Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,3,Mod(353,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.t (of order \(4\), 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: | \(17.4387369191\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 353.15 | ||
Character | \(\chi\) | \(=\) | 640.353 |
Dual form | 640.3.t.a.417.15 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.90859 | 0.636197 | 0.318098 | − | 0.948058i | \(-0.396956\pi\) | ||||
0.318098 | + | 0.948058i | \(0.396956\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.97175 | + | 0.530759i | −0.994350 | + | 0.106152i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.62025 | + | 8.62025i | 1.23146 | + | 1.23146i | 0.963401 | + | 0.268063i | \(0.0863836\pi\) |
0.268063 | + | 0.963401i | \(0.413616\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.35728 | −0.595254 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.35145 | + | 6.35145i | 0.577404 | + | 0.577404i | 0.934187 | − | 0.356783i | \(-0.116126\pi\) |
−0.356783 | + | 0.934187i | \(0.616126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.65056 | −0.511581 | −0.255791 | − | 0.966732i | \(-0.582336\pi\) | ||||
−0.255791 | + | 0.966732i | \(0.582336\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.48903 | + | 1.01300i | −0.632602 | + | 0.0675334i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.36508 | + | 5.36508i | −0.315593 | + | 0.315593i | −0.847072 | − | 0.531479i | \(-0.821637\pi\) |
0.531479 | + | 0.847072i | \(0.321637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.1009 | − | 18.1009i | −0.952677 | − | 0.952677i | 0.0462531 | − | 0.998930i | \(-0.485272\pi\) |
−0.998930 | + | 0.0462531i | \(0.985272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.4525 | + | 16.4525i | 0.783454 | + | 0.783454i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.1730 | + | 16.1730i | −0.703172 | + | 0.703172i | −0.965090 | − | 0.261918i | \(-0.915645\pi\) |
0.261918 | + | 0.965090i | \(0.415645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.4366 | − | 5.27760i | 0.977464 | − | 0.211104i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.4022 | −1.01490 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12.4816 | − | 12.4816i | −0.430400 | − | 0.430400i | 0.458365 | − | 0.888764i | \(-0.348435\pi\) |
−0.888764 | + | 0.458365i | \(0.848435\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.5625 | 0.598792 | 0.299396 | − | 0.954129i | \(-0.403215\pi\) | ||||
0.299396 | + | 0.954129i | \(0.403215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.1223 | + | 12.1223i | 0.367343 | + | 0.367343i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −47.4330 | − | 38.2825i | −1.35523 | − | 1.09378i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −49.8083 | −1.34617 | −0.673085 | − | 0.739565i | \(-0.735031\pi\) | ||||
−0.673085 | + | 0.739565i | \(0.735031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.6932 | −0.325466 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 62.1433i | 1.51569i | 0.652434 | + | 0.757846i | \(0.273748\pi\) | ||||
−0.652434 | + | 0.757846i | \(0.726252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.2720i | 0.750511i | 0.926921 | + | 0.375255i | \(0.122445\pi\) | ||||
−0.926921 | + | 0.375255i | \(0.877555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 26.6351 | − | 2.84343i | 0.591890 | − | 0.0631872i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.2635 | + | 13.2635i | −0.282202 | + | 0.282202i | −0.833986 | − | 0.551785i | \(-0.813947\pi\) |
0.551785 | + | 0.833986i | \(0.313947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 99.6175i | 2.03301i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.2397 | + | 10.2397i | −0.200779 | + | 0.200779i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 64.2436i | 1.21214i | 0.795410 | + | 0.606071i | \(0.207255\pi\) | ||||
−0.795410 | + | 0.606071i | \(0.792745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −34.9489 | − | 28.2067i | −0.635435 | − | 0.512850i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −34.5471 | − | 34.5471i | −0.606090 | − | 0.606090i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.55993 | − | 2.55993i | 0.0433887 | − | 0.0433887i | −0.685080 | − | 0.728468i | \(-0.740233\pi\) |
0.728468 | + | 0.685080i | \(0.240233\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 52.5270 | − | 52.5270i | 0.861098 | − | 0.861098i | −0.130367 | − | 0.991466i | \(-0.541616\pi\) |
0.991466 | + | 0.130367i | \(0.0416157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −46.1811 | − | 46.1811i | −0.733034 | − | 0.733034i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 33.0649 | − | 3.52984i | 0.508691 | − | 0.0543053i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 72.2222i | 1.07794i | 0.842324 | + | 0.538972i | \(0.181187\pi\) | ||||
−0.842324 | + | 0.538972i | \(0.818813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −30.8676 | + | 30.8676i | −0.447356 | + | 0.447356i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 24.3819i | 0.343407i | 0.985149 | + | 0.171703i | \(0.0549270\pi\) | ||||
−0.985149 | + | 0.171703i | \(0.945073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.39841 | − | 1.39841i | 0.0191563 | − | 0.0191563i | −0.697464 | − | 0.716620i | \(-0.745688\pi\) |
0.716620 | + | 0.697464i | \(0.245688\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 46.6394 | − | 10.0728i | 0.621859 | − | 0.134304i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 109.502i | 1.42211i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 90.0709i | − | 1.14014i | −0.821597 | − | 0.570069i | \(-0.806917\pi\) | ||
0.821597 | − | 0.570069i | \(-0.193083\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.08398 | −0.0504195 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.78386 | 0.0455886 | 0.0227943 | − | 0.999740i | \(-0.492744\pi\) | ||||
0.0227943 | + | 0.999740i | \(0.492744\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.8263 | − | 29.5214i | 0.280309 | − | 0.347311i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −23.8222 | − | 23.8222i | −0.273819 | − | 0.273819i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −61.3939 | −0.689819 | −0.344910 | − | 0.938636i | \(-0.612090\pi\) | ||||
−0.344910 | + | 0.938636i | \(0.612090\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −57.3295 | − | 57.3295i | −0.629994 | − | 0.629994i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 35.4283 | 0.380949 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 99.6001 | + | 80.3857i | 1.04842 | + | 0.846166i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 103.182 | − | 103.182i | 1.06373 | − | 1.06373i | 0.0659075 | − | 0.997826i | \(-0.479006\pi\) |
0.997826 | − | 0.0659075i | \(-0.0209942\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −34.0265 | − | 34.0265i | −0.343702 | − | 0.343702i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 92.1665 | + | 92.1665i | 0.912539 | + | 0.912539i | 0.996471 | − | 0.0839323i | \(-0.0267479\pi\) |
−0.0839323 | + | 0.996471i | \(0.526748\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −73.2115 | + | 73.2115i | −0.710791 | + | 0.710791i | −0.966701 | − | 0.255909i | \(-0.917625\pi\) |
0.255909 | + | 0.966701i | \(0.417625\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −90.5302 | − | 73.0655i | −0.862192 | − | 0.695862i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.7853 | 0.166218 | 0.0831089 | − | 0.996540i | \(-0.473515\pi\) | ||||
0.0831089 | + | 0.996540i | \(0.473515\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.64065 | + | 9.64065i | 0.0884463 | + | 0.0884463i | 0.749946 | − | 0.661499i | \(-0.230080\pi\) |
−0.661499 | + | 0.749946i | \(0.730080\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −95.0636 | −0.856429 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −62.4937 | − | 62.4937i | −0.553042 | − | 0.553042i | 0.374276 | − | 0.927317i | \(-0.377891\pi\) |
−0.927317 | + | 0.374276i | \(0.877891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 71.8240 | − | 88.9919i | 0.624556 | − | 0.773842i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 35.6289 | 0.304521 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −92.4967 | −0.777283 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 40.3182i | − | 0.333208i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 118.606i | 0.964278i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −118.691 | + | 39.2089i | −0.949532 | + | 0.313671i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 50.6008 | − | 50.6008i | 0.398432 | − | 0.398432i | −0.479248 | − | 0.877680i | \(-0.659091\pi\) |
0.877680 | + | 0.479248i | \(0.159091\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 61.5939i | 0.477472i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.0987 | + | 22.0987i | −0.168693 | + | 0.168693i | −0.786404 | − | 0.617712i | \(-0.788060\pi\) |
0.617712 | + | 0.786404i | \(0.288060\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 312.068i | − | 2.34637i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 136.237 | − | 14.5440i | 1.00916 | − | 0.107733i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 102.317 | + | 102.317i | 0.746841 | + | 0.746841i | 0.973885 | − | 0.227043i | \(-0.0729059\pi\) |
−0.227043 | + | 0.973885i | \(0.572906\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 83.0087 | − | 83.0087i | 0.597185 | − | 0.597185i | −0.342378 | − | 0.939562i | \(-0.611232\pi\) |
0.939562 | + | 0.342378i | \(0.111232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −25.3145 | + | 25.3145i | −0.179536 | + | 0.179536i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −42.2407 | − | 42.2407i | −0.295389 | − | 0.295389i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 68.6800 | + | 55.4306i | 0.473656 | + | 0.382280i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 190.129i | 1.29339i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −134.149 | + | 134.149i | −0.900331 | + | 0.900331i | −0.995465 | − | 0.0951332i | \(-0.969672\pi\) |
0.0951332 | + | 0.995465i | \(0.469672\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 48.5859i | − | 0.321761i | −0.986974 | − | 0.160881i | \(-0.948567\pi\) | ||
0.986974 | − | 0.160881i | \(-0.0514334\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 28.7423 | − | 28.7423i | 0.187858 | − | 0.187858i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −92.2883 | + | 9.85223i | −0.595408 | + | 0.0635628i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 140.992i | 0.898038i | 0.893522 | + | 0.449019i | \(0.148226\pi\) | ||||
−0.893522 | + | 0.449019i | \(0.851774\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 122.615i | 0.771162i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −278.830 | −1.73186 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 98.2045 | 0.602482 | 0.301241 | − | 0.953548i | \(-0.402599\pi\) | ||||
0.301241 | + | 0.953548i | \(0.402599\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −66.7031 | − | 53.8351i | −0.404261 | − | 0.326273i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.58867 | + | 9.58867i | 0.0574172 | + | 0.0574172i | 0.735232 | − | 0.677815i | \(-0.237073\pi\) |
−0.677815 | + | 0.735232i | \(0.737073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −124.770 | −0.738285 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 96.9714 | + | 96.9714i | 0.567084 | + | 0.567084i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 172.905 | 0.999452 | 0.499726 | − | 0.866184i | \(-0.333434\pi\) | ||||
0.499726 | + | 0.866184i | \(0.333434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 256.144 | + | 165.155i | 1.46368 | + | 0.943744i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.88586 | − | 4.88586i | 0.0276037 | − | 0.0276037i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 47.1828 | + | 47.1828i | 0.263591 | + | 0.263591i | 0.826511 | − | 0.562920i | \(-0.190322\pi\) |
−0.562920 | + | 0.826511i | \(0.690322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −50.7180 | − | 50.7180i | −0.280210 | − | 0.280210i | 0.552983 | − | 0.833193i | \(-0.313489\pi\) |
−0.833193 | + | 0.552983i | \(0.813489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 100.253 | − | 100.253i | 0.547828 | − | 0.547828i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 247.634 | − | 26.4362i | 1.33856 | − | 0.142898i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −68.1521 | −0.364450 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −236.214 | − | 236.214i | −1.24981 | − | 1.24981i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −330.128 | −1.72842 | −0.864210 | − | 0.503132i | \(-0.832181\pi\) | ||||
−0.864210 | + | 0.503132i | \(0.832181\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −150.560 | − | 150.560i | −0.780103 | − | 0.780103i | 0.199745 | − | 0.979848i | \(-0.435989\pi\) |
−0.979848 | + | 0.199745i | \(0.935989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 63.1074 | − | 6.73702i | 0.323627 | − | 0.0345488i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 257.794 | 1.30860 | 0.654299 | − | 0.756236i | \(-0.272964\pi\) | ||||
0.654299 | + | 0.756236i | \(0.272964\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 328.501 | 1.65076 | 0.825378 | − | 0.564580i | \(-0.190962\pi\) | ||||
0.825378 | + | 0.564580i | \(0.190962\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 137.843i | 0.685785i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 215.189i | − | 1.06004i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.9831 | − | 308.961i | −0.160893 | − | 1.50713i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 86.6431 | − | 86.6431i | 0.418566 | − | 0.418566i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 229.933i | − | 1.10016i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 51.3916 | − | 51.3916i | 0.243562 | − | 0.243562i | −0.574760 | − | 0.818322i | \(-0.694905\pi\) |
0.818322 | + | 0.574760i | \(0.194905\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 46.5350i | 0.218474i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.1286 | − | 160.448i | −0.0796681 | − | 0.746270i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 160.014 | + | 160.014i | 0.737390 | + | 0.737390i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.66900 | − | 2.66900i | 0.0121872 | − | 0.0121872i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.6808 | − | 35.6808i | 0.161451 | − | 0.161451i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 200.019 | + | 200.019i | 0.896948 | + | 0.896948i | 0.995165 | − | 0.0982168i | \(-0.0313139\pi\) |
−0.0982168 | + | 0.995165i | \(0.531314\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −130.914 | + | 28.2736i | −0.581839 | + | 0.125660i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 47.5480i | − | 0.209462i | −0.994501 | − | 0.104731i | \(-0.966602\pi\) | ||
0.994501 | − | 0.104731i | \(-0.0333982\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 65.5550 | − | 65.5550i | 0.286266 | − | 0.286266i | −0.549336 | − | 0.835602i | \(-0.685119\pi\) |
0.835602 | + | 0.549336i | \(0.185119\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 208.995i | 0.904739i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 201.087 | − | 201.087i | 0.863035 | − | 0.863035i | −0.128655 | − | 0.991689i | \(-0.541066\pi\) |
0.991689 | + | 0.128655i | \(0.0410659\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 58.9030 | − | 72.9824i | 0.250651 | − | 0.310563i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 171.908i | − | 0.725352i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 245.088i | − | 1.02547i | −0.858546 | − | 0.512737i | \(-0.828632\pi\) | ||
0.858546 | − | 0.512737i | \(-0.171368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 462.483 | 1.91902 | 0.959508 | − | 0.281682i | \(-0.0908922\pi\) | ||||
0.959508 | + | 0.281682i | \(0.0908922\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 238.825 | 0.982819 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −52.8729 | − | 495.273i | −0.215808 | − | 2.02152i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 120.381 | + | 120.381i | 0.487372 | + | 0.487372i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.22183 | 0.0290033 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −53.5564 | − | 53.5564i | −0.213372 | − | 0.213372i | 0.592326 | − | 0.805698i | \(-0.298210\pi\) |
−0.805698 | + | 0.592326i | \(0.798210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −205.444 | −0.812030 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 45.4746 | − | 56.3443i | 0.178332 | − | 0.220958i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 128.524 | − | 128.524i | 0.500092 | − | 0.500092i | −0.411374 | − | 0.911466i | \(-0.634951\pi\) |
0.911466 | + | 0.411374i | \(0.134951\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −429.360 | − | 429.360i | −1.65776 | − | 1.65776i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 66.8674 | + | 66.8674i | 0.256197 | + | 0.256197i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 351.385 | − | 351.385i | 1.33606 | − | 1.33606i | 0.436228 | − | 0.899836i | \(-0.356314\pi\) |
0.899836 | − | 0.436228i | \(-0.143686\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.0979 | − | 319.403i | −0.128671 | − | 1.20529i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −117.176 | −0.438861 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 45.4562 | + | 45.4562i | 0.168982 | + | 0.168982i | 0.786532 | − | 0.617550i | \(-0.211875\pi\) |
−0.617550 | + | 0.786532i | \(0.711875\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −43.2087 | −0.159442 | −0.0797209 | − | 0.996817i | \(-0.525403\pi\) | ||||
−0.0797209 | + | 0.996817i | \(0.525403\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −109.418 | − | 109.418i | −0.400800 | − | 0.400800i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 188.728 | + | 121.687i | 0.686284 | + | 0.442499i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 53.1202 | 0.191770 | 0.0958849 | − | 0.995392i | \(-0.469432\pi\) | ||||
0.0958849 | + | 0.995392i | \(0.469432\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −99.4448 | −0.356433 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 146.320i | 0.520712i | 0.965513 | + | 0.260356i | \(0.0838399\pi\) | ||||
−0.965513 | + | 0.260356i | \(0.916160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 87.7034i | 0.309906i | 0.987922 | + | 0.154953i | \(0.0495226\pi\) | ||||
−0.987922 | + | 0.154953i | \(0.950477\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 190.096 | + | 153.423i | 0.667003 | + | 0.538328i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −535.691 | + | 535.691i | −1.86652 | + | 1.86652i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 231.432i | 0.800802i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 196.932 | − | 196.932i | 0.676744 | − | 0.676744i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 257.077i | 0.877395i | 0.898635 | + | 0.438697i | \(0.144560\pi\) | ||||
−0.898635 | + | 0.438697i | \(0.855440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3686 | + | 14.0861i | −0.0385378 | + | 0.0477493i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −174.044 | − | 174.044i | −0.586005 | − | 0.586005i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 107.559 | − | 107.559i | 0.359730 | − | 0.359730i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −278.192 | + | 278.192i | −0.924227 | + | 0.924227i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 175.908 | + | 175.908i | 0.580555 | + | 0.580555i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −233.272 | + | 289.030i | −0.764826 | + | 0.947640i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 601.105i | 1.95800i | 0.203870 | + | 0.978998i | \(0.434648\pi\) | ||||
−0.203870 | + | 0.978998i | \(0.565352\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −139.731 | + | 139.731i | −0.452203 | + | 0.452203i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.34424i | 0.0236149i | 0.999930 | + | 0.0118075i | \(0.00375852\pi\) | ||||
−0.999930 | + | 0.0118075i | \(0.996241\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −170.573 | + | 170.573i | −0.544962 | + | 0.544962i | −0.924979 | − | 0.380017i | \(-0.875918\pi\) |
0.380017 | + | 0.924979i | \(0.375918\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 254.112 | + | 205.090i | 0.806705 | + | 0.651079i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 266.389i | 0.840345i | 0.907444 | + | 0.420172i | \(0.138030\pi\) | ||||
−0.907444 | + | 0.420172i | \(0.861970\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 158.552i | − | 0.497029i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.9449 | 0.105747 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 194.225 | 0.601316 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −162.517 | + | 35.0990i | −0.500052 | + | 0.107997i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.4000 | + | 18.4000i | 0.0562693 | + | 0.0562693i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −228.669 | −0.695043 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −66.9868 | − | 66.9868i | −0.202377 | − | 0.202377i | 0.598641 | − | 0.801018i | \(-0.295708\pi\) |
−0.801018 | + | 0.598641i | \(0.795708\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 266.837 | 0.801312 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −38.3326 | − | 359.071i | −0.114426 | − | 1.07185i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −167.759 | + | 167.759i | −0.497801 | + | 0.497801i | −0.910753 | − | 0.412952i | \(-0.864498\pi\) |
0.412952 | + | 0.910753i | \(0.364498\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −119.275 | − | 119.275i | −0.351843 | − | 0.351843i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 117.899 | + | 117.899i | 0.345745 | + | 0.345745i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −436.335 | + | 436.335i | −1.27211 | + | 1.27211i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 137.083 | − | 169.849i | 0.397341 | − | 0.492316i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −575.495 | −1.65849 | −0.829243 | − | 0.558888i | \(-0.811228\pi\) | ||||
−0.829243 | + | 0.558888i | \(0.811228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 218.302 | + | 218.302i | 0.625508 | + | 0.625508i | 0.946935 | − | 0.321426i | \(-0.104162\pi\) |
−0.321426 | + | 0.946935i | \(0.604162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 182.240 | 0.519201 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 194.122 | + | 194.122i | 0.549920 | + | 0.549920i | 0.926418 | − | 0.376498i | \(-0.122872\pi\) |
−0.376498 | + | 0.926418i | \(0.622872\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.9409 | − | 121.221i | −0.0364532 | − | 0.341466i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −176.538 | −0.494505 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −545.851 | −1.52048 | −0.760238 | − | 0.649644i | \(-0.774918\pi\) | ||||
−0.760238 | + | 0.649644i | \(0.774918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 294.282i | 0.815186i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 76.9509i | − | 0.211986i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.21033 | + | 7.69477i | −0.0170146 | + | 0.0210816i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 300.825 | − | 300.825i | 0.819686 | − | 0.819686i | −0.166376 | − | 0.986062i | \(-0.553207\pi\) |
0.986062 | + | 0.166376i | \(0.0532065\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 332.919i | − | 0.902221i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −553.796 | + | 553.796i | −1.49271 | + | 1.49271i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 73.3291i | 0.196593i | 0.995157 | + | 0.0982963i | \(0.0313393\pi\) | ||||
−0.995157 | + | 0.0982963i | \(0.968661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −226.533 | + | 74.8336i | −0.604089 | + | 0.199556i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 83.0095 | + | 83.0095i | 0.220184 | + | 0.220184i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 93.5200 | − | 93.5200i | 0.246755 | − | 0.246755i | −0.572883 | − | 0.819637i | \(-0.694175\pi\) |
0.819637 | + | 0.572883i | \(0.194175\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 96.5762 | − | 96.5762i | 0.253481 | − | 0.253481i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 79.4324 | + | 79.4324i | 0.207395 | + | 0.207395i | 0.803159 | − | 0.595764i | \(-0.203151\pi\) |
−0.595764 | + | 0.803159i | \(0.703151\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −58.1193 | − | 544.417i | −0.150959 | − | 1.41407i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 172.890i | − | 0.446744i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 97.6035 | − | 97.6035i | 0.250909 | − | 0.250909i | −0.570434 | − | 0.821343i | \(-0.693225\pi\) |
0.821343 | + | 0.570434i | \(0.193225\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 173.539i | − | 0.443833i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −42.1774 | + | 42.1774i | −0.107322 | + | 0.107322i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.8059 | + | 447.810i | 0.121028 | + | 1.13370i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 299.500i | − | 0.754407i | −0.926130 | − | 0.377204i | \(-0.876886\pi\) | ||
0.926130 | − | 0.377204i | \(-0.123114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 595.610i | − | 1.49276i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −90.9226 | −0.226740 | −0.113370 | − | 0.993553i | \(-0.536164\pi\) | ||||
−0.113370 | + | 0.993553i | \(0.536164\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −123.451 | −0.306331 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.3045 | − | 2.16761i | 0.0501346 | − | 0.00535212i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −316.355 | − | 316.355i | −0.777284 | − | 0.777284i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −657.734 | −1.60815 | −0.804076 | − | 0.594526i | \(-0.797340\pi\) | ||||
−0.804076 | + | 0.594526i | \(0.797340\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 195.282 | + | 195.282i | 0.475138 | + | 0.475138i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.1345 | 0.106863 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.8124 | + | 2.00832i | −0.0453310 | + | 0.00483931i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 158.430 | − | 158.430i | 0.379927 | − | 0.379927i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −145.179 | − | 145.179i | −0.346489 | − | 0.346489i | 0.512311 | − | 0.858800i | \(-0.328790\pi\) |
−0.858800 | + | 0.512311i | \(0.828790\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.6145 | + | 19.6145i | 0.0465904 | + | 0.0465904i | 0.730018 | − | 0.683428i | \(-0.239512\pi\) |
−0.683428 | + | 0.730018i | \(0.739512\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 71.0562 | − | 71.0562i | 0.167982 | − | 0.167982i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −102.790 | + | 159.419i | −0.241858 | + | 0.375104i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 905.592 | 2.12082 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −80.6201 | − | 80.6201i | −0.187926 | − | 0.187926i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −184.193 | −0.427362 | −0.213681 | − | 0.976903i | \(-0.568545\pi\) | ||||
−0.213681 | + | 0.976903i | \(0.568545\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 401.221 | + | 401.221i | 0.926607 | + | 0.926607i | 0.997485 | − | 0.0708779i | \(-0.0225801\pi\) |
−0.0708779 | + | 0.997485i | \(0.522580\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 131.082 | + | 105.794i | 0.301338 | + | 0.243205i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 585.489 | 1.33979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −705.526 | −1.60712 | −0.803561 | − | 0.595223i | \(-0.797064\pi\) | ||||
−0.803561 | + | 0.595223i | \(0.797064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 533.679i | − | 1.21016i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 499.336i | 1.12717i | 0.826058 | + | 0.563585i | \(0.190578\pi\) | ||||
−0.826058 | + | 0.563585i | \(0.809422\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 305.235 | − | 32.5854i | 0.685922 | − | 0.0732256i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −256.036 | + | 256.036i | −0.572788 | + | 0.572788i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 786.125i | 1.75083i | 0.483368 | + | 0.875417i | \(0.339413\pi\) | ||||
−0.483368 | + | 0.875417i | \(0.660587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −394.700 | + | 394.700i | −0.875167 | + | 0.875167i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 92.7306i | − | 0.204703i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 315.456 | + | 254.600i | 0.693310 | + | 0.559560i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 411.045 | + | 411.045i | 0.899443 | + | 0.899443i | 0.995387 | − | 0.0959440i | \(-0.0305870\pi\) |
−0.0959440 | + | 0.995387i | \(0.530587\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 147.015 | − | 147.015i | 0.320294 | − | 0.320294i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −544.187 | + | 544.187i | −1.18045 | + | 1.18045i | −0.200821 | + | 0.979628i | \(0.564361\pi\) |
−0.979628 | + | 0.200821i | \(0.935639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −109.453 | − | 109.453i | −0.236400 | − | 0.236400i | 0.578957 | − | 0.815358i | \(-0.303460\pi\) |
−0.815358 | + | 0.578957i | \(0.803460\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −176.141 | + | 18.8039i | −0.378797 | + | 0.0404384i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 462.541i | − | 0.990452i | −0.868764 | − | 0.495226i | \(-0.835085\pi\) | ||
0.868764 | − | 0.495226i | \(-0.164915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −622.574 | + | 622.574i | −1.32745 | + | 1.32745i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 269.096i | 0.571329i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −204.974 | + | 204.974i | −0.433348 | + | 0.433348i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −537.852 | − | 346.794i | −1.13232 | − | 0.730093i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 344.171i | − | 0.721533i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 127.125i | 0.265397i | 0.991156 | + | 0.132698i | \(0.0423642\pi\) | ||||
−0.991156 | + | 0.132698i | \(0.957636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 331.253 | 0.688675 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −532.172 | −1.10181 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −458.231 | + | 567.761i | −0.944806 | + | 1.17064i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 376.646 | + | 376.646i | 0.773401 | + | 0.773401i | 0.978699 | − | 0.205299i | \(-0.0658165\pi\) |
−0.205299 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 187.432 | 0.383297 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −552.932 | − | 552.932i | −1.12613 | − | 1.12613i | −0.990800 | − | 0.135334i | \(-0.956789\pi\) |
−0.135334 | − | 0.990800i | \(-0.543211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 133.929 | 0.271662 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 187.231 | + | 151.111i | 0.378245 | + | 0.305276i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −210.178 | + | 210.178i | −0.422893 | + | 0.422893i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 308.855 | + | 308.855i | 0.618947 | + | 0.618947i | 0.945261 | − | 0.326314i | \(-0.105807\pi\) |
−0.326314 | + | 0.945261i | \(0.605807\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.3009 | + | 18.3009i | 0.0365286 | + | 0.0365286i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 345.746 | − | 345.746i | 0.687368 | − | 0.687368i | −0.274281 | − | 0.961650i | \(-0.588440\pi\) |
0.961650 | + | 0.274281i | \(0.0884399\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −507.147 | − | 409.310i | −1.00425 | − | 0.810516i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −238.135 | −0.469694 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −156.286 | − | 156.286i | −0.307046 | − | 0.307046i | 0.536717 | − | 0.843762i | \(-0.319664\pi\) |
−0.843762 | + | 0.536717i | \(0.819664\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.1093 | 0.0471807 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 496.003 | + | 496.003i | 0.966867 | + | 0.966867i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 325.132 | − | 402.847i | 0.631324 | − | 0.782227i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −168.485 | −0.325889 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 330.005 | 0.635848 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 483.674i | 0.928358i | 0.885741 | + | 0.464179i | \(0.153651\pi\) | ||||
−0.885741 | + | 0.464179i | \(0.846349\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 114.482i | − | 0.218895i | −0.993993 | − | 0.109448i | \(-0.965092\pi\) | ||
0.993993 | − | 0.109448i | \(-0.0349082\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 488.874 | + | 315.214i | 0.931188 | + | 0.600407i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −99.5895 | + | 99.5895i | −0.188974 | + | 0.188974i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.87038i | 0.0110971i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.7143 | + | 13.7143i | −0.0258273 | + | 0.0258273i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 413.288i | − | 0.775399i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −88.4241 | + | 9.43971i | −0.165279 | + | 0.0176443i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 90.0527 | + | 90.0527i | 0.167696 | + | 0.167696i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −632.715 | + | 632.715i | −1.17387 | + | 1.17387i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 575.569 | − | 575.569i | 1.06390 | − | 1.06390i | 0.0660852 | − | 0.997814i | \(-0.478949\pi\) |
0.997814 | − | 0.0660852i | \(-0.0210509\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −96.7998 | − | 96.7998i | −0.178269 | − | 0.178269i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −53.0478 | − | 42.8140i | −0.0973353 | − | 0.0785579i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1053.61i | − | 1.92616i | −0.269219 | − | 0.963079i | \(-0.586766\pi\) | ||
0.269219 | − | 0.963079i | \(-0.413234\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −281.402 | + | 281.402i | −0.512572 | + | 0.512572i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 451.855i | 0.820063i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 776.434 | − | 776.434i | 1.40404 | − | 1.40404i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 472.632 | − | 50.4559i | 0.851590 | − | 0.0909115i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 680.234i | 1.22125i | 0.791922 | + | 0.610623i | \(0.209081\pi\) | ||||
−0.791922 | + | 0.610623i | \(0.790919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 214.626i | − | 0.383947i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −130.074 | −0.231862 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −408.818 | −0.726142 | −0.363071 | − | 0.931761i | \(-0.618272\pi\) | ||||
−0.363071 | + | 0.931761i | \(0.618272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 343.872 | + | 277.534i | 0.608623 | + | 0.491211i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35.2049 | − | 35.2049i | −0.0620898 | − | 0.0620898i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 324.426 | 0.570169 | 0.285084 | − | 0.958502i | \(-0.407978\pi\) | ||||
0.285084 | + | 0.958502i | \(0.407978\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −124.307 | − | 124.307i | −0.217700 | − | 0.217700i | 0.589829 | − | 0.807528i | \(-0.299195\pi\) |
−0.807528 | + | 0.589829i | \(0.799195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −630.079 | −1.09962 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −309.858 | + | 480.567i | −0.538883 | + | 0.835768i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −303.425 | + | 303.425i | −0.525866 | + | 0.525866i | −0.919337 | − | 0.393471i | \(-0.871274\pi\) |
0.393471 | + | 0.919337i | \(0.371274\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −287.357 | − | 287.357i | −0.496299 | − | 0.496299i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.6178 | + | 32.6178i | 0.0561408 | + | 0.0561408i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −408.040 | + | 408.040i | −0.699897 | + | 0.699897i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −177.138 | + | 18.9104i | −0.302800 | + | 0.0323254i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 279.206 | 0.475649 | 0.237824 | − | 0.971308i | \(-0.423566\pi\) | ||||
0.237824 | + | 0.971308i | \(0.423566\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −335.998 | − | 335.998i | −0.570455 | − | 0.570455i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 492.023 | 0.832526 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −383.903 | − | 383.903i | −0.647392 | − | 0.647392i | 0.304970 | − | 0.952362i | \(-0.401354\pi\) |
−0.952362 | + | 0.304970i | \(0.901354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 459.870 | − | 49.0935i | 0.772892 | − | 0.0825100i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 626.973 | 1.05021 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 169.873 | 0.283594 | 0.141797 | − | 0.989896i | \(-0.454712\pi\) | ||||
0.141797 | + | 0.989896i | \(0.454712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 283.673i | − | 0.472002i | −0.971753 | − | 0.236001i | \(-0.924163\pi\) | ||
0.971753 | − | 0.236001i | \(-0.0758369\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 386.915i | − | 0.641650i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.3992 | + | 200.452i | 0.0353706 | + | 0.331325i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −438.351 | + | 438.351i | −0.722160 | + | 0.722160i | −0.969045 | − | 0.246885i | \(-0.920593\pi\) |
0.246885 | + | 0.969045i | \(0.420593\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 410.707i | − | 0.674396i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 88.2095 | − | 88.2095i | 0.144369 | − | 0.144369i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 165.499i | − | 0.269981i | −0.990847 | − | 0.134991i | \(-0.956900\pi\) | ||
0.990847 | − | 0.134991i | \(-0.0431005\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −62.9513 | − | 589.680i | −0.102360 | − | 0.958830i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 219.108 | + | 219.108i | 0.355118 | + | 0.355118i | 0.862010 | − | 0.506892i | \(-0.169206\pi\) |
−0.506892 | + | 0.862010i | \(0.669206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −365.140 | + | 365.140i | −0.589888 | + | 0.589888i | −0.937601 | − | 0.347713i | \(-0.886958\pi\) |
0.347713 | + | 0.937601i | \(0.386958\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 443.174 | − | 443.174i | 0.713646 | − | 0.713646i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −529.231 | − | 529.231i | −0.849488 | − | 0.849488i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 569.294 | − | 257.933i | 0.910870 | − | 0.412693i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 438.849i | − | 0.699918i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 267.225 | − | 267.225i | 0.424842 | − | 0.424842i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1113.61i | − | 1.76484i | −0.470463 | − | 0.882420i | \(-0.655913\pi\) | ||
0.470463 | − | 0.882420i | \(-0.344087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 98.0856 | − | 98.0856i | 0.154953 | − | 0.154953i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −224.718 | + | 278.431i | −0.353886 | + | 0.438475i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 662.511i | − | 1.04005i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 130.621i | − | 0.204414i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 279.808 | 0.436518 | 0.218259 | − | 0.975891i | \(-0.429962\pi\) | ||||
0.218259 | + | 0.975891i | \(0.429962\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 68.4686 | 0.106483 | 0.0532415 | − | 0.998582i | \(-0.483045\pi\) | ||||
0.0532415 | + | 0.998582i | \(0.483045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −32.6915 | − | 306.230i | −0.0506846 | − | 0.474775i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 60.8229 | + | 60.8229i | 0.0940075 | + | 0.0940075i | 0.752547 | − | 0.658539i | \(-0.228825\pi\) |
−0.658539 | + | 0.752547i | \(0.728825\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.5186 | 0.0501057 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 305.401 | + | 305.401i | 0.469125 | + | 0.469125i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −815.643 | −1.24907 | −0.624536 | − | 0.780996i | \(-0.714712\pi\) | ||||
−0.624536 | + | 0.780996i | \(0.714712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 98.1403 | − | 121.598i | 0.149832 | − | 0.185646i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.49169 | + | 7.49169i | −0.0114029 | + | 0.0114029i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 765.294 | + | 765.294i | 1.16130 | + | 1.16130i | 0.984192 | + | 0.177103i | \(0.0566727\pi\) |
0.177103 | + | 0.984192i | \(0.443327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −423.035 | − | 423.035i | −0.639993 | − | 0.639993i | 0.310561 | − | 0.950553i | \(-0.399483\pi\) |
−0.950553 | + | 0.310561i | \(0.899483\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 68.1000 | − | 68.1000i | 0.102715 | − | 0.102715i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 165.633 | + | 1551.52i | 0.249072 | + | 2.33312i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 403.729 | 0.605290 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 381.755 | + | 381.755i | 0.570636 | + | 0.570636i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 667.245 | 0.994404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −372.278 | − | 372.278i | −0.553162 | − | 0.553162i | 0.374190 | − | 0.927352i | \(-0.377921\pi\) |
−0.927352 | + | 0.374190i | \(0.877921\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −669.616 | + | 144.618i | −0.992023 | + | 0.214249i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −244.469 | −0.361106 | −0.180553 | − | 0.983565i | \(-0.557789\pi\) | ||||
−0.180553 | + | 0.983565i | \(0.557789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1778.91 | 2.61990 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 90.7496i | − | 0.133259i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 434.494i | − | 0.636155i | −0.948065 | − | 0.318077i | \(-0.896963\pi\) | ||
0.948065 | − | 0.318077i | \(-0.103037\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −563.002 | − | 454.390i | −0.821900 | − | 0.663343i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 125.118 | − | 125.118i | 0.182122 | − | 0.182122i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 427.256i | − | 0.620110i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −140.105 | + | 140.105i | −0.202756 | + | 0.202756i | −0.801180 | − | 0.598424i | \(-0.795794\pi\) |
0.598424 | + | 0.801180i | \(0.295794\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 586.634i | − | 0.846514i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −368.641 | + | 456.756i | −0.530419 | + | 0.657203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −333.404 | − | 333.404i | −0.478342 | − | 0.478342i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 383.793 | − | 383.793i | 0.549060 | − | 0.549060i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −333.050 | + | 333.050i | −0.475106 | + | 0.475106i | −0.903563 | − | 0.428456i | \(-0.859058\pi\) |
0.428456 | + | 0.903563i | \(0.359058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 901.572 | + | 901.572i | 1.28246 | + | 1.28246i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 112.422 | − | 139.294i | 0.159463 | − | 0.197579i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1589.00i | 2.24752i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 588.688 | − | 588.688i | 0.830308 | − | 0.830308i | −0.157251 | − | 0.987559i | \(-0.550263\pi\) |
0.987559 | + | 0.157251i | \(0.0502632\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 482.535i | 0.678671i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −300.211 | + | 300.211i | −0.421054 | + | 0.421054i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 232.430 | + | 187.590i | 0.325076 | + | 0.262364i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 467.773i | − | 0.652403i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 837.132i | 1.16430i | 0.813081 | + | 0.582150i | \(0.197788\pi\) | ||||
−0.813081 | + | 0.582150i | \(0.802212\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1262.20 | −1.75063 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 882.690 | 1.22087 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −370.880 | − | 239.135i | −0.511559 | − | 0.329841i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 115.757 | + | 115.757i | 0.159225 | + | 0.159225i | 0.782223 | − | 0.622998i | \(-0.214086\pi\) |
−0.622998 | + | 0.782223i | \(0.714086\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 492.575 | 0.675686 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −173.142 | − | 173.142i | −0.236856 | − | 0.236856i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 123.197 | 0.168073 | 0.0840363 | − | 0.996463i | \(-0.473219\pi\) | ||||
0.0840363 | + | 0.996463i | \(0.473219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −100.913 | − | 945.273i | −0.137296 | − | 1.28609i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −458.716 | + | 458.716i | −0.622410 | + | 0.622410i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 641.523 | + | 641.523i | 0.868096 | + | 0.868096i | 0.992262 | − | 0.124166i | \(-0.0396254\pi\) |
−0.124166 | + | 0.992262i | \(0.539625\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 229.758 | + | 229.758i | 0.310064 | + | 0.310064i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 84.7652 | − | 84.7652i | 0.114085 | − | 0.114085i | −0.647760 | − | 0.761845i | \(-0.724294\pi\) |
0.761845 | + | 0.647760i | \(0.224294\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 595.756 | − | 738.158i | 0.799673 | − | 0.990816i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.2712 | −0.0271368 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 153.314 | + | 153.314i | 0.204691 | + | 0.204691i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −137.548 | −0.183153 | −0.0915766 | − | 0.995798i | \(-0.529191\pi\) | ||||
−0.0915766 | + | 0.995798i | \(0.529191\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −102.217 | − | 102.217i | −0.135747 | − | 0.135747i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.7874 | + | 241.557i | 0.0341555 | + | 0.319943i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −857.792 | −1.13315 | −0.566574 | − | 0.824011i | \(-0.691731\pi\) | ||||
−0.566574 | + | 0.824011i | \(0.691731\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −392.108 | −0.516611 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 353.070i | − | 0.463956i | −0.972721 | − | 0.231978i | \(-0.925480\pi\) | ||
0.972721 | − | 0.231978i | \(-0.0745197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 166.210i | 0.217837i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −127.644 | + | 158.155i | −0.166855 | + | 0.206738i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.0250 | + | 17.0250i | −0.0221968 | + | 0.0221968i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 401.035i | − | 0.521503i | −0.965406 | − | 0.260751i | \(-0.916030\pi\) | ||
0.965406 | − | 0.260751i | \(-0.0839703\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 245.299 | − | 245.299i | 0.318157 | − | 0.318157i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 396.076i | 0.512388i | 0.966625 | + | 0.256194i | \(0.0824686\pi\) | ||||
−0.966625 | + | 0.256194i | \(0.917531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 453.605 | − | 97.9657i | 0.585297 | − | 0.126407i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −819.472 | − | 819.472i | −1.05466 | − | 1.05466i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1124.85 | − | 1124.85i | 1.44396 | − | 1.44396i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −154.860 | + | 154.860i | −0.198285 | + | 0.198285i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 342.023 | + | 342.023i | 0.436811 | + | 0.436811i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −74.8328 | − | 700.977i | −0.0953284 | − | 0.892964i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 184.472i | − | 0.234399i | −0.993108 | − | 0.117200i | \(-0.962608\pi\) | ||
0.993108 | − | 0.117200i | \(-0.0373917\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 670.650 | − | 670.650i | 0.850000 | − | 0.850000i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1077.42i | − | 1.36210i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −349.334 | + | 349.334i | −0.440522 | + | 0.440522i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −65.0788 | − | 609.609i | −0.0818602 | − | 0.766804i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 187.027i | 0.234664i | 0.993093 | + | 0.117332i | \(0.0374341\pi\) | ||||
−0.993093 | + | 0.117332i | \(0.962566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 142.319i | − | 0.178122i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 328.905 | 0.410617 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.7639 | 0.0221219 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1386.27 | − | 147.992i | 1.72208 | − | 0.183840i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 86.7572 | + | 86.7572i | 0.107506 | + | 0.107506i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −356.858 | −0.441110 | −0.220555 | − | 0.975374i | \(-0.570787\pi\) | ||||
−0.220555 | + | 0.975374i | \(0.570787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 882.626 | + | 882.626i | 1.08832 | + | 1.08832i | 0.995702 | + | 0.0926166i | \(0.0295231\pi\) |
0.0926166 | + | 0.995702i | \(0.470477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −82.4677 | −0.101436 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −488.248 | + | 52.1229i | −0.599078 | + | 0.0639545i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 584.150 | − | 584.150i | 0.714994 | − | 0.714994i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 307.130 | + | 307.130i | 0.375006 | + | 0.375006i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.9719 | + | 17.9719i | 0.0218902 | + | 0.0218902i | 0.717967 | − | 0.696077i | \(-0.245073\pi\) |
−0.696077 | + | 0.717967i | \(0.745073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.8905 | + | 36.8905i | −0.0448245 | + | 0.0448245i | −0.729164 | − | 0.684339i | \(-0.760091\pi\) |
0.684339 | + | 0.729164i | \(0.260091\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 360.205 | + | 232.251i | 0.436612 | + | 0.281517i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −837.787 | −1.01304 | −0.506522 | − | 0.862227i | \(-0.669069\pi\) | ||||
−0.506522 | + | 0.862227i | \(0.669069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1129.26 | + | 1129.26i | 1.36219 | + | 1.36219i | 0.871116 | + | 0.491077i | \(0.163397\pi\) |
0.491077 | + | 0.871116i | \(0.336603\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 101.385 | 0.122003 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −534.456 | − | 534.456i | −0.641604 | − | 0.641604i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.7618 | − | 42.5832i | −0.0631877 | − | 0.0509979i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −508.654 | −0.607711 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −949.313 | −1.13148 | −0.565741 | − | 0.824583i | \(-0.691410\pi\) | ||||
−0.565741 | + | 0.824583i | \(0.691410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 529.420i | − | 0.629512i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 279.265i | 0.331275i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 620.326 | − | 66.2229i | 0.734113 | − | 0.0783702i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 347.553 | − | 347.553i | 0.410334 | − | 0.410334i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 167.390i | 0.197161i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 805.547 | − | 805.547i | 0.946589 | − | 0.946589i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 293.712i | 0.344329i | 0.985068 | + | 0.172164i | \(0.0550760\pi\) | ||||
−0.985068 | + | 0.172164i | \(0.944924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −533.586 | − | 430.649i | −0.624077 | − | 0.503683i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −656.737 | − | 656.737i | −0.766321 | − | 0.766321i | 0.211136 | − | 0.977457i | \(-0.432284\pi\) |
−0.977457 | + | 0.211136i | \(0.932284\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1015.37 | + | 1015.37i | −1.18203 | + | 1.18203i | −0.202818 | + | 0.979217i | \(0.565010\pi\) |
−0.979217 | + | 0.202818i | \(0.934990\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1022.41 | + | 1022.41i | −1.18747 | + | 1.18747i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −400.164 | − | 400.164i | −0.463689 | − | 0.463689i | 0.436174 | − | 0.899863i | \(-0.356333\pi\) |
−0.899863 | + | 0.436174i | \(0.856333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −859.641 | + | 91.7710i | −0.993805 | + | 0.106094i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 441.709i | 0.509468i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 572.081 | − | 572.081i | 0.658321 | − | 0.658321i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 480.318i | − | 0.551456i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −552.776 | + | 552.776i | −0.633191 | + | 0.633191i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1361.14 | − | 685.160i | −1.55559 | − | 0.783040i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 532.291i | 0.606945i | 0.952840 | + | 0.303472i | \(0.0981460\pi\) | ||||
−0.952840 | + | 0.303472i | \(0.901854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 490.654i | 0.558196i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1748.05 | 1.98417 | 0.992083 | − | 0.125586i | \(-0.0400812\pi\) | ||||
0.992083 | + | 0.125586i | \(0.0400812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −141.696 | −0.160471 | −0.0802354 | − | 0.996776i | \(-0.525567\pi\) | ||||
−0.0802354 | + | 0.996776i | \(0.525567\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.6981 | + | 26.8845i | −0.0245176 | + | 0.0303780i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 258.995 | + | 258.995i | 0.291990 | + | 0.291990i | 0.837866 | − | 0.545876i | \(-0.183803\pi\) |
−0.545876 | + | 0.837866i | \(0.683803\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 872.383 | 0.981309 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.9392 | − | 25.9392i | −0.0291125 | − | 0.0291125i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 480.161 | 0.537694 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −259.624 | − | 209.538i | −0.290083 | − | 0.234121i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 205.286 | − | 205.286i | 0.228859 | − | 0.228859i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −231.690 | − | 231.690i | −0.257720 | − | 0.257720i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −344.672 | − | 344.672i | −0.382544 | − | 0.382544i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −530.955 | + | 530.955i | −0.587990 | + | 0.587990i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 279.076 | + | 225.238i | 0.308371 | + | 0.248882i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 427.687 | 0.471540 | 0.235770 | − | 0.971809i | \(-0.424239\pi\) | ||||
0.235770 | + | 0.971809i | \(0.424239\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −493.762 | − | 493.762i | −0.543192 | − | 0.543192i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −81.2821 | −0.0892229 | −0.0446114 | − | 0.999004i | \(-0.514205\pi\) | ||||
−0.0446114 | + | 0.999004i | \(0.514205\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0330 | + | 24.0330i | 0.0263231 | + | 0.0263231i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −445.221 | + | 551.640i | −0.486580 | + | 0.602886i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −380.993 | −0.415478 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 314.358 | 0.342065 | 0.171033 | − | 0.985265i | \(-0.445290\pi\) | ||||
0.171033 | + | 0.985265i | \(0.445290\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1147.26i | 1.24567i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 162.153i | − | 0.175680i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1217.14 | + | 262.868i | −1.31583 | + | 0.284182i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 392.215 | − | 392.215i | 0.423101 | − | 0.423101i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 447.538i | − | 0.481742i | −0.970557 | − | 0.240871i | \(-0.922567\pi\) | ||
0.970557 | − | 0.240871i | \(-0.0774330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1803.16 | − | 1803.16i | 1.93680 | − | 1.93680i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.0171i | 0.0150237i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 338.835 | − | 36.1723i | 0.362391 | − | 0.0386870i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −299.777 | − | 299.777i | −0.319932 | − | 0.319932i | 0.528809 | − | 0.848741i | \(-0.322639\pi\) |
−0.848741 | + | 0.528809i | \(0.822639\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −325.554 | + | 325.554i | −0.346703 | + | 0.346703i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 991.114 | − | 991.114i | 1.05326 | − | 1.05326i | 0.0547565 | − | 0.998500i | \(-0.482562\pi\) |
0.998500 | − | 0.0547565i | \(-0.0174382\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1005.04 | − | 1005.04i | −1.06579 | − | 1.06579i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1299.77 | + | 1049.02i | 1.37542 | + | 1.11008i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 22.1486i | − | 0.0233882i | −0.999932 | − | 0.0116941i | \(-0.996278\pi\) | ||
0.999932 | − | 0.0116941i | \(-0.00372243\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.30022 | + | 9.30022i | −0.00980002 | + | 0.00980002i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 508.428i | 0.534625i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1197.38 | − | 1197.38i | 1.25643 | − | 1.25643i | 0.303651 | − | 0.952783i | \(-0.401794\pi\) |
0.952783 | − | 0.303651i | \(-0.0982056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1641.31 | − | 175.218i | 1.71865 | − | 0.183475i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 302.612i | − | 0.316208i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1764.00i | 1.83942i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −616.432 | −0.641449 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −95.2809 | −0.0989417 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 828.457 | + | 668.635i | 0.858505 | + | 0.692886i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −937.022 | − | 937.022i | −0.968998 | − | 0.968998i | 0.0305352 | − | 0.999534i | \(-0.490279\pi\) |
−0.999534 | + | 0.0305352i | \(0.990279\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 370.696 | 0.382555 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1016.28 | − | 1016.28i | −1.04663 | − | 1.04663i | −0.998858 | − | 0.0477733i | \(-0.984787\pi\) |
−0.0477733 | − | 0.998858i | \(-0.515213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1431.11 | 1.47082 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −310.178 | + | 66.9896i | −0.318132 | + | 0.0687073i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −578.640 | + | 578.640i | −0.592262 | + | 0.592262i | −0.938242 | − | 0.345980i | \(-0.887546\pi\) |
0.345980 | + | 0.938242i | \(0.387546\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −389.940 | − | 389.940i | −0.398305 | − | 0.398305i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.6477 | − | 51.6477i | −0.0526480 | − | 0.0526480i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 666.904 | − | 666.904i | 0.678437 | − | 0.678437i | −0.281209 | − | 0.959646i | \(-0.590735\pi\) |
0.959646 | + | 0.281209i | \(0.0907355\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1281.69 | + | 136.826i | −1.30120 | + | 0.138910i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −436.435 | −0.442184 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −521.933 | − | 521.933i | −0.527738 | − | 0.527738i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −573.966 | −0.579178 | −0.289589 | − | 0.957151i | \(-0.593519\pi\) | ||||
−0.289589 | + | 0.957151i | \(0.593519\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −127.850 | − | 127.850i | −0.128752 | − | 0.128752i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1633.22 | + | 174.355i | −1.64143 | + | 0.175231i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −293.423 | −0.294306 | −0.147153 | − | 0.989114i | \(-0.547011\pi\) | ||||
−0.147153 | + | 0.989114i | \(0.547011\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1364.85 | 1.36622 |
(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 | 640.3.t.a.353.15 | 44 | ||
4.3 | odd | 2 | 640.3.t.b.353.8 | 44 | |||
5.2 | odd | 4 | 640.3.i.a.97.8 | 44 | |||
8.3 | odd | 2 | 80.3.t.a.53.17 | yes | 44 | ||
8.5 | even | 2 | 320.3.t.a.113.8 | 44 | |||
16.3 | odd | 4 | 640.3.i.b.33.8 | 44 | |||
16.5 | even | 4 | 320.3.i.a.273.8 | 44 | |||
16.11 | odd | 4 | 80.3.i.a.13.7 | ✓ | 44 | ||
16.13 | even | 4 | 640.3.i.a.33.15 | 44 | |||
20.7 | even | 4 | 640.3.i.b.97.15 | 44 | |||
40.3 | even | 4 | 400.3.i.b.357.16 | 44 | |||
40.19 | odd | 2 | 400.3.t.b.293.6 | 44 | |||
40.27 | even | 4 | 80.3.i.a.37.7 | yes | 44 | ||
40.37 | odd | 4 | 320.3.i.a.177.15 | 44 | |||
80.27 | even | 4 | 80.3.t.a.77.17 | yes | 44 | ||
80.37 | odd | 4 | 320.3.t.a.17.8 | 44 | |||
80.43 | even | 4 | 400.3.t.b.157.6 | 44 | |||
80.59 | odd | 4 | 400.3.i.b.93.16 | 44 | |||
80.67 | even | 4 | 640.3.t.b.417.8 | 44 | |||
80.77 | odd | 4 | inner | 640.3.t.a.417.15 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.i.a.13.7 | ✓ | 44 | 16.11 | odd | 4 | ||
80.3.i.a.37.7 | yes | 44 | 40.27 | even | 4 | ||
80.3.t.a.53.17 | yes | 44 | 8.3 | odd | 2 | ||
80.3.t.a.77.17 | yes | 44 | 80.27 | even | 4 | ||
320.3.i.a.177.15 | 44 | 40.37 | odd | 4 | |||
320.3.i.a.273.8 | 44 | 16.5 | even | 4 | |||
320.3.t.a.17.8 | 44 | 80.37 | odd | 4 | |||
320.3.t.a.113.8 | 44 | 8.5 | even | 2 | |||
400.3.i.b.93.16 | 44 | 80.59 | odd | 4 | |||
400.3.i.b.357.16 | 44 | 40.3 | even | 4 | |||
400.3.t.b.157.6 | 44 | 80.43 | even | 4 | |||
400.3.t.b.293.6 | 44 | 40.19 | odd | 2 | |||
640.3.i.a.33.15 | 44 | 16.13 | even | 4 | |||
640.3.i.a.97.8 | 44 | 5.2 | odd | 4 | |||
640.3.i.b.33.8 | 44 | 16.3 | odd | 4 | |||
640.3.i.b.97.15 | 44 | 20.7 | even | 4 | |||
640.3.t.a.353.15 | 44 | 1.1 | even | 1 | trivial | ||
640.3.t.a.417.15 | 44 | 80.77 | odd | 4 | inner | ||
640.3.t.b.353.8 | 44 | 4.3 | odd | 2 | |||
640.3.t.b.417.8 | 44 | 80.67 | even | 4 |