Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.9 | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.c.2155.16 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.516505i | 0.230988i | 0.993308 | + | 0.115494i | \(0.0368451\pi\) | ||||
−0.993308 | + | 0.115494i | \(0.963155\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.516505 | 0.163333 | ||||||||
\(11\) | −3.09541 | + | 1.19099i | −0.933300 | + | 0.359097i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −2.41249 | −0.669103 | −0.334552 | − | 0.942377i | \(-0.608585\pi\) | ||||
−0.334552 | + | 0.942377i | \(0.608585\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.516505 | 0.133361 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.29986 | 1.77048 | 0.885238 | − | 0.465139i | \(-0.153996\pi\) | ||||
0.885238 | + | 0.465139i | \(0.153996\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −2.57557 | −0.590877 | −0.295438 | − | 0.955362i | \(-0.595466\pi\) | ||||
−0.295438 | + | 0.955362i | \(0.595466\pi\) | |||||||
\(20\) | − | 0.516505i | − | 0.115494i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.19099 | + | 3.09541i | 0.253920 | + | 0.659943i | ||||
\(23\) | −1.88937 | −0.393960 | −0.196980 | − | 0.980407i | \(-0.563113\pi\) | ||||
−0.196980 | + | 0.980407i | \(0.563113\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.73322 | 0.946645 | ||||||||
\(26\) | 2.41249i | 0.473127i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.33100i | − | 0.247160i | −0.992335 | − | 0.123580i | \(-0.960562\pi\) | ||
0.992335 | − | 0.123580i | \(-0.0394376\pi\) | |||||||
\(30\) | − | 0.516505i | − | 0.0943004i | ||||||
\(31\) | 4.58708i | 0.823864i | 0.911215 | + | 0.411932i | \(0.135146\pi\) | ||||
−0.911215 | + | 0.411932i | \(0.864854\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.19099 | + | 3.09541i | 0.207325 | + | 0.538841i | ||||
\(34\) | − | 7.29986i | − | 1.25191i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.34068 | 1.04240 | 0.521200 | − | 0.853434i | \(-0.325484\pi\) | ||||
0.521200 | + | 0.853434i | \(0.325484\pi\) | |||||||
\(38\) | 2.57557i | 0.417813i | ||||||||
\(39\) | 2.41249i | 0.386307i | ||||||||
\(40\) | −0.516505 | −0.0816665 | ||||||||
\(41\) | −2.14721 | −0.335338 | −0.167669 | − | 0.985843i | \(-0.553624\pi\) | ||||
−0.167669 | + | 0.985843i | \(0.553624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.68147i | − | 0.408920i | −0.978875 | − | 0.204460i | \(-0.934456\pi\) | ||
0.978875 | − | 0.204460i | \(-0.0655438\pi\) | |||||||
\(44\) | 3.09541 | − | 1.19099i | 0.466650 | − | 0.179548i | ||||
\(45\) | − | 0.516505i | − | 0.0769959i | ||||||
\(46\) | 1.88937i | 0.278572i | ||||||||
\(47\) | 1.14068i | 0.166385i | 0.996533 | + | 0.0831926i | \(0.0265117\pi\) | ||||
−0.996533 | + | 0.0831926i | \(0.973488\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 4.73322i | − | 0.669379i | ||||||
\(51\) | − | 7.29986i | − | 1.02218i | ||||||
\(52\) | 2.41249 | 0.334552 | ||||||||
\(53\) | 7.15143 | 0.982325 | 0.491162 | − | 0.871068i | \(-0.336572\pi\) | ||||
0.491162 | + | 0.871068i | \(0.336572\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.615152 | − | 1.59879i | −0.0829470 | − | 0.215581i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.57557i | 0.341143i | ||||||||
\(58\) | −1.33100 | −0.174769 | ||||||||
\(59\) | − | 1.00336i | − | 0.130627i | −0.997865 | − | 0.0653134i | \(-0.979195\pi\) | ||
0.997865 | − | 0.0653134i | \(-0.0208047\pi\) | |||||||
\(60\) | −0.516505 | −0.0666804 | ||||||||
\(61\) | −4.50704 | −0.577068 | −0.288534 | − | 0.957470i | \(-0.593168\pi\) | ||||
−0.288534 | + | 0.957470i | \(0.593168\pi\) | |||||||
\(62\) | 4.58708 | 0.582560 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 1.24606i | − | 0.154555i | ||||||
\(66\) | 3.09541 | − | 1.19099i | 0.381018 | − | 0.146601i | ||||
\(67\) | 8.00023 | 0.977384 | 0.488692 | − | 0.872456i | \(-0.337474\pi\) | ||||
0.488692 | + | 0.872456i | \(0.337474\pi\) | |||||||
\(68\) | −7.29986 | −0.885238 | ||||||||
\(69\) | 1.88937i | 0.227453i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.05635 | 1.07479 | 0.537396 | − | 0.843330i | \(-0.319408\pi\) | ||||
0.537396 | + | 0.843330i | \(0.319408\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 5.82214 | 0.681430 | 0.340715 | − | 0.940167i | \(-0.389331\pi\) | ||||
0.340715 | + | 0.940167i | \(0.389331\pi\) | |||||||
\(74\) | − | 6.34068i | − | 0.737089i | ||||||
\(75\) | − | 4.73322i | − | 0.546546i | ||||||
\(76\) | 2.57557 | 0.295438 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.41249 | 0.273160 | ||||||||
\(79\) | − | 17.5335i | − | 1.97268i | −0.164733 | − | 0.986338i | \(-0.552676\pi\) | ||
0.164733 | − | 0.986338i | \(-0.447324\pi\) | |||||||
\(80\) | 0.516505i | 0.0577470i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.14721i | 0.237119i | ||||||||
\(83\) | −3.86307 | −0.424027 | −0.212014 | − | 0.977267i | \(-0.568002\pi\) | ||||
−0.212014 | + | 0.977267i | \(0.568002\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.77041i | 0.408958i | ||||||||
\(86\) | −2.68147 | −0.289150 | ||||||||
\(87\) | −1.33100 | −0.142698 | ||||||||
\(88\) | −1.19099 | − | 3.09541i | −0.126960 | − | 0.329971i | ||||
\(89\) | − | 14.3064i | − | 1.51648i | −0.651976 | − | 0.758240i | \(-0.726060\pi\) | ||
0.651976 | − | 0.758240i | \(-0.273940\pi\) | |||||||
\(90\) | −0.516505 | −0.0544444 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.88937 | 0.196980 | ||||||||
\(93\) | 4.58708 | 0.475658 | ||||||||
\(94\) | 1.14068 | 0.117652 | ||||||||
\(95\) | − | 1.33029i | − | 0.136485i | ||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 3.02541i | − | 0.307184i | −0.988134 | − | 0.153592i | \(-0.950916\pi\) | ||
0.988134 | − | 0.153592i | \(-0.0490841\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.09541 | − | 1.19099i | 0.311100 | − | 0.119699i | ||||
\(100\) | −4.73322 | −0.473322 | ||||||||
\(101\) | 17.0462 | 1.69616 | 0.848078 | − | 0.529872i | \(-0.177760\pi\) | ||||
0.848078 | + | 0.529872i | \(0.177760\pi\) | |||||||
\(102\) | −7.29986 | −0.722793 | ||||||||
\(103\) | 13.4342i | 1.32371i | 0.749633 | + | 0.661854i | \(0.230230\pi\) | ||||
−0.749633 | + | 0.661854i | \(0.769770\pi\) | |||||||
\(104\) | − | 2.41249i | − | 0.236564i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 7.15143i | − | 0.694608i | ||||||
\(107\) | 4.74835i | 0.459040i | 0.973304 | + | 0.229520i | \(0.0737156\pi\) | ||||
−0.973304 | + | 0.229520i | \(0.926284\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 1.61490i | 0.154680i | 0.997005 | + | 0.0773398i | \(0.0246426\pi\) | ||||
−0.997005 | + | 0.0773398i | \(0.975357\pi\) | |||||||
\(110\) | −1.59879 | + | 0.615152i | −0.152439 | + | 0.0586524i | ||||
\(111\) | − | 6.34068i | − | 0.601830i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.4489 | 1.73553 | 0.867763 | − | 0.496978i | \(-0.165557\pi\) | ||||
0.867763 | + | 0.496978i | \(0.165557\pi\) | |||||||
\(114\) | 2.57557 | 0.241224 | ||||||||
\(115\) | − | 0.975866i | − | 0.0910000i | ||||||
\(116\) | 1.33100i | 0.123580i | ||||||||
\(117\) | 2.41249 | 0.223034 | ||||||||
\(118\) | −1.00336 | −0.0923671 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.516505i | 0.0471502i | ||||||||
\(121\) | 8.16309 | − | 7.37320i | 0.742099 | − | 0.670291i | ||||
\(122\) | 4.50704i | 0.408048i | ||||||||
\(123\) | 2.14721i | 0.193607i | ||||||||
\(124\) | − | 4.58708i | − | 0.411932i | ||||||
\(125\) | 5.02725i | 0.449651i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.7652i | − | 1.13273i | −0.824155 | − | 0.566365i | \(-0.808349\pi\) | ||
0.824155 | − | 0.566365i | \(-0.191651\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −2.68147 | −0.236090 | ||||||||
\(130\) | −1.24606 | −0.109287 | ||||||||
\(131\) | −13.1155 | −1.14590 | −0.572952 | − | 0.819589i | \(-0.694202\pi\) | ||||
−0.572952 | + | 0.819589i | \(0.694202\pi\) | |||||||
\(132\) | −1.19099 | − | 3.09541i | −0.103662 | − | 0.269421i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 8.00023i | − | 0.691115i | ||||||
\(135\) | −0.516505 | −0.0444536 | ||||||||
\(136\) | 7.29986i | 0.625957i | ||||||||
\(137\) | 6.94935 | 0.593723 | 0.296861 | − | 0.954921i | \(-0.404060\pi\) | ||||
0.296861 | + | 0.954921i | \(0.404060\pi\) | |||||||
\(138\) | 1.88937 | 0.160834 | ||||||||
\(139\) | −8.43815 | −0.715714 | −0.357857 | − | 0.933776i | \(-0.616493\pi\) | ||||
−0.357857 | + | 0.933776i | \(0.616493\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.14068 | 0.0960626 | ||||||||
\(142\) | − | 9.05635i | − | 0.759992i | ||||||
\(143\) | 7.46762 | − | 2.87325i | 0.624474 | − | 0.240273i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0.687466 | 0.0570910 | ||||||||
\(146\) | − | 5.82214i | − | 0.481844i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.34068 | −0.521200 | ||||||||
\(149\) | − | 5.18030i | − | 0.424387i | −0.977228 | − | 0.212193i | \(-0.931939\pi\) | ||
0.977228 | − | 0.212193i | \(-0.0680607\pi\) | |||||||
\(150\) | −4.73322 | −0.386466 | ||||||||
\(151\) | 14.8174i | 1.20582i | 0.797808 | + | 0.602911i | \(0.205993\pi\) | ||||
−0.797808 | + | 0.602911i | \(0.794007\pi\) | |||||||
\(152\) | − | 2.57557i | − | 0.208906i | ||||||
\(153\) | −7.29986 | −0.590158 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.36925 | −0.190303 | ||||||||
\(156\) | − | 2.41249i | − | 0.193153i | ||||||
\(157\) | − | 0.378604i | − | 0.0302159i | −0.999886 | − | 0.0151079i | \(-0.995191\pi\) | ||
0.999886 | − | 0.0151079i | \(-0.00480919\pi\) | |||||||
\(158\) | −17.5335 | −1.39489 | ||||||||
\(159\) | − | 7.15143i | − | 0.567145i | ||||||
\(160\) | 0.516505 | 0.0408333 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 4.69605 | 0.367823 | 0.183912 | − | 0.982943i | \(-0.441124\pi\) | ||||
0.183912 | + | 0.982943i | \(0.441124\pi\) | |||||||
\(164\) | 2.14721 | 0.167669 | ||||||||
\(165\) | −1.59879 | + | 0.615152i | −0.124466 | + | 0.0478895i | ||||
\(166\) | 3.86307i | 0.299833i | ||||||||
\(167\) | 20.6417 | 1.59730 | 0.798652 | − | 0.601793i | \(-0.205547\pi\) | ||||
0.798652 | + | 0.601793i | \(0.205547\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.17991 | −0.552301 | ||||||||
\(170\) | 3.77041 | 0.289177 | ||||||||
\(171\) | 2.57557 | 0.196959 | ||||||||
\(172\) | 2.68147i | 0.204460i | ||||||||
\(173\) | −12.9992 | −0.988310 | −0.494155 | − | 0.869374i | \(-0.664523\pi\) | ||||
−0.494155 | + | 0.869374i | \(0.664523\pi\) | |||||||
\(174\) | 1.33100i | 0.100903i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.09541 | + | 1.19099i | −0.233325 | + | 0.0897742i | ||||
\(177\) | −1.00336 | −0.0754175 | ||||||||
\(178\) | −14.3064 | −1.07231 | ||||||||
\(179\) | 25.6730 | 1.91889 | 0.959444 | − | 0.281900i | \(-0.0909645\pi\) | ||||
0.959444 | + | 0.281900i | \(0.0909645\pi\) | |||||||
\(180\) | 0.516505i | 0.0384980i | ||||||||
\(181\) | 10.7864i | 0.801750i | 0.916133 | + | 0.400875i | \(0.131294\pi\) | ||||
−0.916133 | + | 0.400875i | \(0.868706\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.50704i | 0.333170i | ||||||||
\(184\) | − | 1.88937i | − | 0.139286i | ||||||
\(185\) | 3.27499i | 0.240782i | ||||||||
\(186\) | − | 4.58708i | − | 0.336341i | ||||||
\(187\) | −22.5960 | + | 8.69405i | −1.65238 | + | 0.635772i | ||||
\(188\) | − | 1.14068i | − | 0.0831926i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.33029 | −0.0965097 | ||||||||
\(191\) | 5.40879 | 0.391367 | 0.195683 | − | 0.980667i | \(-0.437308\pi\) | ||||
0.195683 | + | 0.980667i | \(0.437308\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 6.80675i | − | 0.489960i | −0.969528 | − | 0.244980i | \(-0.921219\pi\) | ||
0.969528 | − | 0.244980i | \(-0.0787814\pi\) | |||||||
\(194\) | −3.02541 | −0.217212 | ||||||||
\(195\) | −1.24606 | −0.0892322 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.3261i | − | 1.37693i | −0.725269 | − | 0.688465i | \(-0.758285\pi\) | ||
0.725269 | − | 0.688465i | \(-0.241715\pi\) | |||||||
\(198\) | −1.19099 | − | 3.09541i | −0.0846400 | − | 0.219981i | ||||
\(199\) | 7.03030i | 0.498364i | 0.968457 | + | 0.249182i | \(0.0801618\pi\) | ||||
−0.968457 | + | 0.249182i | \(0.919838\pi\) | |||||||
\(200\) | 4.73322i | 0.334689i | ||||||||
\(201\) | − | 8.00023i | − | 0.564293i | ||||||
\(202\) | − | 17.0462i | − | 1.19936i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.29986i | 0.511092i | ||||||||
\(205\) | − | 1.10904i | − | 0.0774589i | ||||||
\(206\) | 13.4342 | 0.936003 | ||||||||
\(207\) | 1.88937 | 0.131320 | ||||||||
\(208\) | −2.41249 | −0.167276 | ||||||||
\(209\) | 7.97244 | − | 3.06748i | 0.551465 | − | 0.212182i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.276202i | 0.0190145i | 0.999955 | + | 0.00950725i | \(0.00302630\pi\) | ||||
−0.999955 | + | 0.00950725i | \(0.996974\pi\) | |||||||
\(212\) | −7.15143 | −0.491162 | ||||||||
\(213\) | − | 9.05635i | − | 0.620531i | ||||||
\(214\) | 4.74835 | 0.324590 | ||||||||
\(215\) | 1.38499 | 0.0944555 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.61490 | 0.109375 | ||||||||
\(219\) | − | 5.82214i | − | 0.393424i | ||||||
\(220\) | 0.615152 | + | 1.59879i | 0.0414735 | + | 0.107791i | ||||
\(221\) | −17.6108 | −1.18463 | ||||||||
\(222\) | −6.34068 | −0.425558 | ||||||||
\(223\) | 22.9482i | 1.53673i | 0.640014 | + | 0.768363i | \(0.278929\pi\) | ||||
−0.640014 | + | 0.768363i | \(0.721071\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.73322 | −0.315548 | ||||||||
\(226\) | − | 18.4489i | − | 1.22720i | ||||||
\(227\) | 4.78439 | 0.317551 | 0.158775 | − | 0.987315i | \(-0.449245\pi\) | ||||
0.158775 | + | 0.987315i | \(0.449245\pi\) | |||||||
\(228\) | − | 2.57557i | − | 0.170571i | ||||||
\(229\) | − | 12.8296i | − | 0.847803i | −0.905708 | − | 0.423901i | \(-0.860660\pi\) | ||
0.905708 | − | 0.423901i | \(-0.139340\pi\) | |||||||
\(230\) | −0.975866 | −0.0643467 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.33100 | 0.0873843 | ||||||||
\(233\) | 0.0966329i | 0.00633063i | 0.999995 | + | 0.00316532i | \(0.00100755\pi\) | ||||
−0.999995 | + | 0.00316532i | \(0.998992\pi\) | |||||||
\(234\) | − | 2.41249i | − | 0.157709i | ||||||
\(235\) | −0.589166 | −0.0384330 | ||||||||
\(236\) | 1.00336i | 0.0653134i | ||||||||
\(237\) | −17.5335 | −1.13893 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.8209i | − | 1.02337i | −0.859173 | − | 0.511686i | \(-0.829021\pi\) | ||
0.859173 | − | 0.511686i | \(-0.170979\pi\) | |||||||
\(240\) | 0.516505 | 0.0333402 | ||||||||
\(241\) | −14.5518 | −0.937363 | −0.468682 | − | 0.883367i | \(-0.655271\pi\) | ||||
−0.468682 | + | 0.883367i | \(0.655271\pi\) | |||||||
\(242\) | −7.37320 | − | 8.16309i | −0.473967 | − | 0.524743i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 4.50704 | 0.288534 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.14721 | 0.136901 | ||||||||
\(247\) | 6.21353 | 0.395357 | ||||||||
\(248\) | −4.58708 | −0.291280 | ||||||||
\(249\) | 3.86307i | 0.244812i | ||||||||
\(250\) | 5.02725 | 0.317951 | ||||||||
\(251\) | 20.9000i | 1.31919i | 0.751619 | + | 0.659597i | \(0.229273\pi\) | ||||
−0.751619 | + | 0.659597i | \(0.770727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.84836 | − | 2.25022i | 0.367683 | − | 0.141470i | ||||
\(254\) | −12.7652 | −0.800960 | ||||||||
\(255\) | 3.77041 | 0.236112 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 18.2140i | − | 1.13616i | −0.822973 | − | 0.568080i | \(-0.807686\pi\) | ||
0.822973 | − | 0.568080i | \(-0.192314\pi\) | |||||||
\(258\) | 2.68147i | 0.166941i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.24606i | 0.0772773i | ||||||||
\(261\) | 1.33100i | 0.0823867i | ||||||||
\(262\) | 13.1155i | 0.810276i | ||||||||
\(263\) | − | 15.6132i | − | 0.962751i | −0.876514 | − | 0.481376i | \(-0.840137\pi\) | ||
0.876514 | − | 0.481376i | \(-0.159863\pi\) | |||||||
\(264\) | −3.09541 | + | 1.19099i | −0.190509 | + | 0.0733004i | ||||
\(265\) | 3.69375i | 0.226905i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.3064 | −0.875540 | ||||||||
\(268\) | −8.00023 | −0.488692 | ||||||||
\(269\) | − | 19.8599i | − | 1.21088i | −0.795890 | − | 0.605441i | \(-0.792997\pi\) | ||
0.795890 | − | 0.605441i | \(-0.207003\pi\) | |||||||
\(270\) | 0.516505i | 0.0314335i | ||||||||
\(271\) | 15.7584 | 0.957256 | 0.478628 | − | 0.878018i | \(-0.341134\pi\) | ||||
0.478628 | + | 0.878018i | \(0.341134\pi\) | |||||||
\(272\) | 7.29986 | 0.442619 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 6.94935i | − | 0.419826i | ||||||
\(275\) | −14.6513 | + | 5.63722i | −0.883504 | + | 0.339937i | ||||
\(276\) | − | 1.88937i | − | 0.113727i | ||||||
\(277\) | 20.1002i | 1.20770i | 0.797097 | + | 0.603852i | \(0.206368\pi\) | ||||
−0.797097 | + | 0.603852i | \(0.793632\pi\) | |||||||
\(278\) | 8.43815i | 0.506087i | ||||||||
\(279\) | − | 4.58708i | − | 0.274621i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.3187i | − | 1.45073i | −0.688364 | − | 0.725365i | \(-0.741671\pi\) | ||
0.688364 | − | 0.725365i | \(-0.258329\pi\) | |||||||
\(282\) | − | 1.14068i | − | 0.0679265i | ||||||
\(283\) | 2.29408 | 0.136369 | 0.0681845 | − | 0.997673i | \(-0.478279\pi\) | ||||
0.0681845 | + | 0.997673i | \(0.478279\pi\) | |||||||
\(284\) | −9.05635 | −0.537396 | ||||||||
\(285\) | −1.33029 | −0.0787998 | ||||||||
\(286\) | −2.87325 | − | 7.46762i | −0.169899 | − | 0.441570i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 36.2879 | 2.13458 | ||||||||
\(290\) | − | 0.687466i | − | 0.0403694i | ||||||
\(291\) | −3.02541 | −0.177353 | ||||||||
\(292\) | −5.82214 | −0.340715 | ||||||||
\(293\) | 10.4490 | 0.610438 | 0.305219 | − | 0.952282i | \(-0.401270\pi\) | ||||
0.305219 | + | 0.952282i | \(0.401270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.518242 | 0.0301732 | ||||||||
\(296\) | 6.34068i | 0.368544i | ||||||||
\(297\) | −1.19099 | − | 3.09541i | −0.0691082 | − | 0.179614i | ||||
\(298\) | −5.18030 | −0.300087 | ||||||||
\(299\) | 4.55807 | 0.263600 | ||||||||
\(300\) | 4.73322i | 0.273273i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.8174 | 0.852645 | ||||||||
\(303\) | − | 17.0462i | − | 0.979276i | ||||||
\(304\) | −2.57557 | −0.147719 | ||||||||
\(305\) | − | 2.32791i | − | 0.133296i | ||||||
\(306\) | 7.29986i | 0.417305i | ||||||||
\(307\) | −24.2172 | −1.38215 | −0.691073 | − | 0.722785i | \(-0.742862\pi\) | ||||
−0.691073 | + | 0.722785i | \(0.742862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4342 | 0.764243 | ||||||||
\(310\) | 2.36925i | 0.134564i | ||||||||
\(311\) | − | 7.98705i | − | 0.452904i | −0.974022 | − | 0.226452i | \(-0.927287\pi\) | ||
0.974022 | − | 0.226452i | \(-0.0727126\pi\) | |||||||
\(312\) | −2.41249 | −0.136580 | ||||||||
\(313\) | − | 6.10743i | − | 0.345213i | −0.984991 | − | 0.172606i | \(-0.944781\pi\) | ||
0.984991 | − | 0.172606i | \(-0.0552188\pi\) | |||||||
\(314\) | −0.378604 | −0.0213659 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.5335i | 0.986338i | ||||||||
\(317\) | 15.0861 | 0.847321 | 0.423661 | − | 0.905821i | \(-0.360745\pi\) | ||||
0.423661 | + | 0.905821i | \(0.360745\pi\) | |||||||
\(318\) | −7.15143 | −0.401032 | ||||||||
\(319\) | 1.58521 | + | 4.11998i | 0.0887544 | + | 0.230675i | ||||
\(320\) | − | 0.516505i | − | 0.0288735i | ||||||
\(321\) | 4.74835 | 0.265027 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.8013 | −1.04613 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −11.4188 | −0.633403 | ||||||||
\(326\) | − | 4.69605i | − | 0.260090i | ||||||
\(327\) | 1.61490 | 0.0893043 | ||||||||
\(328\) | − | 2.14721i | − | 0.118560i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.615152 | + | 1.59879i | 0.0338630 | + | 0.0880106i | ||||
\(331\) | 7.60617 | 0.418073 | 0.209036 | − | 0.977908i | \(-0.432967\pi\) | ||||
0.209036 | + | 0.977908i | \(0.432967\pi\) | |||||||
\(332\) | 3.86307 | 0.212014 | ||||||||
\(333\) | −6.34068 | −0.347467 | ||||||||
\(334\) | − | 20.6417i | − | 1.12946i | ||||||
\(335\) | 4.13216i | 0.225764i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7783i | 0.913973i | 0.889474 | + | 0.456987i | \(0.151071\pi\) | ||||
−0.889474 | + | 0.456987i | \(0.848929\pi\) | |||||||
\(338\) | 7.17991i | 0.390536i | ||||||||
\(339\) | − | 18.4489i | − | 1.00201i | ||||||
\(340\) | − | 3.77041i | − | 0.204479i | ||||||
\(341\) | −5.46317 | − | 14.1989i | −0.295847 | − | 0.768912i | ||||
\(342\) | − | 2.57557i | − | 0.139271i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.68147 | 0.144575 | ||||||||
\(345\) | −0.975866 | −0.0525389 | ||||||||
\(346\) | 12.9992i | 0.698841i | ||||||||
\(347\) | − | 7.26500i | − | 0.390005i | −0.980803 | − | 0.195003i | \(-0.937528\pi\) | ||
0.980803 | − | 0.195003i | \(-0.0624716\pi\) | |||||||
\(348\) | 1.33100 | 0.0713490 | ||||||||
\(349\) | −19.0310 | −1.01871 | −0.509354 | − | 0.860557i | \(-0.670116\pi\) | ||||
−0.509354 | + | 0.860557i | \(0.670116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.41249i | − | 0.128769i | ||||||
\(352\) | 1.19099 | + | 3.09541i | 0.0634800 | + | 0.164986i | ||||
\(353\) | 20.1289i | 1.07136i | 0.844422 | + | 0.535678i | \(0.179944\pi\) | ||||
−0.844422 | + | 0.535678i | \(0.820056\pi\) | |||||||
\(354\) | 1.00336i | 0.0533282i | ||||||||
\(355\) | 4.67765i | 0.248264i | ||||||||
\(356\) | 14.3064i | 0.758240i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 25.6730i | − | 1.35686i | ||||||
\(359\) | 17.1576i | 0.905544i | 0.891626 | + | 0.452772i | \(0.149565\pi\) | ||||
−0.891626 | + | 0.452772i | \(0.850435\pi\) | |||||||
\(360\) | 0.516505 | 0.0272222 | ||||||||
\(361\) | −12.3664 | −0.650865 | ||||||||
\(362\) | 10.7864 | 0.566923 | ||||||||
\(363\) | −7.37320 | − | 8.16309i | −0.386992 | − | 0.428451i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.00716i | 0.157402i | ||||||||
\(366\) | 4.50704 | 0.235587 | ||||||||
\(367\) | 1.86109i | 0.0971479i | 0.998820 | + | 0.0485739i | \(0.0154677\pi\) | ||||
−0.998820 | + | 0.0485739i | \(0.984532\pi\) | |||||||
\(368\) | −1.88937 | −0.0984901 | ||||||||
\(369\) | 2.14721 | 0.111779 | ||||||||
\(370\) | 3.27499 | 0.170258 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.58708 | −0.237829 | ||||||||
\(373\) | 14.5431i | 0.753013i | 0.926414 | + | 0.376507i | \(0.122875\pi\) | ||||
−0.926414 | + | 0.376507i | \(0.877125\pi\) | |||||||
\(374\) | 8.69405 | + | 22.5960i | 0.449559 | + | 1.16841i | ||||
\(375\) | 5.02725 | 0.259606 | ||||||||
\(376\) | −1.14068 | −0.0588261 | ||||||||
\(377\) | 3.21101i | 0.165376i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.0016 | −1.59244 | −0.796222 | − | 0.605004i | \(-0.793171\pi\) | ||||
−0.796222 | + | 0.605004i | \(0.793171\pi\) | |||||||
\(380\) | 1.33029i | 0.0682427i | ||||||||
\(381\) | −12.7652 | −0.653981 | ||||||||
\(382\) | − | 5.40879i | − | 0.276738i | ||||||
\(383\) | 18.2949i | 0.934826i | 0.884039 | + | 0.467413i | \(0.154814\pi\) | ||||
−0.884039 | + | 0.467413i | \(0.845186\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.80675 | −0.346454 | ||||||||
\(387\) | 2.68147i | 0.136307i | ||||||||
\(388\) | 3.02541i | 0.153592i | ||||||||
\(389\) | 4.49563 | 0.227938 | 0.113969 | − | 0.993484i | \(-0.463644\pi\) | ||||
0.113969 | + | 0.993484i | \(0.463644\pi\) | |||||||
\(390\) | 1.24606i | 0.0630967i | ||||||||
\(391\) | −13.7921 | −0.697497 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.1155i | 0.661587i | ||||||||
\(394\) | −19.3261 | −0.973637 | ||||||||
\(395\) | 9.05615 | 0.455664 | ||||||||
\(396\) | −3.09541 | + | 1.19099i | −0.155550 | + | 0.0598495i | ||||
\(397\) | 29.5441i | 1.48277i | 0.671077 | + | 0.741387i | \(0.265832\pi\) | ||||
−0.671077 | + | 0.741387i | \(0.734168\pi\) | |||||||
\(398\) | 7.03030 | 0.352397 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.73322 | 0.236661 | ||||||||
\(401\) | −1.94172 | −0.0969648 | −0.0484824 | − | 0.998824i | \(-0.515438\pi\) | ||||
−0.0484824 | + | 0.998824i | \(0.515438\pi\) | |||||||
\(402\) | −8.00023 | −0.399015 | ||||||||
\(403\) | − | 11.0663i | − | 0.551250i | ||||||
\(404\) | −17.0462 | −0.848078 | ||||||||
\(405\) | 0.516505i | 0.0256653i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.6270 | + | 7.55168i | −0.972873 | + | 0.374323i | ||||
\(408\) | 7.29986 | 0.361397 | ||||||||
\(409\) | 3.22431 | 0.159432 | 0.0797160 | − | 0.996818i | \(-0.474599\pi\) | ||||
0.0797160 | + | 0.996818i | \(0.474599\pi\) | |||||||
\(410\) | −1.10904 | −0.0547717 | ||||||||
\(411\) | − | 6.94935i | − | 0.342786i | ||||||
\(412\) | − | 13.4342i | − | 0.661854i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 1.88937i | − | 0.0928573i | ||||||
\(415\) | − | 1.99529i | − | 0.0979451i | ||||||
\(416\) | 2.41249i | 0.118282i | ||||||||
\(417\) | 8.43815i | 0.413218i | ||||||||
\(418\) | −3.06748 | − | 7.97244i | −0.150035 | − | 0.389945i | ||||
\(419\) | 20.1284i | 0.983338i | 0.870782 | + | 0.491669i | \(0.163613\pi\) | ||||
−0.870782 | + | 0.491669i | \(0.836387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0464 | −0.782054 | −0.391027 | − | 0.920379i | \(-0.627880\pi\) | ||||
−0.391027 | + | 0.920379i | \(0.627880\pi\) | |||||||
\(422\) | 0.276202 | 0.0134453 | ||||||||
\(423\) | − | 1.14068i | − | 0.0554617i | ||||||
\(424\) | 7.15143i | 0.347304i | ||||||||
\(425\) | 34.5518 | 1.67601 | ||||||||
\(426\) | −9.05635 | −0.438782 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 4.74835i | − | 0.229520i | ||||||
\(429\) | −2.87325 | − | 7.46762i | −0.138722 | − | 0.360540i | ||||
\(430\) | − | 1.38499i | − | 0.0667902i | ||||||
\(431\) | 28.4344i | 1.36963i | 0.728715 | + | 0.684817i | \(0.240118\pi\) | ||||
−0.728715 | + | 0.684817i | \(0.759882\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 15.4748i | − | 0.743672i | −0.928298 | − | 0.371836i | \(-0.878728\pi\) | ||
0.928298 | − | 0.371836i | \(-0.121272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.687466i | − | 0.0329615i | ||||||
\(436\) | − | 1.61490i | − | 0.0773398i | ||||||
\(437\) | 4.86620 | 0.232782 | ||||||||
\(438\) | −5.82214 | −0.278193 | ||||||||
\(439\) | −2.87850 | −0.137384 | −0.0686918 | − | 0.997638i | \(-0.521882\pi\) | ||||
−0.0686918 | + | 0.997638i | \(0.521882\pi\) | |||||||
\(440\) | 1.59879 | − | 0.615152i | 0.0762194 | − | 0.0293262i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.6108i | 0.837660i | ||||||||
\(443\) | −5.55756 | −0.264048 | −0.132024 | − | 0.991247i | \(-0.542148\pi\) | ||||
−0.132024 | + | 0.991247i | \(0.542148\pi\) | |||||||
\(444\) | 6.34068i | 0.300915i | ||||||||
\(445\) | 7.38934 | 0.350288 | ||||||||
\(446\) | 22.9482 | 1.08663 | ||||||||
\(447\) | −5.18030 | −0.245020 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.7075 | 0.694091 | 0.347046 | − | 0.937848i | \(-0.387185\pi\) | ||||
0.347046 | + | 0.937848i | \(0.387185\pi\) | |||||||
\(450\) | 4.73322i | 0.223126i | ||||||||
\(451\) | 6.64648 | − | 2.55730i | 0.312971 | − | 0.120419i | ||||
\(452\) | −18.4489 | −0.867763 | ||||||||
\(453\) | 14.8174 | 0.696182 | ||||||||
\(454\) | − | 4.78439i | − | 0.224542i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.57557 | −0.120612 | ||||||||
\(457\) | 31.4706i | 1.47213i | 0.676910 | + | 0.736066i | \(0.263319\pi\) | ||||
−0.676910 | + | 0.736066i | \(0.736681\pi\) | |||||||
\(458\) | −12.8296 | −0.599487 | ||||||||
\(459\) | 7.29986i | 0.340728i | ||||||||
\(460\) | 0.975866i | 0.0455000i | ||||||||
\(461\) | 18.8445 | 0.877678 | 0.438839 | − | 0.898566i | \(-0.355390\pi\) | ||||
0.438839 | + | 0.898566i | \(0.355390\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.15933 | 0.239774 | 0.119887 | − | 0.992788i | \(-0.461747\pi\) | ||||
0.119887 | + | 0.992788i | \(0.461747\pi\) | |||||||
\(464\) | − | 1.33100i | − | 0.0617900i | ||||||
\(465\) | 2.36925i | 0.109871i | ||||||||
\(466\) | 0.0966329 | 0.00447643 | ||||||||
\(467\) | − | 14.6712i | − | 0.678900i | −0.940624 | − | 0.339450i | \(-0.889759\pi\) | ||
0.940624 | − | 0.339450i | \(-0.110241\pi\) | |||||||
\(468\) | −2.41249 | −0.111517 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.589166i | 0.0271762i | ||||||||
\(471\) | −0.378604 | −0.0174452 | ||||||||
\(472\) | 1.00336 | 0.0461836 | ||||||||
\(473\) | 3.19360 | + | 8.30023i | 0.146842 | + | 0.381645i | ||||
\(474\) | 17.5335i | 0.805342i | ||||||||
\(475\) | −12.1908 | −0.559350 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.15143 | −0.327442 | ||||||||
\(478\) | −15.8209 | −0.723633 | ||||||||
\(479\) | 26.7570 | 1.22256 | 0.611279 | − | 0.791415i | \(-0.290655\pi\) | ||||
0.611279 | + | 0.791415i | \(0.290655\pi\) | |||||||
\(480\) | − | 0.516505i | − | 0.0235751i | ||||||
\(481\) | −15.2968 | −0.697473 | ||||||||
\(482\) | 14.5518i | 0.662816i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.16309 | + | 7.37320i | −0.371049 | + | 0.335145i | ||||
\(485\) | 1.56264 | 0.0709557 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 18.4972 | 0.838189 | 0.419094 | − | 0.907943i | \(-0.362348\pi\) | ||||
0.419094 | + | 0.907943i | \(0.362348\pi\) | |||||||
\(488\) | − | 4.50704i | − | 0.204024i | ||||||
\(489\) | − | 4.69605i | − | 0.212363i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.5475i | − | 0.521133i | −0.965456 | − | 0.260567i | \(-0.916091\pi\) | ||
0.965456 | − | 0.260567i | \(-0.0839094\pi\) | |||||||
\(492\) | − | 2.14721i | − | 0.0968036i | ||||||
\(493\) | − | 9.71609i | − | 0.437591i | ||||||
\(494\) | − | 6.21353i | − | 0.279560i | ||||||
\(495\) | 0.615152 | + | 1.59879i | 0.0276490 | + | 0.0718603i | ||||
\(496\) | 4.58708i | 0.205966i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.86307 | 0.173108 | ||||||||
\(499\) | −26.7968 | −1.19959 | −0.599796 | − | 0.800153i | \(-0.704752\pi\) | ||||
−0.599796 | + | 0.800153i | \(0.704752\pi\) | |||||||
\(500\) | − | 5.02725i | − | 0.224826i | ||||||
\(501\) | − | 20.6417i | − | 0.922204i | ||||||
\(502\) | 20.9000 | 0.932811 | ||||||||
\(503\) | 29.5306 | 1.31670 | 0.658352 | − | 0.752710i | \(-0.271254\pi\) | ||||
0.658352 | + | 0.752710i | \(0.271254\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.80441i | 0.391791i | ||||||||
\(506\) | −2.25022 | − | 5.84836i | −0.100034 | − | 0.259991i | ||||
\(507\) | 7.17991i | 0.318871i | ||||||||
\(508\) | 12.7652i | 0.566365i | ||||||||
\(509\) | − | 10.4707i | − | 0.464107i | −0.972703 | − | 0.232053i | \(-0.925456\pi\) | ||
0.972703 | − | 0.232053i | \(-0.0745444\pi\) | |||||||
\(510\) | − | 3.77041i | − | 0.166956i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 2.57557i | − | 0.113714i | ||||||
\(514\) | −18.2140 | −0.803387 | ||||||||
\(515\) | −6.93881 | −0.305761 | ||||||||
\(516\) | 2.68147 | 0.118045 | ||||||||
\(517\) | −1.35854 | − | 3.53087i | −0.0597484 | − | 0.155287i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.9992i | 0.570601i | ||||||||
\(520\) | 1.24606 | 0.0546433 | ||||||||
\(521\) | 16.0333i | 0.702433i | 0.936294 | + | 0.351217i | \(0.114232\pi\) | ||||
−0.936294 | + | 0.351217i | \(0.885768\pi\) | |||||||
\(522\) | 1.33100 | 0.0582562 | ||||||||
\(523\) | 39.0430 | 1.70723 | 0.853616 | − | 0.520903i | \(-0.174405\pi\) | ||||
0.853616 | + | 0.520903i | \(0.174405\pi\) | |||||||
\(524\) | 13.1155 | 0.572952 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.6132 | −0.680768 | ||||||||
\(527\) | 33.4850i | 1.45863i | ||||||||
\(528\) | 1.19099 | + | 3.09541i | 0.0518312 | + | 0.134710i | ||||
\(529\) | −19.4303 | −0.844795 | ||||||||
\(530\) | 3.69375 | 0.160446 | ||||||||
\(531\) | 1.00336i | 0.0435423i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.18011 | 0.224375 | ||||||||
\(534\) | 14.3064i | 0.619100i | ||||||||
\(535\) | −2.45254 | −0.106033 | ||||||||
\(536\) | 8.00023i | 0.345557i | ||||||||
\(537\) | − | 25.6730i | − | 1.10787i | ||||||
\(538\) | −19.8599 | −0.856223 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.516505 | 0.0222268 | ||||||||
\(541\) | − | 10.2056i | − | 0.438775i | −0.975638 | − | 0.219387i | \(-0.929594\pi\) | ||
0.975638 | − | 0.219387i | \(-0.0704059\pi\) | |||||||
\(542\) | − | 15.7584i | − | 0.676882i | ||||||
\(543\) | 10.7864 | 0.462890 | ||||||||
\(544\) | − | 7.29986i | − | 0.312979i | ||||||
\(545\) | −0.834104 | −0.0357291 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.4836i | 1.47441i | 0.675668 | + | 0.737206i | \(0.263855\pi\) | ||||
−0.675668 | + | 0.737206i | \(0.736145\pi\) | |||||||
\(548\) | −6.94935 | −0.296861 | ||||||||
\(549\) | 4.50704 | 0.192356 | ||||||||
\(550\) | 5.63722 | + | 14.6513i | 0.240372 | + | 0.624731i | ||||
\(551\) | 3.42808i | 0.146041i | ||||||||
\(552\) | −1.88937 | −0.0804168 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.1002 | 0.853975 | ||||||||
\(555\) | 3.27499 | 0.139015 | ||||||||
\(556\) | 8.43815 | 0.357857 | ||||||||
\(557\) | 5.85427i | 0.248053i | 0.992279 | + | 0.124027i | \(0.0395808\pi\) | ||||
−0.992279 | + | 0.124027i | \(0.960419\pi\) | |||||||
\(558\) | −4.58708 | −0.194187 | ||||||||
\(559\) | 6.46900i | 0.273610i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.69405 | + | 22.5960i | 0.367063 | + | 0.954005i | ||||
\(562\) | −24.3187 | −1.02582 | ||||||||
\(563\) | −7.49773 | −0.315992 | −0.157996 | − | 0.987440i | \(-0.550503\pi\) | ||||
−0.157996 | + | 0.987440i | \(0.550503\pi\) | |||||||
\(564\) | −1.14068 | −0.0480313 | ||||||||
\(565\) | 9.52894i | 0.400885i | ||||||||
\(566\) | − | 2.29408i | − | 0.0964274i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.05635i | 0.379996i | ||||||||
\(569\) | 43.0163i | 1.80334i | 0.432426 | + | 0.901670i | \(0.357658\pi\) | ||||
−0.432426 | + | 0.901670i | \(0.642342\pi\) | |||||||
\(570\) | 1.33029i | 0.0557199i | ||||||||
\(571\) | − | 24.2550i | − | 1.01504i | −0.861640 | − | 0.507521i | \(-0.830562\pi\) | ||
0.861640 | − | 0.507521i | \(-0.169438\pi\) | |||||||
\(572\) | −7.46762 | + | 2.87325i | −0.312237 | + | 0.120136i | ||||
\(573\) | − | 5.40879i | − | 0.225956i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.94279 | −0.372940 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 33.9166i | − | 1.41197i | −0.708228 | − | 0.705984i | \(-0.750505\pi\) | ||
0.708228 | − | 0.705984i | \(-0.249495\pi\) | |||||||
\(578\) | − | 36.2879i | − | 1.50938i | ||||||
\(579\) | −6.80675 | −0.282879 | ||||||||
\(580\) | −0.687466 | −0.0285455 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.02541i | 0.125407i | ||||||||
\(583\) | −22.1366 | + | 8.51728i | −0.916804 | + | 0.352750i | ||||
\(584\) | 5.82214i | 0.240922i | ||||||||
\(585\) | 1.24606i | 0.0515182i | ||||||||
\(586\) | − | 10.4490i | − | 0.431645i | ||||||
\(587\) | − | 13.6010i | − | 0.561372i | −0.959800 | − | 0.280686i | \(-0.909438\pi\) | ||
0.959800 | − | 0.280686i | \(-0.0905619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.8144i | − | 0.486802i | ||||||
\(590\) | − | 0.518242i | − | 0.0213357i | ||||||
\(591\) | −19.3261 | −0.794971 | ||||||||
\(592\) | 6.34068 | 0.260600 | ||||||||
\(593\) | 47.4393 | 1.94810 | 0.974050 | − | 0.226334i | \(-0.0726741\pi\) | ||||
0.974050 | + | 0.226334i | \(0.0726741\pi\) | |||||||
\(594\) | −3.09541 | + | 1.19099i | −0.127006 | + | 0.0488669i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.18030i | 0.212193i | ||||||||
\(597\) | 7.03030 | 0.287731 | ||||||||
\(598\) | − | 4.55807i | − | 0.186393i | ||||||
\(599\) | 30.2176 | 1.23466 | 0.617329 | − | 0.786705i | \(-0.288215\pi\) | ||||
0.617329 | + | 0.786705i | \(0.288215\pi\) | |||||||
\(600\) | 4.73322 | 0.193233 | ||||||||
\(601\) | 40.6902 | 1.65979 | 0.829893 | − | 0.557922i | \(-0.188401\pi\) | ||||
0.829893 | + | 0.557922i | \(0.188401\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.00023 | −0.325795 | ||||||||
\(604\) | − | 14.8174i | − | 0.602911i | ||||||
\(605\) | 3.80829 | + | 4.21627i | 0.154829 | + | 0.171416i | ||||
\(606\) | −17.0462 | −0.692453 | ||||||||
\(607\) | −30.4472 | −1.23581 | −0.617907 | − | 0.786251i | \(-0.712019\pi\) | ||||
−0.617907 | + | 0.786251i | \(0.712019\pi\) | |||||||
\(608\) | 2.57557i | 0.104453i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.32791 | −0.0942542 | ||||||||
\(611\) | − | 2.75187i | − | 0.111329i | ||||||
\(612\) | 7.29986 | 0.295079 | ||||||||
\(613\) | − | 39.9547i | − | 1.61375i | −0.590719 | − | 0.806877i | \(-0.701156\pi\) | ||
0.590719 | − | 0.806877i | \(-0.298844\pi\) | |||||||
\(614\) | 24.2172i | 0.977325i | ||||||||
\(615\) | −1.10904 | −0.0447209 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.0978 | 0.527299 | 0.263649 | − | 0.964619i | \(-0.415074\pi\) | ||||
0.263649 | + | 0.964619i | \(0.415074\pi\) | |||||||
\(618\) | − | 13.4342i | − | 0.540402i | ||||||
\(619\) | − | 38.3268i | − | 1.54048i | −0.637753 | − | 0.770241i | \(-0.720136\pi\) | ||
0.637753 | − | 0.770241i | \(-0.279864\pi\) | |||||||
\(620\) | 2.36925 | 0.0951513 | ||||||||
\(621\) | − | 1.88937i | − | 0.0758177i | ||||||
\(622\) | −7.98705 | −0.320251 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.41249i | 0.0965767i | ||||||||
\(625\) | 21.0695 | 0.842781 | ||||||||
\(626\) | −6.10743 | −0.244102 | ||||||||
\(627\) | −3.06748 | − | 7.97244i | −0.122503 | − | 0.318389i | ||||
\(628\) | 0.378604i | 0.0151079i | ||||||||
\(629\) | 46.2860 | 1.84554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.88637 | −0.114905 | −0.0574523 | − | 0.998348i | \(-0.518298\pi\) | ||||
−0.0574523 | + | 0.998348i | \(0.518298\pi\) | |||||||
\(632\) | 17.5335 | 0.697446 | ||||||||
\(633\) | 0.276202 | 0.0109780 | ||||||||
\(634\) | − | 15.0861i | − | 0.599147i | ||||||
\(635\) | 6.59329 | 0.261647 | ||||||||
\(636\) | 7.15143i | 0.283573i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.11998 | − | 1.58521i | 0.163112 | − | 0.0627589i | ||||
\(639\) | −9.05635 | −0.358264 | ||||||||
\(640\) | −0.516505 | −0.0204166 | ||||||||
\(641\) | 29.2123 | 1.15382 | 0.576908 | − | 0.816809i | \(-0.304259\pi\) | ||||
0.576908 | + | 0.816809i | \(0.304259\pi\) | |||||||
\(642\) | − | 4.74835i | − | 0.187402i | ||||||
\(643\) | 18.8359i | 0.742816i | 0.928470 | + | 0.371408i | \(0.121125\pi\) | ||||
−0.928470 | + | 0.371408i | \(0.878875\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.38499i | − | 0.0545339i | ||||||
\(646\) | 18.8013i | 0.739727i | ||||||||
\(647\) | − | 15.1888i | − | 0.597134i | −0.954389 | − | 0.298567i | \(-0.903491\pi\) | ||
0.954389 | − | 0.298567i | \(-0.0965086\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 1.19500 | + | 3.10582i | 0.0469077 | + | 0.121914i | ||||
\(650\) | 11.4188i | 0.447883i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.69605 | −0.183912 | ||||||||
\(653\) | −21.0264 | −0.822825 | −0.411413 | − | 0.911449i | \(-0.634964\pi\) | ||||
−0.411413 | + | 0.911449i | \(0.634964\pi\) | |||||||
\(654\) | − | 1.61490i | − | 0.0631477i | ||||||
\(655\) | − | 6.77419i | − | 0.264690i | ||||||
\(656\) | −2.14721 | −0.0838344 | ||||||||
\(657\) | −5.82214 | −0.227143 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 25.9809i | − | 1.01207i | −0.862513 | − | 0.506036i | \(-0.831110\pi\) | ||
0.862513 | − | 0.506036i | \(-0.168890\pi\) | |||||||
\(660\) | 1.59879 | − | 0.615152i | 0.0622329 | − | 0.0239447i | ||||
\(661\) | 18.2876i | 0.711307i | 0.934618 | + | 0.355653i | \(0.115742\pi\) | ||||
−0.934618 | + | 0.355653i | \(0.884258\pi\) | |||||||
\(662\) | − | 7.60617i | − | 0.295622i | ||||||
\(663\) | 17.6108i | 0.683947i | ||||||||
\(664\) | − | 3.86307i | − | 0.149916i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.34068i | 0.245696i | ||||||||
\(667\) | 2.51474i | 0.0973713i | ||||||||
\(668\) | −20.6417 | −0.798652 | ||||||||
\(669\) | 22.9482 | 0.887230 | ||||||||
\(670\) | 4.13216 | 0.159639 | ||||||||
\(671\) | 13.9511 | − | 5.36784i | 0.538577 | − | 0.207223i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.0446i | 1.19668i | 0.801242 | + | 0.598340i | \(0.204173\pi\) | ||||
−0.801242 | + | 0.598340i | \(0.795827\pi\) | |||||||
\(674\) | 16.7783 | 0.646277 | ||||||||
\(675\) | 4.73322i | 0.182182i | ||||||||
\(676\) | 7.17991 | 0.276151 | ||||||||
\(677\) | 7.98432 | 0.306862 | 0.153431 | − | 0.988159i | \(-0.450968\pi\) | ||||
0.153431 | + | 0.988159i | \(0.450968\pi\) | |||||||
\(678\) | −18.4489 | −0.708526 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.77041 | −0.144589 | ||||||||
\(681\) | − | 4.78439i | − | 0.183338i | ||||||
\(682\) | −14.1989 | + | 5.46317i | −0.543703 | + | 0.209195i | ||||
\(683\) | −9.95220 | −0.380810 | −0.190405 | − | 0.981706i | \(-0.560980\pi\) | ||||
−0.190405 | + | 0.981706i | \(0.560980\pi\) | |||||||
\(684\) | −2.57557 | −0.0984795 | ||||||||
\(685\) | 3.58937i | 0.137143i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.8296 | −0.489479 | ||||||||
\(688\) | − | 2.68147i | − | 0.102230i | ||||||
\(689\) | −17.2527 | −0.657276 | ||||||||
\(690\) | 0.975866i | 0.0371506i | ||||||||
\(691\) | 22.8178i | 0.868030i | 0.900906 | + | 0.434015i | \(0.142904\pi\) | ||||
−0.900906 | + | 0.434015i | \(0.857096\pi\) | |||||||
\(692\) | 12.9992 | 0.494155 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.26500 | −0.275776 | ||||||||
\(695\) | − | 4.35834i | − | 0.165321i | ||||||
\(696\) | − | 1.33100i | − | 0.0504513i | ||||||
\(697\) | −15.6743 | −0.593707 | ||||||||
\(698\) | 19.0310i | 0.720335i | ||||||||
\(699\) | 0.0966329 | 0.00365499 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.0953i | 1.89207i | 0.324059 | + | 0.946037i | \(0.394952\pi\) | ||||
−0.324059 | + | 0.946037i | \(0.605048\pi\) | |||||||
\(702\) | −2.41249 | −0.0910534 | ||||||||
\(703\) | −16.3309 | −0.615930 | ||||||||
\(704\) | 3.09541 | − | 1.19099i | 0.116663 | − | 0.0448871i | ||||
\(705\) | 0.589166i | 0.0221893i | ||||||||
\(706\) | 20.1289 | 0.757563 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.00336 | 0.0377087 | ||||||||
\(709\) | 39.4466 | 1.48145 | 0.740725 | − | 0.671808i | \(-0.234482\pi\) | ||||
0.740725 | + | 0.671808i | \(0.234482\pi\) | |||||||
\(710\) | 4.67765 | 0.175549 | ||||||||
\(711\) | 17.5335i | 0.657559i | ||||||||
\(712\) | 14.3064 | 0.536156 | ||||||||
\(713\) | − | 8.66668i | − | 0.324570i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.48404 | + | 3.85706i | 0.0555001 | + | 0.144246i | ||||
\(716\) | −25.6730 | −0.959444 | ||||||||
\(717\) | −15.8209 | −0.590844 | ||||||||
\(718\) | 17.1576 | 0.640316 | ||||||||
\(719\) | 49.2461i | 1.83657i | 0.395922 | + | 0.918284i | \(0.370425\pi\) | ||||
−0.395922 | + | 0.918284i | \(0.629575\pi\) | |||||||
\(720\) | − | 0.516505i | − | 0.0192490i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.3664i | 0.460231i | ||||||||
\(723\) | 14.5518i | 0.541187i | ||||||||
\(724\) | − | 10.7864i | − | 0.400875i | ||||||
\(725\) | − | 6.29991i | − | 0.233973i | ||||||
\(726\) | −8.16309 | + | 7.37320i | −0.302961 | + | 0.273645i | ||||
\(727\) | − | 12.9593i | − | 0.480633i | −0.970695 | − | 0.240316i | \(-0.922749\pi\) | ||
0.970695 | − | 0.240316i | \(-0.0772512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 3.00716 | 0.111300 | ||||||||
\(731\) | − | 19.5743i | − | 0.723983i | ||||||
\(732\) | − | 4.50704i | − | 0.166585i | ||||||
\(733\) | 15.2932 | 0.564869 | 0.282434 | − | 0.959287i | \(-0.408858\pi\) | ||||
0.282434 | + | 0.959287i | \(0.408858\pi\) | |||||||
\(734\) | 1.86109 | 0.0686939 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.88937i | 0.0696430i | ||||||||
\(737\) | −24.7640 | + | 9.52820i | −0.912193 | + | 0.350976i | ||||
\(738\) | − | 2.14721i | − | 0.0790398i | ||||||
\(739\) | 43.9489i | 1.61669i | 0.588711 | + | 0.808344i | \(0.299636\pi\) | ||||
−0.588711 | + | 0.808344i | \(0.700364\pi\) | |||||||
\(740\) | − | 3.27499i | − | 0.120391i | ||||||
\(741\) | − | 6.21353i | − | 0.228260i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.8447i | − | 1.05821i | −0.848557 | − | 0.529104i | \(-0.822528\pi\) | ||
0.848557 | − | 0.529104i | \(-0.177472\pi\) | |||||||
\(744\) | 4.58708i | 0.168171i | ||||||||
\(745\) | 2.67565 | 0.0980282 | ||||||||
\(746\) | 14.5431 | 0.532461 | ||||||||
\(747\) | 3.86307 | 0.141342 | ||||||||
\(748\) | 22.5960 | − | 8.69405i | 0.826192 | − | 0.317886i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 5.02725i | − | 0.183569i | ||||||
\(751\) | 1.64654 | 0.0600832 | 0.0300416 | − | 0.999549i | \(-0.490436\pi\) | ||||
0.0300416 | + | 0.999549i | \(0.490436\pi\) | |||||||
\(752\) | 1.14068i | 0.0415963i | ||||||||
\(753\) | 20.9000 | 0.761637 | ||||||||
\(754\) | 3.21101 | 0.116938 | ||||||||
\(755\) | −7.65325 | −0.278530 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.2401 | 1.06275 | 0.531375 | − | 0.847137i | \(-0.321676\pi\) | ||||
0.531375 | + | 0.847137i | \(0.321676\pi\) | |||||||
\(758\) | 31.0016i | 1.12603i | ||||||||
\(759\) | −2.25022 | − | 5.84836i | −0.0816777 | − | 0.212282i | ||||
\(760\) | 1.33029 | 0.0482549 | ||||||||
\(761\) | −7.95411 | −0.288336 | −0.144168 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144168 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(762\) | 12.7652i | 0.462435i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.40879 | −0.195683 | ||||||||
\(765\) | − | 3.77041i | − | 0.136319i | ||||||
\(766\) | 18.2949 | 0.661022 | ||||||||
\(767\) | 2.42060i | 0.0874028i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −48.7306 | −1.75727 | −0.878635 | − | 0.477494i | \(-0.841545\pi\) | ||||
−0.878635 | + | 0.477494i | \(0.841545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.2140 | −0.655963 | ||||||||
\(772\) | 6.80675i | 0.244980i | ||||||||
\(773\) | 28.0705i | 1.00963i | 0.863229 | + | 0.504813i | \(0.168439\pi\) | ||||
−0.863229 | + | 0.504813i | \(0.831561\pi\) | |||||||
\(774\) | 2.68147 | 0.0963834 | ||||||||
\(775\) | 21.7117i | 0.779906i | ||||||||
\(776\) | 3.02541 | 0.108606 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 4.49563i | − | 0.161176i | ||||||
\(779\) | 5.53029 | 0.198143 | ||||||||
\(780\) | 1.24606 | 0.0446161 | ||||||||
\(781\) | −28.0331 | + | 10.7860i | −1.00310 | + | 0.385954i | ||||
\(782\) | 13.7921i | 0.493205i | ||||||||
\(783\) | 1.33100 | 0.0475660 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.195551 | 0.00697950 | ||||||||
\(786\) | 13.1155 | 0.467813 | ||||||||
\(787\) | −52.3968 | −1.86774 | −0.933872 | − | 0.357608i | \(-0.883592\pi\) | ||||
−0.933872 | + | 0.357608i | \(0.883592\pi\) | |||||||
\(788\) | 19.3261i | 0.688465i | ||||||||
\(789\) | −15.6132 | −0.555845 | ||||||||
\(790\) | − | 9.05615i | − | 0.322203i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.19099 | + | 3.09541i | 0.0423200 | + | 0.109990i | ||||
\(793\) | 10.8732 | 0.386118 | ||||||||
\(794\) | 29.5441 | 1.04848 | ||||||||
\(795\) | 3.69375 | 0.131004 | ||||||||
\(796\) | − | 7.03030i | − | 0.249182i | ||||||
\(797\) | 30.1448i | 1.06778i | 0.845553 | + | 0.533891i | \(0.179271\pi\) | ||||
−0.845553 | + | 0.533891i | \(0.820729\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.32680i | 0.294581i | ||||||||
\(800\) | − | 4.73322i | − | 0.167345i | ||||||
\(801\) | 14.3064i | 0.505493i | ||||||||
\(802\) | 1.94172i | 0.0685645i | ||||||||
\(803\) | −18.0219 | + | 6.93411i | −0.635979 | + | 0.244700i | ||||
\(804\) | 8.00023i | 0.282146i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.0663 | −0.389793 | ||||||||
\(807\) | −19.8599 | −0.699103 | ||||||||
\(808\) | 17.0462i | 0.599682i | ||||||||
\(809\) | − | 31.6620i | − | 1.11318i | −0.830788 | − | 0.556589i | \(-0.812110\pi\) | ||
0.830788 | − | 0.556589i | \(-0.187890\pi\) | |||||||
\(810\) | 0.516505 | 0.0181481 | ||||||||
\(811\) | 32.9219 | 1.15605 | 0.578023 | − | 0.816021i | \(-0.303824\pi\) | ||||
0.578023 | + | 0.816021i | \(0.303824\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 15.7584i | − | 0.552672i | ||||||
\(814\) | 7.55168 | + | 19.6270i | 0.264686 | + | 0.687925i | ||||
\(815\) | 2.42553i | 0.0849627i | ||||||||
\(816\) | − | 7.29986i | − | 0.255546i | ||||||
\(817\) | 6.90631i | 0.241621i | ||||||||
\(818\) | − | 3.22431i | − | 0.112735i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.10904i | 0.0387294i | ||||||||
\(821\) | 22.4729i | 0.784308i | 0.919900 | + | 0.392154i | \(0.128270\pi\) | ||||
−0.919900 | + | 0.392154i | \(0.871730\pi\) | |||||||
\(822\) | −6.94935 | −0.242386 | ||||||||
\(823\) | −1.90917 | −0.0665495 | −0.0332748 | − | 0.999446i | \(-0.510594\pi\) | ||||
−0.0332748 | + | 0.999446i | \(0.510594\pi\) | |||||||
\(824\) | −13.4342 | −0.468002 | ||||||||
\(825\) | 5.63722 | + | 14.6513i | 0.196263 | + | 0.510091i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.2948i | 0.914359i | 0.889374 | + | 0.457179i | \(0.151140\pi\) | ||||
−0.889374 | + | 0.457179i | \(0.848860\pi\) | |||||||
\(828\) | −1.88937 | −0.0656600 | ||||||||
\(829\) | 0.890046i | 0.0309126i | 0.999881 | + | 0.0154563i | \(0.00492008\pi\) | ||||
−0.999881 | + | 0.0154563i | \(0.995080\pi\) | |||||||
\(830\) | −1.99529 | −0.0692577 | ||||||||
\(831\) | 20.1002 | 0.697268 | ||||||||
\(832\) | 2.41249 | 0.0836379 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.43815 | 0.292189 | ||||||||
\(835\) | 10.6615i | 0.368958i | ||||||||
\(836\) | −7.97244 | + | 3.06748i | −0.275733 | + | 0.106091i | ||||
\(837\) | −4.58708 | −0.158553 | ||||||||
\(838\) | 20.1284 | 0.695325 | ||||||||
\(839\) | − | 6.18078i | − | 0.213384i | −0.994292 | − | 0.106692i | \(-0.965974\pi\) | ||
0.994292 | − | 0.106692i | \(-0.0340259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2284 | 0.938912 | ||||||||
\(842\) | 16.0464i | 0.552996i | ||||||||
\(843\) | −24.3187 | −0.837580 | ||||||||
\(844\) | − | 0.276202i | − | 0.00950725i | ||||||
\(845\) | − | 3.70846i | − | 0.127575i | ||||||
\(846\) | −1.14068 | −0.0392174 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.15143 | 0.245581 | ||||||||
\(849\) | − | 2.29408i | − | 0.0787327i | ||||||
\(850\) | − | 34.5518i | − | 1.18512i | ||||||
\(851\) | −11.9799 | −0.410664 | ||||||||
\(852\) | 9.05635i | 0.310266i | ||||||||
\(853\) | −37.4345 | −1.28173 | −0.640867 | − | 0.767652i | \(-0.721425\pi\) | ||||
−0.640867 | + | 0.767652i | \(0.721425\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.33029i | 0.0454951i | ||||||||
\(856\) | −4.74835 | −0.162295 | ||||||||
\(857\) | −25.3397 | −0.865587 | −0.432793 | − | 0.901493i | \(-0.642472\pi\) | ||||
−0.432793 | + | 0.901493i | \(0.642472\pi\) | |||||||
\(858\) | −7.46762 | + | 2.87325i | −0.254940 | + | 0.0980910i | ||||
\(859\) | − | 20.6952i | − | 0.706109i | −0.935603 | − | 0.353055i | \(-0.885143\pi\) | ||
0.935603 | − | 0.353055i | \(-0.114857\pi\) | |||||||
\(860\) | −1.38499 | −0.0472278 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.4344 | 0.968478 | ||||||||
\(863\) | −37.7053 | −1.28350 | −0.641752 | − | 0.766913i | \(-0.721792\pi\) | ||||
−0.641752 | + | 0.766913i | \(0.721792\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | − | 6.71414i | − | 0.228288i | ||||||
\(866\) | −15.4748 | −0.525855 | ||||||||
\(867\) | − | 36.2879i | − | 1.23240i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.8823 | + | 54.2734i | 0.708382 | + | 1.84110i | ||||
\(870\) | −0.687466 | −0.0233073 | ||||||||
\(871\) | −19.3004 | −0.653971 | ||||||||
\(872\) | −1.61490 | −0.0546875 | ||||||||
\(873\) | 3.02541i | 0.102395i | ||||||||
\(874\) | − | 4.86620i | − | 0.164602i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.82214i | 0.196712i | ||||||||
\(877\) | 18.8756i | 0.637384i | 0.947858 | + | 0.318692i | \(0.103244\pi\) | ||||
−0.947858 | + | 0.318692i | \(0.896756\pi\) | |||||||
\(878\) | 2.87850i | 0.0971448i | ||||||||
\(879\) | − | 10.4490i | − | 0.352436i | ||||||
\(880\) | −0.615152 | − | 1.59879i | −0.0207368 | − | 0.0538953i | ||||
\(881\) | − | 53.5511i | − | 1.80418i | −0.431545 | − | 0.902092i | \(-0.642031\pi\) | ||
0.431545 | − | 0.902092i | \(-0.357969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.7180 | 0.899131 | 0.449566 | − | 0.893247i | \(-0.351579\pi\) | ||||
0.449566 | + | 0.893247i | \(0.351579\pi\) | |||||||
\(884\) | 17.6108 | 0.592315 | ||||||||
\(885\) | − | 0.518242i | − | 0.0174205i | ||||||
\(886\) | 5.55756i | 0.186710i | ||||||||
\(887\) | −9.98396 | −0.335229 | −0.167614 | − | 0.985853i | \(-0.553606\pi\) | ||||
−0.167614 | + | 0.985853i | \(0.553606\pi\) | |||||||
\(888\) | 6.34068 | 0.212779 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.38934i | − | 0.247691i | ||||||
\(891\) | −3.09541 | + | 1.19099i | −0.103700 | + | 0.0398997i | ||||
\(892\) | − | 22.9482i | − | 0.768363i | ||||||
\(893\) | − | 2.93790i | − | 0.0983132i | ||||||
\(894\) | 5.18030i | 0.173255i | ||||||||
\(895\) | 13.2602i | 0.443240i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 4.55807i | − | 0.152190i | ||||||
\(898\) | − | 14.7075i | − | 0.490797i | ||||||
\(899\) | 6.10540 | 0.203626 | ||||||||
\(900\) | 4.73322 | 0.157774 | ||||||||
\(901\) | 52.2044 | 1.73918 | ||||||||
\(902\) | −2.55730 | − | 6.64648i | −0.0851489 | − | 0.221304i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.4489i | 0.613601i | ||||||||
\(905\) | −5.57124 | −0.185194 | ||||||||
\(906\) | − | 14.8174i | − | 0.492275i | ||||||
\(907\) | −17.8142 | −0.591510 | −0.295755 | − | 0.955264i | \(-0.595571\pi\) | ||||
−0.295755 | + | 0.955264i | \(0.595571\pi\) | |||||||
\(908\) | −4.78439 | −0.158775 | ||||||||
\(909\) | −17.0462 | −0.565385 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.9803 | −0.396925 | −0.198463 | − | 0.980108i | \(-0.563595\pi\) | ||||
−0.198463 | + | 0.980108i | \(0.563595\pi\) | |||||||
\(912\) | 2.57557i | 0.0852857i | ||||||||
\(913\) | 11.9578 | − | 4.60088i | 0.395745 | − | 0.152267i | ||||
\(914\) | 31.4706 | 1.04095 | ||||||||
\(915\) | −2.32791 | −0.0769582 | ||||||||
\(916\) | 12.8296i | 0.423901i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.29986 | 0.240931 | ||||||||
\(919\) | − | 18.5312i | − | 0.611287i | −0.952146 | − | 0.305644i | \(-0.901128\pi\) | ||
0.952146 | − | 0.305644i | \(-0.0988716\pi\) | |||||||
\(920\) | 0.975866 | 0.0321734 | ||||||||
\(921\) | 24.2172i | 0.797982i | ||||||||
\(922\) | − | 18.8445i | − | 0.620612i | ||||||
\(923\) | −21.8483 | −0.719146 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0118 | 0.986783 | ||||||||
\(926\) | − | 5.15933i | − | 0.169546i | ||||||
\(927\) | − | 13.4342i | − | 0.441236i | ||||||
\(928\) | −1.33100 | −0.0436922 | ||||||||
\(929\) | − | 1.15853i | − | 0.0380101i | −0.999819 | − | 0.0190050i | \(-0.993950\pi\) | ||
0.999819 | − | 0.0190050i | \(-0.00604986\pi\) | |||||||
\(930\) | 2.36925 | 0.0776907 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 0.0966329i | − | 0.00316532i | ||||||
\(933\) | −7.98705 | −0.261484 | ||||||||
\(934\) | −14.6712 | −0.480055 | ||||||||
\(935\) | −4.49052 | − | 11.6709i | −0.146856 | − | 0.381681i | ||||
\(936\) | 2.41249i | 0.0788546i | ||||||||
\(937\) | 54.5037 | 1.78056 | 0.890280 | − | 0.455414i | \(-0.150509\pi\) | ||||
0.890280 | + | 0.455414i | \(0.150509\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.10743 | −0.199309 | ||||||||
\(940\) | 0.589166 | 0.0192165 | ||||||||
\(941\) | −19.3839 | −0.631896 | −0.315948 | − | 0.948776i | \(-0.602323\pi\) | ||||
−0.315948 | + | 0.948776i | \(0.602323\pi\) | |||||||
\(942\) | 0.378604i | 0.0123356i | ||||||||
\(943\) | 4.05686 | 0.132110 | ||||||||
\(944\) | − | 1.00336i | − | 0.0326567i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.30023 | − | 3.19360i | 0.269864 | − | 0.103833i | ||||
\(947\) | −20.0226 | −0.650647 | −0.325324 | − | 0.945603i | \(-0.605473\pi\) | ||||
−0.325324 | + | 0.945603i | \(0.605473\pi\) | |||||||
\(948\) | 17.5335 | 0.569463 | ||||||||
\(949\) | −14.0458 | −0.455947 | ||||||||
\(950\) | 12.1908i | 0.395520i | ||||||||
\(951\) | − | 15.0861i | − | 0.489201i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 46.5508i | − | 1.50793i | −0.656915 | − | 0.753964i | \(-0.728139\pi\) | ||
0.656915 | − | 0.753964i | \(-0.271861\pi\) | |||||||
\(954\) | 7.15143i | 0.231536i | ||||||||
\(955\) | 2.79367i | 0.0904009i | ||||||||
\(956\) | 15.8209i | 0.511686i | ||||||||
\(957\) | 4.11998 | − | 1.58521i | 0.133180 | − | 0.0512424i | ||||
\(958\) | − | 26.7570i | − | 0.864480i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.516505 | −0.0166701 | ||||||||
\(961\) | 9.95869 | 0.321248 | ||||||||
\(962\) | 15.2968i | 0.493188i | ||||||||
\(963\) | − | 4.74835i | − | 0.153013i | ||||||
\(964\) | 14.5518 | 0.468682 | ||||||||
\(965\) | 3.51571 | 0.113175 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.0366i | 0.837280i | 0.908152 | + | 0.418640i | \(0.137493\pi\) | ||||
−0.908152 | + | 0.418640i | \(0.862507\pi\) | |||||||
\(968\) | 7.37320 | + | 8.16309i | 0.236983 | + | 0.262372i | ||||
\(969\) | 18.8013i | 0.603985i | ||||||||
\(970\) | − | 1.56264i | − | 0.0501732i | ||||||
\(971\) | − | 39.1267i | − | 1.25564i | −0.778360 | − | 0.627818i | \(-0.783948\pi\) | ||
0.778360 | − | 0.627818i | \(-0.216052\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 18.4972i | − | 0.592689i | ||||||
\(975\) | 11.4188i | 0.365695i | ||||||||
\(976\) | −4.50704 | −0.144267 | ||||||||
\(977\) | 19.8640 | 0.635507 | 0.317753 | − | 0.948173i | \(-0.397072\pi\) | ||||
0.317753 | + | 0.948173i | \(0.397072\pi\) | |||||||
\(978\) | −4.69605 | −0.150163 | ||||||||
\(979\) | 17.0388 | + | 44.2842i | 0.544563 | + | 1.41533i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.61490i | − | 0.0515598i | ||||||
\(982\) | −11.5475 | −0.368497 | ||||||||
\(983\) | − | 22.4112i | − | 0.714805i | −0.933950 | − | 0.357402i | \(-0.883662\pi\) | ||
0.933950 | − | 0.357402i | \(-0.116338\pi\) | |||||||
\(984\) | −2.14721 | −0.0684505 | ||||||||
\(985\) | 9.98204 | 0.318054 | ||||||||
\(986\) | −9.71609 | −0.309423 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.21353 | −0.197679 | ||||||||
\(989\) | 5.06628i | 0.161098i | ||||||||
\(990\) | 1.59879 | − | 0.615152i | 0.0508129 | − | 0.0195508i | ||||
\(991\) | −26.7246 | −0.848935 | −0.424467 | − | 0.905443i | \(-0.639539\pi\) | ||||
−0.424467 | + | 0.905443i | \(0.639539\pi\) | |||||||
\(992\) | 4.58708 | 0.145640 | ||||||||
\(993\) | − | 7.60617i | − | 0.241375i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.63118 | −0.115116 | ||||||||
\(996\) | − | 3.86307i | − | 0.122406i | ||||||
\(997\) | 21.2635 | 0.673421 | 0.336711 | − | 0.941608i | \(-0.390686\pi\) | ||||
0.336711 | + | 0.941608i | \(0.390686\pi\) | |||||||
\(998\) | 26.7968i | 0.848239i | ||||||||
\(999\) | 6.34068i | 0.200610i |
(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 | 3234.2.e.c.2155.9 | ✓ | 24 | |
7.6 | odd | 2 | 3234.2.e.d.2155.4 | yes | 24 | ||
11.10 | odd | 2 | 3234.2.e.d.2155.21 | yes | 24 | ||
77.76 | even | 2 | inner | 3234.2.e.c.2155.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.e.c.2155.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
3234.2.e.c.2155.16 | yes | 24 | 77.76 | even | 2 | inner | |
3234.2.e.d.2155.4 | yes | 24 | 7.6 | odd | 2 | ||
3234.2.e.d.2155.21 | yes | 24 | 11.10 | odd | 2 |