Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(1567,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.b (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: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.3 | ||
Root | \(0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1567 |
Dual form | 2352.2.b.i.1567.2 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.765367i | 0.342282i | 0.985247 | + | 0.171141i | \(0.0547454\pi\) | ||||
−0.985247 | + | 0.171141i | \(0.945255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.16478i | − 0.652707i | −0.945248 | − | 0.326354i | \(-0.894180\pi\) | ||||
0.945248 | − | 0.326354i | \(-0.105820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.317025i | 0.0879270i | 0.999033 | + | 0.0439635i | \(0.0139985\pi\) | ||||
−0.999033 | + | 0.0439635i | \(0.986001\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 0.765367i | − 0.197617i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.37849i | − 0.819405i | −0.912219 | − | 0.409702i | \(-0.865633\pi\) | ||||
0.912219 | − | 0.409702i | \(-0.134367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.22625i | 1.08975i | 0.838518 | + | 0.544874i | \(0.183423\pi\) | ||||
−0.838518 | + | 0.544874i | \(0.816577\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.41421 | 0.882843 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.58579 | −0.480168 | −0.240084 | − | 0.970752i | \(-0.577175\pi\) | ||||
−0.240084 | + | 0.970752i | \(0.577175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.65685 | −0.297580 | −0.148790 | − | 0.988869i | \(-0.547538\pi\) | ||||
−0.148790 | + | 0.988869i | \(0.547538\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.16478i | 0.376841i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.41421 | −0.232495 | −0.116248 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116248 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 0.317025i | − 0.0507647i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.99162i | 0.935734i | 0.883799 | + | 0.467867i | \(0.154977\pi\) | ||||
−0.883799 | + | 0.467867i | \(0.845023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.39104i | − 1.12712i | −0.826074 | − | 0.563561i | \(-0.809431\pi\) | ||||
0.826074 | − | 0.563561i | \(-0.190569\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.765367i | 0.114094i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.65685 | −1.40860 | −0.704298 | − | 0.709904i | \(-0.748738\pi\) | ||||
−0.704298 | + | 0.709904i | \(0.748738\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.37849i | 0.473084i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.65685 | 0.227586 | 0.113793 | − | 0.993504i | \(-0.463700\pi\) | ||||
0.113793 | + | 0.993504i | \(0.463700\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.65685 | 0.223410 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.65685 | 0.749269 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.65685 | −0.736460 | −0.368230 | − | 0.929735i | \(-0.620036\pi\) | ||||
−0.368230 | + | 0.929735i | \(0.620036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.07401i | 0.905734i | 0.891578 | + | 0.452867i | \(0.149599\pi\) | ||||
−0.891578 | + | 0.452867i | \(0.850401\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.242641 | −0.0300959 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.7206i | − 1.43190i | −0.698152 | − | 0.715950i | \(-0.745994\pi\) | ||||
0.698152 | − | 0.715950i | \(-0.254006\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 5.22625i | − 0.629167i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 15.6788i | − 1.86073i | −0.366640 | − | 0.930363i | \(-0.619492\pi\) | ||||
0.366640 | − | 0.930363i | \(-0.380508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.62567i | 0.775476i | 0.921770 | + | 0.387738i | \(0.126743\pi\) | ||||
−0.921770 | + | 0.387738i | \(0.873257\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.41421 | −0.509709 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5140i | 1.52044i | 0.649665 | + | 0.760220i | \(0.274909\pi\) | ||||
−0.649665 | + | 0.760220i | \(0.725091\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.34315 | −0.696251 | −0.348125 | − | 0.937448i | \(-0.613182\pi\) | ||||
−0.348125 | + | 0.937448i | \(0.613182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58579 | 0.280468 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.58579 | 0.277225 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 11.4036i | − 1.20878i | −0.796690 | − | 0.604389i | \(-0.793417\pi\) | ||||
0.796690 | − | 0.604389i | \(-0.206583\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.65685 | 0.171808 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 4.32957i | − 0.444204i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 3.82683i | − 0.388556i | −0.980946 | − | 0.194278i | \(-0.937764\pi\) | ||||
0.980946 | − | 0.194278i | \(-0.0622364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 2.16478i | − 0.217569i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 16.6298i | − 1.65473i | −0.561665 | − | 0.827365i | \(-0.689839\pi\) | ||||
0.561665 | − | 0.827365i | \(-0.310161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0000 | −1.18240 | −0.591198 | − | 0.806527i | \(-0.701345\pi\) | ||||
−0.591198 | + | 0.806527i | \(0.701345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.95815i | 0.382649i | 0.981527 | + | 0.191324i | \(0.0612783\pi\) | ||||
−0.981527 | + | 0.191324i | \(0.938722\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.72792 | −0.452853 | −0.226426 | − | 0.974028i | \(-0.572704\pi\) | ||||
−0.226426 | + | 0.974028i | \(0.572704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.41421 | 0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.9706 | −1.59646 | −0.798228 | − | 0.602355i | \(-0.794229\pi\) | ||||
−0.798228 | + | 0.602355i | \(0.794229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.317025i | 0.0293090i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.31371 | 0.573973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.99162i | − 0.540246i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.20533i | 0.644464i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 13.5140i | − 1.19917i | −0.800311 | − | 0.599586i | \(-0.795332\pi\) | ||||
0.800311 | − | 0.599586i | \(-0.204668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.39104i | 0.650744i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3137 | −1.33796 | −0.668982 | − | 0.743278i | \(-0.733270\pi\) | ||||
−0.668982 | + | 0.743278i | \(0.733270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 0.765367i | − 0.0658723i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4142 | −1.14605 | −0.573027 | − | 0.819537i | \(-0.694231\pi\) | ||||
−0.573027 | + | 0.819537i | \(0.694231\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6569 | −1.49763 | −0.748817 | − | 0.662776i | \(-0.769378\pi\) | ||||
−0.748817 | + | 0.662776i | \(0.769378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.65685 | 0.813254 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.686292 | 0.0573906 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 1.97908i | − 0.164353i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.9706 | −1.06259 | −0.531295 | − | 0.847187i | \(-0.678294\pi\) | ||||
−0.531295 | + | 0.847187i | \(0.678294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.12293i | 0.498277i | 0.968468 | + | 0.249139i | \(0.0801475\pi\) | ||||
−0.968468 | + | 0.249139i | \(0.919852\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 3.37849i | − 0.273135i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.26810i | − 0.101856i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.9134i | 1.19022i | 0.803645 | + | 0.595109i | \(0.202891\pi\) | ||||
−0.803645 | + | 0.595109i | \(0.797109\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.65685 | −0.131397 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.12293i | 0.479585i | 0.970824 | + | 0.239793i | \(0.0770795\pi\) | ||||
−0.970824 | + | 0.239793i | \(0.922921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.65685 | −0.128986 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.65685 | 0.747270 | 0.373635 | − | 0.927576i | \(-0.378111\pi\) | ||||
0.373635 | + | 0.927576i | \(0.378111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8995 | 0.992269 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.65685 | −0.432590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 9.42450i | − 0.716532i | −0.933620 | − | 0.358266i | \(-0.883368\pi\) | ||||
0.933620 | − | 0.358266i | \(-0.116632\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.65685 | 0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 20.0083i | − 1.49549i | −0.663985 | − | 0.747746i | \(-0.731136\pi\) | ||||
0.663985 | − | 0.747746i | \(-0.268864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 16.1815i | − 1.20276i | −0.798963 | − | 0.601380i | \(-0.794618\pi\) | ||||
0.798963 | − | 0.601380i | \(-0.205382\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 7.07401i | − 0.522926i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 1.08239i | − 0.0795791i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.31371 | −0.534831 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8854i | 1.00471i | 0.864661 | + | 0.502356i | \(0.167533\pi\) | ||||
−0.864661 | + | 0.502356i | \(0.832467\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.31371 | 0.238526 | 0.119263 | − | 0.992863i | \(-0.461947\pi\) | ||||
0.119263 | + | 0.992863i | \(0.461947\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.242641 | 0.0173759 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.3137 | −1.80353 | −0.901764 | − | 0.432230i | \(-0.857727\pi\) | ||||
−0.901764 | + | 0.432230i | \(0.857727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.65685 | −0.401004 | −0.200502 | − | 0.979693i | \(-0.564257\pi\) | ||||
−0.200502 | + | 0.979693i | \(0.564257\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.7206i | 0.826708i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.58579 | −0.320285 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.22625i | 0.363250i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.2459i | 0.847065i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.39104i | 0.508820i | 0.967096 | + | 0.254410i | \(0.0818813\pi\) | ||||
−0.967096 | + | 0.254410i | \(0.918119\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.6788i | 1.07429i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.65685 | 0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 6.62567i | − 0.447721i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.07107 | 0.0720478 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.3137 | 1.29334 | 0.646671 | − | 0.762769i | \(-0.276161\pi\) | ||||
0.646671 | + | 0.762769i | \(0.276161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.41421 | 0.294281 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.31371 | 0.219939 | 0.109969 | − | 0.993935i | \(-0.464925\pi\) | ||||
0.109969 | + | 0.993935i | \(0.464925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4.72352i | − 0.312139i | −0.987746 | − | 0.156069i | \(-0.950118\pi\) | ||||
0.987746 | − | 0.156069i | \(-0.0498824\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.242641 | 0.0158959 | 0.00794796 | − | 0.999968i | \(-0.497470\pi\) | ||||
0.00794796 | + | 0.999968i | \(0.497470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7.39104i | − 0.482138i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 13.5140i | − 0.877827i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 0.896683i | − 0.0580016i | −0.999579 | − | 0.0290008i | \(-0.990767\pi\) | ||||
0.999579 | − | 0.0290008i | \(-0.00923254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 3.11586i | − 0.200710i | −0.994952 | − | 0.100355i | \(-0.968002\pi\) | ||||
0.994952 | − | 0.100355i | \(-0.0319979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.79337i | − 0.114109i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.34315 | 0.401981 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.97056 | −0.566217 | −0.283108 | − | 0.959088i | \(-0.591366\pi\) | ||||
−0.283108 | + | 0.959088i | \(0.591366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3137 | 0.711287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.58579 | −0.161928 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 18.9803i | − 1.18396i | −0.805953 | − | 0.591980i | \(-0.798346\pi\) | ||||
0.805953 | − | 0.591980i | \(-0.201654\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.58579 | −0.160056 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.1313i | 1.61132i | 0.592377 | + | 0.805661i | \(0.298190\pi\) | ||||
−0.592377 | + | 0.805661i | \(0.701810\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.26810i | 0.0778988i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.4036i | 0.697888i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 25.1802i | − 1.53526i | −0.640892 | − | 0.767631i | \(-0.721435\pi\) | ||||
0.640892 | − | 0.767631i | \(-0.278565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.65685 | 0.586612 | 0.293306 | − | 0.956019i | \(-0.405245\pi\) | ||||
0.293306 | + | 0.956019i | \(0.405245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 9.55582i | − 0.576238i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.31371 | −0.559607 | −0.279803 | − | 0.960057i | \(-0.590269\pi\) | ||||
−0.279803 | + | 0.960057i | \(0.590269\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.65685 | −0.0991933 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.3848 | −1.33536 | −0.667682 | − | 0.744447i | \(-0.732713\pi\) | ||||
−0.667682 | + | 0.744447i | \(0.732713\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.32957i | 0.256462i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.58579 | 0.328576 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.82683i | 0.224333i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.4119i | 1.83510i | 0.397617 | + | 0.917552i | \(0.369837\pi\) | ||||
−0.397617 | + | 0.917552i | \(0.630163\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 4.32957i | − 0.252077i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.16478i | 0.125614i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.65685 | −0.0958184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.6298i | 0.955359i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.41421 | −0.310017 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.31371 | −0.189123 | −0.0945617 | − | 0.995519i | \(-0.530145\pi\) | ||||
−0.0945617 | + | 0.995519i | \(0.530145\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.0000 | 0.682656 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8770i | 1.12351i | 0.827302 | + | 0.561757i | \(0.189875\pi\) | ||||
−0.827302 | + | 0.561757i | \(0.810125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.31371 | −0.298448 | −0.149224 | − | 0.988803i | \(-0.547677\pi\) | ||||
−0.149224 | + | 0.988803i | \(0.547677\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.59767i | 0.313409i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 3.95815i | − 0.220922i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.1116i | 1.06340i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.39942i | 0.0776257i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.72792 | 0.261455 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 25.2346i | − 1.38702i | −0.720448 | − | 0.693509i | \(-0.756064\pi\) | ||||
0.720448 | − | 0.693509i | \(-0.243936\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.41421 | −0.0774984 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.97056 | 0.490114 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.7279 | 1.12912 | 0.564561 | − | 0.825391i | \(-0.309046\pi\) | ||||
0.564561 | + | 0.825391i | \(0.309046\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.9706 | 0.921714 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.58673i | 0.194232i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.43289i | 0.184287i | 0.995746 | + | 0.0921435i | \(0.0293718\pi\) | ||||
−0.995746 | + | 0.0921435i | \(0.970628\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 20.7737i | − 1.11199i | −0.831186 | − | 0.555995i | \(-0.812337\pi\) | ||||
0.831186 | − | 0.555995i | \(-0.187663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 0.317025i | − 0.0169216i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 14.9134i | − 0.793760i | −0.917871 | − | 0.396880i | \(-0.870093\pi\) | ||||
0.917871 | − | 0.396880i | \(-0.129907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | 0.636894 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 15.6788i | − 0.827493i | −0.910392 | − | 0.413747i | \(-0.864220\pi\) | ||||
0.910392 | − | 0.413747i | \(-0.135780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.31371 | −0.331384 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.07107 | −0.265432 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.6569 | 1.13048 | 0.565239 | − | 0.824927i | \(-0.308784\pi\) | ||||
0.565239 | + | 0.824927i | \(0.308784\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.99162i | 0.311911i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.6274 | 1.79294 | 0.896470 | − | 0.443105i | \(-0.146123\pi\) | ||||
0.896470 | + | 0.443105i | \(0.146123\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 7.20533i | − 0.372081i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 0.819760i | − 0.0422198i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.1509i | 1.70285i | 0.524479 | + | 0.851423i | \(0.324260\pi\) | ||||
−0.524479 | + | 0.851423i | \(0.675740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.5140i | 0.692342i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.2843 | 1.85404 | 0.927020 | − | 0.375012i | \(-0.122362\pi\) | ||||
0.927020 | + | 0.375012i | \(0.122362\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 7.39104i | − 0.375707i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0416 | 1.01615 | 0.508076 | − | 0.861313i | \(-0.330357\pi\) | ||||
0.508076 | + | 0.861313i | \(0.330357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.6569 | 0.892946 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.3137 | 0.772474 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.3431 | −0.520420 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.4287i | 0.975097i | 0.873096 | + | 0.487548i | \(0.162109\pi\) | ||||
−0.873096 | + | 0.487548i | \(0.837891\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.8701 | −1.14208 | −0.571038 | − | 0.820924i | \(-0.693459\pi\) | ||||
−0.571038 | + | 0.820924i | \(0.693459\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.525265i | − 0.0261653i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.765367i | 0.0380314i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.06147i | 0.151751i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.89377i | 0.390322i | 0.980771 | + | 0.195161i | \(0.0625229\pi\) | ||||
−0.980771 | + | 0.195161i | \(0.937477\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4142 | 0.661674 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 4.85483i | − 0.238314i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.6569 | 0.864660 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.6274 | −1.10542 | −0.552711 | − | 0.833373i | \(-0.686407\pi\) | ||||
−0.552711 | + | 0.833373i | \(0.686407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.68629 | −0.325870 | −0.162935 | − | 0.986637i | \(-0.552096\pi\) | ||||
−0.162935 | + | 0.986637i | \(0.552096\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.65685 | −0.469532 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 14.9134i | − 0.723406i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.686292 | −0.0331345 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1535i | 0.729918i | 0.931024 | + | 0.364959i | \(0.118917\pi\) | ||||
−0.931024 | + | 0.364959i | \(0.881083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.87285i | 0.474459i | 0.971454 | + | 0.237229i | \(0.0762393\pi\) | ||||
−0.971454 | + | 0.237229i | \(0.923761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.97908i | 0.0948894i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 29.5641i | − 1.41424i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.6274 | 1.07995 | 0.539974 | − | 0.841682i | \(-0.318434\pi\) | ||||
0.539974 | + | 0.841682i | \(0.318434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 26.1313i | − 1.24153i | −0.783995 | − | 0.620767i | \(-0.786821\pi\) | ||||
0.783995 | − | 0.620767i | \(-0.213179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.72792 | 0.413743 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.9706 | 0.613487 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.6569 | −1.39959 | −0.699797 | − | 0.714342i | \(-0.746726\pi\) | ||||
−0.699797 | + | 0.714342i | \(0.746726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.9706 | 0.610760 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 6.12293i | − 0.287681i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.3137 | −0.903457 | −0.451729 | − | 0.892155i | \(-0.649192\pi\) | ||||
−0.451729 | + | 0.892155i | \(0.649192\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.37849i | 0.157695i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.2066i | 1.12741i | 0.825975 | + | 0.563706i | \(0.190625\pi\) | ||||
−0.825975 | + | 0.563706i | \(0.809375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.79337i | − 0.0833448i | −0.999131 | − | 0.0416724i | \(-0.986731\pi\) | ||||
0.999131 | − | 0.0416724i | \(-0.0132686\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.26810i | 0.0588068i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3137 | 0.893732 | 0.446866 | − | 0.894601i | \(-0.352540\pi\) | ||||
0.446866 | + | 0.894601i | \(0.352540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 14.9134i | − 0.687173i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.0000 | −0.735681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.9706 | −1.14573 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.65685 | 0.0758621 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.6274 | 1.21664 | 0.608319 | − | 0.793693i | \(-0.291844\pi\) | ||||
0.608319 | + | 0.793693i | \(0.291844\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 0.448342i | − 0.0204426i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.92893 | 0.132996 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.6871i | 1.61714i | 0.588403 | + | 0.808568i | \(0.299757\pi\) | ||||
−0.588403 | + | 0.808568i | \(0.700243\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 6.12293i | − 0.276889i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4107i | 0.650344i | 0.945655 | + | 0.325172i | \(0.105422\pi\) | ||||
−0.945655 | + | 0.325172i | \(0.894578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.73606i | 0.393452i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.65685 | 0.0744701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 17.3183i | − 0.775272i | −0.921812 | − | 0.387636i | \(-0.873292\pi\) | ||||
0.921812 | − | 0.387636i | \(-0.126708\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.65685 | −0.431436 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.6569 | 1.67904 | 0.839518 | − | 0.543332i | \(-0.182837\pi\) | ||||
0.839518 | + | 0.543332i | \(0.182837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.7279 | 0.566385 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8995 | −0.572887 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5069i | 0.465710i | 0.972511 | + | 0.232855i | \(0.0748068\pi\) | ||||
−0.972511 | + | 0.232855i | \(0.925193\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.65685 | 0.249756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 9.18440i | − 0.404713i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.9050i | 0.919401i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.42450i | 0.413690i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.66205i | 0.0728157i | 0.999337 | + | 0.0364079i | \(0.0115915\pi\) | ||||
−0.999337 | + | 0.0364079i | \(0.988408\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.6274 | 0.464704 | 0.232352 | − | 0.972632i | \(-0.425358\pi\) | ||||
0.232352 | + | 0.972632i | \(0.425358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.59767i | 0.243838i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.31371 | −0.187553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.65685 | −0.245487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.89949 | −0.0822763 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.02944 | −0.130974 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.0083i | 0.863423i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.0000 | −0.515920 | −0.257960 | − | 0.966156i | \(-0.583050\pi\) | ||||
−0.257960 | + | 0.966156i | \(0.583050\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.1815i | 0.694414i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 3.61859i | − 0.155004i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.8322i | 1.31829i | 0.752015 | + | 0.659146i | \(0.229082\pi\) | ||||
−0.752015 | + | 0.659146i | \(0.770918\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.07401i | 0.301911i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.6274 | 0.623149 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.08239i | 0.0459450i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.3137 | 0.903091 | 0.451545 | − | 0.892248i | \(-0.350873\pi\) | ||||
0.451545 | + | 0.892248i | \(0.350873\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.34315 | 0.0991045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.31371 | 0.308785 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.9706 | 1.38954 | 0.694772 | − | 0.719230i | \(-0.255505\pi\) | ||||
0.694772 | + | 0.719230i | \(0.255505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 12.9887i | − 0.546439i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.58579 | 0.108402 | 0.0542009 | − | 0.998530i | \(-0.482739\pi\) | ||||
0.0542009 | + | 0.998530i | \(0.482739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.1731i | 0.927916i | 0.885857 | + | 0.463958i | \(0.153571\pi\) | ||||
−0.885857 | + | 0.463958i | \(0.846429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 13.8854i | − 0.580070i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.0698i | 0.962077i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 12.9343i | − 0.538463i | −0.963076 | − | 0.269231i | \(-0.913230\pi\) | ||||
0.963076 | − | 0.269231i | \(-0.0867696\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.31371 | −0.137713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 3.58673i | − 0.148547i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.242641 | −0.0100320 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.97056 | −0.370255 | −0.185127 | − | 0.982715i | \(-0.559270\pi\) | ||||
−0.185127 | + | 0.982715i | \(0.559270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.37258 | 0.386191 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.3137 | 1.04127 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 23.1242i | − 0.949596i | −0.880095 | − | 0.474798i | \(-0.842521\pi\) | ||||
0.880095 | − | 0.474798i | \(-0.157479\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.65685 | 0.231520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.55582i | 0.390440i | 0.980759 | + | 0.195220i | \(0.0625421\pi\) | ||||
−0.980759 | + | 0.195220i | \(0.937458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 44.1061i | − 1.79913i | −0.436791 | − | 0.899563i | \(-0.643885\pi\) | ||||
0.436791 | − | 0.899563i | \(-0.356115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 11.7206i | − 0.477300i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.83230i | 0.196461i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.3137 | 1.75805 | 0.879025 | − | 0.476776i | \(-0.158195\pi\) | ||||
0.879025 | + | 0.476776i | \(0.158195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 3.06147i | − 0.123854i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.24264 | −0.171359 | −0.0856793 | − | 0.996323i | \(-0.527306\pi\) | ||||
−0.0856793 | + | 0.996323i | \(0.527306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.58579 | 0.184917 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.55635 | −0.143173 | −0.0715866 | − | 0.997434i | \(-0.522806\pi\) | ||||
−0.0715866 | + | 0.997434i | \(0.522806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.3431 | −1.21959 | −0.609797 | − | 0.792558i | \(-0.708749\pi\) | ||||
−0.609797 | + | 0.792558i | \(0.708749\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5.22625i | − 0.209722i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.5563 | 0.662254 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 12.2459i | − 0.489053i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.77791i | 0.190508i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 6.12293i | − 0.243750i | −0.992545 | − | 0.121875i | \(-0.961109\pi\) | ||||
0.992545 | − | 0.121875i | \(-0.0388907\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 7.39104i | − 0.293767i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.3431 | 0.410455 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 15.6788i | − 0.620242i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.8701 | −1.53527 | −0.767637 | − | 0.640884i | \(-0.778568\pi\) | ||||
−0.767637 | + | 0.640884i | \(0.778568\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.6569 | 0.854063 | 0.427031 | − | 0.904237i | \(-0.359559\pi\) | ||||
0.427031 | + | 0.904237i | \(0.359559\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.65685 | −0.222738 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.9706 | −0.509925 | −0.254963 | − | 0.966951i | \(-0.582063\pi\) | ||||
−0.254963 | + | 0.966951i | \(0.582063\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.2459i | 0.480692i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.0711 | 1.37244 | 0.686218 | − | 0.727395i | \(-0.259269\pi\) | ||||
0.686218 | + | 0.727395i | \(0.259269\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 11.7206i | − 0.457962i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.62567i | 0.258492i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.5223i | 1.30584i | 0.757425 | + | 0.652922i | \(0.226457\pi\) | ||||
−0.757425 | + | 0.652922i | \(0.773543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.7624i | 1.31321i | 0.754237 | + | 0.656603i | \(0.228007\pi\) | ||||
−0.754237 | + | 0.656603i | \(0.771993\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.07107 | −0.0415968 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 13.5140i | − 0.523263i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.3137 | −0.746711 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3137 | 0.591179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.07107 | −0.272570 | −0.136285 | − | 0.990670i | \(-0.543516\pi\) | ||||
−0.136285 | + | 0.990670i | \(0.543516\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.41421 | −0.169903 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.82683i | 0.147077i | 0.997292 | + | 0.0735386i | \(0.0234292\pi\) | ||||
−0.997292 | + | 0.0735386i | \(0.976571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.31371 | −0.126982 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.8017i | 0.834219i | 0.908856 | + | 0.417109i | \(0.136957\pi\) | ||||
−0.908856 | + | 0.417109i | \(0.863043\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 10.2668i | − 0.392274i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.72352i | 0.180213i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.525265i | 0.0200110i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.65685 | 0.0630297 | 0.0315149 | − | 0.999503i | \(-0.489967\pi\) | ||||
0.0315149 | + | 0.999503i | \(0.489967\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 13.5140i | − 0.512614i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.2426 | 0.766745 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.242641 | −0.00917751 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.38478 | 0.241150 | 0.120575 | − | 0.992704i | \(-0.461526\pi\) | ||||
0.120575 | + | 0.992704i | \(0.461526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.00000 | 0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.39104i | 0.278363i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.8995 | −1.27312 | −0.636561 | − | 0.771226i | \(-0.719644\pi\) | ||||
−0.636561 | + | 0.771226i | \(0.719644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.5140i | 0.506814i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8.65914i | − 0.324287i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.525265i | 0.0196438i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.896683i | 0.0334872i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.2843 | −0.756476 | −0.378238 | − | 0.925708i | \(-0.623470\pi\) | ||||
−0.378238 | + | 0.925708i | \(0.623470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.11586i | 0.115880i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.4142 | −0.423913 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.9706 | −0.481052 | −0.240526 | − | 0.970643i | \(-0.577320\pi\) | ||||
−0.240526 | + | 0.970643i | \(0.577320\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.9706 | −0.923570 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 51.1257i | − 1.88837i | −0.329413 | − | 0.944186i | \(-0.606851\pi\) | ||||
0.329413 | − | 0.944186i | \(-0.393149\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.3726 | −0.934611 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 41.8100i | − 1.53801i | −0.639245 | − | 0.769003i | \(-0.720753\pi\) | ||||
0.639245 | − | 0.769003i | \(-0.279247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.79337i | 0.0658810i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 29.1927i | − 1.07098i | −0.844542 | − | 0.535489i | \(-0.820127\pi\) | ||||
0.844542 | − | 0.535489i | \(-0.179873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 9.92724i | − 0.363706i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.34315 | −0.232084 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2960i | 1.03254i | 0.856427 | + | 0.516269i | \(0.172679\pi\) | ||||
−0.856427 | + | 0.516269i | \(0.827321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.97056 | 0.326905 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.68629 | −0.170552 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.3848 | −0.377441 | −0.188721 | − | 0.982031i | \(-0.560434\pi\) | ||||
−0.188721 | + | 0.982031i | \(0.560434\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.3137 | −0.410662 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 12.5629i | − 0.455405i | −0.973731 | − | 0.227702i | \(-0.926879\pi\) | ||||
0.973731 | − | 0.227702i | \(-0.0731213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.58579 | 0.0934893 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.79337i | − 0.0647547i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.5963i | 1.46394i | 0.681337 | + | 0.731970i | \(0.261399\pi\) | ||||
−0.681337 | + | 0.731970i | \(0.738601\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9803i | 0.683560i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 8.68167i | − 0.312258i | −0.987737 | − | 0.156129i | \(-0.950098\pi\) | ||||
0.987737 | − | 0.156129i | \(-0.0499015\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.31371 | −0.262716 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 33.8937i | − 1.21437i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.9411 | −1.21451 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.58579 | 0.0924085 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.4142 | −0.407391 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.3137 | 0.831044 | 0.415522 | − | 0.909583i | \(-0.363599\pi\) | ||||
0.415522 | + | 0.909583i | \(0.363599\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 26.1313i | − 0.930297i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.24264 | −0.0796385 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.26810i | − 0.0449749i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.48181i | − 0.0879102i | −0.999034 | − | 0.0439551i | \(-0.986004\pi\) | ||||
0.999034 | − | 0.0439551i | \(-0.0139959\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.6256i | 1.15421i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 11.4036i | − 0.402926i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.3431 | 0.506159 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.1802i | 0.886384i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.0000 | −0.351581 | −0.175791 | − | 0.984428i | \(-0.556248\pi\) | ||||
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.65685 | 0.0581800 | 0.0290900 | − | 0.999577i | \(-0.490739\pi\) | ||||
0.0290900 | + | 0.999577i | \(0.490739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.65685 | −0.338681 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.68629 | −0.164154 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.8100i | 1.46275i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.3137 | −0.883455 | −0.441727 | − | 0.897149i | \(-0.645634\pi\) | ||||
−0.441727 | + | 0.897149i | \(0.645634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.4190i | 1.19977i | 0.800086 | + | 0.599885i | \(0.204787\pi\) | ||||
−0.800086 | + | 0.599885i | \(0.795213\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.55582i | 0.332691i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 12.6173i | − 0.438746i | −0.975641 | − | 0.219373i | \(-0.929599\pi\) | ||||
0.975641 | − | 0.219373i | \(-0.0704012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.7473i | 0.755315i | 0.925945 | + | 0.377657i | \(0.123270\pi\) | ||||
−0.925945 | + | 0.377657i | \(0.876730\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.31371 | 0.323089 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.39104i | 0.255777i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.65685 | 0.0572693 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.9411 | −1.03368 | −0.516841 | − | 0.856081i | \(-0.672892\pi\) | ||||
−0.516841 | + | 0.856081i | \(0.672892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3137 | −0.769438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.3848 | 0.770973 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.87285i | 0.339636i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 7.39104i | − 0.253361i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 5.46635i | − 0.187164i | −0.995612 | − | 0.0935822i | \(-0.970168\pi\) | ||||
0.995612 | − | 0.0935822i | \(-0.0298318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 4.32957i | − 0.148068i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.6159i | 1.62653i | 0.581894 | + | 0.813264i | \(0.302312\pi\) | ||||
−0.581894 | + | 0.813264i | \(0.697688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.6274 | −1.31795 | −0.658975 | − | 0.752165i | \(-0.729010\pi\) | ||||
−0.658975 | + | 0.752165i | \(0.729010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.7289i | 1.08007i | 0.841644 | + | 0.540033i | \(0.181588\pi\) | ||||
−0.841644 | + | 0.540033i | \(0.818412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.21320 | 0.245256 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.58579 | −0.189703 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.2548 | 0.992402 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.71573 | 0.125903 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 3.82683i | − 0.129519i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.2426 | 1.22383 | 0.611914 | − | 0.790925i | \(-0.290400\pi\) | ||||
0.611914 | + | 0.790925i | \(0.290400\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 31.4119i | − 1.05950i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 50.7862i | − 1.71103i | −0.517778 | − | 0.855515i | \(-0.673241\pi\) | ||||
0.517778 | − | 0.855515i | \(-0.326759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 16.5754i | − 0.557808i | −0.960319 | − | 0.278904i | \(-0.910029\pi\) | ||||
0.960319 | − | 0.278904i | \(-0.0899711\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.32957i | 0.145537i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.6863 | −0.828885 | −0.414442 | − | 0.910076i | \(-0.636023\pi\) | ||||
−0.414442 | + | 0.910076i | \(0.636023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.16478i | − 0.0725230i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 54.6274 | 1.82804 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.3137 | 0.511881 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.65685 | 0.0553208 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.28427 | 0.142888 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 5.59767i | − 0.186485i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.3848 | 0.411684 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.79337i | 0.0595477i | 0.999557 | + | 0.0297739i | \(0.00947872\pi\) | ||||
−0.999557 | + | 0.0297739i | \(0.990521\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 16.6298i | − 0.551577i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 26.6565i | − 0.883170i | −0.897219 | − | 0.441585i | \(-0.854416\pi\) | ||||
0.897219 | − | 0.441585i | \(-0.145584\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.7315i | 0.454448i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.41421 | 0.178988 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 29.0389i | − 0.957904i | −0.877841 | − | 0.478952i | \(-0.841017\pi\) | ||||
0.877841 | − | 0.478952i | \(-0.158983\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.31371 | 0.109190 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.97056 | 0.163608 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.24264 | −0.205257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.0000 | −0.394132 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.8310i | 0.453780i | 0.973920 | + | 0.226890i | \(0.0728558\pi\) | ||||
−0.973920 | + | 0.226890i | \(0.927144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.00000 | 0.130954 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 5.59767i | − 0.183063i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 3.82683i | − 0.125017i | −0.998044 | − | 0.0625086i | \(-0.980090\pi\) | ||||
0.998044 | − | 0.0625086i | \(-0.0199101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 19.8770i | − 0.648662i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 11.0322i | − 0.359638i | −0.983700 | − | 0.179819i | \(-0.942449\pi\) | ||||
0.983700 | − | 0.179819i | \(-0.0575512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.3137 | −1.01971 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.3771i | 1.24709i | 0.781788 | + | 0.623545i | \(0.214308\pi\) | ||||
−0.781788 | + | 0.623545i | \(0.785692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.10051 | −0.0681853 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.31371 | 0.172309 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0000 | 1.23094 | 0.615470 | − | 0.788160i | \(-0.288966\pi\) | ||||
0.615470 | + | 0.788160i | \(0.288966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.6274 | −0.343895 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5.59767i | − 0.180947i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2548 | −0.911446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.95815i | 0.127550i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.53620i | 0.0816433i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 49.9439i | − 1.60609i | −0.595920 | − | 0.803044i | \(-0.703213\pi\) | ||||
0.595920 | − | 0.803044i | \(-0.296787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 19.1116i | − 0.613954i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.0294 | −0.353951 | −0.176976 | − | 0.984215i | \(-0.556631\pi\) | ||||
−0.176976 | + | 0.984215i | \(0.556631\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1.39942i | − 0.0448172i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.1838 | −1.34958 | −0.674789 | − | 0.738011i | \(-0.735765\pi\) | ||||
−0.674789 | + | 0.738011i | \(0.735765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.6863 | −0.788977 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.72792 | −0.150951 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.5980 | −0.752659 | −0.376329 | − | 0.926486i | \(-0.622814\pi\) | ||||
−0.376329 | + | 0.926486i | \(0.622814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 19.3743i | − 0.617316i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.6274 | 1.22828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 15.3073i | − 0.486254i | −0.969995 | − | 0.243127i | \(-0.921827\pi\) | ||||
0.969995 | − | 0.243127i | \(-0.0781731\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.2346i | 0.800795i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 4.32957i | − 0.137257i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 48.8071i | − 1.54574i | −0.634567 | − | 0.772868i | \(-0.718821\pi\) | ||||
0.634567 | − | 0.772868i | \(-0.281179\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.41421 | 0.0447437 |
(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 | 2352.2.b.i.1567.3 | yes | 4 | |
3.2 | odd | 2 | 7056.2.b.u.1567.2 | 4 | |||
4.3 | odd | 2 | 2352.2.b.j.1567.3 | yes | 4 | ||
7.2 | even | 3 | 2352.2.bl.s.31.3 | 8 | |||
7.3 | odd | 6 | 2352.2.bl.p.607.3 | 8 | |||
7.4 | even | 3 | 2352.2.bl.s.607.2 | 8 | |||
7.5 | odd | 6 | 2352.2.bl.p.31.2 | 8 | |||
7.6 | odd | 2 | 2352.2.b.j.1567.2 | yes | 4 | ||
12.11 | even | 2 | 7056.2.b.t.1567.2 | 4 | |||
21.20 | even | 2 | 7056.2.b.t.1567.3 | 4 | |||
28.3 | even | 6 | 2352.2.bl.s.607.3 | 8 | |||
28.11 | odd | 6 | 2352.2.bl.p.607.2 | 8 | |||
28.19 | even | 6 | 2352.2.bl.s.31.2 | 8 | |||
28.23 | odd | 6 | 2352.2.bl.p.31.3 | 8 | |||
28.27 | even | 2 | inner | 2352.2.b.i.1567.2 | ✓ | 4 | |
84.83 | odd | 2 | 7056.2.b.u.1567.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.2.b.i.1567.2 | ✓ | 4 | 28.27 | even | 2 | inner | |
2352.2.b.i.1567.3 | yes | 4 | 1.1 | even | 1 | trivial | |
2352.2.b.j.1567.2 | yes | 4 | 7.6 | odd | 2 | ||
2352.2.b.j.1567.3 | yes | 4 | 4.3 | odd | 2 | ||
2352.2.bl.p.31.2 | 8 | 7.5 | odd | 6 | |||
2352.2.bl.p.31.3 | 8 | 28.23 | odd | 6 | |||
2352.2.bl.p.607.2 | 8 | 28.11 | odd | 6 | |||
2352.2.bl.p.607.3 | 8 | 7.3 | odd | 6 | |||
2352.2.bl.s.31.2 | 8 | 28.19 | even | 6 | |||
2352.2.bl.s.31.3 | 8 | 7.2 | even | 3 | |||
2352.2.bl.s.607.2 | 8 | 7.4 | even | 3 | |||
2352.2.bl.s.607.3 | 8 | 28.3 | even | 6 | |||
7056.2.b.t.1567.2 | 4 | 12.11 | even | 2 | |||
7056.2.b.t.1567.3 | 4 | 21.20 | even | 2 | |||
7056.2.b.u.1567.2 | 4 | 3.2 | odd | 2 | |||
7056.2.b.u.1567.3 | 4 | 84.83 | odd | 2 |