Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.10 | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.l.1873.10 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.43592 | 1.53659 | 0.768294 | − | 0.640097i | \(-0.221106\pi\) | ||||
0.768294 | + | 0.640097i | \(0.221106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.83889 | − | 1.90223i | 0.695036 | − | 0.718975i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.40938 | 1.32948 | 0.664739 | − | 0.747076i | \(-0.268543\pi\) | ||||
0.664739 | + | 0.747076i | \(0.268543\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.49401 | + | 2.58771i | 0.414365 | + | 0.717701i | 0.995362 | − | 0.0962048i | \(-0.0306704\pi\) |
−0.580997 | + | 0.813906i | \(0.697337\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.542270 | − | 0.939239i | −0.131520 | − | 0.227799i | 0.792743 | − | 0.609556i | \(-0.208652\pi\) |
−0.924263 | + | 0.381757i | \(0.875319\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.74273 | − | 6.48261i | 0.858642 | − | 1.48721i | −0.0145824 | − | 0.999894i | \(-0.504642\pi\) |
0.873225 | − | 0.487318i | \(-0.162025\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.32558 | −0.901945 | −0.450972 | − | 0.892538i | \(-0.648923\pi\) | ||||
−0.450972 | + | 0.892538i | \(0.648923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.80552 | 1.36110 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.68485 | + | 2.91825i | −0.312870 | + | 0.541906i | −0.978982 | − | 0.203945i | \(-0.934624\pi\) |
0.666113 | + | 0.745851i | \(0.267957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.68734 | − | 8.11872i | 0.841872 | − | 1.45816i | −0.0464389 | − | 0.998921i | \(-0.514787\pi\) |
0.888311 | − | 0.459243i | \(-0.151879\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.31828 | − | 6.53590i | 1.06798 | − | 1.10477i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50767 | + | 4.34341i | −0.412258 | + | 0.714052i | −0.995136 | − | 0.0985079i | \(-0.968593\pi\) |
0.582878 | + | 0.812559i | \(0.301926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.20160 | + | 2.08122i | 0.187658 | + | 0.325033i | 0.944469 | − | 0.328601i | \(-0.106577\pi\) |
−0.756811 | + | 0.653634i | \(0.773244\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.31412 | + | 5.74023i | −0.505399 | + | 0.875377i | 0.494581 | + | 0.869131i | \(0.335321\pi\) |
−0.999980 | + | 0.00624563i | \(0.998012\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.50415 | − | 2.60527i | −0.219403 | − | 0.380018i | 0.735222 | − | 0.677826i | \(-0.237078\pi\) |
−0.954626 | + | 0.297808i | \(0.903744\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.236948 | − | 6.99599i | −0.0338498 | − | 0.999427i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.530699 | + | 0.919198i | 0.0728971 | + | 0.126262i | 0.900170 | − | 0.435539i | \(-0.143442\pi\) |
−0.827273 | + | 0.561801i | \(0.810109\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.1502 | 2.04286 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.20470 | + | 10.7468i | −0.807783 | + | 1.39912i | 0.106614 | + | 0.994301i | \(0.465999\pi\) |
−0.914396 | + | 0.404820i | \(0.867334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.71334 | + | 4.69965i | 0.347408 | + | 0.601728i | 0.985788 | − | 0.167993i | \(-0.0537286\pi\) |
−0.638380 | + | 0.769721i | \(0.720395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.13331 | + | 8.89115i | 0.636708 | + | 1.10281i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.66999 | − | 2.89251i | 0.204022 | − | 0.353376i | −0.745799 | − | 0.666171i | \(-0.767932\pi\) |
0.949821 | + | 0.312795i | \(0.101265\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9064 | −1.53171 | −0.765857 | − | 0.643011i | \(-0.777685\pi\) | ||||
−0.765857 | + | 0.643011i | \(0.777685\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.21382 | − | 14.2267i | −0.961355 | − | 1.66511i | −0.719106 | − | 0.694901i | \(-0.755448\pi\) |
−0.242249 | − | 0.970214i | \(-0.577885\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.10837 | − | 8.38764i | 0.924035 | − | 0.955861i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.17516 | − | 2.03543i | −0.132216 | − | 0.229004i | 0.792315 | − | 0.610113i | \(-0.208876\pi\) |
−0.924530 | + | 0.381108i | \(0.875542\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.60602 | + | 2.78171i | −0.176283 | + | 0.305332i | −0.940605 | − | 0.339504i | \(-0.889741\pi\) |
0.764321 | + | 0.644836i | \(0.223074\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.86319 | − | 3.22715i | −0.202092 | − | 0.350033i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.67524 | + | 9.82981i | −0.601575 | + | 1.04196i | 0.391008 | + | 0.920387i | \(0.372126\pi\) |
−0.992583 | + | 0.121570i | \(0.961207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.66974 | + | 1.91656i | 0.804008 | + | 0.200910i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.8597 | − | 22.2737i | 1.31938 | − | 2.28523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.40321 | + | 11.0907i | −0.650148 | + | 1.12609i | 0.332939 | + | 0.942948i | \(0.391960\pi\) |
−0.983087 | + | 0.183140i | \(0.941374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.776221 | 0.0772369 | 0.0386184 | − | 0.999254i | \(-0.487704\pi\) | ||||
0.0386184 | + | 0.999254i | \(0.487704\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.28262 | −0.224913 | −0.112457 | − | 0.993657i | \(-0.535872\pi\) | ||||
−0.112457 | + | 0.993657i | \(0.535872\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.27468 | + | 3.93986i | −0.219901 | + | 0.380880i | −0.954778 | − | 0.297321i | \(-0.903907\pi\) |
0.734876 | + | 0.678201i | \(0.237240\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.36710 | + | 4.09994i | 0.226727 | + | 0.392703i | 0.956836 | − | 0.290627i | \(-0.0938640\pi\) |
−0.730109 | + | 0.683331i | \(0.760531\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.175367 | − | 0.303745i | −0.0164972 | − | 0.0285740i | 0.857659 | − | 0.514219i | \(-0.171918\pi\) |
−0.874156 | + | 0.485645i | \(0.838585\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.8623 | −1.38592 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.78382 | − | 0.695638i | −0.255193 | − | 0.0637691i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.44261 | 0.767510 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.20360 | 0.554867 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4175 | −1.10187 | −0.550935 | − | 0.834548i | \(-0.685729\pi\) | ||||
−0.550935 | + | 0.834548i | \(0.685729\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.7430 | 1.37548 | 0.687738 | − | 0.725959i | \(-0.258604\pi\) | ||||
0.687738 | + | 0.725959i | \(0.258604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.44891 | − | 19.0404i | −0.472481 | − | 1.65101i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.23020 | 0.361410 | 0.180705 | − | 0.983537i | \(-0.442162\pi\) | ||||
0.180705 | + | 0.983537i | \(0.442162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.80367 | − | 16.9805i | −0.831537 | − | 1.44026i | −0.896819 | − | 0.442397i | \(-0.854128\pi\) |
0.0652824 | − | 0.997867i | \(-0.479205\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.58767 | + | 11.4102i | 0.550889 | + | 0.954167i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.78902 | + | 10.0269i | −0.480752 | + | 0.832686i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.72651 | 0.796827 | 0.398414 | − | 0.917206i | \(-0.369561\pi\) | ||||
0.398414 | + | 0.917206i | \(0.369561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.82148 | 0.799261 | 0.399630 | − | 0.916676i | \(-0.369138\pi\) | ||||
0.399630 | + | 0.916676i | \(0.369138\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.1053 | − | 27.8952i | 1.29361 | − | 2.24060i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.02041 | − | 10.4277i | 0.480481 | − | 0.832218i | −0.519268 | − | 0.854611i | \(-0.673795\pi\) |
0.999749 | + | 0.0223936i | \(0.00712870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.95427 | + | 8.22824i | −0.626884 | + | 0.648476i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.885601 | + | 1.53391i | −0.0693656 | + | 0.120145i | −0.898622 | − | 0.438723i | \(-0.855431\pi\) |
0.829257 | + | 0.558868i | \(0.188764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.86350 | − | 13.6200i | −0.608496 | − | 1.05395i | −0.991489 | − | 0.130194i | \(-0.958440\pi\) |
0.382993 | − | 0.923751i | \(-0.374893\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.03584 | − | 3.52618i | 0.156603 | − | 0.271245i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.40313 | + | 16.2867i | 0.714907 | + | 1.23825i | 0.962996 | + | 0.269517i | \(0.0868642\pi\) |
−0.248089 | + | 0.968737i | \(0.579802\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5146 | − | 12.9456i | 0.946016 | − | 0.978599i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.34201 | + | 5.78853i | 0.249794 | + | 0.432655i | 0.963468 | − | 0.267822i | \(-0.0863039\pi\) |
−0.713675 | + | 0.700477i | \(0.752971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.73726 | 0.352117 | 0.176059 | − | 0.984380i | \(-0.443665\pi\) | ||||
0.176059 | + | 0.984380i | \(0.443665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.61613 | + | 14.9236i | −0.633471 | + | 1.09720i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.39107 | − | 4.14146i | −0.174853 | − | 0.302853i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5347 | + | 19.9786i | 0.834618 | + | 1.44560i | 0.894341 | + | 0.447386i | \(0.147645\pi\) |
−0.0597224 | + | 0.998215i | \(0.519022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.15352 | + | 15.8544i | −0.658885 | + | 1.14122i | 0.322020 | + | 0.946733i | \(0.395638\pi\) |
−0.980905 | + | 0.194489i | \(0.937695\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.5866 | −1.03925 | −0.519625 | − | 0.854395i | \(-0.673928\pi\) | ||||
−0.519625 | + | 0.854395i | \(0.673928\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.912102 | + | 1.57981i | 0.0646572 | + | 0.111990i | 0.896542 | − | 0.442959i | \(-0.146071\pi\) |
−0.831885 | + | 0.554949i | \(0.812738\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.45292 | + | 8.57133i | 0.172161 | + | 0.601590i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.12858 | + | 7.15091i | 0.288352 | + | 0.499441i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.5031 | − | 28.5843i | 1.14155 | − | 1.97721i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.77359 | + | 4.80400i | 0.190942 | + | 0.330721i | 0.945563 | − | 0.325440i | \(-0.105512\pi\) |
−0.754621 | + | 0.656161i | \(0.772179\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.3870 | + | 19.7229i | −0.776590 | + | 1.34509i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.82413 | − | 23.8458i | −0.463252 | − | 1.61876i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.62032 | − | 2.80647i | 0.108994 | − | 0.188784i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.01726 | + | 10.4222i | −0.402946 | + | 0.697922i | −0.994080 | − | 0.108651i | \(-0.965347\pi\) |
0.591134 | + | 0.806573i | \(0.298680\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.1567 | −0.873240 | −0.436620 | − | 0.899646i | \(-0.643825\pi\) | ||||
−0.436620 | + | 0.899646i | \(0.643825\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4832 | 0.824912 | 0.412456 | − | 0.910978i | \(-0.364671\pi\) | ||||
0.412456 | + | 0.910978i | \(0.364671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.01687 | − | 3.49332i | 0.132130 | − | 0.228855i | −0.792368 | − | 0.610044i | \(-0.791152\pi\) |
0.924497 | + | 0.381189i | \(0.124485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.16814 | − | 8.95149i | −0.337133 | − | 0.583931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8679 | + | 24.0200i | 0.897043 | + | 1.55372i | 0.831256 | + | 0.555890i | \(0.187623\pi\) |
0.0657873 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9134 | 1.54040 | 0.770199 | − | 0.637803i | \(-0.220157\pi\) | ||||
0.770199 | + | 0.637803i | \(0.220157\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.814135 | − | 24.0376i | −0.0520131 | − | 1.53571i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.3668 | 1.42316 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.33510 | −0.210509 | −0.105255 | − | 0.994445i | \(-0.533566\pi\) | ||||
−0.105255 | + | 0.994445i | \(0.533566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.0731 | −1.19912 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.8691 | 1.36416 | 0.682078 | − | 0.731280i | \(-0.261077\pi\) | ||||
0.682078 | + | 0.731280i | \(0.261077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.65082 | + | 12.7572i | 0.226851 | + | 0.792695i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.51044 | 0.339788 | 0.169894 | − | 0.985462i | \(-0.445657\pi\) | ||||
0.169894 | + | 0.985462i | \(0.445657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82344 | + | 3.15829i | 0.112013 | + | 0.194012i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.37393 | − | 5.84382i | −0.205712 | − | 0.356304i | 0.744647 | − | 0.667458i | \(-0.232618\pi\) |
−0.950359 | + | 0.311154i | \(0.899284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.21944 | + | 10.7724i | −0.377804 | + | 0.654376i | −0.990742 | − | 0.135755i | \(-0.956654\pi\) |
0.612938 | + | 0.790131i | \(0.289987\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.0081 | 1.80956 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.71890 | −0.583952 | −0.291976 | − | 0.956426i | \(-0.594313\pi\) | ||||
−0.291976 | + | 0.956426i | \(0.594313\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.66772 | − | 16.7450i | 0.576728 | − | 0.998922i | −0.419124 | − | 0.907929i | \(-0.637663\pi\) |
0.995852 | − | 0.0909928i | \(-0.0290040\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.15450 | − | 7.19581i | 0.246959 | − | 0.427746i | −0.715721 | − | 0.698386i | \(-0.753902\pi\) |
0.962681 | + | 0.270640i | \(0.0872352\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.16857 | + | 1.54144i | 0.364119 | + | 0.0909882i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.91189 | − | 13.7038i | 0.465405 | − | 0.806105i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.97318 | + | 6.88175i | 0.232116 | + | 0.402036i | 0.958430 | − | 0.285326i | \(-0.0921019\pi\) |
−0.726315 | + | 0.687362i | \(0.758769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.3188 | + | 36.9253i | −1.24123 | + | 2.14987i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.46247 | − | 11.1933i | −0.373734 | − | 0.647327i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.82491 | + | 16.8599i | 0.278103 | + | 0.971788i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.32281 | + | 16.1476i | 0.533823 | + | 0.924608i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.9180 | 1.53629 | 0.768145 | − | 0.640276i | \(-0.221180\pi\) | ||||
0.768145 | + | 0.640276i | \(0.221180\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.67458 | + | 8.09662i | −0.265071 | + | 0.459117i | −0.967582 | − | 0.252556i | \(-0.918729\pi\) |
0.702511 | + | 0.711673i | \(0.252062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.91902 | − | 13.7161i | −0.447610 | − | 0.775282i | 0.550620 | − | 0.834756i | \(-0.314391\pi\) |
−0.998230 | + | 0.0594734i | \(0.981058\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.2296 | − | 24.6463i | −0.799213 | − | 1.38428i | −0.920130 | − | 0.391614i | \(-0.871917\pi\) |
0.120917 | − | 0.992663i | \(-0.461417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.42916 | + | 12.8677i | −0.415953 | + | 0.720452i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.11829 | −0.451714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1675 | + | 17.6107i | 0.563994 | + | 0.976865i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.72180 | − | 1.92957i | −0.425716 | − | 0.106381i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.79521 | − | 16.9658i | −0.538393 | − | 0.932524i | −0.998991 | − | 0.0449153i | \(-0.985698\pi\) |
0.460598 | − | 0.887609i | \(-0.347635\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.73794 | − | 9.93841i | 0.313497 | − | 0.542993i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.73059 | + | 15.1218i | 0.475586 | + | 0.823739i | 0.999609 | − | 0.0279654i | \(-0.00890283\pi\) |
−0.524023 | + | 0.851704i | \(0.675569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.6683 | − | 35.7985i | 1.11925 | − | 1.93860i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.7437 | − | 12.4141i | −0.742090 | − | 0.670301i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.72509 | − | 16.8443i | 0.522070 | − | 0.904252i | −0.477600 | − | 0.878577i | \(-0.658493\pi\) |
0.999670 | − | 0.0256747i | \(-0.00817340\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.91419 | − | 11.9757i | 0.370108 | − | 0.641046i | −0.619474 | − | 0.785018i | \(-0.712654\pi\) |
0.989582 | + | 0.143971i | \(0.0459872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.8459 | −0.630493 | −0.315247 | − | 0.949010i | \(-0.602087\pi\) | ||||
−0.315247 | + | 0.949010i | \(0.602087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.3455 | −2.35361 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.628489 | + | 1.08858i | −0.0331704 | + | 0.0574528i | −0.882134 | − | 0.470998i | \(-0.843894\pi\) |
0.848964 | + | 0.528451i | \(0.177227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5161 | − | 32.0709i | −0.974533 | − | 1.68794i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.2220 | − | 48.8819i | −1.47721 | − | 2.55860i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.2386 | 0.795446 | 0.397723 | − | 0.917505i | \(-0.369800\pi\) | ||||
0.397723 | + | 0.917505i | \(0.369800\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.72442 | + | 0.680795i | 0.141445 | + | 0.0353451i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.3351 | 0.897579 | 0.448789 | − | 0.893638i | \(-0.351855\pi\) | ||||
0.448789 | + | 0.893638i | \(0.351855\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0688 | −0.518569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6319 | −0.802955 | −0.401478 | − | 0.915869i | \(-0.631503\pi\) | ||||
−0.401478 | + | 0.915869i | \(0.631503\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8123 | −0.910166 | −0.455083 | − | 0.890449i | \(-0.650390\pi\) | ||||
−0.455083 | + | 0.890449i | \(0.650390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.8597 | − | 28.8192i | 1.41986 | − | 1.46876i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.4148 | −1.49139 | −0.745695 | − | 0.666288i | \(-0.767882\pi\) | ||||
−0.745695 | + | 0.666288i | \(0.767882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.34563 | + | 4.06275i | 0.118624 | + | 0.205462i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.03774 | − | 6.99357i | −0.203161 | − | 0.351885i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.55930 | + | 2.70079i | −0.0782592 | + | 0.135549i | −0.902499 | − | 0.430692i | \(-0.858270\pi\) |
0.824240 | + | 0.566241i | \(0.191603\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.7226 | 1.78390 | 0.891950 | − | 0.452134i | \(-0.149337\pi\) | ||||
0.891950 | + | 0.452134i | \(0.149337\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.0118 | 1.39537 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0572 | + | 19.1517i | −0.548087 | + | 0.949315i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.90826 | + | 8.50135i | −0.242698 | + | 0.420365i | −0.961482 | − | 0.274869i | \(-0.911366\pi\) |
0.718784 | + | 0.695233i | \(0.244699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.03320 | + | 31.5651i | 0.444494 | + | 1.55321i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.51814 | + | 9.55771i | −0.270875 | + | 0.469169i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.09812 | + | 10.5623i | 0.297913 | + | 0.516000i | 0.975658 | − | 0.219297i | \(-0.0703762\pi\) |
−0.677746 | + | 0.735297i | \(0.737043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.10015 | + | 8.83373i | −0.248566 | + | 0.430529i | −0.963128 | − | 0.269043i | \(-0.913293\pi\) |
0.714562 | + | 0.699572i | \(0.246626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.69043 | − | 6.39201i | −0.179012 | − | 0.310058i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.9293 | + | 3.48075i | 0.674088 | + | 0.168445i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.70254 | − | 9.87710i | −0.274682 | − | 0.475763i | 0.695373 | − | 0.718649i | \(-0.255239\pi\) |
−0.970055 | + | 0.242886i | \(0.921906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.2391 | 1.26097 | 0.630486 | − | 0.776201i | \(-0.282856\pi\) | ||||
0.630486 | + | 0.776201i | \(0.282856\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.1895 | + | 28.0410i | −0.774448 | + | 1.34138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.4777 | + | 19.8800i | 0.547801 | + | 0.948819i | 0.998425 | + | 0.0561054i | \(0.0178683\pi\) |
−0.450624 | + | 0.892714i | \(0.648798\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.2013 | − | 19.4012i | −0.532188 | − | 0.921777i | −0.999294 | − | 0.0375758i | \(-0.988036\pi\) |
0.467105 | − | 0.884202i | \(-0.345297\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.4997 | + | 33.7744i | −0.924372 | + | 1.60106i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0576 | −0.805000 | −0.402500 | − | 0.915420i | \(-0.631859\pi\) | ||||
−0.402500 | + | 0.915420i | \(0.631859\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.29829 | + | 9.17690i | 0.249487 | + | 0.432123i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.3526 | + | 6.58514i | 1.23543 | + | 0.308716i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.77365 | − | 8.26820i | −0.223302 | − | 0.386770i | 0.732507 | − | 0.680760i | \(-0.238350\pi\) |
−0.955809 | + | 0.293990i | \(0.905017\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1213 | + | 17.5305i | −0.471394 | + | 0.816478i | −0.999464 | − | 0.0327222i | \(-0.989582\pi\) |
0.528070 | + | 0.849201i | \(0.322916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.81948 | + | 13.5437i | 0.363402 | + | 0.629431i | 0.988518 | − | 0.151101i | \(-0.0482818\pi\) |
−0.625116 | + | 0.780532i | \(0.714948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.96638 | + | 5.13793i | −0.137268 | + | 0.237755i | −0.926461 | − | 0.376390i | \(-0.877165\pi\) |
0.789194 | + | 0.614144i | \(0.210499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.43128 | − | 8.49571i | −0.112266 | − | 0.392295i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.6132 | + | 25.3108i | −0.671917 | + | 1.16379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.4712 | − | 44.1175i | 1.16870 | − | 2.02425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3942 | −0.794760 | −0.397380 | − | 0.917654i | \(-0.630080\pi\) | ||||
−0.397380 | + | 0.917654i | \(0.630080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.9860 | −0.683301 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.0009 | + | 38.1067i | −0.999009 | + | 1.73033i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.76967 | + | 16.9216i | 0.442706 | + | 0.766790i | 0.997889 | − | 0.0649386i | \(-0.0206851\pi\) |
−0.555183 | + | 0.831728i | \(0.687352\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.16702 | − | 10.6816i | −0.278314 | − | 0.482054i | 0.692652 | − | 0.721272i | \(-0.256442\pi\) |
−0.970966 | + | 0.239218i | \(0.923109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.65458 | 0.164594 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.7336 | + | 24.5510i | −1.06460 | + | 1.10126i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.5462 | −0.830240 | −0.415120 | − | 0.909767i | \(-0.636260\pi\) | ||||
−0.415120 | + | 0.909767i | \(0.636260\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.3264 | −0.638782 | −0.319391 | − | 0.947623i | \(-0.603478\pi\) | ||||
−0.319391 | + | 0.947623i | \(0.603478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.66703 | 0.118681 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8611 | 0.747356 | 0.373678 | − | 0.927559i | \(-0.378097\pi\) | ||||
0.373678 | + | 0.927559i | \(0.378097\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.1669 | − | 10.5369i | −1.86535 | − | 0.466125i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.84290 | −0.345599 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.63238 | − | 11.4876i | −0.291692 | − | 0.505225i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8132 | − | 18.7291i | −0.473737 | − | 0.820536i | 0.525811 | − | 0.850601i | \(-0.323762\pi\) |
−0.999548 | + | 0.0300652i | \(0.990428\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.27472 | + | 14.3322i | −0.361828 | + | 0.626705i | −0.988262 | − | 0.152770i | \(-0.951181\pi\) |
0.626433 | + | 0.779475i | \(0.284514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.1672 | −0.442891 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.28939 | −0.186495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.59040 | + | 6.21876i | −0.155517 | + | 0.269364i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.81560 | + | 13.5370i | −0.337898 | + | 0.585256i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.04479 | − | 30.8480i | −0.0450025 | − | 1.32872i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9542 | + | 20.7053i | −0.513952 | + | 0.890191i | 0.485917 | + | 0.874005i | \(0.338486\pi\) |
−0.999869 | + | 0.0161861i | \(0.994848\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.13317 | + | 14.0871i | 0.348387 | + | 0.603423i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8193 | − | 25.6678i | 0.633627 | − | 1.09747i | −0.353177 | − | 0.935556i | \(-0.614899\pi\) |
0.986804 | − | 0.161918i | \(-0.0517679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6119 | + | 21.8445i | 0.537286 | + | 0.930607i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.03285 | − | 1.50752i | −0.256543 | − | 0.0641064i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.8366 | + | 18.7695i | 0.459160 | + | 0.795288i | 0.998917 | − | 0.0465330i | \(-0.0148173\pi\) |
−0.539757 | + | 0.841821i | \(0.681484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.8054 | −0.837679 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.07782 | + | 12.2591i | −0.298294 | + | 0.516661i | −0.975746 | − | 0.218906i | \(-0.929751\pi\) |
0.677451 | + | 0.735567i | \(0.263084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.602548 | − | 1.04364i | −0.0253494 | − | 0.0439064i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.0178 | − | 29.4757i | −0.713422 | − | 1.23568i | −0.963565 | − | 0.267475i | \(-0.913811\pi\) |
0.250143 | − | 0.968209i | \(-0.419522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.67485 | + | 4.63298i | −0.111939 | + | 0.193884i | −0.916552 | − | 0.399915i | \(-0.869039\pi\) |
0.804613 | + | 0.593800i | \(0.202373\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.4378 | −1.22764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1865 | + | 19.3756i | 0.465699 | + | 0.806615i | 0.999233 | − | 0.0391640i | \(-0.0124695\pi\) |
−0.533533 | + | 0.845779i | \(0.679136\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.33814 | + | 8.17027i | 0.0970026 | + | 0.338960i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.34005 | + | 4.05309i | 0.0969151 | + | 0.167862i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.49899 | + | 4.32839i | −0.103145 | + | 0.178652i | −0.912979 | − | 0.408007i | \(-0.866224\pi\) |
0.809834 | + | 0.586659i | \(0.199557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.0870 | − | 60.7724i | −1.44573 | − | 2.50408i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.1698 | + | 21.0788i | −0.499755 | + | 0.865601i | −1.00000 | 0.000282582i | \(-0.999910\pi\) | |
0.500245 | + | 0.865884i | \(0.333243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.56498 | − | 2.39015i | −0.392126 | − | 0.0979868i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.1073 | + | 40.0230i | −0.944137 | + | 1.63529i | −0.186668 | + | 0.982423i | \(0.559769\pi\) |
−0.757469 | + | 0.652871i | \(0.773564\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.6163 | + | 28.7803i | −0.677792 | + | 1.17397i | 0.297852 | + | 0.954612i | \(0.403730\pi\) |
−0.975644 | + | 0.219359i | \(0.929603\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.0081 | 1.17935 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.8635 | −1.78036 | −0.890182 | − | 0.455604i | \(-0.849423\pi\) | ||||
−0.890182 | + | 0.455604i | \(0.849423\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.49445 | − | 7.78462i | 0.181826 | − | 0.314932i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.81569 | + | 3.14487i | 0.0733351 | + | 0.127020i | 0.900361 | − | 0.435144i | \(-0.143302\pi\) |
−0.827026 | + | 0.562164i | \(0.809969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.4542 | − | 18.1073i | −0.420872 | − | 0.728971i | 0.575153 | − | 0.818046i | \(-0.304942\pi\) |
−0.996025 | + | 0.0890744i | \(0.971609\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9490 | −0.962592 | −0.481296 | − | 0.876558i | \(-0.659834\pi\) | ||||
−0.481296 | + | 0.876558i | \(0.659834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.26238 | + | 28.8716i | 0.331025 | + | 1.15672i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.7125 | −0.508501 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.43933 | 0.216880 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.06918 | 0.241610 | 0.120805 | − | 0.992676i | \(-0.461452\pi\) | ||||
0.120805 | + | 0.992676i | \(0.461452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.6653 | −1.69312 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.7496 | − | 11.0653i | 0.703264 | − | 0.438422i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.3881 | 0.686790 | 0.343395 | − | 0.939191i | \(-0.388423\pi\) | ||||
0.343395 | + | 0.939191i | \(0.388423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.66411 | − | 16.7387i | −0.381115 | − | 0.660111i | 0.610107 | − | 0.792319i | \(-0.291127\pi\) |
−0.991222 | + | 0.132208i | \(0.957793\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.7041 | + | 22.0042i | 0.499451 | + | 0.865075i | 1.00000 | 0.000633482i | \(-0.000201644\pi\) | |
−0.500549 | + | 0.865708i | \(0.666868\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.3588 | + | 47.3869i | −1.07393 | + | 1.86010i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.8127 | 1.01013 | 0.505065 | − | 0.863081i | \(-0.331468\pi\) | ||||
0.505065 | + | 0.863081i | \(0.331468\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 54.0918 | 2.11354 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.62598 | − | 14.9406i | 0.336020 | − | 0.582004i | −0.647660 | − | 0.761930i | \(-0.724252\pi\) |
0.983680 | + | 0.179925i | \(0.0575856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.48175 | + | 11.2267i | −0.252111 | + | 0.436669i | −0.964107 | − | 0.265515i | \(-0.914458\pi\) |
0.711996 | + | 0.702184i | \(0.247791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.7220 | − | 65.4210i | −0.726008 | − | 2.53692i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.28797 | − | 12.6231i | 0.282191 | − | 0.488769i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9641 | + | 20.7225i | 0.461871 | + | 0.799984i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.8060 | + | 36.0371i | −0.802013 | + | 1.38913i | 0.116277 | + | 0.993217i | \(0.462904\pi\) |
−0.918289 | + | 0.395910i | \(0.870429\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.0999 | − | 19.2256i | −0.426605 | − | 0.738901i | 0.569964 | − | 0.821669i | \(-0.306957\pi\) |
−0.996569 | + | 0.0827688i | \(0.973624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.32221 | + | 32.5750i | 0.357753 | + | 1.25011i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.60315 | − | 7.97289i | −0.176135 | − | 0.305074i | 0.764419 | − | 0.644720i | \(-0.223026\pi\) |
−0.940553 | + | 0.339646i | \(0.889693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.5346 | 0.555338 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.58574 | + | 2.74659i | −0.0604120 | + | 0.104637i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0293 | − | 34.6917i | −0.761949 | − | 1.31974i | −0.941844 | − | 0.336049i | \(-0.890909\pi\) |
0.179895 | − | 0.983686i | \(-0.442424\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.6846 | − | 58.3434i | −1.27773 | − | 2.21309i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.30318 | − | 2.25717i | 0.0493614 | − | 0.0854964i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.3868 | −1.29877 | −0.649385 | − | 0.760459i | \(-0.724974\pi\) | ||||
−0.649385 | + | 0.760459i | \(0.724974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.7711 | + | 32.5124i | 0.707964 | + | 1.22623i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.42739 | − | 1.47655i | 0.0536824 | − | 0.0555314i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.5920 | − | 18.3459i | −0.397791 | − | 0.688994i | 0.595662 | − | 0.803235i | \(-0.296890\pi\) |
−0.993453 | + | 0.114241i | \(0.963556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.2755 | + | 35.1181i | −0.759322 | + | 1.31518i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.6347 | + | 39.2044i | 0.846489 | + | 1.46616i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.5994 | + | 37.4113i | −0.805523 | + | 1.39521i | 0.110414 | + | 0.993886i | \(0.464782\pi\) |
−0.915937 | + | 0.401321i | \(0.868551\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.19750 | + | 4.34207i | −0.156323 | + | 0.161707i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.4663 | + | 19.8602i | −0.425848 | + | 0.737590i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.5571 | + | 35.6059i | −0.762420 | + | 1.32055i | 0.179180 | + | 0.983816i | \(0.442656\pi\) |
−0.941600 | + | 0.336734i | \(0.890678\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.18860 | 0.265880 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.0851 | 1.92381 | 0.961903 | − | 0.273390i | \(-0.0881451\pi\) | ||||
0.961903 | + | 0.273390i | \(0.0881451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.36361 | − | 12.7541i | 0.271242 | − | 0.469805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.18624 | − | 12.4469i | −0.264350 | − | 0.457868i | 0.703043 | − | 0.711147i | \(-0.251824\pi\) |
−0.967393 | + | 0.253279i | \(0.918491\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.3167 | − | 36.9216i | −0.782034 | − | 1.35452i | −0.930755 | − | 0.365643i | \(-0.880849\pi\) |
0.148721 | − | 0.988879i | \(-0.452484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.4195 | 1.22440 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.31162 | + | 11.5719i | 0.121004 | + | 0.422829i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.9692 | 1.38552 | 0.692758 | − | 0.721171i | \(-0.256396\pi\) | ||||
0.692758 | + | 0.721171i | \(0.256396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.7458 | 1.22813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6692 | 1.00565 | 0.502827 | − | 0.864387i | \(-0.332293\pi\) | ||||
0.502827 | + | 0.864387i | \(0.332293\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.9442 | −0.432977 | −0.216488 | − | 0.976285i | \(-0.569460\pi\) | ||||
−0.216488 | + | 0.976285i | \(0.569460\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1519 | + | 3.03658i | 0.439927 | + | 0.109932i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.0796 | −1.33887 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.4026 | − | 30.1422i | −0.627554 | − | 1.08695i | −0.988041 | − | 0.154191i | \(-0.950723\pi\) |
0.360487 | − | 0.932764i | \(-0.382610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5014 | + | 23.3851i | 0.485611 | + | 0.841103i | 0.999863 | − | 0.0165363i | \(-0.00526391\pi\) |
−0.514253 | + | 0.857639i | \(0.671931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.8998 | − | 55.2521i | 1.14587 | − | 1.98471i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.9890 | 0.644523 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −56.9094 | −2.03638 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.6856 | − | 35.8286i | 0.738302 | − | 1.27878i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6420 | − | 18.4325i | 0.379347 | − | 0.657048i | −0.611621 | − | 0.791151i | \(-0.709482\pi\) |
0.990967 | + | 0.134104i | \(0.0428155\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.900275 | − | 0.224966i | −0.0320101 | − | 0.00799887i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.10754 | + | 14.0427i | −0.287907 | + | 0.498670i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.3062 | + | 17.8508i | 0.365064 | + | 0.632309i | 0.988786 | − | 0.149337i | \(-0.0477138\pi\) |
−0.623723 | + | 0.781646i | \(0.714381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.63131 | + | 2.82552i | −0.0577117 | + | 0.0999597i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.2178 | − | 62.7311i | −1.27810 | − | 2.21373i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.3302 | + | 28.2715i | −0.963263 | + | 0.996440i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.54223 | − | 4.40328i | −0.0893802 | − | 0.154811i | 0.817869 | − | 0.575404i | \(-0.195155\pi\) |
−0.907249 | + | 0.420593i | \(0.861822\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.58775 | 0.266442 | 0.133221 | − | 0.991086i | \(-0.457468\pi\) | ||||
0.133221 | + | 0.991086i | \(0.457468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.04285 | + | 5.27037i | −0.106586 | + | 0.184613i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.8078 | + | 42.9683i | 0.867914 | + | 1.50327i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.1348 | + | 17.5540i | 0.353706 | + | 0.612637i | 0.986896 | − | 0.161360i | \(-0.0515879\pi\) |
−0.633189 | + | 0.773997i | \(0.718255\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8955 | − | 18.8716i | 0.379794 | − | 0.657823i | −0.611238 | − | 0.791447i | \(-0.709328\pi\) |
0.991032 | + | 0.133624i | \(0.0426615\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.3796 | 0.917307 | 0.458654 | − | 0.888615i | \(-0.348332\pi\) | ||||
0.458654 | + | 0.888615i | \(0.348332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.33400 | + | 16.1670i | 0.324183 | + | 0.561502i | 0.981347 | − | 0.192246i | \(-0.0615773\pi\) |
−0.657164 | + | 0.753748i | \(0.728244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.44242 | + | 4.01627i | −0.223216 | + | 0.139155i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.0183 | − | 46.7971i | −0.935007 | − | 1.61948i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5265 | − | 21.6966i | 0.432464 | − | 0.749050i | −0.564621 | − | 0.825351i | \(-0.690977\pi\) |
0.997085 | + | 0.0763004i | \(0.0243108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.82253 | + | 15.2811i | 0.304225 | + | 0.526934i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.99499 | − | 12.1157i | 0.240635 | − | 0.416792i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.5250 | − | 16.0598i | 0.533447 | − | 0.551820i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.8471 | − | 18.7877i | 0.371834 | − | 0.644035i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2219 | + | 33.2933i | −0.658146 | + | 1.13994i | 0.322949 | + | 0.946416i | \(0.395326\pi\) |
−0.981095 | + | 0.193526i | \(0.938008\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0060 | 0.410117 | 0.205058 | − | 0.978750i | \(-0.434262\pi\) | ||||
0.205058 | + | 0.978750i | \(0.434262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.6031 | 0.430012 | 0.215006 | − | 0.976613i | \(-0.431023\pi\) | ||||
0.215006 | + | 0.976613i | \(0.431023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.210643 | + | 0.364845i | −0.00717038 | + | 0.0124195i | −0.869588 | − | 0.493777i | \(-0.835616\pi\) |
0.862418 | + | 0.506197i | \(0.168949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.3084 | + | 55.9597i | 1.09852 | + | 1.90269i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.18171 | − | 8.97499i | −0.175778 | − | 0.304456i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.97995 | 0.338158 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.4078 | − | 11.8007i | 0.385653 | − | 0.398936i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.78685 | 0.0603376 | 0.0301688 | − | 0.999545i | \(-0.490396\pi\) | ||||
0.0301688 | + | 0.999545i | \(0.490396\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.8891 | 1.68081 | 0.840403 | − | 0.541962i | \(-0.182318\pi\) | ||||
0.840403 | + | 0.541962i | \(0.182318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.7935 | −1.17090 | −0.585448 | − | 0.810710i | \(-0.699081\pi\) | ||||
−0.585448 | + | 0.810710i | \(0.699081\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.8080 | 0.799396 | 0.399698 | − | 0.916647i | \(-0.369115\pi\) | ||||
0.399698 | + | 0.916647i | \(0.369115\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.8344 | + | 23.6208i | −0.765840 | + | 0.792217i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.5186 | −0.753556 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.4829 | + | 19.8889i | 0.383830 | + | 0.664813i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.7950 | + | 27.3577i | 0.526792 | + | 0.912431i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.575564 | − | 0.996907i | 0.0191748 | − | 0.0332118i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.2768 | 0.541060 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.2813 | −1.13829 | −0.569146 | − | 0.822237i | \(-0.692726\pi\) | ||||
−0.569146 | + | 0.822237i | \(0.692726\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.9839 | − | 25.9529i | 0.496438 | − | 0.859857i | −0.503553 | − | 0.863964i | \(-0.667974\pi\) |
0.999992 | + | 0.00410771i | \(0.00130753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.08154 | + | 12.2656i | −0.234365 | + | 0.405932i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.9498 | − | 29.9469i | 0.956006 | − | 0.988933i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.391037 | − | 0.677296i | 0.0128991 | − | 0.0223419i | −0.859504 | − | 0.511129i | \(-0.829227\pi\) |
0.872403 | + | 0.488787i | \(0.162561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.2824 | − | 33.3981i | −0.634688 | − | 1.09931i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0660 | + | 29.5591i | −0.561126 | + | 0.971898i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.76620 | − | 11.7194i | −0.221992 | − | 0.384501i | 0.733421 | − | 0.679775i | \(-0.237922\pi\) |
−0.955413 | + | 0.295274i | \(0.904589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.2391 | − | 24.6481i | −1.51542 | − | 0.807808i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.21552 | − | 14.2297i | −0.268676 | − | 0.465361i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.27674 | −0.0743777 | −0.0371889 | − | 0.999308i | \(-0.511840\pi\) | ||||
−0.0371889 | + | 0.999308i | \(0.511840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.07720 | + | 7.06192i | −0.132913 | + | 0.230212i | −0.924798 | − | 0.380458i | \(-0.875766\pi\) |
0.791885 | + | 0.610670i | \(0.209100\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.19759 | − | 9.00249i | −0.169257 | − | 0.293161i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.93553 | − | 6.81654i | −0.127888 | − | 0.221508i | 0.794970 | − | 0.606648i | \(-0.207486\pi\) |
−0.922858 | + | 0.385140i | \(0.874153\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.5431 | − | 42.5099i | 0.796703 | − | 1.37993i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.1097 | −1.39646 | −0.698230 | − | 0.715873i | \(-0.746029\pi\) | ||||
−0.698230 | + | 0.715873i | \(0.746029\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.6321 | + | 68.6448i | 1.28246 | + | 2.22129i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.77888 | − | 8.04680i | 0.251193 | − | 0.259845i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4424 | − | 49.2636i | −0.917496 | − | 1.58915i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31.4507 | + | 54.4742i | −1.01243 | + | 1.75359i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.9537 | − | 24.1684i | −0.448719 | − | 0.777205i | 0.549584 | − | 0.835439i | \(-0.314786\pi\) |
−0.998303 | + | 0.0582340i | \(0.981453\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0705 | − | 36.4952i | 0.676185 | − | 1.17119i | −0.299936 | − | 0.953959i | \(-0.596965\pi\) |
0.976121 | − | 0.217228i | \(-0.0697015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.3286 | − | 12.5764i | −1.61346 | − | 0.403181i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.92747 | + | 11.9987i | −0.221629 | + | 0.383873i | −0.955303 | − | 0.295629i | \(-0.904471\pi\) |
0.733674 | + | 0.679502i | \(0.237804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.0243 | + | 43.3433i | −0.799780 | + | 1.38526i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.95876 | 0.253845 | 0.126923 | − | 0.991913i | \(-0.459490\pi\) | ||||
0.126923 | + | 0.991913i | \(0.459490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.1182 | −1.59690 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3355 | − | 24.8298i | 0.455842 | − | 0.789542i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.36428 | − | 7.55916i | −0.138636 | − | 0.240125i | 0.788345 | − | 0.615234i | \(-0.210938\pi\) |
−0.926981 | + | 0.375109i | \(0.877605\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.13391 | + | 5.42809i | 0.0993515 | + | 0.172082i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.30379 | −0.0729619 | −0.0364810 | − | 0.999334i | \(-0.511615\pi\) | ||||
−0.0364810 | + | 0.999334i | \(0.511615\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3024.2.t.l.289.10 | 22 | ||
3.2 | odd | 2 | 1008.2.t.k.961.7 | 22 | |||
4.3 | odd | 2 | 1512.2.t.d.289.10 | 22 | |||
7.4 | even | 3 | 3024.2.q.k.2881.2 | 22 | |||
9.4 | even | 3 | 3024.2.q.k.2305.2 | 22 | |||
9.5 | odd | 6 | 1008.2.q.k.625.10 | 22 | |||
12.11 | even | 2 | 504.2.t.d.457.5 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.q.k.529.10 | 22 | |||
28.11 | odd | 6 | 1512.2.q.c.1369.2 | 22 | |||
36.23 | even | 6 | 504.2.q.d.121.2 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.q.c.793.2 | 22 | |||
63.4 | even | 3 | inner | 3024.2.t.l.1873.10 | 22 | ||
63.32 | odd | 6 | 1008.2.t.k.193.7 | 22 | |||
84.11 | even | 6 | 504.2.q.d.25.2 | ✓ | 22 | ||
252.67 | odd | 6 | 1512.2.t.d.361.10 | 22 | |||
252.95 | even | 6 | 504.2.t.d.193.5 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.2 | ✓ | 22 | 84.11 | even | 6 | ||
504.2.q.d.121.2 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.d.193.5 | yes | 22 | 252.95 | even | 6 | ||
504.2.t.d.457.5 | yes | 22 | 12.11 | even | 2 | ||
1008.2.q.k.529.10 | 22 | 21.11 | odd | 6 | |||
1008.2.q.k.625.10 | 22 | 9.5 | odd | 6 | |||
1008.2.t.k.193.7 | 22 | 63.32 | odd | 6 | |||
1008.2.t.k.961.7 | 22 | 3.2 | odd | 2 | |||
1512.2.q.c.793.2 | 22 | 36.31 | odd | 6 | |||
1512.2.q.c.1369.2 | 22 | 28.11 | odd | 6 | |||
1512.2.t.d.289.10 | 22 | 4.3 | odd | 2 | |||
1512.2.t.d.361.10 | 22 | 252.67 | odd | 6 | |||
3024.2.q.k.2305.2 | 22 | 9.4 | even | 3 | |||
3024.2.q.k.2881.2 | 22 | 7.4 | even | 3 | |||
3024.2.t.l.289.10 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.l.1873.10 | 22 | 63.4 | even | 3 | inner |