Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(361,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.bs (of order \(6\), degree \(2\), 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: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.3 | ||
Root | \(1.35234 + 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.901 |
Dual form | 1170.2.bs.h.361.3 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.34233 | + | 1.35234i | −0.885317 | + | 0.511138i | −0.872408 | − | 0.488779i | \(-0.837443\pi\) |
−0.0129093 | + | 0.999917i | \(0.504109\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −2.59808 | − | 1.50000i | −0.783349 | − | 0.452267i | 0.0542666 | − | 0.998526i | \(-0.482718\pi\) |
−0.837616 | + | 0.546259i | \(0.816051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.34233 | − | 1.35234i | −0.926995 | − | 0.375073i | ||||
\(14\) | −2.70469 | −0.722858 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.34233 | + | 3.08440i | −1.22561 | + | 0.707609i | −0.966109 | − | 0.258133i | \(-0.916893\pi\) |
−0.259505 | + | 0.965742i | \(0.583559\pi\) | |||||||
\(20\) | 0.866025 | − | 0.500000i | 0.193649 | − | 0.111803i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | −3.95042 | + | 6.84233i | −0.823720 | + | 1.42672i | 0.0791743 | + | 0.996861i | \(0.474772\pi\) |
−0.902894 | + | 0.429863i | \(0.858562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.21837 | − | 2.84233i | −0.435058 | − | 0.557427i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.34233 | − | 1.35234i | −0.442659 | − | 0.255569i | ||||
\(29\) | 1.24573 | − | 2.15767i | 0.231327 | − | 0.400669i | −0.726872 | − | 0.686773i | \(-0.759027\pi\) |
0.958199 | + | 0.286103i | \(0.0923601\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.972638i | 0.174691i | 0.996178 | + | 0.0873455i | \(0.0278384\pi\) | ||||
−0.996178 | + | 0.0873455i | \(0.972162\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.35234 | + | 2.34233i | 0.228588 | + | 0.395926i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | − | 0.866025i | −0.246598 | − | 0.142374i | 0.371607 | − | 0.928390i | \(-0.378807\pi\) |
−0.618206 | + | 0.786016i | \(0.712140\pi\) | |||||||
\(38\) | −6.16879 | −1.00071 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 5.19615 | + | 3.00000i | 0.811503 | + | 0.468521i | 0.847477 | − | 0.530831i | \(-0.178120\pi\) |
−0.0359748 | + | 0.999353i | \(0.511454\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.84233 | − | 8.38716i | −0.738448 | − | 1.27903i | −0.953194 | − | 0.302360i | \(-0.902226\pi\) |
0.214746 | − | 0.976670i | \(-0.431108\pi\) | |||||||
\(44\) | − | 3.00000i | − | 0.452267i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.84233 | + | 3.95042i | −1.00885 | + | 0.582458i | ||||
\(47\) | 3.00000i | 0.437595i | 0.975770 | + | 0.218797i | \(0.0702134\pi\) | ||||
−0.975770 | + | 0.218797i | \(0.929787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.157671 | − | 0.273094i | 0.0225244 | − | 0.0390134i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.500000 | − | 3.57071i | −0.0693375 | − | 0.495169i | ||||
\(53\) | 2.70469 | 0.371518 | 0.185759 | − | 0.982595i | \(-0.440526\pi\) | ||||
0.185759 | + | 0.982595i | \(0.440526\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | + | 2.59808i | −0.202260 | + | 0.350325i | ||||
\(56\) | −1.35234 | − | 2.34233i | −0.180715 | − | 0.313007i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.15767 | − | 1.24573i | 0.283316 | − | 0.163573i | ||||
\(59\) | 6.65511 | − | 3.84233i | 0.866421 | − | 0.500229i | 0.000264050 | − | 1.00000i | \(-0.499916\pi\) |
0.866157 | + | 0.499771i | \(0.166583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.68466 | − | 11.5782i | −0.855883 | − | 1.48243i | −0.875824 | − | 0.482631i | \(-0.839681\pi\) |
0.0199408 | − | 0.999801i | \(-0.493652\pi\) | |||||||
\(62\) | −0.486319 | + | 0.842329i | −0.0617626 | + | 0.106976i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.35234 | + | 3.34233i | −0.167738 | + | 0.414565i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.68466 | − | 0.972638i | −0.205814 | − | 0.118827i | 0.393551 | − | 0.919303i | \(-0.371247\pi\) |
−0.599364 | + | 0.800476i | \(0.704580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.70469i | 0.323272i | ||||||||
\(71\) | −5.19615 | + | 3.00000i | −0.616670 | + | 0.356034i | −0.775571 | − | 0.631260i | \(-0.782538\pi\) |
0.158901 | + | 0.987294i | \(0.449205\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | −0.866025 | − | 1.50000i | −0.100673 | − | 0.174371i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.34233 | − | 3.08440i | −0.612807 | − | 0.353804i | ||||
\(77\) | 8.11407 | 0.924684 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.68466 | 0.639574 | 0.319787 | − | 0.947489i | \(-0.396389\pi\) | ||||
0.319787 | + | 0.947489i | \(0.396389\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | + | 5.19615i | 0.331295 | + | 0.573819i | ||||
\(83\) | 15.3693i | 1.68700i | 0.537128 | + | 0.843501i | \(0.319509\pi\) | ||||
−0.537128 | + | 0.843501i | \(0.680491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 9.68466i | − | 1.04432i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −4.05703 | − | 2.34233i | −0.430045 | − | 0.248286i | 0.269321 | − | 0.963050i | \(-0.413201\pi\) |
−0.699366 | + | 0.714764i | \(0.746534\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.65767 | − | 1.35234i | 1.01240 | − | 0.141764i | ||||
\(92\) | −7.90084 | −0.823720 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.50000 | + | 2.59808i | −0.154713 | + | 0.267971i | ||||
\(95\) | 3.08440 | + | 5.34233i | 0.316452 | + | 0.548111i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.68466 | + | 4.43674i | −0.780259 | + | 0.450483i | −0.836522 | − | 0.547933i | \(-0.815415\pi\) |
0.0562632 | + | 0.998416i | \(0.482081\pi\) | |||||||
\(98\) | 0.273094 | − | 0.157671i | 0.0275866 | − | 0.0159272i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 5.40938 | − | 9.36932i | 0.538253 | − | 0.932282i | −0.460745 | − | 0.887533i | \(-0.652418\pi\) |
0.998998 | − | 0.0447493i | \(-0.0142489\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.6847 | −1.44692 | −0.723461 | − | 0.690365i | \(-0.757450\pi\) | ||||
−0.723461 | + | 0.690365i | \(0.757450\pi\) | |||||||
\(104\) | 1.35234 | − | 3.34233i | 0.132608 | − | 0.327742i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.34233 | + | 1.35234i | 0.227507 | + | 0.131351i | ||||
\(107\) | 2.70469 | − | 4.68466i | 0.261472 | − | 0.452883i | −0.705161 | − | 0.709047i | \(-0.749125\pi\) |
0.966633 | + | 0.256164i | \(0.0824587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3376i | 1.18173i | 0.806772 | + | 0.590863i | \(0.201213\pi\) | ||||
−0.806772 | + | 0.590863i | \(0.798787\pi\) | |||||||
\(110\) | −2.59808 | + | 1.50000i | −0.247717 | + | 0.143019i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 2.70469i | − | 0.255569i | ||||||
\(113\) | −1.24573 | − | 2.15767i | −0.117189 | − | 0.202977i | 0.801464 | − | 0.598043i | \(-0.204055\pi\) |
−0.918653 | + | 0.395067i | \(0.870722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.84233 | + | 3.95042i | 0.638050 | + | 0.368379i | ||||
\(116\) | 2.49146 | 0.231327 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.68466 | 0.707430 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | − | 13.3693i | − | 1.21040i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.842329 | + | 0.486319i | −0.0756434 | + | 0.0436727i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.34233 | + | 2.32498i | −0.119112 | + | 0.206309i | −0.919416 | − | 0.393286i | \(-0.871338\pi\) |
0.800304 | + | 0.599595i | \(0.204672\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.84233 | + | 2.21837i | −0.249289 | + | 0.194564i | ||||
\(131\) | 20.9978 | 1.83459 | 0.917295 | − | 0.398209i | \(-0.130368\pi\) | ||||
0.917295 | + | 0.398209i | \(0.130368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.34233 | − | 14.4493i | 0.723372 | − | 1.25292i | ||||
\(134\) | −0.972638 | − | 1.68466i | −0.0840231 | − | 0.145532i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.0474 | − | 9.84233i | 1.45646 | − | 0.840887i | 0.457624 | − | 0.889146i | \(-0.348701\pi\) |
0.998835 | + | 0.0482589i | \(0.0153672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.65767 | − | 8.06732i | −0.395058 | − | 0.684261i | 0.598050 | − | 0.801459i | \(-0.295942\pi\) |
−0.993109 | + | 0.117197i | \(0.962609\pi\) | |||||||
\(140\) | −1.35234 | + | 2.34233i | −0.114294 | + | 0.197963i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 6.65511 | + | 8.52699i | 0.556528 | + | 0.713063i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.15767 | − | 1.24573i | −0.179185 | − | 0.103452i | ||||
\(146\) | −3.46410 | + | 6.00000i | −0.286691 | + | 0.496564i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.73205i | − | 0.142374i | ||||||
\(149\) | −8.93335 | + | 5.15767i | −0.731848 | + | 0.422533i | −0.819098 | − | 0.573654i | \(-0.805526\pi\) |
0.0872496 | + | 0.996186i | \(0.472192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.2829i | − | 1.16232i | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||
0.813788 | − | 0.581161i | \(-0.197401\pi\) | |||||||
\(152\) | −3.08440 | − | 5.34233i | −0.250177 | − | 0.433320i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.02699 | + | 4.05703i | 0.566251 | + | 0.326925i | ||||
\(155\) | 0.972638 | 0.0781242 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.36932 | 0.667944 | 0.333972 | − | 0.942583i | \(-0.391611\pi\) | ||||
0.333972 | + | 0.942583i | \(0.391611\pi\) | |||||||
\(158\) | 4.92306 | + | 2.84233i | 0.391658 | + | 0.226124i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | − | 21.3693i | − | 1.68414i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.8423 | + | 9.14657i | −1.24087 | + | 0.716415i | −0.969271 | − | 0.245996i | \(-0.920885\pi\) |
−0.271596 | + | 0.962411i | \(0.587552\pi\) | |||||||
\(164\) | 6.00000i | 0.468521i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.68466 | + | 13.3102i | −0.596445 | + | 1.03307i | ||||
\(167\) | 5.51599 | + | 3.18466i | 0.426840 | + | 0.246436i | 0.698000 | − | 0.716098i | \(-0.254074\pi\) |
−0.271159 | + | 0.962534i | \(0.587407\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.34233 | + | 9.03996i | 0.718641 | + | 0.695382i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.84233 | − | 8.38716i | 0.369224 | − | 0.639515i | ||||
\(173\) | 4.05703 | + | 7.02699i | 0.308451 | + | 0.534252i | 0.978024 | − | 0.208494i | \(-0.0668562\pi\) |
−0.669573 | + | 0.742746i | \(0.733523\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34233 | − | 1.35234i | 0.177063 | − | 0.102228i | ||||
\(176\) | 2.59808 | − | 1.50000i | 0.195837 | − | 0.113067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.34233 | − | 4.05703i | −0.175565 | − | 0.304087i | ||||
\(179\) | −6.44188 | + | 11.1577i | −0.481489 | + | 0.833963i | −0.999774 | − | 0.0212443i | \(-0.993237\pi\) |
0.518285 | + | 0.855208i | \(0.326571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.36932 | 0.399098 | 0.199549 | − | 0.979888i | \(-0.436052\pi\) | ||||
0.199549 | + | 0.979888i | \(0.436052\pi\) | |||||||
\(182\) | 9.03996 | + | 3.65767i | 0.670086 | + | 0.271125i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.84233 | − | 3.95042i | −0.504423 | − | 0.291229i | ||||
\(185\) | −0.866025 | + | 1.50000i | −0.0636715 | + | 0.110282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.59808 | + | 1.50000i | −0.189484 | + | 0.109399i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.16879i | 0.447531i | ||||||||
\(191\) | −10.6055 | − | 18.3693i | −0.767389 | − | 1.32916i | −0.938974 | − | 0.343988i | \(-0.888222\pi\) |
0.171585 | − | 0.985169i | \(-0.445111\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.6847 | + | 7.90084i | 0.985043 | + | 0.568715i | 0.903789 | − | 0.427978i | \(-0.140774\pi\) |
0.0812543 | + | 0.996693i | \(0.474107\pi\) | |||||||
\(194\) | −8.87348 | −0.637079 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.315342 | 0.0225244 | ||||||||
\(197\) | −17.3673 | − | 10.0270i | −1.23737 | − | 0.714393i | −0.268811 | − | 0.963193i | \(-0.586631\pi\) |
−0.968555 | + | 0.248800i | \(0.919964\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.68466 | + | 15.0423i | 0.615639 | + | 1.06632i | 0.990272 | + | 0.139145i | \(0.0444354\pi\) |
−0.374633 | + | 0.927173i | \(0.622231\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.36932 | − | 5.40938i | 0.659223 | − | 0.380602i | ||||
\(203\) | 6.73863i | 0.472959i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | −12.7173 | − | 7.34233i | −0.886055 | − | 0.511564i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.84233 | − | 2.21837i | 0.197080 | − | 0.153816i | ||||
\(209\) | 18.5064 | 1.28011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.34233 | − | 5.78908i | 0.230095 | − | 0.398537i | −0.727741 | − | 0.685853i | \(-0.759429\pi\) |
0.957836 | + | 0.287316i | \(0.0927628\pi\) | |||||||
\(212\) | 1.35234 | + | 2.34233i | 0.0928794 | + | 0.160872i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.68466 | − | 2.70469i | 0.320237 | − | 0.184889i | ||||
\(215\) | −8.38716 | + | 4.84233i | −0.572000 | + | 0.330244i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.31534 | − | 2.27824i | −0.0892912 | − | 0.154657i | ||||
\(218\) | −6.16879 | + | 10.6847i | −0.417803 | + | 0.723656i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.00000 | −0.202260 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.65767 | + | 3.84381i | 0.445831 | + | 0.257400i | 0.706068 | − | 0.708144i | \(-0.250467\pi\) |
−0.260237 | + | 0.965545i | \(0.583801\pi\) | |||||||
\(224\) | 1.35234 | − | 2.34233i | 0.0903573 | − | 0.156503i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 2.49146i | − | 0.165730i | ||||||
\(227\) | −2.91791 | + | 1.68466i | −0.193669 | + | 0.111815i | −0.593699 | − | 0.804687i | \(-0.702333\pi\) |
0.400030 | + | 0.916502i | \(0.369000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.1940i | 1.73095i | 0.500954 | + | 0.865474i | \(0.332982\pi\) | ||||
−0.500954 | + | 0.865474i | \(0.667018\pi\) | |||||||
\(230\) | 3.95042 | + | 6.84233i | 0.260483 | + | 0.451170i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.15767 | + | 1.24573i | 0.141658 | + | 0.0817863i | ||||
\(233\) | 12.8838 | 0.844044 | 0.422022 | − | 0.906586i | \(-0.361321\pi\) | ||||
0.422022 | + | 0.906586i | \(0.361321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 6.65511 | + | 3.84233i | 0.433211 | + | 0.250114i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.7386i | 1.60021i | 0.599861 | + | 0.800105i | \(0.295223\pi\) | ||||
−0.599861 | + | 0.800105i | \(0.704777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.81534 | + | 3.35749i | −0.374599 | + | 0.216275i | −0.675466 | − | 0.737391i | \(-0.736057\pi\) |
0.300867 | + | 0.953666i | \(0.402724\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.68466 | − | 11.5782i | 0.427941 | − | 0.741216i | ||||
\(245\) | −0.273094 | − | 0.157671i | −0.0174473 | − | 0.0100732i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.0270 | − | 3.08440i | 1.40154 | − | 0.196255i | ||||
\(248\) | −0.972638 | −0.0617626 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | −2.59808 | − | 4.50000i | −0.163989 | − | 0.284037i | 0.772307 | − | 0.635250i | \(-0.219103\pi\) |
−0.936296 | + | 0.351212i | \(0.885770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.5270 | − | 11.8513i | 1.29052 | − | 0.745082i | ||||
\(254\) | −2.32498 | + | 1.34233i | −0.145882 | + | 0.0842252i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −11.6380 | + | 20.1577i | −0.725961 | + | 1.25740i | 0.232617 | + | 0.972569i | \(0.425271\pi\) |
−0.958577 | + | 0.284832i | \(0.908062\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.68466 | 0.291091 | ||||||||
\(260\) | −3.57071 | + | 0.500000i | −0.221446 | + | 0.0310087i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.1847 | + | 10.4989i | 1.12345 | + | 0.648625i | ||||
\(263\) | −15.9083 | + | 27.5540i | −0.980947 | + | 1.69905i | −0.322228 | + | 0.946662i | \(0.604432\pi\) |
−0.658719 | + | 0.752389i | \(0.728901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.70469i | − | 0.166148i | ||||||
\(266\) | 14.4493 | − | 8.34233i | 0.885946 | − | 0.511501i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 1.94528i | − | 0.118827i | ||||||
\(269\) | −5.40938 | − | 9.36932i | −0.329816 | − | 0.571257i | 0.652659 | − | 0.757651i | \(-0.273653\pi\) |
−0.982475 | + | 0.186394i | \(0.940320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5270 | + | 6.65511i | 0.700215 | + | 0.404269i | 0.807427 | − | 0.589967i | \(-0.200859\pi\) |
−0.107213 | + | 0.994236i | \(0.534193\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.6847 | 1.18919 | ||||||||
\(275\) | 2.59808 | + | 1.50000i | 0.156670 | + | 0.0904534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | − | 9.31534i | − | 0.558697i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.34233 | + | 1.35234i | −0.139981 | + | 0.0808180i | ||||
\(281\) | − | 24.7386i | − | 1.47578i | −0.674919 | − | 0.737892i | \(-0.735822\pi\) | ||
0.674919 | − | 0.737892i | \(-0.264178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.52699 | − | 11.3051i | 0.387989 | − | 0.672017i | −0.604190 | − | 0.796840i | \(-0.706503\pi\) |
0.992179 | + | 0.124824i | \(0.0398365\pi\) | |||||||
\(284\) | −5.19615 | − | 3.00000i | −0.308335 | − | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.50000 | + | 10.7121i | 0.0886969 | + | 0.633422i | ||||
\(287\) | −16.2281 | −0.957916 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | −1.24573 | − | 2.15767i | −0.0731519 | − | 0.126703i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | + | 3.46410i | −0.351123 | + | 0.202721i | ||||
\(293\) | −19.6455 | + | 11.3423i | −1.14770 | + | 0.662626i | −0.948326 | − | 0.317297i | \(-0.897225\pi\) |
−0.199376 | + | 0.979923i | \(0.563891\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.84233 | − | 6.65511i | −0.223709 | − | 0.387475i | ||||
\(296\) | 0.866025 | − | 1.50000i | 0.0503367 | − | 0.0871857i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.3153 | −0.597552 | ||||||||
\(299\) | 22.4568 | − | 17.5270i | 1.29871 | − | 1.01361i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.6847 | + | 13.0970i | 1.30752 | + | 0.754898i | ||||
\(302\) | 7.14143 | − | 12.3693i | 0.410943 | − | 0.711774i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.16879i | − | 0.353804i | ||||||
\(305\) | −11.5782 | + | 6.68466i | −0.662964 | + | 0.382762i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.2829i | 0.815166i | 0.913168 | + | 0.407583i | \(0.133628\pi\) | ||||
−0.913168 | + | 0.407583i | \(0.866372\pi\) | |||||||
\(308\) | 4.05703 | + | 7.02699i | 0.231171 | + | 0.400400i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.842329 | + | 0.486319i | 0.0478411 | + | 0.0276211i | ||||
\(311\) | 4.98293 | 0.282556 | 0.141278 | − | 0.989970i | \(-0.454879\pi\) | ||||
0.141278 | + | 0.989970i | \(0.454879\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.36932 | −0.303492 | −0.151746 | − | 0.988420i | \(-0.548490\pi\) | ||||
−0.151746 | + | 0.988420i | \(0.548490\pi\) | |||||||
\(314\) | 7.24804 | + | 4.18466i | 0.409031 | + | 0.236154i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.84233 | + | 4.92306i | 0.159894 | + | 0.276944i | ||||
\(317\) | − | 29.4233i | − | 1.65258i | −0.563247 | − | 0.826288i | \(-0.690448\pi\) | ||
0.563247 | − | 0.826288i | \(-0.309552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.47301 | + | 3.73720i | −0.362419 | + | 0.209243i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.6847 | − | 18.5064i | 0.595433 | − | 1.03132i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.34233 | + | 1.35234i | 0.185399 | + | 0.0750146i | ||||
\(326\) | −18.2931 | −1.01316 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.00000 | + | 5.19615i | −0.165647 | + | 0.286910i | ||||
\(329\) | −4.05703 | − | 7.02699i | −0.223671 | − | 0.387410i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.05398 | − | 4.64996i | 0.442687 | − | 0.255585i | −0.262050 | − | 0.965054i | \(-0.584399\pi\) |
0.704737 | + | 0.709469i | \(0.251065\pi\) | |||||||
\(332\) | −13.3102 | + | 7.68466i | −0.730493 | + | 0.421750i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.18466 | + | 5.51599i | 0.174257 | + | 0.301822i | ||||
\(335\) | −0.972638 | + | 1.68466i | −0.0531409 | + | 0.0920427i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.3693 | −1.59985 | −0.799924 | − | 0.600101i | \(-0.795127\pi\) | ||||
−0.799924 | + | 0.600101i | \(0.795127\pi\) | |||||||
\(338\) | 3.57071 | + | 12.5000i | 0.194221 | + | 0.679910i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.45896 | − | 2.52699i | 0.0790070 | − | 0.136844i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.0799i | − | 0.976224i | ||||||
\(344\) | 8.38716 | − | 4.84233i | 0.452205 | − | 0.261081i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.11407i | 0.436215i | ||||||||
\(347\) | −2.49146 | − | 4.31534i | −0.133749 | − | 0.231660i | 0.791370 | − | 0.611337i | \(-0.209368\pi\) |
−0.925119 | + | 0.379678i | \(0.876035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.0540 | − | 16.7743i | −1.55522 | − | 0.897909i | −0.997703 | − | 0.0677460i | \(-0.978419\pi\) |
−0.557521 | − | 0.830163i | \(-0.688247\pi\) | |||||||
\(350\) | 2.70469 | 0.144572 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 13.3102 | + | 7.68466i | 0.708431 | + | 0.409013i | 0.810480 | − | 0.585766i | \(-0.199206\pi\) |
−0.102049 | + | 0.994779i | \(0.532540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | + | 5.19615i | 0.159223 | + | 0.275783i | ||||
\(356\) | − | 4.68466i | − | 0.248286i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.1577 | + | 6.44188i | −0.589701 | + | 0.340464i | ||||
\(359\) | − | 2.63068i | − | 0.138842i | −0.997587 | − | 0.0694211i | \(-0.977885\pi\) | ||
0.997587 | − | 0.0694211i | \(-0.0221152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.52699 | − | 16.5012i | 0.501420 | − | 0.868486i | ||||
\(362\) | 4.64996 | + | 2.68466i | 0.244397 | + | 0.141103i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.00000 | + | 7.68762i | 0.314485 | + | 0.402941i | ||||
\(365\) | 6.92820 | 0.362639 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.6847 | + | 20.2384i | −0.609934 | + | 1.05644i | 0.381317 | + | 0.924445i | \(0.375471\pi\) |
−0.991251 | + | 0.131992i | \(0.957863\pi\) | |||||||
\(368\) | −3.95042 | − | 6.84233i | −0.205930 | − | 0.356681i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.50000 | + | 0.866025i | −0.0779813 | + | 0.0450225i | ||||
\(371\) | −6.33527 | + | 3.65767i | −0.328911 | + | 0.189897i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.526988 | + | 0.912769i | 0.0272864 | + | 0.0472614i | 0.879346 | − | 0.476183i | \(-0.157980\pi\) |
−0.852060 | + | 0.523445i | \(0.824647\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | −7.08156 | + | 5.52699i | −0.364719 | + | 0.284654i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.288354 | − | 0.166481i | −0.0148117 | − | 0.00855157i | 0.492576 | − | 0.870270i | \(-0.336055\pi\) |
−0.507388 | + | 0.861718i | \(0.669389\pi\) | |||||||
\(380\) | −3.08440 | + | 5.34233i | −0.158226 | + | 0.274056i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 21.2111i | − | 1.08525i | ||||||
\(383\) | −6.65511 | + | 3.84233i | −0.340060 | + | 0.196334i | −0.660299 | − | 0.751003i | \(-0.729570\pi\) |
0.320238 | + | 0.947337i | \(0.396237\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 8.11407i | − | 0.413531i | ||||||
\(386\) | 7.90084 | + | 13.6847i | 0.402142 | + | 0.696531i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.68466 | − | 4.43674i | −0.390129 | − | 0.225241i | ||||
\(389\) | −24.1290 | −1.22339 | −0.611694 | − | 0.791095i | \(-0.709512\pi\) | ||||
−0.611694 | + | 0.791095i | \(0.709512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.273094 | + | 0.157671i | 0.0137933 | + | 0.00796358i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0270 | − | 17.3673i | −0.505152 | − | 0.874950i | ||||
\(395\) | − | 5.68466i | − | 0.286026i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.1847 | + | 17.4271i | −1.51492 | + | 0.874642i | −0.515078 | + | 0.857143i | \(0.672237\pi\) |
−0.999847 | + | 0.0174986i | \(0.994430\pi\) | |||||||
\(398\) | 17.3693i | 0.870645i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −1.77879 | − | 1.02699i | −0.0888288 | − | 0.0512853i | 0.454928 | − | 0.890528i | \(-0.349665\pi\) |
−0.543756 | + | 0.839243i | \(0.682998\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.31534 | − | 3.25088i | 0.0655218 | − | 0.161938i | ||||
\(404\) | 10.8188 | 0.538253 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.36932 | + | 5.83583i | −0.167216 | + | 0.289627i | ||||
\(407\) | 2.59808 | + | 4.50000i | 0.128782 | + | 0.223057i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.7116 | + | 6.76172i | −0.579104 | + | 0.334346i | −0.760777 | − | 0.649013i | \(-0.775182\pi\) |
0.181673 | + | 0.983359i | \(0.441849\pi\) | |||||||
\(410\) | 5.19615 | − | 3.00000i | 0.256620 | − | 0.148159i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.34233 | − | 12.7173i | −0.361731 | − | 0.626536i | ||||
\(413\) | −10.3923 | + | 18.0000i | −0.511372 | + | 0.885722i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.3693 | 0.754450 | ||||||||
\(416\) | 3.57071 | − | 0.500000i | 0.175069 | − | 0.0245145i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.0270 | + | 9.25319i | 0.783906 | + | 0.452588i | ||||
\(419\) | −0.213225 | + | 0.369317i | −0.0104167 | + | 0.0180423i | −0.871187 | − | 0.490952i | \(-0.836649\pi\) |
0.860770 | + | 0.508994i | \(0.169982\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.6204i | − | 1.29740i | −0.761044 | − | 0.648700i | \(-0.775313\pi\) | ||
0.761044 | − | 0.648700i | \(-0.224687\pi\) | |||||||
\(422\) | 5.78908 | − | 3.34233i | 0.281808 | − | 0.162702i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.70469i | 0.131351i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.3153 | + | 18.0799i | 1.51546 | + | 0.874949i | ||||
\(428\) | 5.40938 | 0.261472 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.68466 | −0.467036 | ||||||||
\(431\) | −2.91791 | − | 1.68466i | −0.140551 | − | 0.0811471i | 0.428076 | − | 0.903743i | \(-0.359192\pi\) |
−0.568627 | + | 0.822596i | \(0.692525\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6847 | + | 30.6307i | 0.849870 | + | 1.47202i | 0.881323 | + | 0.472514i | \(0.156653\pi\) |
−0.0314530 | + | 0.999505i | \(0.510013\pi\) | |||||||
\(434\) | − | 2.63068i | − | 0.126277i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.6847 | + | 6.16879i | −0.511702 | + | 0.295431i | ||||
\(437\) | − | 48.7386i | − | 2.33149i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.31534 | − | 5.74234i | 0.158233 | − | 0.274067i | −0.775999 | − | 0.630734i | \(-0.782754\pi\) |
0.934231 | + | 0.356667i | \(0.116087\pi\) | |||||||
\(440\) | −2.59808 | − | 1.50000i | −0.123858 | − | 0.0715097i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3923 | −0.493753 | −0.246877 | − | 0.969047i | \(-0.579404\pi\) | ||||
−0.246877 | + | 0.969047i | \(0.579404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.34233 | + | 4.05703i | −0.111037 | + | 0.192322i | ||||
\(446\) | 3.84381 | + | 6.65767i | 0.182010 | + | 0.315250i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.34233 | − | 1.35234i | 0.110665 | − | 0.0638923i | ||||
\(449\) | 24.8416 | − | 14.3423i | 1.17235 | − | 0.676856i | 0.218117 | − | 0.975923i | \(-0.430008\pi\) |
0.954232 | + | 0.299066i | \(0.0966751\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 1.24573 | − | 2.15767i | 0.0585943 | − | 0.101488i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.36932 | −0.158130 | ||||||||
\(455\) | −1.35234 | − | 9.65767i | −0.0633989 | − | 0.452759i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.00000 | − | 1.73205i | −0.140334 | − | 0.0810219i | 0.428189 | − | 0.903689i | \(-0.359152\pi\) |
−0.568523 | + | 0.822667i | \(0.692485\pi\) | |||||||
\(458\) | −13.0970 | + | 22.6847i | −0.611982 | + | 1.05998i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.90084i | 0.368379i | ||||||||
\(461\) | −3.73720 | + | 2.15767i | −0.174059 | + | 0.100493i | −0.584498 | − | 0.811395i | \(-0.698709\pi\) |
0.410440 | + | 0.911888i | \(0.365375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.0845i | 1.39815i | 0.715050 | + | 0.699074i | \(0.246404\pi\) | ||||
−0.715050 | + | 0.699074i | \(0.753596\pi\) | |||||||
\(464\) | 1.24573 | + | 2.15767i | 0.0578316 | + | 0.100167i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.1577 | + | 6.44188i | 0.516869 | + | 0.298415i | ||||
\(467\) | 21.6375 | 1.00126 | 0.500632 | − | 0.865660i | \(-0.333101\pi\) | ||||
0.500632 | + | 0.865660i | \(0.333101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.26137 | 0.242947 | ||||||||
\(470\) | 2.59808 | + | 1.50000i | 0.119840 | + | 0.0691898i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.84233 | + | 6.65511i | 0.176858 | + | 0.306326i | ||||
\(473\) | 29.0540i | 1.33590i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.34233 | − | 3.08440i | 0.245123 | − | 0.141522i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.3693 | + | 21.4243i | −0.565759 | + | 0.979924i | ||||
\(479\) | −23.7025 | − | 13.6847i | −1.08300 | − | 0.625268i | −0.151293 | − | 0.988489i | \(-0.548344\pi\) |
−0.931703 | + | 0.363221i | \(0.881677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.84233 | + | 4.92306i | 0.175195 | + | 0.224472i | ||||
\(482\) | −6.71498 | −0.305859 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 4.43674 | + | 7.68466i | 0.201462 | + | 0.348942i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.3423 | + | 10.0126i | −0.785856 | + | 0.453714i | −0.838502 | − | 0.544899i | \(-0.816568\pi\) |
0.0526457 | + | 0.998613i | \(0.483235\pi\) | |||||||
\(488\) | 11.5782 | − | 6.68466i | 0.524119 | − | 0.302600i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.157671 | − | 0.273094i | −0.00712284 | − | 0.0123371i | ||||
\(491\) | −6.54850 | + | 11.3423i | −0.295530 | + | 0.511872i | −0.975108 | − | 0.221731i | \(-0.928829\pi\) |
0.679578 | + | 0.733603i | \(0.262163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 20.6181 | + | 8.34233i | 0.927653 | + | 0.375339i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.842329 | − | 0.486319i | −0.0378217 | − | 0.0218364i | ||||
\(497\) | 8.11407 | − | 14.0540i | 0.363966 | − | 0.630407i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 32.0298i | − | 1.43385i | −0.697150 | − | 0.716926i | \(-0.745549\pi\) | ||
0.697150 | − | 0.716926i | \(-0.254451\pi\) | |||||||
\(500\) | −0.866025 | + | 0.500000i | −0.0387298 | + | 0.0223607i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 5.19615i | − | 0.231916i | ||||||
\(503\) | −14.2361 | − | 24.6577i | −0.634757 | − | 1.09943i | −0.986567 | − | 0.163360i | \(-0.947767\pi\) |
0.351810 | − | 0.936072i | \(-0.385566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.36932 | − | 5.40938i | −0.416929 | − | 0.240714i | ||||
\(506\) | 23.7025 | 1.05371 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.68466 | −0.119112 | ||||||||
\(509\) | −8.93335 | − | 5.15767i | −0.395964 | − | 0.228610i | 0.288777 | − | 0.957396i | \(-0.406751\pi\) |
−0.684741 | + | 0.728787i | \(0.740085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.36932 | − | 16.2281i | −0.414474 | − | 0.717890i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.1577 | + | 11.6380i | −0.889117 | + | 0.513332i | ||||
\(515\) | 14.6847i | 0.647083i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.50000 | − | 7.79423i | 0.197910 | − | 0.342790i | ||||
\(518\) | 4.05703 | + | 2.34233i | 0.178256 | + | 0.102916i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.34233 | − | 1.35234i | −0.146571 | − | 0.0593042i | ||||
\(521\) | 13.0970 | 0.573790 | 0.286895 | − | 0.957962i | \(-0.407377\pi\) | ||||
0.286895 | + | 0.957962i | \(0.407377\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.526988 | + | 0.912769i | −0.0230436 | + | 0.0399126i | −0.877317 | − | 0.479911i | \(-0.840669\pi\) |
0.854274 | + | 0.519824i | \(0.174002\pi\) | |||||||
\(524\) | 10.4989 | + | 18.1847i | 0.458647 | + | 0.794400i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.5540 | + | 15.9083i | −1.20141 | + | 0.693635i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7116 | − | 34.1416i | −0.857028 | − | 1.48442i | ||||
\(530\) | 1.35234 | − | 2.34233i | 0.0587421 | − | 0.101744i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.6847 | 0.723372 | ||||||||
\(533\) | −13.3102 | − | 17.0540i | −0.576530 | − | 0.738690i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.68466 | − | 2.70469i | −0.202535 | − | 0.116934i | ||||
\(536\) | 0.972638 | − | 1.68466i | 0.0420116 | − | 0.0727662i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10.8188i | − | 0.466430i | ||||||
\(539\) | −0.819281 | + | 0.473012i | −0.0352889 | + | 0.0203741i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0504i | 1.72190i | 0.508689 | + | 0.860950i | \(0.330130\pi\) | ||||
−0.508689 | + | 0.860950i | \(0.669870\pi\) | |||||||
\(542\) | 6.65511 | + | 11.5270i | 0.285861 | + | 0.495127i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.3376 | 0.528484 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.1080 | −1.37284 | −0.686418 | − | 0.727207i | \(-0.740818\pi\) | ||||
−0.686418 | + | 0.727207i | \(0.740818\pi\) | |||||||
\(548\) | 17.0474 | + | 9.84233i | 0.728229 | + | 0.420443i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.50000 | + | 2.59808i | 0.0639602 | + | 0.110782i | ||||
\(551\) | 15.3693i | 0.654755i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.3153 | + | 7.68762i | −0.566226 | + | 0.326911i | ||||
\(554\) | 1.00000i | 0.0424859i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.65767 | − | 8.06732i | 0.197529 | − | 0.342131i | ||||
\(557\) | 1.13912 | + | 0.657671i | 0.0482660 | + | 0.0278664i | 0.523939 | − | 0.851756i | \(-0.324462\pi\) |
−0.475673 | + | 0.879622i | \(0.657795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.84233 | + | 34.5811i | 0.204809 | + | 1.46263i | ||||
\(560\) | −2.70469 | −0.114294 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.3693 | − | 21.4243i | 0.521768 | − | 0.903729i | ||||
\(563\) | 12.8838 | + | 22.3153i | 0.542986 | + | 0.940480i | 0.998731 | + | 0.0503689i | \(0.0160397\pi\) |
−0.455745 | + | 0.890111i | \(0.650627\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.15767 | + | 1.24573i | −0.0907739 | + | 0.0524083i | ||||
\(566\) | 11.3051 | − | 6.52699i | 0.475188 | − | 0.274350i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | − | 5.19615i | −0.125877 | − | 0.218026i | ||||
\(569\) | 14.6626 | − | 25.3963i | 0.614687 | − | 1.06467i | −0.375753 | − | 0.926720i | \(-0.622616\pi\) |
0.990439 | − | 0.137949i | \(-0.0440509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0540 | −1.67621 | −0.838103 | − | 0.545511i | \(-0.816335\pi\) | ||||
−0.838103 | + | 0.545511i | \(0.816335\pi\) | |||||||
\(572\) | −4.05703 | + | 10.0270i | −0.169633 | + | 0.419249i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.0540 | − | 8.11407i | −0.586602 | − | 0.338675i | ||||
\(575\) | 3.95042 | − | 6.84233i | 0.164744 | − | 0.285345i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 29.2316i | − | 1.21693i | −0.793581 | − | 0.608465i | \(-0.791786\pi\) | ||
0.793581 | − | 0.608465i | \(-0.208214\pi\) | |||||||
\(578\) | 14.7224 | − | 8.50000i | 0.612372 | − | 0.353553i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 2.49146i | − | 0.103452i | ||||||
\(581\) | −20.7846 | − | 36.0000i | −0.862291 | − | 1.49353i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.02699 | − | 4.05703i | −0.291028 | − | 0.168025i | ||||
\(584\) | −6.92820 | −0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.6847 | −0.937095 | ||||||||
\(587\) | −8.11407 | − | 4.68466i | −0.334903 | − | 0.193357i | 0.323113 | − | 0.946361i | \(-0.395271\pi\) |
−0.658016 | + | 0.753004i | \(0.728604\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00000 | − | 5.19615i | −0.123613 | − | 0.214104i | ||||
\(590\) | − | 7.68466i | − | 0.316372i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.50000 | − | 0.866025i | 0.0616496 | − | 0.0355934i | ||||
\(593\) | − | 38.4233i | − | 1.57786i | −0.614486 | − | 0.788928i | \(-0.710637\pi\) | ||
0.614486 | − | 0.788928i | \(-0.289363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.93335 | − | 5.15767i | −0.365924 | − | 0.211266i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.2116 | − | 3.95042i | 1.15366 | − | 0.161545i | ||||
\(599\) | −0.426450 | −0.0174243 | −0.00871215 | − | 0.999962i | \(-0.502773\pi\) | ||||
−0.00871215 | + | 0.999962i | \(0.502773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.5000 | − | 30.3109i | 0.713840 | − | 1.23641i | −0.249565 | − | 0.968358i | \(-0.580288\pi\) |
0.963405 | − | 0.268049i | \(-0.0863789\pi\) | |||||||
\(602\) | 13.0970 | + | 22.6847i | 0.533794 | + | 0.924558i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.3693 | − | 7.14143i | 0.503300 | − | 0.290581i | ||||
\(605\) | −1.73205 | + | 1.00000i | −0.0704179 | + | 0.0406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.97301 | − | 5.14941i | −0.120671 | − | 0.209008i | 0.799362 | − | 0.600850i | \(-0.205171\pi\) |
−0.920032 | + | 0.391842i | \(0.871838\pi\) | |||||||
\(608\) | 3.08440 | − | 5.34233i | 0.125089 | − | 0.216660i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.3693 | −0.541308 | ||||||||
\(611\) | 4.05703 | − | 10.0270i | 0.164130 | − | 0.405649i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.5000 | − | 6.06218i | −0.424091 | − | 0.244849i | 0.272735 | − | 0.962089i | \(-0.412072\pi\) |
−0.696826 | + | 0.717240i | \(0.745405\pi\) | |||||||
\(614\) | −7.14143 | + | 12.3693i | −0.288205 | + | 0.499185i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.11407i | 0.326925i | ||||||||
\(617\) | −11.8513 | + | 6.84233i | −0.477114 | + | 0.275462i | −0.719213 | − | 0.694790i | \(-0.755497\pi\) |
0.242099 | + | 0.970252i | \(0.422164\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.13114i | − | 0.125851i | −0.998018 | − | 0.0629256i | \(-0.979957\pi\) | ||
0.998018 | − | 0.0629256i | \(-0.0200431\pi\) | |||||||
\(620\) | 0.486319 | + | 0.842329i | 0.0195310 | + | 0.0338288i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.31534 | + | 2.49146i | 0.173029 | + | 0.0998986i | ||||
\(623\) | 12.6705 | 0.507635 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.64996 | − | 2.68466i | −0.185850 | − | 0.107301i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.18466 | + | 7.24804i | 0.166986 | + | 0.289228i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6847 | + | 11.3649i | −0.783634 | + | 0.452431i | −0.837717 | − | 0.546105i | \(-0.816110\pi\) |
0.0540827 | + | 0.998536i | \(0.482777\pi\) | |||||||
\(632\) | 5.68466i | 0.226124i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.7116 | − | 25.4813i | 0.584274 | − | 1.01199i | ||||
\(635\) | 2.32498 | + | 1.34233i | 0.0922641 | + | 0.0532687i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.896305 | + | 0.699544i | −0.0355129 | + | 0.0277170i | ||||
\(638\) | −7.47439 | −0.295914 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −19.8587 | − | 34.3963i | −0.784372 | − | 1.35857i | −0.929373 | − | 0.369141i | \(-0.879652\pi\) |
0.145001 | − | 0.989431i | \(-0.453681\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.0540 | + | 16.7743i | −1.14578 | + | 0.661515i | −0.947855 | − | 0.318703i | \(-0.896753\pi\) |
−0.197922 | + | 0.980218i | \(0.563419\pi\) | |||||||
\(644\) | 18.5064 | − | 10.6847i | 0.729253 | − | 0.421035i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.3673 | + | 30.0810i | −0.682777 | + | 1.18260i | 0.291353 | + | 0.956616i | \(0.405895\pi\) |
−0.974130 | + | 0.225989i | \(0.927439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.0540 | −0.904948 | ||||||||
\(650\) | 2.21837 | + | 2.84233i | 0.0870116 | + | 0.111485i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.8423 | − | 9.14657i | −0.620433 | − | 0.358207i | ||||
\(653\) | 11.5314 | − | 19.9730i | 0.451259 | − | 0.781604i | −0.547205 | − | 0.836999i | \(-0.684308\pi\) |
0.998465 | + | 0.0553942i | \(0.0176416\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 20.9978i | − | 0.820453i | ||||||
\(656\) | −5.19615 | + | 3.00000i | −0.202876 | + | 0.117130i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 8.11407i | − | 0.316319i | ||||||
\(659\) | 16.8342 | + | 29.1577i | 0.655767 | + | 1.13582i | 0.981701 | + | 0.190429i | \(0.0609879\pi\) |
−0.325934 | + | 0.945393i | \(0.605679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.00000 | + | 5.19615i | 0.350059 | + | 0.202107i | 0.664711 | − | 0.747100i | \(-0.268554\pi\) |
−0.314652 | + | 0.949207i | \(0.601888\pi\) | |||||||
\(662\) | 9.29993 | 0.361452 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.3693 | −0.596445 | ||||||||
\(665\) | −14.4493 | − | 8.34233i | −0.560321 | − | 0.323502i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.84233 | + | 17.0474i | 0.381097 | + | 0.660079i | ||||
\(668\) | 6.36932i | 0.246436i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.68466 | + | 0.972638i | −0.0650840 | + | 0.0375763i | ||||
\(671\) | 40.1080i | 1.54835i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.0000 | + | 27.7128i | −0.616755 | + | 1.06825i | 0.373319 | + | 0.927703i | \(0.378220\pi\) |
−0.990074 | + | 0.140548i | \(0.955114\pi\) | |||||||
\(674\) | −25.4346 | − | 14.6847i | −0.979703 | − | 0.565632i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.15767 | + | 12.6107i | −0.121449 | + | 0.485026i | ||||
\(677\) | 36.5863 | 1.40613 | 0.703063 | − | 0.711128i | \(-0.251815\pi\) | ||||
0.703063 | + | 0.711128i | \(0.251815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 20.7846i | 0.460518 | − | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.52699 | − | 1.45896i | 0.0967634 | − | 0.0558664i | ||||
\(683\) | −2.27824 | + | 1.31534i | −0.0871744 | + | 0.0503301i | −0.542954 | − | 0.839763i | \(-0.682694\pi\) |
0.455779 | + | 0.890093i | \(0.349361\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.84233 | − | 17.0474i | −0.376056 | − | 0.651348i | ||||
\(686\) | 9.03996 | − | 15.6577i | 0.345147 | − | 0.597813i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.68466 | 0.369224 | ||||||||
\(689\) | −9.03996 | − | 3.65767i | −0.344395 | − | 0.139346i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.02699 | − | 2.32498i | −0.153194 | − | 0.0884465i | 0.421444 | − | 0.906855i | \(-0.361524\pi\) |
−0.574637 | + | 0.818408i | \(0.694857\pi\) | |||||||
\(692\) | −4.05703 | + | 7.02699i | −0.154225 | + | 0.267126i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 4.98293i | − | 0.189149i | ||||||
\(695\) | −8.06732 | + | 4.65767i | −0.306011 | + | 0.176676i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −16.7743 | − | 29.0540i | −0.634917 | − | 1.09971i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.34233 | + | 1.35234i | 0.0885317 | + | 0.0511138i | ||||
\(701\) | 23.2761 | 0.879125 | 0.439563 | − | 0.898212i | \(-0.355133\pi\) | ||||
0.439563 | + | 0.898212i | \(0.355133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6847 | 0.402980 | ||||||||
\(704\) | 2.59808 | + | 1.50000i | 0.0979187 | + | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.68466 | + | 13.3102i | 0.289216 | + | 0.500937i | ||||
\(707\) | 29.2614i | 1.10049i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.3693 | + | 15.8017i | −1.02788 | + | 0.593445i | −0.916376 | − | 0.400320i | \(-0.868899\pi\) |
−0.111501 | + | 0.993764i | \(0.535566\pi\) | |||||||
\(710\) | 6.00000i | 0.225176i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.34233 | − | 4.05703i | 0.0877825 | − | 0.152044i | ||||
\(713\) | −6.65511 | − | 3.84233i | −0.249236 | − | 0.143896i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.52699 | − | 6.65511i | 0.318891 | − | 0.248887i | ||||
\(716\) | −12.8838 | −0.481489 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.31534 | − | 2.27824i | 0.0490881 | − | 0.0850231i | ||||
\(719\) | 4.98293 | + | 8.63068i | 0.185832 | + | 0.321870i | 0.943857 | − | 0.330356i | \(-0.107169\pi\) |
−0.758025 | + | 0.652226i | \(0.773835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.3963 | − | 19.8587i | 1.28099 | − | 0.739577i | ||||
\(722\) | 16.5012 | − | 9.52699i | 0.614112 | − | 0.354558i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.68466 | + | 4.64996i | 0.0997745 | + | 0.172815i | ||||
\(725\) | −1.24573 | + | 2.15767i | −0.0462653 | + | 0.0801339i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.6847 | −1.36056 | −0.680279 | − | 0.732953i | \(-0.738142\pi\) | ||||
−0.680279 | + | 0.732953i | \(0.738142\pi\) | |||||||
\(728\) | 1.35234 | + | 9.65767i | 0.0501212 | + | 0.357937i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | + | 3.46410i | 0.222070 | + | 0.128212i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.5269i | − | 0.979795i | −0.871780 | − | 0.489898i | \(-0.837034\pi\) | ||
0.871780 | − | 0.489898i | \(-0.162966\pi\) | |||||||
\(734\) | −20.2384 | + | 11.6847i | −0.747014 | + | 0.431289i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.90084i | − | 0.291229i | ||||||
\(737\) | 2.91791 | + | 5.05398i | 0.107483 | + | 0.186166i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.97301 | + | 1.13912i | 0.0725784 | + | 0.0419032i | 0.535850 | − | 0.844313i | \(-0.319991\pi\) |
−0.463272 | + | 0.886216i | \(0.653325\pi\) | |||||||
\(740\) | −1.73205 | −0.0636715 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.31534 | −0.268555 | ||||||||
\(743\) | −17.0474 | − | 9.84233i | −0.625409 | − | 0.361080i | 0.153563 | − | 0.988139i | \(-0.450925\pi\) |
−0.778972 | + | 0.627059i | \(0.784259\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.15767 | + | 8.93335i | 0.188962 | + | 0.327293i | ||||
\(746\) | 1.05398i | 0.0385888i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.6307i | 0.534594i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.8423 | − | 30.9038i | 0.651076 | − | 1.12770i | −0.331786 | − | 0.943355i | \(-0.607651\pi\) |
0.982862 | − | 0.184342i | \(-0.0590154\pi\) | |||||||
\(752\) | −2.59808 | − | 1.50000i | −0.0947421 | − | 0.0546994i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.89630 | + | 1.24573i | −0.323984 | + | 0.0453669i | ||||
\(755\) | −14.2829 | −0.519806 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0270 | + | 31.2237i | −0.655202 | + | 1.13484i | 0.326641 | + | 0.945148i | \(0.394083\pi\) |
−0.981843 | + | 0.189695i | \(0.939250\pi\) | |||||||
\(758\) | −0.166481 | − | 0.288354i | −0.00604687 | − | 0.0104735i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.34233 | + | 3.08440i | −0.193787 | + | 0.111883i | ||||
\(761\) | −12.1711 | + | 7.02699i | −0.441202 | + | 0.254728i | −0.704107 | − | 0.710094i | \(-0.748653\pi\) |
0.262905 | + | 0.964822i | \(0.415319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.6847 | − | 28.8987i | −0.604025 | − | 1.04620i | ||||
\(764\) | 10.6055 | − | 18.3693i | 0.383695 | − | 0.664579i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.68466 | −0.277658 | ||||||||
\(767\) | −27.4397 | + | 3.84233i | −0.990791 | + | 0.138738i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.2116 | − | 11.0918i | −0.692790 | − | 0.399982i | 0.111867 | − | 0.993723i | \(-0.464317\pi\) |
−0.804656 | + | 0.593741i | \(0.797650\pi\) | |||||||
\(770\) | 4.05703 | − | 7.02699i | 0.146205 | − | 0.253235i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.8017i | 0.568715i | ||||||||
\(773\) | 35.2339 | − | 20.3423i | 1.26728 | − | 0.731663i | 0.292805 | − | 0.956172i | \(-0.405411\pi\) |
0.974472 | + | 0.224509i | \(0.0720780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.972638i | − | 0.0349382i | ||||||
\(776\) | −4.43674 | − | 7.68466i | −0.159270 | − | 0.275863i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.8963 | − | 12.0645i | −0.749169 | − | 0.432533i | ||||
\(779\) | −37.0127 | −1.32612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | 0.644091 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.157671 | + | 0.273094i | 0.00563110 | + | 0.00975335i | ||||
\(785\) | − | 8.36932i | − | 0.298714i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.84233 | − | 2.21837i | 0.136964 | − | 0.0790763i | −0.429952 | − | 0.902852i | \(-0.641470\pi\) |
0.566916 | + | 0.823775i | \(0.308136\pi\) | |||||||
\(788\) | − | 20.0540i | − | 0.714393i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.84233 | − | 4.92306i | 0.101126 | − | 0.175155i | ||||
\(791\) | 5.83583 | + | 3.36932i | 0.207498 | + | 0.119799i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.68466 | + | 47.7380i | 0.237379 | + | 1.69523i | ||||
\(794\) | −34.8542 | −1.23693 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.68466 | + | 15.0423i | −0.307820 | + | 0.533159i | ||||
\(797\) | 10.8188 | + | 18.7386i | 0.383220 | + | 0.663756i | 0.991521 | − | 0.129950i | \(-0.0414818\pi\) |
−0.608301 | + | 0.793707i | \(0.708148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.02699 | − | 1.77879i | −0.0362642 | − | 0.0628114i | ||||
\(803\) | 10.3923 | − | 18.0000i | 0.366736 | − | 0.635206i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.3693 | −0.753169 | ||||||||
\(806\) | 2.76456 | − | 2.15767i | 0.0973774 | − | 0.0760007i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.36932 | + | 5.40938i | 0.329611 | + | 0.190301i | ||||
\(809\) | 10.3923 | − | 18.0000i | 0.365374 | − | 0.632846i | −0.623462 | − | 0.781854i | \(-0.714274\pi\) |
0.988836 | + | 0.149007i | \(0.0476078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.3799i | 0.961437i | 0.876875 | + | 0.480718i | \(0.159624\pi\) | ||||
−0.876875 | + | 0.480718i | \(0.840376\pi\) | |||||||
\(812\) | −5.83583 | + | 3.36932i | −0.204797 | + | 0.118240i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.19615i | 0.182125i | ||||||||
\(815\) | 9.14657 | + | 15.8423i | 0.320390 | + | 0.554933i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.7386 | + | 29.8713i | 1.81011 | + | 1.04506i | ||||
\(818\) | −13.5234 | −0.472836 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 35.5538 | + | 20.5270i | 1.24084 | + | 0.716397i | 0.969264 | − | 0.246022i | \(-0.0791234\pi\) |
0.271571 | + | 0.962418i | \(0.412457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.65767 | + | 9.79937i | 0.197214 | + | 0.341585i | 0.947624 | − | 0.319388i | \(-0.103477\pi\) |
−0.750410 | + | 0.660973i | \(0.770144\pi\) | |||||||
\(824\) | − | 14.6847i | − | 0.511564i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | + | 10.3923i | −0.626300 | + | 0.361595i | ||||
\(827\) | − | 14.6307i | − | 0.508759i | −0.967105 | − | 0.254379i | \(-0.918129\pi\) | ||
0.967105 | − | 0.254379i | \(-0.0818712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3693 | + | 30.0845i | −0.603261 | + | 1.04488i | 0.389062 | + | 0.921211i | \(0.372799\pi\) |
−0.992324 | + | 0.123668i | \(0.960534\pi\) | |||||||
\(830\) | 13.3102 | + | 7.68466i | 0.462004 | + | 0.266738i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.34233 | + | 1.35234i | 0.115874 | + | 0.0468841i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.18466 | − | 5.51599i | 0.110210 | − | 0.190889i | ||||
\(836\) | 9.25319 | + | 16.0270i | 0.320028 | + | 0.554305i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.369317 | + | 0.213225i | −0.0127578 | + | 0.00736574i | ||||
\(839\) | −42.2089 | + | 24.3693i | −1.45721 | + | 0.841322i | −0.998873 | − | 0.0474549i | \(-0.984889\pi\) |
−0.458340 | + | 0.888777i | \(0.651556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.3963 | + | 19.7390i | 0.392976 | + | 0.680654i | ||||
\(842\) | 13.3102 | − | 23.0540i | 0.458700 | − | 0.794492i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.68466 | 0.230095 | ||||||||
\(845\) | 9.03996 | − | 9.34233i | 0.310984 | − | 0.321386i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.68466 | + | 2.70469i | 0.160967 | + | 0.0929342i | ||||
\(848\) | −1.35234 | + | 2.34233i | −0.0464397 | + | 0.0804359i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.8513 | − | 6.84233i | 0.406256 | − | 0.234552i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.49146i | 0.0853061i | 0.999090 | + | 0.0426530i | \(0.0135810\pi\) | ||||
−0.999090 | + | 0.0426530i | \(0.986419\pi\) | |||||||
\(854\) | 18.0799 | + | 31.3153i | 0.618682 | + | 1.07159i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.68466 | + | 2.70469i | 0.160118 | + | 0.0924444i | ||||
\(857\) | −12.8838 | −0.440101 | −0.220051 | − | 0.975488i | \(-0.570622\pi\) | ||||
−0.220051 | + | 0.975488i | \(0.570622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.0540 | 0.615994 | 0.307997 | − | 0.951387i | \(-0.400341\pi\) | ||||
0.307997 | + | 0.951387i | \(0.400341\pi\) | |||||||
\(860\) | −8.38716 | − | 4.84233i | −0.286000 | − | 0.165122i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.68466 | − | 2.91791i | −0.0573797 | − | 0.0993845i | ||||
\(863\) | 28.3153i | 0.963865i | 0.876208 | + | 0.481933i | \(0.160065\pi\) | ||||
−0.876208 | + | 0.481933i | \(0.839935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.02699 | − | 4.05703i | 0.238925 | − | 0.137943i | ||||
\(866\) | 35.3693i | 1.20190i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.31534 | − | 2.27824i | 0.0446456 | − | 0.0773285i | ||||
\(869\) | −14.7692 | − | 8.52699i | −0.501010 | − | 0.289258i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.31534 | + | 5.52911i | 0.146220 | + | 0.187347i | ||||
\(872\) | −12.3376 | −0.417803 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.3693 | − | 42.2089i | 0.824304 | − | 1.42774i | ||||
\(875\) | −1.35234 | − | 2.34233i | −0.0457176 | − | 0.0791852i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.84233 | + | 5.68247i | −0.332352 | + | 0.191883i | −0.656885 | − | 0.753991i | \(-0.728126\pi\) |
0.324533 | + | 0.945874i | \(0.394793\pi\) | |||||||
\(878\) | 5.74234 | − | 3.31534i | 0.193795 | − | 0.111887i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.50000 | − | 2.59808i | −0.0505650 | − | 0.0875811i | ||||
\(881\) | −17.1540 | + | 29.7116i | −0.577934 | + | 1.00101i | 0.417782 | + | 0.908547i | \(0.362808\pi\) |
−0.995716 | + | 0.0924636i | \(0.970526\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.3153 | 0.481750 | 0.240875 | − | 0.970556i | \(-0.422566\pi\) | ||||
0.240875 | + | 0.970556i | \(0.422566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.00000 | − | 5.19615i | −0.302361 | − | 0.174568i | ||||
\(887\) | 23.3827 | − | 40.5000i | 0.785114 | − | 1.35986i | −0.143817 | − | 0.989604i | \(-0.545938\pi\) |
0.928931 | − | 0.370253i | \(-0.120729\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.26117i | − | 0.243532i | ||||||
\(890\) | −4.05703 | + | 2.34233i | −0.135992 | + | 0.0785151i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.68762i | 0.257400i | ||||||||
\(893\) | −9.25319 | − | 16.0270i | −0.309646 | − | 0.536323i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1577 | + | 6.44188i | 0.372960 | + | 0.215328i | ||||
\(896\) | 2.70469 | 0.0903573 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.6847 | 0.957219 | ||||||||
\(899\) | 2.09863 | + | 1.21165i | 0.0699933 | + | 0.0404107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 18.0000i | − | 0.599334i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.15767 | − | 1.24573i | 0.0717631 | − | 0.0414324i | ||||
\(905\) | − | 5.36932i | − | 0.178482i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.1577 | − | 26.2539i | 0.503302 | − | 0.871745i | −0.496691 | − | 0.867928i | \(-0.665452\pi\) |
0.999993 | − | 0.00381726i | \(-0.00121507\pi\) | |||||||
\(908\) | −2.91791 | − | 1.68466i | −0.0968344 | − | 0.0559074i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.65767 | − | 9.03996i | 0.121251 | − | 0.299672i | ||||
\(911\) | −37.4392 | −1.24042 | −0.620208 | − | 0.784437i | \(-0.712952\pi\) | ||||
−0.620208 | + | 0.784437i | \(0.712952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.0540 | − | 39.9307i | 0.762975 | − | 1.32151i | ||||
\(914\) | −1.73205 | − | 3.00000i | −0.0572911 | − | 0.0992312i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.6847 | + | 13.0970i | −0.749522 | + | 0.432737i | ||||
\(917\) | −49.1838 | + | 28.3963i | −1.62419 | + | 0.937729i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.684658 | − | 1.18586i | −0.0225848 | − | 0.0391180i | 0.854512 | − | 0.519431i | \(-0.173856\pi\) |
−0.877097 | + | 0.480313i | \(0.840523\pi\) | |||||||
\(920\) | −3.95042 | + | 6.84233i | −0.130242 | + | 0.225585i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.31534 | −0.142118 | ||||||||
\(923\) | 21.4243 | − | 3.00000i | 0.705189 | − | 0.0987462i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.50000 | + | 0.866025i | 0.0493197 | + | 0.0284747i | ||||
\(926\) | −15.0423 | + | 26.0540i | −0.494320 | + | 0.856187i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.49146i | 0.0817863i | ||||||||
\(929\) | −39.2910 | + | 22.6847i | −1.28910 | + | 0.744260i | −0.978493 | − | 0.206280i | \(-0.933864\pi\) |
−0.310602 | + | 0.950540i | \(0.600531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.94528i | 0.0637538i | ||||||||
\(932\) | 6.44188 | + | 11.1577i | 0.211011 | + | 0.365482i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.7386 | + | 10.8188i | 0.613147 | + | 0.354000i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.7386 | 0.938850 | 0.469425 | − | 0.882972i | \(-0.344461\pi\) | ||||
0.469425 | + | 0.882972i | \(0.344461\pi\) | |||||||
\(938\) | 4.55648 | + | 2.63068i | 0.148774 | + | 0.0858948i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.50000 | + | 2.59808i | 0.0489246 | + | 0.0847399i | ||||
\(941\) | 27.3693i | 0.892214i | 0.894980 | + | 0.446107i | \(0.147190\pi\) | ||||
−0.894980 | + | 0.446107i | \(0.852810\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.0540 | + | 23.7025i | −1.33690 | + | 0.771860i | ||||
\(944\) | 7.68466i | 0.250114i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.5270 | + | 25.1615i | −0.472313 | + | 0.818070i | ||||
\(947\) | 31.8166 | + | 18.3693i | 1.03390 | + | 0.596923i | 0.918100 | − | 0.396350i | \(-0.129723\pi\) |
0.115801 | + | 0.993272i | \(0.463057\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.36932 | − | 23.1563i | 0.304141 | − | 0.751686i | ||||
\(950\) | 6.16879 | 0.200142 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.1615 | − | 43.5810i | −0.815060 | − | 1.41173i | −0.909285 | − | 0.416175i | \(-0.863370\pi\) |
0.0942243 | − | 0.995551i | \(-0.469963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.3693 | + | 10.6055i | −0.594417 | + | 0.343187i | ||||
\(956\) | −21.4243 | + | 12.3693i | −0.692911 | + | 0.400052i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.6847 | − | 23.7025i | −0.442131 | − | 0.765794i | ||||
\(959\) | −26.6204 | + | 46.1080i | −0.859619 | + | 1.48890i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0540 | 0.969483 | ||||||||
\(962\) | 0.866025 | + | 6.18466i | 0.0279218 | + | 0.199401i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.81534 | − | 3.35749i | −0.187300 | − | 0.108137i | ||||
\(965\) | 7.90084 | − | 13.6847i | 0.254337 | − | 0.440525i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.64996i | 0.149533i | 0.997201 | + | 0.0747664i | \(0.0238211\pi\) | ||||
−0.997201 | + | 0.0747664i | \(0.976179\pi\) | |||||||
\(968\) | 1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.87348i | 0.284910i | ||||||||
\(971\) | −1.13912 | − | 1.97301i | −0.0365561 | − | 0.0633170i | 0.847169 | − | 0.531324i | \(-0.178305\pi\) |
−0.883725 | + | 0.468007i | \(0.844972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.8196 | + | 12.5976i | 0.699504 | + | 0.403859i | ||||
\(974\) | −20.0252 | −0.641649 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.3693 | 0.427941 | ||||||||
\(977\) | 25.8012 | + | 14.8963i | 0.825452 | + | 0.476575i | 0.852293 | − | 0.523065i | \(-0.175211\pi\) |
−0.0268408 | + | 0.999640i | \(0.508545\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.02699 | + | 12.1711i | 0.224583 | + | 0.388990i | ||||
\(980\) | − | 0.315342i | − | 0.0100732i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11.3423 | + | 6.54850i | −0.361948 | + | 0.208971i | ||||
\(983\) | − | 33.0000i | − | 1.05254i | −0.850319 | − | 0.526268i | \(-0.823591\pi\) | ||
0.850319 | − | 0.526268i | \(-0.176409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0270 | + | 17.3673i | −0.319486 | + | 0.553367i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.6847 | + | 17.5337i | 0.435367 | + | 0.557822i | ||||
\(989\) | 76.5169 | 2.43310 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.8963 | − | 44.8537i | 0.822623 | − | 1.42483i | −0.0810991 | − | 0.996706i | \(-0.525843\pi\) |
0.903722 | − | 0.428119i | \(-0.140824\pi\) | |||||||
\(992\) | −0.486319 | − | 0.842329i | −0.0154406 | − | 0.0267440i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.0540 | − | 8.11407i | 0.445765 | − | 0.257363i | ||||
\(995\) | 15.0423 | − | 8.68466i | 0.476872 | − | 0.275322i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.7116 | − | 42.8018i | −0.782626 | − | 1.35555i | −0.930407 | − | 0.366527i | \(-0.880547\pi\) |
0.147782 | − | 0.989020i | \(-0.452787\pi\) | |||||||
\(998\) | 16.0149 | − | 27.7386i | 0.506943 | − | 0.878051i | ||||
\(999\) | 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 | 1170.2.bs.h.901.3 | yes | 8 | |
3.2 | odd | 2 | inner | 1170.2.bs.h.901.1 | yes | 8 | |
13.10 | even | 6 | inner | 1170.2.bs.h.361.3 | yes | 8 | |
39.23 | odd | 6 | inner | 1170.2.bs.h.361.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.bs.h.361.1 | ✓ | 8 | 39.23 | odd | 6 | inner | |
1170.2.bs.h.361.3 | yes | 8 | 13.10 | even | 6 | inner | |
1170.2.bs.h.901.1 | yes | 8 | 3.2 | odd | 2 | inner | |
1170.2.bs.h.901.3 | yes | 8 | 1.1 | even | 1 | trivial |