Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(97,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, 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("224.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4694952902656.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 20x^{6} + 56x^{4} + 20x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.5 | ||
Root | \(-0.590371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.97 |
Dual form | 224.3.c.a.97.4 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.56056i | 0.520186i | 0.965584 | + | 0.260093i | \(0.0837532\pi\) | ||||
−0.965584 | + | 0.260093i | \(0.916247\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.23038i | − | 0.646076i | −0.946386 | − | 0.323038i | \(-0.895296\pi\) | ||
0.946386 | − | 0.323038i | \(-0.104704\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.38162 | − | 6.12900i | −0.483088 | − | 0.875572i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.56466 | 0.729407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.93481 | −0.357710 | −0.178855 | − | 0.983875i | \(-0.557239\pi\) | ||||
−0.178855 | + | 0.983875i | \(0.557239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 14.1051i | − | 1.08500i | −0.840054 | − | 0.542502i | \(-0.817477\pi\) | ||
0.840054 | − | 0.542502i | \(-0.182523\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.04119 | 0.336079 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 26.1633i | − | 1.53902i | −0.638637 | − | 0.769508i | \(-0.720501\pi\) | ||
0.638637 | − | 0.769508i | \(-0.279499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.6974i | 0.563023i | 0.959558 | + | 0.281512i | \(0.0908358\pi\) | ||||
−0.959558 | + | 0.281512i | \(0.909164\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.56466 | − | 5.27721i | 0.455460 | − | 0.251296i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.9054 | 0.908929 | 0.454465 | − | 0.890765i | \(-0.349831\pi\) | ||||
0.454465 | + | 0.890765i | \(0.349831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.5647 | 0.582586 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 24.2895i | 0.899613i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.1293 | 0.452735 | 0.226368 | − | 0.974042i | \(-0.427315\pi\) | ||||
0.226368 | + | 0.974042i | \(0.427315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 39.8951i | − | 1.28694i | −0.765472 | − | 0.643470i | \(-0.777494\pi\) | ||
0.765472 | − | 0.643470i | \(-0.222506\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.14050i | − | 0.186076i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −19.7990 | + | 10.9239i | −0.565685 | + | 0.312112i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.12932 | −0.0305222 | −0.0152611 | − | 0.999884i | \(-0.504858\pi\) | ||||
−0.0152611 | + | 0.999884i | \(0.504858\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 22.0118 | 0.564404 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.36709i | − | 0.0577339i | −0.999583 | − | 0.0288670i | \(-0.990810\pi\) | ||
0.999583 | − | 0.0288670i | \(-0.00918992\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −59.2720 | −1.37842 | −0.689210 | − | 0.724562i | \(-0.742042\pi\) | ||||
−0.689210 | + | 0.724562i | \(0.742042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 21.2063i | − | 0.471252i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 33.6529i | − | 0.716019i | −0.933718 | − | 0.358010i | \(-0.883456\pi\) | ||
0.933718 | − | 0.358010i | \(-0.116544\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26.1293 | + | 41.4519i | −0.533251 | + | 0.845957i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 40.8293 | 0.800575 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −30.0000 | −0.566038 | −0.283019 | − | 0.959114i | \(-0.591336\pi\) | ||||
−0.283019 | + | 0.959114i | \(0.591336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.7109i | 0.231108i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.6940 | −0.292877 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 63.3035i | 1.07294i | 0.843919 | + | 0.536470i | \(0.180243\pi\) | ||||
−0.843919 | + | 0.536470i | \(0.819757\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 103.149i | 1.69097i | 0.533997 | + | 0.845486i | \(0.320689\pi\) | ||||
−0.533997 | + | 0.845486i | \(0.679311\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −22.1992 | − | 40.2348i | −0.352368 | − | 0.638648i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −45.5647 | −0.700995 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 28.7750 | 0.429477 | 0.214739 | − | 0.976672i | \(-0.431110\pi\) | ||||
0.214739 | + | 0.976672i | \(0.431110\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 32.6240i | 0.472812i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −90.3847 | −1.27302 | −0.636512 | − | 0.771267i | \(-0.719623\pi\) | ||||
−0.636512 | + | 0.771267i | \(0.719623\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 62.5607i | 0.856996i | 0.903543 | + | 0.428498i | \(0.140957\pi\) | ||||
−0.903543 | + | 0.428498i | \(0.859043\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.7290i | 0.303053i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.3060 | + | 24.1164i | 0.172805 | + | 0.313201i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 139.084 | 1.76055 | 0.880276 | − | 0.474462i | \(-0.157357\pi\) | ||||
0.880276 | + | 0.474462i | \(0.157357\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 21.1767 | 0.261441 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 109.441i | − | 1.31856i | −0.751896 | − | 0.659282i | \(-0.770860\pi\) | ||
0.751896 | − | 0.659282i | \(-0.229140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −84.5173 | −0.994321 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.4891i | 0.235506i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.04683i | − | 0.0229981i | −0.999934 | − | 0.0114991i | \(-0.996340\pi\) | ||
0.999934 | − | 0.0114991i | \(-0.00366034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −86.4499 | + | 47.6979i | −0.949999 | + | 0.524153i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 62.2586 | 0.669448 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 34.5568 | 0.363756 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 90.7708i | 0.935782i | 0.883786 | + | 0.467891i | \(0.154986\pi\) | ||||
−0.883786 | + | 0.467891i | \(0.845014\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.8307 | −0.260916 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.91773i | 0.0585914i | 0.999571 | + | 0.0292957i | \(0.00932644\pi\) | ||||
−0.999571 | + | 0.0292957i | \(0.990674\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 101.638i | 0.986777i | 0.869809 | + | 0.493389i | \(0.164242\pi\) | ||||
−0.869809 | + | 0.493389i | \(0.835758\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −17.0474 | − | 30.8975i | −0.162356 | − | 0.294262i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 180.279 | 1.68485 | 0.842424 | − | 0.538815i | \(-0.181128\pi\) | ||||
0.842424 | + | 0.538815i | \(0.181128\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −132.259 | −1.21338 | −0.606691 | − | 0.794938i | \(-0.707503\pi\) | ||||
−0.606691 | + | 0.794938i | \(0.707503\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.76237i | − | 0.0158772i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 111.211 | 0.984170 | 0.492085 | − | 0.870547i | \(-0.336235\pi\) | ||||
0.492085 | + | 0.870547i | \(0.336235\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 67.5322i | − | 0.587237i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 92.5949i | − | 0.791409i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −160.355 | + | 88.4742i | −1.34752 | + | 0.743481i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −105.517 | −0.872044 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.69398 | 0.0300324 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 127.809i | − | 1.02247i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −110.434 | −0.869556 | −0.434778 | − | 0.900538i | \(-0.643173\pi\) | ||||
−0.434778 | + | 0.900538i | \(0.643173\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 92.4974i | − | 0.717034i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 200.357i | − | 1.52944i | −0.644362 | − | 0.764721i | \(-0.722877\pi\) | ||
0.644362 | − | 0.764721i | \(-0.277123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 65.5647 | − | 36.1747i | 0.492967 | − | 0.271990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 78.4644 | 0.581218 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 214.517 | 1.56582 | 0.782910 | − | 0.622135i | \(-0.213735\pi\) | ||||
0.782910 | + | 0.622135i | \(0.213735\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 47.6979i | − | 0.343150i | −0.985171 | − | 0.171575i | \(-0.945114\pi\) | ||
0.985171 | − | 0.171575i | \(-0.0548857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 52.5173 | 0.372463 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 55.5007i | 0.388117i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 42.4127i | − | 0.292501i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −64.6881 | − | 40.7763i | −0.440055 | − | 0.277390i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 214.517 | 1.43971 | 0.719857 | − | 0.694123i | \(-0.244208\pi\) | ||||
0.719857 | + | 0.694123i | \(0.244208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −55.8279 | −0.369721 | −0.184861 | − | 0.982765i | \(-0.559183\pi\) | ||||
−0.184861 | + | 0.982765i | \(0.559183\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 171.753i | − | 1.12257i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −128.876 | −0.831460 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 130.594i | 0.831807i | 0.909409 | + | 0.415903i | \(0.136535\pi\) | ||||
−0.909409 | + | 0.415903i | \(0.863465\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 46.8167i | − | 0.294445i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −70.6940 | − | 128.129i | −0.439093 | − | 0.795833i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 296.610 | 1.81969 | 0.909847 | − | 0.414945i | \(-0.136199\pi\) | ||||
0.909847 | + | 0.414945i | \(0.136199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19.8361 | −0.120219 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 266.102i | 1.59343i | 0.604358 | + | 0.796713i | \(0.293430\pi\) | ||||
−0.604358 | + | 0.796713i | \(0.706570\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −29.9526 | −0.177234 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 70.2251i | 0.410673i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 292.113i | − | 1.68851i | −0.535940 | − | 0.844256i | \(-0.680043\pi\) | ||
0.535940 | − | 0.844256i | \(-0.319957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −49.2521 | − | 89.2668i | −0.281441 | − | 0.510096i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −98.7887 | −0.558128 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 219.377 | 1.22557 | 0.612785 | − | 0.790250i | \(-0.290049\pi\) | ||||
0.612785 | + | 0.790250i | \(0.290049\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 173.577i | 0.958990i | 0.877545 | + | 0.479495i | \(0.159180\pi\) | ||||
−0.877545 | + | 0.479495i | \(0.840820\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −160.970 | −0.879620 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.64813i | 0.0197196i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 102.948i | 0.550521i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 148.871 | − | 82.1380i | 0.787676 | − | 0.434592i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 154.823 | 0.810591 | 0.405296 | − | 0.914186i | \(-0.367169\pi\) | ||||
0.405296 | + | 0.914186i | \(0.367169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 164.435 | 0.851997 | 0.425998 | − | 0.904724i | \(-0.359923\pi\) | ||||
0.425998 | + | 0.904724i | \(0.359923\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 71.1063i | − | 0.364648i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −58.8707 | −0.298836 | −0.149418 | − | 0.988774i | \(-0.547740\pi\) | ||||
−0.149418 | + | 0.988774i | \(0.547740\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.81626i | − | 0.0493279i | −0.999696 | − | 0.0246640i | \(-0.992148\pi\) | ||
0.999696 | − | 0.0246640i | \(-0.00785158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 44.9050i | 0.223408i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −44.3983 | − | 80.4696i | −0.218711 | − | 0.396402i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.64660 | −0.0373005 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 137.237 | 0.662979 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 42.0924i | − | 0.201399i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −167.484 | −0.793762 | −0.396881 | − | 0.917870i | \(-0.629907\pi\) | ||||
−0.396881 | + | 0.917870i | \(0.629907\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 141.051i | − | 0.662209i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 191.471i | 0.890563i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −244.517 | + | 134.910i | −1.12681 | + | 0.621705i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −97.6296 | −0.445797 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −369.035 | −1.66984 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 172.971i | − | 0.775654i | −0.921732 | − | 0.387827i | \(-0.873226\pi\) | ||
0.921732 | − | 0.387827i | \(-0.126774\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 95.6120 | 0.424942 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 358.854i | − | 1.58086i | −0.612555 | − | 0.790428i | \(-0.709858\pi\) | ||
0.612555 | − | 0.790428i | \(-0.290142\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 239.786i | 1.04710i | 0.851995 | + | 0.523550i | \(0.175393\pi\) | ||||
−0.851995 | + | 0.523550i | \(0.824607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −37.6351 | + | 20.7648i | −0.162923 | + | 0.0898910i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.4827 | −0.109368 | −0.0546839 | − | 0.998504i | \(-0.517415\pi\) | ||||
−0.0546839 | + | 0.998504i | \(0.517415\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −108.712 | −0.462602 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 217.048i | 0.915815i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −40.0887 | −0.167735 | −0.0838676 | − | 0.996477i | \(-0.526727\pi\) | ||||
−0.0838676 | + | 0.996477i | \(0.526727\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 399.356i | 1.65708i | 0.559932 | + | 0.828538i | \(0.310827\pi\) | ||||
−0.559932 | + | 0.828538i | \(0.689173\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 251.653i | 1.03561i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 133.905 | + | 84.4076i | 0.546552 | + | 0.344521i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 150.888 | 0.610883 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 170.789 | 0.685899 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 373.781i | 1.48917i | 0.667530 | + | 0.744583i | \(0.267351\pi\) | ||||
−0.667530 | + | 0.744583i | \(0.732649\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −82.2586 | −0.325133 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 131.894i | − | 0.517232i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 189.729i | 0.738245i | 0.929381 | + | 0.369123i | \(0.120342\pi\) | ||||
−0.929381 | + | 0.369123i | \(0.879658\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.81893 | + | 6.92160i | 0.0147449 | + | 0.0267243i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 86.1895 | 0.330228 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28.8909 | −0.109851 | −0.0549256 | − | 0.998490i | \(-0.517492\pi\) | ||||
−0.0549256 | + | 0.998490i | \(0.517492\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 96.9113i | 0.365703i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.19420 | 0.0119633 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 132.766i | 0.493553i | 0.969072 | + | 0.246776i | \(0.0793713\pi\) | ||||
−0.969072 | + | 0.246776i | \(0.920629\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 333.004i | − | 1.22880i | −0.788996 | − | 0.614399i | \(-0.789399\pi\) | ||
0.788996 | − | 0.614399i | \(-0.210601\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −74.4353 | − | 134.910i | −0.272657 | − | 0.494176i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −57.3092 | −0.208397 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −436.940 | −1.57740 | −0.788700 | − | 0.614778i | \(-0.789245\pi\) | ||||
−0.788700 | + | 0.614778i | \(0.789245\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 261.898i | − | 0.938702i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −154.517 | −0.549884 | −0.274942 | − | 0.961461i | \(-0.588659\pi\) | ||||
−0.274942 | + | 0.961461i | \(0.588659\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 421.907i | 1.49084i | 0.666597 | + | 0.745418i | \(0.267750\pi\) | ||||
−0.666597 | + | 0.745418i | \(0.732250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 53.9279i | 0.189221i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.5079 | + | 8.00460i | −0.0505502 | + | 0.0278906i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −395.517 | −1.36857 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −141.653 | −0.486780 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 170.639i | − | 0.582386i | −0.956664 | − | 0.291193i | \(-0.905948\pi\) | ||
0.956664 | − | 0.291193i | \(-0.0940522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 204.494 | 0.693201 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 95.5747i | − | 0.321800i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 294.871i | − | 0.986192i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 200.435 | + | 363.278i | 0.665898 | + | 1.20690i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.23496 | −0.0304784 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 333.211 | 1.09250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 261.470i | 0.851693i | 0.904795 | + | 0.425846i | \(0.140024\pi\) | ||||
−0.904795 | + | 0.425846i | \(0.859976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −158.612 | −0.513308 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.92160i | − | 0.0222560i | −0.999938 | − | 0.0111280i | \(-0.996458\pi\) | ||
0.999938 | − | 0.0111280i | \(-0.00354222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 65.0531i | − | 0.207837i | −0.994586 | − | 0.103919i | \(-0.966862\pi\) | ||
0.994586 | − | 0.103919i | \(-0.0331382\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −129.974 | + | 71.7117i | −0.412615 | + | 0.227656i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 65.6466 | 0.207087 | 0.103544 | − | 0.994625i | \(-0.466982\pi\) | ||||
0.103544 | + | 0.994625i | \(0.466982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −51.6614 | −0.161948 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 281.335i | 0.876434i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 279.880 | 0.866502 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 205.435i | − | 0.632109i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 206.397i | − | 0.631184i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −206.259 | + | 113.801i | −0.626926 | + | 0.345900i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −76.2426 | −0.230340 | −0.115170 | − | 0.993346i | \(-0.536741\pi\) | ||||
−0.115170 | + | 0.993346i | \(0.536741\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.41360 | −0.0222631 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 92.9541i | − | 0.277475i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 182.177 | 0.540584 | 0.270292 | − | 0.962778i | \(-0.412880\pi\) | ||||
0.270292 | + | 0.962778i | \(0.412880\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 173.552i | 0.511952i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 156.980i | 0.460351i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 342.418 | + | 19.9722i | 0.998303 | + | 0.0582280i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 105.388 | 0.305472 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5355 | 0.0390073 | 0.0195037 | − | 0.999810i | \(-0.493791\pi\) | ||||
0.0195037 | + | 0.999810i | \(0.493791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 350.134i | − | 1.00325i | −0.865085 | − | 0.501625i | \(-0.832736\pi\) | ||
0.865085 | − | 0.501625i | \(-0.167264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 342.605 | 0.976084 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 572.390i | − | 1.62150i | −0.585392 | − | 0.810750i | \(-0.699060\pi\) | ||
0.585392 | − | 0.810750i | \(-0.300940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 291.977i | 0.822470i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −138.069 | − | 250.243i | −0.386748 | − | 0.700960i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −458.196 | −1.27631 | −0.638156 | − | 0.769907i | \(-0.720303\pi\) | ||||
−0.638156 | + | 0.769907i | \(0.720303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 246.565 | 0.683005 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 164.666i | − | 0.453625i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 202.095 | 0.553684 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 272.394i | 0.742217i | 0.928590 | + | 0.371108i | \(0.121022\pi\) | ||||
−0.928590 | + | 0.371108i | \(0.878978\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 15.5392i | − | 0.0421115i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 101.449 | + | 183.870i | 0.273446 | + | 0.495607i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 705.974 | 1.89269 | 0.946346 | − | 0.323154i | \(-0.104743\pi\) | ||||
0.946346 | + | 0.323154i | \(0.104743\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 199.453 | 0.531875 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 185.190i | − | 0.491220i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.41603 | 0.0142903 | 0.00714516 | − | 0.999974i | \(-0.497726\pi\) | ||||
0.00714516 | + | 0.999974i | \(0.497726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 172.338i | − | 0.452331i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 127.286i | 0.332340i | 0.986097 | + | 0.166170i | \(0.0531401\pi\) | ||||
−0.986097 | + | 0.166170i | \(0.946860\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 77.9052 | − | 42.9835i | 0.202351 | − | 0.111645i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −389.101 | −1.00543 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −49.8361 | −0.128113 | −0.0640567 | − | 0.997946i | \(-0.520404\pi\) | ||||
−0.0640567 | + | 0.997946i | \(0.520404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 546.953i | − | 1.39886i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 312.668 | 0.795594 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 449.293i | − | 1.13745i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 112.172i | − | 0.282549i | −0.989970 | − | 0.141275i | \(-0.954880\pi\) | ||
0.989970 | − | 0.141275i | \(-0.0451201\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 56.4527 | + | 102.317i | 0.141485 | + | 0.256435i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −583.375 | −1.45480 | −0.727400 | − | 0.686213i | \(-0.759272\pi\) | ||||
−0.727400 | + | 0.686213i | \(0.759272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −562.723 | −1.39633 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 68.4087i | − | 0.168910i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.44366 | 0.0109181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 179.815i | − | 0.439646i | −0.975540 | − | 0.219823i | \(-0.929452\pi\) | ||
0.975540 | − | 0.219823i | \(-0.0705479\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 334.767i | 0.814517i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 387.987 | − | 214.068i | 0.939436 | − | 0.518325i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −353.535 | −0.851892 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 74.4353 | 0.178502 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 297.515i | − | 0.710060i | −0.934855 | − | 0.355030i | \(-0.884471\pi\) | ||
0.934855 | − | 0.355030i | \(-0.115529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −198.707 | −0.471988 | −0.235994 | − | 0.971755i | \(-0.575835\pi\) | ||||
−0.235994 | + | 0.971755i | \(0.575835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 220.920i | − | 0.522269i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 381.059i | − | 0.896610i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 632.202 | − | 348.812i | 1.48057 | − | 0.816889i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −86.6120 | −0.201893 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −128.136 | −0.297299 | −0.148649 | − | 0.988890i | \(-0.547493\pi\) | ||||
−0.148649 | + | 0.988890i | \(0.547493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 593.568i | − | 1.37083i | −0.728154 | − | 0.685414i | \(-0.759621\pi\) | ||
0.728154 | − | 0.685414i | \(-0.240379\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 66.1874 | 0.152155 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 223.634i | 0.511748i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 88.9764i | 0.202680i | 0.994852 | + | 0.101340i | \(0.0323130\pi\) | ||||
−0.994852 | + | 0.101340i | \(0.967687\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −171.530 | + | 272.118i | −0.388957 | + | 0.617047i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −508.626 | −1.14814 | −0.574070 | − | 0.818806i | \(-0.694636\pi\) | ||||
−0.574070 | + | 0.818806i | \(0.694636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.61204 | −0.0148585 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 334.767i | 0.748919i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2241 | 0.0517240 | 0.0258620 | − | 0.999666i | \(-0.491767\pi\) | ||||
0.0258620 | + | 0.999666i | \(0.491767\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.31405i | 0.0206520i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 87.1227i | − | 0.192324i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 154.082 | + | 279.266i | 0.338642 | + | 0.613771i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 273.306 | 0.598044 | 0.299022 | − | 0.954246i | \(-0.403340\pi\) | ||||
0.299022 | + | 0.954246i | \(0.403340\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 635.494 | 1.38452 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 141.273i | 0.306450i | 0.988191 | + | 0.153225i | \(0.0489659\pi\) | ||||
−0.988191 | + | 0.153225i | \(0.951034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5953 | 0.0380028 | 0.0190014 | − | 0.999819i | \(-0.493951\pi\) | ||||
0.0190014 | + | 0.999819i | \(0.493951\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 201.119i | − | 0.432514i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 295.073i | − | 0.631849i | −0.948784 | − | 0.315924i | \(-0.897685\pi\) | ||
0.948784 | − | 0.315924i | \(-0.102315\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −97.3060 | − | 176.362i | −0.207476 | − | 0.376038i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −203.799 | −0.432694 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 233.224 | 0.493074 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 155.805i | 0.328010i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −196.940 | −0.412872 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 785.694i | 1.64028i | 0.572163 | + | 0.820140i | \(0.306104\pi\) | ||||
−0.572163 | + | 0.820140i | \(0.693896\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9291i | 0.0331167i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 199.953 | − | 110.322i | 0.413981 | − | 0.228410i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 293.224 | 0.604586 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −503.451 | −1.03378 | −0.516890 | − | 0.856052i | \(-0.672910\pi\) | ||||
−0.516890 | + | 0.856052i | \(0.672910\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 462.877i | 0.946579i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 851.213 | 1.73363 | 0.866816 | − | 0.498628i | \(-0.166163\pi\) | ||||
0.866816 | + | 0.498628i | \(0.166163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 343.506i | − | 0.696767i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 83.4429i | 0.168571i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 305.647 | + | 553.968i | 0.614983 | + | 1.11462i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −393.990 | −0.789559 | −0.394779 | − | 0.918776i | \(-0.629179\pi\) | ||||
−0.394779 | + | 0.918776i | \(0.629179\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −415.268 | −0.828877 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 389.312i | 0.773980i | 0.922084 | + | 0.386990i | \(0.126485\pi\) | ||||
−0.922084 | + | 0.386990i | \(0.873515\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.1165 | 0.0378545 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 46.7428i | − | 0.0921948i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 519.840i | 1.02130i | 0.859790 | + | 0.510649i | \(0.170595\pi\) | ||||
−0.859790 | + | 0.510649i | \(0.829405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 383.435 | − | 211.556i | 0.750362 | − | 0.414005i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −259.836 | −0.506503 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 328.329 | 0.637533 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 132.418i | 0.256127i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 455.858 | 0.878340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 930.043i | 1.78511i | 0.450938 | + | 0.892555i | \(0.351090\pi\) | ||||
−0.450938 | + | 0.892555i | \(0.648910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1007.90i | − | 1.92715i | −0.267442 | − | 0.963574i | \(-0.586178\pi\) | ||
0.267442 | − | 0.963574i | \(-0.413822\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 139.306 | − | 76.8608i | 0.265345 | − | 0.146401i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1043.79 | −1.98062 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −91.9654 | −0.173848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 415.566i | 0.782610i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.3880 | −0.0626416 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 582.368i | − | 1.08854i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 342.350i | 0.637524i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 102.814 | − | 163.105i | 0.190749 | − | 0.302607i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −629.293 | −1.16320 | −0.581602 | − | 0.813474i | \(-0.697574\pi\) | ||||
−0.581602 | + | 0.813474i | \(0.697574\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −270.877 | −0.498853 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 427.245i | 0.783936i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 227.728 | 0.416322 | 0.208161 | − | 0.978095i | \(-0.433252\pi\) | ||||
0.208161 | + | 0.978095i | \(0.433252\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 677.140i | 1.23341i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 140.450i | 0.254901i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −470.328 | − | 852.444i | −0.850502 | − | 1.54149i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.69312 | −0.0102579 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −452.259 | −0.811954 | −0.405977 | − | 0.913883i | \(-0.633069\pi\) | ||||
−0.405977 | + | 0.913883i | \(0.633069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 836.035i | 1.49559i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −160.656 | −0.286373 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 123.008i | − | 0.218487i | −0.994015 | − | 0.109244i | \(-0.965157\pi\) | ||
0.994015 | − | 0.109244i | \(-0.0348429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 359.254i | − | 0.635848i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −71.6115 | − | 129.792i | −0.126299 | − | 0.228910i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 317.823 | 0.558565 | 0.279282 | − | 0.960209i | \(-0.409903\pi\) | ||||
0.279282 | + | 0.960209i | \(0.409903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −934.353 | −1.63635 | −0.818173 | − | 0.574972i | \(-0.805013\pi\) | ||||
−0.818173 | + | 0.574972i | \(0.805013\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 241.610i | 0.421658i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 304.480 | 0.529530 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 382.661i | 0.663190i | 0.943422 | + | 0.331595i | \(0.107587\pi\) | ||||
−0.943422 | + | 0.331595i | \(0.892413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 256.611i | 0.443197i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −670.763 | + | 370.087i | −1.15450 | + | 0.636983i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 118.044 | 0.202477 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −299.116 | −0.511310 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 962.844i | − | 1.64028i | −0.572163 | − | 0.820140i | \(-0.693896\pi\) | ||
0.572163 | − | 0.820140i | \(-0.306104\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 426.776 | 0.724577 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 91.8711i | − | 0.155450i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 136.511i | − | 0.230205i | −0.993354 | − | 0.115102i | \(-0.963280\pi\) | ||
0.993354 | − | 0.115102i | \(-0.0367196\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 285.805 | + | 518.007i | 0.480345 | + | 0.870599i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.3188 | 0.0256597 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 120.150 | 0.200585 | 0.100292 | − | 0.994958i | \(-0.468022\pi\) | ||||
0.100292 | + | 0.994958i | \(0.468022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 145.464i | 0.242037i | 0.992650 | + | 0.121019i | \(0.0386161\pi\) | ||||
−0.992650 | + | 0.121019i | \(0.961384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 188.898 | 0.313264 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 340.861i | 0.563406i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 839.885i | 1.38367i | 0.722058 | + | 0.691833i | \(0.243196\pi\) | ||||
−0.722058 | + | 0.691833i | \(0.756804\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 125.577 | − | 69.2862i | 0.206203 | − | 0.113770i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −474.676 | −0.776884 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 948.397 | 1.54714 | 0.773570 | − | 0.633711i | \(-0.218469\pi\) | ||||
0.773570 | + | 0.633711i | \(0.218469\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 11.9330i | − | 0.0194032i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1029.28 | −1.66820 | −0.834101 | − | 0.551612i | \(-0.814013\pi\) | ||||
−0.834101 | + | 0.551612i | \(0.814013\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 729.440i | − | 1.17842i | −0.807981 | − | 0.589208i | \(-0.799440\pi\) | ||
0.807981 | − | 0.589208i | \(-0.200560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 507.782i | 0.817684i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.5450 | + | 6.92160i | −0.0201365 | + | 0.0111101i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −48.7542 | −0.0780067 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 65.6876 | 0.104765 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.5467i | 0.0469741i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 528.907 | 0.838204 | 0.419102 | − | 0.907939i | \(-0.362345\pi\) | ||||
0.419102 | + | 0.907939i | \(0.362345\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 261.368i | − | 0.412904i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 356.742i | 0.561799i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 584.681 | + | 368.556i | 0.917867 | + | 0.578580i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −593.345 | −0.928552 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −191.047 | −0.298046 | −0.149023 | − | 0.988834i | \(-0.547613\pi\) | ||||
−0.149023 | + | 0.988834i | \(0.547613\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 113.192i | 0.176037i | 0.996119 | + | 0.0880187i | \(0.0280535\pi\) | ||||
−0.996119 | + | 0.0880187i | \(0.971946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −298.802 | −0.463258 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.5293i | 0.0178197i | 0.999960 | + | 0.00890984i | \(0.00283613\pi\) | ||||
−0.999960 | + | 0.00890984i | \(0.997164\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 249.087i | − | 0.383801i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −210.535 | − | 381.583i | −0.323402 | − | 0.586149i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −714.845 | −1.09471 | −0.547355 | − | 0.836901i | \(-0.684365\pi\) | ||||
−0.547355 | + | 0.836901i | \(0.684365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −647.228 | −0.988135 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 410.690i | 0.625099i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.7379 | 0.0466432 | 0.0233216 | − | 0.999728i | \(-0.492576\pi\) | ||||
0.0233216 | + | 0.999728i | \(0.492576\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 177.796i | − | 0.268980i | −0.990915 | − | 0.134490i | \(-0.957060\pi\) | ||
0.990915 | − | 0.134490i | \(-0.0429397\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 575.900i | − | 0.868627i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −116.858 | − | 211.799i | −0.175726 | − | 0.318494i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 274.473 | 0.411504 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 269.931 | 0.403484 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 405.873i | − | 0.604878i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 899.362 | 1.33635 | 0.668174 | − | 0.744005i | \(-0.267076\pi\) | ||||
0.668174 | + | 0.744005i | \(0.267076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 353.769i | 0.524102i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 639.977i | − | 0.945313i | −0.881247 | − | 0.472657i | \(-0.843295\pi\) | ||
0.881247 | − | 0.472657i | \(-0.156705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 556.335 | − | 306.952i | 0.819344 | − | 0.452065i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 560.013 | 0.822339 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 459.196 | 0.672322 | 0.336161 | − | 0.941805i | \(-0.390871\pi\) | ||||
0.336161 | + | 0.941805i | \(0.390871\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 692.972i | − | 1.01164i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −374.200 | −0.544687 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 423.152i | 0.614153i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 795.387i | 1.15107i | 0.817778 | + | 0.575533i | \(0.195205\pi\) | ||||
−0.817778 | + | 0.575533i | \(0.804795\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 87.3495 | + | 158.316i | 0.126045 | + | 0.228451i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −154.082 | −0.221701 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −61.9309 | −0.0888535 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 39.7673i | − | 0.0568916i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 645.810 | 0.921270 | 0.460635 | − | 0.887590i | \(-0.347622\pi\) | ||||
0.460635 | + | 0.887590i | \(0.347622\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.0808i | − | 0.0171847i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 169.651i | − | 0.240639i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.2698 | − | 20.0115i | 0.0513009 | − | 0.0283048i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 418.000 | 0.589563 | 0.294781 | − | 0.955565i | \(-0.404753\pi\) | ||||
0.294781 | + | 0.955565i | \(0.404753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 913.037 | 1.28416 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 834.022i | − | 1.16974i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 179.288 | 0.250753 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 62.5607i | − | 0.0872534i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 258.373i | − | 0.359351i | −0.983726 | − | 0.179675i | \(-0.942495\pi\) | ||
0.983726 | − | 0.179675i | \(-0.0575047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 622.940 | − | 343.701i | 0.863994 | − | 0.476701i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −623.217 | −0.861988 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 191.224 | 0.263757 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 345.892i | − | 0.475780i | −0.971292 | − | 0.237890i | \(-0.923544\pi\) | ||
0.971292 | − | 0.237890i | \(-0.0764558\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −202.129 | −0.277269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1550.75i | 2.12141i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1100.86i | − | 1.50186i | −0.660382 | − | 0.750930i | \(-0.729606\pi\) | ||
0.660382 | − | 0.750930i | \(-0.270394\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −131.723 | + | 208.967i | −0.179215 | + | 0.284309i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −113.224 | −0.153628 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −538.142 | −0.728203 | −0.364101 | − | 0.931359i | \(-0.618624\pi\) | ||||
−0.364101 | + | 0.931359i | \(0.618624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 235.470i | 0.317773i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −73.5300 | −0.0989637 | −0.0494819 | − | 0.998775i | \(-0.515757\pi\) | ||||
−0.0494819 | + | 0.998775i | \(0.515757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 692.972i | − | 0.930164i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 718.442i | − | 0.961770i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −609.634 | − | 1104.93i | −0.813930 | − | 1.47521i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1198.49 | 1.59586 | 0.797932 | − | 0.602747i | \(-0.205927\pi\) | ||||
0.797932 | + | 0.602747i | \(0.205927\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −583.306 | −0.774643 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 180.345i | 0.238868i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −172.259 | −0.227554 | −0.113777 | − | 0.993506i | \(-0.536295\pi\) | ||||
−0.113777 | + | 0.993506i | \(0.536295\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 128.369i | − | 0.169130i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 899.967i | 1.18261i | 0.806448 | + | 0.591305i | \(0.201387\pi\) | ||||
−0.806448 | + | 0.591305i | \(0.798613\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 447.248 | + | 810.613i | 0.586171 | + | 1.06240i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −554.827 | −0.725264 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 892.899 | 1.16415 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1170.05i | − | 1.52152i | −0.649031 | − | 0.760762i | \(-0.724826\pi\) | ||
0.649031 | − | 0.760762i | \(-0.275174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −296.083 | −0.384025 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 684.116i | − | 0.885014i | −0.896765 | − | 0.442507i | \(-0.854089\pi\) | ||
0.896765 | − | 0.442507i | \(-0.145911\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 581.059i | − | 0.749753i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.8016 | + | 5.95966i | −0.0139016 | + | 0.00767009i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.3218 | 0.0325056 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 355.647 | 0.455373 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 318.905i | 0.407286i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 421.867 | 0.537410 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 709.630i | 0.901690i | 0.892602 | + | 0.450845i | \(0.148877\pi\) | ||||
−0.892602 | + | 0.450845i | \(0.851123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 45.0859i | − | 0.0571430i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −376.074 | − | 681.614i | −0.475441 | − | 0.861712i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1454.93 | 1.83471 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −151.236 | −0.190234 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1173.92i | 1.47293i | 0.676478 | + | 0.736463i | \(0.263506\pi\) | ||||
−0.676478 | + | 0.736463i | \(0.736494\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −880.470 | −1.10197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13.4368i | − | 0.0167750i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 246.164i | − | 0.306556i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −413.905 | + | 228.368i | −0.514168 | + | 0.283687i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −207.189 | −0.256739 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −123.211 | −0.152301 | −0.0761503 | − | 0.997096i | \(-0.524263\pi\) | ||||
−0.0761503 | + | 0.997096i | \(0.524263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 295.753i | − | 0.364676i | −0.983236 | − | 0.182338i | \(-0.941633\pi\) | ||
0.983236 | − | 0.182338i | \(-0.0583666\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 519.672 | 0.639203 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 958.162i | − | 1.17566i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 634.059i | − | 0.776082i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −567.514 | + | 313.121i | −0.692936 | + | 0.382321i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 692.750 | 0.843788 | 0.421894 | − | 0.906645i | \(-0.361365\pi\) | ||||
0.421894 | + | 0.906645i | \(0.361365\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −631.980 | −0.767897 | −0.383949 | − | 0.923354i | \(-0.625436\pi\) | ||||
−0.383949 | + | 0.923354i | \(0.625436\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 89.4342i | − | 0.108405i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1074.28 | −1.29900 | −0.649501 | − | 0.760360i | \(-0.725022\pi\) | ||||
−0.649501 | + | 0.760360i | \(0.725022\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 474.866i | − | 0.572817i | −0.958108 | − | 0.286409i | \(-0.907539\pi\) | ||
0.958108 | − | 0.286409i | \(-0.0924615\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 681.870i | − | 0.820541i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1084.52 | + | 683.629i | 1.30194 | + | 0.820683i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 859.610 | 1.02947 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 969.035 | 1.15775 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 137.181i | − | 0.163506i | −0.996653 | − | 0.0817528i | \(-0.973948\pi\) | ||
0.996653 | − | 0.0817528i | \(-0.0260518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −668.621 | −0.795031 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 241.133i | − | 0.286042i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 96.7583i | 0.114507i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 356.819 | + | 646.716i | 0.421274 | + | 0.763537i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −658.410 | −0.775512 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.6089 | −0.0277425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 586.940i | − | 0.688089i | −0.938953 | − | 0.344045i | \(-0.888203\pi\) | ||
0.938953 | − | 0.344045i | \(-0.111797\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 226.854 | 0.265326 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 861.341i | − | 1.00507i | −0.864558 | − | 0.502533i | \(-0.832402\pi\) | ||
0.864558 | − | 0.502533i | \(-0.167598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 253.465i | 0.295070i | 0.989057 | + | 0.147535i | \(0.0471339\pi\) | ||||
−0.989057 | + | 0.147535i | \(0.952866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.4916 | − | 22.6404i | −0.0145083 | − | 0.0262955i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 600.447 | 0.695767 | 0.347883 | − | 0.937538i | \(-0.386901\pi\) | ||||
0.347883 | + | 0.937538i | \(0.386901\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −943.634 | −1.09091 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 617.227i | − | 0.711912i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −547.268 | −0.629767 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 405.873i | − | 0.465985i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 595.880i | 0.682565i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −783.340 | + | 432.201i | −0.895246 | + | 0.493943i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1156.61 | −1.31883 | −0.659414 | − | 0.751780i | \(-0.729196\pi\) | ||||
−0.659414 | + | 0.751780i | \(0.729196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 266.292 | 0.302949 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 57.7013i | − | 0.0654952i | −0.999464 | − | 0.0327476i | \(-0.989574\pi\) | ||
0.999464 | − | 0.0327476i | \(-0.0104257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −590.053 | −0.668237 | −0.334118 | − | 0.942531i | \(-0.608439\pi\) | ||||
−0.334118 | + | 0.942531i | \(0.608439\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 319.125i | 0.360593i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1077.85i | 1.21516i | 0.794258 | + | 0.607580i | \(0.207860\pi\) | ||||
−0.794258 | + | 0.607580i | \(0.792140\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 373.444 | + | 676.848i | 0.420072 | + | 0.761359i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −83.3263 | −0.0935199 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 360.000 | 0.403135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 708.670i | − | 0.791810i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 460.164 | 0.513003 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 523.796i | − | 0.582643i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 784.898i | 0.871141i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −566.917 | + | 312.791i | −0.627815 | + | 0.346391i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 560.720 | 0.619580 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 132.793 | 0.146409 | 0.0732045 | − | 0.997317i | \(-0.476677\pi\) | ||||
0.0732045 | + | 0.997317i | \(0.476677\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.8479i | 0.0427369i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1173.87 | 1.28855 | 0.644274 | − | 0.764794i | \(-0.277160\pi\) | ||||
0.644274 | + | 0.764794i | \(0.277160\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 430.629i | 0.471664i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 519.995i | 0.568301i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1227.99 | + | 677.530i | −1.33914 | + | 0.738855i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1166.90 | 1.26975 | 0.634875 | − | 0.772615i | \(-0.281052\pi\) | ||||
0.634875 | + | 0.772615i | \(0.281052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −408.038 | −0.443039 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1274.88i | 1.38124i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4482 | −0.0177818 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 667.219i | 0.719762i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 679.675i | 0.731619i | 0.930690 | + | 0.365810i | \(0.119208\pi\) | ||||
−0.930690 | + | 0.365810i | \(0.880792\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −443.429 | − | 279.517i | −0.476294 | − | 0.300233i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.8016 | 0.0115772 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 332.559 | 0.355678 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1411.66i | 1.50658i | 0.657691 | + | 0.753288i | \(0.271533\pi\) | ||||
−0.657691 | + | 0.753288i | \(0.728467\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 101.519 | 0.108114 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 607.408i | 0.645493i | 0.946486 | + | 0.322746i | \(0.104606\pi\) | ||||
−0.946486 | + | 0.322746i | \(0.895394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 49.4849i | − | 0.0524761i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −265.337 | − | 480.909i | −0.280780 | − | 0.508898i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 954.000 | 1.00739 | 0.503696 | − | 0.863881i | \(-0.331973\pi\) | ||||
0.503696 | + | 0.863881i | \(0.331973\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 882.423 | 0.929845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 102.445i | 0.107724i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1105.48 | −1.16000 | −0.580001 | − | 0.814615i | \(-0.696948\pi\) | ||||
−0.580001 | + | 0.814615i | \(0.696948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 500.136i | − | 0.523703i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 80.6205i | − | 0.0842430i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −725.415 | − | 1314.78i | −0.756429 | − | 1.37099i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −630.621 | −0.656213 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1183.47 | 1.22894 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 531.188i | − | 0.550454i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1508.91 | −1.56040 | −0.780201 | − | 0.625529i | \(-0.784883\pi\) | ||||
−0.780201 | + | 0.625529i | \(0.784883\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 436.769i | 0.450742i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1059.05i | 1.09068i | 0.838216 | + | 0.545338i | \(0.183599\pi\) | ||||
−0.838216 | + | 0.545338i | \(0.816401\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −292.341 | + | 161.296i | −0.300453 | + | 0.165772i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 320.594 | 0.328814 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1164.21 | −1.19161 | −0.595807 | − | 0.803127i | \(-0.703168\pi\) | ||||
−0.595807 | + | 0.803127i | \(0.703168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.05389i | 0.00822665i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −868.233 | −0.885049 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 674.013i | 0.685669i | 0.939396 | + | 0.342835i | \(0.111387\pi\) | ||||
−0.939396 | + | 0.342835i | \(0.888613\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 190.175i | 0.193071i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −177.593 | − | 321.878i | −0.179932 | − | 0.326118i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1239.10 | −1.25289 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1482.70 | −1.49617 | −0.748084 | − | 0.663604i | \(-0.769026\pi\) | ||||
−0.748084 | + | 0.663604i | \(0.769026\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 118.981i | − | 0.119820i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.7102 | −0.0318696 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 102.564i | 0.102873i | 0.998676 | + | 0.0514365i | \(0.0163800\pi\) | ||||
−0.998676 | + | 0.0514365i | \(0.983620\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 27.4307i | − | 0.0274581i |
(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 | 224.3.c.a.97.5 | yes | 8 | |
3.2 | odd | 2 | 2016.3.f.c.1441.5 | 8 | |||
4.3 | odd | 2 | inner | 224.3.c.a.97.3 | ✓ | 8 | |
7.6 | odd | 2 | inner | 224.3.c.a.97.4 | yes | 8 | |
8.3 | odd | 2 | 448.3.c.g.321.6 | 8 | |||
8.5 | even | 2 | 448.3.c.g.321.4 | 8 | |||
12.11 | even | 2 | 2016.3.f.c.1441.6 | 8 | |||
21.20 | even | 2 | 2016.3.f.c.1441.3 | 8 | |||
28.27 | even | 2 | inner | 224.3.c.a.97.6 | yes | 8 | |
56.13 | odd | 2 | 448.3.c.g.321.5 | 8 | |||
56.27 | even | 2 | 448.3.c.g.321.3 | 8 | |||
84.83 | odd | 2 | 2016.3.f.c.1441.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.c.a.97.3 | ✓ | 8 | 4.3 | odd | 2 | inner | |
224.3.c.a.97.4 | yes | 8 | 7.6 | odd | 2 | inner | |
224.3.c.a.97.5 | yes | 8 | 1.1 | even | 1 | trivial | |
224.3.c.a.97.6 | yes | 8 | 28.27 | even | 2 | inner | |
448.3.c.g.321.3 | 8 | 56.27 | even | 2 | |||
448.3.c.g.321.4 | 8 | 8.5 | even | 2 | |||
448.3.c.g.321.5 | 8 | 56.13 | odd | 2 | |||
448.3.c.g.321.6 | 8 | 8.3 | odd | 2 | |||
2016.3.f.c.1441.3 | 8 | 21.20 | even | 2 | |||
2016.3.f.c.1441.4 | 8 | 84.83 | odd | 2 | |||
2016.3.f.c.1441.5 | 8 | 3.2 | odd | 2 | |||
2016.3.f.c.1441.6 | 8 | 12.11 | even | 2 |