Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(1025,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 34x^{6} + 345x^{4} + 1064x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.8 | ||
Root | \(4.27138i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1025 |
Dual form | 1216.3.e.n.1025.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.27138i | 1.42379i | 0.702284 | + | 0.711897i | \(0.252164\pi\) | ||||
−0.702284 | + | 0.711897i | \(0.747836\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.92033 | 1.58407 | 0.792033 | − | 0.610478i | \(-0.209023\pi\) | ||||
0.792033 | + | 0.610478i | \(0.209023\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.75693 | −0.822418 | −0.411209 | − | 0.911541i | \(-0.634893\pi\) | ||||
−0.411209 | + | 0.911541i | \(0.634893\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.24469 | −1.02719 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.5691 | −1.50628 | −0.753139 | − | 0.657862i | \(-0.771461\pi\) | ||||
−0.753139 | + | 0.657862i | \(0.771461\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 7.95976i | − | 0.612289i | −0.951985 | − | 0.306145i | \(-0.900961\pi\) | ||
0.951985 | − | 0.306145i | \(-0.0990391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 33.8307i | 2.25538i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.1650 | −1.06853 | −0.534265 | − | 0.845317i | \(-0.679412\pi\) | ||||
−0.534265 | + | 0.845317i | \(0.679412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.595968 | − | 18.9907i | −0.0313668 | − | 0.999508i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 24.5900i | − | 1.17095i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.02853 | −0.305588 | −0.152794 | − | 0.988258i | \(-0.548827\pi\) | ||||
−0.152794 | + | 0.988258i | \(0.548827\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 37.7316 | 1.50927 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.04517i | − | 0.0387101i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 30.4768i | − | 1.05092i | −0.850817 | − | 0.525462i | \(-0.823892\pi\) | ||
0.850817 | − | 0.525462i | \(-0.176108\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 34.9967i | − | 1.12893i | −0.825458 | − | 0.564464i | \(-0.809083\pi\) | ||
0.825458 | − | 0.564464i | \(-0.190917\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 70.7727i | − | 2.14463i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −45.5968 | −1.30276 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 58.6635i | − | 1.58550i | −0.609547 | − | 0.792750i | \(-0.708649\pi\) | ||
0.609547 | − | 0.792750i | \(-0.291351\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 33.9992 | 0.871774 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.7686i | 0.994355i | 0.867649 | + | 0.497178i | \(0.165630\pi\) | ||||
−0.867649 | + | 0.497178i | \(0.834370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.5739 | 0.292417 | 0.146209 | − | 0.989254i | \(-0.453293\pi\) | ||||
0.146209 | + | 0.989254i | \(0.453293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −73.2210 | −1.62713 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −88.8974 | −1.89144 | −0.945718 | − | 0.324990i | \(-0.894639\pi\) | ||||
−0.945718 | + | 0.324990i | \(0.894639\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.8578 | −0.323628 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 77.5897i | − | 1.52137i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 62.8130i | 1.18515i | 0.805515 | + | 0.592575i | \(0.201889\pi\) | ||||
−0.805515 | + | 0.592575i | \(0.798111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −131.232 | −2.38604 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 81.1163 | − | 2.54561i | 1.42309 | − | 0.0446598i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 51.2763i | 0.869089i | 0.900650 | + | 0.434545i | \(0.143091\pi\) | ||||
−0.900650 | + | 0.434545i | \(0.856909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 68.1970 | 1.11798 | 0.558992 | − | 0.829173i | \(-0.311188\pi\) | ||||
0.558992 | + | 0.829173i | \(0.311188\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 53.2210 | 0.844778 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 63.0439i | − | 0.969907i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 82.5313i | − | 1.23181i | −0.787820 | − | 0.615905i | \(-0.788791\pi\) | ||
0.787820 | − | 0.615905i | \(-0.211209\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 30.0215i | − | 0.435095i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 21.9213i | − | 0.308750i | −0.988012 | − | 0.154375i | \(-0.950664\pi\) | ||
0.988012 | − | 0.154375i | \(-0.0493364\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −57.3956 | −0.786241 | −0.393121 | − | 0.919487i | \(-0.628605\pi\) | ||||
−0.393121 | + | 0.919487i | \(0.628605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 161.166i | 2.14888i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 95.3868 | 1.23879 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 88.3089i | 1.11783i | 0.829223 | + | 0.558917i | \(0.188783\pi\) | ||||
−0.829223 | + | 0.558917i | \(0.811217\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −78.7379 | −0.972073 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.720460 | −0.00868024 | −0.00434012 | − | 0.999991i | \(-0.501382\pi\) | ||||
−0.00434012 | + | 0.999991i | \(0.501382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −143.873 | −1.69262 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 130.178 | 1.49630 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 30.1376i | − | 0.338624i | −0.985562 | − | 0.169312i | \(-0.945845\pi\) | ||
0.985562 | − | 0.169312i | \(-0.0541546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 45.8238i | 0.503558i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 149.484 | 1.60736 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.72027 | − | 150.412i | −0.0496870 | − | 1.58329i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 169.956i | 1.75213i | 0.482195 | + | 0.876064i | \(0.339840\pi\) | ||||
−0.482195 | + | 0.876064i | \(0.660160\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 153.176 | 1.54723 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −111.727 | −1.10621 | −0.553104 | − | 0.833112i | \(-0.686557\pi\) | ||||
−0.553104 | + | 0.833112i | \(0.686557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 23.7725i | − | 0.230801i | −0.993319 | − | 0.115401i | \(-0.963185\pi\) | ||
0.993319 | − | 0.115401i | \(-0.0368152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 194.761i | − | 1.85487i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 70.3801i | 0.657758i | 0.944372 | + | 0.328879i | \(0.106671\pi\) | ||||
−0.944372 | + | 0.328879i | \(0.893329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 21.0005i | 0.192665i | 0.995349 | + | 0.0963327i | \(0.0307113\pi\) | ||||
−0.995349 | + | 0.0963327i | \(0.969289\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 250.574 | 2.25742 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 223.885i | − | 1.98128i | −0.136494 | − | 0.990641i | \(-0.543584\pi\) | ||
0.136494 | − | 0.990641i | \(-0.456416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −55.6683 | −0.484072 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 73.5856i | 0.628936i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 104.575 | 0.878779 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 153.534 | 1.26887 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −174.138 | −1.41576 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 100.839 | 0.806710 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 37.2567i | 0.293360i | 0.989184 | + | 0.146680i | \(0.0468588\pi\) | ||||
−0.989184 | + | 0.146680i | \(0.953141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 53.7081i | 0.416342i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 33.3254 | 0.254393 | 0.127196 | − | 0.991878i | \(-0.459402\pi\) | ||||
0.127196 | + | 0.991878i | \(0.459402\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.43095 | + | 109.328i | 0.0257966 | + | 0.822013i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 8.27812i | − | 0.0613194i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −227.044 | −1.65726 | −0.828629 | − | 0.559799i | \(-0.810878\pi\) | ||||
−0.828629 | + | 0.559799i | \(0.810878\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 239.245 | 1.72119 | 0.860593 | − | 0.509293i | \(-0.170093\pi\) | ||||
0.860593 | + | 0.509293i | \(0.170093\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 379.715i | − | 2.69301i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 131.886i | 0.922278i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 241.386i | − | 1.66473i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 67.7347i | − | 0.460780i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −142.214 | −0.954459 | −0.477229 | − | 0.878779i | \(-0.658359\pi\) | ||||
−0.477229 | + | 0.878779i | \(0.658359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 88.4519i | − | 0.585774i | −0.956147 | − | 0.292887i | \(-0.905384\pi\) | ||
0.956147 | − | 0.292887i | \(-0.0946160\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 167.930 | 1.09758 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 277.186i | − | 1.78830i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −45.8364 | −0.291952 | −0.145976 | − | 0.989288i | \(-0.546632\pi\) | ||||
−0.145976 | + | 0.989288i | \(0.546632\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −268.298 | −1.68741 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 40.4627 | 0.251321 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −50.0387 | −0.306986 | −0.153493 | − | 0.988150i | \(-0.549052\pi\) | ||||
−0.153493 | + | 0.988150i | \(0.549052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 560.543i | − | 3.39723i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 147.739i | − | 0.884663i | −0.896852 | − | 0.442332i | \(-0.854151\pi\) | ||
0.896852 | − | 0.442332i | \(-0.145849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 105.642 | 0.625102 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.50954 | + | 175.563i | 0.0322196 | + | 1.02668i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 221.272i | − | 1.27903i | −0.768778 | − | 0.639515i | \(-0.779135\pi\) | ||
0.768778 | − | 0.639515i | \(-0.220865\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −217.218 | −1.24125 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −219.020 | −1.23740 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 119.436i | 0.667241i | 0.942707 | + | 0.333621i | \(0.108270\pi\) | ||||
−0.942707 | + | 0.333621i | \(0.891730\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.14798i | − | 0.0173921i | −0.999962 | − | 0.00869606i | \(-0.997232\pi\) | ||
0.999962 | − | 0.00869606i | \(-0.00276808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 291.296i | 1.59178i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 464.634i | − | 2.51154i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 300.977 | 1.60950 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.01699i | 0.0318359i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 213.295 | 1.11673 | 0.558364 | − | 0.829596i | \(-0.311429\pi\) | ||||
0.558364 | + | 0.829596i | \(0.311429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 104.442i | 0.541150i | 0.962699 | + | 0.270575i | \(0.0872138\pi\) | ||||
−0.962699 | + | 0.270575i | \(0.912786\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 269.285 | 1.38095 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 268.231 | 1.36158 | 0.680789 | − | 0.732479i | \(-0.261637\pi\) | ||||
0.680789 | + | 0.732479i | \(0.261637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.33565 | 0.0167621 | 0.00838103 | − | 0.999965i | \(-0.497332\pi\) | ||||
0.00838103 | + | 0.999965i | \(0.497332\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 352.522 | 1.75384 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 175.453i | 0.864299i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 322.900i | 1.57512i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64.9766 | 0.313897 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.87463 | + | 314.657i | 0.0472470 | + | 1.50554i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 188.650i | − | 0.894075i | −0.894515 | − | 0.447037i | \(-0.852479\pi\) | ||
0.894515 | − | 0.447037i | \(-0.147521\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 93.6340 | 0.439596 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 99.5898 | 0.463208 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 201.474i | 0.928450i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 245.159i | − | 1.11945i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 144.589i | 0.654250i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 43.0515i | − | 0.193056i | −0.995330 | − | 0.0965281i | \(-0.969226\pi\) | ||
0.995330 | − | 0.0965281i | \(-0.0307738\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −348.817 | −1.55030 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 107.923i | − | 0.475433i | −0.971335 | − | 0.237717i | \(-0.923601\pi\) | ||
0.971335 | − | 0.237717i | \(-0.0763990\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −173.435 | −0.757360 | −0.378680 | − | 0.925528i | \(-0.623622\pi\) | ||||
−0.378680 | + | 0.925528i | \(0.623622\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 407.433i | 1.76378i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.95848 | −0.0298647 | −0.0149324 | − | 0.999889i | \(-0.504753\pi\) | ||||
−0.0149324 | + | 0.999889i | \(0.504753\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −704.097 | −2.99616 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −377.201 | −1.59157 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −55.8581 | −0.233716 | −0.116858 | − | 0.993149i | \(-0.537282\pi\) | ||||
−0.116858 | + | 0.993149i | \(0.537282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 156.862i | 0.650880i | 0.945563 | + | 0.325440i | \(0.105512\pi\) | ||||
−0.945563 | + | 0.325440i | \(0.894488\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 345.726i | − | 1.42274i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −125.599 | −0.512649 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −151.161 | + | 4.74377i | −0.611988 | + | 0.0192055i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.07736i | − | 0.0123589i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −99.2555 | −0.395440 | −0.197720 | − | 0.980258i | \(-0.563354\pi\) | ||||
−0.197720 | + | 0.980258i | \(0.563354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 116.456 | 0.460301 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 614.536i | − | 2.40995i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.8601i | 0.108405i | 0.998530 | + | 0.0542026i | \(0.0172617\pi\) | ||||
−0.998530 | + | 0.0542026i | \(0.982738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 337.721i | 1.30394i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 281.749i | 1.07950i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −378.378 | −1.43870 | −0.719349 | − | 0.694649i | \(-0.755560\pi\) | ||||
−0.719349 | + | 0.694649i | \(0.755560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 497.500i | 1.87736i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 128.729 | 0.482131 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 132.873i | 0.493950i | 0.969022 | + | 0.246975i | \(0.0794366\pi\) | ||||
−0.969022 | + | 0.246975i | \(0.920563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 186.215 | 0.687140 | 0.343570 | − | 0.939127i | \(-0.388364\pi\) | ||||
0.343570 | + | 0.939127i | \(0.388364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −195.731 | −0.716962 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −625.177 | −2.27337 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −44.9078 | −0.162122 | −0.0810611 | − | 0.996709i | \(-0.525831\pi\) | ||||
−0.0810611 | + | 0.996709i | \(0.525831\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 323.534i | 1.15962i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 344.957i | 1.22761i | 0.789459 | + | 0.613803i | \(0.210361\pi\) | ||||
−0.789459 | + | 0.613803i | \(0.789639\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −181.986 | −0.643059 | −0.321530 | − | 0.946900i | \(-0.604197\pi\) | ||||
−0.321530 | + | 0.946900i | \(0.604197\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 642.468 | − | 20.1621i | 2.25427 | − | 0.0707440i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 234.702i | − | 0.817776i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.9680 | 0.141758 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −725.949 | −2.49467 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.4268i | 0.0389992i | 0.999810 | + | 0.0194996i | \(0.00620731\pi\) | ||||
−0.999810 | + | 0.0194996i | \(0.993793\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 406.125i | 1.37669i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.3175i | 0.0583082i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 55.9455i | 0.187109i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −72.3873 | −0.240489 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 477.228i | − | 1.57501i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 540.143 | 1.77096 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 66.7163i | − | 0.217317i | −0.994079 | − | 0.108659i | \(-0.965344\pi\) | ||
0.994079 | − | 0.108659i | \(-0.0346555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 101.542 | 0.328613 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −456.827 | −1.46890 | −0.734449 | − | 0.678664i | \(-0.762559\pi\) | ||||
−0.734449 | + | 0.678664i | \(0.762559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −571.983 | −1.82742 | −0.913711 | − | 0.406364i | \(-0.866797\pi\) | ||||
−0.913711 | + | 0.406364i | \(0.866797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 421.528 | 1.33818 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 564.021i | 1.77925i | 0.456695 | + | 0.889623i | \(0.349033\pi\) | ||||
−0.456695 | + | 0.889623i | \(0.650967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 504.972i | 1.58298i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −300.620 | −0.936512 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8258 | + | 344.966i | 0.0335163 | + | 1.06800i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 300.335i | − | 0.924107i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −89.7013 | −0.274316 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 511.776 | 1.55555 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 101.354i | 0.306206i | 0.988210 | + | 0.153103i | \(0.0489267\pi\) | ||||
−0.988210 | + | 0.153103i | \(0.951073\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 542.326i | 1.62861i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 653.675i | − | 1.95127i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 251.262i | − | 0.745583i | −0.927915 | − | 0.372792i | \(-0.878401\pi\) | ||
0.927915 | − | 0.372792i | \(-0.121599\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 956.297 | 2.82094 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 579.863i | 1.70048i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 373.382 | 1.08858 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 237.781i | − | 0.689219i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 382.247 | 1.10158 | 0.550788 | − | 0.834645i | \(-0.314327\pi\) | ||||
0.550788 | + | 0.834645i | \(0.314327\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.1254 | 0.0719925 | 0.0359963 | − | 0.999352i | \(-0.488540\pi\) | ||||
0.0359963 | + | 0.999352i | \(0.488540\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.31934 | −0.0237018 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 140.407 | 0.397754 | 0.198877 | − | 0.980024i | \(-0.436271\pi\) | ||||
0.198877 | + | 0.980024i | \(0.436271\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 173.624i | − | 0.489081i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 446.678i | 1.25120i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 51.9710 | 0.144766 | 0.0723830 | − | 0.997377i | \(-0.476940\pi\) | ||||
0.0723830 | + | 0.997377i | \(0.476940\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −360.290 | + | 22.6357i | −0.998032 | + | 0.0627026i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 655.800i | 1.80661i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −454.592 | −1.24546 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −211.340 | −0.575857 | −0.287929 | − | 0.957652i | \(-0.592967\pi\) | ||||
−0.287929 | + | 0.957652i | \(0.592967\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 376.893i | − | 1.02139i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 361.610i | − | 0.974689i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 530.062i | − | 1.42108i | −0.703657 | − | 0.710539i | \(-0.748451\pi\) | ||
0.703657 | − | 0.710539i | \(-0.251549\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 430.721i | 1.14859i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −242.588 | −0.643470 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 498.205i | 1.31453i | 0.753661 | + | 0.657263i | \(0.228286\pi\) | ||||
−0.753661 | + | 0.657263i | \(0.771714\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −159.138 | −0.417684 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 626.130i | − | 1.63480i | −0.576067 | − | 0.817402i | \(-0.695413\pi\) | ||
0.576067 | − | 0.817402i | \(-0.304587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 755.495 | 1.96233 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −116.242 | −0.300368 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 209.215 | 0.537828 | 0.268914 | − | 0.963164i | \(-0.413335\pi\) | ||||
0.268914 | + | 0.963164i | \(0.413335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 127.673 | 0.326531 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 142.346i | 0.362203i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 699.436i | 1.77072i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 355.260 | 0.894861 | 0.447430 | − | 0.894319i | \(-0.352339\pi\) | ||||
0.447430 | + | 0.894319i | \(0.352339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −466.981 | + | 14.6549i | −1.17038 | + | 0.0367290i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 335.760i | 0.837308i | 0.908146 | + | 0.418654i | \(0.137498\pi\) | ||||
−0.908146 | + | 0.418654i | \(0.862502\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −278.566 | −0.691230 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −623.630 | −1.53983 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 971.998i | 2.38820i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 267.604i | 0.654289i | 0.944974 | + | 0.327144i | \(0.106086\pi\) | ||||
−0.944974 | + | 0.327144i | \(0.893914\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 969.792i | − | 2.35959i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 295.194i | − | 0.714755i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.70628 | −0.0137501 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1021.91i | 2.45061i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 460.072 | 1.09802 | 0.549012 | − | 0.835815i | \(-0.315004\pi\) | ||||
0.549012 | + | 0.835815i | \(0.315004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.7047i | − | 0.0278021i | −0.999903 | − | 0.0139011i | \(-0.995575\pi\) | ||
0.999903 | − | 0.0139011i | \(-0.00442499\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 821.830 | 1.94286 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −685.396 | −1.61270 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −392.605 | −0.919450 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −563.334 | −1.31313 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 262.531i | − | 0.609121i | −0.952493 | − | 0.304560i | \(-0.901490\pi\) | ||
0.952493 | − | 0.304560i | \(-0.0985095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 476.152i | − | 1.09966i | −0.835277 | − | 0.549829i | \(-0.814693\pi\) | ||
0.835277 | − | 0.549829i | \(-0.185307\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1031.05 | 2.37024 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.18878 | + | 133.476i | 0.00958531 | + | 0.305438i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 712.061i | − | 1.62201i | −0.585042 | − | 0.811003i | \(-0.698922\pi\) | ||
0.585042 | − | 0.811003i | \(-0.301078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 146.600 | 0.332427 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −771.711 | −1.74201 | −0.871006 | − | 0.491272i | \(-0.836532\pi\) | ||||
−0.871006 | + | 0.491272i | \(0.836532\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 238.699i | − | 0.536403i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 607.452i | − | 1.35895i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 318.364i | − | 0.709050i | −0.935047 | − | 0.354525i | \(-0.884643\pi\) | ||
0.935047 | − | 0.354525i | \(-0.115357\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 675.496i | − | 1.49777i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 377.812 | 0.834022 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 362.939i | 0.797669i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 548.540 | 1.20031 | 0.600153 | − | 0.799885i | \(-0.295106\pi\) | ||||
0.600153 | + | 0.799885i | \(0.295106\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.9856i | 0.0413630i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −233.459 | −0.506419 | −0.253209 | − | 0.967412i | \(-0.581486\pi\) | ||||
−0.253209 | + | 0.967412i | \(0.581486\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −315.936 | −0.682367 | −0.341183 | − | 0.939997i | \(-0.610828\pi\) | ||||
−0.341183 | + | 0.939997i | \(0.610828\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1183.97 | 2.54616 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −340.599 | −0.729335 | −0.364667 | − | 0.931138i | \(-0.618817\pi\) | ||||
−0.364667 | + | 0.931138i | \(0.618817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 475.126i | 1.01306i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 195.785i | − | 0.415679i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −208.338 | −0.440462 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.4869 | − | 716.548i | −0.0473407 | − | 1.50852i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 580.687i | − | 1.21737i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 414.927 | 0.866236 | 0.433118 | − | 0.901337i | \(-0.357413\pi\) | ||||
0.433118 | + | 0.901337i | \(0.357413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −466.947 | −0.970784 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 172.832i | 0.357830i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1346.11i | 2.77549i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 173.832i | 0.356945i | 0.983945 | + | 0.178473i | \(0.0571156\pi\) | ||||
−0.983945 | + | 0.178473i | \(0.942884\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 213.734i | − | 0.437084i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 436.406 | 0.888811 | 0.444406 | − | 0.895826i | \(-0.353415\pi\) | ||||
0.444406 | + | 0.895826i | \(0.353415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 553.612i | 1.12294i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1213.20 | 2.45092 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 126.199i | 0.253922i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.6139 | −0.0653585 | −0.0326792 | − | 0.999466i | \(-0.510404\pi\) | ||||
−0.0326792 | + | 0.999466i | \(0.510404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 631.048 | 1.25958 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −464.682 | −0.923820 | −0.461910 | − | 0.886927i | \(-0.652836\pi\) | ||||
−0.461910 | + | 0.886927i | \(0.652836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −884.914 | −1.75231 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 451.238i | 0.890016i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 428.140i | − | 0.841140i | −0.907260 | − | 0.420570i | \(-0.861830\pi\) | ||
0.907260 | − | 0.420570i | \(-0.138170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 330.422 | 0.646619 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.8485 | + | 0.622891i | −0.0386911 | + | 0.00121421i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 188.286i | − | 0.365604i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1472.95 | 2.84903 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 945.138 | 1.82108 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 336.826i | 0.646499i | 0.946314 | + | 0.323250i | \(0.104775\pi\) | ||||
−0.946314 | + | 0.323250i | \(0.895225\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 850.674i | 1.62653i | 0.581895 | + | 0.813264i | \(0.302311\pi\) | ||||
−0.581895 | + | 0.813264i | \(0.697689\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 927.822i | − | 1.76728i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 635.717i | 1.20629i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −479.600 | −0.906616 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 474.033i | − | 0.892718i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 324.508 | 0.608833 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 557.434i | 1.04193i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −510.157 | −0.950014 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 262.749 | 0.487474 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.9805 | −0.0609620 | −0.0304810 | − | 0.999535i | \(-0.509704\pi\) | ||||
−0.0304810 | + | 0.999535i | \(0.509704\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.4462 | 0.0247628 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 166.331i | 0.305195i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 811.240i | − | 1.48307i | −0.670914 | − | 0.741535i | \(-0.734098\pi\) | ||
0.670914 | − | 0.741535i | \(-0.265902\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −630.461 | −1.14838 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −578.774 | + | 18.1632i | −1.05041 | + | 0.0329641i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 508.388i | − | 0.919327i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1984.63 | 3.57591 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −942.150 | −1.69147 | −0.845736 | − | 0.533602i | \(-0.820838\pi\) | ||||
−0.845736 | + | 0.533602i | \(0.820838\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 100.086i | − | 0.179044i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1285.59i | 2.29160i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 193.631i | − | 0.343927i | −0.985103 | − | 0.171964i | \(-0.944989\pi\) | ||
0.985103 | − | 0.171964i | \(-0.0550111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1773.24i | − | 3.13848i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 453.288 | 0.799450 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1072.23i | 1.88440i | 0.335047 | + | 0.942202i | \(0.391248\pi\) | ||||
−0.335047 | + | 0.942202i | \(0.608752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −470.870 | −0.824641 | −0.412321 | − | 0.911039i | \(-0.635282\pi\) | ||||
−0.412321 | + | 0.911039i | \(0.635282\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 911.065i | 1.58999i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −265.198 | −0.461214 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 863.970 | 1.49735 | 0.748675 | − | 0.662938i | \(-0.230691\pi\) | ||||
0.748675 | + | 0.662938i | \(0.230691\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −446.111 | −0.770486 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.14764 | 0.00713879 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1040.75i | − | 1.78517i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 582.822i | 0.996277i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −478.667 | −0.815446 | −0.407723 | − | 0.913106i | \(-0.633677\pi\) | ||||
−0.407723 | + | 0.913106i | \(0.633677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −664.611 | + | 20.8569i | −1.12837 | + | 0.0354108i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1145.72i | 1.93861i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −444.287 | −0.749219 | −0.374610 | − | 0.927183i | \(-0.622223\pi\) | ||||
−0.374610 | + | 0.927183i | \(0.622223\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 828.266 | 1.39204 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.2478i | 0.0238657i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 644.065i | 1.07523i | 0.843189 | + | 0.537617i | \(0.180675\pi\) | ||||
−0.843189 | + | 0.537617i | \(0.819325\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 858.767i | − | 1.42890i | −0.699688 | − | 0.714449i | \(-0.746678\pi\) | ||
0.699688 | − | 0.714449i | \(-0.253322\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 762.976i | 1.26530i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1216.04 | 2.00998 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 570.384i | 0.939677i | 0.882752 | + | 0.469839i | \(0.155688\pi\) | ||||
−0.882752 | + | 0.469839i | \(0.844312\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −749.425 | −1.23058 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 707.603i | 1.15811i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 225.808 | 0.368366 | 0.184183 | − | 0.982892i | \(-0.441036\pi\) | ||||
0.184183 | + | 0.982892i | \(0.441036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1379.23 | −2.24265 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 484.705 | 0.785583 | 0.392792 | − | 0.919628i | \(-0.371509\pi\) | ||||
0.392792 | + | 0.919628i | \(0.371509\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.30576 | −0.00695599 | −0.00347799 | − | 0.999994i | \(-0.501107\pi\) | ||||
−0.00347799 | + | 0.999994i | \(0.501107\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.34604i | 0.0118294i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 173.500i | 0.278491i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −144.615 | −0.231384 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1344.02 | + | 42.1783i | −2.14357 | + | 0.0672700i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1065.62i | 1.69415i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −428.682 | −0.679370 | −0.339685 | − | 0.940539i | \(-0.610320\pi\) | ||||
−0.339685 | + | 0.940539i | \(0.610320\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 805.795 | 1.27298 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 295.086i | 0.464702i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 126.224i | 0.198154i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 202.655i | 0.317144i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.2734i | 0.0441083i | 0.999757 | + | 0.0220542i | \(0.00702063\pi\) | ||||
−0.999757 | + | 0.0220542i | \(0.992979\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −555.039 | −0.863202 | −0.431601 | − | 0.902065i | \(-0.642051\pi\) | ||||
−0.431601 | + | 0.902065i | \(0.642051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 425.386i | 0.659513i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −258.218 | −0.399101 | −0.199550 | − | 0.979888i | \(-0.563948\pi\) | ||||
−0.199550 | + | 0.979888i | \(0.563948\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 849.599i | − | 1.30909i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −860.571 | −1.32192 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −889.632 | −1.36238 | −0.681189 | − | 0.732108i | \(-0.738537\pi\) | ||||
−0.681189 | + | 0.732108i | \(0.738537\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 263.948 | 0.402975 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 530.605 | 0.807618 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 611.017i | − | 0.927188i | −0.886048 | − | 0.463594i | \(-0.846560\pi\) | ||
0.886048 | − | 0.463594i | \(-0.153440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 114.885i | − | 0.173805i | −0.996217 | − | 0.0869025i | \(-0.972303\pi\) | ||
0.996217 | − | 0.0869025i | \(-0.0276969\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −617.596 | −0.931517 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27.1742 | + | 865.912i | 0.0408635 | + | 1.30212i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 214.207i | 0.321150i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 183.889 | 0.274872 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1129.96 | −1.68399 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 365.864i | − | 0.543631i | −0.962349 | − | 0.271815i | \(-0.912376\pi\) | ||
0.962349 | − | 0.271815i | \(-0.0876240\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 39.4361i | − | 0.0584239i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 42.7480i | − | 0.0631433i | −0.999501 | − | 0.0315716i | \(-0.989949\pi\) | ||
0.999501 | − | 0.0315716i | \(-0.0100512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 978.427i | − | 1.44098i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 460.982 | 0.676919 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 862.409i | − | 1.26268i | −0.775507 | − | 0.631339i | \(-0.782506\pi\) | ||
0.775507 | − | 0.631339i | \(-0.217494\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1798.27 | −2.62521 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 740.808i | − | 1.07832i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 499.976 | 0.725655 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −84.3258 | −0.122034 | −0.0610172 | − | 0.998137i | \(-0.519434\pi\) | ||||
−0.0610172 | + | 0.998137i | \(0.519434\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −881.822 | −1.27247 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1894.90 | 2.72647 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 740.562i | − | 1.06250i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 29.7223i | − | 0.0425212i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 87.4458 | 0.124744 | 0.0623722 | − | 0.998053i | \(-0.480133\pi\) | ||||
0.0623722 | + | 0.998053i | \(0.480133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1114.06 | + | 34.9616i | −1.58472 | + | 0.0497320i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 3007.47i | − | 4.26591i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 643.204 | 0.909765 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 588.263 | 0.829709 | 0.414854 | − | 0.909888i | \(-0.363833\pi\) | ||||
0.414854 | + | 0.909888i | \(0.363833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 816.389i | − | 1.14823i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 245.976i | 0.344987i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1044.58i | 1.46095i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 238.591i | − | 0.332763i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −356.156 | −0.495349 | −0.247674 | − | 0.968843i | \(-0.579666\pi\) | ||||
−0.247674 | + | 0.968843i | \(0.579666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 136.857i | 0.189815i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −670.018 | −0.926719 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1149.94i | − | 1.58612i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −177.681 | −0.244403 | −0.122202 | − | 0.992505i | \(-0.538995\pi\) | ||||
−0.122202 | + | 0.992505i | \(0.538995\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 768.087 | 1.05362 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −228.406 | −0.312457 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 942.078 | 1.28524 | 0.642618 | − | 0.766187i | \(-0.277848\pi\) | ||||
0.642618 | + | 0.766187i | \(0.277848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 536.481i | − | 0.729906i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1367.46i | 1.85545i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 578.070 | 0.782233 | 0.391116 | − | 0.920341i | \(-0.372089\pi\) | ||||
0.391116 | + | 0.920341i | \(0.372089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.2624 | − | 645.666i | −0.0273447 | − | 0.871345i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 124.430i | − | 0.167470i | −0.996488 | − | 0.0837349i | \(-0.973315\pi\) | ||
0.996488 | − | 0.0837349i | \(-0.0266849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1126.38 | −1.51193 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.66043 | 0.00891624 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 405.173i | − | 0.540952i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 774.593i | − | 1.03141i | −0.856765 | − | 0.515707i | \(-0.827529\pi\) | ||
0.856765 | − | 0.515707i | \(-0.172471\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 423.958i | − | 0.563025i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 700.569i | − | 0.927905i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −551.096 | −0.727999 | −0.364000 | − | 0.931399i | \(-0.618589\pi\) | ||||
−0.364000 | + | 0.931399i | \(0.618589\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 497.429i | 0.655374i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −453.591 | −0.596046 | −0.298023 | − | 0.954559i | \(-0.596327\pi\) | ||||
−0.298023 | + | 0.954559i | \(0.596327\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 120.899i | − | 0.158452i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1330.06 | 1.73864 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 408.147 | 0.532134 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1000.00 | 1.30039 | 0.650197 | − | 0.759766i | \(-0.274686\pi\) | ||||
0.650197 | + | 0.759766i | \(0.274686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −119.001 | −0.154347 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 757.916i | 0.980486i | 0.871586 | + | 0.490243i | \(0.163092\pi\) | ||||
−0.871586 | + | 0.490243i | \(0.836908\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1320.48i | − | 1.70385i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1442.54 | −1.85655 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 774.221 | − | 24.2968i | 0.993866 | − | 0.0311897i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 363.215i | 0.465063i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.8536 | −0.0406814 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −363.040 | −0.462471 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 384.175i | − | 0.488151i | −0.969756 | − | 0.244075i | \(-0.921516\pi\) | ||
0.969756 | − | 0.244075i | \(-0.0784845\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1616.19i | − | 2.04841i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1288.89i | 1.62944i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 542.832i | − | 0.684530i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2125.01 | −2.67297 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 566.234i | 0.710457i | 0.934780 | + | 0.355228i | \(0.115597\pi\) | ||||
−0.934780 | + | 0.355228i | \(0.884403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1614.82 | 2.02106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 278.612i | 0.347831i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 950.991 | 1.18430 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 320.478 | 0.398110 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −567.550 | −0.703283 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −357.919 | −0.442422 | −0.221211 | − | 0.975226i | \(-0.571001\pi\) | ||||
−0.221211 | + | 0.975226i | \(0.571001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 903.689i | 1.11429i | 0.830415 | + | 0.557145i | \(0.188103\pi\) | ||||
−0.830415 | + | 0.557145i | \(0.811897\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 795.395i | 0.978346i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −396.323 | −0.486286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.49367 | − | 238.787i | −0.00917218 | − | 0.292273i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 423.627i | − | 0.517249i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 853.605 | 1.03971 | 0.519857 | − | 0.854253i | \(-0.325985\pi\) | ||||
0.519857 | + | 0.854253i | \(0.325985\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −173.599 | −0.210934 | −0.105467 | − | 0.994423i | \(-0.533634\pi\) | ||||
−0.105467 | + | 0.994423i | \(0.533634\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2670.37i | − | 3.23681i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1114.69i | 1.34787i | 0.738789 | + | 0.673937i | \(0.235398\pi\) | ||||
−0.738789 | + | 0.673937i | \(0.764602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1382.86i | − | 1.66810i | −0.551686 | − | 0.834052i | \(-0.686015\pi\) | ||
0.551686 | − | 0.834052i | \(-0.313985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 191.818i | − | 0.230828i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 288.057 | 0.345807 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1170.14i | − | 1.40136i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.5777 | −0.0437009 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1132.53i | − | 1.34986i | −0.737882 | − | 0.674929i | \(-0.764174\pi\) | ||
0.737882 | − | 0.674929i | \(-0.235826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −87.8353 | −0.104441 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1473.44 | −1.74786 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 836.721 | 0.990202 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −883.881 | −1.04354 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 777.331i | − | 0.915584i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 412.318i | 0.484510i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −403.013 | −0.472465 | −0.236232 | − | 0.971697i | \(-0.575913\pi\) | ||||
−0.236232 | + | 0.971697i | \(0.575913\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 43.6374 | + | 1390.51i | 0.0510379 | + | 1.62633i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 873.926i | 1.01975i | 0.860248 | + | 0.509875i | \(0.170308\pi\) | ||||
−0.860248 | + | 0.509875i | \(0.829692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1159.36 | 1.34966 | 0.674828 | − | 0.737975i | \(-0.264218\pi\) | ||||
0.674828 | + | 0.737975i | \(0.264218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1002.50 | 1.16434 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.7815i | 0.0426206i | 0.999773 | + | 0.0213103i | \(0.00678379\pi\) | ||||
−0.999773 | + | 0.0213103i | \(0.993216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1752.55i | − | 2.02607i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 174.990i | 0.201834i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1463.20i | − | 1.68377i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −656.929 | −0.754224 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1571.19i | − | 1.79977i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −580.521 | −0.663453 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 247.696i | − | 0.282435i | −0.989979 | − | 0.141218i | \(-0.954898\pi\) | ||
0.989979 | − | 0.141218i | \(-0.0451017\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −48.8081 | −0.0555269 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −882.282 | −1.00146 | −0.500728 | − | 0.865605i | \(-0.666934\pi\) | ||||
−0.500728 | + | 0.865605i | \(0.666934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −241.560 | −0.273567 | −0.136784 | − | 0.990601i | \(-0.543677\pi\) | ||||
−0.136784 | + | 0.990601i | \(0.543677\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1734.71 | −1.96013 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1060.17i | 1.19523i | 0.801782 | + | 0.597617i | \(0.203886\pi\) | ||||
−0.801782 | + | 0.597617i | \(0.796114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 214.484i | − | 0.241265i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1304.61 | 1.46421 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 52.9801 | + | 1688.22i | 0.0593282 | + | 1.89050i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 945.974i | 1.05695i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −238.964 | −0.266404 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1066.59 | −1.18642 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1141.00i | − | 1.26637i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 309.194i | − | 0.342407i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 24.9330i | − | 0.0275503i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 590.873i | 0.651459i | 0.945463 | + | 0.325729i | \(0.105610\pi\) | ||||
−0.945463 | + | 0.325729i | \(0.894390\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1032.88 | 1.13628 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 442.176i | − | 0.485374i | −0.970105 | − | 0.242687i | \(-0.921971\pi\) | ||
0.970105 | − | 0.242687i | \(-0.0780288\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.9373 | 0.0130749 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2307.16i | 2.52148i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −191.852 | −0.209217 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 951.533 | 1.03540 | 0.517700 | − | 0.855562i | \(-0.326788\pi\) | ||||
0.517700 | + | 0.855562i | \(0.326788\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 284.971 | 0.309415 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −174.488 | −0.189044 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2213.47i | − | 2.39294i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 219.770i | 0.237076i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 518.679 | 0.558320 | 0.279160 | − | 0.960245i | \(-0.409944\pi\) | ||||
0.279160 | + | 0.960245i | \(0.409944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.45074 | + | 301.150i | 0.0101512 | + | 0.323469i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1951.28i | − | 2.09141i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2383.84 | 2.54956 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1238.36 | 1.32162 | 0.660809 | − | 0.750554i | \(-0.270213\pi\) | ||||
0.660809 | + | 0.750554i | \(0.270213\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2443.16i | − | 2.60187i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 492.751i | − | 0.523646i | −0.965116 | − | 0.261823i | \(-0.915676\pi\) | ||
0.965116 | − | 0.261823i | \(-0.0843236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 286.543i | − | 0.303863i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 47.6565i | 0.0504302i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −270.266 | −0.285392 | −0.142696 | − | 0.989767i | \(-0.545577\pi\) | ||||
−0.142696 | + | 0.989767i | \(0.545577\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 456.856i | 0.481407i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2409.15 | −2.53328 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1576.70i | 1.65446i | 0.561860 | + | 0.827232i | \(0.310086\pi\) | ||||
−0.561860 | + | 0.827232i | \(0.689914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1689.37 | 1.76897 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2156.93 | −2.25384 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1307.08 | 1.36296 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −263.772 | −0.274477 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 650.643i | − | 0.675641i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 827.215i | 0.857218i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 533.968 | 0.552190 | 0.276095 | − | 0.961130i | \(-0.410960\pi\) | ||||
0.276095 | + | 0.961130i | \(0.410960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1473.48 | + | 46.2410i | −1.52062 | + | 0.0477203i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 431.827i | − | 0.444724i | −0.974964 | − | 0.222362i | \(-0.928623\pi\) | ||
0.974964 | − | 0.222362i | \(-0.0713767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1377.32 | −1.41553 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1282.84 | 1.31574 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 666.524i | − | 0.682215i | −0.940024 | − | 0.341107i | \(-0.889198\pi\) | ||
0.940024 | − | 0.341107i | \(-0.110802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 499.351i | 0.510062i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 194.143i | − | 0.197904i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 16.4228i | − | 0.0167068i | −0.999965 | − | 0.00835338i | \(-0.997341\pi\) | ||
0.999965 | − | 0.00835338i | \(-0.00265900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2124.48 | 2.15683 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2185.99i | 2.21478i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −88.3764 | −0.0893593 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 505.687i | 0.510280i | 0.966904 | + | 0.255140i | \(0.0821215\pi\) | ||||
−0.966904 | + | 0.255140i | \(0.917879\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −432.923 | −0.435974 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.4195 | 0.0265522 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −682.491 | −0.684545 | −0.342272 | − | 0.939601i | \(-0.611197\pi\) | ||||
−0.342272 | + | 0.939601i | \(0.611197\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −61.3135 | −0.0613749 |
(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 | 1216.3.e.n.1025.8 | 8 | ||
4.3 | odd | 2 | 1216.3.e.m.1025.1 | 8 | |||
8.3 | odd | 2 | 152.3.e.b.113.8 | yes | 8 | ||
8.5 | even | 2 | 304.3.e.g.113.1 | 8 | |||
19.18 | odd | 2 | inner | 1216.3.e.n.1025.1 | 8 | ||
24.5 | odd | 2 | 2736.3.o.p.721.8 | 8 | |||
24.11 | even | 2 | 1368.3.o.b.721.8 | 8 | |||
76.75 | even | 2 | 1216.3.e.m.1025.8 | 8 | |||
152.37 | odd | 2 | 304.3.e.g.113.8 | 8 | |||
152.75 | even | 2 | 152.3.e.b.113.1 | ✓ | 8 | ||
456.227 | odd | 2 | 1368.3.o.b.721.7 | 8 | |||
456.341 | even | 2 | 2736.3.o.p.721.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.3.e.b.113.1 | ✓ | 8 | 152.75 | even | 2 | ||
152.3.e.b.113.8 | yes | 8 | 8.3 | odd | 2 | ||
304.3.e.g.113.1 | 8 | 8.5 | even | 2 | |||
304.3.e.g.113.8 | 8 | 152.37 | odd | 2 | |||
1216.3.e.m.1025.1 | 8 | 4.3 | odd | 2 | |||
1216.3.e.m.1025.8 | 8 | 76.75 | even | 2 | |||
1216.3.e.n.1025.1 | 8 | 19.18 | odd | 2 | inner | ||
1216.3.e.n.1025.8 | 8 | 1.1 | even | 1 | trivial | ||
1368.3.o.b.721.7 | 8 | 456.227 | odd | 2 | |||
1368.3.o.b.721.8 | 8 | 24.11 | even | 2 | |||
2736.3.o.p.721.7 | 8 | 456.341 | even | 2 | |||
2736.3.o.p.721.8 | 8 | 24.5 | odd | 2 |