 | − | 0.160518i | ||||
\(785\) | −3.11018 | −0.111007 | ||||||||
\(786\) | 16.6483 | 0.593826 | ||||||||
\(787\) | −42.9391 | −1.53061 | −0.765307 | − | 0.643666i | \(-0.777413\pi\) | ||||
−0.765307 | + | 0.643666i | \(0.777413\pi\) | |||||||
\(788\) | 59.7493 | 2.12848 | ||||||||
\(789\) | −11.3465 | −0.403946 | ||||||||
\(790\) | − | 37.2866i | − | 1.32660i | ||||||
\(791\) | −3.71113 | + | 32.2966i | −0.131952 | + | 1.14834i | ||||
\(792\) | 2.93048i | 0.104130i | ||||||||
\(793\) | − | 16.2995i | − | 0.578812i | ||||||
\(794\) | 26.8929i | 0.954392i | ||||||||
\(795\) | 21.1344 | 0.749558 | ||||||||
\(796\) | 58.2401 | 2.06427 | ||||||||
\(797\) | 13.6729 | 0.484320 | 0.242160 | − | 0.970236i | \(-0.422144\pi\) | ||||
0.242160 | + | 0.970236i | \(0.422144\pi\) | |||||||
\(798\) | 4.02792 | − | 35.0536i | 0.142587 | − | 1.24088i | ||||
\(799\) | 2.51847i | 0.0890969i | ||||||||
\(800\) | −8.31528 | −0.293990 | ||||||||
\(801\) | 0.0511154 | 0.00180607 | ||||||||
\(802\) | 20.1642i | 0.712024i | ||||||||
\(803\) | −2.71428 | −0.0957847 | ||||||||
\(804\) | −24.0662 | −0.848751 | ||||||||
\(805\) | −24.0286 | − | 7.74621i | −0.846898 | − | 0.273018i | ||||
\(806\) | −63.9644 | −2.25305 | ||||||||
\(807\) | −8.79588 | −0.309629 | ||||||||
\(808\) | 12.7500i | 0.448544i | ||||||||
\(809\) | −3.49924 | −0.123027 | −0.0615134 | − | 0.998106i | \(-0.519593\pi\) | ||||
−0.0615134 | + | 0.998106i | \(0.519593\pi\) | |||||||
\(810\) | 4.20801 | 0.147855 | ||||||||
\(811\) | − | 12.6266i | − | 0.443381i | −0.975117 | − | 0.221691i | \(-0.928843\pi\) | ||
0.975117 | − | 0.221691i | \(-0.0711575\pi\) | |||||||
\(812\) | −16.8196 | − | 1.93270i | −0.590253 | − | 0.0678246i | ||||
\(813\) | 32.1142 | 1.12629 | ||||||||
\(814\) | 41.4853 | 1.45406 | ||||||||
\(815\) | 5.06697 | 0.177488 | ||||||||
\(816\) | − | 1.25923i | − | 0.0440820i | ||||||
\(817\) | 79.8488i | 2.79355i | ||||||||
\(818\) | 12.2445i | 0.428120i | ||||||||
\(819\) | −1.43675 | + | 12.5035i | −0.0502040 | + | 0.436908i | ||||
\(820\) | 52.0936i | 1.81919i | ||||||||
\(821\) | −21.9038 | −0.764449 | −0.382224 | − | 0.924070i | \(-0.624842\pi\) | ||||
−0.382224 | + | 0.924070i | \(0.624842\pi\) | |||||||
\(822\) | −37.6698 | −1.31388 | ||||||||
\(823\) | 6.07306 | 0.211694 | 0.105847 | − | 0.994382i | \(-0.466245\pi\) | ||||
0.105847 | + | 0.994382i | \(0.466245\pi\) | |||||||
\(824\) | −6.46503 | −0.225220 | ||||||||
\(825\) | 3.05101 | 0.106223 | ||||||||
\(826\) | 4.08749 | − | 35.5720i | 0.142222 | − | 1.23771i | ||||
\(827\) | 18.4339i | 0.641009i | 0.947247 | + | 0.320505i | \(0.103852\pi\) | ||||
−0.947247 | + | 0.320505i | \(0.896148\pi\) | |||||||
\(828\) | −11.6289 | − | 2.32643i | −0.404131 | − | 0.0808489i | ||||
\(829\) | − | 39.9666i | − | 1.38810i | −0.719928 | − | 0.694049i | \(-0.755825\pi\) | ||
0.719928 | − | 0.694049i | \(-0.244175\pi\) | |||||||
\(830\) | 20.2493 | 0.702862 | ||||||||
\(831\) | − | 1.39058i | − | 0.0482386i | ||||||
\(832\) | 53.4200i | 1.85201i | ||||||||
\(833\) | 3.03272 | + | 0.706289i | 0.105077 | + | 0.0244715i | ||||
\(834\) | −3.15604 | −0.109285 | ||||||||
\(835\) | 6.11587i | 0.211648i | ||||||||
\(836\) | 45.6957i | 1.58042i | ||||||||
\(837\) | 6.35793 | 0.219762 | ||||||||
\(838\) | −8.49786 | −0.293554 | ||||||||
\(839\) | 33.0863 | 1.14227 | 0.571133 | − | 0.820857i | \(-0.306504\pi\) | ||||
0.571133 | + | 0.820857i | \(0.306504\pi\) | |||||||
\(840\) | −0.600945 | + | 5.22982i | −0.0207346 | + | 0.180446i | ||||
\(841\) | −22.3036 | −0.769089 | ||||||||
\(842\) | 25.0457i | 0.863133i | ||||||||
\(843\) | 17.4361 | 0.600532 | ||||||||
\(844\) | −4.69417 | −0.161580 | ||||||||
\(845\) | 19.1585 | 0.659072 | ||||||||
\(846\) | 11.9736i | 0.411661i | ||||||||
\(847\) | 6.34051 | + | 0.728573i | 0.217863 | + | 0.0250341i | ||||
\(848\) | − | 30.0681i | − | 1.03254i | ||||||
\(849\) | 18.3645i | 0.630267i | ||||||||
\(850\) | 0.979487 | 0.0335961 | ||||||||
\(851\) | −6.29735 | + | 31.4779i | −0.215870 | + | 1.07905i | ||||
\(852\) | 21.6546i | 0.741873i | ||||||||
\(853\) | 47.9861i | 1.64301i | 0.570200 | + | 0.821506i | \(0.306866\pi\) | ||||
−0.570200 | + | 0.821506i | \(0.693134\pi\) | |||||||
\(854\) | −19.0474 | − | 2.18869i | −0.651788 | − | 0.0748953i | ||||
\(855\) | 12.5466 | 0.429085 | ||||||||
\(856\) | 13.0506i | 0.446060i | ||||||||
\(857\) | − | 29.4487i | − | 1.00595i | −0.864302 | − | 0.502974i | \(-0.832239\pi\) | ||
0.864302 | − | 0.502974i | \(-0.167761\pi\) | |||||||
\(858\) | − | 29.4824i | − | 1.00651i | ||||||
\(859\) | − | 22.4721i | − | 0.766739i | −0.923595 | − | 0.383369i | \(-0.874764\pi\) | ||
0.923595 | − | 0.383369i | \(-0.125236\pi\) | |||||||
\(860\) | − | 62.3029i | − | 2.12451i | ||||||
\(861\) | 27.8294 | + | 3.19781i | 0.948424 | + | 0.108981i | ||||
\(862\) | 56.8282i | 1.93558i | ||||||||
\(863\) | 22.4332 | 0.763636 | 0.381818 | − | 0.924238i | \(-0.375298\pi\) | ||||
0.381818 | + | 0.924238i | \(0.375298\pi\) | |||||||
\(864\) | − | 7.98680i | − | 0.271716i | ||||||
\(865\) | − | 12.4341i | − | 0.422772i | ||||||
\(866\) | −7.95877 | −0.270450 | ||||||||
\(867\) | − | 16.8021i | − | 0.570630i | ||||||
\(868\) | −4.74853 | + | 41.3248i | −0.161176 | + | 1.40266i | ||||
\(869\) | 25.9666 | 0.880858 | ||||||||
\(870\) | − | 10.8893i | − | 0.369180i | ||||||
\(871\) | 46.2961 | 1.56868 | ||||||||
\(872\) | 9.80166i | 0.331926i | ||||||||
\(873\) | 17.4237 | 0.589703 | ||||||||
\(874\) | −62.7155 | − | 12.5466i | −2.12138 | − | 0.424396i | ||||
\(875\) | 31.5940 | + | 3.63039i | 1.06807 | + | 0.122729i | ||||
\(876\) | −2.29039 | −0.0773851 | ||||||||
\(877\) | −28.8929 | −0.975642 | −0.487821 | − | 0.872944i | \(-0.662208\pi\) | ||||
−0.487821 | + | 0.872944i | \(0.662208\pi\) | |||||||
\(878\) | 84.9201i | 2.86591i | ||||||||
\(879\) | 1.70995i | 0.0576750i | ||||||||
\(880\) | 16.5055i | 0.556400i | ||||||||
\(881\) | −47.0960 | −1.58670 | −0.793352 | − | 0.608763i | \(-0.791666\pi\) | ||||
−0.793352 | + | 0.608763i | \(0.791666\pi\) | |||||||
\(882\) | 14.4185 | + | 3.35793i | 0.485496 | + | 0.113067i | ||||
\(883\) | 24.0147 | 0.808160 | 0.404080 | − | 0.914724i | \(-0.367592\pi\) | ||||
0.404080 | + | 0.914724i | \(0.367592\pi\) | |||||||
\(884\) | − | 5.23274i | − | 0.175996i | ||||||
\(885\) | 12.7321 | 0.427986 | ||||||||
\(886\) | −47.5823 | −1.59856 | ||||||||
\(887\) | 34.6872i | 1.16468i | 0.812944 | + | 0.582341i | \(0.197863\pi\) | ||||
−0.812944 | + | 0.582341i | \(0.802137\pi\) | |||||||
\(888\) | 6.69366 | 0.224624 | ||||||||
\(889\) | −10.0179 | − | 1.15113i | −0.335988 | − | 0.0386076i | ||||
\(890\) | −0.215094 | −0.00720997 | ||||||||
\(891\) | 2.93048i | 0.0981749i | ||||||||
\(892\) | 12.8517i | 0.430308i | ||||||||
\(893\) | 35.7005i | 1.19467i | ||||||||
\(894\) | 8.77903 | 0.293615 | ||||||||
\(895\) | 37.1431 | 1.24156 | ||||||||
\(896\) | 20.4400 | + | 2.34871i | 0.682852 | + | 0.0784649i | ||||
\(897\) | 22.3704 | + | 4.47534i | 0.746926 | + | 0.149427i | ||||
\(898\) | −27.6810 | −0.923726 | ||||||||
\(899\) | − | 16.4527i | − | 0.548727i | ||||||
\(900\) | 2.57454 | 0.0858179 | ||||||||
\(901\) | 4.72505i | 0.157414i | ||||||||
\(902\) | −65.6197 | −2.18490 | ||||||||
\(903\) | −33.2834 | − | 3.82452i | −1.10760 | − | 0.127272i | ||||
\(904\) | − | 12.2873i | − | 0.408670i | ||||||
\(905\) | −33.6040 | −1.11703 | ||||||||
\(906\) | 8.63360i | 0.286832i | ||||||||
\(907\) | 0.667596i | 0.0221672i | 0.999939 | + | 0.0110836i | \(0.00352809\pi\) | ||||
−0.999939 | + | 0.0110836i | \(0.996472\pi\) | |||||||
\(908\) | −2.54851 | −0.0845752 | ||||||||
\(909\) | 12.7500i | 0.422891i | ||||||||
\(910\) | 6.04585 | − | 52.6149i | 0.200418 | − | 1.74417i | ||||
\(911\) | 21.5623i | 0.714391i | 0.934030 | + | 0.357195i | \(0.116267\pi\) | ||||
−0.934030 | + | 0.357195i | \(0.883733\pi\) | |||||||
\(912\) | − | 17.8502i | − | 0.591080i | ||||||
\(913\) | 14.1017i | 0.466698i | ||||||||
\(914\) | 54.8510i | 1.81431i | ||||||||
\(915\) | − | 6.81756i | − | 0.225381i | ||||||
\(916\) | −31.8782 | −1.05329 | ||||||||
\(917\) | −2.37754 | + | 20.6909i | −0.0785133 | + | 0.683274i | ||||
\(918\) | 0.940794i | 0.0310508i | ||||||||
\(919\) | 53.4346i | 1.76265i | 0.472515 | + | 0.881323i | \(0.343346\pi\) | ||||
−0.472515 | + | 0.881323i | \(0.656654\pi\) | |||||||
\(920\) | 9.35682 | + | 1.87189i | 0.308485 | + | 0.0617143i | ||||
\(921\) | 5.34696 | 0.176188 | ||||||||
\(922\) | 40.6825i | 1.33981i | ||||||||
\(923\) | − | 41.6568i | − | 1.37115i | ||||||
\(924\) | −19.0474 | − | 2.18869i | −0.626613 | − | 0.0720025i | ||||
\(925\) | − | 6.96896i | − | 0.229138i | ||||||
\(926\) | 50.0272 | 1.64400 | ||||||||
\(927\) | −6.46503 | −0.212339 | ||||||||
\(928\) | −20.6678 | −0.678453 | ||||||||
\(929\) | 10.3602i | 0.339906i | 0.985452 | + | 0.169953i | \(0.0543616\pi\) | ||||
−0.985452 | + | 0.169953i | \(0.945638\pi\) | |||||||
\(930\) | −26.7542 | −0.877306 | ||||||||
\(931\) | 42.9902 | + | 10.0120i | 1.40895 | + | 0.328130i | ||||
\(932\) | 54.8517 | 1.79673 | ||||||||
\(933\) | −1.72906 | −0.0566068 | ||||||||
\(934\) | 78.9822 | 2.58438 | ||||||||
\(935\) | − | 2.59375i | − | 0.0848247i | ||||||
\(936\) | − | 4.75698i | − | 0.155487i | ||||||
\(937\) | 45.0880 | 1.47296 | 0.736480 | − | 0.676459i | \(-0.236486\pi\) | ||||
0.736480 | + | 0.676459i | \(0.236486\pi\) | |||||||
\(938\) | 6.21661 | − | 54.1010i | 0.202980 | − | 1.76646i | ||||
\(939\) | 5.54253i | 0.180874i | ||||||||
\(940\) | − | 27.8557i | − | 0.908552i | ||||||
\(941\) | −9.15891 | −0.298572 | −0.149286 | − | 0.988794i | \(-0.547697\pi\) | ||||
−0.149286 | + | 0.988794i | \(0.547697\pi\) | |||||||
\(942\) | − | 3.30591i | − | 0.107712i | ||||||
\(943\) | 9.96088 | − | 49.7904i | 0.324371 | − | 1.62140i | ||||
\(944\) | − | 18.1142i | − | 0.589567i | ||||||
\(945\) | −0.600945 | + | 5.22982i | −0.0195487 | + | 0.170126i | ||||
\(946\) | 78.4799 | 2.55160 | ||||||||
\(947\) | 5.97359 | 0.194116 | 0.0970578 | − | 0.995279i | \(-0.469057\pi\) | ||||
0.0970578 | + | 0.995279i | \(0.469057\pi\) | |||||||
\(948\) | 21.9114 | 0.711651 | ||||||||
\(949\) | 4.40602 | 0.143025 | ||||||||
\(950\) | 13.8847 | 0.450479 | ||||||||
\(951\) | − | 8.88509i | − | 0.288119i | ||||||
\(952\) | −1.16924 | − | 0.134354i | −0.0378953 | − | 0.00435445i | ||||
\(953\) | − | 46.3268i | − | 1.50067i | −0.661056 | − | 0.750337i | \(-0.729891\pi\) | ||
0.661056 | − | 0.750337i | \(-0.270109\pi\) | |||||||
\(954\) | 22.4644i | 0.727312i | ||||||||
\(955\) | − | 11.0279i | − | 0.356855i | ||||||
\(956\) | 34.8656 | 1.12764 | ||||||||
\(957\) | 7.58334 | 0.245134 | ||||||||
\(958\) | 50.2120 | 1.62227 | ||||||||
\(959\) | 5.37961 | − | 46.8168i | 0.173717 | − | 1.51179i | ||||
\(960\) | 22.3439i | 0.721145i | ||||||||
\(961\) | −9.42323 | −0.303975 | ||||||||
\(962\) | −67.3421 | −2.17120 | ||||||||
\(963\) | 13.0506i | 0.420549i | ||||||||
\(964\) | −39.5638 | −1.27426 | ||||||||
\(965\) | 17.7466 | 0.571282 | ||||||||
\(966\) | 8.23370 | − | 25.5408i | 0.264915 | − | 0.821762i | ||||
\(967\) | 24.3774 | 0.783923 | 0.391962 | − | 0.919982i | \(-0.371797\pi\) | ||||
0.391962 | + | 0.919982i | \(0.371797\pi\) | |||||||
\(968\) | −2.41226 | −0.0775329 | ||||||||
\(969\) | 2.80507i | 0.0901118i | ||||||||
\(970\) | −73.3191 | −2.35413 | ||||||||
\(971\) | −6.12032 | −0.196410 | −0.0982052 | − | 0.995166i | \(-0.531310\pi\) | ||||
−0.0982052 | + | 0.995166i | \(0.531310\pi\) | |||||||
\(972\) | 2.47283i | 0.0793162i | ||||||||
\(973\) | 0.450713 | − | 3.92239i | 0.0144492 | − | 0.125746i | ||||
\(974\) | −72.3782 | −2.31915 | ||||||||
\(975\) | −4.95263 | −0.158611 | ||||||||
\(976\) | −9.69943 | −0.310471 | ||||||||
\(977\) | − | 40.3636i | − | 1.29135i | −0.763614 | − | 0.645674i | \(-0.776577\pi\) | ||
0.763614 | − | 0.645674i | \(-0.223423\pi\) | |||||||
\(978\) | 5.38585i | 0.172221i | ||||||||
\(979\) | − | 0.149793i | − | 0.00478740i | ||||||
\(980\) | −33.5436 | − | 7.81197i | −1.07151 | − | 0.249544i | ||||
\(981\) | 9.80166i | 0.312943i | ||||||||
\(982\) | 9.11491 | 0.290868 | ||||||||
\(983\) | −24.8112 | −0.791355 | −0.395677 | − | 0.918390i | \(-0.629490\pi\) | ||||
−0.395677 | + | 0.918390i | \(0.629490\pi\) | |||||||
\(984\) | −10.5877 | −0.337525 | ||||||||
\(985\) | −48.0755 | −1.53181 | ||||||||
\(986\) | 2.43453 | 0.0775312 | ||||||||
\(987\) | −14.8811 | − | 1.70995i | −0.473669 | − | 0.0544282i | ||||
\(988\) | − | 74.1766i | − | 2.35987i | ||||||
\(989\) | −11.9130 | + | 59.5484i | −0.378812 | + | 1.89353i | ||||
\(990\) | − | 12.3315i | − | 0.391921i | ||||||
\(991\) | 39.5412 | 1.25607 | 0.628033 | − | 0.778186i | \(-0.283860\pi\) | ||||
0.628033 | + | 0.778186i | \(0.283860\pi\) | |||||||
\(992\) | 50.7795i | 1.61225i | ||||||||
\(993\) | − | 15.1491i | − | 0.480741i | ||||||
\(994\) | −48.6795 | − | 5.59365i | −1.54402 | − | 0.177420i | ||||
\(995\) | −46.8612 | −1.48560 | ||||||||
\(996\) | 11.8995i | 0.377049i | ||||||||
\(997\) | − | 27.8021i | − | 0.880502i | −0.897875 | − | 0.440251i | \(-0.854889\pi\) | ||
0.897875 | − | 0.440251i | \(-0.145111\pi\) | |||||||
\(998\) | −64.6033 | −2.04498 | ||||||||
\(999\) | 6.69366 | 0.211778 |
(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 | 483.2.h.b.160.3 | yes | 12 | |
3.2 | odd | 2 | 1449.2.h.h.1126.12 | 12 | |||
7.6 | odd | 2 | inner | 483.2.h.b.160.2 | yes | 12 | |
21.20 | even | 2 | 1449.2.h.h.1126.10 | 12 | |||
23.22 | odd | 2 | inner | 483.2.h.b.160.4 | yes | 12 | |
69.68 | even | 2 | 1449.2.h.h.1126.9 | 12 | |||
161.160 | even | 2 | inner | 483.2.h.b.160.1 | ✓ | 12 | |
483.482 | odd | 2 | 1449.2.h.h.1126.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.h.b.160.1 | ✓ | 12 | 161.160 | even | 2 | inner | |
483.2.h.b.160.2 | yes | 12 | 7.6 | odd | 2 | inner | |
483.2.h.b.160.3 | yes | 12 | 1.1 | even | 1 | trivial | |
483.2.h.b.160.4 | yes | 12 | 23.22 | odd | 2 | inner | |
1449.2.h.h.1126.9 | 12 | 69.68 | even | 2 | |||
1449.2.h.h.1126.10 | 12 | 21.20 | even | 2 | |||
1449.2.h.h.1126.11 | 12 | 483.482 | odd | 2 | |||
1449.2.h.h.1126.12 | 12 | 3.2 | odd | 2 |