Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,3,Mod(55,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("126.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.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: | \(3.43325133094\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 32x^{2} + 289 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.3 | ||
Root | \(-0.707107 + 4.06202i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.55 |
Dual form | 126.3.c.a.55.4 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 8.12404i | − | 1.62481i | −0.583095 | − | 0.812404i | \(-0.698159\pi\) | ||
0.583095 | − | 0.812404i | \(-0.301841\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00000 | − | 5.74456i | −0.571429 | − | 0.820652i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 11.4891i | − | 1.14891i | ||||||
\(11\) | 12.7279 | 1.15708 | 0.578542 | − | 0.815653i | \(-0.303622\pi\) | ||||
0.578542 | + | 0.815653i | \(0.303622\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.9783i | 1.76756i | 0.467905 | + | 0.883779i | \(0.345009\pi\) | ||||
−0.467905 | + | 0.883779i | \(0.654991\pi\) | |||||||
\(14\) | −5.65685 | − | 8.12404i | −0.404061 | − | 0.580288i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 8.12404i | − | 0.477885i | −0.971034 | − | 0.238942i | \(-0.923199\pi\) | ||
0.971034 | − | 0.238942i | \(-0.0768007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.4891i | 0.604691i | 0.953198 | + | 0.302345i | \(0.0977696\pi\) | ||||
−0.953198 | + | 0.302345i | \(0.902230\pi\) | |||||||
\(20\) | − | 16.2481i | − | 0.812404i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.0000 | 0.818182 | ||||||||
\(23\) | 21.2132 | 0.922313 | 0.461157 | − | 0.887319i | \(-0.347435\pi\) | ||||
0.461157 | + | 0.887319i | \(0.347435\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −41.0000 | −1.64000 | ||||||||
\(26\) | 32.4962i | 1.24985i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.00000 | − | 11.4891i | −0.285714 | − | 0.410326i | ||||
\(29\) | −33.9411 | −1.17038 | −0.585192 | − | 0.810895i | \(-0.698981\pi\) | ||||
−0.585192 | + | 0.810895i | \(0.698981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 11.4891i | − | 0.337915i | ||||||
\(35\) | −46.6690 | + | 32.4962i | −1.33340 | + | 0.928462i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.0000 | 0.432432 | 0.216216 | − | 0.976346i | \(-0.430628\pi\) | ||||
0.216216 | + | 0.976346i | \(0.430628\pi\) | |||||||
\(38\) | 16.2481i | 0.427581i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 22.9783i | − | 0.574456i | ||||||
\(41\) | 56.8683i | 1.38703i | 0.720442 | + | 0.693515i | \(0.243939\pi\) | ||||
−0.720442 | + | 0.693515i | \(0.756061\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.0000 | 1.20930 | 0.604651 | − | 0.796490i | \(-0.293313\pi\) | ||||
0.604651 | + | 0.796490i | \(0.293313\pi\) | |||||||
\(44\) | 25.4558 | 0.578542 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 30.0000 | 0.652174 | ||||||||
\(47\) | − | 32.4962i | − | 0.691408i | −0.938344 | − | 0.345704i | \(-0.887640\pi\) | ||
0.938344 | − | 0.345704i | \(-0.112360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.0000 | + | 45.9565i | −0.346939 | + | 0.937888i | ||||
\(50\) | −57.9828 | −1.15966 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 45.9565i | 0.883779i | ||||||||
\(53\) | −16.9706 | −0.320199 | −0.160100 | − | 0.987101i | \(-0.551182\pi\) | ||||
−0.160100 | + | 0.987101i | \(0.551182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 103.402i | − | 1.88004i | ||||||
\(56\) | −11.3137 | − | 16.2481i | −0.202031 | − | 0.290144i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −48.0000 | −0.827586 | ||||||||
\(59\) | 32.4962i | 0.550782i | 0.961332 | + | 0.275391i | \(0.0888074\pi\) | ||||
−0.961332 | + | 0.275391i | \(0.911193\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 22.9783i | − | 0.376693i | −0.982103 | − | 0.188346i | \(-0.939687\pi\) | ||
0.982103 | − | 0.188346i | \(-0.0603127\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 186.676 | 2.87194 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52.0000 | −0.776119 | −0.388060 | − | 0.921634i | \(-0.626855\pi\) | ||||
−0.388060 | + | 0.921634i | \(0.626855\pi\) | |||||||
\(68\) | − | 16.2481i | − | 0.238942i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −66.0000 | + | 45.9565i | −0.942857 | + | 0.656521i | ||||
\(71\) | −89.0955 | −1.25487 | −0.627433 | − | 0.778671i | \(-0.715894\pi\) | ||||
−0.627433 | + | 0.778671i | \(0.715894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 45.9565i | 0.629541i | 0.949168 | + | 0.314771i | \(0.101928\pi\) | ||||
−0.949168 | + | 0.314771i | \(0.898072\pi\) | |||||||
\(74\) | 22.6274 | 0.305776 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 22.9783i | 0.302345i | ||||||||
\(77\) | −50.9117 | − | 73.1163i | −0.661191 | − | 0.949563i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 104.000 | 1.31646 | 0.658228 | − | 0.752819i | \(-0.271306\pi\) | ||||
0.658228 | + | 0.752819i | \(0.271306\pi\) | |||||||
\(80\) | − | 32.4962i | − | 0.406202i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 80.4239i | 0.980779i | ||||||||
\(83\) | − | 162.481i | − | 1.95760i | −0.204819 | − | 0.978800i | \(-0.565661\pi\) | ||
0.204819 | − | 0.978800i | \(-0.434339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −66.0000 | −0.776471 | ||||||||
\(86\) | 73.5391 | 0.855106 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 36.0000 | 0.409091 | ||||||||
\(89\) | 73.1163i | 0.821532i | 0.911741 | + | 0.410766i | \(0.134739\pi\) | ||||
−0.911741 | + | 0.410766i | \(0.865261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 132.000 | − | 91.9130i | 1.45055 | − | 1.01003i | ||||
\(92\) | 42.4264 | 0.461157 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 45.9565i | − | 0.488899i | ||||||
\(95\) | 93.3381 | 0.982506 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 91.9130i | 0.947557i | 0.880644 | + | 0.473778i | \(0.157110\pi\) | ||||
−0.880644 | + | 0.473778i | \(0.842890\pi\) | |||||||
\(98\) | −24.0416 | + | 64.9923i | −0.245323 | + | 0.663187i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −82.0000 | −0.820000 | ||||||||
\(101\) | − | 121.861i | − | 1.20654i | −0.797537 | − | 0.603270i | \(-0.793864\pi\) | ||
0.797537 | − | 0.603270i | \(-0.206136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 91.9130i | − | 0.892359i | −0.894943 | − | 0.446180i | \(-0.852784\pi\) | ||
0.894943 | − | 0.446180i | \(-0.147216\pi\) | |||||||
\(104\) | 64.9923i | 0.624926i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −24.0000 | −0.226415 | ||||||||
\(107\) | 123.037 | 1.14987 | 0.574937 | − | 0.818197i | \(-0.305026\pi\) | ||||
0.574937 | + | 0.818197i | \(0.305026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −62.0000 | −0.568807 | −0.284404 | − | 0.958705i | \(-0.591796\pi\) | ||||
−0.284404 | + | 0.958705i | \(0.591796\pi\) | |||||||
\(110\) | − | 146.233i | − | 1.32939i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −16.0000 | − | 22.9783i | −0.142857 | − | 0.205163i | ||||
\(113\) | −118.794 | −1.05127 | −0.525637 | − | 0.850709i | \(-0.676173\pi\) | ||||
−0.525637 | + | 0.850709i | \(0.676173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 172.337i | − | 1.49858i | ||||||
\(116\) | −67.8823 | −0.585192 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 45.9565i | 0.389462i | ||||||||
\(119\) | −46.6690 | + | 32.4962i | −0.392177 | + | 0.273077i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 41.0000 | 0.338843 | ||||||||
\(122\) | − | 32.4962i | − | 0.266362i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 129.985i | 1.03988i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −64.0000 | −0.503937 | −0.251969 | − | 0.967735i | \(-0.581078\pi\) | ||||
−0.251969 | + | 0.967735i | \(0.581078\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 264.000 | 2.03077 | ||||||||
\(131\) | 97.4885i | 0.744187i | 0.928195 | + | 0.372093i | \(0.121360\pi\) | ||||
−0.928195 | + | 0.372093i | \(0.878640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 66.0000 | − | 45.9565i | 0.496241 | − | 0.345538i | ||||
\(134\) | −73.5391 | −0.548799 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 22.9783i | − | 0.168958i | ||||||
\(137\) | 33.9411 | 0.247745 | 0.123873 | − | 0.992298i | \(-0.460469\pi\) | ||||
0.123873 | + | 0.992298i | \(0.460469\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 183.826i | 1.32249i | 0.750170 | + | 0.661245i | \(0.229971\pi\) | ||||
−0.750170 | + | 0.661245i | \(0.770029\pi\) | |||||||
\(140\) | −93.3381 | + | 64.9923i | −0.666701 | + | 0.464231i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −126.000 | −0.887324 | ||||||||
\(143\) | 292.465i | 2.04521i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 275.739i | 1.90165i | ||||||||
\(146\) | 64.9923i | 0.445153i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32.0000 | 0.216216 | ||||||||
\(149\) | −186.676 | −1.25286 | −0.626430 | − | 0.779478i | \(-0.715485\pi\) | ||||
−0.626430 | + | 0.779478i | \(0.715485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −32.0000 | −0.211921 | −0.105960 | − | 0.994370i | \(-0.533792\pi\) | ||||
−0.105960 | + | 0.994370i | \(0.533792\pi\) | |||||||
\(152\) | 32.4962i | 0.213790i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −72.0000 | − | 103.402i | −0.467532 | − | 0.671442i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 68.9348i | 0.439075i | 0.975604 | + | 0.219537i | \(0.0704548\pi\) | ||||
−0.975604 | + | 0.219537i | \(0.929545\pi\) | |||||||
\(158\) | 147.078 | 0.930875 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 45.9565i | − | 0.287228i | ||||||
\(161\) | −84.8528 | − | 121.861i | −0.527036 | − | 0.756898i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −124.000 | −0.760736 | −0.380368 | − | 0.924835i | \(-0.624203\pi\) | ||||
−0.380368 | + | 0.924835i | \(0.624203\pi\) | |||||||
\(164\) | 113.737i | 0.693515i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 229.783i | − | 1.38423i | ||||||
\(167\) | − | 129.985i | − | 0.778351i | −0.921164 | − | 0.389175i | \(-0.872760\pi\) | ||
0.921164 | − | 0.389175i | \(-0.127240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −359.000 | −2.12426 | ||||||||
\(170\) | −93.3381 | −0.549048 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 104.000 | 0.604651 | ||||||||
\(173\) | 73.1163i | 0.422638i | 0.977417 | + | 0.211319i | \(0.0677759\pi\) | ||||
−0.977417 | + | 0.211319i | \(0.932224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 164.000 | + | 235.527i | 0.937143 | + | 1.34587i | ||||
\(176\) | 50.9117 | 0.289271 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 103.402i | 0.580911i | ||||||||
\(179\) | −156.978 | −0.876970 | −0.438485 | − | 0.898738i | \(-0.644485\pi\) | ||||
−0.438485 | + | 0.898738i | \(0.644485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 252.761i | − | 1.39647i | −0.715869 | − | 0.698234i | \(-0.753969\pi\) | ||
0.715869 | − | 0.698234i | \(-0.246031\pi\) | |||||||
\(182\) | 186.676 | − | 129.985i | 1.02569 | − | 0.714201i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 60.0000 | 0.326087 | ||||||||
\(185\) | − | 129.985i | − | 0.702620i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 103.402i | − | 0.552953i | ||||||
\(188\) | − | 64.9923i | − | 0.345704i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 132.000 | 0.694737 | ||||||||
\(191\) | −12.7279 | −0.0666383 | −0.0333192 | − | 0.999445i | \(-0.510608\pi\) | ||||
−0.0333192 | + | 0.999445i | \(0.510608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −224.000 | −1.16062 | −0.580311 | − | 0.814395i | \(-0.697069\pi\) | ||||
−0.580311 | + | 0.814395i | \(0.697069\pi\) | |||||||
\(194\) | 129.985i | 0.670024i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −34.0000 | + | 91.9130i | −0.173469 | + | 0.468944i | ||||
\(197\) | 305.470 | 1.55061 | 0.775305 | − | 0.631587i | \(-0.217596\pi\) | ||||
0.775305 | + | 0.631587i | \(0.217596\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 264.250i | 1.32789i | 0.747782 | + | 0.663944i | \(0.231119\pi\) | ||||
−0.747782 | + | 0.663944i | \(0.768881\pi\) | |||||||
\(200\) | −115.966 | −0.579828 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 172.337i | − | 0.853153i | ||||||
\(203\) | 135.765 | + | 194.977i | 0.668791 | + | 0.960477i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 462.000 | 2.25366 | ||||||||
\(206\) | − | 129.985i | − | 0.630993i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 91.9130i | 0.441889i | ||||||||
\(209\) | 146.233i | 0.699678i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 124.000 | 0.587678 | 0.293839 | − | 0.955855i | \(-0.405067\pi\) | ||||
0.293839 | + | 0.955855i | \(0.405067\pi\) | |||||||
\(212\) | −33.9411 | −0.160100 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 174.000 | 0.813084 | ||||||||
\(215\) | − | 422.450i | − | 1.96488i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −87.6812 | −0.402208 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 206.804i | − | 0.940019i | ||||||
\(221\) | 186.676 | 0.844689 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 172.337i | − | 0.772811i | −0.922329 | − | 0.386406i | \(-0.873717\pi\) | ||
0.922329 | − | 0.386406i | \(-0.126283\pi\) | |||||||
\(224\) | −22.6274 | − | 32.4962i | −0.101015 | − | 0.145072i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −168.000 | −0.743363 | ||||||||
\(227\) | − | 389.954i | − | 1.71786i | −0.512094 | − | 0.858929i | \(-0.671130\pi\) | ||
0.512094 | − | 0.858929i | \(-0.328870\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 206.804i | − | 0.903075i | −0.892252 | − | 0.451538i | \(-0.850876\pi\) | ||
0.892252 | − | 0.451538i | \(-0.149124\pi\) | |||||||
\(230\) | − | 243.721i | − | 1.05966i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −96.0000 | −0.413793 | ||||||||
\(233\) | −186.676 | −0.801185 | −0.400593 | − | 0.916256i | \(-0.631196\pi\) | ||||
−0.400593 | + | 0.916256i | \(0.631196\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −264.000 | −1.12340 | ||||||||
\(236\) | 64.9923i | 0.275391i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −66.0000 | + | 45.9565i | −0.277311 | + | 0.193095i | ||||
\(239\) | 258.801 | 1.08285 | 0.541425 | − | 0.840749i | \(-0.317885\pi\) | ||||
0.541425 | + | 0.840749i | \(0.317885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 45.9565i | 0.190691i | 0.995444 | + | 0.0953454i | \(0.0303956\pi\) | ||||
−0.995444 | + | 0.0953454i | \(0.969604\pi\) | |||||||
\(242\) | 57.9828 | 0.239598 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 45.9565i | − | 0.188346i | ||||||
\(245\) | 373.352 | + | 138.109i | 1.52389 | + | 0.563709i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −264.000 | −1.06883 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 183.826i | 0.735304i | ||||||||
\(251\) | 64.9923i | 0.258933i | 0.991584 | + | 0.129467i | \(0.0413265\pi\) | ||||
−0.991584 | + | 0.129467i | \(0.958673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 270.000 | 1.06719 | ||||||||
\(254\) | −90.5097 | −0.356337 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 268.093i | − | 1.04316i | −0.853201 | − | 0.521582i | \(-0.825342\pi\) | ||
0.853201 | − | 0.521582i | \(-0.174658\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −64.0000 | − | 91.9130i | −0.247104 | − | 0.354876i | ||||
\(260\) | 373.352 | 1.43597 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 137.870i | 0.526219i | ||||||||
\(263\) | −428.507 | −1.62930 | −0.814652 | − | 0.579951i | \(-0.803072\pi\) | ||||
−0.814652 | + | 0.579951i | \(0.803072\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 137.870i | 0.520262i | ||||||||
\(266\) | 93.3381 | − | 64.9923i | 0.350895 | − | 0.244332i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −104.000 | −0.388060 | ||||||||
\(269\) | 203.101i | 0.755022i | 0.926005 | + | 0.377511i | \(0.123220\pi\) | ||||
−0.926005 | + | 0.377511i | \(0.876780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 91.9130i | 0.339162i | 0.985516 | + | 0.169581i | \(0.0542415\pi\) | ||||
−0.985516 | + | 0.169581i | \(0.945759\pi\) | |||||||
\(272\) | − | 32.4962i | − | 0.119471i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 48.0000 | 0.175182 | ||||||||
\(275\) | −521.845 | −1.89762 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 272.000 | 0.981949 | 0.490975 | − | 0.871174i | \(-0.336641\pi\) | ||||
0.490975 | + | 0.871174i | \(0.336641\pi\) | |||||||
\(278\) | 259.969i | 0.935141i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −132.000 | + | 91.9130i | −0.471429 | + | 0.328261i | ||||
\(281\) | −50.9117 | −0.181180 | −0.0905902 | − | 0.995888i | \(-0.528875\pi\) | ||||
−0.0905902 | + | 0.995888i | \(0.528875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 103.402i | − | 0.365379i | −0.983171 | − | 0.182689i | \(-0.941520\pi\) | ||
0.983171 | − | 0.182689i | \(-0.0584802\pi\) | |||||||
\(284\) | −178.191 | −0.627433 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 413.609i | 1.44618i | ||||||||
\(287\) | 326.683 | − | 227.473i | 1.13827 | − | 0.792589i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 223.000 | 0.771626 | ||||||||
\(290\) | 389.954i | 1.34467i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 91.9130i | 0.314771i | ||||||||
\(293\) | 8.12404i | 0.0277271i | 0.999904 | + | 0.0138635i | \(0.00441305\pi\) | ||||
−0.999904 | + | 0.0138635i | \(0.995587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 264.000 | 0.894915 | ||||||||
\(296\) | 45.2548 | 0.152888 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −264.000 | −0.885906 | ||||||||
\(299\) | 487.442i | 1.63024i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −208.000 | − | 298.717i | −0.691030 | − | 0.992416i | ||||
\(302\) | −45.2548 | −0.149850 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 45.9565i | 0.151173i | ||||||||
\(305\) | −186.676 | −0.612053 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 379.141i | 1.23499i | 0.786576 | + | 0.617494i | \(0.211852\pi\) | ||||
−0.786576 | + | 0.617494i | \(0.788148\pi\) | |||||||
\(308\) | −101.823 | − | 146.233i | −0.330595 | − | 0.474781i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 357.458i | 1.14938i | 0.818371 | + | 0.574691i | \(0.194878\pi\) | ||||
−0.818371 | + | 0.574691i | \(0.805122\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 183.826i | − | 0.587304i | −0.955912 | − | 0.293652i | \(-0.905129\pi\) | ||
0.955912 | − | 0.293652i | \(-0.0948706\pi\) | |||||||
\(314\) | 97.4885i | 0.310473i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 208.000 | 0.658228 | ||||||||
\(317\) | −356.382 | −1.12423 | −0.562116 | − | 0.827058i | \(-0.690013\pi\) | ||||
−0.562116 | + | 0.827058i | \(0.690013\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −432.000 | −1.35423 | ||||||||
\(320\) | − | 64.9923i | − | 0.203101i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −120.000 | − | 172.337i | −0.372671 | − | 0.535208i | ||||
\(323\) | 93.3381 | 0.288972 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 942.108i | − | 2.89879i | ||||||
\(326\) | −175.362 | −0.537922 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 160.848i | 0.490389i | ||||||||
\(329\) | −186.676 | + | 129.985i | −0.567405 | + | 0.395090i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.0120846 | 0.00604230 | − | 0.999982i | \(-0.498077\pi\) | ||||
0.00604230 | + | 0.999982i | \(0.498077\pi\) | |||||||
\(332\) | − | 324.962i | − | 0.978800i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 183.826i | − | 0.550377i | ||||||
\(335\) | 422.450i | 1.26104i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 82.0000 | 0.243323 | 0.121662 | − | 0.992572i | \(-0.461178\pi\) | ||||
0.121662 | + | 0.992572i | \(0.461178\pi\) | |||||||
\(338\) | −507.703 | −1.50208 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −132.000 | −0.388235 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 332.000 | − | 86.1684i | 0.967930 | − | 0.251220i | ||||
\(344\) | 147.078 | 0.427553 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 103.402i | 0.298850i | ||||||||
\(347\) | 555.786 | 1.60169 | 0.800844 | − | 0.598873i | \(-0.204384\pi\) | ||||
0.800844 | + | 0.598873i | \(0.204384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 160.848i | − | 0.460882i | −0.973086 | − | 0.230441i | \(-0.925983\pi\) | ||
0.973086 | − | 0.230441i | \(-0.0740168\pi\) | |||||||
\(350\) | 231.931 | + | 333.086i | 0.662660 | + | 0.951673i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 72.0000 | 0.204545 | ||||||||
\(353\) | 138.109i | 0.391243i | 0.980680 | + | 0.195621i | \(0.0626723\pi\) | ||||
−0.980680 | + | 0.195621i | \(0.937328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 723.815i | 2.03892i | ||||||||
\(356\) | 146.233i | 0.410766i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −222.000 | −0.620112 | ||||||||
\(359\) | −224.860 | −0.626351 | −0.313175 | − | 0.949695i | \(-0.601393\pi\) | ||||
−0.313175 | + | 0.949695i | \(0.601393\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 229.000 | 0.634349 | ||||||||
\(362\) | − | 357.458i | − | 0.987452i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 264.000 | − | 183.826i | 0.725275 | − | 0.505016i | ||||
\(365\) | 373.352 | 1.02288 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 195.315i | 0.532194i | 0.963946 | + | 0.266097i | \(0.0857341\pi\) | ||||
−0.963946 | + | 0.266097i | \(0.914266\pi\) | |||||||
\(368\) | 84.8528 | 0.230578 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 183.826i | − | 0.496827i | ||||||
\(371\) | 67.8823 | + | 97.4885i | 0.182971 | + | 0.262772i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 530.000 | 1.42091 | 0.710456 | − | 0.703742i | \(-0.248489\pi\) | ||||
0.710456 | + | 0.703742i | \(0.248489\pi\) | |||||||
\(374\) | − | 146.233i | − | 0.390997i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 91.9130i | − | 0.244449i | ||||||
\(377\) | − | 779.908i | − | 2.06872i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 196.000 | 0.517150 | 0.258575 | − | 0.965991i | \(-0.416747\pi\) | ||||
0.258575 | + | 0.965991i | \(0.416747\pi\) | |||||||
\(380\) | 186.676 | 0.491253 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.0000 | −0.0471204 | ||||||||
\(383\) | 32.4962i | 0.0848464i | 0.999100 | + | 0.0424232i | \(0.0135078\pi\) | ||||
−0.999100 | + | 0.0424232i | \(0.986492\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −594.000 | + | 413.609i | −1.54286 | + | 1.07431i | ||||
\(386\) | −316.784 | −0.820684 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 183.826i | 0.473778i | ||||||||
\(389\) | −644.881 | −1.65779 | −0.828896 | − | 0.559402i | \(-0.811031\pi\) | ||||
−0.828896 | + | 0.559402i | \(0.811031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 172.337i | − | 0.440759i | ||||||
\(392\) | −48.0833 | + | 129.985i | −0.122661 | + | 0.331593i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 432.000 | 1.09645 | ||||||||
\(395\) | − | 844.900i | − | 2.13899i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 758.282i | − | 1.91003i | −0.296556 | − | 0.955015i | \(-0.595838\pi\) | ||
0.296556 | − | 0.955015i | \(-0.404162\pi\) | |||||||
\(398\) | 373.706i | 0.938959i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −164.000 | −0.410000 | ||||||||
\(401\) | −33.9411 | −0.0846412 | −0.0423206 | − | 0.999104i | \(-0.513475\pi\) | ||||
−0.0423206 | + | 0.999104i | \(0.513475\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 243.721i | − | 0.603270i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 192.000 | + | 275.739i | 0.472906 | + | 0.679160i | ||||
\(407\) | 203.647 | 0.500361 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 735.304i | 1.79781i | 0.438144 | + | 0.898905i | \(0.355636\pi\) | ||||
−0.438144 | + | 0.898905i | \(0.644364\pi\) | |||||||
\(410\) | 653.367 | 1.59358 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 183.826i | − | 0.446180i | ||||||
\(413\) | 186.676 | − | 129.985i | 0.452000 | − | 0.314733i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1320.00 | −3.18072 | ||||||||
\(416\) | 129.985i | 0.312463i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 206.804i | 0.494747i | ||||||||
\(419\) | − | 32.4962i | − | 0.0775565i | −0.999248 | − | 0.0387782i | \(-0.987653\pi\) | ||
0.999248 | − | 0.0387782i | \(-0.0123466\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −496.000 | −1.17815 | −0.589074 | − | 0.808079i | \(-0.700507\pi\) | ||||
−0.589074 | + | 0.808079i | \(0.700507\pi\) | |||||||
\(422\) | 175.362 | 0.415551 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −48.0000 | −0.113208 | ||||||||
\(425\) | 333.086i | 0.783731i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −132.000 | + | 91.9130i | −0.309133 | + | 0.215253i | ||||
\(428\) | 246.073 | 0.574937 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 597.435i | − | 1.38938i | ||||||
\(431\) | 462.448 | 1.07296 | 0.536482 | − | 0.843912i | \(-0.319753\pi\) | ||||
0.536482 | + | 0.843912i | \(0.319753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 137.870i | 0.318405i | 0.987246 | + | 0.159203i | \(0.0508923\pi\) | ||||
−0.987246 | + | 0.159203i | \(0.949108\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −124.000 | −0.284404 | ||||||||
\(437\) | 243.721i | 0.557714i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 172.337i | 0.392567i | 0.980547 | + | 0.196283i | \(0.0628873\pi\) | ||||
−0.980547 | + | 0.196283i | \(0.937113\pi\) | |||||||
\(440\) | − | 292.465i | − | 0.664694i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 264.000 | 0.597285 | ||||||||
\(443\) | 394.566 | 0.890667 | 0.445334 | − | 0.895365i | \(-0.353085\pi\) | ||||
0.445334 | + | 0.895365i | \(0.353085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 594.000 | 1.33483 | ||||||||
\(446\) | − | 243.721i | − | 0.546460i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −32.0000 | − | 45.9565i | −0.0714286 | − | 0.102581i | ||||
\(449\) | 50.9117 | 0.113389 | 0.0566945 | − | 0.998392i | \(-0.481944\pi\) | ||||
0.0566945 | + | 0.998392i | \(0.481944\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 723.815i | 1.60491i | ||||||||
\(452\) | −237.588 | −0.525637 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 551.478i | − | 1.21471i | ||||||
\(455\) | −746.705 | − | 1072.37i | −1.64111 | − | 2.35686i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 130.000 | 0.284464 | 0.142232 | − | 0.989833i | \(-0.454572\pi\) | ||||
0.142232 | + | 0.989833i | \(0.454572\pi\) | |||||||
\(458\) | − | 292.465i | − | 0.638571i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 344.674i | − | 0.749291i | ||||||
\(461\) | − | 723.039i | − | 1.56842i | −0.620499 | − | 0.784208i | \(-0.713070\pi\) | ||
0.620499 | − | 0.784208i | \(-0.286930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 80.0000 | 0.172786 | 0.0863931 | − | 0.996261i | \(-0.472466\pi\) | ||||
0.0863931 | + | 0.996261i | \(0.472466\pi\) | |||||||
\(464\) | −135.765 | −0.292596 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −264.000 | −0.566524 | ||||||||
\(467\) | 194.977i | 0.417509i | 0.977968 | + | 0.208755i | \(0.0669410\pi\) | ||||
−0.977968 | + | 0.208755i | \(0.933059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 208.000 | + | 298.717i | 0.443497 | + | 0.636924i | ||||
\(470\) | −373.352 | −0.794367 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 91.9130i | 0.194731i | ||||||||
\(473\) | 661.852 | 1.39926 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 471.054i | − | 0.991693i | ||||||
\(476\) | −93.3381 | + | 64.9923i | −0.196088 | + | 0.136538i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 366.000 | 0.765690 | ||||||||
\(479\) | 422.450i | 0.881942i | 0.897521 | + | 0.440971i | \(0.145366\pi\) | ||||
−0.897521 | + | 0.440971i | \(0.854634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 367.652i | 0.764349i | ||||||||
\(482\) | 64.9923i | 0.134839i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 82.0000 | 0.169421 | ||||||||
\(485\) | 746.705 | 1.53960 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 904.000 | 1.85626 | 0.928131 | − | 0.372253i | \(-0.121415\pi\) | ||||
0.928131 | + | 0.372253i | \(0.121415\pi\) | |||||||
\(488\) | − | 64.9923i | − | 0.133181i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 528.000 | + | 195.315i | 1.07755 | + | 0.398602i | ||||
\(491\) | −420.021 | −0.855441 | −0.427720 | − | 0.903911i | \(-0.640683\pi\) | ||||
−0.427720 | + | 0.903911i | \(0.640683\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 275.739i | 0.559308i | ||||||||
\(494\) | −373.352 | −0.755774 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 356.382 | + | 511.814i | 0.717066 | + | 1.02981i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −716.000 | −1.43487 | −0.717435 | − | 0.696626i | \(-0.754684\pi\) | ||||
−0.717435 | + | 0.696626i | \(0.754684\pi\) | |||||||
\(500\) | 259.969i | 0.519938i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 91.9130i | 0.183094i | ||||||||
\(503\) | 812.404i | 1.61512i | 0.589787 | + | 0.807558i | \(0.299212\pi\) | ||||
−0.589787 | + | 0.807558i | \(0.700788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −990.000 | −1.96040 | ||||||||
\(506\) | 381.838 | 0.754620 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −128.000 | −0.251969 | ||||||||
\(509\) | − | 186.853i | − | 0.367098i | −0.983011 | − | 0.183549i | \(-0.941241\pi\) | ||
0.983011 | − | 0.183549i | \(-0.0587586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 264.000 | − | 183.826i | 0.516634 | − | 0.359738i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 379.141i | − | 0.737629i | ||||||
\(515\) | −746.705 | −1.44991 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 413.609i | − | 0.800016i | ||||||
\(518\) | −90.5097 | − | 129.985i | −0.174729 | − | 0.250936i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 528.000 | 1.01538 | ||||||||
\(521\) | 593.055i | 1.13830i | 0.822233 | + | 0.569150i | \(0.192728\pi\) | ||||
−0.822233 | + | 0.569150i | \(0.807272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 735.304i | − | 1.40594i | −0.711222 | − | 0.702968i | \(-0.751858\pi\) | ||
0.711222 | − | 0.702968i | \(-0.248142\pi\) | |||||||
\(524\) | 194.977i | 0.372093i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −606.000 | −1.15209 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −79.0000 | −0.149338 | ||||||||
\(530\) | 194.977i | 0.367881i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 132.000 | − | 91.9130i | 0.248120 | − | 0.172769i | ||||
\(533\) | −1306.73 | −2.45166 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 999.554i | − | 1.86833i | ||||||
\(536\) | −147.078 | −0.274400 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 287.228i | 0.533881i | ||||||||
\(539\) | −216.375 | + | 584.931i | −0.401437 | + | 1.08521i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 272.000 | 0.502773 | 0.251386 | − | 0.967887i | \(-0.419114\pi\) | ||||
0.251386 | + | 0.967887i | \(0.419114\pi\) | |||||||
\(542\) | 129.985i | 0.239824i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 45.9565i | − | 0.0844789i | ||||||
\(545\) | 503.690i | 0.924203i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 644.000 | 1.17733 | 0.588665 | − | 0.808377i | \(-0.299654\pi\) | ||||
0.588665 | + | 0.808377i | \(0.299654\pi\) | |||||||
\(548\) | 67.8823 | 0.123873 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −738.000 | −1.34182 | ||||||||
\(551\) | − | 389.954i | − | 0.707720i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −416.000 | − | 597.435i | −0.752260 | − | 1.08035i | ||||
\(554\) | 384.666 | 0.694343 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 367.652i | 0.661245i | ||||||||
\(557\) | −152.735 | −0.274210 | −0.137105 | − | 0.990557i | \(-0.543780\pi\) | ||||
−0.137105 | + | 0.990557i | \(0.543780\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1194.87i | 2.13751i | ||||||||
\(560\) | −186.676 | + | 129.985i | −0.333350 | + | 0.232115i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −72.0000 | −0.128114 | ||||||||
\(563\) | − | 877.396i | − | 1.55843i | −0.626757 | − | 0.779215i | \(-0.715618\pi\) | ||
0.626757 | − | 0.779215i | \(-0.284382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 965.087i | 1.70812i | ||||||||
\(566\) | − | 146.233i | − | 0.258362i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −252.000 | −0.443662 | ||||||||
\(569\) | 933.381 | 1.64039 | 0.820194 | − | 0.572085i | \(-0.193865\pi\) | ||||
0.820194 | + | 0.572085i | \(0.193865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 260.000 | 0.455342 | 0.227671 | − | 0.973738i | \(-0.426889\pi\) | ||||
0.227671 | + | 0.973738i | \(0.426889\pi\) | |||||||
\(572\) | 584.931i | 1.02261i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 462.000 | − | 321.696i | 0.804878 | − | 0.560445i | ||||
\(575\) | −869.741 | −1.51259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 505.522i | − | 0.876120i | −0.898946 | − | 0.438060i | \(-0.855666\pi\) | ||
0.898946 | − | 0.438060i | \(-0.144334\pi\) | |||||||
\(578\) | 315.370 | 0.545622 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 551.478i | 0.950824i | ||||||||
\(581\) | −933.381 | + | 649.923i | −1.60651 | + | 1.11863i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −216.000 | −0.370497 | ||||||||
\(584\) | 129.985i | 0.222576i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.4891i | 0.0196060i | ||||||||
\(587\) | 194.977i | 0.332158i | 0.986112 | + | 0.166079i | \(0.0531107\pi\) | ||||
−0.986112 | + | 0.166079i | \(0.946889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 373.352 | 0.632801 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 64.0000 | 0.108108 | ||||||||
\(593\) | − | 138.109i | − | 0.232898i | −0.993197 | − | 0.116449i | \(-0.962849\pi\) | ||
0.993197 | − | 0.116449i | \(-0.0371512\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 264.000 | + | 379.141i | 0.443697 | + | 0.637212i | ||||
\(596\) | −373.352 | −0.626430 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 689.348i | 1.15276i | ||||||||
\(599\) | 453.963 | 0.757867 | 0.378934 | − | 0.925424i | \(-0.376291\pi\) | ||||
0.378934 | + | 0.925424i | \(0.376291\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 827.217i | 1.37640i | 0.725521 | + | 0.688201i | \(0.241599\pi\) | ||||
−0.725521 | + | 0.688201i | \(0.758401\pi\) | |||||||
\(602\) | −294.156 | − | 422.450i | −0.488632 | − | 0.701744i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −64.0000 | −0.105960 | ||||||||
\(605\) | − | 333.086i | − | 0.550555i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 356.163i | − | 0.586759i | −0.955996 | − | 0.293380i | \(-0.905220\pi\) | ||
0.955996 | − | 0.293380i | \(-0.0947800\pi\) | |||||||
\(608\) | 64.9923i | 0.106895i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −264.000 | −0.432787 | ||||||||
\(611\) | 746.705 | 1.22210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 878.000 | 1.43230 | 0.716150 | − | 0.697946i | \(-0.245903\pi\) | ||||
0.716150 | + | 0.697946i | \(0.245903\pi\) | |||||||
\(614\) | 536.187i | 0.873268i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −144.000 | − | 206.804i | −0.233766 | − | 0.335721i | ||||
\(617\) | 101.823 | 0.165030 | 0.0825149 | − | 0.996590i | \(-0.473705\pi\) | ||||
0.0825149 | + | 0.996590i | \(0.473705\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 735.304i | − | 1.18789i | −0.804506 | − | 0.593945i | \(-0.797570\pi\) | ||
0.804506 | − | 0.593945i | \(-0.202430\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 505.522i | 0.812736i | ||||||||
\(623\) | 420.021 | − | 292.465i | 0.674192 | − | 0.469447i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.0000 | 0.0496000 | ||||||||
\(626\) | − | 259.969i | − | 0.415286i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 137.870i | 0.219537i | ||||||||
\(629\) | − | 129.985i | − | 0.206653i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.0253566 | −0.0126783 | − | 0.999920i | \(-0.504036\pi\) | ||||
−0.0126783 | + | 0.999920i | \(0.504036\pi\) | |||||||
\(632\) | 294.156 | 0.465437 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −504.000 | −0.794953 | ||||||||
\(635\) | 519.938i | 0.818801i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1056.00 | − | 390.630i | −1.65777 | − | 0.613234i | ||||
\(638\) | −610.940 | −0.957587 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 91.9130i | − | 0.143614i | ||||||
\(641\) | −67.8823 | −0.105901 | −0.0529503 | − | 0.998597i | \(-0.516862\pi\) | ||||
−0.0529503 | + | 0.998597i | \(0.516862\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 930.619i | − | 1.44731i | −0.690163 | − | 0.723654i | \(-0.742461\pi\) | ||
0.690163 | − | 0.723654i | \(-0.257539\pi\) | |||||||
\(644\) | −169.706 | − | 243.721i | −0.263518 | − | 0.378449i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 132.000 | 0.204334 | ||||||||
\(647\) | 584.931i | 0.904066i | 0.892001 | + | 0.452033i | \(0.149301\pi\) | ||||
−0.892001 | + | 0.452033i | \(0.850699\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 413.609i | 0.637301i | ||||||||
\(650\) | − | 1332.34i | − | 2.04976i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −248.000 | −0.380368 | ||||||||
\(653\) | 84.8528 | 0.129943 | 0.0649715 | − | 0.997887i | \(-0.479304\pi\) | ||||
0.0649715 | + | 0.997887i | \(0.479304\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 792.000 | 1.20916 | ||||||||
\(656\) | 227.473i | 0.346758i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −264.000 | + | 183.826i | −0.401216 | + | 0.279371i | ||||
\(659\) | 700.036 | 1.06227 | 0.531135 | − | 0.847287i | \(-0.321766\pi\) | ||||
0.531135 | + | 0.847287i | \(0.321766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 114.891i | − | 0.173814i | −0.996216 | − | 0.0869072i | \(-0.972302\pi\) | ||
0.996216 | − | 0.0869072i | \(-0.0276983\pi\) | |||||||
\(662\) | 5.65685 | 0.00854510 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 459.565i | − | 0.692116i | ||||||
\(665\) | −373.352 | − | 536.187i | −0.561432 | − | 0.806296i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −720.000 | −1.07946 | ||||||||
\(668\) | − | 259.969i | − | 0.389175i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 597.435i | 0.891693i | ||||||||
\(671\) | − | 292.465i | − | 0.435865i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −368.000 | −0.546805 | −0.273403 | − | 0.961900i | \(-0.588149\pi\) | ||||
−0.273403 | + | 0.961900i | \(0.588149\pi\) | |||||||
\(674\) | 115.966 | 0.172056 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −718.000 | −1.06213 | ||||||||
\(677\) | − | 1048.00i | − | 1.54801i | −0.633181 | − | 0.774004i | \(-0.718251\pi\) | ||
0.633181 | − | 0.774004i | \(-0.281749\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 528.000 | − | 367.652i | 0.777614 | − | 0.541461i | ||||
\(680\) | −186.676 | −0.274524 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 258.801 | 0.378918 | 0.189459 | − | 0.981889i | \(-0.439327\pi\) | ||||
0.189459 | + | 0.981889i | \(0.439327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 275.739i | − | 0.402539i | ||||||
\(686\) | 469.519 | − | 121.861i | 0.684430 | − | 0.177639i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 208.000 | 0.302326 | ||||||||
\(689\) | − | 389.954i | − | 0.565971i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1102.96i | − | 1.59617i | −0.602542 | − | 0.798087i | \(-0.705846\pi\) | ||
0.602542 | − | 0.798087i | \(-0.294154\pi\) | |||||||
\(692\) | 146.233i | 0.211319i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 786.000 | 1.13256 | ||||||||
\(695\) | 1493.41 | 2.14879 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 462.000 | 0.662841 | ||||||||
\(698\) | − | 227.473i | − | 0.325893i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 328.000 | + | 471.054i | 0.468571 | + | 0.672934i | ||||
\(701\) | −390.323 | −0.556809 | −0.278404 | − | 0.960464i | \(-0.589806\pi\) | ||||
−0.278404 | + | 0.960464i | \(0.589806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 183.826i | 0.261488i | ||||||||
\(704\) | 101.823 | 0.144635 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 195.315i | 0.276650i | ||||||||
\(707\) | −700.036 | + | 487.442i | −0.990150 | + | 0.689452i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 238.000 | 0.335684 | 0.167842 | − | 0.985814i | \(-0.446320\pi\) | ||||
0.167842 | + | 0.985814i | \(0.446320\pi\) | |||||||
\(710\) | 1023.63i | 1.44173i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 206.804i | 0.290455i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2376.00 | 3.32308 | ||||||||
\(716\) | −313.955 | −0.438485 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −318.000 | −0.442897 | ||||||||
\(719\) | − | 1137.37i | − | 1.58187i | −0.611899 | − | 0.790936i | \(-0.709594\pi\) | ||
0.611899 | − | 0.790936i | \(-0.290406\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −528.000 | + | 367.652i | −0.732316 | + | 0.509920i | ||||
\(722\) | 323.855 | 0.448553 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 505.522i | − | 0.698234i | ||||||
\(725\) | 1391.59 | 1.91943 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 275.739i | − | 0.379283i | −0.981853 | − | 0.189642i | \(-0.939267\pi\) | ||
0.981853 | − | 0.189642i | \(-0.0607326\pi\) | |||||||
\(728\) | 373.352 | − | 259.969i | 0.512847 | − | 0.357101i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 528.000 | 0.723288 | ||||||||
\(731\) | − | 422.450i | − | 0.577907i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 206.804i | − | 0.282134i | −0.990000 | − | 0.141067i | \(-0.954947\pi\) | ||
0.990000 | − | 0.141067i | \(-0.0450533\pi\) | |||||||
\(734\) | 276.217i | 0.376318i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 120.000 | 0.163043 | ||||||||
\(737\) | −661.852 | −0.898035 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1348.00 | −1.82409 | −0.912043 | − | 0.410094i | \(-0.865496\pi\) | ||||
−0.912043 | + | 0.410094i | \(0.865496\pi\) | |||||||
\(740\) | − | 259.969i | − | 0.351310i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 96.0000 | + | 137.870i | 0.129380 | + | 0.185808i | ||||
\(743\) | −182.434 | −0.245536 | −0.122768 | − | 0.992435i | \(-0.539177\pi\) | ||||
−0.122768 | + | 0.992435i | \(0.539177\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1516.56i | 2.03566i | ||||||||
\(746\) | 749.533 | 1.00474 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 206.804i | − | 0.276476i | ||||||
\(749\) | −492.146 | − | 706.791i | −0.657071 | − | 0.943647i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 232.000 | 0.308921 | 0.154461 | − | 0.987999i | \(-0.450636\pi\) | ||||
0.154461 | + | 0.987999i | \(0.450636\pi\) | |||||||
\(752\) | − | 129.985i | − | 0.172852i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 1102.96i | − | 1.46281i | ||||||
\(755\) | 259.969i | 0.344330i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −434.000 | −0.573316 | −0.286658 | − | 0.958033i | \(-0.592544\pi\) | ||||
−0.286658 | + | 0.958033i | \(0.592544\pi\) | |||||||
\(758\) | 277.186 | 0.365681 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 264.000 | 0.347368 | ||||||||
\(761\) | 56.8683i | 0.0747283i | 0.999302 | + | 0.0373642i | \(0.0118962\pi\) | ||||
−0.999302 | + | 0.0373642i | \(0.988104\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 248.000 | + | 356.163i | 0.325033 | + | 0.466793i | ||||
\(764\) | −25.4558 | −0.0333192 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45.9565i | 0.0599954i | ||||||||
\(767\) | −746.705 | −0.973539 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 505.522i | − | 0.657375i | −0.944439 | − | 0.328688i | \(-0.893394\pi\) | ||
0.944439 | − | 0.328688i | \(-0.106606\pi\) | |||||||
\(770\) | −840.043 | + | 584.931i | −1.09096 | + | 0.759650i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −448.000 | −0.580311 | ||||||||
\(773\) | − | 8.12404i | − | 0.0105098i | −0.999986 | − | 0.00525488i | \(-0.998327\pi\) | ||
0.999986 | − | 0.00525488i | \(-0.00167269\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 259.969i | 0.335012i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −912.000 | −1.17224 | ||||||||
\(779\) | −653.367 | −0.838725 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1134.00 | −1.45198 | ||||||||
\(782\) | − | 243.721i | − | 0.311664i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −68.0000 | + | 183.826i | −0.0867347 | + | 0.234472i | ||||
\(785\) | 560.029 | 0.713412 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 919.130i | 1.16789i | 0.811793 | + | 0.583945i | \(0.198492\pi\) | ||||
−0.811793 | + | 0.583945i | \(0.801508\pi\) | |||||||
\(788\) | 610.940 | 0.775305 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 1194.87i | − | 1.51249i | ||||||
\(791\) | 475.176 | + | 682.419i | 0.600728 | + | 0.862730i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 528.000 | 0.665826 | ||||||||
\(794\) | − | 1072.37i | − | 1.35060i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 528.500i | 0.663944i | ||||||||
\(797\) | 706.791i | 0.886815i | 0.896320 | + | 0.443407i | \(0.146230\pi\) | ||||
−0.896320 | + | 0.443407i | \(0.853770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −264.000 | −0.330413 | ||||||||
\(800\) | −231.931 | −0.289914 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −48.0000 | −0.0598504 | ||||||||
\(803\) | 584.931i | 0.728432i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −990.000 | + | 689.348i | −1.22981 | + | 0.856332i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 344.674i | − | 0.426576i | ||||||
\(809\) | −899.440 | −1.11179 | −0.555896 | − | 0.831252i | \(-0.687625\pi\) | ||||
−0.555896 | + | 0.831252i | \(0.687625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1102.96i | − | 1.36000i | −0.733214 | − | 0.679998i | \(-0.761981\pi\) | ||
0.733214 | − | 0.679998i | \(-0.238019\pi\) | |||||||
\(812\) | 271.529 | + | 389.954i | 0.334395 | + | 0.480239i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 288.000 | 0.353808 | ||||||||
\(815\) | 1007.38i | 1.23605i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 597.435i | 0.731254i | ||||||||
\(818\) | 1039.88i | 1.27124i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 924.000 | 1.12683 | ||||||||
\(821\) | 186.676 | 0.227377 | 0.113688 | − | 0.993516i | \(-0.463733\pi\) | ||||
0.113688 | + | 0.993516i | \(0.463733\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −424.000 | −0.515188 | −0.257594 | − | 0.966253i | \(-0.582930\pi\) | ||||
−0.257594 | + | 0.966253i | \(0.582930\pi\) | |||||||
\(824\) | − | 259.969i | − | 0.315497i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 264.000 | − | 183.826i | 0.319613 | − | 0.222550i | ||||
\(827\) | −1073.39 | −1.29793 | −0.648965 | − | 0.760818i | \(-0.724798\pi\) | ||||
−0.648965 | + | 0.760818i | \(0.724798\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 850.195i | 1.02557i | 0.858518 | + | 0.512784i | \(0.171386\pi\) | ||||
−0.858518 | + | 0.512784i | \(0.828614\pi\) | |||||||
\(830\) | −1866.76 | −2.24911 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 183.826i | 0.220945i | ||||||||
\(833\) | 373.352 | + | 138.109i | 0.448202 | + | 0.165797i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1056.00 | −1.26467 | ||||||||
\(836\) | 292.465i | 0.349839i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 45.9565i | − | 0.0548407i | ||||||
\(839\) | − | 1299.85i | − | 1.54928i | −0.632402 | − | 0.774640i | \(-0.717931\pi\) | ||
0.632402 | − | 0.774640i | \(-0.282069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | −701.450 | −0.833076 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 248.000 | 0.293839 | ||||||||
\(845\) | 2916.53i | 3.45151i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −164.000 | − | 235.527i | −0.193625 | − | 0.278072i | ||||
\(848\) | −67.8823 | −0.0800498 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 471.054i | 0.554181i | ||||||||
\(851\) | 339.411 | 0.398838 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1401.67i | 1.64323i | 0.570044 | + | 0.821614i | \(0.306926\pi\) | ||||
−0.570044 | + | 0.821614i | \(0.693074\pi\) | |||||||
\(854\) | −186.676 | + | 129.985i | −0.218590 | + | 0.152207i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 348.000 | 0.406542 | ||||||||
\(857\) | 186.853i | 0.218031i | 0.994040 | + | 0.109016i | \(0.0347699\pi\) | ||||
−0.994040 | + | 0.109016i | \(0.965230\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 471.054i | 0.548375i | 0.961676 | + | 0.274188i | \(0.0884089\pi\) | ||||
−0.961676 | + | 0.274188i | \(0.911591\pi\) | |||||||
\(860\) | − | 844.900i | − | 0.982442i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 654.000 | 0.758701 | ||||||||
\(863\) | −1166.73 | −1.35194 | −0.675971 | − | 0.736928i | \(-0.736276\pi\) | ||||
−0.675971 | + | 0.736928i | \(0.736276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 594.000 | 0.686705 | ||||||||
\(866\) | 194.977i | 0.225147i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1323.70 | 1.52325 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1194.87i | − | 1.37184i | ||||||
\(872\) | −175.362 | −0.201104 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 344.674i | 0.394364i | ||||||||
\(875\) | 746.705 | − | 519.938i | 0.853377 | − | 0.594215i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 350.000 | 0.399088 | 0.199544 | − | 0.979889i | \(-0.436054\pi\) | ||||
0.199544 | + | 0.979889i | \(0.436054\pi\) | |||||||
\(878\) | 243.721i | 0.277587i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 413.609i | − | 0.470010i | ||||||
\(881\) | 268.093i | 0.304306i | 0.988357 | + | 0.152153i | \(0.0486206\pi\) | ||||
−0.988357 | + | 0.152153i | \(0.951379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 412.000 | 0.466591 | 0.233296 | − | 0.972406i | \(-0.425049\pi\) | ||||
0.233296 | + | 0.972406i | \(0.425049\pi\) | |||||||
\(884\) | 373.352 | 0.422344 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 558.000 | 0.629797 | ||||||||
\(887\) | 1039.88i | 1.17235i | 0.810183 | + | 0.586176i | \(0.199367\pi\) | ||||
−0.810183 | + | 0.586176i | \(0.800633\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 256.000 | + | 367.652i | 0.287964 | + | 0.413557i | ||||
\(890\) | 840.043 | 0.943868 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 344.674i | − | 0.386406i | ||||||
\(893\) | 373.352 | 0.418088 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1275.29i | 1.42491i | ||||||||
\(896\) | −45.2548 | − | 64.9923i | −0.0505076 | − | 0.0725361i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 72.0000 | 0.0801782 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 137.870i | 0.153018i | ||||||||
\(902\) | 1023.63i | 1.13484i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −336.000 | −0.371681 | ||||||||
\(905\) | −2053.44 | −2.26899 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 436.000 | 0.480706 | 0.240353 | − | 0.970686i | \(-0.422737\pi\) | ||||
0.240353 | + | 0.970686i | \(0.422737\pi\) | |||||||
\(908\) | − | 779.908i | − | 0.858929i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1056.00 | − | 1516.56i | −1.16044 | − | 1.66655i | ||||
\(911\) | −326.683 | −0.358599 | −0.179299 | − | 0.983795i | \(-0.557383\pi\) | ||||
−0.179299 | + | 0.983795i | \(0.557383\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2068.04i | − | 2.26511i | ||||||
\(914\) | 183.848 | 0.201146 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 413.609i | − | 0.451538i | ||||||
\(917\) | 560.029 | − | 389.954i | 0.610718 | − | 0.425250i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −224.000 | −0.243743 | −0.121872 | − | 0.992546i | \(-0.538890\pi\) | ||||
−0.121872 | + | 0.992546i | \(0.538890\pi\) | |||||||
\(920\) | − | 487.442i | − | 0.529829i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1022.53i | − | 1.10904i | ||||||
\(923\) | − | 2047.26i | − | 2.21805i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −656.000 | −0.709189 | ||||||||
\(926\) | 113.137 | 0.122178 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −192.000 | −0.206897 | ||||||||
\(929\) | − | 788.032i | − | 0.848258i | −0.905602 | − | 0.424129i | \(-0.860580\pi\) | ||
0.905602 | − | 0.424129i | \(-0.139420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −528.000 | − | 195.315i | −0.567132 | − | 0.209791i | ||||
\(932\) | −373.352 | −0.400593 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 275.739i | 0.295224i | ||||||||
\(935\) | −840.043 | −0.898442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 505.522i | − | 0.539511i | −0.962929 | − | 0.269755i | \(-0.913057\pi\) | ||
0.962929 | − | 0.269755i | \(-0.0869428\pi\) | |||||||
\(938\) | 294.156 | + | 422.450i | 0.313600 | + | 0.450373i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −528.000 | −0.561702 | ||||||||
\(941\) | − | 333.086i | − | 0.353970i | −0.984214 | − | 0.176985i | \(-0.943366\pi\) | ||
0.984214 | − | 0.176985i | \(-0.0566344\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1206.36i | 1.27928i | ||||||||
\(944\) | 129.985i | 0.137696i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 936.000 | 0.989429 | ||||||||
\(947\) | 46.6690 | 0.0492809 | 0.0246405 | − | 0.999696i | \(-0.492156\pi\) | ||||
0.0246405 | + | 0.999696i | \(0.492156\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1056.00 | −1.11275 | ||||||||
\(950\) | − | 666.171i | − | 0.701233i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −132.000 | + | 91.9130i | −0.138655 | + | 0.0965473i | ||||
\(953\) | −101.823 | −0.106845 | −0.0534225 | − | 0.998572i | \(-0.517013\pi\) | ||||
−0.0534225 | + | 0.998572i | \(0.517013\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 103.402i | 0.108274i | ||||||||
\(956\) | 517.602 | 0.541425 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 597.435i | 0.623627i | ||||||||
\(959\) | −135.765 | − | 194.977i | −0.141569 | − | 0.203313i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 961.000 | 1.00000 | ||||||||
\(962\) | 519.938i | 0.540477i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 91.9130i | 0.0953454i | ||||||||
\(965\) | 1819.78i | 1.88579i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −664.000 | −0.686660 | −0.343330 | − | 0.939215i | \(-0.611555\pi\) | ||||
−0.343330 | + | 0.939215i | \(0.611555\pi\) | |||||||
\(968\) | 115.966 | 0.119799 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1056.00 | 1.08866 | ||||||||
\(971\) | − | 844.900i | − | 0.870134i | −0.900398 | − | 0.435067i | \(-0.856725\pi\) | ||
0.900398 | − | 0.435067i | \(-0.143275\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1056.00 | − | 735.304i | 1.08530 | − | 0.755708i | ||||
\(974\) | 1278.45 | 1.31258 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 91.9130i | − | 0.0941732i | ||||||
\(977\) | −424.264 | −0.434252 | −0.217126 | − | 0.976144i | \(-0.569668\pi\) | ||||
−0.217126 | + | 0.976144i | \(0.569668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 930.619i | 0.950581i | ||||||||
\(980\) | 746.705 | + | 276.217i | 0.761944 | + | 0.281854i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −594.000 | −0.604888 | ||||||||
\(983\) | 1104.87i | 1.12398i | 0.827145 | + | 0.561988i | \(0.189963\pi\) | ||||
−0.827145 | + | 0.561988i | \(0.810037\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2481.65i | − | 2.51944i | ||||||
\(986\) | 389.954i | 0.395491i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −528.000 | −0.534413 | ||||||||
\(989\) | 1103.09 | 1.11536 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 592.000 | 0.597376 | 0.298688 | − | 0.954351i | \(-0.403451\pi\) | ||||
0.298688 | + | 0.954351i | \(0.403451\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 504.000 | + | 723.815i | 0.507042 | + | 0.728184i | ||||
\(995\) | 2146.78 | 2.15756 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 344.674i | − | 0.345711i | −0.984947 | − | 0.172855i | \(-0.944701\pi\) | ||
0.984947 | − | 0.172855i | \(-0.0552993\pi\) | |||||||
\(998\) | −1012.58 | −1.01461 | ||||||||
\(999\) | 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 | 126.3.c.a.55.3 | yes | 4 | |
3.2 | odd | 2 | inner | 126.3.c.a.55.2 | yes | 4 | |
4.3 | odd | 2 | 1008.3.f.i.433.2 | 4 | |||
7.2 | even | 3 | 882.3.n.i.325.1 | 8 | |||
7.3 | odd | 6 | 882.3.n.i.19.1 | 8 | |||
7.4 | even | 3 | 882.3.n.i.19.2 | 8 | |||
7.5 | odd | 6 | 882.3.n.i.325.2 | 8 | |||
7.6 | odd | 2 | inner | 126.3.c.a.55.4 | yes | 4 | |
12.11 | even | 2 | 1008.3.f.i.433.4 | 4 | |||
21.2 | odd | 6 | 882.3.n.i.325.4 | 8 | |||
21.5 | even | 6 | 882.3.n.i.325.3 | 8 | |||
21.11 | odd | 6 | 882.3.n.i.19.3 | 8 | |||
21.17 | even | 6 | 882.3.n.i.19.4 | 8 | |||
21.20 | even | 2 | inner | 126.3.c.a.55.1 | ✓ | 4 | |
28.27 | even | 2 | 1008.3.f.i.433.3 | 4 | |||
84.83 | odd | 2 | 1008.3.f.i.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.c.a.55.1 | ✓ | 4 | 21.20 | even | 2 | inner | |
126.3.c.a.55.2 | yes | 4 | 3.2 | odd | 2 | inner | |
126.3.c.a.55.3 | yes | 4 | 1.1 | even | 1 | trivial | |
126.3.c.a.55.4 | yes | 4 | 7.6 | odd | 2 | inner | |
882.3.n.i.19.1 | 8 | 7.3 | odd | 6 | |||
882.3.n.i.19.2 | 8 | 7.4 | even | 3 | |||
882.3.n.i.19.3 | 8 | 21.11 | odd | 6 | |||
882.3.n.i.19.4 | 8 | 21.17 | even | 6 | |||
882.3.n.i.325.1 | 8 | 7.2 | even | 3 | |||
882.3.n.i.325.2 | 8 | 7.5 | odd | 6 | |||
882.3.n.i.325.3 | 8 | 21.5 | even | 6 | |||
882.3.n.i.325.4 | 8 | 21.2 | odd | 6 | |||
1008.3.f.i.433.1 | 4 | 84.83 | odd | 2 | |||
1008.3.f.i.433.2 | 4 | 4.3 | odd | 2 | |||
1008.3.f.i.433.3 | 4 | 28.27 | even | 2 | |||
1008.3.f.i.433.4 | 4 | 12.11 | even | 2 |