Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(191,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.h (of order \(2\), degree \(1\), not 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: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 480) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.191 |
Dual form | 960.2.h.b.191.2 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70711 | − | 0.292893i | −0.985599 | − | 0.169102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.585786i | 0.221406i | 0.993854 | + | 0.110703i | \(0.0353103\pi\) | ||||
−0.993854 | + | 0.110703i | \(0.964690\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | + | 1.00000i | 0.942809 | + | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.82843 | −0.852803 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.292893 | + | 1.70711i | −0.0756247 | + | 0.440773i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.65685i | 0.886917i | 0.896295 | + | 0.443459i | \(0.146249\pi\) | ||||
−0.896295 | + | 0.443459i | \(0.853751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843i | 0.648886i | 0.945905 | + | 0.324443i | \(0.105177\pi\) | ||||
−0.945905 | + | 0.324443i | \(0.894823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.171573 | − | 1.00000i | 0.0374403 | − | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.58579 | 0.956203 | 0.478101 | − | 0.878305i | \(-0.341325\pi\) | ||||
0.478101 | + | 0.878305i | \(0.341325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.53553 | − | 2.53553i | −0.872864 | − | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.00000i | − | 1.48556i | −0.669534 | − | 0.742781i | \(-0.733506\pi\) | ||
0.669534 | − | 0.742781i | \(-0.266494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.65685i | − | 1.01600i | −0.861357 | − | 0.508001i | \(-0.830385\pi\) | ||
0.861357 | − | 0.508001i | \(-0.169615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.82843 | + | 0.828427i | 0.840521 | + | 0.144211i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.585786 | 0.0990160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.6569 | 1.91638 | 0.958188 | − | 0.286141i | \(-0.0923726\pi\) | ||||
0.958188 | + | 0.286141i | \(0.0923726\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.41421 | − | 0.585786i | −0.546712 | − | 0.0938009i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.00000i | − | 0.312348i | −0.987730 | − | 0.156174i | \(-0.950084\pi\) | ||
0.987730 | − | 0.156174i | \(-0.0499160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8995i | 1.81466i | 0.420424 | + | 0.907328i | \(0.361882\pi\) | ||||
−0.420424 | + | 0.907328i | \(0.638118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | − | 2.82843i | 0.149071 | − | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.24264 | 0.327123 | 0.163561 | − | 0.986533i | \(-0.447702\pi\) | ||||
0.163561 | + | 0.986533i | \(0.447702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65685 | 0.950979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.07107 | − | 6.24264i | 0.149979 | − | 0.874145i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.65685i | 1.05175i | 0.850562 | + | 0.525875i | \(0.176262\pi\) | ||||
−0.850562 | + | 0.525875i | \(0.823738\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.82843i | 0.381385i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.828427 | − | 4.82843i | 0.109728 | − | 0.639541i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.65685 | 1.25722 | 0.628608 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.65685 | 0.724286 | 0.362143 | − | 0.932123i | \(-0.382045\pi\) | ||||
0.362143 | + | 0.932123i | \(0.382045\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.585786 | + | 1.65685i | −0.0738022 | + | 0.208744i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.00000i | − | 0.248069i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.0711i | − | 1.59689i | −0.602071 | − | 0.798443i | \(-0.705658\pi\) | ||
0.602071 | − | 0.798443i | \(-0.294342\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.82843 | − | 1.34315i | −0.942432 | − | 0.161696i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.82843 | 0.810385 | 0.405193 | − | 0.914231i | \(-0.367204\pi\) | ||||
0.405193 | + | 0.914231i | \(0.367204\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.34315 | 0.508327 | 0.254163 | − | 0.967161i | \(-0.418200\pi\) | ||||
0.254163 | + | 0.967161i | \(0.418200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.70711 | + | 0.292893i | 0.197120 | + | 0.0338204i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.65685i | − | 0.188816i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.4853i | − | 1.40470i | −0.711830 | − | 0.702352i | \(-0.752133\pi\) | ||
0.711830 | − | 0.702352i | \(-0.247867\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.07107 | 0.995679 | 0.497840 | − | 0.867269i | \(-0.334127\pi\) | ||||
0.497840 | + | 0.867269i | \(0.334127\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65685 | 0.396642 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.34315 | + | 13.6569i | −0.251212 | + | 1.46417i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.3137i | − | 1.62325i | −0.584179 | − | 0.811625i | \(-0.698583\pi\) | ||
0.584179 | − | 0.811625i | \(-0.301417\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.17157i | 0.122814i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.65685 | + | 9.65685i | −0.171808 | + | 1.00137i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.82843 | 0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.9706 | −1.52003 | −0.760015 | − | 0.649905i | \(-0.774809\pi\) | ||||
−0.760015 | + | 0.649905i | \(0.774809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.00000 | − | 2.82843i | −0.804030 | − | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.3137i | 1.52377i | 0.647712 | + | 0.761885i | \(0.275726\pi\) | ||||
−0.647712 | + | 0.761885i | \(0.724274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.24264i | 0.615106i | 0.951531 | + | 0.307553i | \(0.0995101\pi\) | ||||
−0.951531 | + | 0.307553i | \(0.900490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | − | 0.171573i | −0.0975900 | − | 0.0167438i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.5858 | 1.21671 | 0.608357 | − | 0.793664i | \(-0.291829\pi\) | ||||
0.608357 | + | 0.793664i | \(0.291829\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.34315 | −0.607563 | −0.303782 | − | 0.952742i | \(-0.598249\pi\) | ||||
−0.303782 | + | 0.952742i | \(0.598249\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.8995 | − | 3.41421i | −1.88878 | − | 0.324063i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000i | 0.940721i | 0.882474 | + | 0.470360i | \(0.155876\pi\) | ||||
−0.882474 | + | 0.470360i | \(0.844124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.58579i | − | 0.427627i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.65685 | + | 2.00000i | 0.522976 | + | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.14214 | −0.196369 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.585786 | + | 3.41421i | −0.0528186 | + | 0.307849i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.92893i | − | 0.259901i | −0.991521 | − | 0.129950i | \(-0.958518\pi\) | ||
0.991521 | − | 0.129950i | \(-0.0414818\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.48528 | − | 20.3137i | 0.306862 | − | 1.78852i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.17157 | 0.451842 | 0.225921 | − | 0.974146i | \(-0.427461\pi\) | ||||
0.225921 | + | 0.974146i | \(0.427461\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.65685 | −0.143667 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.53553 | + | 4.53553i | −0.218224 | + | 0.390357i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.31371i | 0.453981i | 0.973897 | + | 0.226990i | \(0.0728886\pi\) | ||||
−0.973897 | + | 0.226990i | \(0.927111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.8284i | 1.59701i | 0.601991 | + | 0.798503i | \(0.294374\pi\) | ||||
−0.601991 | + | 0.798503i | \(0.705626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.82843 | − | 0.656854i | −0.322412 | − | 0.0553171i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.3640 | − | 1.94975i | −0.937284 | − | 0.160812i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.31371i | − | 0.763009i | −0.924367 | − | 0.381504i | \(-0.875406\pi\) | ||
0.924367 | − | 0.381504i | \(-0.124594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.65685 | + | 10.3431i | −0.295639 | + | 0.836194i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.65685 | −0.454369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.65685 | −0.291849 | −0.145924 | − | 0.989296i | \(-0.546616\pi\) | ||||
−0.145924 | + | 0.989296i | \(0.546616\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.24264 | − | 13.0711i | 0.177853 | − | 1.03660i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.68629i | 0.211709i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.75736i | 0.137647i | 0.997629 | + | 0.0688235i | \(0.0219245\pi\) | ||||
−0.997629 | + | 0.0688235i | \(0.978075\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.828427 | − | 4.82843i | 0.0644930 | − | 0.375893i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.72792 | −0.520622 | −0.260311 | − | 0.965525i | \(-0.583825\pi\) | ||||
−0.260311 | + | 0.965525i | \(0.583825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | + | 8.00000i | −0.216295 | + | 0.611775i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000i | 0.152057i | 0.997106 | + | 0.0760286i | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.585786i | − | 0.0442813i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.4853 | − | 2.82843i | −1.23911 | − | 0.212598i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.34315 | −0.474109 | −0.237054 | − | 0.971496i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971496i | \(0.576182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.3137 | −0.989600 | −0.494800 | − | 0.869007i | \(-0.664759\pi\) | ||||
−0.494800 | + | 0.869007i | \(0.664759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.65685 | − | 1.65685i | −0.713855 | − | 0.122478i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 11.6569i | − | 0.857029i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10.3431i | − | 0.756366i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.48528 | − | 2.65685i | 0.108038 | − | 0.193258i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1421 | 0.733859 | 0.366930 | − | 0.930249i | \(-0.380409\pi\) | ||||
0.366930 | + | 0.930249i | \(0.380409\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.65685 | 0.263226 | 0.131613 | − | 0.991301i | \(-0.457984\pi\) | ||||
0.131613 | + | 0.991301i | \(0.457984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.585786 | + | 3.41421i | −0.0419490 | + | 0.244497i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.9706i | − | 0.781620i | −0.920471 | − | 0.390810i | \(-0.872195\pi\) | ||
0.920471 | − | 0.390810i | \(-0.127805\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.1716i | 1.21726i | 0.793454 | + | 0.608630i | \(0.208281\pi\) | ||||
−0.793454 | + | 0.608630i | \(0.791719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.82843 | + | 22.3137i | −0.270036 | + | 1.57389i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.68629 | 0.328913 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.9706 | + | 4.58579i | 0.901516 | + | 0.318734i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.00000i | − | 0.553372i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.0000i | − | 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.6569 | − | 2.00000i | −0.798714 | − | 0.137038i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.8995 | 0.811539 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.31371 | 0.224949 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.41421 | − | 1.27208i | −0.501006 | − | 0.0859591i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.31371i | 0.491973i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.8995i | − | 0.796849i | −0.917201 | − | 0.398425i | \(-0.869557\pi\) | ||
0.917201 | − | 0.398425i | \(-0.130443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.82843 | − | 1.00000i | −0.188562 | − | 0.0666667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.58579 | −0.304369 | −0.152185 | − | 0.988352i | \(-0.548631\pi\) | ||||
−0.152185 | + | 0.988352i | \(0.548631\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.3137 | −1.67278 | −0.836388 | − | 0.548137i | \(-0.815337\pi\) | ||||
−0.836388 | + | 0.548137i | \(0.815337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.485281 | + | 2.82843i | −0.0319292 | + | 0.186097i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.9706i | 1.76690i | 0.468525 | + | 0.883450i | \(0.344786\pi\) | ||||
−0.468525 | + | 0.883450i | \(0.655214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.24264i | − | 0.146294i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.65685 | + | 21.3137i | −0.237538 | + | 1.38447i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6569 | 0.883388 | 0.441694 | − | 0.897166i | \(-0.354378\pi\) | ||||
0.441694 | + | 0.897166i | \(0.354378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.65685 | −0.106727 | −0.0533637 | − | 0.998575i | \(-0.516994\pi\) | ||||
−0.0533637 | + | 0.998575i | \(0.516994\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.2929 | − | 11.7071i | −0.660289 | − | 0.751011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.65685i | − | 0.425291i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.65685i | 0.359937i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.4853 | − | 2.65685i | −0.981340 | − | 0.168371i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.4853 | −1.04054 | −0.520271 | − | 0.854001i | \(-0.674169\pi\) | ||||
−0.520271 | + | 0.854001i | \(0.674169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.9706 | −0.815452 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.24264 | − | 1.07107i | −0.390929 | − | 0.0670729i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.0000i | 1.37232i | 0.727450 | + | 0.686161i | \(0.240706\pi\) | ||||
−0.727450 | + | 0.686161i | \(0.759294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.82843i | 0.424298i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | − | 22.6274i | 0.495188 | − | 1.40060i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.89949 | 0.487104 | 0.243552 | − | 0.969888i | \(-0.421687\pi\) | ||||
0.243552 | + | 0.969888i | \(0.421687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.65685 | 0.470357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.48528 | + | 26.1421i | −0.274495 | + | 1.59987i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 18.0000i | − | 1.09748i | −0.835993 | − | 0.548740i | \(-0.815108\pi\) | ||
0.835993 | − | 0.548740i | \(-0.184892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6569i | 0.829595i | 0.909914 | + | 0.414797i | \(0.136148\pi\) | ||||
−0.909914 | + | 0.414797i | \(0.863852\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.343146 | − | 2.00000i | 0.0207681 | − | 0.121046i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.82843 | 0.170561 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.343146 | −0.0206176 | −0.0103088 | − | 0.999947i | \(-0.503281\pi\) | ||||
−0.0103088 | + | 0.999947i | \(0.503281\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.65685 | − | 16.0000i | 0.338667 | − | 0.957895i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.31371i | − | 0.555609i | −0.960638 | − | 0.277805i | \(-0.910393\pi\) | ||
0.960638 | − | 0.277805i | \(-0.0896068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 17.5563i | − | 1.04362i | −0.853063 | − | 0.521808i | \(-0.825258\pi\) | ||
0.853063 | − | 0.521808i | \(-0.174742\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.82843 | − | 0.828427i | −0.286011 | − | 0.0490718i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.17157 | 0.0691558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.62742 | 0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.5563 | + | 4.38478i | 1.49814 | + | 0.257040i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.0000i | 1.28525i | 0.766179 | + | 0.642627i | \(0.222155\pi\) | ||||
−0.766179 | + | 0.642627i | \(0.777845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.65685i | − | 0.562244i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.8284 | + | 7.17157i | 0.744381 | + | 0.416137i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.17157 | 0.530406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.97056 | −0.401777 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.48528 | − | 26.1421i | 0.257673 | − | 1.50183i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.65685i | − | 0.323911i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.8995i | − | 0.679140i | −0.940581 | − | 0.339570i | \(-0.889718\pi\) | ||
0.940581 | − | 0.339570i | \(-0.110282\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.82843 | − | 10.6569i | 0.104016 | − | 0.606247i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.4853 | 1.61525 | 0.807626 | − | 0.589695i | \(-0.200752\pi\) | ||||
0.807626 | + | 0.589695i | \(0.200752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.31371 | −0.300349 | −0.150174 | − | 0.988660i | \(-0.547983\pi\) | ||||
−0.150174 | + | 0.988660i | \(0.547983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.65685 | + | 0.585786i | 0.0933532 | + | 0.0330053i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 11.6569i | − | 0.654714i | −0.944901 | − | 0.327357i | \(-0.893842\pi\) | ||
0.944901 | − | 0.327357i | \(-0.106158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.6274i | 1.26689i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.4853 | − | 3.68629i | −1.19919 | − | 0.205749i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3431 | −0.575508 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.8284 | + | 1.85786i | 0.598813 | + | 0.102740i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.31371i | 0.0724271i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.3137i | 1.72116i | 0.509318 | + | 0.860579i | \(0.329898\pi\) | ||||
−0.509318 | + | 0.860579i | \(0.670102\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.9706 | + | 11.6569i | 1.80678 | + | 0.638792i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.0711 | −0.714149 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.3137 | 0.725244 | 0.362622 | − | 0.931936i | \(-0.381882\pi\) | ||||
0.362622 | + | 0.931936i | \(0.381882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.92893 | − | 17.0711i | 0.159078 | − | 0.927173i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.34315 | + | 7.82843i | −0.0723125 | + | 0.421468i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.6985 | 1.70166 | 0.850832 | − | 0.525438i | \(-0.176099\pi\) | ||||
0.850832 | + | 0.525438i | \(0.176099\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.6274 | 1.53239 | 0.766195 | − | 0.642608i | \(-0.222148\pi\) | ||||
0.766195 | + | 0.642608i | \(0.222148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.07107 | − | 5.07107i | −0.484178 | − | 0.270674i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 6.82843i | − | 0.362415i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.65685 | + | 0.627417i | 0.193541 | + | 0.0332064i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.3431 | −0.968114 | −0.484057 | − | 0.875036i | \(-0.660837\pi\) | ||||
−0.484057 | + | 0.875036i | \(0.660837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.12132 | + | 0.878680i | 0.268800 | + | 0.0461187i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.34315i | − | 0.227331i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 29.0711i | − | 1.51750i | −0.651383 | − | 0.758749i | \(-0.725811\pi\) | ||
0.651383 | − | 0.758749i | \(-0.274189\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | − | 5.65685i | 0.104116 | − | 0.294484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.48528 | −0.232864 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.34315 | 0.431992 | 0.215996 | − | 0.976394i | \(-0.430700\pi\) | ||||
0.215996 | + | 0.976394i | \(0.430700\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.292893 | − | 1.70711i | 0.0151249 | − | 0.0881546i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16.0000i | − | 0.824042i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.1421i | − | 0.726433i | −0.931705 | − | 0.363216i | \(-0.881679\pi\) | ||
0.931705 | − | 0.363216i | \(-0.118321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.857864 | + | 5.00000i | −0.0439497 | + | 0.256158i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.41421 | 0.174458 | 0.0872291 | − | 0.996188i | \(-0.472199\pi\) | ||||
0.0872291 | + | 0.996188i | \(0.472199\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.65685 | −0.0844411 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.8995 | + | 33.6569i | −0.604885 | + | 1.71087i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 13.3137i | − | 0.675032i | −0.941320 | − | 0.337516i | \(-0.890413\pi\) | ||
0.941320 | − | 0.337516i | \(-0.109587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7696i | 0.848073i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.82843 | − | 1.51472i | −0.445335 | − | 0.0764074i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.4853 | −0.628203 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.6274 | −1.23601 | −0.618007 | − | 0.786172i | \(-0.712060\pi\) | ||||
−0.618007 | + | 0.786172i | \(0.712060\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.82843 | + | 0.485281i | 0.141598 | + | 0.0242945i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.00000i | − | 0.399501i | −0.979847 | − | 0.199750i | \(-0.935987\pi\) | ||
0.979847 | − | 0.199750i | \(-0.0640132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11.3137i | − | 0.563576i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.65685 | − | 7.00000i | 0.281091 | − | 0.347833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.9706 | −1.63429 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.65685 | −0.279713 | −0.139857 | − | 0.990172i | \(-0.544664\pi\) | ||||
−0.139857 | + | 0.990172i | \(0.544664\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.55635 | − | 9.07107i | 0.0767690 | − | 0.447443i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.65685i | 0.278356i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9.07107i | − | 0.445281i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.51472 | − | 32.1421i | 0.270057 | − | 1.57401i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.9706 | 0.827095 | 0.413547 | − | 0.910483i | \(-0.364290\pi\) | ||||
0.413547 | + | 0.910483i | \(0.364290\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.34315 | + | 2.24264i | 0.308414 | + | 0.109041i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.65685i | − | 0.177383i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.31371i | 0.160362i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.65685 | + | 1.65685i | 0.466237 | + | 0.0799937i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4853 | −1.37209 | −0.686044 | − | 0.727560i | \(-0.740654\pi\) | ||||
−0.686044 | + | 0.727560i | \(0.740654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.34315 | 0.208718 | 0.104359 | − | 0.994540i | \(-0.466721\pi\) | ||||
0.104359 | + | 0.994540i | \(0.466721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.6569 | + | 2.34315i | 0.654796 | + | 0.112345i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.9706i | 0.620466i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.8284i | 1.08954i | 0.838585 | + | 0.544771i | \(0.183383\pi\) | ||||
−0.838585 | + | 0.544771i | \(0.816617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.8284 | + | 6.65685i | 0.896592 | + | 0.316993i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.1005 | −0.764958 | −0.382479 | − | 0.923964i | \(-0.624930\pi\) | ||||
−0.382479 | + | 0.923964i | \(0.624930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.3137 | −0.725939 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.72792 | + | 15.8995i | −0.129026 | + | 0.752020i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000i | 0.0943858i | 0.998886 | + | 0.0471929i | \(0.0150276\pi\) | ||||
−0.998886 | + | 0.0471929i | \(0.984972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.65685i | 0.266371i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.17157 | 0.0549242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3137 | 0.809901 | 0.404951 | − | 0.914339i | \(-0.367289\pi\) | ||||
0.404951 | + | 0.914339i | \(0.367289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.27208 | − | 16.5858i | 0.432784 | − | 0.774158i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.6274i | 0.867565i | 0.901018 | + | 0.433783i | \(0.142821\pi\) | ||||
−0.901018 | + | 0.433783i | \(0.857179\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.4142i | 1.08815i | 0.839036 | + | 0.544075i | \(0.183119\pi\) | ||||
−0.839036 | + | 0.544075i | \(0.816881\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.65685 | + | 1.65685i | 0.447826 | + | 0.0768348i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.1005 | −0.745043 | −0.372521 | − | 0.928024i | \(-0.621507\pi\) | ||||
−0.372521 | + | 0.928024i | \(0.621507\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.65685 | 0.353561 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.24264 | + | 1.07107i | 0.287646 | + | 0.0493522i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 33.6569i | − | 1.54754i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.82843i | − | 0.129777i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.65685 | + | 21.6569i | −0.350583 | + | 0.991599i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.9706 | −1.50646 | −0.753232 | − | 0.657755i | \(-0.771506\pi\) | ||||
−0.753232 | + | 0.657755i | \(0.771506\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.3137 | 1.06301 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.786797 | − | 4.58579i | 0.0358005 | − | 0.208661i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.9706i | 0.679778i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 27.8995i | − | 1.26425i | −0.774868 | − | 0.632123i | \(-0.782184\pi\) | ||
0.774868 | − | 0.632123i | \(-0.217816\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.514719 | − | 3.00000i | 0.0232764 | − | 0.135665i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.1127 | −1.04306 | −0.521531 | − | 0.853232i | \(-0.674639\pi\) | ||||
−0.521531 | + | 0.853232i | \(0.674639\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.2548 | 1.31757 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.82843 | + | 8.00000i | −0.127128 | + | 0.359573i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000i | 0.179425i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.4558i | − | 0.781431i | −0.920512 | − | 0.390715i | \(-0.872228\pi\) | ||
0.920512 | − | 0.390715i | \(-0.127772\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.4853 | + | 1.97056i | 0.513125 | + | 0.0880383i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.2132 | −1.92678 | −0.963391 | − | 0.268101i | \(-0.913604\pi\) | ||||
−0.963391 | + | 0.268101i | \(0.913604\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.3137 | 0.681451 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.3640 | + | 2.63604i | 0.682337 | + | 0.117071i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 22.6274i | − | 1.00294i | −0.865174 | − | 0.501471i | \(-0.832792\pi\) | ||
0.865174 | − | 0.501471i | \(-0.167208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.54416i | 0.112547i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.17157 | − | 12.8284i | 0.316633 | − | 0.566389i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.24264 | 0.275084 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.34315 | −0.278971 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.585786 | − | 3.41421i | 0.0257132 | − | 0.149867i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16.0000i | − | 0.700973i | −0.936568 | − | 0.350486i | \(-0.886016\pi\) | ||
0.936568 | − | 0.350486i | \(-0.113984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.58579i | 0.375430i | 0.982224 | + | 0.187715i | \(0.0601082\pi\) | ||||
−0.982224 | + | 0.187715i | \(0.939892\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.171573 | + | 1.00000i | −0.00748805 | + | 0.0436436i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.6863 | 0.901109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.97056 | −0.0856766 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.3137 | + | 9.65685i | 1.18531 | + | 0.419072i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.00000i | − | 0.173259i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 12.5858i | − | 0.544131i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.8284 | + | 1.85786i | 0.467281 | + | 0.0801728i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.8284 | −0.810998 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.3137 | 1.60424 | 0.802121 | − | 0.597162i | \(-0.203705\pi\) | ||||
0.802121 | + | 0.597162i | \(0.203705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.7279 | + | 3.89949i | 0.975348 | + | 0.167343i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.34315i | 0.271711i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.0416i | 1.28449i | 0.766501 | + | 0.642244i | \(0.221996\pi\) | ||||
−0.766501 | + | 0.642244i | \(0.778004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.0000 | + | 5.65685i | 0.682863 | + | 0.241429i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.6274 | 0.963960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.31371 | 0.311011 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.41421 | + | 19.8995i | −0.144925 | + | 0.844687i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.0000i | − | 0.762684i | −0.924434 | − | 0.381342i | \(-0.875462\pi\) | ||
0.924434 | − | 0.381342i | \(-0.124538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.7990i | 1.00659i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.02944 | + | 17.6569i | −0.127903 | + | 0.745473i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.55635 | −0.234172 | −0.117086 | − | 0.993122i | \(-0.537355\pi\) | ||||
−0.117086 | + | 0.993122i | \(0.537355\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | 0.420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.31371 | + | 4.10051i | −0.139163 | + | 0.172205i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.6274i | 0.697058i | 0.937298 | + | 0.348529i | \(0.113319\pi\) | ||||
−0.937298 | + | 0.348529i | \(0.886681\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 40.2843i | − | 1.68584i | −0.538036 | − | 0.842922i | \(-0.680833\pi\) | ||
0.538036 | − | 0.842922i | \(-0.319167\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.3137 | − | 2.97056i | −0.723291 | − | 0.124097i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.58579 | −0.191241 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000 | 0.915872 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.24264 | − | 1.07107i | −0.259435 | − | 0.0445121i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.31371i | 0.220450i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 21.6569i | − | 0.896935i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | − | 5.65685i | 0.0826898 | − | 0.233882i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.72792 | 0.277691 | 0.138846 | − | 0.990314i | \(-0.455661\pi\) | ||||
0.138846 | + | 0.990314i | \(0.455661\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.21320 | + | 18.7279i | −0.132174 | + | 0.770364i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.6274i | 0.518546i | 0.965804 | + | 0.259273i | \(0.0834829\pi\) | ||||
−0.965804 | + | 0.259273i | \(0.916517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.14214i | 0.0878190i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.02944 | − | 29.3137i | 0.205841 | − | 1.19973i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.6274 | 0.597660 | 0.298830 | − | 0.954306i | \(-0.403404\pi\) | ||||
0.298830 | + | 0.954306i | \(0.403404\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9706 | −1.18173 | −0.590867 | − | 0.806769i | \(-0.701214\pi\) | ||||
−0.590867 | + | 0.806769i | \(0.701214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.0711 | − | 36.9706i | 0.532295 | − | 1.50556i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.00000i | 0.121967i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.9289i | − | 1.09301i | −0.837455 | − | 0.546506i | \(-0.815958\pi\) | ||
0.837455 | − | 0.546506i | \(-0.184042\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | − | 1.37258i | −0.324176 | − | 0.0556199i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.48528 | 0.181455 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6863 | 0.593174 | 0.296587 | − | 0.955006i | \(-0.404152\pi\) | ||||
0.296587 | + | 0.955006i | \(0.404152\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.41421 | + | 0.585786i | 0.137674 | + | 0.0236212i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.65685i | − | 0.308253i | −0.988051 | − | 0.154127i | \(-0.950744\pi\) | ||
0.988051 | − | 0.154127i | \(-0.0492564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.4558i | 1.34470i | 0.740232 | + | 0.672352i | \(0.234716\pi\) | ||||
−0.740232 | + | 0.672352i | \(0.765284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.7990 | − | 11.6274i | −0.834635 | − | 0.466592i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.97056 | 0.359398 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.34315 | + | 13.6569i | −0.0935762 | + | 0.545402i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.6274i | 1.69967i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.3137i | − | 0.768867i | −0.923153 | − | 0.384433i | \(-0.874397\pi\) | ||
0.923153 | − | 0.384433i | \(-0.125603\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.51472 | + | 20.4853i | −0.139698 | + | 0.814217i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.92893 | −0.116231 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.3137 | 0.527508 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.3137 | + | 6.82843i | 0.764038 | + | 0.270128i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.3137i | 0.683850i | 0.939727 | + | 0.341925i | \(0.111079\pi\) | ||||
−0.939727 | + | 0.341925i | \(0.888921\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.8995i | 1.41574i | 0.706344 | + | 0.707869i | \(0.250343\pi\) | ||||
−0.706344 | + | 0.707869i | \(0.749657\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.3137 | − | 3.48528i | −0.799851 | − | 0.137233i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.2426 | −1.66073 | −0.830365 | − | 0.557220i | \(-0.811868\pi\) | ||||
−0.830365 | + | 0.557220i | \(0.811868\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.3137 | −1.07216 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.65685 | − | 0.970563i | −0.221710 | − | 0.0380394i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 43.6569i | − | 1.70842i | −0.519924 | − | 0.854212i | \(-0.674040\pi\) | ||
0.519924 | − | 0.854212i | \(-0.325960\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 5.17157i | − | 0.202070i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.2843 | + | 4.34315i | 0.479255 | + | 0.169442i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.6569 | −1.31108 | −0.655542 | − | 0.755158i | \(-0.727560\pi\) | ||||
−0.655542 | + | 0.755158i | \(0.727560\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6569 | −0.842354 | −0.421177 | − | 0.906978i | \(-0.638383\pi\) | ||||
−0.421177 | + | 0.906978i | \(0.638383\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.14214 | − | 12.4853i | 0.0831937 | − | 0.484888i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.65685i | 0.0642501i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 36.6863i | − | 1.42050i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.48528 | + | 20.3137i | −0.134749 | + | 0.785373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.0000 | −0.617673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.6569 | −1.37447 | −0.687235 | − | 0.726435i | \(-0.741176\pi\) | ||||
−0.687235 | + | 0.726435i | \(0.741176\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.53553 | + | 2.53553i | 0.174573 | + | 0.0975927i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6569i | 0.448009i | 0.974588 | + | 0.224005i | \(0.0719131\pi\) | ||||
−0.974588 | + | 0.224005i | \(0.928087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.76955i | − | 0.336545i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.82843 | + | 1.34315i | 0.299986 | + | 0.0514695i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.5563 | 0.824831 | 0.412415 | − | 0.910996i | \(-0.364685\pi\) | ||||
0.412415 | + | 0.910996i | \(0.364685\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.31371 | 0.203026 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 43.2132 | + | 7.41421i | 1.64869 | + | 0.282870i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.3137i | 0.583406i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2843i | 0.619483i | 0.950821 | + | 0.309741i | \(0.100242\pi\) | ||||
−0.950821 | + | 0.309741i | \(0.899758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.65685 | − | 4.68629i | 0.0629387 | − | 0.178017i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.8284 | 0.714203 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.31371 | 0.277026 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.89949 | − | 46.0416i | 0.298786 | − | 1.74145i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 51.9411i | − | 1.96179i | −0.194540 | − | 0.980895i | \(-0.562321\pi\) | ||
0.194540 | − | 0.980895i | \(-0.437679\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.9706i | 1.24351i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.656854 | + | 3.82843i | −0.0247386 | + | 0.144187i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.97056 | −0.337373 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.3137 | 0.950676 | 0.475338 | − | 0.879803i | \(-0.342326\pi\) | ||||
0.475338 | + | 0.879803i | \(0.342326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.4853 | − | 35.3137i | 0.468235 | − | 1.32437i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 25.9411i | − | 0.971503i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685i | 0.211554i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.3137 | − | 4.00000i | −0.870666 | − | 0.149383i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.2843 | 1.65152 | 0.825762 | − | 0.564018i | \(-0.190745\pi\) | ||||
0.825762 | + | 0.564018i | \(0.190745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.65685 | −0.136188 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.82843 | + | 0.485281i | 0.105190 | + | 0.0180478i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.00000i | 0.297113i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 48.1838i | − | 1.78704i | −0.449026 | − | 0.893518i | \(-0.648229\pi\) | ||
0.449026 | − | 0.893518i | \(-0.351771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43.5147 | −1.60945 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.9706 | −1.58715 | −0.793577 | − | 0.608470i | \(-0.791784\pi\) | ||||
−0.793577 | + | 0.608470i | \(0.791784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.94975 | + | 11.3640i | −0.0719175 | + | 0.419166i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.9706i | 1.36183i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.4853i | 1.19499i | 0.801872 | + | 0.597495i | \(0.203837\pi\) | ||||
−0.801872 | + | 0.597495i | \(0.796163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.65685 | − | 9.65685i | 0.0608661 | − | 0.354753i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.7279 | 1.12730 | 0.563649 | − | 0.826014i | \(-0.309397\pi\) | ||||
0.563649 | + | 0.826014i | \(0.309397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.31371 | −0.341228 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.6569 | + | 9.07107i | 0.938735 | + | 0.331893i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.37258i | 0.269388i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.62742i | − | 0.241838i | −0.992662 | − | 0.120919i | \(-0.961416\pi\) | ||
0.992662 | − | 0.120919i | \(-0.0385841\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.1421 | + | 4.82843i | 1.02556 | + | 0.175958i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.6569 | −1.00521 | −0.502603 | − | 0.864517i | \(-0.667624\pi\) | ||||
−0.502603 | + | 0.864517i | \(0.667624\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.1421 | + | 3.79899i | 0.803709 | + | 0.137895i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 11.3137i | − | 0.410122i | −0.978749 | − | 0.205061i | \(-0.934261\pi\) | ||
0.978749 | − | 0.205061i | \(-0.0657392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.71573i | − | 0.134518i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.3431 | + | 3.65685i | 0.373957 | + | 0.132214i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.3137 | 0.697378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.68629 | 0.0968701 | 0.0484351 | − | 0.998826i | \(-0.484577\pi\) | ||||
0.0484351 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.44365 | − | 37.5563i | 0.232062 | − | 1.35256i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 30.2843i | − | 1.08925i | −0.838680 | − | 0.544625i | \(-0.816672\pi\) | ||
0.838680 | − | 0.544625i | \(-0.183328\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685i | 0.203200i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.00000 | − | 11.6569i | 0.0717496 | − | 0.418187i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.65685 | 0.202678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.3137 | −0.691099 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.2843 | + | 36.2843i | −0.724901 | + | 1.29669i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.65685i | 0.130519i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.55635i | − | 0.340647i | −0.985388 | − | 0.170324i | \(-0.945519\pi\) | ||
0.985388 | − | 0.170324i | \(-0.0544813\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.4853 | − | 2.31371i | −0.480089 | − | 0.0823702i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.85786 | −0.208282 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.3137 | 0.401762 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.0711 | − | 2.24264i | −0.463583 | − | 0.0795383i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.97056i | 0.105223i | 0.998615 | + | 0.0526114i | \(0.0167545\pi\) | ||||
−0.998615 | + | 0.0526114i | \(0.983246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.20101i | 0.290131i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.3137 | − | 43.3137i | 0.541083 | − | 1.53041i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.2843 | −0.433503 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.68629 | 0.0946793 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.27208 | + | 30.7279i | −0.185586 | + | 1.08167i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 18.6274i | − | 0.654905i | −0.944868 | − | 0.327453i | \(-0.893810\pi\) | ||
0.944868 | − | 0.327453i | \(-0.106190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.62742i | − | 0.0922611i | −0.998935 | − | 0.0461305i | \(-0.985311\pi\) | ||
0.998935 | − | 0.0461305i | \(-0.0146890\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00000 | − | 23.3137i | 0.140286 | − | 0.817647i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.75736 | 0.0615576 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.6569 | −1.17750 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.17157 | + | 3.31371i | −0.0409381 | + | 0.115790i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 16.6274i | − | 0.580301i | −0.956981 | − | 0.290150i | \(-0.906295\pi\) | ||
0.956981 | − | 0.290150i | \(-0.0937053\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.8995i | 1.25138i | 0.780073 | + | 0.625689i | \(0.215182\pi\) | ||||
−0.780073 | + | 0.625689i | \(0.784818\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.82843 | − | 0.828427i | −0.168104 | − | 0.0288421i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.4142 | −0.953286 | −0.476643 | − | 0.879097i | \(-0.658146\pi\) | ||||
−0.476643 | + | 0.879097i | \(0.658146\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.9706 | −0.728338 | −0.364169 | − | 0.931333i | \(-0.618647\pi\) | ||||
−0.364169 | + | 0.931333i | \(0.618647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.585786 | + | 0.100505i | 0.0203207 | + | 0.00348648i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.3431i | 0.843440i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.72792i | 0.232829i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.3431 | + | 25.6569i | −0.495772 | + | 0.886831i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.9411 | −1.72416 | −0.862080 | − | 0.506773i | \(-0.830838\pi\) | ||||
−0.862080 | + | 0.506773i | \(0.830838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.0000 | −1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.72792 | + | 15.8995i | −0.0939546 | + | 0.547608i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000i | 0.309609i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.75736i | − | 0.0603836i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.14214 | + | 29.9706i | −0.176478 | + | 1.02859i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.4558 | 1.83244 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.9411 | 0.682771 | 0.341386 | − | 0.939923i | \(-0.389104\pi\) | ||||
0.341386 | + | 0.939923i | \(0.389104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.00000 | + | 2.82843i | 0.273594 | + | 0.0967302i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0000i | 0.341593i | 0.985306 | + | 0.170797i | \(0.0546341\pi\) | ||||
−0.985306 | + | 0.170797i | \(0.945366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24.4853i | − | 0.835427i | −0.908579 | − | 0.417714i | \(-0.862832\pi\) | ||
0.908579 | − | 0.417714i | \(-0.137168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00000 | − | 0.343146i | −0.0681598 | − | 0.0116944i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.5563 | −0.461463 | −0.230732 | − | 0.973017i | \(-0.574112\pi\) | ||||
−0.230732 | + | 0.973017i | \(0.574112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.19239 | − | 1.06245i | −0.210305 | − | 0.0360826i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.3137i | 1.19794i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 26.1421i | − | 0.885792i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.3431 | − | 14.9706i | −1.43310 | − | 0.506677i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.585786 | −0.0198032 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.3431 | 0.416798 | 0.208399 | − | 0.978044i | \(-0.433175\pi\) | ||||
0.208399 | + | 0.978044i | \(0.433175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.44365 | − | 37.5563i | 0.217339 | − | 1.26674i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16.6274i | − | 0.560192i | −0.959972 | − | 0.280096i | \(-0.909634\pi\) | ||
0.959972 | − | 0.280096i | \(-0.0903663\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.7279i | 0.899466i | 0.893163 | + | 0.449733i | \(0.148481\pi\) | ||||
−0.893163 | + | 0.449733i | \(0.851519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.82843 | + | 16.4853i | −0.0950765 | + | 0.554147i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.89949 | −0.265239 | −0.132620 | − | 0.991167i | \(-0.542339\pi\) | ||||
−0.132620 | + | 0.991167i | \(0.542339\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.71573 | 0.0575437 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.7990 | − | 16.0000i | −0.663291 | − | 0.536020i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.34315i | 0.212265i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.34315i | 0.212028i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.6569 | − | 2.68629i | −0.522767 | − | 0.0896927i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.2548 | −1.50933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.0000 | −0.932815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.8995 | + | 2.04163i | 0.395990 | + | 0.0679412i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3137i | 0.442563i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 13.0711i | − | 0.434018i | −0.976170 | − | 0.217009i | \(-0.930370\pi\) | ||
0.976170 | − | 0.217009i | \(-0.0696300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.3137 | + | 43.3137i | −0.507924 | + | 1.43663i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.1127 | −1.69344 | −0.846720 | − | 0.532039i | \(-0.821426\pi\) | ||||
−0.846720 | + | 0.532039i | \(0.821426\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.6569 | −0.849118 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.65685 | + | 9.65685i | −0.0547739 | + | 0.319246i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.02944i | 0.100041i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.5147i | − | 0.907627i | −0.891097 | − | 0.453813i | \(-0.850063\pi\) | ||
0.891097 | − | 0.453813i | \(-0.149937\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.48528 | + | 20.3137i | −0.114844 | + | 0.669359i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.6569 | 0.449521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.6569 | −0.383275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.24264 | + | 17.6569i | −0.205035 | + | 0.579927i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.0000i | 1.50921i | 0.656179 | + | 0.754606i | \(0.272172\pi\) | ||||
−0.656179 | + | 0.754606i | \(0.727828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.8284i | 0.617077i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −48.6274 | − | 8.34315i | −1.59199 | − | 0.273142i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.3431 | −0.338257 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.5980 | −1.35895 | −0.679473 | − | 0.733700i | \(-0.737792\pi\) | ||||
−0.679473 | + | 0.733700i | \(0.737792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.07107 | + | 1.55635i | 0.296023 | + | 0.0507895i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0000i | 0.391189i | 0.980685 | + | 0.195594i | \(0.0626636\pi\) | ||||
−0.980685 | + | 0.195594i | \(0.937336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 9.17157i | − | 0.298668i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.65685 | − | 1.48528i | −0.0864275 | − | 0.0483162i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.2132 | −0.624345 | −0.312173 | − | 0.950025i | \(-0.601057\pi\) | ||||
−0.312173 | + | 0.950025i | \(0.601057\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.68629 | 0.281969 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.41421 | + | 19.8995i | −0.110713 | + | 0.645285i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.68629i | − | 0.0870175i | −0.999053 | − | 0.0435088i | \(-0.986146\pi\) | ||
0.999053 | − | 0.0435088i | \(-0.0138536\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 10.1421i | − | 0.328192i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.62742 | − | 38.6274i | 0.214234 | − | 1.24865i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.11270 | −0.100514 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.5980 | + | 12.5858i | 1.14713 | + | 0.405571i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 3.65685i | − | 0.117718i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.58579i | 0.276100i | 0.990425 | + | 0.138050i | \(0.0440835\pi\) | ||||
−0.990425 | + | 0.138050i | \(0.955916\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.6569 | + | 3.02944i | 0.567220 | + | 0.0973195i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.5147 | −0.497891 | −0.248946 | − | 0.968517i | \(-0.580084\pi\) | ||||
−0.248946 | + | 0.968517i | \(0.580084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0294 | −0.353588 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.41421 | + | 0.585786i | 0.109342 | + | 0.0187602i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 54.9706i | − | 1.75866i | −0.476209 | − | 0.879332i | \(-0.657989\pi\) | ||
0.476209 | − | 0.879332i | \(-0.342011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.3137i | 1.38431i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.9411 | − | 6.34315i | −0.572816 | − | 0.202521i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.9289 | −0.986480 | −0.493240 | − | 0.869893i | \(-0.664188\pi\) | ||||
−0.493240 | + | 0.869893i | \(0.664188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.9706 | −0.349551 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.384776 | − | 2.24264i | 0.0122476 | − | 0.0713840i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54.5685i | 1.73518i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.2843i | 0.898479i | 0.893411 | + | 0.449240i | \(0.148305\pi\) | ||||
−0.893411 | + | 0.449240i | \(0.851695\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.17157 | − | 53.4558i | 0.291051 | − | 1.69637i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.1716 | 0.544375 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0000 | 0.570066 | 0.285033 | − | 0.958518i | \(-0.407995\pi\) | ||||
0.285033 | + | 0.958518i | \(0.407995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −52.8701 | − | 29.5563i | −1.67273 | − | 0.935122i |
(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 | 960.2.h.b.191.1 | 4 | ||
3.2 | odd | 2 | 960.2.h.f.191.3 | 4 | |||
4.3 | odd | 2 | 960.2.h.f.191.4 | 4 | |||
8.3 | odd | 2 | 480.2.h.b.191.1 | ✓ | 4 | ||
8.5 | even | 2 | 480.2.h.d.191.4 | yes | 4 | ||
12.11 | even | 2 | inner | 960.2.h.b.191.2 | 4 | ||
24.5 | odd | 2 | 480.2.h.b.191.2 | yes | 4 | ||
24.11 | even | 2 | 480.2.h.d.191.3 | yes | 4 | ||
40.3 | even | 4 | 2400.2.o.i.2399.1 | 4 | |||
40.13 | odd | 4 | 2400.2.o.b.2399.4 | 4 | |||
40.19 | odd | 2 | 2400.2.h.e.1151.4 | 4 | |||
40.27 | even | 4 | 2400.2.o.c.2399.4 | 4 | |||
40.29 | even | 2 | 2400.2.h.b.1151.1 | 4 | |||
40.37 | odd | 4 | 2400.2.o.j.2399.1 | 4 | |||
120.29 | odd | 2 | 2400.2.h.e.1151.3 | 4 | |||
120.53 | even | 4 | 2400.2.o.c.2399.3 | 4 | |||
120.59 | even | 2 | 2400.2.h.b.1151.2 | 4 | |||
120.77 | even | 4 | 2400.2.o.i.2399.2 | 4 | |||
120.83 | odd | 4 | 2400.2.o.j.2399.2 | 4 | |||
120.107 | odd | 4 | 2400.2.o.b.2399.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.2.h.b.191.1 | ✓ | 4 | 8.3 | odd | 2 | ||
480.2.h.b.191.2 | yes | 4 | 24.5 | odd | 2 | ||
480.2.h.d.191.3 | yes | 4 | 24.11 | even | 2 | ||
480.2.h.d.191.4 | yes | 4 | 8.5 | even | 2 | ||
960.2.h.b.191.1 | 4 | 1.1 | even | 1 | trivial | ||
960.2.h.b.191.2 | 4 | 12.11 | even | 2 | inner | ||
960.2.h.f.191.3 | 4 | 3.2 | odd | 2 | |||
960.2.h.f.191.4 | 4 | 4.3 | odd | 2 | |||
2400.2.h.b.1151.1 | 4 | 40.29 | even | 2 | |||
2400.2.h.b.1151.2 | 4 | 120.59 | even | 2 | |||
2400.2.h.e.1151.3 | 4 | 120.29 | odd | 2 | |||
2400.2.h.e.1151.4 | 4 | 40.19 | odd | 2 | |||
2400.2.o.b.2399.3 | 4 | 120.107 | odd | 4 | |||
2400.2.o.b.2399.4 | 4 | 40.13 | odd | 4 | |||
2400.2.o.c.2399.3 | 4 | 120.53 | even | 4 | |||
2400.2.o.c.2399.4 | 4 | 40.27 | even | 4 | |||
2400.2.o.i.2399.1 | 4 | 40.3 | even | 4 | |||
2400.2.o.i.2399.2 | 4 | 120.77 | even | 4 | |||
2400.2.o.j.2399.1 | 4 | 40.37 | odd | 4 | |||
2400.2.o.j.2399.2 | 4 | 120.83 | odd | 4 |