Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(2255,2352)]
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, 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("2352.2255");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.7808145554\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2255.3 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.2255 |
Dual form | 2352.2.h.k.2255.2 |
$q$-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 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.00000i | − | 0.894427i | −0.894427 | − | 0.447214i | \(-0.852416\pi\) | ||
0.894427 | − | 0.447214i | \(-0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41421 | 0.392232 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843 | − | 2.00000i | 0.730297 | − | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.24264 | −0.884652 | −0.442326 | − | 0.896854i | \(-0.645847\pi\) | ||||
−0.442326 | + | 0.896854i | \(0.645847\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528i | 1.57568i | 0.615882 | + | 0.787839i | \(0.288800\pi\) | ||||
−0.615882 | + | 0.787839i | \(0.711200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48528i | 1.52400i | 0.647576 | + | 0.762001i | \(0.275783\pi\) | ||||
−0.647576 | + | 0.762001i | \(0.724217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.24264 | − | 6.00000i | −0.738549 | − | 1.04447i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.41421 | + | 2.00000i | 0.226455 | + | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000i | 1.56174i | 0.624695 | + | 0.780869i | \(0.285223\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.0000i | − | 1.82998i | −0.403473 | − | 0.914991i | \(-0.632197\pi\) | ||
0.403473 | − | 0.914991i | \(-0.367803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.65685 | + | 2.00000i | 0.843274 | + | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.82843 | + | 2.00000i | −0.396059 | + | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65685i | 0.777029i | 0.921443 | + | 0.388514i | \(0.127012\pi\) | ||||
−0.921443 | + | 0.388514i | \(0.872988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.48528i | 1.14416i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.41421 | 0.181071 | 0.0905357 | − | 0.995893i | \(-0.471142\pi\) | ||||
0.0905357 | + | 0.995893i | \(0.471142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.82843i | − | 0.350823i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000i | 1.46603i | 0.680211 | + | 0.733017i | \(0.261888\pi\) | ||||
−0.680211 | + | 0.733017i | \(0.738112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.24264 | − | 6.00000i | −0.510754 | − | 0.722315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7279 | 1.51053 | 0.755263 | − | 0.655422i | \(-0.227509\pi\) | ||||
0.755263 | + | 0.655422i | \(0.227509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.89949 | −1.15865 | −0.579324 | − | 0.815097i | \(-0.696683\pi\) | ||||
−0.579324 | + | 0.815097i | \(0.696683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | + | 1.41421i | 0.115470 | + | 0.163299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000i | 1.35011i | 0.737769 | + | 0.675053i | \(0.235879\pi\) | ||||
−0.737769 | + | 0.675053i | \(0.764121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.0000 | + | 8.48528i | −1.28654 | + | 0.909718i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000i | 0.212000i | 0.994366 | + | 0.106000i | \(0.0338043\pi\) | ||||
−0.994366 | + | 0.106000i | \(0.966196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.0000 | + | 8.48528i | −1.24434 | + | 0.879883i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.07107 | 0.717958 | 0.358979 | − | 0.933346i | \(-0.383125\pi\) | ||||
0.358979 | + | 0.933346i | \(0.383125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | − | 12.0000i | 0.426401 | − | 1.20605i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.00000i | 0.199007i | 0.995037 | + | 0.0995037i | \(0.0317255\pi\) | ||||
−0.995037 | + | 0.0995037i | \(0.968274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.48528i | 0.836080i | 0.908429 | + | 0.418040i | \(0.137283\pi\) | ||||
−0.908429 | + | 0.418040i | \(0.862717\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.24264 | 0.410152 | 0.205076 | − | 0.978746i | \(-0.434256\pi\) | ||||
0.205076 | + | 0.978746i | \(0.434256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0000 | 1.14939 | 0.574696 | − | 0.818367i | \(-0.305120\pi\) | ||||
0.574696 | + | 0.818367i | \(0.305120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | + | 8.48528i | 0.569495 | + | 0.805387i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.3137i | − | 1.06430i | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||
0.846649 | − | 0.532152i | \(-0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.48528i | 0.791257i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41421 | + | 4.00000i | −0.130744 | + | 0.369800i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.1421 | + | 10.0000i | −1.27515 | + | 0.901670i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0000i | − | 1.07331i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.0000i | − | 1.06483i | −0.846484 | − | 0.532414i | \(-0.821285\pi\) | ||
0.846484 | − | 0.532414i | \(-0.178715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.9706 | − | 12.0000i | 1.49417 | − | 1.05654i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0000 | 1.57267 | 0.786334 | − | 0.617802i | \(-0.211977\pi\) | ||||
0.786334 | + | 0.617802i | \(0.211977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.82843 | + | 10.0000i | 0.243432 | + | 0.860663i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.48528i | − | 0.724947i | −0.931994 | − | 0.362473i | \(-0.881932\pi\) | ||
0.931994 | − | 0.362473i | \(-0.118068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.48528i | 0.719712i | 0.933008 | + | 0.359856i | \(0.117174\pi\) | ||||
−0.933008 | + | 0.359856i | \(0.882826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | − | 8.48528i | −0.505291 | − | 0.714590i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00000 | −0.501745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.9706 | 1.40933 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.3137i | − | 0.926855i | −0.886135 | − | 0.463428i | \(-0.846619\pi\) | ||
0.886135 | − | 0.463428i | \(-0.153381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.65685 | − | 2.00000i | −0.457330 | − | 0.161690i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.9706 | 1.36311 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.3848 | −1.46726 | −0.733632 | − | 0.679546i | \(-0.762177\pi\) | ||||
−0.733632 | + | 0.679546i | \(0.762177\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.00000 | + | 5.65685i | −0.634441 | + | 0.448618i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.0000 | + | 8.48528i | −0.934199 | + | 0.660578i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.0000i | 1.67263i | 0.548250 | + | 0.836315i | \(0.315294\pi\) | ||||
−0.548250 | + | 0.836315i | \(0.684706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0000 | − | 16.9706i | −0.901975 | − | 1.27559i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.24264 | −0.317110 | −0.158555 | − | 0.987350i | \(-0.550683\pi\) | ||||
−0.158555 | + | 0.987350i | \(0.550683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.41421 | −0.105118 | −0.0525588 | − | 0.998618i | \(-0.516738\pi\) | ||||
−0.0525588 | + | 0.998618i | \(0.516738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.41421 | + | 2.00000i | 0.104542 | + | 0.147844i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 12.0000i | − | 0.882258i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.48528i | − | 0.620505i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7279 | −0.920960 | −0.460480 | − | 0.887670i | \(-0.652323\pi\) | ||||
−0.460480 | + | 0.887670i | \(0.652323\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.00000 | 0.287926 | 0.143963 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143963 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.00000 | − | 2.82843i | 0.286446 | − | 0.202548i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.65685i | − | 0.403034i | −0.979485 | − | 0.201517i | \(-0.935413\pi\) | ||
0.979485 | − | 0.201517i | \(-0.0645872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.9706i | 1.20301i | 0.798869 | + | 0.601506i | \(0.205432\pi\) | ||||
−0.798869 | + | 0.601506i | \(0.794568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.9706 | + | 12.0000i | −1.19701 | + | 0.846415i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.0000 | 1.39686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.24264 | − | 12.0000i | 0.294884 | − | 0.834058i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.0000i | − | 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.7279 | + | 18.0000i | 0.872103 | + | 1.23334i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.0000 | −1.63679 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.89949 | − | 14.0000i | −0.668946 | − | 0.946032i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.82843i | 0.190261i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | + | 2.82843i | −0.0666667 | + | 0.188562i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.07107 | 0.467269 | 0.233635 | − | 0.972324i | \(-0.424938\pi\) | ||||
0.233635 | + | 0.972324i | \(0.424938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.48528i | 0.555889i | 0.960597 | + | 0.277945i | \(0.0896532\pi\) | ||||
−0.960597 | + | 0.277945i | \(0.910347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000i | 0.782794i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.9706 | + | 12.0000i | −1.10236 | + | 0.779484i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.2132 | −1.37217 | −0.686084 | − | 0.727522i | \(-0.740672\pi\) | ||||
−0.686084 | + | 0.727522i | \(0.740672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.0416 | −1.54866 | −0.774329 | − | 0.632783i | \(-0.781912\pi\) | ||||
−0.774329 | + | 0.632783i | \(0.781912\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 8.48528i | −0.380235 | − | 0.537733i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.00000 | + | 5.65685i | 0.250490 | + | 0.354246i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 14.0000i | − | 0.873296i | −0.899632 | − | 0.436648i | \(-0.856166\pi\) | ||
0.899632 | − | 0.436648i | \(-0.143834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.0000 | − | 8.48528i | −1.48556 | − | 0.525226i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.24264 | 0.261612 | 0.130806 | − | 0.991408i | \(-0.458243\pi\) | ||||
0.130806 | + | 0.991408i | \(0.458243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.3137 | 0.694996 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.82843 | + | 2.00000i | −0.173097 | + | 0.122398i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 10.0000i | − | 0.609711i | −0.952399 | − | 0.304855i | \(-0.901392\pi\) | ||
0.952399 | − | 0.304855i | \(-0.0986081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.48528i | 0.515444i | 0.966219 | + | 0.257722i | \(0.0829719\pi\) | ||||
−0.966219 | + | 0.257722i | \(0.917028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.24264 | −0.255841 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.00000 | 0.480673 | 0.240337 | − | 0.970690i | \(-0.422742\pi\) | ||||
0.240337 | + | 0.970690i | \(0.422742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.0000 | − | 8.48528i | −1.43684 | − | 0.508001i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.48528i | − | 0.506189i | −0.967442 | − | 0.253095i | \(-0.918552\pi\) | ||
0.967442 | − | 0.253095i | \(-0.0814484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 16.9706i | − | 1.00880i | −0.863472 | − | 0.504398i | \(-0.831715\pi\) | ||
0.863472 | − | 0.504398i | \(-0.168285\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.07107 | + | 10.0000i | 0.414513 | + | 0.586210i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.0000i | − | 1.28525i | −0.766179 | − | 0.642627i | \(-0.777845\pi\) | ||
0.766179 | − | 0.642627i | \(-0.222155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000i | 1.39733i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.2132 | − | 6.00000i | 1.23091 | − | 0.348155i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.82843 | + | 2.00000i | −0.162489 | + | 0.114897i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.82843i | − | 0.161955i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.9706i | − | 0.968561i | −0.874913 | − | 0.484281i | \(-0.839081\pi\) | ||
0.874913 | − | 0.484281i | \(-0.160919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | + | 8.48528i | −0.682656 | + | 0.482711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | −0.340229 | −0.170114 | − | 0.985424i | \(-0.554414\pi\) | ||||
−0.170114 | + | 0.985424i | \(0.554414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.5563 | 0.879297 | 0.439648 | − | 0.898170i | \(-0.355103\pi\) | ||||
0.439648 | + | 0.898170i | \(0.355103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.2843i | 1.58860i | 0.607524 | + | 0.794301i | \(0.292163\pi\) | ||||
−0.607524 | + | 0.794301i | \(0.707837\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.0000i | − | 2.01561i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.24264 | + | 6.00000i | 0.236801 | + | 0.334887i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.41421 | 0.0784465 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0000 | + | 16.9706i | 0.663602 | + | 0.938474i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.0000i | − | 1.31916i | −0.751635 | − | 0.659580i | \(-0.770734\pi\) | ||
0.751635 | − | 0.659580i | \(-0.229266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.00000 | + | 16.9706i | −0.328798 | + | 0.929981i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.0000 | 1.31126 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0000 | − | 11.3137i | 0.869001 | − | 0.614476i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 36.0000i | − | 1.94951i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.0000 | + | 8.48528i | −0.646058 | + | 0.456832i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.2132 | −1.13878 | −0.569392 | − | 0.822066i | \(-0.692821\pi\) | ||||
−0.569392 | + | 0.822066i | \(0.692821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.5269 | 1.74113 | 0.870563 | − | 0.492057i | \(-0.163755\pi\) | ||||
0.870563 | + | 0.492057i | \(0.163755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.07107 | + | 2.00000i | −0.377426 | + | 0.106752i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.0000i | 1.80964i | 0.425797 | + | 0.904819i | \(0.359994\pi\) | ||||
−0.425797 | + | 0.904819i | \(0.640006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 25.4558i | − | 1.35106i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.7279 | 0.671754 | 0.335877 | − | 0.941906i | \(-0.390967\pi\) | ||||
0.335877 | + | 0.941906i | \(0.390967\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | + | 9.89949i | 0.367405 | + | 0.519589i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.7990i | 1.03633i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.9706i | − | 0.885856i | −0.896557 | − | 0.442928i | \(-0.853940\pi\) | ||
0.896557 | − | 0.442928i | \(-0.146060\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.2843 | − | 10.0000i | −1.47242 | − | 0.520579i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0000 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.9706 | − | 12.0000i | 0.876356 | − | 0.619677i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000i | 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000i | 1.23280i | 0.787434 | + | 0.616399i | \(0.211409\pi\) | ||||
−0.787434 | + | 0.616399i | \(0.788591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.9706 | − | 12.0000i | 0.869428 | − | 0.614779i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 33.9411 | + | 12.0000i | 1.72532 | + | 0.609994i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 25.4558i | − | 1.29066i | −0.763903 | − | 0.645331i | \(-0.776719\pi\) | ||
0.763903 | − | 0.645331i | \(-0.223281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.48528i | − | 0.429119i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0000 | + | 25.4558i | 0.907980 | + | 1.28408i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.0000 | 1.20757 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.07107 | −0.354887 | −0.177443 | − | 0.984131i | \(-0.556783\pi\) | ||||
−0.177443 | + | 0.984131i | \(0.556783\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.48528i | 0.423735i | 0.977298 | + | 0.211867i | \(0.0679545\pi\) | ||||
−0.977298 | + | 0.211867i | \(0.932046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000i | 0.597763i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.3137 | + | 14.0000i | −0.562183 | + | 0.695666i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.4558 | −1.26180 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.8701 | −1.32864 | −0.664319 | − | 0.747449i | \(-0.731279\pi\) | ||||
−0.664319 | + | 0.747449i | \(0.731279\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | − | 8.48528i | 0.591916 | − | 0.418548i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000i | 0.589057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0000 | + | 8.48528i | −0.587643 | + | 0.415526i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000 | − | 16.9706i | 0.291730 | − | 0.825137i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000i | 0.0970143i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.00000 | − | 8.48528i | −0.289683 | − | 0.409673i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.6985 | 1.43053 | 0.715263 | − | 0.698856i | \(-0.246307\pi\) | ||||
0.715263 | + | 0.698856i | \(0.246307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.5269 | −1.56314 | −0.781572 | − | 0.623815i | \(-0.785582\pi\) | ||||
−0.781572 | + | 0.623815i | \(0.785582\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.9706 | + | 24.0000i | 0.813676 | + | 1.15071i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.9411i | 1.61992i | 0.586484 | + | 0.809961i | \(0.300512\pi\) | ||||
−0.586484 | + | 0.809961i | \(0.699488\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.1838 | 1.81417 | 0.907083 | − | 0.420952i | \(-0.138304\pi\) | ||||
0.907083 | + | 0.420952i | \(0.138304\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.00000 | 0.189618 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.0000 | − | 11.3137i | 0.756774 | − | 0.535120i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.65685i | 0.266963i | 0.991051 | + | 0.133482i | \(0.0426157\pi\) | ||||
−0.991051 | + | 0.133482i | \(0.957384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 42.4264i | − | 1.99778i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0000 | 0.467780 | 0.233890 | − | 0.972263i | \(-0.424854\pi\) | ||||
0.233890 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.82843 | − | 10.0000i | −0.132020 | − | 0.466760i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.0000i | 1.58354i | 0.610821 | + | 0.791769i | \(0.290840\pi\) | ||||
−0.610821 | + | 0.791769i | \(0.709160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000i | 1.11537i | 0.830051 | + | 0.557687i | \(0.188311\pi\) | ||||
−0.830051 | + | 0.557687i | \(0.811689\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.9706 | + | 24.0000i | 0.786991 | + | 1.11297i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.3848 | − | 26.0000i | −0.847126 | − | 1.19802i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 50.9117i | 2.34092i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.0000 | − | 5.65685i | −0.732590 | − | 0.259010i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0000 | −0.822441 | −0.411220 | − | 0.911536i | \(-0.634897\pi\) | ||||
−0.411220 | + | 0.911536i | \(0.634897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.48528 | 0.386896 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 14.1421i | − | 0.642161i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.0000i | − | 1.08754i | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||
0.839233 | − | 0.543772i | \(-0.183004\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.2132 | −0.957338 | −0.478669 | − | 0.877995i | \(-0.658881\pi\) | ||||
−0.478669 | + | 0.877995i | \(0.658881\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.9706 | −0.764316 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −24.0000 | − | 8.48528i | −1.07872 | − | 0.381385i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | − | 25.4558i | −0.804181 | − | 1.13728i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0000 | − | 15.5563i | −0.488527 | − | 0.690882i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 10.0000i | − | 0.443242i | −0.975133 | − | 0.221621i | \(-0.928865\pi\) | ||
0.975133 | − | 0.221621i | \(-0.0711348\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.9706 | 0.747812 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.4558 | 1.11955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31.1127 | + | 22.0000i | −1.36570 | + | 0.965693i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 14.0000i | − | 0.613351i | −0.951814 | − | 0.306676i | \(-0.900783\pi\) | ||
0.951814 | − | 0.306676i | \(-0.0992167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 25.4558i | − | 1.11311i | −0.830812 | − | 0.556553i | \(-0.812124\pi\) | ||
0.830812 | − | 0.556553i | \(-0.187876\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.9706 | −0.739249 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.00000 | −0.217391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | − | 33.9411i | 0.520756 | − | 1.47292i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.1421i | 0.612564i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.48528i | − | 0.366851i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.24264 | − | 6.00000i | −0.183083 | − | 0.258919i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0000 | 0.687894 | 0.343947 | − | 0.938989i | \(-0.388236\pi\) | ||||
0.343947 | + | 0.938989i | \(0.388236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.41421 | − | 2.00000i | −0.0606897 | − | 0.0858282i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 24.0000i | − | 1.02805i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.41421 | + | 4.00000i | −0.0603572 | + | 0.170716i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.9706 | − | 12.0000i | 0.720360 | − | 0.509372i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 5.65685i | − | 0.239689i | −0.992793 | − | 0.119844i | \(-0.961760\pi\) | ||
0.992793 | − | 0.119844i | \(-0.0382395\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16.9706i | − | 0.717778i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | − | 8.48528i | 0.506640 | − | 0.358249i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.6274 | −0.951943 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.48528i | 0.355722i | 0.984056 | + | 0.177861i | \(0.0569177\pi\) | ||||
−0.984056 | + | 0.177861i | \(0.943082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000i | 0.502184i | 0.967963 | + | 0.251092i | \(0.0807897\pi\) | ||||
−0.967963 | + | 0.251092i | \(0.919210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.7279 | − | 18.0000i | −0.531717 | − | 0.751961i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.24264 | −0.176930 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.89949 | 0.412121 | 0.206061 | − | 0.978539i | \(-0.433936\pi\) | ||||
0.206061 | + | 0.978539i | \(0.433936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.00000 | + | 5.65685i | 0.166234 | + | 0.235091i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.0000i | − | 0.993978i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.00000 | + | 2.82843i | 0.330759 | + | 0.116941i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.00000 | − | 5.65685i | 0.329076 | − | 0.232692i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.0000i | 1.06769i | 0.845582 | + | 0.533846i | \(0.179254\pi\) | ||||
−0.845582 | + | 0.533846i | \(0.820746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.0000 | + | 16.9706i | −0.982255 | + | 0.694559i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.6690 | 1.90685 | 0.953423 | − | 0.301637i | \(-0.0975331\pi\) | ||||
0.953423 | + | 0.301637i | \(0.0975331\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5563 | 0.634557 | 0.317278 | − | 0.948332i | \(-0.397231\pi\) | ||||
0.317278 | + | 0.948332i | \(0.397231\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.9411 | − | 12.0000i | −1.38219 | − | 0.488678i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 14.0000i | − | 0.569181i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.48528 | −0.343278 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.0000 | 1.45403 | 0.727013 | − | 0.686624i | \(-0.240908\pi\) | ||||
0.727013 | + | 0.686624i | \(0.240908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.0000 | + | 28.2843i | 0.806478 | + | 1.14053i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.48528i | − | 0.341605i | −0.985305 | − | 0.170802i | \(-0.945364\pi\) | ||
0.985305 | − | 0.170802i | \(-0.0546359\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.48528i | − | 0.341052i | −0.985353 | − | 0.170526i | \(-0.945453\pi\) | ||
0.985353 | − | 0.170526i | \(-0.0545467\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.2132 | − | 6.00000i | 0.851257 | − | 0.240772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000i | 0.478471i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000i | 0.955425i | 0.878516 | + | 0.477712i | \(0.158534\pi\) | ||||
−0.878516 | + | 0.477712i | \(0.841466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.9706 | − | 12.0000i | 0.674519 | − | 0.476957i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.0000 | −0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.7279 | + | 36.0000i | −0.503509 | + | 1.42414i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 42.4264i | − | 1.67574i | −0.545868 | − | 0.837871i | \(-0.683800\pi\) | ||
0.545868 | − | 0.837871i | \(-0.316200\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 33.9411i | − | 1.33851i | −0.743034 | − | 0.669254i | \(-0.766614\pi\) | ||
0.743034 | − | 0.669254i | \(-0.233386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.0000 | − | 33.9411i | −0.944999 | − | 1.33643i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.0000 | 1.17942 | 0.589711 | − | 0.807614i | \(-0.299242\pi\) | ||||
0.589711 | + | 0.807614i | \(0.299242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.9117 | 1.99846 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 25.4558i | − | 0.996164i | −0.867130 | − | 0.498082i | \(-0.834038\pi\) | ||
0.867130 | − | 0.498082i | \(-0.165962\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 36.0000i | − | 1.40664i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.89949 | − | 28.0000i | 0.386216 | − | 1.09238i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.24264 | 0.165270 | 0.0826349 | − | 0.996580i | \(-0.473666\pi\) | ||||
0.0826349 | + | 0.996580i | \(0.473666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41421 | −0.0550065 | −0.0275033 | − | 0.999622i | \(-0.508756\pi\) | ||||
−0.0275033 | + | 0.999622i | \(0.508756\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.00000 | + | 2.82843i | −0.155347 | + | 0.109847i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 36.0000i | − | 1.39393i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | −0.231627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0000 | −1.15642 | −0.578208 | − | 0.815890i | \(-0.696248\pi\) | ||||
−0.578208 | + | 0.815890i | \(0.696248\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.00000 | + | 1.41421i | −0.192450 | + | 0.0544331i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.0000i | 1.30673i | 0.757045 | + | 0.653363i | \(0.226642\pi\) | ||||
−0.757045 | + | 0.653363i | \(0.773358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | + | 16.9706i | 0.459841 | + | 0.650313i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.6985 | −1.13638 | −0.568190 | − | 0.822897i | \(-0.692356\pi\) | ||||
−0.568190 | + | 0.822897i | \(0.692356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.9706 | −0.648412 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.07107 | + | 10.0000i | 0.269778 | + | 0.381524i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.00000i | 0.304776i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 25.4558i | − | 0.968386i | −0.874961 | − | 0.484193i | \(-0.839113\pi\) | ||
0.874961 | − | 0.484193i | \(-0.160887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9706 | 0.643730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.0000 | −0.757554 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0000 | + | 8.48528i | −0.453882 | + | 0.320943i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 42.4264i | − | 1.60242i | −0.598381 | − | 0.801212i | \(-0.704189\pi\) | ||
0.598381 | − | 0.801212i | \(-0.295811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.9706 | + | 12.0000i | −0.639148 | + | 0.451946i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0000 | −0.450669 | −0.225335 | − | 0.974281i | \(-0.572348\pi\) | ||||
−0.225335 | + | 0.974281i | \(0.572348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.9411 | − | 12.0000i | −1.27289 | − | 0.450035i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 36.0000i | − | 1.34821i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000i | 0.448775i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.2132 | − | 30.0000i | −0.792222 | − | 1.12037i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.0416 | − | 34.0000i | −0.894118 | − | 1.26447i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.48528i | 0.315135i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.48528i | 0.314702i | 0.987543 | + | 0.157351i | \(0.0502953\pi\) | ||||
−0.987543 | + | 0.157351i | \(0.949705\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | 0.887672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.89949 | −0.365646 | −0.182823 | − | 0.983146i | \(-0.558524\pi\) | ||||
−0.182823 | + | 0.983146i | \(0.558524\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 50.9117i | − | 1.87536i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.0000i | − | 0.882854i | −0.897297 | − | 0.441427i | \(-0.854472\pi\) | ||
0.897297 | − | 0.441427i | \(-0.145528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.7279 | 0.466942 | 0.233471 | − | 0.972364i | \(-0.424992\pi\) | ||||
0.233471 | + | 0.972364i | \(0.424992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.6274 | −0.829004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | − | 16.9706i | 0.219529 | − | 0.620920i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000i | 0.437886i | 0.975738 | + | 0.218943i | \(0.0702609\pi\) | ||||
−0.975738 | + | 0.218943i | \(0.929739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000 | + | 16.9706i | 0.437304 | + | 0.618442i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.0000 | 1.30844 | 0.654221 | − | 0.756303i | \(-0.272997\pi\) | ||||
0.654221 | + | 0.756303i | \(0.272997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.0000 | + | 25.4558i | 0.653359 | + | 0.923989i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0000i | 0.507500i | 0.967270 | + | 0.253750i | \(0.0816640\pi\) | ||||
−0.967270 | + | 0.253750i | \(0.918336\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | + | 11.3137i | −0.144620 | + | 0.409048i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.9706 | −0.612772 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.0416 | −0.866963 | −0.433482 | − | 0.901162i | \(-0.642715\pi\) | ||||
−0.433482 | + | 0.901162i | \(0.642715\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.7990 | − | 14.0000i | 0.713043 | − | 0.504198i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.0000i | 0.359675i | 0.983696 | + | 0.179838i | \(0.0575572\pi\) | ||||
−0.983696 | + | 0.179838i | \(0.942443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.48528i | 0.304800i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.0000 | −1.93227 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.0000 | − | 42.4264i | −0.428845 | − | 1.51620i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.7696i | 1.31236i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.48528i | 0.302468i | 0.988498 | + | 0.151234i | \(0.0483246\pi\) | ||||
−0.988498 | + | 0.151234i | \(0.951675\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.24264 | + | 6.00000i | 0.151042 | + | 0.213606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000 | 0.0710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.3137 | + | 16.0000i | 0.401256 | + | 0.567462i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.0000i | 1.34603i | 0.739629 | + | 0.673015i | \(0.235001\pi\) | ||||
−0.739629 | + | 0.673015i | \(0.764999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.0000i | − | 0.424529i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.65685 | − | 2.00000i | −0.199875 | − | 0.0706665i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.0000 | 1.48215 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.1421 | − | 10.0000i | 0.497827 | − | 0.352017i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.2548i | 1.59108i | 0.605904 | + | 0.795538i | \(0.292811\pi\) | ||||
−0.605904 | + | 0.795538i | \(0.707189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.4558i | 0.893876i | 0.894565 | + | 0.446938i | \(0.147485\pi\) | ||||
−0.894565 | + | 0.446938i | \(0.852515\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | + | 8.48528i | −0.420858 | + | 0.297592i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 22.6274i | − | 0.789702i | −0.918745 | − | 0.394851i | \(-0.870796\pi\) | ||
0.918745 | − | 0.394851i | \(-0.129204\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.0000i | 1.25488i | 0.778664 | + | 0.627441i | \(0.215897\pi\) | ||||
−0.778664 | + | 0.627441i | \(0.784103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.24264 | − | 6.00000i | −0.147710 | − | 0.208893i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.2132 | −0.737655 | −0.368828 | − | 0.929498i | \(-0.620241\pi\) | ||||
−0.368828 | + | 0.929498i | \(0.620241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.8701 | 0.933236 | 0.466618 | − | 0.884459i | \(-0.345472\pi\) | ||||
0.466618 | + | 0.884459i | \(0.345472\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.00000 | + | 11.3137i | 0.277517 | + | 0.392468i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.0000i | 1.24583i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.0000 | − | 42.4264i | −0.414781 | − | 1.46647i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.00000 | 0.207143 | 0.103572 | − | 0.994622i | \(-0.466973\pi\) | ||||
0.103572 | + | 0.994622i | \(0.466973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.0000 | −1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000 | − | 8.48528i | 0.413302 | − | 0.292249i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.0000i | 0.756823i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.0000 | − | 16.9706i | 0.823678 | − | 0.582428i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.4558 | −0.872615 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.07107 | 0.242109 | 0.121054 | − | 0.992646i | \(-0.461372\pi\) | ||||
0.121054 | + | 0.992646i | \(0.461372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 10.0000i | − | 0.341593i | −0.985306 | − | 0.170797i | \(-0.945366\pi\) | ||
0.985306 | − | 0.170797i | \(-0.0546341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.9117i | 1.73708i | 0.495615 | + | 0.868542i | \(0.334943\pi\) | ||||
−0.495615 | + | 0.868542i | \(0.665057\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.7279 | −0.433264 | −0.216632 | − | 0.976253i | \(-0.569507\pi\) | ||||
−0.216632 | + | 0.976253i | \(0.569507\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.0000 | 1.49604 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | + | 18.3848i | 0.441503 | + | 0.624380i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 50.9117i | − | 1.72706i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9706i | 0.575026i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.07107 | + | 20.0000i | −0.239319 | + | 0.676897i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0000 | 0.405211 | 0.202606 | − | 0.979260i | \(-0.435059\pi\) | ||||
0.202606 | + | 0.979260i | \(0.435059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.1127 | − | 22.0000i | 1.04941 | − | 0.742042i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0000i | 0.471672i | 0.971793 | + | 0.235836i | \(0.0757828\pi\) | ||||
−0.971793 | + | 0.235836i | \(0.924217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 48.0000i | − | 1.61533i | −0.589643 | − | 0.807664i | \(-0.700731\pi\) | ||
0.589643 | − | 0.807664i | \(-0.299269\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.9411 | + | 24.0000i | −1.14092 | + | 0.806751i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.0000 | −1.41022 | −0.705111 | − | 0.709097i | \(-0.749103\pi\) | ||||
−0.705111 | + | 0.709097i | \(0.749103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.6985 | + | 24.0000i | 0.994937 | + | 0.804030i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.48528i | 0.283632i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | − | 8.48528i | −0.200334 | − | 0.283315i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −72.0000 | −2.40133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.3137 | −0.376914 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.82843i | 0.0940201i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0000i | 0.796907i | 0.917189 | + | 0.398453i | \(0.130453\pi\) | ||||
−0.917189 | + | 0.398453i | \(0.869547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.65685 | − | 2.00000i | −0.187626 | − | 0.0663358i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24264 | 0.140565 | 0.0702825 | − | 0.997527i | \(-0.477610\pi\) | ||||
0.0702825 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.4558 | 0.842465 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.00000 | − | 2.82843i | 0.132236 | − | 0.0935049i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0000i | 0.395843i | 0.980218 | + | 0.197922i | \(0.0634192\pi\) | ||||
−0.980218 | + | 0.197922i | \(0.936581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0000 | − | 16.9706i | 0.790827 | − | 0.559199i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.0000 | 0.592477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.0000 | − | 8.48528i | −0.788263 | − | 0.278693i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0000i | 0.459325i | 0.973270 | + | 0.229663i | \(0.0737623\pi\) | ||||
−0.973270 | + | 0.229663i | \(0.926238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.00000 | − | 8.48528i | −0.196431 | − | 0.277796i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.9706 | −0.554997 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.3553 | −1.15501 | −0.577504 | − | 0.816388i | \(-0.695973\pi\) | ||||
−0.577504 | + | 0.816388i | \(0.695973\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.5563 | + | 22.0000i | 0.507662 | + | 0.717943i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 22.0000i | − | 0.717180i | −0.933495 | − | 0.358590i | \(-0.883258\pi\) | ||
0.933495 | − | 0.358590i | \(-0.116742\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 42.4264i | − | 1.38159i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.6690 | −1.51654 | −0.758270 | − | 0.651940i | \(-0.773955\pi\) | ||||
−0.758270 | + | 0.651940i | \(0.773955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0000 | −0.454459 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.0000 | + | 28.2843i | −1.29709 | + | 0.917180i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.2548i | 1.46595i | 0.680257 | + | 0.732974i | \(0.261868\pi\) | ||||
−0.680257 | + | 0.732974i | \(0.738132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.4558i | 0.823732i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 50.9117 | − | 36.0000i | 1.64574 | − | 1.16371i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −41.0000 | −1.32258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.24264 | + | 12.0000i | −0.136717 | + | 0.386695i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 8.00000i | − | 0.257529i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12.0000i | − | 0.385894i | −0.981209 | − | 0.192947i | \(-0.938195\pi\) | ||
0.981209 | − | 0.192947i | \(-0.0618045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | 0.577647 | 0.288824 | − | 0.957382i | \(-0.406736\pi\) | ||||
0.288824 | + | 0.957382i | \(0.406736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.41421 | + | 2.00000i | 0.0452911 | + | 0.0640513i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 25.4558i | − | 0.814405i | −0.913338 | − | 0.407202i | \(-0.866504\pi\) | ||
0.913338 | − | 0.407202i | \(-0.133496\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.48528i | − | 0.271191i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.0000 | + | 33.9411i | −0.383131 | + | 1.08366i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.0000 | −1.53096 | −0.765481 | − | 0.643458i | \(-0.777499\pi\) | ||||
−0.765481 | + | 0.643458i | \(0.777499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.3137 | −0.360485 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.9117i | 1.61890i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0000i | 1.14358i | 0.820401 | + | 0.571789i | \(0.193750\pi\) | ||||
−0.820401 | + | 0.571789i | \(0.806250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.9411 | − | 24.0000i | 1.07709 | − | 0.761617i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.9411 | 1.07601 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.0416 | 0.761406 | 0.380703 | − | 0.924697i | \(-0.375682\pi\) | ||||
0.380703 | + | 0.924697i | \(0.375682\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.0000 | + | 8.48528i | −0.949158 | + | 0.268462i |
(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.h.k.2255.3 | yes | 4 | |
3.2 | odd | 2 | 2352.2.h.f.2255.4 | yes | 4 | ||
4.3 | odd | 2 | 2352.2.h.f.2255.1 | ✓ | 4 | ||
7.6 | odd | 2 | 2352.2.h.f.2255.2 | yes | 4 | ||
12.11 | even | 2 | inner | 2352.2.h.k.2255.2 | yes | 4 | |
21.20 | even | 2 | inner | 2352.2.h.k.2255.1 | yes | 4 | |
28.27 | even | 2 | inner | 2352.2.h.k.2255.4 | yes | 4 | |
84.83 | odd | 2 | 2352.2.h.f.2255.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.2.h.f.2255.1 | ✓ | 4 | 4.3 | odd | 2 | ||
2352.2.h.f.2255.2 | yes | 4 | 7.6 | odd | 2 | ||
2352.2.h.f.2255.3 | yes | 4 | 84.83 | odd | 2 | ||
2352.2.h.f.2255.4 | yes | 4 | 3.2 | odd | 2 | ||
2352.2.h.k.2255.1 | yes | 4 | 21.20 | even | 2 | inner | |
2352.2.h.k.2255.2 | yes | 4 | 12.11 | even | 2 | inner | |
2352.2.h.k.2255.3 | yes | 4 | 1.1 | even | 1 | trivial | |
2352.2.h.k.2255.4 | yes | 4 | 28.27 | even | 2 | inner |