Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(145,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cg (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.145 |
Dual form | 1008.3.cg.l.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.74264 | − | 1.58346i | −0.548528 | − | 0.316693i | 0.200000 | − | 0.979796i | \(-0.435906\pi\) |
−0.748528 | + | 0.663103i | \(0.769239\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.24264 | + | 6.63103i | 0.320377 | + | 0.947290i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.62132 | + | 11.4685i | 0.601938 | + | 1.04259i | 0.992527 | + | 0.122022i | \(0.0389380\pi\) |
−0.390589 | + | 0.920565i | \(0.627729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.49333i | − | 0.422563i | −0.977425 | − | 0.211282i | \(-0.932236\pi\) | ||
0.977425 | − | 0.211282i | \(-0.0677638\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.7426 | − | 6.77962i | 0.690744 | − | 0.398801i | −0.113147 | − | 0.993578i | \(-0.536093\pi\) |
0.803891 | + | 0.594777i | \(0.202760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.621320 | + | 0.358719i | 0.0327011 | + | 0.0188800i | 0.516261 | − | 0.856431i | \(-0.327323\pi\) |
−0.483560 | + | 0.875311i | \(0.660657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.13604 | − | 1.96768i | 0.0493930 | − | 0.0855512i | −0.840272 | − | 0.542165i | \(-0.817605\pi\) |
0.889665 | + | 0.456614i | \(0.150938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.48528 | − | 12.9649i | −0.299411 | − | 0.518596i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −20.4853 | −0.706389 | −0.353195 | − | 0.935550i | \(-0.614905\pi\) | ||||
−0.353195 | + | 0.935550i | \(0.614905\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −21.3198 | + | 12.3090i | −0.687736 | + | 0.397064i | −0.802763 | − | 0.596298i | \(-0.796638\pi\) |
0.115028 | + | 0.993362i | \(0.463304\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.34924 | − | 21.7377i | 0.124264 | − | 0.621076i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.4706 | + | 56.2407i | −0.877583 | + | 1.52002i | −0.0235970 | + | 0.999722i | \(0.507512\pi\) |
−0.853986 | + | 0.520296i | \(0.825821\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.0308i | 0.512946i | 0.966551 | + | 0.256473i | \(0.0825605\pi\) | ||||
−0.966551 | + | 0.256473i | \(0.917439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.48528 | −0.150820 | −0.0754102 | − | 0.997153i | \(-0.524027\pi\) | ||||
−0.0754102 | + | 0.997153i | \(0.524027\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 41.3787 | + | 23.8900i | 0.880397 | + | 0.508298i | 0.870789 | − | 0.491656i | \(-0.163608\pi\) |
0.00960801 | + | 0.999954i | \(0.496942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −38.9411 | + | 29.7420i | −0.794717 | + | 0.606980i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.0147 | + | 19.0781i | 0.207825 | + | 0.359963i | 0.951029 | − | 0.309101i | \(-0.100028\pi\) |
−0.743204 | + | 0.669065i | \(0.766695\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 41.9385i | − | 0.762518i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −72.5330 | + | 41.8770i | −1.22937 | + | 0.709779i | −0.966899 | − | 0.255160i | \(-0.917872\pi\) |
−0.262474 | + | 0.964939i | \(0.584538\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.3823 | + | 33.1297i | 0.940693 | + | 0.543109i | 0.890177 | − | 0.455614i | \(-0.150580\pi\) |
0.0505153 | + | 0.998723i | \(0.483914\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.69848 | + | 15.0662i | −0.133823 | + | 0.231788i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 46.3198 | + | 80.2283i | 0.691340 | + | 1.19744i | 0.971399 | + | 0.237454i | \(0.0763128\pi\) |
−0.280058 | + | 0.959983i | \(0.590354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −48.4264 | −0.682062 | −0.341031 | − | 0.940052i | \(-0.610776\pi\) | ||||
−0.341031 | + | 0.940052i | \(0.610776\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 113.441 | − | 65.4953i | 1.55399 | − | 0.897195i | 0.556177 | − | 0.831064i | \(-0.312268\pi\) |
0.997811 | − | 0.0661316i | \(-0.0210657\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −61.1985 | + | 69.6258i | −0.794786 | + | 0.904231i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −38.1066 | + | 66.0026i | −0.482362 | + | 0.835476i | −0.999795 | − | 0.0202482i | \(-0.993554\pi\) |
0.517433 | + | 0.855724i | \(0.326888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 107.981i | 1.30098i | 0.759514 | + | 0.650491i | \(0.225437\pi\) | ||||
−0.759514 | + | 0.650491i | \(0.774563\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −42.9411 | −0.505190 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 145.412 | + | 83.9535i | 1.63384 | + | 0.943297i | 0.982894 | + | 0.184173i | \(0.0589606\pi\) |
0.650945 | + | 0.759125i | \(0.274373\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 36.4264 | − | 12.3196i | 0.400290 | − | 0.135380i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.13604 | − | 1.96768i | −0.0119583 | − | 0.0207124i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 25.5816i | 0.263728i | 0.991268 | + | 0.131864i | \(0.0420962\pi\) | ||||
−0.991268 | + | 0.131864i | \(0.957904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −24.6838 | + | 14.2512i | −0.244394 | + | 0.141101i | −0.617194 | − | 0.786811i | \(-0.711731\pi\) |
0.372801 | + | 0.927911i | \(0.378397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −48.9228 | − | 28.2456i | −0.474979 | − | 0.274229i | 0.243343 | − | 0.969940i | \(-0.421756\pi\) |
−0.718322 | + | 0.695711i | \(0.755089\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −23.8051 | + | 41.2316i | −0.222477 | + | 0.385342i | −0.955560 | − | 0.294798i | \(-0.904748\pi\) |
0.733082 | + | 0.680140i | \(0.238081\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −37.6543 | − | 65.2192i | −0.345453 | − | 0.598341i | 0.639983 | − | 0.768389i | \(-0.278941\pi\) |
−0.985436 | + | 0.170047i | \(0.945608\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −85.4558 | −0.756246 | −0.378123 | − | 0.925755i | \(-0.623430\pi\) | ||||
−0.378123 | + | 0.925755i | \(0.623430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.23149 | + | 3.59775i | −0.0541869 | + | 0.0312848i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 71.2904 | + | 62.6616i | 0.599079 | + | 0.526568i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27.1838 | + | 47.0837i | −0.224659 | + | 0.389121i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 126.584i | 1.01267i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 60.6619 | 0.477653 | 0.238826 | − | 0.971062i | \(-0.423237\pi\) | ||||
0.238826 | + | 0.971062i | \(0.423237\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −115.136 | − | 66.4738i | −0.878901 | − | 0.507434i | −0.00860515 | − | 0.999963i | \(-0.502739\pi\) |
−0.870296 | + | 0.492529i | \(0.836072\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.985281 | + | 4.92447i | −0.00740813 | + | 0.0370261i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −58.7132 | − | 101.694i | −0.428564 | − | 0.742294i | 0.568182 | − | 0.822903i | \(-0.307647\pi\) |
−0.996746 | + | 0.0806089i | \(0.974314\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 68.5857i | − | 0.493422i | −0.969089 | − | 0.246711i | \(-0.920650\pi\) | ||
0.969089 | − | 0.246711i | \(-0.0793499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 63.0000 | − | 36.3731i | 0.440559 | − | 0.254357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 56.1838 | + | 32.4377i | 0.387474 | + | 0.223708i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.1985 | + | 22.8604i | −0.0885804 | + | 0.153426i | −0.906911 | − | 0.421322i | \(-0.861566\pi\) |
0.818331 | + | 0.574747i | \(0.194900\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −67.1066 | − | 116.232i | −0.444415 | − | 0.769749i | 0.553597 | − | 0.832785i | \(-0.313255\pi\) |
−0.998011 | + | 0.0630363i | \(0.979922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 77.9634 | 0.502990 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −196.323 | + | 113.347i | −1.25047 | + | 0.721958i | −0.971202 | − | 0.238256i | \(-0.923424\pi\) |
−0.279265 | + | 0.960214i | \(0.590091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.5955 | + | 3.12032i | 0.0968662 | + | 0.0193808i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −45.9889 | + | 79.6550i | −0.282140 | + | 0.488681i | −0.971912 | − | 0.235346i | \(-0.924378\pi\) |
0.689771 | + | 0.724027i | \(0.257711\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 203.482i | 1.21845i | 0.792996 | + | 0.609227i | \(0.208520\pi\) | ||||
−0.792996 | + | 0.609227i | \(0.791480\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 138.823 | 0.821440 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −61.3234 | − | 35.4051i | −0.354470 | − | 0.204654i | 0.312182 | − | 0.950022i | \(-0.398940\pi\) |
−0.666652 | + | 0.745369i | \(0.732273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 69.1838 | − | 78.7107i | 0.395336 | − | 0.449775i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −54.4081 | − | 94.2376i | −0.303956 | − | 0.526467i | 0.673072 | − | 0.739577i | \(-0.264974\pi\) |
−0.977028 | + | 0.213109i | \(0.931641\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 99.6607i | − | 0.550611i | −0.961357 | − | 0.275306i | \(-0.911221\pi\) | ||
0.961357 | − | 0.275306i | \(-0.0887791\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 178.110 | − | 102.832i | 0.962758 | − | 0.555848i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 155.504 | + | 89.7800i | 0.831570 | + | 0.480107i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −34.9523 | + | 60.5391i | −0.182996 | + | 0.316959i | −0.942899 | − | 0.333077i | \(-0.891913\pi\) |
0.759903 | + | 0.650036i | \(0.225246\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.1690 | + | 28.0056i | 0.0837774 | + | 0.145107i | 0.904870 | − | 0.425689i | \(-0.139968\pi\) |
−0.821092 | + | 0.570796i | \(0.806635\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −277.103 | −1.40661 | −0.703306 | − | 0.710887i | \(-0.748294\pi\) | ||||
−0.703306 | + | 0.710887i | \(0.748294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −145.011 | + | 83.7222i | −0.728699 | + | 0.420715i | −0.817946 | − | 0.575295i | \(-0.804887\pi\) |
0.0892469 | + | 0.996010i | \(0.471554\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −45.9411 | − | 135.839i | −0.226311 | − | 0.669155i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33.3015 | − | 57.6799i | 0.162446 | − | 0.281365i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.50079i | 0.0454583i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 128.073 | 0.606982 | 0.303491 | − | 0.952834i | \(-0.401848\pi\) | ||||
0.303491 | + | 0.952834i | \(0.401848\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.7868 | + | 10.2692i | 0.0827293 | + | 0.0477638i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −129.434 | − | 113.768i | −0.596470 | − | 0.524275i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37.2426 | − | 64.5061i | −0.168519 | − | 0.291883i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 417.169i | 1.87071i | 0.353705 | + | 0.935357i | \(0.384922\pi\) | ||||
−0.353705 | + | 0.935357i | \(0.615078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 201.143 | − | 116.130i | 0.886093 | − | 0.511586i | 0.0134307 | − | 0.999910i | \(-0.495725\pi\) |
0.872663 | + | 0.488324i | \(0.162391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −72.4188 | − | 41.8110i | −0.316239 | − | 0.182581i | 0.333476 | − | 0.942759i | \(-0.391778\pi\) |
−0.649715 | + | 0.760178i | \(0.725112\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 109.537 | − | 189.723i | 0.470114 | − | 0.814261i | −0.529302 | − | 0.848434i | \(-0.677546\pi\) |
0.999416 | + | 0.0341721i | \(0.0108794\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −75.6579 | − | 131.043i | −0.321949 | − | 0.557631i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 193.103 | 0.807961 | 0.403980 | − | 0.914768i | \(-0.367626\pi\) | ||||
0.403980 | + | 0.914768i | \(0.367626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 42.8970 | − | 24.7666i | 0.177996 | − | 0.102766i | −0.408355 | − | 0.912823i | \(-0.633897\pi\) |
0.586351 | + | 0.810057i | \(0.300564\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 153.897 | − | 19.9098i | 0.628151 | − | 0.0812646i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.97056 | − | 3.41311i | 0.00797799 | − | 0.0138183i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 162.524i | 0.647507i | 0.946141 | + | 0.323754i | \(0.104945\pi\) | ||||
−0.946141 | + | 0.323754i | \(0.895055\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0883 | 0.118926 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 85.8747 | + | 49.5798i | 0.334143 | + | 0.192917i | 0.657679 | − | 0.753298i | \(-0.271538\pi\) |
−0.323536 | + | 0.946216i | \(0.604872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −445.753 | − | 89.1857i | −1.72106 | − | 0.344346i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −217.173 | − | 376.154i | −0.825751 | − | 1.43024i | −0.901344 | − | 0.433105i | \(-0.857418\pi\) |
0.0755923 | − | 0.997139i | \(-0.475915\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 69.7657i | − | 0.263267i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 79.1619 | − | 45.7041i | 0.294282 | − | 0.169904i | −0.345589 | − | 0.938386i | \(-0.612321\pi\) |
0.639871 | + | 0.768482i | \(0.278988\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.8051 | − | 8.54772i | −0.0546313 | − | 0.0315414i | 0.472436 | − | 0.881365i | \(-0.343375\pi\) |
−0.527067 | + | 0.849824i | \(0.676708\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 99.1249 | − | 171.689i | 0.360454 | − | 0.624325i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 200.206 | + | 346.766i | 0.722764 | + | 1.25186i | 0.959888 | + | 0.280385i | \(0.0904620\pi\) |
−0.237124 | + | 0.971479i | \(0.576205\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 538.690 | 1.91705 | 0.958524 | − | 0.285012i | \(-0.0919976\pi\) | ||||
0.958524 | + | 0.285012i | \(0.0919976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 267.783 | − | 154.604i | 0.946229 | − | 0.546306i | 0.0543215 | − | 0.998523i | \(-0.482700\pi\) |
0.891907 | + | 0.452218i | \(0.149367\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −139.456 | + | 47.1645i | −0.485909 | + | 0.164336i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −52.5736 | + | 91.0601i | −0.181916 | + | 0.315087i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 327.391i | − | 1.11738i | −0.829378 | − | 0.558688i | \(-0.811305\pi\) | ||
0.829378 | − | 0.558688i | \(-0.188695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 265.243 | 0.899128 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.8091 | − | 6.24063i | −0.0361508 | − | 0.0208717i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.5442 | − | 43.0041i | −0.0483195 | − | 0.142871i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −104.919 | − | 181.725i | −0.343998 | − | 0.595821i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 256.140i | − | 0.834331i | −0.908831 | − | 0.417165i | \(-0.863024\pi\) | ||
0.908831 | − | 0.417165i | \(-0.136976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 187.349 | − | 108.166i | 0.602409 | − | 0.347801i | −0.167580 | − | 0.985859i | \(-0.553595\pi\) |
0.769989 | + | 0.638057i | \(0.220262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 135.809 | + | 78.4092i | 0.433893 | + | 0.250509i | 0.701004 | − | 0.713157i | \(-0.252736\pi\) |
−0.267110 | + | 0.963666i | \(0.586069\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −224.015 | + | 388.005i | −0.706671 | + | 1.22399i | 0.259414 | + | 0.965766i | \(0.416471\pi\) |
−0.966085 | + | 0.258224i | \(0.916863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −135.640 | − | 234.935i | −0.425203 | − | 0.736472i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.72792 | 0.0301174 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −71.2203 | + | 41.1191i | −0.219140 | + | 0.126520i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −65.6177 | + | 327.960i | −0.199446 | + | 0.996839i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.5036 | + | 47.6376i | −0.0830924 | + | 0.143920i | −0.904577 | − | 0.426311i | \(-0.859813\pi\) |
0.821484 | + | 0.570231i | \(0.193146\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 293.383i | − | 0.875770i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −111.632 | −0.331254 | −0.165627 | − | 0.986189i | \(-0.552965\pi\) | ||||
−0.165627 | + | 0.986189i | \(0.552965\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −282.331 | − | 163.004i | −0.827949 | − | 0.478016i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −284.551 | − | 191.519i | −0.829596 | − | 0.558365i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −188.628 | − | 326.714i | −0.543598 | − | 0.941539i | −0.998694 | − | 0.0510967i | \(-0.983728\pi\) |
0.455096 | − | 0.890442i | \(-0.349605\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 204.034i | − | 0.584624i | −0.956323 | − | 0.292312i | \(-0.905575\pi\) | ||
0.956323 | − | 0.292312i | \(-0.0944246\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 361.198 | − | 208.538i | 1.02323 | − | 0.590759i | 0.108189 | − | 0.994130i | \(-0.465495\pi\) |
0.915036 | + | 0.403371i | \(0.132162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 132.816 | + | 76.6815i | 0.374130 | + | 0.216004i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 89.4153 | − | 154.872i | 0.249068 | − | 0.431398i | −0.714200 | − | 0.699942i | \(-0.753209\pi\) |
0.963267 | + | 0.268544i | \(0.0865425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −180.243 | − | 312.189i | −0.499287 | − | 0.864791i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −414.838 | −1.13654 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 544.724 | − | 314.497i | 1.48426 | − | 0.856939i | 0.484422 | − | 0.874835i | \(-0.339030\pi\) |
0.999840 | + | 0.0178960i | \(0.00569679\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −101.805 | + | 115.824i | −0.274407 | + | 0.312194i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 127.779 | − | 221.320i | 0.342572 | − | 0.593351i | −0.642338 | − | 0.766422i | \(-0.722035\pi\) |
0.984910 | + | 0.173070i | \(0.0553687\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 112.532i | 0.298494i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −219.750 | −0.579816 | −0.289908 | − | 0.957055i | \(-0.593625\pi\) | ||||
−0.289908 | + | 0.957055i | \(0.593625\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.7534 | − | 8.51785i | −0.0385205 | − | 0.0222398i | 0.480616 | − | 0.876931i | \(-0.340413\pi\) |
−0.519137 | + | 0.854691i | \(0.673746\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 278.095 | − | 94.0530i | 0.722326 | − | 0.244293i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −76.1102 | − | 131.827i | −0.195656 | − | 0.338886i | 0.751459 | − | 0.659779i | \(-0.229350\pi\) |
−0.947115 | + | 0.320893i | \(0.896017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 30.8076i | − | 0.0787919i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 209.025 | − | 120.681i | 0.529178 | − | 0.305521i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −322.786 | − | 186.361i | −0.813064 | − | 0.469423i | 0.0349549 | − | 0.999389i | \(-0.488871\pi\) |
−0.848019 | + | 0.529966i | \(0.822205\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 325.786 | − | 564.279i | 0.812435 | − | 1.40718i | −0.0987205 | − | 0.995115i | \(-0.531475\pi\) |
0.911155 | − | 0.412063i | \(-0.135192\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 67.6173 | + | 117.117i | 0.167785 | + | 0.290612i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −859.992 | −2.11300 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 462.081 | − | 266.782i | 1.12978 | − | 0.652280i | 0.185902 | − | 0.982568i | \(-0.440479\pi\) |
0.943880 | + | 0.330289i | \(0.107146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −440.353 | − | 387.054i | −1.06623 | − | 0.937176i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 170.985 | − | 296.154i | 0.412012 | − | 0.713625i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 534.252i | 1.27507i | 0.770423 | + | 0.637533i | \(0.220045\pi\) | ||||
−0.770423 | + | 0.637533i | \(0.779955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 157.220 | 0.373445 | 0.186723 | − | 0.982413i | \(-0.440213\pi\) | ||||
0.186723 | + | 0.982413i | \(0.440213\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −175.794 | − | 101.495i | −0.413633 | − | 0.238811i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −90.9960 | + | 454.801i | −0.213105 | + | 1.06511i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 114.268 | + | 197.918i | 0.265123 | + | 0.459207i | 0.967596 | − | 0.252504i | \(-0.0812541\pi\) |
−0.702473 | + | 0.711711i | \(0.747921\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 47.5549i | − | 0.109827i | −0.998491 | − | 0.0549133i | \(-0.982512\pi\) | ||
0.998491 | − | 0.0549133i | \(-0.0174882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.41169 | − | 0.815039i | 0.00323041 | − | 0.00186508i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 63.9594 | + | 36.9270i | 0.145693 | + | 0.0841161i | 0.571075 | − | 0.820898i | \(-0.306527\pi\) |
−0.425381 | + | 0.905014i | \(0.639860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −117.320 | + | 203.204i | −0.264830 | + | 0.458699i | −0.967519 | − | 0.252798i | \(-0.918649\pi\) |
0.702689 | + | 0.711497i | \(0.251983\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −265.875 | − | 460.508i | −0.597471 | − | 1.03485i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 255.161 | 0.568288 | 0.284144 | − | 0.958782i | \(-0.408291\pi\) | ||||
0.284144 | + | 0.958782i | \(0.408291\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −241.191 | + | 139.252i | −0.534791 | + | 0.308762i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −119.412 | − | 23.8918i | −0.262444 | − | 0.0525095i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 72.8675 | − | 126.210i | 0.159448 | − | 0.276171i | −0.775222 | − | 0.631689i | \(-0.782362\pi\) |
0.934670 | + | 0.355518i | \(0.115695\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 888.329i | 1.92696i | 0.267777 | + | 0.963481i | \(0.413711\pi\) | ||||
−0.267777 | + | 0.963481i | \(0.586289\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −234.014 | −0.505430 | −0.252715 | − | 0.967541i | \(-0.581324\pi\) | ||||
−0.252715 | + | 0.967541i | \(0.581324\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 681.231 | + | 393.309i | 1.45874 | + | 0.842204i | 0.998950 | − | 0.0458237i | \(-0.0145912\pi\) |
0.459790 | + | 0.888028i | \(0.347925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −428.117 | + | 487.071i | −0.912830 | + | 1.03853i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −42.9411 | − | 74.3762i | −0.0907846 | − | 0.157244i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 10.7405i | − | 0.0226115i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 638.202 | − | 368.466i | 1.33236 | − | 0.769240i | 0.346702 | − | 0.937975i | \(-0.387302\pi\) |
0.985661 | + | 0.168735i | \(0.0539682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 308.948 | + | 178.371i | 0.642304 | + | 0.370834i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.5076 | − | 70.1612i | 0.0835208 | − | 0.144662i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 135.349 | + | 234.432i | 0.277925 | + | 0.481379i | 0.970869 | − | 0.239612i | \(-0.0770202\pi\) |
−0.692944 | + | 0.720991i | \(0.743687\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 760.161 | 1.54819 | 0.774094 | − | 0.633070i | \(-0.218206\pi\) | ||||
0.774094 | + | 0.633070i | \(0.218206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −240.551 | + | 138.882i | −0.487934 | + | 0.281709i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −108.603 | − | 321.117i | −0.218517 | − | 0.646111i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 62.7462 | − | 108.680i | 0.125744 | − | 0.217795i | −0.796280 | − | 0.604929i | \(-0.793202\pi\) |
0.922023 | + | 0.387134i | \(0.126535\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 117.083i | − | 0.232770i | −0.993204 | − | 0.116385i | \(-0.962869\pi\) | ||
0.993204 | − | 0.116385i | \(-0.0371306\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 90.2649 | 0.178742 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 574.110 | + | 331.463i | 1.12792 | + | 0.651204i | 0.943410 | − | 0.331627i | \(-0.107598\pi\) |
0.184507 | + | 0.982831i | \(0.440931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 688.709 | + | 605.349i | 1.34777 | + | 1.18464i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 89.4518 | + | 154.935i | 0.173693 | + | 0.300845i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 632.733i | 1.22386i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.8229 | − | 23.5691i | 0.0783550 | − | 0.0452383i | −0.460311 | − | 0.887758i | \(-0.652262\pi\) |
0.538666 | + | 0.842520i | \(0.318929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −432.554 | − | 249.735i | −0.827064 | − | 0.477506i | 0.0257824 | − | 0.999668i | \(-0.491792\pi\) |
−0.852846 | + | 0.522162i | \(0.825126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −166.901 | + | 289.080i | −0.316699 | + | 0.548539i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 261.919 | + | 453.657i | 0.495121 | + | 0.857574i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 115.529 | 0.216752 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 130.578 | − | 75.3890i | 0.244070 | − | 0.140914i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −598.937 | − | 249.663i | −1.11120 | − | 0.463197i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −249.405 | + | 431.981i | −0.461007 | + | 0.798487i | −0.999011 | − | 0.0444550i | \(-0.985845\pi\) |
0.538005 | + | 0.842942i | \(0.319178\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 238.497i | 0.437609i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 279.897 | 0.511694 | 0.255847 | − | 0.966717i | \(-0.417646\pi\) | ||||
0.255847 | + | 0.966717i | \(0.417646\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7279 | − | 7.34847i | −0.0230997 | − | 0.0133366i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −523.124 | − | 104.666i | −0.945976 | − | 0.189269i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −130.890 | − | 226.708i | −0.234991 | − | 0.407016i | 0.724279 | − | 0.689507i | \(-0.242173\pi\) |
−0.959270 | + | 0.282491i | \(0.908839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.6258i | 0.0637312i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −420.076 | + | 242.531i | −0.746139 | + | 0.430784i | −0.824297 | − | 0.566157i | \(-0.808429\pi\) |
0.0781581 | + | 0.996941i | \(0.475096\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 234.375 | + | 135.316i | 0.414822 | + | 0.239498i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −227.000 | + | 393.175i | −0.398945 | + | 0.690993i | −0.993596 | − | 0.112991i | \(-0.963957\pi\) |
0.594651 | + | 0.803984i | \(0.297290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −115.769 | − | 200.517i | −0.202747 | − | 0.351168i | 0.746666 | − | 0.665200i | \(-0.231654\pi\) |
−0.949413 | + | 0.314032i | \(0.898320\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.0143 | −0.0591553 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 564.014 | − | 325.634i | 0.977494 | − | 0.564356i | 0.0759812 | − | 0.997109i | \(-0.475791\pi\) |
0.901513 | + | 0.432753i | \(0.142458\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −716.029 | + | 242.164i | −1.23241 | + | 0.416805i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −145.864 | + | 252.644i | −0.250195 | + | 0.433351i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 823.029i | − | 1.40209i | −0.713116 | − | 0.701046i | \(-0.752717\pi\) | ||
0.713116 | − | 0.701046i | \(-0.247283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.6619 | −0.0299863 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 700.110 | + | 404.209i | 1.18062 | + | 0.681634i | 0.956159 | − | 0.292848i | \(-0.0946031\pi\) |
0.224465 | + | 0.974482i | \(0.427936\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −96.3015 | − | 284.744i | −0.161851 | − | 0.478561i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −265.422 | − | 459.725i | −0.443109 | − | 0.767488i | 0.554809 | − | 0.831978i | \(-0.312791\pi\) |
−0.997918 | + | 0.0644900i | \(0.979458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 936.503i | 1.55824i | 0.626874 | + | 0.779121i | \(0.284334\pi\) | ||||
−0.626874 | + | 0.779121i | \(0.715666\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 149.111 | − | 86.0890i | 0.246464 | − | 0.142296i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −521.452 | − | 301.060i | −0.859064 | − | 0.495981i | 0.00463474 | − | 0.999989i | \(-0.498525\pi\) |
−0.863699 | + | 0.504008i | \(0.831858\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 131.235 | − | 227.307i | 0.214788 | − | 0.372024i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −548.448 | − | 949.940i | −0.894695 | − | 1.54966i | −0.834181 | − | 0.551491i | \(-0.814059\pi\) |
−0.0605142 | − | 0.998167i | \(-0.519274\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 432.956 | 0.701712 | 0.350856 | − | 0.936429i | \(-0.385891\pi\) | ||||
0.350856 | + | 0.936429i | \(0.385891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −194.951 | + | 112.555i | −0.314946 | + | 0.181834i | −0.649137 | − | 0.760671i | \(-0.724870\pi\) |
0.334192 | + | 0.942505i | \(0.391537\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −230.592 | + | 1152.51i | −0.370131 | + | 1.84993i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.3091 | − | 23.0520i | 0.0212945 | − | 0.0368832i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 880.552i | 1.39992i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −750.514 | −1.18940 | −0.594702 | − | 0.803946i | \(-0.702730\pi\) | ||||
−0.594702 | + | 0.803946i | \(0.702730\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −166.374 | − | 96.0560i | −0.262006 | − | 0.151269i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 163.383 | + | 213.916i | 0.256488 | + | 0.335818i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −580.926 | − | 1006.19i | −0.906281 | − | 1.56973i | −0.819188 | − | 0.573525i | \(-0.805575\pi\) |
−0.0870937 | − | 0.996200i | \(-0.527758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 121.957i | 0.189669i | 0.995493 | + | 0.0948347i | \(0.0302322\pi\) | ||||
−0.995493 | + | 0.0948347i | \(0.969768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −137.504 | + | 79.3877i | −0.212525 | + | 0.122701i | −0.602484 | − | 0.798131i | \(-0.705822\pi\) |
0.389959 | + | 0.920832i | \(0.372489\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −960.529 | − | 554.561i | −1.48001 | − | 0.854486i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −195.471 | + | 338.565i | −0.299342 | + | 0.518476i | −0.975986 | − | 0.217835i | \(-0.930101\pi\) |
0.676643 | + | 0.736311i | \(0.263434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 210.518 | + | 364.628i | 0.321401 | + | 0.556683i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −331.955 | −0.503726 | −0.251863 | − | 0.967763i | \(-0.581043\pi\) | ||||
−0.251863 | + | 0.967763i | \(0.581043\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 561.029 | − | 323.910i | 0.848758 | − | 0.490031i | −0.0114736 | − | 0.999934i | \(-0.503652\pi\) |
0.860232 | + | 0.509904i | \(0.170319\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.5000 | − | 11.9459i | 0.0157895 | − | 0.0179638i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.2721 | + | 40.3084i | −0.0348907 | + | 0.0604324i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 877.448i | 1.30767i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 100.956 | 0.150009 | 0.0750047 | − | 0.997183i | \(-0.476103\pi\) | ||||
0.0750047 | + | 0.997183i | \(0.476103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −643.610 | − | 371.588i | −0.950679 | − | 0.548875i | −0.0573873 | − | 0.998352i | \(-0.518277\pi\) |
−0.893292 | + | 0.449477i | \(0.851610\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −169.632 | + | 57.3704i | −0.249827 | + | 0.0844924i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.21721 | − | 3.84032i | −0.00324628 | − | 0.00562272i | 0.864398 | − | 0.502809i | \(-0.167700\pi\) |
−0.867644 | + | 0.497186i | \(0.834367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 371.881i | 0.542892i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 104.802 | − | 60.5074i | 0.152107 | − | 0.0878192i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 846.253 | + | 488.584i | 1.22468 | + | 0.707069i | 0.965912 | − | 0.258871i | \(-0.0833506\pi\) |
0.258767 | + | 0.965940i | \(0.416684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −108.603 | + | 188.106i | −0.156263 | + | 0.270656i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 142.581 | + | 246.957i | 0.204563 | + | 0.354314i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 840.177 | 1.19854 | 0.599270 | − | 0.800547i | \(-0.295458\pi\) | ||||
0.599270 | + | 0.800547i | \(0.295458\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.3492 | + | 23.2956i | −0.0573958 | + | 0.0331375i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −149.857 | − | 131.719i | −0.211962 | − | 0.186306i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −341.279 | + | 591.112i | −0.481352 | + | 0.833727i | −0.999771 | − | 0.0214003i | \(-0.993188\pi\) |
0.518419 | + | 0.855127i | \(0.326521\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 55.9340i | 0.0784488i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −230.382 | −0.322212 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 119.187 | + | 68.8126i | 0.165768 | + | 0.0957060i | 0.580589 | − | 0.814197i | \(-0.302822\pi\) |
−0.414821 | + | 0.909903i | \(0.636156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 77.5812 | − | 387.754i | 0.107602 | − | 0.537800i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 153.338 | + | 265.589i | 0.211501 | + | 0.366330i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 264.137i | 0.363325i | 0.983361 | + | 0.181662i | \(0.0581478\pi\) | ||||
−0.983361 | + | 0.181662i | \(0.941852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −76.1543 | + | 43.9677i | −0.104178 | + | 0.0601474i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 501.705 | + | 289.660i | 0.684455 | + | 0.395170i | 0.801531 | − | 0.597953i | \(-0.204019\pi\) |
−0.117077 | + | 0.993123i | \(0.537352\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −613.397 | + | 1062.43i | −0.832288 | + | 1.44157i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −99.0477 | − | 171.556i | −0.134029 | − | 0.232146i | 0.791197 | − | 0.611562i | \(-0.209458\pi\) |
−0.925226 | + | 0.379416i | \(0.876125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 976.690 | 1.31452 | 0.657261 | − | 0.753663i | \(-0.271715\pi\) | ||||
0.657261 | + | 0.753663i | \(0.271715\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 72.3974 | − | 41.7987i | 0.0971777 | − | 0.0561056i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −326.794 | − | 65.3845i | −0.436308 | − | 0.0872958i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −417.665 | + | 723.417i | −0.556145 | + | 0.963272i | 0.441668 | + | 0.897178i | \(0.354387\pi\) |
−0.997813 | + | 0.0660933i | \(0.978947\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 425.044i | 0.562972i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 104.221 | 0.137677 | 0.0688383 | − | 0.997628i | \(-0.478071\pi\) | ||||
0.0688383 | + | 0.997628i | \(0.478071\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 473.785 | + | 273.540i | 0.622583 | + | 0.359448i | 0.777874 | − | 0.628420i | \(-0.216298\pi\) |
−0.155291 | + | 0.987869i | \(0.549632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 348.025 | − | 395.950i | 0.456128 | − | 0.518939i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 230.044 | + | 398.447i | 0.299927 | + | 0.519488i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 341.205i | 0.443700i | 0.975081 | + | 0.221850i | \(0.0712095\pi\) | ||||
−0.975081 | + | 0.221850i | \(0.928790\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 425.213 | − | 245.497i | 0.550081 | − | 0.317590i | −0.199074 | − | 0.979985i | \(-0.563793\pi\) |
0.749155 | + | 0.662395i | \(0.230460\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 319.169 | + | 184.273i | 0.411832 | + | 0.237771i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.54416 | + | 13.0669i | −0.00968441 | + | 0.0167739i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −320.647 | − | 555.376i | −0.410559 | − | 0.711109i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 717.926 | 0.914555 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −260.202 | + | 150.228i | −0.330625 | + | 0.190887i | −0.656119 | − | 0.754658i | \(-0.727803\pi\) |
0.325493 | + | 0.945544i | \(0.394470\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −191.647 | − | 566.660i | −0.242284 | − | 0.716385i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 181.992 | − | 315.219i | 0.229498 | − | 0.397502i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 370.072i | − | 0.464331i | −0.972676 | − | 0.232165i | \(-0.925419\pi\) | ||
0.972676 | − | 0.232165i | \(-0.0745811\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 647.860 | 0.810838 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1502.26 | + | 867.330i | 1.87081 | + | 1.08011i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.8318 | − | 33.2528i | −0.0469960 | − | 0.0413078i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 245.618 | + | 425.422i | 0.303607 | + | 0.525862i | 0.976950 | − | 0.213468i | \(-0.0684758\pi\) |
−0.673344 | + | 0.739330i | \(0.735142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 156.802i | 0.193344i | 0.995316 | + | 0.0966722i | \(0.0308199\pi\) | ||||
−0.995316 | + | 0.0966722i | \(0.969180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 252.262 | − | 145.643i | 0.309524 | − | 0.178704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.02944 | − | 2.32640i | −0.00493199 | − | 0.00284749i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −215.316 | + | 372.939i | −0.262261 | + | 0.454249i | −0.966842 | − | 0.255374i | \(-0.917801\pi\) |
0.704581 | + | 0.709623i | \(0.251135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −354.371 | − | 613.788i | −0.430584 | − | 0.745793i | 0.566340 | − | 0.824172i | \(-0.308359\pi\) |
−0.996924 | + | 0.0783785i | \(0.975026\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1460.10 | −1.76554 | −0.882770 | − | 0.469805i | \(-0.844324\pi\) | ||||
−0.882770 | + | 0.469805i | \(0.844324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −223.095 | + | 128.804i | −0.269113 | + | 0.155373i | −0.628485 | − | 0.777822i | \(-0.716325\pi\) |
0.359371 | + | 0.933195i | \(0.382991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −255.632 | + | 613.256i | −0.306881 | + | 0.736202i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 322.206 | − | 558.077i | 0.385876 | − | 0.668356i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 213.621i | 0.254613i | 0.991863 | + | 0.127307i | \(0.0406332\pi\) | ||||
−0.991863 | + | 0.127307i | \(0.959367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −421.353 | −0.501015 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −380.743 | − | 219.822i | −0.450583 | − | 0.260144i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −373.177 | − | 74.6646i | −0.440586 | − | 0.0881519i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 73.7756 | + | 127.783i | 0.0866929 | + | 0.150156i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1127.37i | 1.32165i | 0.750539 | + | 0.660826i | \(0.229794\pi\) | ||||
−0.750539 | + | 0.660826i | \(0.770206\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1100.22 | + | 635.212i | −1.28380 | + | 0.741204i | −0.977541 | − | 0.210744i | \(-0.932412\pi\) |
−0.306261 | + | 0.951947i | \(0.599078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 221.488 | + | 127.876i | 0.257844 | + | 0.148867i | 0.623351 | − | 0.781942i | \(-0.285771\pi\) |
−0.365506 | + | 0.930809i | \(0.619104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −557.364 | + | 965.382i | −0.645844 | + | 1.11863i | 0.338262 | + | 0.941052i | \(0.390161\pi\) |
−0.984106 | + | 0.177583i | \(0.943172\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 112.125 | + | 194.207i | 0.129625 | + | 0.224516i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1009.26 | −1.16141 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 440.720 | − | 254.450i | 0.505993 | − | 0.292135i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −839.382 | + | 283.882i | −0.959294 | + | 0.324437i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 550.904 | − | 954.194i | 0.628169 | − | 1.08802i | −0.359750 | − | 0.933049i | \(-0.617138\pi\) |
0.987919 | − | 0.154972i | \(-0.0495286\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 217.067i | 0.246387i | 0.992383 | + | 0.123194i | \(0.0393136\pi\) | ||||
−0.992383 | + | 0.123194i | \(0.960686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 516.544 | 0.584988 | 0.292494 | − | 0.956267i | \(-0.405515\pi\) | ||||
0.292494 | + | 0.956267i | \(0.405515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −978.445 | − | 564.905i | −1.10309 | − | 0.636872i | −0.166062 | − | 0.986115i | \(-0.553105\pi\) |
−0.937032 | + | 0.349243i | \(0.886439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 136.043 | + | 402.251i | 0.153029 | + | 0.452476i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.1396 | + | 29.6867i | 0.0191933 | + | 0.0332438i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 344.613i | 0.385043i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 436.742 | − | 252.153i | 0.485809 | − | 0.280482i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 258.684 | + | 149.351i | 0.287107 | + | 0.165762i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −157.809 | + | 273.333i | −0.174375 | + | 0.302026i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.0111 | + | 51.9808i | 0.0330884 | + | 0.0573107i | 0.882095 | − | 0.471071i | \(-0.156132\pi\) |
−0.849007 | + | 0.528382i | \(0.822799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1422.25 | 1.56120 | 0.780598 | − | 0.625033i | \(-0.214915\pi\) | ||||
0.780598 | + | 0.625033i | \(0.214915\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1238.38 | + | 714.980i | −1.35639 | + | 0.783111i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 182.581 | − | 912.547i | 0.199107 | − | 0.995144i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 834.849 | − | 1446.00i | 0.908432 | − | 1.57345i | 0.0921886 | − | 0.995742i | \(-0.470614\pi\) |
0.816243 | − | 0.577708i | \(-0.196053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 266.022i | 0.288215i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 972.205 | 1.05103 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −839.058 | − | 484.430i | −0.903184 | − | 0.521453i | −0.0249519 | − | 0.999689i | \(-0.507943\pi\) |
−0.878232 | + | 0.478235i | \(0.841277\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.8640 | + | 4.51039i | −0.0374479 | + | 0.00484468i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −284.327 | − | 492.469i | −0.304093 | − | 0.526705i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1212.57i | − | 1.29410i | −0.762449 | − | 0.647049i | \(-0.776003\pi\) | ||
0.762449 | − | 0.647049i | \(-0.223997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1293.90 | − | 747.032i | 1.37502 | − | 0.793870i | 0.383468 | − | 0.923554i | \(-0.374730\pi\) |
0.991555 | + | 0.129684i | \(0.0413963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.3818 | + | 23.8918i | 0.0438832 | + | 0.0253360i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −387.731 | + | 671.570i | −0.409431 | + | 0.709155i | −0.994826 | − | 0.101593i | \(-0.967606\pi\) |
0.585395 | + | 0.810748i | \(0.300939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −359.787 | − | 623.169i | −0.379122 | − | 0.656659i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1055.40 | −1.10745 | −0.553723 | − | 0.832701i | \(-0.686794\pi\) | ||||
−0.553723 | + | 0.832701i | \(0.686794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 191.723 | − | 110.691i | 0.200757 | − | 0.115907i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 542.665 | − | 617.393i | 0.565866 | − | 0.643788i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −177.477 | + | 307.400i | −0.184680 | + | 0.319875i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 102.412i | − | 0.106127i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1221.63 | −1.26332 | −0.631661 | − | 0.775245i | \(-0.717627\pi\) | ||||
−0.631661 | + | 0.775245i | \(0.717627\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −455.753 | − | 263.129i | −0.469365 | − | 0.270988i | 0.246609 | − | 0.969115i | \(-0.420684\pi\) |
−0.715974 | + | 0.698127i | \(0.754017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 454.794 | − | 153.813i | 0.467414 | − | 0.158081i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −500.051 | − | 866.114i | −0.511823 | − | 0.886504i | −0.999906 | − | 0.0137065i | \(-0.995637\pi\) |
0.488083 | − | 0.872797i | \(-0.337696\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2223.53i | 2.27123i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 931.584 | − | 537.850i | 0.947695 | − | 0.547152i | 0.0553306 | − | 0.998468i | \(-0.482379\pi\) |
0.892364 | + | 0.451316i | \(0.149045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 759.993 | + | 438.782i | 0.771566 | + | 0.445464i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.36753 | + | 12.7609i | −0.00744948 | + | 0.0129029i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −938.017 | − | 1624.69i | −0.946536 | − | 1.63945i | −0.752646 | − | 0.658426i | \(-0.771223\pi\) |
−0.193891 | − | 0.981023i | \(-0.562111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 530.285 | 0.532949 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 504.221 | − | 291.112i | 0.505738 | − | 0.291988i | −0.225342 | − | 0.974280i | \(-0.572350\pi\) |
0.731080 | + | 0.682292i | \(0.239017\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1008.3.cg.l.145.1 | 4 | ||
3.2 | odd | 2 | 112.3.s.b.33.2 | 4 | |||
4.3 | odd | 2 | 126.3.n.c.19.1 | 4 | |||
7.3 | odd | 6 | inner | 1008.3.cg.l.577.1 | 4 | ||
12.11 | even | 2 | 14.3.d.a.5.2 | yes | 4 | ||
21.2 | odd | 6 | 784.3.c.e.97.4 | 4 | |||
21.5 | even | 6 | 784.3.c.e.97.1 | 4 | |||
21.11 | odd | 6 | 784.3.s.c.129.1 | 4 | |||
21.17 | even | 6 | 112.3.s.b.17.2 | 4 | |||
21.20 | even | 2 | 784.3.s.c.705.1 | 4 | |||
24.5 | odd | 2 | 448.3.s.c.257.1 | 4 | |||
24.11 | even | 2 | 448.3.s.d.257.2 | 4 | |||
28.3 | even | 6 | 126.3.n.c.73.1 | 4 | |||
28.11 | odd | 6 | 882.3.n.b.325.1 | 4 | |||
28.19 | even | 6 | 882.3.c.f.685.3 | 4 | |||
28.23 | odd | 6 | 882.3.c.f.685.4 | 4 | |||
28.27 | even | 2 | 882.3.n.b.19.1 | 4 | |||
60.23 | odd | 4 | 350.3.i.a.299.1 | 8 | |||
60.47 | odd | 4 | 350.3.i.a.299.4 | 8 | |||
60.59 | even | 2 | 350.3.k.a.201.1 | 4 | |||
84.11 | even | 6 | 98.3.d.a.31.2 | 4 | |||
84.23 | even | 6 | 98.3.b.b.97.1 | 4 | |||
84.47 | odd | 6 | 98.3.b.b.97.2 | 4 | |||
84.59 | odd | 6 | 14.3.d.a.3.2 | ✓ | 4 | ||
84.83 | odd | 2 | 98.3.d.a.19.2 | 4 | |||
168.59 | odd | 6 | 448.3.s.d.129.2 | 4 | |||
168.101 | even | 6 | 448.3.s.c.129.1 | 4 | |||
420.59 | odd | 6 | 350.3.k.a.101.1 | 4 | |||
420.143 | even | 12 | 350.3.i.a.199.4 | 8 | |||
420.227 | even | 12 | 350.3.i.a.199.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.3.d.a.3.2 | ✓ | 4 | 84.59 | odd | 6 | ||
14.3.d.a.5.2 | yes | 4 | 12.11 | even | 2 | ||
98.3.b.b.97.1 | 4 | 84.23 | even | 6 | |||
98.3.b.b.97.2 | 4 | 84.47 | odd | 6 | |||
98.3.d.a.19.2 | 4 | 84.83 | odd | 2 | |||
98.3.d.a.31.2 | 4 | 84.11 | even | 6 | |||
112.3.s.b.17.2 | 4 | 21.17 | even | 6 | |||
112.3.s.b.33.2 | 4 | 3.2 | odd | 2 | |||
126.3.n.c.19.1 | 4 | 4.3 | odd | 2 | |||
126.3.n.c.73.1 | 4 | 28.3 | even | 6 | |||
350.3.i.a.199.1 | 8 | 420.227 | even | 12 | |||
350.3.i.a.199.4 | 8 | 420.143 | even | 12 | |||
350.3.i.a.299.1 | 8 | 60.23 | odd | 4 | |||
350.3.i.a.299.4 | 8 | 60.47 | odd | 4 | |||
350.3.k.a.101.1 | 4 | 420.59 | odd | 6 | |||
350.3.k.a.201.1 | 4 | 60.59 | even | 2 | |||
448.3.s.c.129.1 | 4 | 168.101 | even | 6 | |||
448.3.s.c.257.1 | 4 | 24.5 | odd | 2 | |||
448.3.s.d.129.2 | 4 | 168.59 | odd | 6 | |||
448.3.s.d.257.2 | 4 | 24.11 | even | 2 | |||
784.3.c.e.97.1 | 4 | 21.5 | even | 6 | |||
784.3.c.e.97.4 | 4 | 21.2 | odd | 6 | |||
784.3.s.c.129.1 | 4 | 21.11 | odd | 6 | |||
784.3.s.c.705.1 | 4 | 21.20 | even | 2 | |||
882.3.c.f.685.3 | 4 | 28.19 | even | 6 | |||
882.3.c.f.685.4 | 4 | 28.23 | odd | 6 | |||
882.3.n.b.19.1 | 4 | 28.27 | even | 2 | |||
882.3.n.b.325.1 | 4 | 28.11 | odd | 6 | |||
1008.3.cg.l.145.1 | 4 | 1.1 | even | 1 | trivial | ||
1008.3.cg.l.577.1 | 4 | 7.3 | odd | 6 | inner |