Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3087,2,Mod(3086,3087)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3087, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3087.3086");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3087 = 3^{2} \cdot 7^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3087.c (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: | \(24.6498191040\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3086.17 | ||
Character | \(\chi\) | \(=\) | 3087.3086 |
Dual form | 3087.2.c.c.3086.18 |
$q$-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 \(\left(\mathbb{Z}/3087\mathbb{Z}\right)^\times\).
\(n\) | \(344\) | \(2404\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.06406i | − 0.752407i | −0.926537 | − | 0.376203i | \(-0.877229\pi\) | ||||
0.926537 | − | 0.376203i | \(-0.122771\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.867767 | 0.433884 | ||||||||
\(5\) | 3.23675 | 1.44752 | 0.723759 | − | 0.690053i | \(-0.242413\pi\) | ||||
0.723759 | + | 0.690053i | \(0.242413\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 3.05149i | − 1.07886i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 3.44411i | − 1.08912i | ||||||||
\(11\) | − 0.699431i | − 0.210886i | −0.994425 | − | 0.105443i | \(-0.966374\pi\) | ||||
0.994425 | − | 0.105443i | \(-0.0336261\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.71931i | − 0.754200i | −0.926173 | − | 0.377100i | \(-0.876921\pi\) | ||||
0.926173 | − | 0.377100i | \(-0.123079\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.51144 | −0.377861 | ||||||||
\(17\) | −6.50168 | −1.57689 | −0.788444 | − | 0.615107i | \(-0.789113\pi\) | ||||
−0.788444 | + | 0.615107i | \(0.789113\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.581246i | 0.133347i | 0.997775 | + | 0.0666735i | \(0.0212386\pi\) | ||||
−0.997775 | + | 0.0666735i | \(0.978761\pi\) | |||||||
\(20\) | 2.80875 | 0.628055 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.744240 | −0.158672 | ||||||||
\(23\) | − 0.742427i | − 0.154807i | −0.997000 | − | 0.0774033i | \(-0.975337\pi\) | ||||
0.997000 | − | 0.0774033i | \(-0.0246629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47655 | 1.09531 | ||||||||
\(26\) | −2.89352 | −0.567465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.65157i | − 1.23516i | −0.786506 | − | 0.617582i | \(-0.788112\pi\) | ||||
0.786506 | − | 0.617582i | \(-0.211888\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.87219i | − 1.59349i | −0.604314 | − | 0.796746i | \(-0.706553\pi\) | ||||
0.604314 | − | 0.796746i | \(-0.293447\pi\) | |||||||
\(32\) | − 4.49470i | − 0.794559i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.91820i | 1.18646i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.66798 | 0.274214 | 0.137107 | − | 0.990556i | \(-0.456220\pi\) | ||||
0.137107 | + | 0.990556i | \(0.456220\pi\) | |||||||
\(38\) | 0.618483 | 0.100331 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 9.87691i | − 1.56168i | ||||||||
\(41\) | −3.71552 | −0.580267 | −0.290134 | − | 0.956986i | \(-0.593700\pi\) | ||||
−0.290134 | + | 0.956986i | \(0.593700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.59897 | −0.853835 | −0.426917 | − | 0.904291i | \(-0.640400\pi\) | ||||
−0.426917 | + | 0.904291i | \(0.640400\pi\) | |||||||
\(44\) | − 0.606944i | − 0.0915002i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.789990 | −0.116478 | ||||||||
\(47\) | −2.32997 | −0.339861 | −0.169931 | − | 0.985456i | \(-0.554354\pi\) | ||||
−0.169931 | + | 0.985456i | \(0.554354\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 5.82740i | − 0.824119i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.35973i | − 0.327235i | ||||||||
\(53\) | − 6.07261i | − 0.834138i | −0.908875 | − | 0.417069i | \(-0.863057\pi\) | ||||
0.908875 | − | 0.417069i | \(-0.136943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.26388i | − 0.305262i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.07769 | −0.929347 | ||||||||
\(59\) | −0.355771 | −0.0463175 | −0.0231587 | − | 0.999732i | \(-0.507372\pi\) | ||||
−0.0231587 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7351i | 1.50252i | 0.660007 | + | 0.751260i | \(0.270553\pi\) | ||||
−0.660007 | + | 0.751260i | \(0.729447\pi\) | |||||||
\(62\) | −9.44058 | −1.19895 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.80554 | −0.975693 | ||||||||
\(65\) | − 8.80172i | − 1.09172i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.4957 | 1.89310 | 0.946552 | − | 0.322550i | \(-0.104540\pi\) | ||||
0.946552 | + | 0.322550i | \(0.104540\pi\) | |||||||
\(68\) | −5.64194 | −0.684186 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 8.84942i | − 1.05023i | −0.851030 | − | 0.525117i | \(-0.824022\pi\) | ||||
0.851030 | − | 0.525117i | \(-0.175978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.2339i | 1.66596i | 0.553305 | + | 0.832979i | \(0.313366\pi\) | ||||
−0.553305 | + | 0.832979i | \(0.686634\pi\) | |||||||
\(74\) | − 1.77484i | − 0.206321i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.504386i | 0.0578571i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.775773 | −0.0872813 | −0.0436406 | − | 0.999047i | \(-0.513896\pi\) | ||||
−0.0436406 | + | 0.999047i | \(0.513896\pi\) | |||||||
\(80\) | −4.89217 | −0.546961 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.95356i | 0.436597i | ||||||||
\(83\) | 16.5058 | 1.81175 | 0.905873 | − | 0.423549i | \(-0.139216\pi\) | ||||
0.905873 | + | 0.423549i | \(0.139216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.0443 | −2.28257 | ||||||||
\(86\) | 5.95766i | 0.642431i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.13431 | −0.227518 | ||||||||
\(89\) | 3.83377 | 0.406379 | 0.203189 | − | 0.979139i | \(-0.434869\pi\) | ||||
0.203189 | + | 0.979139i | \(0.434869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 0.644254i | − 0.0671681i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.47924i | 0.255714i | ||||||||
\(95\) | 1.88135i | 0.193022i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 10.4610i | − 1.06215i | −0.847325 | − | 0.531075i | \(-0.821788\pi\) | ||||
0.847325 | − | 0.531075i | \(-0.178212\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.75237 | 0.475237 | ||||||||
\(101\) | 15.7643 | 1.56861 | 0.784304 | − | 0.620377i | \(-0.213020\pi\) | ||||
0.784304 | + | 0.620377i | \(0.213020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.5477i | 1.33490i | 0.744655 | + | 0.667449i | \(0.232614\pi\) | ||||
−0.744655 | + | 0.667449i | \(0.767386\pi\) | |||||||
\(104\) | −8.29794 | −0.813680 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.46165 | −0.627611 | ||||||||
\(107\) | 13.3360i | 1.28924i | 0.764504 | + | 0.644619i | \(0.222984\pi\) | ||||
−0.764504 | + | 0.644619i | \(0.777016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.28866 | 0.889692 | 0.444846 | − | 0.895607i | \(-0.353258\pi\) | ||||
0.444846 | + | 0.895607i | \(0.353258\pi\) | |||||||
\(110\) | −2.40892 | −0.229681 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 5.86335i | − 0.551578i | −0.961218 | − | 0.275789i | \(-0.911061\pi\) | ||||
0.961218 | − | 0.275789i | \(-0.0889391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.40305i | − 0.224086i | ||||||||
\(116\) | − 5.77201i | − 0.535918i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.378564i | 0.0348496i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5108 | 0.955527 | ||||||||
\(122\) | 12.4868 | 1.13051 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 7.69900i | − 0.691390i | ||||||||
\(125\) | 1.54247 | 0.137963 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1902 | −0.904237 | −0.452119 | − | 0.891958i | \(-0.649332\pi\) | ||||
−0.452119 | + | 0.891958i | \(0.649332\pi\) | |||||||
\(128\) | − 0.683809i | − 0.0604407i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.36559 | −0.821417 | ||||||||
\(131\) | 12.3920 | 1.08270 | 0.541348 | − | 0.840799i | \(-0.317914\pi\) | ||||
0.541348 | + | 0.840799i | \(0.317914\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 16.4885i | − 1.42439i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.8398i | 1.70125i | ||||||||
\(137\) | − 1.53066i | − 0.130773i | −0.997860 | − | 0.0653864i | \(-0.979172\pi\) | ||||
0.997860 | − | 0.0653864i | \(-0.0208280\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.4423i | 1.73389i | 0.498403 | + | 0.866945i | \(0.333920\pi\) | ||||
−0.498403 | + | 0.866945i | \(0.666080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.41635 | −0.790203 | ||||||||
\(143\) | −1.90197 | −0.159051 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 21.5295i | − 1.78792i | ||||||||
\(146\) | 15.1458 | 1.25348 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.44742 | 0.118977 | ||||||||
\(149\) | − 16.0703i | − 1.31653i | −0.752786 | − | 0.658266i | \(-0.771290\pi\) | ||||
0.752786 | − | 0.658266i | \(-0.228710\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.6504 | 0.948098 | 0.474049 | − | 0.880499i | \(-0.342792\pi\) | ||||
0.474049 | + | 0.880499i | \(0.342792\pi\) | |||||||
\(152\) | 1.77367 | 0.143863 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 28.7171i | − 2.30661i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2146i | 1.21426i | 0.794603 | + | 0.607129i | \(0.207679\pi\) | ||||
−0.794603 | + | 0.607129i | \(0.792321\pi\) | |||||||
\(158\) | 0.825472i | 0.0656711i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 14.5482i | − 1.15014i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.7335 | 1.38900 | 0.694499 | − | 0.719494i | \(-0.255626\pi\) | ||||
0.694499 | + | 0.719494i | \(0.255626\pi\) | |||||||
\(164\) | −3.22421 | −0.251769 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 17.5632i | − 1.36317i | ||||||||
\(167\) | −12.0363 | −0.931393 | −0.465697 | − | 0.884944i | \(-0.654196\pi\) | ||||
−0.465697 | + | 0.884944i | \(0.654196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.60537 | 0.431182 | ||||||||
\(170\) | 22.3925i | 1.71742i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.85860 | −0.370465 | ||||||||
\(173\) | 10.9940 | 0.835859 | 0.417930 | − | 0.908479i | \(-0.362756\pi\) | ||||
0.417930 | + | 0.908479i | \(0.362756\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.05715i | 0.0796858i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 4.07938i | − 0.305762i | ||||||||
\(179\) | 11.2624i | 0.841792i | 0.907109 | + | 0.420896i | \(0.138284\pi\) | ||||
−0.907109 | + | 0.420896i | \(0.861716\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.65897i | 0.123310i | 0.998098 | + | 0.0616550i | \(0.0196379\pi\) | ||||
−0.998098 | + | 0.0616550i | \(0.980362\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.26551 | −0.167015 | ||||||||
\(185\) | 5.39884 | 0.396930 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.54748i | 0.332544i | ||||||||
\(188\) | −2.02187 | −0.147460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.00188 | 0.145231 | ||||||||
\(191\) | − 8.47446i | − 0.613190i | −0.951840 | − | 0.306595i | \(-0.900810\pi\) | ||||
0.951840 | − | 0.306595i | \(-0.0991897\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.6179 | −1.70005 | −0.850025 | − | 0.526742i | \(-0.823413\pi\) | ||||
−0.850025 | + | 0.526742i | \(0.823413\pi\) | |||||||
\(194\) | −11.1311 | −0.799169 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 20.1961i | − 1.43891i | −0.694537 | − | 0.719457i | \(-0.744391\pi\) | ||||
0.694537 | − | 0.719457i | \(-0.255609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.55682i | 0.110360i | 0.998476 | + | 0.0551799i | \(0.0175732\pi\) | ||||
−0.998476 | + | 0.0551799i | \(0.982427\pi\) | |||||||
\(200\) | − 16.7116i | − 1.18169i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 16.7742i | − 1.18023i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0262 | −0.839948 | ||||||||
\(206\) | 14.4157 | 1.00439 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.11008i | 0.284983i | ||||||||
\(209\) | 0.406542 | 0.0281211 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.92376 | 0.476651 | 0.238326 | − | 0.971185i | \(-0.423401\pi\) | ||||
0.238326 | + | 0.971185i | \(0.423401\pi\) | |||||||
\(212\) | − 5.26962i | − 0.361919i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.1903 | 0.970032 | ||||||||
\(215\) | −18.1225 | −1.23594 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 9.88373i | − 0.669411i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 1.96453i | − 0.132448i | ||||||||
\(221\) | 17.6801i | 1.18929i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.2781i | 1.62578i | 0.582417 | + | 0.812890i | \(0.302107\pi\) | ||||
−0.582417 | + | 0.812890i | \(0.697893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.23898 | −0.415011 | ||||||||
\(227\) | −5.74207 | −0.381115 | −0.190557 | − | 0.981676i | \(-0.561029\pi\) | ||||
−0.190557 | + | 0.981676i | \(0.561029\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.2897i | 1.34078i | 0.742007 | + | 0.670392i | \(0.233874\pi\) | ||||
−0.742007 | + | 0.670392i | \(0.766126\pi\) | |||||||
\(230\) | −2.55700 | −0.168604 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.2972 | −1.33258 | ||||||||
\(233\) | 12.3784i | 0.810936i | 0.914109 | + | 0.405468i | \(0.132891\pi\) | ||||
−0.914109 | + | 0.405468i | \(0.867109\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.54154 | −0.491956 | ||||||||
\(236\) | −0.308727 | −0.0200964 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.2647i | 1.18144i | 0.806875 | + | 0.590722i | \(0.201157\pi\) | ||||
−0.806875 | + | 0.590722i | \(0.798843\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 23.2883i | − 1.50013i | −0.661364 | − | 0.750065i | \(-0.730022\pi\) | ||||
0.661364 | − | 0.750065i | \(-0.269978\pi\) | |||||||
\(242\) | − 11.1842i | − 0.718945i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.1833i | 0.651919i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.58059 | 0.100570 | ||||||||
\(248\) | −27.0734 | −1.71916 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.64129i | − 0.103804i | ||||||||
\(251\) | −12.7841 | −0.806923 | −0.403462 | − | 0.914997i | \(-0.632193\pi\) | ||||
−0.403462 | + | 0.914997i | \(0.632193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.519276 | −0.0326466 | ||||||||
\(254\) | 10.8431i | 0.680355i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.3387 | −1.02117 | ||||||||
\(257\) | 6.55775 | 0.409061 | 0.204530 | − | 0.978860i | \(-0.434433\pi\) | ||||
0.204530 | + | 0.978860i | \(0.434433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 7.63784i | − 0.473679i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 13.1859i | − 0.814628i | ||||||||
\(263\) | 29.7935i | 1.83715i | 0.395249 | + | 0.918574i | \(0.370658\pi\) | ||||
−0.395249 | + | 0.918574i | \(0.629342\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 19.6555i | − 1.20743i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.4467 | 0.821387 | ||||||||
\(269\) | 1.43750 | 0.0876460 | 0.0438230 | − | 0.999039i | \(-0.486046\pi\) | ||||
0.0438230 | + | 0.999039i | \(0.486046\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4973i | 0.941396i | 0.882294 | + | 0.470698i | \(0.155998\pi\) | ||||
−0.882294 | + | 0.470698i | \(0.844002\pi\) | |||||||
\(272\) | 9.82692 | 0.595845 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.62872 | −0.0983944 | ||||||||
\(275\) | − 3.83047i | − 0.230986i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.71075 | 0.102789 | 0.0513945 | − | 0.998678i | \(-0.483633\pi\) | ||||
0.0513945 | + | 0.998678i | \(0.483633\pi\) | |||||||
\(278\) | 21.7519 | 1.30459 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 4.30417i | − 0.256765i | −0.991725 | − | 0.128383i | \(-0.959021\pi\) | ||||
0.991725 | − | 0.128383i | \(-0.0409785\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8.76848i | − 0.521232i | −0.965443 | − | 0.260616i | \(-0.916074\pi\) | ||||
0.965443 | − | 0.260616i | \(-0.0839257\pi\) | |||||||
\(284\) | − 7.67924i | − 0.455679i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.02382i | 0.119671i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.2718 | 1.48658 | ||||||||
\(290\) | −22.9087 | −1.34525 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.3518i | 0.722832i | ||||||||
\(293\) | −31.5105 | −1.84086 | −0.920432 | − | 0.390903i | \(-0.872163\pi\) | ||||
−0.920432 | + | 0.390903i | \(0.872163\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.15154 | −0.0670454 | ||||||||
\(296\) | − 5.08983i | − 0.295840i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.0998 | −0.990568 | ||||||||
\(299\) | −2.01889 | −0.116755 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 12.3968i | − 0.713355i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 0.878521i | − 0.0503867i | ||||||||
\(305\) | 37.9834i | 2.17492i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.13806i | − 0.122026i | −0.998137 | − | 0.0610128i | \(-0.980567\pi\) | ||||
0.998137 | − | 0.0610128i | \(-0.0194330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −30.5568 | −1.73551 | ||||||||
\(311\) | −11.4164 | −0.647367 | −0.323683 | − | 0.946165i | \(-0.604921\pi\) | ||||
−0.323683 | + | 0.946165i | \(0.604921\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 9.39656i | − 0.531125i | −0.964094 | − | 0.265563i | \(-0.914442\pi\) | ||||
0.964094 | − | 0.265563i | \(-0.0855577\pi\) | |||||||
\(314\) | 16.1893 | 0.913617 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.673191 | −0.0378699 | ||||||||
\(317\) | − 6.03447i | − 0.338930i | −0.985536 | − | 0.169465i | \(-0.945796\pi\) | ||||
0.985536 | − | 0.169465i | \(-0.0542039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.65231 | −0.260480 | ||||||||
\(320\) | −25.2646 | −1.41233 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.77907i | − 0.210273i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 14.8924i | − 0.826083i | ||||||||
\(326\) | − 18.8696i | − 1.04509i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.3379i | 0.626030i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.51343 | −0.248081 | −0.124040 | − | 0.992277i | \(-0.539585\pi\) | ||||
−0.124040 | + | 0.992277i | \(0.539585\pi\) | |||||||
\(332\) | 14.3232 | 0.786087 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.8073i | 0.700787i | ||||||||
\(335\) | 50.1558 | 2.74030 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.262350 | −0.0142911 | −0.00714556 | − | 0.999974i | \(-0.502275\pi\) | ||||
−0.00714556 | + | 0.999974i | \(0.502275\pi\) | |||||||
\(338\) | − 5.96447i | − 0.324424i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −18.2616 | −0.990372 | ||||||||
\(341\) | −6.20549 | −0.336046 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 17.0852i | 0.921172i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 11.6983i | − 0.628907i | ||||||||
\(347\) | − 5.73283i | − 0.307755i | −0.988090 | − | 0.153877i | \(-0.950824\pi\) | ||||
0.988090 | − | 0.153877i | \(-0.0491761\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 11.7082i | − 0.626726i | −0.949633 | − | 0.313363i | \(-0.898544\pi\) | ||||
0.949633 | − | 0.313363i | \(-0.101456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.14374 | −0.167562 | ||||||||
\(353\) | −9.25250 | −0.492461 | −0.246230 | − | 0.969211i | \(-0.579192\pi\) | ||||
−0.246230 | + | 0.969211i | \(0.579192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 28.6434i | − 1.52023i | ||||||||
\(356\) | 3.32682 | 0.176321 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.9839 | 0.633370 | ||||||||
\(359\) | − 19.8213i | − 1.04613i | −0.852294 | − | 0.523064i | \(-0.824789\pi\) | ||||
0.852294 | − | 0.523064i | \(-0.175211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.6622 | 0.982219 | ||||||||
\(362\) | 1.76525 | 0.0927793 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 46.0717i | 2.41150i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.86165i | 0.0971773i | 0.998819 | + | 0.0485887i | \(0.0154723\pi\) | ||||
−0.998819 | + | 0.0485887i | \(0.984528\pi\) | |||||||
\(368\) | 1.12214i | 0.0584954i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 5.74471i | − 0.298653i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.5179 | −1.32127 | −0.660634 | − | 0.750708i | \(-0.729712\pi\) | ||||
−0.660634 | + | 0.750708i | \(0.729712\pi\) | |||||||
\(374\) | 4.83881 | 0.250209 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.10988i | 0.366664i | ||||||||
\(377\) | −18.0877 | −0.931562 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.7502 | −1.32270 | −0.661350 | − | 0.750078i | \(-0.730016\pi\) | ||||
−0.661350 | + | 0.750078i | \(0.730016\pi\) | |||||||
\(380\) | 1.63257i | 0.0837492i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.01736 | −0.461369 | ||||||||
\(383\) | −12.7085 | −0.649374 | −0.324687 | − | 0.945822i | \(-0.605259\pi\) | ||||
−0.324687 | + | 0.945822i | \(0.605259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.1309i | 1.27913i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 9.07768i | − 0.460849i | ||||||||
\(389\) | 27.8265i | 1.41086i | 0.708781 | + | 0.705429i | \(0.249246\pi\) | ||||
−0.708781 | + | 0.705429i | \(0.750754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.82702i | 0.244113i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.4900 | −1.08265 | ||||||||
\(395\) | −2.51098 | −0.126341 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 13.8127i | − 0.693241i | −0.938005 | − | 0.346620i | \(-0.887329\pi\) | ||||
0.938005 | − | 0.346620i | \(-0.112671\pi\) | |||||||
\(398\) | 1.65655 | 0.0830354 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.27750 | −0.413875 | ||||||||
\(401\) | 2.27378i | 0.113547i | 0.998387 | + | 0.0567736i | \(0.0180813\pi\) | ||||
−0.998387 | + | 0.0567736i | \(0.981919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.1262 | −1.20181 | ||||||||
\(404\) | 13.6798 | 0.680593 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.16664i | − 0.0578281i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 17.8055i | − 0.880423i | −0.897894 | − | 0.440212i | \(-0.854903\pi\) | ||||
0.897894 | − | 0.440212i | \(-0.145097\pi\) | |||||||
\(410\) | 12.7967i | 0.631983i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.7563i | 0.579191i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 53.4251 | 2.62254 | ||||||||
\(416\) | −12.2225 | −0.599256 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 0.432586i | − 0.0211585i | ||||||||
\(419\) | 4.85817 | 0.237337 | 0.118668 | − | 0.992934i | \(-0.462137\pi\) | ||||
0.118668 | + | 0.992934i | \(0.462137\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.40414 | −0.360856 | −0.180428 | − | 0.983588i | \(-0.557748\pi\) | ||||
−0.180428 | + | 0.983588i | \(0.557748\pi\) | |||||||
\(422\) | − 7.36732i | − 0.358636i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.5305 | −0.899921 | ||||||||
\(425\) | −35.6067 | −1.72718 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.5725i | 0.559380i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.2835i | 0.929931i | ||||||||
\(431\) | − 31.0308i | − 1.49470i | −0.664429 | − | 0.747351i | \(-0.731325\pi\) | ||||
0.664429 | − | 0.747351i | \(-0.268675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 27.0645i | − 1.30064i | −0.759662 | − | 0.650318i | \(-0.774636\pi\) | ||||
0.759662 | − | 0.650318i | \(-0.225364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.06040 | 0.386023 | ||||||||
\(437\) | 0.431533 | 0.0206430 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 26.9454i | − 1.28604i | −0.765851 | − | 0.643018i | \(-0.777682\pi\) | ||||
0.765851 | − | 0.643018i | \(-0.222318\pi\) | |||||||
\(440\) | −6.90822 | −0.329336 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.8127 | 0.894829 | ||||||||
\(443\) | − 0.652931i | − 0.0310217i | −0.999880 | − | 0.0155108i | \(-0.995063\pi\) | ||||
0.999880 | − | 0.0155108i | \(-0.00493745\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.4090 | 0.588241 | ||||||||
\(446\) | 25.8334 | 1.22325 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 23.3074i | − 1.09994i | −0.835183 | − | 0.549972i | \(-0.814638\pi\) | ||||
0.835183 | − | 0.549972i | \(-0.185362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.59875i | 0.122371i | ||||||||
\(452\) | − 5.08803i | − 0.239321i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.10993i | 0.286753i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.4707 | −1.70603 | −0.853015 | − | 0.521887i | \(-0.825228\pi\) | ||||
−0.853015 | + | 0.521887i | \(0.825228\pi\) | |||||||
\(458\) | 21.5896 | 1.00881 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 2.08529i | − 0.0972271i | ||||||||
\(461\) | −26.3678 | −1.22807 | −0.614035 | − | 0.789279i | \(-0.710455\pi\) | ||||
−0.614035 | + | 0.789279i | \(0.710455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5599 | 0.816076 | 0.408038 | − | 0.912965i | \(-0.366213\pi\) | ||||
0.408038 | + | 0.912965i | \(0.366213\pi\) | |||||||
\(464\) | 10.0535i | 0.466721i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.1714 | 0.610154 | ||||||||
\(467\) | 25.0005 | 1.15689 | 0.578444 | − | 0.815722i | \(-0.303660\pi\) | ||||
0.578444 | + | 0.815722i | \(0.303660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.02468i | 0.370151i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.08563i | 0.0499703i | ||||||||
\(473\) | 3.91609i | 0.180062i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.18322i | 0.146056i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.4348 | 0.888927 | ||||||||
\(479\) | 1.73499 | 0.0792738 | 0.0396369 | − | 0.999214i | \(-0.487380\pi\) | ||||
0.0396369 | + | 0.999214i | \(0.487380\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 4.53575i | − 0.206813i | ||||||||
\(482\) | −24.7802 | −1.12871 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.12093 | 0.414588 | ||||||||
\(485\) | − 33.8595i | − 1.53748i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.8737 | −0.583361 | −0.291681 | − | 0.956516i | \(-0.594214\pi\) | ||||
−0.291681 | + | 0.956516i | \(0.594214\pi\) | |||||||
\(488\) | 35.8094 | 1.62101 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.7852i | 1.75035i | 0.483804 | + | 0.875176i | \(0.339255\pi\) | ||||
−0.483804 | + | 0.875176i | \(0.660745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.2463i | 1.94772i | ||||||||
\(494\) | − 1.68185i | − 0.0756698i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.4098i | 0.602119i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.5167 | 1.00799 | 0.503993 | − | 0.863708i | \(-0.331864\pi\) | ||||
0.503993 | + | 0.863708i | \(0.331864\pi\) | |||||||
\(500\) | 1.33851 | 0.0598598 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.6031i | 0.607135i | ||||||||
\(503\) | 0.431101 | 0.0192218 | 0.00961091 | − | 0.999954i | \(-0.496941\pi\) | ||||
0.00961091 | + | 0.999954i | \(0.496941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 51.0251 | 2.27059 | ||||||||
\(506\) | 0.552543i | 0.0245636i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.84276 | −0.392334 | ||||||||
\(509\) | 33.6247 | 1.49039 | 0.745194 | − | 0.666847i | \(-0.232357\pi\) | ||||
0.745194 | + | 0.666847i | \(0.232357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0178i | 0.707894i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 6.97786i | − 0.307780i | ||||||||
\(515\) | 43.8506i | 1.93229i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.62966i | 0.0716722i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −26.8583 | −1.17782 | ||||||||
\(521\) | −20.0638 | −0.879012 | −0.439506 | − | 0.898240i | \(-0.644846\pi\) | ||||
−0.439506 | + | 0.898240i | \(0.644846\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 0.242504i | − 0.0106040i | −0.999986 | − | 0.00530198i | \(-0.998312\pi\) | ||||
0.999986 | − | 0.00530198i | \(-0.00168768\pi\) | |||||||
\(524\) | 10.7534 | 0.469764 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.7022 | 1.38228 | ||||||||
\(527\) | 57.6841i | 2.51276i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4488 | 0.976035 | ||||||||
\(530\) | −20.9147 | −0.908479 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.1037i | 0.437638i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.1653i | 1.86620i | ||||||||
\(536\) | − 47.2850i | − 2.04240i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 1.52959i | − 0.0659455i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.51687 | 0.194195 | 0.0970977 | − | 0.995275i | \(-0.469044\pi\) | ||||
0.0970977 | + | 0.995275i | \(0.469044\pi\) | |||||||
\(542\) | 16.4902 | 0.708313 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 29.2231i | 1.25293i | ||||||||
\(545\) | 30.0651 | 1.28785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.5555 | 1.22094 | 0.610472 | − | 0.792038i | \(-0.290980\pi\) | ||||
0.610472 | + | 0.792038i | \(0.290980\pi\) | |||||||
\(548\) | − 1.32825i | − 0.0567402i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.07587 | −0.173796 | ||||||||
\(551\) | 3.86620 | 0.164706 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 1.82035i | − 0.0773392i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.7391i | 0.752307i | ||||||||
\(557\) | 28.7904i | 1.21989i | 0.792445 | + | 0.609944i | \(0.208808\pi\) | ||||
−0.792445 | + | 0.609944i | \(0.791192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.2253i | 0.643962i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.57991 | −0.193192 | ||||||||
\(563\) | 29.9049 | 1.26034 | 0.630171 | − | 0.776456i | \(-0.282985\pi\) | ||||
0.630171 | + | 0.776456i | \(0.282985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 18.9782i | − 0.798419i | ||||||||
\(566\) | −9.33023 | −0.392179 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.0039 | −1.13306 | ||||||||
\(569\) | − 25.6498i | − 1.07529i | −0.843170 | − | 0.537647i | \(-0.819313\pi\) | ||||
0.843170 | − | 0.537647i | \(-0.180687\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.5885 | 1.28009 | 0.640045 | − | 0.768338i | \(-0.278916\pi\) | ||||
0.640045 | + | 0.768338i | \(0.278916\pi\) | |||||||
\(572\) | −1.65047 | −0.0690095 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 4.06594i | − 0.169561i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 33.9163i | − 1.41195i | −0.708236 | − | 0.705976i | \(-0.750509\pi\) | ||||
0.708236 | − | 0.705976i | \(-0.249491\pi\) | |||||||
\(578\) | − 26.8908i | − 1.11851i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 18.6826i | − 0.775751i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.24738 | −0.175908 | ||||||||
\(584\) | 43.4347 | 1.79734 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.5292i | 1.38508i | ||||||||
\(587\) | 13.6861 | 0.564885 | 0.282443 | − | 0.959284i | \(-0.408855\pi\) | ||||
0.282443 | + | 0.959284i | \(0.408855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.15693 | 0.212487 | ||||||||
\(590\) | 1.22532i | 0.0504455i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.52106 | −0.103615 | ||||||||
\(593\) | −45.1939 | −1.85589 | −0.927945 | − | 0.372716i | \(-0.878426\pi\) | ||||
−0.927945 | + | 0.372716i | \(0.878426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 13.9453i | − 0.571222i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.14822i | 0.0878474i | ||||||||
\(599\) | 35.8228i | 1.46368i | 0.681476 | + | 0.731841i | \(0.261339\pi\) | ||||
−0.681476 | + | 0.731841i | \(0.738661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.05781i | 0.0839400i | 0.999119 | + | 0.0419700i | \(0.0133634\pi\) | ||||
−0.999119 | + | 0.0419700i | \(0.986637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.1099 | 0.411364 | ||||||||
\(605\) | 34.0208 | 1.38314 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.8987i | 0.929428i | 0.885461 | + | 0.464714i | \(0.153843\pi\) | ||||
−0.885461 | + | 0.464714i | \(0.846157\pi\) | |||||||
\(608\) | 2.61253 | 0.105952 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 40.4168 | 1.63643 | ||||||||
\(611\) | 6.33591i | 0.256324i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.20196 | −0.331274 | −0.165637 | − | 0.986187i | \(-0.552968\pi\) | ||||
−0.165637 | + | 0.986187i | \(0.552968\pi\) | |||||||
\(614\) | −2.27503 | −0.0918129 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.5639i | 1.23046i | 0.788349 | + | 0.615228i | \(0.210936\pi\) | ||||
−0.788349 | + | 0.615228i | \(0.789064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.4160i | 1.90581i | 0.303270 | + | 0.952905i | \(0.401922\pi\) | ||||
−0.303270 | + | 0.952905i | \(0.598078\pi\) | |||||||
\(620\) | − 24.9197i | − 1.00080i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.1478i | 0.487083i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.3902 | −0.895606 | ||||||||
\(626\) | −9.99854 | −0.399622 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.2028i | 0.526847i | ||||||||
\(629\) | −10.8447 | −0.432405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.1614 | 1.35994 | 0.679972 | − | 0.733238i | \(-0.261992\pi\) | ||||
0.679972 | + | 0.733238i | \(0.261992\pi\) | |||||||
\(632\) | 2.36726i | 0.0941647i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.42107 | −0.255013 | ||||||||
\(635\) | −32.9833 | −1.30890 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.95036i | 0.195987i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 2.21332i | − 0.0874891i | ||||||||
\(641\) | − 33.9597i | − 1.34133i | −0.741761 | − | 0.670664i | \(-0.766009\pi\) | ||||
0.741761 | − | 0.670664i | \(-0.233991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.2852i | 1.07602i | 0.842937 | + | 0.538012i | \(0.180824\pi\) | ||||
−0.842937 | + | 0.538012i | \(0.819176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.02118 | −0.158211 | ||||||||
\(647\) | −15.1250 | −0.594625 | −0.297313 | − | 0.954780i | \(-0.596090\pi\) | ||||
−0.297313 | + | 0.954780i | \(0.596090\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.248838i | 0.00976773i | ||||||||
\(650\) | −15.8465 | −0.621551 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.3886 | 0.602663 | ||||||||
\(653\) | − 34.6919i | − 1.35760i | −0.734325 | − | 0.678799i | \(-0.762501\pi\) | ||||
0.734325 | − | 0.678799i | \(-0.237499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.1099 | 1.56722 | ||||||||
\(656\) | 5.61581 | 0.219260 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.0377i | 1.55965i | 0.625998 | + | 0.779824i | \(0.284692\pi\) | ||||
−0.625998 | + | 0.779824i | \(0.715308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0584i | 0.935763i | 0.883791 | + | 0.467881i | \(0.154983\pi\) | ||||
−0.883791 | + | 0.467881i | \(0.845017\pi\) | |||||||
\(662\) | 4.80258i | 0.186658i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 50.3673i | − 1.95463i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.93830 | −0.191212 | ||||||||
\(668\) | −10.4447 | −0.404116 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 53.3690i | − 2.06182i | ||||||||
\(671\) | 8.20786 | 0.316861 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.1204 | −0.582847 | −0.291423 | − | 0.956594i | \(-0.594129\pi\) | ||||
−0.291423 | + | 0.956594i | \(0.594129\pi\) | |||||||
\(674\) | 0.279157i | 0.0107527i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.86416 | 0.187083 | ||||||||
\(677\) | −7.65304 | −0.294130 | −0.147065 | − | 0.989127i | \(-0.546983\pi\) | ||||
−0.147065 | + | 0.989127i | \(0.546983\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 64.2164i | 2.46259i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.60304i | 0.252843i | ||||||||
\(683\) | − 19.1173i | − 0.731502i | −0.930713 | − | 0.365751i | \(-0.880812\pi\) | ||||
0.930713 | − | 0.365751i | \(-0.119188\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 4.95435i | − 0.189296i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.46253 | 0.322631 | ||||||||
\(689\) | −16.5133 | −0.629107 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 21.1450i | − 0.804392i | −0.915554 | − | 0.402196i | \(-0.868247\pi\) | ||||
0.915554 | − | 0.402196i | \(-0.131753\pi\) | |||||||
\(692\) | 9.54025 | 0.362666 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.10010 | −0.231557 | ||||||||
\(695\) | 66.1665i | 2.50984i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.1571 | 0.915016 | ||||||||
\(698\) | −12.4583 | −0.471553 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.99602i | 0.226466i | 0.993568 | + | 0.113233i | \(0.0361207\pi\) | ||||
−0.993568 | + | 0.113233i | \(0.963879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.969507i | 0.0365657i | ||||||||
\(704\) | 5.45944i | 0.205760i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.84525i | 0.370531i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.2002 | 1.09664 | 0.548318 | − | 0.836270i | \(-0.315268\pi\) | ||||
0.548318 | + | 0.836270i | \(0.315268\pi\) | |||||||
\(710\) | −30.4784 | −1.14383 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 11.6987i | − 0.438428i | ||||||||
\(713\) | −6.58695 | −0.246683 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.15620 | −0.230229 | ||||||||
\(716\) | 9.77315i | 0.365240i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.0911 | −0.787113 | ||||||||
\(719\) | −7.31249 | −0.272710 | −0.136355 | − | 0.990660i | \(-0.543539\pi\) | ||||
−0.136355 | + | 0.990660i | \(0.543539\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 19.8577i | − 0.739028i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.43960i | 0.0535022i | ||||||||
\(725\) | − 36.4276i | − 1.35289i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.8932i | 0.700710i | 0.936617 | + | 0.350355i | \(0.113939\pi\) | ||||
−0.936617 | + | 0.350355i | \(0.886061\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 49.0233 | 1.81443 | ||||||||
\(731\) | 36.4027 | 1.34640 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.2662i | 1.30259i | 0.758826 | + | 0.651294i | \(0.225773\pi\) | ||||
−0.758826 | + | 0.651294i | \(0.774227\pi\) | |||||||
\(734\) | 1.98091 | 0.0731169 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.33699 | −0.123003 | ||||||||
\(737\) | − 10.8382i | − 0.399230i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.4234 | 1.45021 | 0.725106 | − | 0.688637i | \(-0.241791\pi\) | ||||
0.725106 | + | 0.688637i | \(0.241791\pi\) | |||||||
\(740\) | 4.68494 | 0.172222 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.3303i | 0.599101i | 0.954080 | + | 0.299551i | \(0.0968368\pi\) | ||||
−0.954080 | + | 0.299551i | \(0.903163\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 52.0156i | − 1.90570i | ||||||||
\(746\) | 27.1527i | 0.994131i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.94615i | 0.144286i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.3426 | −0.377406 | −0.188703 | − | 0.982034i | \(-0.560428\pi\) | ||||
−0.188703 | + | 0.982034i | \(0.560428\pi\) | |||||||
\(752\) | 3.52162 | 0.128420 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.2464i | 0.700914i | ||||||||
\(755\) | 37.7095 | 1.37239 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1500 | 0.805054 | 0.402527 | − | 0.915408i | \(-0.368132\pi\) | ||||
0.402527 | + | 0.915408i | \(0.368132\pi\) | |||||||
\(758\) | 27.3999i | 0.995209i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.74091 | 0.208245 | ||||||||
\(761\) | −12.3923 | −0.449221 | −0.224610 | − | 0.974449i | \(-0.572111\pi\) | ||||
−0.224610 | + | 0.974449i | \(0.572111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 7.35386i | − 0.266053i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.5227i | 0.488593i | ||||||||
\(767\) | 0.967452i | 0.0349327i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 54.4250i | − 1.96261i | −0.192448 | − | 0.981307i | \(-0.561643\pi\) | ||||
0.192448 | − | 0.981307i | \(-0.438357\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.4948 | −0.737624 | ||||||||
\(773\) | −35.6261 | −1.28138 | −0.640690 | − | 0.767800i | \(-0.721352\pi\) | ||||
−0.640690 | + | 0.767800i | \(0.721352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 48.5890i | − 1.74537i | ||||||||
\(776\) | −31.9215 | −1.14591 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.6092 | 1.06154 | ||||||||
\(779\) | − 2.15963i | − 0.0773769i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.18956 | −0.221480 | ||||||||
\(782\) | 5.13626 | 0.183672 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 49.2459i | 1.75766i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 29.8669i | − 1.06464i | −0.846543 | − | 0.532320i | \(-0.821320\pi\) | ||||
0.846543 | − | 0.532320i | \(-0.178680\pi\) | |||||||
\(788\) | − 17.5255i | − 0.624322i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.67185i | 0.0950601i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.9112 | 1.13320 | ||||||||
\(794\) | −14.6976 | −0.521599 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.35095i | 0.0478833i | ||||||||
\(797\) | 39.0290 | 1.38248 | 0.691239 | − | 0.722626i | \(-0.257065\pi\) | ||||
0.691239 | + | 0.722626i | \(0.257065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.1487 | 0.535923 | ||||||||
\(800\) | − 24.6155i | − 0.870288i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.41945 | 0.0854337 | ||||||||
\(803\) | 9.95567 | 0.351328 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.6718i | 0.904252i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 48.1046i | − 1.69231i | ||||||||
\(809\) | 15.5843i | 0.547914i | 0.961742 | + | 0.273957i | \(0.0883325\pi\) | ||||
−0.961742 | + | 0.273957i | \(0.911667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 19.2285i | − 0.675206i | −0.941289 | − | 0.337603i | \(-0.890384\pi\) | ||||
0.941289 | − | 0.337603i | \(-0.109616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.24138 | −0.0435103 | ||||||||
\(815\) | 57.3990 | 2.01060 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3.25438i | − 0.113856i | ||||||||
\(818\) | −18.9462 | −0.662437 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.4360 | −0.364440 | ||||||||
\(821\) | 5.35524i | 0.186899i | 0.995624 | + | 0.0934496i | \(0.0297894\pi\) | ||||
−0.995624 | + | 0.0934496i | \(0.970211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0188996 | 0.000658797 0 | 0.000329399 | − | 1.00000i | \(-0.499895\pi\) | ||||
0.000329399 | 1.00000i | \(0.499895\pi\) | ||||||||
\(824\) | 41.3408 | 1.44017 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.3217i | 0.463240i | 0.972806 | + | 0.231620i | \(0.0744026\pi\) | ||||
−0.972806 | + | 0.231620i | \(0.925597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 8.78111i | − 0.304981i | −0.988305 | − | 0.152490i | \(-0.951271\pi\) | ||||
0.988305 | − | 0.152490i | \(-0.0487293\pi\) | |||||||
\(830\) | − 56.8478i | − 1.97322i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.2257i | 0.735868i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.9583 | −1.34821 | ||||||||
\(836\) | 0.352784 | 0.0122013 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 5.16940i | − 0.178574i | ||||||||
\(839\) | −22.2873 | −0.769441 | −0.384721 | − | 0.923033i | \(-0.625702\pi\) | ||||
−0.384721 | + | 0.923033i | \(0.625702\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2433 | −0.525633 | ||||||||
\(842\) | 7.87848i | 0.271510i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.00821 | 0.206811 | ||||||||
\(845\) | 18.1432 | 0.624144 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.17842i | 0.315188i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 37.8879i | 1.29954i | ||||||||
\(851\) | − 1.23835i | − 0.0424502i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.41899i | − 0.0828248i | −0.999142 | − | 0.0414124i | \(-0.986814\pi\) | ||||
0.999142 | − | 0.0414124i | \(-0.0131857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 40.6946 | 1.39091 | ||||||||
\(857\) | −27.5213 | −0.940109 | −0.470054 | − | 0.882637i | \(-0.655766\pi\) | ||||
−0.470054 | + | 0.882637i | \(0.655766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5133i | 0.870502i | 0.900309 | + | 0.435251i | \(0.143340\pi\) | ||||
−0.900309 | + | 0.435251i | \(0.856660\pi\) | |||||||
\(860\) | −15.7261 | −0.536255 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.0188 | −1.12462 | ||||||||
\(863\) | − 27.2351i | − 0.927093i | −0.886073 | − | 0.463547i | \(-0.846577\pi\) | ||||
0.886073 | − | 0.463547i | \(-0.153423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.5849 | 1.20992 | ||||||||
\(866\) | −28.7984 | −0.978608 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.542600i | 0.0184064i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 42.1377i | − 1.42778i | ||||||||
\(872\) | − 28.3442i | − 0.959857i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 0.459178i | − 0.0155319i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.5486 | −1.60560 | −0.802800 | − | 0.596248i | \(-0.796658\pi\) | ||||
−0.802800 | + | 0.596248i | \(0.796658\pi\) | |||||||
\(878\) | −28.6717 | −0.967622 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.42174i | 0.115347i | ||||||||
\(881\) | 28.6217 | 0.964290 | 0.482145 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482145 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.03859 | 0.203215 | 0.101607 | − | 0.994825i | \(-0.467601\pi\) | ||||
0.101607 | + | 0.994825i | \(0.467601\pi\) | |||||||
\(884\) | 15.3422i | 0.516013i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.694761 | −0.0233409 | ||||||||
\(887\) | 28.9776 | 0.972974 | 0.486487 | − | 0.873688i | \(-0.338278\pi\) | ||||
0.486487 | + | 0.873688i | \(0.338278\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 13.2039i | − 0.442597i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.0677i | 0.705400i | ||||||||
\(893\) | − 1.35429i | − 0.0453195i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.4536i | 1.21851i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.8006 | −0.827606 | ||||||||
\(899\) | −59.0140 | −1.96823 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.4822i | 1.31534i | ||||||||
\(902\) | 2.76524 | 0.0920724 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.8920 | −0.595078 | ||||||||
\(905\) | 5.36966i | 0.178494i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.2651 | 1.07134 | 0.535672 | − | 0.844426i | \(-0.320058\pi\) | ||||
0.535672 | + | 0.844426i | \(0.320058\pi\) | |||||||
\(908\) | −4.98278 | −0.165359 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 3.28593i | − 0.108868i | −0.998517 | − | 0.0544338i | \(-0.982665\pi\) | ||||
0.998517 | − | 0.0544338i | \(-0.0173354\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 11.5447i | − 0.382073i | ||||||||
\(914\) | 38.8072i | 1.28363i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.6068i | 0.581744i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.1217 | 1.65336 | 0.826681 | − | 0.562670i | \(-0.190226\pi\) | ||||
0.826681 | + | 0.562670i | \(0.190226\pi\) | |||||||
\(920\) | −7.33288 | −0.241758 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.0570i | 0.924008i | ||||||||
\(923\) | −24.0643 | −0.792086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.13478 | 0.300350 | ||||||||
\(926\) | − 18.6848i | − 0.614021i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.8968 | −0.981411 | ||||||||
\(929\) | 23.9594 | 0.786081 | 0.393041 | − | 0.919521i | \(-0.371423\pi\) | ||||
0.393041 | + | 0.919521i | \(0.371423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.7416i | 0.351852i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 26.6022i | − 0.870450i | ||||||||
\(935\) | 14.7190i | 0.481364i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.8400i | 1.04017i | 0.854115 | + | 0.520084i | \(0.174099\pi\) | ||||
−0.854115 | + | 0.520084i | \(0.825901\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.54430 | −0.213452 | ||||||||
\(941\) | −11.9469 | −0.389457 | −0.194729 | − | 0.980857i | \(-0.562383\pi\) | ||||
−0.194729 | + | 0.980857i | \(0.562383\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.75850i | 0.0898293i | ||||||||
\(944\) | 0.537729 | 0.0175016 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.16698 | 0.135480 | ||||||||
\(947\) | 29.7866i | 0.967935i | 0.875086 | + | 0.483968i | \(0.160805\pi\) | ||||
−0.875086 | + | 0.483968i | \(0.839195\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.7065 | 1.25647 | ||||||||
\(950\) | 3.38715 | 0.109894 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.8959i | 1.29235i | 0.763188 | + | 0.646177i | \(0.223633\pi\) | ||||
−0.763188 | + | 0.646177i | \(0.776367\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 27.4297i | − 0.887604i | ||||||||
\(956\) | 15.8495i | 0.512609i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 1.84614i | − 0.0596462i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −47.7158 | −1.53922 | ||||||||
\(962\) | −4.82633 | −0.155607 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 20.2088i | − 0.650882i | ||||||||
\(965\) | −76.4451 | −2.46085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.8294 | −1.47378 | −0.736888 | − | 0.676015i | \(-0.763705\pi\) | ||||
−0.736888 | + | 0.676015i | \(0.763705\pi\) | |||||||
\(968\) | − 32.0736i | − 1.03088i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −36.0287 | −1.15681 | ||||||||
\(971\) | 35.9104 | 1.15242 | 0.576209 | − | 0.817302i | \(-0.304531\pi\) | ||||
0.576209 | + | 0.817302i | \(0.304531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13.6984i | 0.438925i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 17.7369i | − 0.567744i | ||||||||
\(977\) | − 10.7437i | − 0.343722i | −0.985121 | − | 0.171861i | \(-0.945022\pi\) | ||||
0.985121 | − | 0.171861i | \(-0.0549780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 2.68146i | − 0.0856998i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 41.2700 | 1.31698 | ||||||||
\(983\) | 32.9206 | 1.05000 | 0.525002 | − | 0.851101i | \(-0.324064\pi\) | ||||
0.525002 | + | 0.851101i | \(0.324064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 65.3698i | − 2.08286i | ||||||||
\(986\) | 46.0169 | 1.46548 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.37158 | 0.0436358 | ||||||||
\(989\) | 4.15682i | 0.132179i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8152 | 0.534151 | 0.267076 | − | 0.963676i | \(-0.413943\pi\) | ||||
0.267076 | + | 0.963676i | \(0.413943\pi\) | |||||||
\(992\) | −39.8779 | −1.26612 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.03902i | 0.159748i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.9743i | 1.29767i | 0.760930 | + | 0.648834i | \(0.224743\pi\) | ||||
−0.760930 | + | 0.648834i | \(0.775257\pi\) | |||||||
\(998\) | − 23.9592i | − 0.758416i | ||||||||
\(999\) | 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 | 3087.2.c.c.3086.17 | yes | 24 | |
3.2 | odd | 2 | inner | 3087.2.c.c.3086.8 | yes | 24 | |
7.6 | odd | 2 | inner | 3087.2.c.c.3086.7 | ✓ | 24 | |
21.20 | even | 2 | inner | 3087.2.c.c.3086.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3087.2.c.c.3086.7 | ✓ | 24 | 7.6 | odd | 2 | inner | |
3087.2.c.c.3086.8 | yes | 24 | 3.2 | odd | 2 | inner | |
3087.2.c.c.3086.17 | yes | 24 | 1.1 | even | 1 | trivial | |
3087.2.c.c.3086.18 | yes | 24 | 21.20 | even | 2 | inner |