Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(269,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.n (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.269 |
Dual form | 370.2.n.c.359.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.86603 | − | 1.23205i | 0.834512 | − | 0.550990i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.36603 | − | 1.36603i | 0.894274 | − | 0.516309i | 0.0189356 | − | 0.999821i | \(-0.493972\pi\) |
0.875338 | + | 0.483512i | \(0.160639\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −2.23205 | + | 0.133975i | −0.705836 | + | 0.0423665i | ||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.26795 | − | 0.732051i | 0.351666 | − | 0.203034i | −0.313753 | − | 0.949505i | \(-0.601586\pi\) |
0.665419 | + | 0.746470i | \(0.268253\pi\) | |||||||
\(14\) | −2.73205 | −0.730171 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | − | 0.866025i | −0.363803 | − | 0.210042i | 0.306944 | − | 0.951727i | \(-0.400693\pi\) |
−0.670748 | + | 0.741685i | \(0.734027\pi\) | |||||||
\(18\) | 2.59808 | − | 1.50000i | 0.612372 | − | 0.353553i | ||||
\(19\) | 0.633975 | + | 1.09808i | 0.145444 | + | 0.251916i | 0.929538 | − | 0.368725i | \(-0.120206\pi\) |
−0.784095 | + | 0.620641i | \(0.786872\pi\) | |||||||
\(20\) | 2.00000 | + | 1.00000i | 0.447214 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.09808 | − | 0.633975i | −0.234111 | − | 0.135164i | ||||
\(23\) | − | 1.46410i | − | 0.305286i | −0.988281 | − | 0.152643i | \(-0.951221\pi\) | ||
0.988281 | − | 0.152643i | \(-0.0487785\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96410 | − | 4.59808i | 0.392820 | − | 0.919615i | ||||
\(26\) | −1.46410 | −0.287134 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.36603 | + | 1.36603i | 0.447137 | + | 0.258155i | ||||
\(29\) | 1.73205 | 0.321634 | 0.160817 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160817 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.66025 | 1.37582 | 0.687911 | − | 0.725795i | \(-0.258528\pi\) | ||||
0.687911 | + | 0.725795i | \(0.258528\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.866025 | + | 1.50000i | 0.148522 | + | 0.257248i | ||||
\(35\) | 2.73205 | − | 5.46410i | 0.461801 | − | 0.923602i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 2.59808 | − | 5.50000i | 0.427121 | − | 0.904194i | ||||
\(38\) | − | 1.26795i | − | 0.205689i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.23205 | − | 1.86603i | −0.194804 | − | 0.295045i | ||||
\(41\) | −2.96410 | − | 5.13397i | −0.462915 | − | 0.801792i | 0.536190 | − | 0.844097i | \(-0.319863\pi\) |
−0.999105 | + | 0.0423053i | \(0.986530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.73205i | 1.33163i | 0.746119 | + | 0.665813i | \(0.231915\pi\) | ||||
−0.746119 | + | 0.665813i | \(0.768085\pi\) | |||||||
\(44\) | 0.633975 | + | 1.09808i | 0.0955753 | + | 0.165541i | ||||
\(45\) | 0.401924 | + | 6.69615i | 0.0599153 | + | 0.998203i | ||||
\(46\) | −0.732051 | + | 1.26795i | −0.107935 | + | 0.186949i | ||||
\(47\) | − | 6.73205i | − | 0.981971i | −0.871168 | − | 0.490985i | \(-0.836637\pi\) | ||
0.871168 | − | 0.490985i | \(-0.163363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.232051 | − | 0.401924i | 0.0331501 | − | 0.0574177i | ||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.26795 | + | 0.732051i | 0.175833 | + | 0.101517i | ||||
\(53\) | −7.26795 | − | 4.19615i | −0.998330 | − | 0.576386i | −0.0905760 | − | 0.995890i | \(-0.528871\pi\) |
−0.907754 | + | 0.419504i | \(0.862204\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.36603 | − | 1.56218i | 0.319035 | − | 0.210644i | ||||
\(56\) | −1.36603 | − | 2.36603i | −0.182543 | − | 0.316173i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.50000 | − | 0.866025i | −0.196960 | − | 0.113715i | ||||
\(59\) | −4.73205 | + | 8.19615i | −0.616061 | + | 1.06705i | 0.374137 | + | 0.927373i | \(0.377939\pi\) |
−0.990197 | + | 0.139675i | \(0.955394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.86603 | − | 6.69615i | −0.494994 | − | 0.857354i | 0.504990 | − | 0.863125i | \(-0.331496\pi\) |
−0.999983 | + | 0.00577101i | \(0.998163\pi\) | |||||||
\(62\) | −6.63397 | − | 3.83013i | −0.842516 | − | 0.486427i | ||||
\(63\) | 8.19615i | 1.03262i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.46410 | − | 2.92820i | 0.181599 | − | 0.363199i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.56218 | + | 4.36603i | −0.923867 | + | 0.533395i | −0.884867 | − | 0.465844i | \(-0.845751\pi\) |
−0.0390004 | + | 0.999239i | \(0.512417\pi\) | |||||||
\(68\) | − | 1.73205i | − | 0.210042i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.09808 | + | 3.36603i | −0.609337 | + | 0.402317i | ||||
\(71\) | 4.56218 | + | 7.90192i | 0.541431 | + | 0.937786i | 0.998822 | + | 0.0485203i | \(0.0154506\pi\) |
−0.457391 | + | 0.889266i | \(0.651216\pi\) | |||||||
\(72\) | 2.59808 | + | 1.50000i | 0.306186 | + | 0.176777i | ||||
\(73\) | 11.8564i | 1.38769i | 0.720126 | + | 0.693844i | \(0.244084\pi\) | ||||
−0.720126 | + | 0.693844i | \(0.755916\pi\) | |||||||
\(74\) | −5.00000 | + | 3.46410i | −0.581238 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.633975 | + | 1.09808i | −0.0727219 | + | 0.125958i | ||||
\(77\) | 3.00000 | − | 1.73205i | 0.341882 | − | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.83013 | + | 13.5622i | 0.880958 | + | 1.52586i | 0.850277 | + | 0.526335i | \(0.176434\pi\) |
0.0306808 | + | 0.999529i | \(0.490232\pi\) | |||||||
\(80\) | 0.133975 | + | 2.23205i | 0.0149788 | + | 0.249551i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 5.92820i | 0.654661i | ||||||||
\(83\) | −2.19615 | − | 1.26795i | −0.241059 | − | 0.139176i | 0.374604 | − | 0.927185i | \(-0.377779\pi\) |
−0.615663 | + | 0.788009i | \(0.711112\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.86603 | + | 0.232051i | −0.419329 | + | 0.0251694i | ||||
\(86\) | 4.36603 | − | 7.56218i | 0.470801 | − | 0.815451i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.26795i | − | 0.135164i | ||||||
\(89\) | −3.23205 | + | 5.59808i | −0.342597 | + | 0.593395i | −0.984914 | − | 0.173044i | \(-0.944640\pi\) |
0.642317 | + | 0.766439i | \(0.277973\pi\) | |||||||
\(90\) | 3.00000 | − | 6.00000i | 0.316228 | − | 0.632456i | ||||
\(91\) | 2.00000 | − | 3.46410i | 0.209657 | − | 0.363137i | ||||
\(92\) | 1.26795 | − | 0.732051i | 0.132193 | − | 0.0763216i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.36603 | + | 5.83013i | −0.347179 | + | 0.601332i | ||||
\(95\) | 2.53590 | + | 1.26795i | 0.260178 | + | 0.130089i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.19615i | 0.730659i | 0.930878 | + | 0.365329i | \(0.119044\pi\) | ||||
−0.930878 | + | 0.365329i | \(0.880956\pi\) | |||||||
\(98\) | −0.401924 | + | 0.232051i | −0.0406004 | + | 0.0234407i | ||||
\(99\) | −1.90192 | + | 3.29423i | −0.191151 | + | 0.331082i | ||||
\(100\) | 4.96410 | − | 0.598076i | 0.496410 | − | 0.0598076i | ||||
\(101\) | 0.267949 | 0.0266619 | 0.0133310 | − | 0.999911i | \(-0.495756\pi\) | ||||
0.0133310 | + | 0.999911i | \(0.495756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.80385i | 0.374804i | 0.982283 | + | 0.187402i | \(0.0600067\pi\) | ||||
−0.982283 | + | 0.187402i | \(0.939993\pi\) | |||||||
\(104\) | −0.732051 | − | 1.26795i | −0.0717835 | − | 0.124333i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.19615 | + | 7.26795i | 0.407566 | + | 0.705926i | ||||
\(107\) | −5.36603 | + | 3.09808i | −0.518753 | + | 0.299502i | −0.736424 | − | 0.676520i | \(-0.763487\pi\) |
0.217671 | + | 0.976022i | \(0.430154\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.40192 | + | 2.42820i | −0.134280 | + | 0.232580i | −0.925322 | − | 0.379182i | \(-0.876205\pi\) |
0.791042 | + | 0.611762i | \(0.209539\pi\) | |||||||
\(110\) | −2.83013 | + | 0.169873i | −0.269842 | + | 0.0161968i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.73205i | 0.258155i | ||||||||
\(113\) | −14.6603 | − | 8.46410i | −1.37912 | − | 0.796236i | −0.387067 | − | 0.922052i | \(-0.626512\pi\) |
−0.992054 | + | 0.125816i | \(0.959845\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.80385 | − | 2.73205i | −0.168210 | − | 0.254765i | ||||
\(116\) | 0.866025 | + | 1.50000i | 0.0804084 | + | 0.139272i | ||||
\(117\) | 4.39230i | 0.406069i | ||||||||
\(118\) | 8.19615 | − | 4.73205i | 0.754517 | − | 0.435621i | ||||
\(119\) | −4.73205 | −0.433786 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 7.73205i | 0.700027i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.83013 | + | 6.63397i | 0.343956 | + | 0.595749i | ||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 4.09808 | − | 7.09808i | 0.365086 | − | 0.632347i | ||||
\(127\) | −9.46410 | − | 5.46410i | −0.839803 | − | 0.484861i | 0.0173941 | − | 0.999849i | \(-0.494463\pi\) |
−0.857197 | + | 0.514988i | \(0.827796\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.73205 | + | 1.80385i | −0.239617 | + | 0.158208i | ||||
\(131\) | −1.46410 | + | 2.53590i | −0.127919 | + | 0.221562i | −0.922870 | − | 0.385111i | \(-0.874163\pi\) |
0.794951 | + | 0.606674i | \(0.207496\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | + | 1.73205i | 0.260133 | + | 0.150188i | ||||
\(134\) | 8.73205 | 0.754334 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.866025 | + | 1.50000i | −0.0742611 | + | 0.128624i | ||||
\(137\) | − | 1.73205i | − | 0.147979i | −0.997259 | − | 0.0739895i | \(-0.976427\pi\) | ||
0.997259 | − | 0.0739895i | \(-0.0235731\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.46410 | − | 9.46410i | 0.463459 | − | 0.802735i | −0.535671 | − | 0.844426i | \(-0.679941\pi\) |
0.999131 | + | 0.0416919i | \(0.0132748\pi\) | |||||||
\(140\) | 6.09808 | − | 0.366025i | 0.515382 | − | 0.0309348i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 9.12436i | − | 0.765699i | ||||||
\(143\) | 1.60770 | − | 0.928203i | 0.134442 | − | 0.0776203i | ||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | 3.23205 | − | 2.13397i | 0.268407 | − | 0.177217i | ||||
\(146\) | 5.92820 | − | 10.2679i | 0.490622 | − | 0.849782i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.06218 | − | 0.500000i | 0.498308 | − | 0.0410997i | ||||
\(149\) | −11.5885 | −0.949363 | −0.474682 | − | 0.880158i | \(-0.657437\pi\) | ||||
−0.474682 | + | 0.880158i | \(0.657437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.26795 | + | 9.12436i | 0.428700 | + | 0.742530i | 0.996758 | − | 0.0804588i | \(-0.0256385\pi\) |
−0.568058 | + | 0.822988i | \(0.692305\pi\) | |||||||
\(152\) | 1.09808 | − | 0.633975i | 0.0890657 | − | 0.0514221i | ||||
\(153\) | 4.50000 | − | 2.59808i | 0.363803 | − | 0.210042i | ||||
\(154\) | −3.46410 | −0.279145 | ||||||||
\(155\) | 14.2942 | − | 9.43782i | 1.14814 | − | 0.758064i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7224 | + | 8.50000i | 1.17498 | + | 0.678374i | 0.954847 | − | 0.297097i | \(-0.0960183\pi\) |
0.220131 | + | 0.975470i | \(0.429352\pi\) | |||||||
\(158\) | − | 15.6603i | − | 1.24586i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | − | 2.00000i | 0.0790569 | − | 0.158114i | ||||
\(161\) | −2.00000 | − | 3.46410i | −0.157622 | − | 0.273009i | ||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | −7.90192 | − | 4.56218i | −0.618926 | − | 0.357337i | 0.157524 | − | 0.987515i | \(-0.449649\pi\) |
−0.776451 | + | 0.630178i | \(0.782982\pi\) | |||||||
\(164\) | 2.96410 | − | 5.13397i | 0.231457 | − | 0.400896i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.26795 | + | 2.19615i | 0.0984119 | + | 0.170454i | ||||
\(167\) | 15.4641 | − | 8.92820i | 1.19665 | − | 0.690885i | 0.236842 | − | 0.971548i | \(-0.423888\pi\) |
0.959806 | + | 0.280663i | \(0.0905544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.42820 | + | 9.40192i | −0.417554 | + | 0.723225i | ||||
\(170\) | 3.46410 | + | 1.73205i | 0.265684 | + | 0.132842i | ||||
\(171\) | −3.80385 | −0.290887 | ||||||||
\(172\) | −7.56218 | + | 4.36603i | −0.576611 | + | 0.332906i | ||||
\(173\) | −0.0621778 | − | 0.0358984i | −0.00472729 | − | 0.00272930i | 0.497634 | − | 0.867387i | \(-0.334202\pi\) |
−0.502362 | + | 0.864658i | \(0.667535\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.63397 | − | 13.5622i | −0.123517 | − | 1.02520i | ||||
\(176\) | −0.633975 | + | 1.09808i | −0.0477876 | + | 0.0827706i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.59808 | − | 3.23205i | 0.419594 | − | 0.242252i | ||||
\(179\) | 14.9282 | 1.11579 | 0.557893 | − | 0.829913i | \(-0.311610\pi\) | ||||
0.557893 | + | 0.829913i | \(0.311610\pi\) | |||||||
\(180\) | −5.59808 | + | 3.69615i | −0.417256 | + | 0.275495i | ||||
\(181\) | −5.79423 | − | 10.0359i | −0.430682 | − | 0.745962i | 0.566251 | − | 0.824233i | \(-0.308393\pi\) |
−0.996932 | + | 0.0782707i | \(0.975060\pi\) | |||||||
\(182\) | −3.46410 | + | 2.00000i | −0.256776 | + | 0.148250i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.46410 | −0.107935 | ||||||||
\(185\) | −1.92820 | − | 13.4641i | −0.141764 | − | 0.989900i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.90192 | − | 1.09808i | −0.139082 | − | 0.0802993i | ||||
\(188\) | 5.83013 | − | 3.36603i | 0.425206 | − | 0.245493i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.56218 | − | 2.36603i | −0.113332 | − | 0.171650i | ||||
\(191\) | −19.3205 | −1.39798 | −0.698991 | − | 0.715130i | \(-0.746367\pi\) | ||||
−0.698991 | + | 0.715130i | \(0.746367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.6603i | 1.19923i | 0.800288 | + | 0.599616i | \(0.204680\pi\) | ||||
−0.800288 | + | 0.599616i | \(0.795320\pi\) | |||||||
\(194\) | 3.59808 | − | 6.23205i | 0.258327 | − | 0.447435i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.464102 | 0.0331501 | ||||||||
\(197\) | 5.25833 | + | 3.03590i | 0.374641 | + | 0.216299i | 0.675484 | − | 0.737375i | \(-0.263935\pi\) |
−0.300843 | + | 0.953674i | \(0.597268\pi\) | |||||||
\(198\) | 3.29423 | − | 1.90192i | 0.234111 | − | 0.135164i | ||||
\(199\) | −1.80385 | −0.127871 | −0.0639357 | − | 0.997954i | \(-0.520365\pi\) | ||||
−0.0639357 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(200\) | −4.59808 | − | 1.96410i | −0.325133 | − | 0.138883i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.232051 | − | 0.133975i | −0.0163270 | − | 0.00942642i | ||||
\(203\) | 4.09808 | − | 2.36603i | 0.287629 | − | 0.166062i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8564 | − | 5.92820i | −0.828087 | − | 0.414044i | ||||
\(206\) | 1.90192 | − | 3.29423i | 0.132513 | − | 0.229520i | ||||
\(207\) | 3.80385 | + | 2.19615i | 0.264386 | + | 0.152643i | ||||
\(208\) | 1.46410i | 0.101517i | ||||||||
\(209\) | 0.803848 | + | 1.39230i | 0.0556033 | + | 0.0963077i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0526 | 1.24279 | 0.621395 | − | 0.783498i | \(-0.286566\pi\) | ||||
0.621395 | + | 0.783498i | \(0.286566\pi\) | |||||||
\(212\) | − | 8.39230i | − | 0.576386i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.19615 | 0.423560 | ||||||||
\(215\) | 10.7583 | + | 16.2942i | 0.733712 | + | 1.11126i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.1244 | − | 10.4641i | 1.23036 | − | 0.710350i | ||||
\(218\) | 2.42820 | − | 1.40192i | 0.164459 | − | 0.0949503i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.53590 | + | 1.26795i | 0.170970 | + | 0.0854851i | ||||
\(221\) | −2.53590 | −0.170583 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.07180i | − | 0.0717728i | −0.999356 | − | 0.0358864i | \(-0.988575\pi\) | ||
0.999356 | − | 0.0358864i | \(-0.0114255\pi\) | |||||||
\(224\) | 1.36603 | − | 2.36603i | 0.0912714 | − | 0.158087i | ||||
\(225\) | 9.00000 | + | 12.0000i | 0.600000 | + | 0.800000i | ||||
\(226\) | 8.46410 | + | 14.6603i | 0.563024 | + | 0.975186i | ||||
\(227\) | −3.75833 | + | 2.16987i | −0.249449 | + | 0.144020i | −0.619512 | − | 0.784987i | \(-0.712669\pi\) |
0.370063 | + | 0.929007i | \(0.379336\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7942 | − | 22.1603i | −0.845466 | − | 1.46439i | −0.885216 | − | 0.465181i | \(-0.845989\pi\) |
0.0397491 | − | 0.999210i | \(-0.487344\pi\) | |||||||
\(230\) | 0.196152 | + | 3.26795i | 0.0129339 | + | 0.215482i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.73205i | − | 0.113715i | ||||||
\(233\) | − | 13.7321i | − | 0.899617i | −0.893125 | − | 0.449808i | \(-0.851492\pi\) | ||
0.893125 | − | 0.449808i | \(-0.148508\pi\) | |||||||
\(234\) | 2.19615 | − | 3.80385i | 0.143567 | − | 0.248665i | ||||
\(235\) | −8.29423 | − | 12.5622i | −0.541056 | − | 0.819466i | ||||
\(236\) | −9.46410 | −0.616061 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.09808 | + | 2.36603i | 0.265639 | + | 0.153367i | ||||
\(239\) | −7.29423 | + | 12.6340i | −0.471824 | + | 0.817224i | −0.999480 | − | 0.0322343i | \(-0.989738\pi\) |
0.527656 | + | 0.849458i | \(0.323071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.73205 | + | 15.1244i | 0.562481 | + | 0.974245i | 0.997279 | + | 0.0737175i | \(0.0234863\pi\) |
−0.434798 | + | 0.900528i | \(0.643180\pi\) | |||||||
\(242\) | 8.13397 | + | 4.69615i | 0.522872 | + | 0.301880i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.86603 | − | 6.69615i | 0.247497 | − | 0.428677i | ||||
\(245\) | −0.0621778 | − | 1.03590i | −0.00397240 | − | 0.0661811i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.60770 | + | 0.928203i | 0.102295 | + | 0.0590602i | ||||
\(248\) | − | 7.66025i | − | 0.486427i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.76795 | + | 10.5263i | −0.238306 | + | 0.665740i | ||||
\(251\) | 11.8038 | 0.745052 | 0.372526 | − | 0.928022i | \(-0.378492\pi\) | ||||
0.372526 | + | 0.928022i | \(0.378492\pi\) | |||||||
\(252\) | −7.09808 | + | 4.09808i | −0.447137 | + | 0.258155i | ||||
\(253\) | − | 1.85641i | − | 0.116711i | ||||||
\(254\) | 5.46410 | + | 9.46410i | 0.342848 | + | 0.593831i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 11.0885 | + | 6.40192i | 0.691679 | + | 0.399341i | 0.804241 | − | 0.594304i | \(-0.202572\pi\) |
−0.112562 | + | 0.993645i | \(0.535906\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.36603 | − | 16.5622i | −0.0848807 | − | 1.02912i | ||||
\(260\) | 3.26795 | − | 0.196152i | 0.202670 | − | 0.0121649i | ||||
\(261\) | −2.59808 | + | 4.50000i | −0.160817 | + | 0.278543i | ||||
\(262\) | 2.53590 | − | 1.46410i | 0.156668 | − | 0.0904525i | ||||
\(263\) | −7.85641 | + | 4.53590i | −0.484447 | + | 0.279695i | −0.722268 | − | 0.691614i | \(-0.756900\pi\) |
0.237821 | + | 0.971309i | \(0.423567\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.7321 | + | 1.12436i | −1.15070 | + | 0.0690686i | ||||
\(266\) | −1.73205 | − | 3.00000i | −0.106199 | − | 0.183942i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.56218 | − | 4.36603i | −0.461934 | − | 0.266697i | ||||
\(269\) | 17.8564 | 1.08872 | 0.544362 | − | 0.838850i | \(-0.316772\pi\) | ||||
0.544362 | + | 0.838850i | \(0.316772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.36603 | + | 7.56218i | −0.265217 | + | 0.459370i | −0.967620 | − | 0.252410i | \(-0.918777\pi\) |
0.702403 | + | 0.711779i | \(0.252110\pi\) | |||||||
\(272\) | 1.50000 | − | 0.866025i | 0.0909509 | − | 0.0525105i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.866025 | + | 1.50000i | −0.0523185 | + | 0.0906183i | ||||
\(275\) | 2.49038 | − | 5.83013i | 0.150176 | − | 0.351570i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.20577 | + | 0.696152i | −0.0724478 | + | 0.0418277i | −0.535786 | − | 0.844354i | \(-0.679985\pi\) |
0.463339 | + | 0.886181i | \(0.346651\pi\) | |||||||
\(278\) | −9.46410 | + | 5.46410i | −0.567619 | + | 0.327715i | ||||
\(279\) | −11.4904 | + | 19.9019i | −0.687911 | + | 1.19150i | ||||
\(280\) | −5.46410 | − | 2.73205i | −0.326543 | − | 0.163271i | ||||
\(281\) | 1.50000 | − | 2.59808i | 0.0894825 | − | 0.154988i | −0.817810 | − | 0.575488i | \(-0.804812\pi\) |
0.907293 | + | 0.420500i | \(0.138145\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.02628 | − | 2.90192i | 0.298781 | − | 0.172501i | −0.343114 | − | 0.939294i | \(-0.611482\pi\) |
0.641895 | + | 0.766792i | \(0.278148\pi\) | |||||||
\(284\) | −4.56218 | + | 7.90192i | −0.270715 | + | 0.468893i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.85641 | −0.109772 | ||||||||
\(287\) | −14.0263 | − | 8.09808i | −0.827945 | − | 0.478014i | ||||
\(288\) | 3.00000i | 0.176777i | ||||||||
\(289\) | −7.00000 | − | 12.1244i | −0.411765 | − | 0.713197i | ||||
\(290\) | −3.86603 | + | 0.232051i | −0.227021 | + | 0.0136265i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.2679 | + | 5.92820i | −0.600886 | + | 0.346922i | ||||
\(293\) | −24.9904 | + | 14.4282i | −1.45995 | + | 0.842905i | −0.999008 | − | 0.0445239i | \(-0.985823\pi\) |
−0.460945 | + | 0.887429i | \(0.652490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.26795 | + | 21.1244i | 0.0738229 | + | 1.22991i | ||||
\(296\) | −5.50000 | − | 2.59808i | −0.319681 | − | 0.151010i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.0359 | + | 5.79423i | 0.581364 | + | 0.335651i | ||||
\(299\) | −1.07180 | − | 1.85641i | −0.0619836 | − | 0.107359i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9282 | + | 20.6603i | 0.687530 | + | 1.19084i | ||||
\(302\) | − | 10.5359i | − | 0.606273i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.26795 | −0.0727219 | ||||||||
\(305\) | −15.4641 | − | 7.73205i | −0.885472 | − | 0.442736i | ||||
\(306\) | −5.19615 | −0.297044 | ||||||||
\(307\) | 6.87564i | 0.392414i | 0.980563 | + | 0.196207i | \(0.0628624\pi\) | ||||
−0.980563 | + | 0.196207i | \(0.937138\pi\) | |||||||
\(308\) | 3.00000 | + | 1.73205i | 0.170941 | + | 0.0986928i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.0981 | + | 1.02628i | −0.971105 | + | 0.0582888i | ||||
\(311\) | −2.36603 | + | 4.09808i | −0.134165 | + | 0.232381i | −0.925278 | − | 0.379289i | \(-0.876169\pi\) |
0.791113 | + | 0.611670i | \(0.209502\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.42820 | − | 1.40192i | −0.137250 | − | 0.0792414i | 0.429803 | − | 0.902923i | \(-0.358583\pi\) |
−0.567053 | + | 0.823681i | \(0.691916\pi\) | |||||||
\(314\) | −8.50000 | − | 14.7224i | −0.479683 | − | 0.830835i | ||||
\(315\) | 10.0981 | + | 15.2942i | 0.568962 | + | 0.861732i | ||||
\(316\) | −7.83013 | + | 13.5622i | −0.440479 | + | 0.762932i | ||||
\(317\) | −12.4019 | − | 7.16025i | −0.696561 | − | 0.402160i | 0.109504 | − | 0.993986i | \(-0.465074\pi\) |
−0.806065 | + | 0.591826i | \(0.798407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.19615 | 0.122961 | ||||||||
\(320\) | −1.86603 | + | 1.23205i | −0.104314 | + | 0.0688737i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.00000i | 0.222911i | ||||||||
\(323\) | − | 2.19615i | − | 0.122197i | ||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | −0.875644 | − | 7.26795i | −0.0485720 | − | 0.403153i | ||||
\(326\) | 4.56218 | + | 7.90192i | 0.252676 | + | 0.437647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.13397 | + | 2.96410i | −0.283476 | + | 0.163665i | ||||
\(329\) | −9.19615 | − | 15.9282i | −0.507000 | − | 0.878150i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1962 | − | 17.6603i | 0.560431 | − | 0.970695i | −0.437027 | − | 0.899448i | \(-0.643969\pi\) |
0.997459 | − | 0.0712472i | \(-0.0226979\pi\) | |||||||
\(332\) | − | 2.53590i | − | 0.139176i | ||||||
\(333\) | 10.3923 | + | 15.0000i | 0.569495 | + | 0.821995i | ||||
\(334\) | −17.8564 | −0.977059 | ||||||||
\(335\) | −8.73205 | + | 17.4641i | −0.477083 | + | 0.954166i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.03590 | − | 0.598076i | 0.0564290 | − | 0.0325793i | −0.471520 | − | 0.881855i | \(-0.656295\pi\) |
0.527949 | + | 0.849276i | \(0.322961\pi\) | |||||||
\(338\) | 9.40192 | − | 5.42820i | 0.511397 | − | 0.295255i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.13397 | − | 3.23205i | −0.115731 | − | 0.175283i | ||||
\(341\) | 9.71281 | 0.525978 | ||||||||
\(342\) | 3.29423 | + | 1.90192i | 0.178131 | + | 0.102844i | ||||
\(343\) | 17.8564i | 0.964155i | ||||||||
\(344\) | 8.73205 | 0.470801 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.0358984 | + | 0.0621778i | 0.00192991 | + | 0.00334270i | ||||
\(347\) | 27.7128i | 1.48770i | 0.668346 | + | 0.743851i | \(0.267003\pi\) | ||||
−0.668346 | + | 0.743851i | \(0.732997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7942 | − | 29.0885i | 0.898974 | − | 1.55707i | 0.0701672 | − | 0.997535i | \(-0.477647\pi\) |
0.828807 | − | 0.559534i | \(-0.189020\pi\) | |||||||
\(350\) | −5.36603 | + | 12.5622i | −0.286826 | + | 0.671477i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.09808 | − | 0.633975i | 0.0585277 | − | 0.0337910i | ||||
\(353\) | −11.8923 | − | 6.86603i | −0.632964 | − | 0.365442i | 0.148935 | − | 0.988847i | \(-0.452415\pi\) |
−0.781899 | + | 0.623405i | \(0.785749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.2487 | + | 9.12436i | 0.968541 | + | 0.484271i | ||||
\(356\) | −6.46410 | −0.342597 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.9282 | − | 7.46410i | −0.683277 | − | 0.394490i | ||||
\(359\) | 17.4641 | 0.921720 | 0.460860 | − | 0.887473i | \(-0.347541\pi\) | ||||
0.460860 | + | 0.887473i | \(0.347541\pi\) | |||||||
\(360\) | 6.69615 | − | 0.401924i | 0.352918 | − | 0.0211832i | ||||
\(361\) | 8.69615 | − | 15.0622i | 0.457692 | − | 0.792746i | ||||
\(362\) | 11.5885i | 0.609076i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 14.6077 | + | 22.1244i | 0.764602 | + | 1.15804i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.3205 | + | 16.9282i | −1.53052 | + | 0.883645i | −0.531180 | + | 0.847259i | \(0.678251\pi\) |
−0.999338 | + | 0.0363862i | \(0.988415\pi\) | |||||||
\(368\) | 1.26795 | + | 0.732051i | 0.0660964 | + | 0.0381608i | ||||
\(369\) | 17.7846 | 0.925830 | ||||||||
\(370\) | −5.06218 | + | 12.6244i | −0.263170 | + | 0.656309i | ||||
\(371\) | −22.9282 | −1.19037 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.866025 | − | 0.500000i | 0.0448411 | − | 0.0258890i | −0.477412 | − | 0.878680i | \(-0.658425\pi\) |
0.522253 | + | 0.852791i | \(0.325092\pi\) | |||||||
\(374\) | 1.09808 | + | 1.90192i | 0.0567802 | + | 0.0983461i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.73205 | −0.347179 | ||||||||
\(377\) | 2.19615 | − | 1.26795i | 0.113108 | − | 0.0653027i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.2942 | − | 31.6865i | 0.939711 | − | 1.62763i | 0.173702 | − | 0.984798i | \(-0.444427\pi\) |
0.766009 | − | 0.642830i | \(-0.222240\pi\) | |||||||
\(380\) | 0.169873 | + | 2.83013i | 0.00871430 | + | 0.145182i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.7321 | + | 9.66025i | 0.856086 | + | 0.494262i | ||||
\(383\) | −13.4378 | + | 7.75833i | −0.686641 | + | 0.396432i | −0.802352 | − | 0.596851i | \(-0.796418\pi\) |
0.115712 | + | 0.993283i | \(0.463085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.46410 | − | 6.92820i | 0.176547 | − | 0.353094i | ||||
\(386\) | 8.33013 | − | 14.4282i | 0.423992 | − | 0.734376i | ||||
\(387\) | −22.6865 | − | 13.0981i | −1.15322 | − | 0.665813i | ||||
\(388\) | −6.23205 | + | 3.59808i | −0.316384 | + | 0.182665i | ||||
\(389\) | −4.13397 | − | 7.16025i | −0.209601 | − | 0.363039i | 0.741988 | − | 0.670413i | \(-0.233883\pi\) |
−0.951589 | + | 0.307374i | \(0.900550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.26795 | + | 2.19615i | −0.0641229 | + | 0.111064i | ||||
\(392\) | −0.401924 | − | 0.232051i | −0.0203002 | − | 0.0117203i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.03590 | − | 5.25833i | −0.152946 | − | 0.264911i | ||||
\(395\) | 31.3205 | + | 15.6603i | 1.57591 | + | 0.787953i | ||||
\(396\) | −3.80385 | −0.191151 | ||||||||
\(397\) | − | 0.0717968i | − | 0.00360338i | −0.999998 | − | 0.00180169i | \(-0.999427\pi\) | ||
0.999998 | − | 0.00180169i | \(-0.000573496\pi\) | |||||||
\(398\) | 1.56218 | + | 0.901924i | 0.0783049 | + | 0.0452094i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | 15.3205 | 0.765070 | 0.382535 | − | 0.923941i | \(-0.375051\pi\) | ||||
0.382535 | + | 0.923941i | \(0.375051\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.71281 | − | 5.60770i | 0.483830 | − | 0.279339i | ||||
\(404\) | 0.133975 | + | 0.232051i | 0.00666549 | + | 0.0115450i | ||||
\(405\) | −18.0000 | − | 9.00000i | −0.894427 | − | 0.447214i | ||||
\(406\) | −4.73205 | −0.234848 | ||||||||
\(407\) | 3.29423 | − | 6.97372i | 0.163289 | − | 0.345674i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.89230 | + | 3.27757i | −0.0935685 | + | 0.162065i | −0.909010 | − | 0.416774i | \(-0.863161\pi\) |
0.815442 | + | 0.578839i | \(0.196494\pi\) | |||||||
\(410\) | 7.30385 | + | 11.0622i | 0.360711 | + | 0.546322i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.29423 | + | 1.90192i | −0.162295 | + | 0.0937011i | ||||
\(413\) | 25.8564i | 1.27231i | ||||||||
\(414\) | −2.19615 | − | 3.80385i | −0.107935 | − | 0.186949i | ||||
\(415\) | −5.66025 | + | 0.339746i | −0.277851 | + | 0.0166775i | ||||
\(416\) | 0.732051 | − | 1.26795i | 0.0358917 | − | 0.0621663i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.60770i | − | 0.0786349i | ||||||
\(419\) | 14.0981 | − | 24.4186i | 0.688736 | − | 1.19293i | −0.283511 | − | 0.958969i | \(-0.591499\pi\) |
0.972247 | − | 0.233957i | \(-0.0751675\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.5167 | −0.804973 | −0.402486 | − | 0.915426i | \(-0.631854\pi\) | ||||
−0.402486 | + | 0.915426i | \(0.631854\pi\) | |||||||
\(422\) | −15.6340 | − | 9.02628i | −0.761050 | − | 0.439392i | ||||
\(423\) | 17.4904 | + | 10.0981i | 0.850411 | + | 0.490985i | ||||
\(424\) | −4.19615 | + | 7.26795i | −0.203783 | + | 0.352963i | ||||
\(425\) | −6.92820 | + | 5.19615i | −0.336067 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.2942 | − | 10.5622i | −0.885320 | − | 0.511140i | ||||
\(428\) | −5.36603 | − | 3.09808i | −0.259377 | − | 0.149751i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.16987 | − | 19.4904i | −0.0564163 | − | 0.939910i | ||||
\(431\) | −6.36603 | − | 11.0263i | −0.306641 | − | 0.531117i | 0.670985 | − | 0.741471i | \(-0.265872\pi\) |
−0.977625 | + | 0.210354i | \(0.932538\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.3731i | − | 1.55575i | −0.628419 | − | 0.777875i | \(-0.716298\pi\) | ||
0.628419 | − | 0.777875i | \(-0.283702\pi\) | |||||||
\(434\) | −20.9282 | −1.00459 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.80385 | −0.134280 | ||||||||
\(437\) | 1.60770 | − | 0.928203i | 0.0769065 | − | 0.0444020i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.9282 | − | 29.3205i | −0.807939 | − | 1.39939i | −0.914289 | − | 0.405063i | \(-0.867250\pi\) |
0.106350 | − | 0.994329i | \(-0.466084\pi\) | |||||||
\(440\) | −1.56218 | − | 2.36603i | −0.0744739 | − | 0.112796i | ||||
\(441\) | 0.696152 | + | 1.20577i | 0.0331501 | + | 0.0574177i | ||||
\(442\) | 2.19615 | + | 1.26795i | 0.104460 | + | 0.0603102i | ||||
\(443\) | − | 24.7846i | − | 1.17755i | −0.808296 | − | 0.588776i | \(-0.799610\pi\) | ||
0.808296 | − | 0.588776i | \(-0.200390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.866025 | + | 14.4282i | 0.0410535 | + | 0.683962i | ||||
\(446\) | −0.535898 | + | 0.928203i | −0.0253755 | + | 0.0439517i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.36603 | + | 1.36603i | −0.111784 | + | 0.0645386i | ||||
\(449\) | 21.1244 | + | 36.5885i | 0.996920 | + | 1.72672i | 0.566378 | + | 0.824145i | \(0.308344\pi\) |
0.430542 | + | 0.902571i | \(0.358323\pi\) | |||||||
\(450\) | −1.79423 | − | 14.8923i | −0.0845807 | − | 0.702030i | ||||
\(451\) | −3.75833 | − | 6.50962i | −0.176973 | − | 0.306526i | ||||
\(452\) | − | 16.9282i | − | 0.796236i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.33975 | 0.203674 | ||||||||
\(455\) | −0.535898 | − | 8.92820i | −0.0251233 | − | 0.418561i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.62436 | − | 4.40192i | 0.356652 | − | 0.205913i | −0.310959 | − | 0.950423i | \(-0.600650\pi\) |
0.667611 | + | 0.744510i | \(0.267317\pi\) | |||||||
\(458\) | 25.5885i | 1.19567i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.46410 | − | 2.92820i | 0.0682641 | − | 0.136528i | ||||
\(461\) | −16.8564 | + | 29.1962i | −0.785081 | + | 1.35980i | 0.143869 | + | 0.989597i | \(0.454045\pi\) |
−0.928951 | + | 0.370204i | \(0.879288\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1699 | − | 10.4904i | 0.844426 | − | 0.487529i | −0.0143405 | − | 0.999897i | \(-0.504565\pi\) |
0.858766 | + | 0.512368i | \(0.171232\pi\) | |||||||
\(464\) | −0.866025 | + | 1.50000i | −0.0402042 | + | 0.0696358i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.86603 | + | 11.8923i | −0.318062 | + | 0.550900i | ||||
\(467\) | 14.5359i | 0.672641i | 0.941748 | + | 0.336321i | \(0.109183\pi\) | ||||
−0.941748 | + | 0.336321i | \(0.890817\pi\) | |||||||
\(468\) | −3.80385 | + | 2.19615i | −0.175833 | + | 0.101517i | ||||
\(469\) | −11.9282 | + | 20.6603i | −0.550793 | + | 0.954002i | ||||
\(470\) | 0.901924 | + | 15.0263i | 0.0416026 | + | 0.693111i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.19615 | + | 4.73205i | 0.377258 | + | 0.217810i | ||||
\(473\) | 11.0718i | 0.509082i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.29423 | − | 0.758330i | 0.288799 | − | 0.0347946i | ||||
\(476\) | −2.36603 | − | 4.09808i | −0.108447 | − | 0.187835i | ||||
\(477\) | 21.8038 | − | 12.5885i | 0.998330 | − | 0.576386i | ||||
\(478\) | 12.6340 | − | 7.29423i | 0.577865 | − | 0.333630i | ||||
\(479\) | −1.26795 | + | 2.19615i | −0.0579341 | + | 0.100345i | −0.893538 | − | 0.448988i | \(-0.851785\pi\) |
0.835604 | + | 0.549333i | \(0.185118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.732051 | − | 8.87564i | −0.0333786 | − | 0.404695i | ||||
\(482\) | − | 17.4641i | − | 0.795468i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.69615 | − | 8.13397i | −0.213461 | − | 0.369726i | ||||
\(485\) | 8.86603 | + | 13.4282i | 0.402585 | + | 0.609743i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 33.4641i | − | 1.51640i | −0.652020 | − | 0.758202i | \(-0.726078\pi\) | ||
0.652020 | − | 0.758202i | \(-0.273922\pi\) | |||||||
\(488\) | −6.69615 | + | 3.86603i | −0.303121 | + | 0.175007i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.464102 | + | 0.928203i | −0.0209660 | + | 0.0419319i | ||||
\(491\) | −29.6603 | −1.33855 | −0.669274 | − | 0.743015i | \(-0.733395\pi\) | ||||
−0.669274 | + | 0.743015i | \(0.733395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.59808 | − | 1.50000i | −0.117011 | − | 0.0675566i | ||||
\(494\) | −0.928203 | − | 1.60770i | −0.0417618 | − | 0.0723336i | ||||
\(495\) | 0.509619 | + | 8.49038i | 0.0229057 | + | 0.381614i | ||||
\(496\) | −3.83013 | + | 6.63397i | −0.171978 | + | 0.297874i | ||||
\(497\) | 21.5885 | + | 12.4641i | 0.968375 | + | 0.559091i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.75833 | − | 6.50962i | −0.168246 | − | 0.291411i | 0.769557 | − | 0.638578i | \(-0.220477\pi\) |
−0.937803 | + | 0.347167i | \(0.887144\pi\) | |||||||
\(500\) | 8.52628 | − | 7.23205i | 0.381307 | − | 0.323427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.2224 | − | 5.90192i | −0.456249 | − | 0.263416i | ||||
\(503\) | 12.1699 | + | 7.02628i | 0.542628 | + | 0.313286i | 0.746143 | − | 0.665785i | \(-0.231903\pi\) |
−0.203515 | + | 0.979072i | \(0.565237\pi\) | |||||||
\(504\) | 8.19615 | 0.365086 | ||||||||
\(505\) | 0.500000 | − | 0.330127i | 0.0222497 | − | 0.0146905i | ||||
\(506\) | −0.928203 | + | 1.60770i | −0.0412637 | + | 0.0714708i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 10.9282i | − | 0.484861i | ||||||
\(509\) | 20.2583 | − | 35.0885i | 0.897935 | − | 1.55527i | 0.0678047 | − | 0.997699i | \(-0.478401\pi\) |
0.830130 | − | 0.557570i | \(-0.188266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.1962 | + | 28.0526i | 0.716476 | + | 1.24097i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.40192 | − | 11.0885i | −0.282377 | − | 0.489091i | ||||
\(515\) | 4.68653 | + | 7.09808i | 0.206513 | + | 0.312779i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.53590i | − | 0.375408i | ||||||
\(518\) | −7.09808 | + | 15.0263i | −0.311872 | + | 0.660217i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.92820 | − | 1.46410i | −0.128410 | − | 0.0642051i | ||||
\(521\) | 17.1244 | + | 29.6603i | 0.750232 | + | 1.29944i | 0.947710 | + | 0.319132i | \(0.103391\pi\) |
−0.197479 | + | 0.980307i | \(0.563275\pi\) | |||||||
\(522\) | 4.50000 | − | 2.59808i | 0.196960 | − | 0.113715i | ||||
\(523\) | 10.7321 | − | 6.19615i | 0.469280 | − | 0.270939i | −0.246658 | − | 0.969102i | \(-0.579333\pi\) |
0.715938 | + | 0.698164i | \(0.245999\pi\) | |||||||
\(524\) | −2.92820 | −0.127919 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.07180 | 0.395549 | ||||||||
\(527\) | −11.4904 | − | 6.63397i | −0.500529 | − | 0.288980i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8564 | 0.906800 | ||||||||
\(530\) | 16.7846 | + | 8.39230i | 0.729077 | + | 0.364538i | ||||
\(531\) | −14.1962 | − | 24.5885i | −0.616061 | − | 1.06705i | ||||
\(532\) | 3.46410i | 0.150188i | ||||||||
\(533\) | −7.51666 | − | 4.33975i | −0.325583 | − | 0.187975i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.19615 | + | 12.3923i | −0.267883 | + | 0.535766i | ||||
\(536\) | 4.36603 | + | 7.56218i | 0.188584 | + | 0.326636i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.4641 | − | 8.92820i | −0.666705 | − | 0.384922i | ||||
\(539\) | 0.294229 | − | 0.509619i | 0.0126733 | − | 0.0219508i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.2679 | 1.04336 | 0.521680 | − | 0.853141i | \(-0.325305\pi\) | ||||
0.521680 | + | 0.853141i | \(0.325305\pi\) | |||||||
\(542\) | 7.56218 | − | 4.36603i | 0.324823 | − | 0.187537i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.73205 | −0.0742611 | ||||||||
\(545\) | 0.375644 | + | 6.25833i | 0.0160908 | + | 0.268077i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 43.3731i | − | 1.85450i | −0.374445 | − | 0.927249i | \(-0.622167\pi\) | ||
0.374445 | − | 0.927249i | \(-0.377833\pi\) | |||||||
\(548\) | 1.50000 | − | 0.866025i | 0.0640768 | − | 0.0369948i | ||||
\(549\) | 23.1962 | 0.989988 | ||||||||
\(550\) | −5.07180 | + | 3.80385i | −0.216262 | + | 0.162197i | ||||
\(551\) | 1.09808 | + | 1.90192i | 0.0467796 | + | 0.0810247i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.0526 | + | 21.3923i | 1.57564 | + | 0.909693i | ||||
\(554\) | 1.39230 | 0.0591534 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.9282 | 0.463459 | ||||||||
\(557\) | 13.7942 | + | 7.96410i | 0.584480 | + | 0.337450i | 0.762912 | − | 0.646502i | \(-0.223769\pi\) |
−0.178432 | + | 0.983952i | \(0.557102\pi\) | |||||||
\(558\) | 19.9019 | − | 11.4904i | 0.842516 | − | 0.486427i | ||||
\(559\) | 6.39230 | + | 11.0718i | 0.270366 | + | 0.468287i | ||||
\(560\) | 3.36603 | + | 5.09808i | 0.142241 | + | 0.215433i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.59808 | + | 1.50000i | −0.109593 | + | 0.0632737i | ||||
\(563\) | 5.85641i | 0.246818i | 0.992356 | + | 0.123409i | \(0.0393827\pi\) | ||||
−0.992356 | + | 0.123409i | \(0.960617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.7846 | + | 2.26795i | −1.58961 | + | 0.0954133i | ||||
\(566\) | −5.80385 | −0.243954 | ||||||||
\(567\) | −21.2942 | − | 12.2942i | −0.894274 | − | 0.516309i | ||||
\(568\) | 7.90192 | − | 4.56218i | 0.331557 | − | 0.191425i | ||||
\(569\) | −43.1051 | −1.80706 | −0.903530 | − | 0.428524i | \(-0.859034\pi\) | ||||
−0.903530 | + | 0.428524i | \(0.859034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.1244 | − | 22.7321i | 0.549237 | − | 0.951307i | −0.449090 | − | 0.893487i | \(-0.648252\pi\) |
0.998327 | − | 0.0578201i | \(-0.0184150\pi\) | |||||||
\(572\) | 1.60770 | + | 0.928203i | 0.0672211 | + | 0.0388101i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.09808 | + | 14.0263i | 0.338007 | + | 0.585446i | ||||
\(575\) | −6.73205 | − | 2.87564i | −0.280746 | − | 0.119923i | ||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | 1.73205 | + | 1.00000i | 0.0721062 | + | 0.0416305i | 0.535620 | − | 0.844459i | \(-0.320078\pi\) |
−0.463513 | + | 0.886090i | \(0.653411\pi\) | |||||||
\(578\) | 14.0000i | 0.582323i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.46410 | + | 1.73205i | 0.143839 | + | 0.0719195i | ||||
\(581\) | −6.92820 | −0.287430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.21539 | − | 5.32051i | −0.381662 | − | 0.220353i | ||||
\(584\) | 11.8564 | 0.490622 | ||||||||
\(585\) | 5.41154 | + | 8.19615i | 0.223740 | + | 0.338869i | ||||
\(586\) | 28.8564 | 1.19205 | ||||||||
\(587\) | 16.3923 | − | 9.46410i | 0.676583 | − | 0.390625i | −0.121983 | − | 0.992532i | \(-0.538925\pi\) |
0.798566 | + | 0.601907i | \(0.205592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.85641 | + | 8.41154i | 0.200105 | + | 0.346592i | ||||
\(590\) | 9.46410 | − | 18.9282i | 0.389631 | − | 0.779262i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.46410 | + | 5.00000i | 0.142374 | + | 0.205499i | ||||
\(593\) | − | 19.7321i | − | 0.810298i | −0.914251 | − | 0.405149i | \(-0.867220\pi\) | ||
0.914251 | − | 0.405149i | \(-0.132780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.83013 | + | 5.83013i | −0.362000 | + | 0.239012i | ||||
\(596\) | −5.79423 | − | 10.0359i | −0.237341 | − | 0.411086i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.14359i | 0.0876581i | ||||||||
\(599\) | −0.0262794 | − | 0.0455173i | −0.00107375 | − | 0.00185979i | 0.865488 | − | 0.500930i | \(-0.167008\pi\) |
−0.866562 | + | 0.499070i | \(0.833675\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.6244 | + | 32.2583i | −0.759703 | + | 1.31584i | 0.183299 | + | 0.983057i | \(0.441322\pi\) |
−0.943002 | + | 0.332787i | \(0.892011\pi\) | |||||||
\(602\) | − | 23.8564i | − | 0.972315i | ||||||
\(603\) | − | 26.1962i | − | 1.06679i | ||||||
\(604\) | −5.26795 | + | 9.12436i | −0.214350 | + | 0.371265i | ||||
\(605\) | −17.5263 | + | 11.5718i | −0.712545 | + | 0.470460i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.9019 | + | 13.2224i | 0.929560 | + | 0.536682i | 0.886673 | − | 0.462398i | \(-0.153011\pi\) |
0.0428879 | + | 0.999080i | \(0.486344\pi\) | |||||||
\(608\) | 1.09808 | + | 0.633975i | 0.0445329 | + | 0.0257111i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.52628 | + | 14.4282i | 0.385708 | + | 0.584181i | ||||
\(611\) | −4.92820 | − | 8.53590i | −0.199374 | − | 0.345325i | ||||
\(612\) | 4.50000 | + | 2.59808i | 0.181902 | + | 0.105021i | ||||
\(613\) | −27.9904 | − | 16.1603i | −1.13052 | − | 0.652707i | −0.186455 | − | 0.982464i | \(-0.559700\pi\) |
−0.944066 | + | 0.329757i | \(0.893033\pi\) | |||||||
\(614\) | 3.43782 | − | 5.95448i | 0.138739 | − | 0.240303i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.73205 | − | 3.00000i | −0.0697863 | − | 0.120873i | ||||
\(617\) | 28.3923 | + | 16.3923i | 1.14303 | + | 0.659929i | 0.947179 | − | 0.320704i | \(-0.103920\pi\) |
0.195852 | + | 0.980634i | \(0.437253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.4449 | −1.22368 | −0.611841 | − | 0.790981i | \(-0.709571\pi\) | ||||
−0.611841 | + | 0.790981i | \(0.709571\pi\) | |||||||
\(620\) | 15.3205 | + | 7.66025i | 0.615286 | + | 0.307643i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.09808 | − | 2.36603i | 0.164318 | − | 0.0948690i | ||||
\(623\) | 17.6603i | 0.707543i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | 1.40192 | + | 2.42820i | 0.0560321 | + | 0.0970505i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.0000i | 0.678374i | ||||||||
\(629\) | −8.66025 | + | 6.00000i | −0.345307 | + | 0.239236i | ||||
\(630\) | −1.09808 | − | 18.2942i | −0.0437484 | − | 0.728860i | ||||
\(631\) | −6.39230 | + | 11.0718i | −0.254474 | + | 0.440761i | −0.964752 | − | 0.263159i | \(-0.915236\pi\) |
0.710279 | + | 0.703920i | \(0.248569\pi\) | |||||||
\(632\) | 13.5622 | − | 7.83013i | 0.539474 | − | 0.311466i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.16025 | + | 12.4019i | 0.284370 | + | 0.492543i | ||||
\(635\) | −24.3923 | + | 1.46410i | −0.967979 | + | 0.0581011i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.679492i | − | 0.0269225i | ||||||
\(638\) | −1.90192 | − | 1.09808i | −0.0752979 | − | 0.0434733i | ||||
\(639\) | −27.3731 | −1.08286 | ||||||||
\(640\) | 2.23205 | − | 0.133975i | 0.0882296 | − | 0.00529581i | ||||
\(641\) | 14.3564 | − | 24.8660i | 0.567044 | − | 0.982149i | −0.429812 | − | 0.902918i | \(-0.641420\pi\) |
0.996856 | − | 0.0792307i | \(-0.0252464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 39.6603i | − | 1.56405i | −0.623248 | − | 0.782024i | \(-0.714187\pi\) | ||
0.623248 | − | 0.782024i | \(-0.285813\pi\) | |||||||
\(644\) | 2.00000 | − | 3.46410i | 0.0788110 | − | 0.136505i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.09808 | + | 1.90192i | −0.0432032 | + | 0.0748302i | ||||
\(647\) | −6.75833 | + | 3.90192i | −0.265697 | + | 0.153400i | −0.626931 | − | 0.779075i | \(-0.715689\pi\) |
0.361233 | + | 0.932475i | \(0.382356\pi\) | |||||||
\(648\) | −7.79423 | + | 4.50000i | −0.306186 | + | 0.176777i | ||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | −2.87564 | + | 6.73205i | −0.112792 | + | 0.264053i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 9.12436i | − | 0.357337i | ||||||
\(653\) | 36.6506 | − | 21.1603i | 1.43425 | − | 0.828065i | 0.436809 | − | 0.899554i | \(-0.356109\pi\) |
0.997441 | + | 0.0714896i | \(0.0227753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.392305 | + | 6.53590i | 0.0153286 | + | 0.255379i | ||||
\(656\) | 5.92820 | 0.231457 | ||||||||
\(657\) | −30.8038 | − | 17.7846i | −1.20177 | − | 0.693844i | ||||
\(658\) | 18.3923i | 0.717007i | ||||||||
\(659\) | −7.26795 | − | 12.5885i | −0.283119 | − | 0.490377i | 0.689032 | − | 0.724731i | \(-0.258036\pi\) |
−0.972151 | + | 0.234354i | \(0.924703\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.1340 | + | 33.1410i | 0.744225 | + | 1.28904i | 0.950556 | + | 0.310554i | \(0.100514\pi\) |
−0.206330 | + | 0.978482i | \(0.566152\pi\) | |||||||
\(662\) | −17.6603 | + | 10.1962i | −0.686385 | + | 0.396285i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.26795 | + | 2.19615i | −0.0492060 | + | 0.0852272i | ||||
\(665\) | 7.73205 | − | 0.464102i | 0.299836 | − | 0.0179971i | ||||
\(666\) | −1.50000 | − | 18.1865i | −0.0581238 | − | 0.704714i | ||||
\(667\) | − | 2.53590i | − | 0.0981904i | ||||||
\(668\) | 15.4641 | + | 8.92820i | 0.598324 | + | 0.345443i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.2942 | − | 10.7583i | 0.629501 | − | 0.415631i | ||||
\(671\) | −4.90192 | − | 8.49038i | −0.189237 | − | 0.327768i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.5885 | + | 19.3923i | −1.29474 | + | 0.747518i | −0.979490 | − | 0.201490i | \(-0.935422\pi\) |
−0.315249 | + | 0.949009i | \(0.602088\pi\) | |||||||
\(674\) | −1.19615 | −0.0460741 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8564 | −0.417554 | ||||||||
\(677\) | 39.0000i | 1.49889i | 0.662066 | + | 0.749446i | \(0.269680\pi\) | ||||
−0.662066 | + | 0.749446i | \(0.730320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.83013 | + | 17.0263i | 0.377246 | + | 0.653409i | ||||
\(680\) | 0.232051 | + | 3.86603i | 0.00889874 | + | 0.148255i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.41154 | − | 4.85641i | −0.322095 | − | 0.185961i | ||||
\(683\) | 13.5622 | + | 7.83013i | 0.518942 | + | 0.299611i | 0.736502 | − | 0.676436i | \(-0.236476\pi\) |
−0.217559 | + | 0.976047i | \(0.569810\pi\) | |||||||
\(684\) | −1.90192 | − | 3.29423i | −0.0727219 | − | 0.125958i | ||||
\(685\) | −2.13397 | − | 3.23205i | −0.0815350 | − | 0.123490i | ||||
\(686\) | 8.92820 | − | 15.4641i | 0.340880 | − | 0.590422i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.56218 | − | 4.36603i | −0.288305 | − | 0.166453i | ||||
\(689\) | −12.2872 | −0.468105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.90192 | − | 10.2224i | 0.224520 | − | 0.388880i | −0.731655 | − | 0.681675i | \(-0.761252\pi\) |
0.956175 | + | 0.292795i | \(0.0945853\pi\) | |||||||
\(692\) | − | 0.0717968i | − | 0.00272930i | ||||||
\(693\) | 10.3923i | 0.394771i | ||||||||
\(694\) | 13.8564 | − | 24.0000i | 0.525982 | − | 0.911028i | ||||
\(695\) | −1.46410 | − | 24.3923i | −0.0555365 | − | 0.925253i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.2679i | 0.388926i | ||||||||
\(698\) | −29.0885 | + | 16.7942i | −1.10101 | + | 0.635671i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.9282 | − | 8.19615i | 0.413047 | − | 0.309785i | ||||
\(701\) | 15.3923 | − | 26.6603i | 0.581359 | − | 1.00694i | −0.413959 | − | 0.910295i | \(-0.635854\pi\) |
0.995319 | − | 0.0966485i | \(-0.0308123\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.68653 | − | 0.633975i | 0.289903 | − | 0.0239108i | ||||
\(704\) | −1.26795 | −0.0477876 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.86603 | + | 11.8923i | 0.258406 | + | 0.447573i | ||||
\(707\) | 0.633975 | − | 0.366025i | 0.0238431 | − | 0.0137658i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.07180 | −0.0402522 | −0.0201261 | − | 0.999797i | \(-0.506407\pi\) | ||||
−0.0201261 | + | 0.999797i | \(0.506407\pi\) | |||||||
\(710\) | −11.2417 | − | 17.0263i | −0.421892 | − | 0.638985i | ||||
\(711\) | −46.9808 | −1.76192 | ||||||||
\(712\) | 5.59808 | + | 3.23205i | 0.209797 | + | 0.121126i | ||||
\(713\) | − | 11.2154i | − | 0.420020i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.85641 | − | 3.71281i | 0.0694257 | − | 0.138851i | ||||
\(716\) | 7.46410 | + | 12.9282i | 0.278947 | + | 0.483150i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.1244 | − | 8.73205i | −0.564436 | − | 0.325877i | ||||
\(719\) | 6.19615 | − | 10.7321i | 0.231077 | − | 0.400238i | −0.727048 | − | 0.686587i | \(-0.759108\pi\) |
0.958125 | + | 0.286349i | \(0.0924416\pi\) | |||||||
\(720\) | −6.00000 | − | 3.00000i | −0.223607 | − | 0.111803i | ||||
\(721\) | 5.19615 | + | 9.00000i | 0.193515 | + | 0.335178i | ||||
\(722\) | −15.0622 | + | 8.69615i | −0.560556 | + | 0.323637i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.79423 | − | 10.0359i | 0.215341 | − | 0.372981i | ||||
\(725\) | 3.40192 | − | 7.96410i | 0.126344 | − | 0.295779i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.1244 | + | 19.1244i | −1.22851 | + | 0.709283i | −0.966719 | − | 0.255840i | \(-0.917648\pi\) |
−0.261795 | + | 0.965123i | \(0.584315\pi\) | |||||||
\(728\) | −3.46410 | − | 2.00000i | −0.128388 | − | 0.0741249i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −1.58846 | − | 26.4641i | −0.0587914 | − | 0.979480i | ||||
\(731\) | 7.56218 | − | 13.0981i | 0.279697 | − | 0.484450i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.1244 | − | 8.73205i | 0.558631 | − | 0.322526i | −0.193965 | − | 0.981008i | \(-0.562135\pi\) |
0.752596 | + | 0.658483i | \(0.228801\pi\) | |||||||
\(734\) | 33.8564 | 1.24966 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.732051 | − | 1.26795i | −0.0269838 | − | 0.0467372i | ||||
\(737\) | −9.58846 | + | 5.53590i | −0.353195 | + | 0.203917i | ||||
\(738\) | −15.4019 | − | 8.89230i | −0.566953 | − | 0.327330i | ||||
\(739\) | −30.9282 | −1.13771 | −0.568856 | − | 0.822437i | \(-0.692614\pi\) | ||||
−0.568856 | + | 0.822437i | \(0.692614\pi\) | |||||||
\(740\) | 10.6962 | − | 8.40192i | 0.393198 | − | 0.308861i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.8564 | + | 11.4641i | 0.728952 | + | 0.420860i | ||||
\(743\) | −22.2224 | + | 12.8301i | −0.815262 | + | 0.470692i | −0.848780 | − | 0.528746i | \(-0.822662\pi\) |
0.0335179 | + | 0.999438i | \(0.489329\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.6244 | + | 14.2776i | −0.792255 | + | 0.523090i | ||||
\(746\) | −1.00000 | −0.0366126 | ||||||||
\(747\) | 6.58846 | − | 3.80385i | 0.241059 | − | 0.139176i | ||||
\(748\) | − | 2.19615i | − | 0.0802993i | ||||||
\(749\) | −8.46410 | + | 14.6603i | −0.309272 | + | 0.535674i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.1962 | 1.10187 | 0.550937 | − | 0.834547i | \(-0.314271\pi\) | ||||
0.550937 | + | 0.834547i | \(0.314271\pi\) | |||||||
\(752\) | 5.83013 | + | 3.36603i | 0.212603 | + | 0.122746i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.53590 | −0.0923520 | ||||||||
\(755\) | 21.0718 | + | 10.5359i | 0.766881 | + | 0.383441i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.33013 | − | 0.767949i | −0.0483443 | − | 0.0279116i | 0.475633 | − | 0.879644i | \(-0.342219\pi\) |
−0.523977 | + | 0.851732i | \(0.675552\pi\) | |||||||
\(758\) | −31.6865 | + | 18.2942i | −1.15091 | + | 0.664476i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.26795 | − | 2.53590i | 0.0459934 | − | 0.0919867i | ||||
\(761\) | −0.500000 | + | 0.866025i | −0.0181250 | + | 0.0313934i | −0.874946 | − | 0.484221i | \(-0.839103\pi\) |
0.856821 | + | 0.515615i | \(0.172436\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.66025i | 0.277320i | ||||||||
\(764\) | −9.66025 | − | 16.7321i | −0.349496 | − | 0.605344i | ||||
\(765\) | 5.19615 | − | 10.3923i | 0.187867 | − | 0.375735i | ||||
\(766\) | 15.5167 | 0.560640 | ||||||||
\(767\) | 13.8564i | 0.500326i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.60770 | 0.130097 | 0.0650484 | − | 0.997882i | \(-0.479280\pi\) | ||||
0.0650484 | + | 0.997882i | \(0.479280\pi\) | |||||||
\(770\) | −6.46410 | + | 4.26795i | −0.232950 | + | 0.153806i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.4282 | + | 8.33013i | −0.519282 | + | 0.299808i | ||||
\(773\) | 35.3827 | − | 20.4282i | 1.27263 | − | 0.734751i | 0.297145 | − | 0.954832i | \(-0.403965\pi\) |
0.975482 | + | 0.220081i | \(0.0706321\pi\) | |||||||
\(774\) | 13.0981 | + | 22.6865i | 0.470801 | + | 0.815451i | ||||
\(775\) | 15.0455 | − | 35.2224i | 0.540451 | − | 1.26523i | ||||
\(776\) | 7.19615 | 0.258327 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.26795i | 0.296420i | ||||||||
\(779\) | 3.75833 | − | 6.50962i | 0.134656 | − | 0.233231i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.78461 | + | 10.0192i | 0.206990 | + | 0.358517i | ||||
\(782\) | 2.19615 | − | 1.26795i | 0.0785343 | − | 0.0453418i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.232051 | + | 0.401924i | 0.00828753 | + | 0.0143544i | ||||
\(785\) | 37.9449 | − | 2.27757i | 1.35431 | − | 0.0812899i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.5692i | 1.62437i | 0.583402 | + | 0.812184i | \(0.301721\pi\) | ||||
−0.583402 | + | 0.812184i | \(0.698279\pi\) | |||||||
\(788\) | 6.07180i | 0.216299i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19.2942 | − | 29.2224i | −0.686458 | − | 1.03969i | ||||
\(791\) | −46.2487 | −1.64441 | ||||||||
\(792\) | 3.29423 | + | 1.90192i | 0.117055 | + | 0.0675819i | ||||
\(793\) | −9.80385 | − | 5.66025i | −0.348145 | − | 0.201002i | ||||
\(794\) | −0.0358984 | + | 0.0621778i | −0.00127399 | + | 0.00220661i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.901924 | − | 1.56218i | −0.0319678 | − | 0.0553699i | ||||
\(797\) | 22.9808 | + | 13.2679i | 0.814020 | + | 0.469975i | 0.848350 | − | 0.529436i | \(-0.177596\pi\) |
−0.0343297 | + | 0.999411i | \(0.510930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.83013 | + | 10.0981i | −0.206255 | + | 0.357244i | ||||
\(800\) | −0.598076 | − | 4.96410i | −0.0211452 | − | 0.175507i | ||||
\(801\) | −9.69615 | − | 16.7942i | −0.342597 | − | 0.593395i | ||||
\(802\) | −13.2679 | − | 7.66025i | −0.468508 | − | 0.270493i | ||||
\(803\) | 15.0333i | 0.530514i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | − | 4.00000i | −0.281963 | − | 0.140981i | ||||
\(806\) | −11.2154 | −0.395045 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 0.267949i | − | 0.00942642i | ||||||
\(809\) | 5.66025 | + | 9.80385i | 0.199004 | + | 0.344685i | 0.948206 | − | 0.317657i | \(-0.102896\pi\) |
−0.749202 | + | 0.662342i | \(0.769563\pi\) | |||||||
\(810\) | 11.0885 | + | 16.7942i | 0.389609 | + | 0.590089i | ||||
\(811\) | 20.1962 | + | 34.9808i | 0.709183 | + | 1.22834i | 0.965161 | + | 0.261658i | \(0.0842693\pi\) |
−0.255978 | + | 0.966683i | \(0.582397\pi\) | |||||||
\(812\) | 4.09808 | + | 2.36603i | 0.143814 | + | 0.0830312i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.33975 | + | 4.39230i | −0.222208 | + | 0.153950i | ||||
\(815\) | −20.3660 | + | 1.22243i | −0.713391 | + | 0.0428199i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.58846 | + | 5.53590i | −0.335458 | + | 0.193677i | ||||
\(818\) | 3.27757 | − | 1.89230i | 0.114597 | − | 0.0661629i | ||||
\(819\) | 6.00000 | + | 10.3923i | 0.209657 | + | 0.363137i | ||||
\(820\) | −0.794229 | − | 13.2321i | −0.0277357 | − | 0.462083i | ||||
\(821\) | −14.0000 | − | 24.2487i | −0.488603 | − | 0.846286i | 0.511311 | − | 0.859396i | \(-0.329160\pi\) |
−0.999914 | + | 0.0131101i | \(0.995827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.4449 | + | 25.6603i | 1.54925 | + | 0.894460i | 0.998199 | + | 0.0599890i | \(0.0191066\pi\) |
0.551052 | + | 0.834471i | \(0.314227\pi\) | |||||||
\(824\) | 3.80385 | 0.132513 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9282 | − | 22.3923i | 0.449830 | − | 0.779128i | ||||
\(827\) | −44.7846 | + | 25.8564i | −1.55731 | + | 0.899115i | −0.559801 | + | 0.828627i | \(0.689122\pi\) |
−0.997513 | + | 0.0704882i | \(0.977544\pi\) | |||||||
\(828\) | 4.39230i | 0.152643i | ||||||||
\(829\) | −22.4641 | + | 38.9090i | −0.780210 | + | 1.35136i | 0.151608 | + | 0.988441i | \(0.451555\pi\) |
−0.931819 | + | 0.362924i | \(0.881779\pi\) | |||||||
\(830\) | 5.07180 | + | 2.53590i | 0.176045 | + | 0.0880223i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.26795 | + | 0.732051i | −0.0439582 | + | 0.0253793i | ||||
\(833\) | −0.696152 | + | 0.401924i | −0.0241203 | + | 0.0139258i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.8564 | − | 35.7128i | 0.617946 | − | 1.23589i | ||||
\(836\) | −0.803848 | + | 1.39230i | −0.0278016 | + | 0.0481539i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.4186 | + | 14.0981i | −0.843526 | + | 0.487010i | ||||
\(839\) | −26.1962 | + | 45.3731i | −0.904392 | + | 1.56645i | −0.0826598 | + | 0.996578i | \(0.526341\pi\) |
−0.821732 | + | 0.569874i | \(0.806992\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | 14.3038 | + | 8.25833i | 0.492943 | + | 0.284601i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.02628 | + | 15.6340i | 0.310697 | + | 0.538144i | ||||
\(845\) | 1.45448 | + | 24.2321i | 0.0500357 | + | 0.833608i | ||||
\(846\) | −10.0981 | − | 17.4904i | −0.347179 | − | 0.601332i | ||||
\(847\) | −22.2224 | + | 12.8301i | −0.763572 | + | 0.440848i | ||||
\(848\) | 7.26795 | − | 4.19615i | 0.249582 | − | 0.144096i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.59808 | − | 1.03590i | 0.294912 | − | 0.0355310i | ||||
\(851\) | −8.05256 | − | 3.80385i | −0.276038 | − | 0.130394i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.7750 | − | 26.4282i | −1.56731 | − | 0.904884i | −0.996482 | − | 0.0838122i | \(-0.973290\pi\) |
−0.570824 | − | 0.821072i | \(-0.693376\pi\) | |||||||
\(854\) | 10.5622 | + | 18.2942i | 0.361430 | + | 0.626016i | ||||
\(855\) | −7.09808 | + | 4.68653i | −0.242749 | + | 0.160276i | ||||
\(856\) | 3.09808 | + | 5.36603i | 0.105890 | + | 0.183407i | ||||
\(857\) | 32.5167i | 1.11075i | 0.831601 | + | 0.555374i | \(0.187425\pi\) | ||||
−0.831601 | + | 0.555374i | \(0.812575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.0526 | −1.29834 | −0.649168 | − | 0.760645i | \(-0.724883\pi\) | ||||
−0.649168 | + | 0.760645i | \(0.724883\pi\) | |||||||
\(860\) | −8.73205 | + | 17.4641i | −0.297760 | + | 0.595521i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.7321i | 0.433655i | ||||||||
\(863\) | −15.8038 | − | 9.12436i | −0.537969 | − | 0.310597i | 0.206286 | − | 0.978492i | \(-0.433862\pi\) |
−0.744256 | + | 0.667895i | \(0.767196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.160254 | + | 0.00961894i | −0.00544880 | + | 0.000327054i | ||||
\(866\) | −16.1865 | + | 28.0359i | −0.550041 | + | 0.952699i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.1244 | + | 10.4641i | 0.615181 | + | 0.355175i | ||||
\(869\) | 9.92820 | + | 17.1962i | 0.336791 | + | 0.583340i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.39230 | + | 11.0718i | −0.216595 | + | 0.375154i | ||||
\(872\) | 2.42820 | + | 1.40192i | 0.0822293 | + | 0.0474751i | ||||
\(873\) | −18.6962 | − | 10.7942i | −0.632769 | − | 0.365329i | ||||
\(874\) | −1.85641 | −0.0627939 | ||||||||
\(875\) | −19.7583 | − | 23.2942i | −0.667953 | − | 0.787489i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 27.1051i | − | 0.915275i | −0.889139 | − | 0.457637i | \(-0.848696\pi\) | ||
0.889139 | − | 0.457637i | \(-0.151304\pi\) | |||||||
\(878\) | 33.8564i | 1.14260i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.169873 | + | 2.83013i | 0.00572642 | + | 0.0954036i | ||||
\(881\) | −8.76795 | − | 15.1865i | −0.295400 | − | 0.511647i | 0.679678 | − | 0.733511i | \(-0.262119\pi\) |
−0.975078 | + | 0.221863i | \(0.928786\pi\) | |||||||
\(882\) | − | 1.39230i | − | 0.0468813i | ||||||
\(883\) | 17.6603 | − | 10.1962i | 0.594315 | − | 0.343128i | −0.172487 | − | 0.985012i | \(-0.555180\pi\) |
0.766802 | + | 0.641884i | \(0.221847\pi\) | |||||||
\(884\) | −1.26795 | − | 2.19615i | −0.0426457 | − | 0.0738646i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.3923 | + | 21.4641i | −0.416328 | + | 0.721101i | ||||
\(887\) | − | 5.46410i | − | 0.183467i | −0.995784 | − | 0.0917333i | \(-0.970759\pi\) | ||
0.995784 | − | 0.0917333i | \(-0.0292407\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.8564 | −1.00135 | ||||||||
\(890\) | 6.46410 | − | 12.9282i | 0.216677 | − | 0.433354i | ||||
\(891\) | −5.70577 | − | 9.88269i | −0.191151 | − | 0.331082i | ||||
\(892\) | 0.928203 | − | 0.535898i | 0.0310785 | − | 0.0179432i | ||||
\(893\) | 7.39230 | − | 4.26795i | 0.247374 | − | 0.142821i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.8564 | − | 18.3923i | 0.931137 | − | 0.614787i | ||||
\(896\) | 2.73205 | 0.0912714 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 42.2487i | − | 1.40986i | ||||||
\(899\) | 13.2679 | 0.442511 | ||||||||
\(900\) | −5.89230 | + | 13.7942i | −0.196410 | + | 0.459808i | ||||
\(901\) | 7.26795 | + | 12.5885i | 0.242130 | + | 0.419382i | ||||
\(902\) | 7.51666i | 0.250277i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.46410 | + | 14.6603i | −0.281512 | + | 0.487593i | ||||
\(905\) | −23.1769 | − | 11.5885i | −0.770427 | − | 0.385213i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.83013 | + | 1.63397i | −0.0939728 | + | 0.0542552i | −0.546250 | − | 0.837622i | \(-0.683945\pi\) |
0.452277 | + | 0.891877i | \(0.350612\pi\) | |||||||
\(908\) | −3.75833 | − | 2.16987i | −0.124725 | − | 0.0720098i | ||||
\(909\) | −0.401924 | + | 0.696152i | −0.0133310 | + | 0.0230899i | ||||
\(910\) | −4.00000 | + | 8.00000i | −0.132599 | + | 0.265197i | ||||
\(911\) | 18.9282 | 0.627119 | 0.313560 | − | 0.949568i | \(-0.398478\pi\) | ||||
0.313560 | + | 0.949568i | \(0.398478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.78461 | − | 1.60770i | −0.0921571 | − | 0.0532069i | ||||
\(914\) | −8.80385 | −0.291205 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.7942 | − | 22.1603i | 0.422733 | − | 0.732195i | ||||
\(917\) | 8.00000i | 0.264183i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.0333 | 1.81538 | 0.907691 | − | 0.419639i | \(-0.137843\pi\) | ||||
0.907691 | + | 0.419639i | \(0.137843\pi\) | |||||||
\(920\) | −2.73205 | + | 1.80385i | −0.0900730 | + | 0.0594711i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.1962 | − | 16.8564i | 0.961524 | − | 0.555136i | ||||
\(923\) | 11.5692 | + | 6.67949i | 0.380805 | + | 0.219858i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.1865 | − | 22.7487i | −0.663729 | − | 0.747973i | ||||
\(926\) | −20.9808 | −0.689471 | ||||||||
\(927\) | −9.88269 | − | 5.70577i | −0.324590 | − | 0.187402i | ||||
\(928\) | 1.50000 | − | 0.866025i | 0.0492399 | − | 0.0284287i | ||||
\(929\) | 14.7679 | + | 25.5788i | 0.484521 | + | 0.839214i | 0.999842 | − | 0.0177827i | \(-0.00566070\pi\) |
−0.515321 | + | 0.856997i | \(0.672327\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.588457 | 0.0192859 | ||||||||
\(932\) | 11.8923 | − | 6.86603i | 0.389545 | − | 0.224904i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.26795 | − | 12.5885i | 0.237815 | − | 0.411907i | ||||
\(935\) | −4.90192 | + | 0.294229i | −0.160310 | + | 0.00962231i | ||||
\(936\) | 4.39230 | 0.143567 | ||||||||
\(937\) | −31.7487 | − | 18.3301i | −1.03719 | − | 0.598819i | −0.118150 | − | 0.992996i | \(-0.537697\pi\) |
−0.919035 | + | 0.394177i | \(0.871030\pi\) | |||||||
\(938\) | 20.6603 | − | 11.9282i | 0.674581 | − | 0.389470i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.73205 | − | 13.4641i | 0.219575 | − | 0.439151i | ||||
\(941\) | 9.33013 | − | 16.1603i | 0.304153 | − | 0.526809i | −0.672919 | − | 0.739716i | \(-0.734960\pi\) |
0.977072 | + | 0.212907i | \(0.0682931\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.51666 | + | 4.33975i | −0.244776 | + | 0.141322i | ||||
\(944\) | −4.73205 | − | 8.19615i | −0.154015 | − | 0.266762i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.53590 | − | 9.58846i | 0.179988 | − | 0.311748i | ||||
\(947\) | −11.0718 | − | 6.39230i | −0.359785 | − | 0.207722i | 0.309201 | − | 0.950997i | \(-0.399938\pi\) |
−0.668986 | + | 0.743275i | \(0.733272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.67949 | + | 15.0333i | 0.281748 | + | 0.488002i | ||||
\(950\) | −5.83013 | − | 2.49038i | −0.189154 | − | 0.0807986i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.73205i | 0.153367i | ||||||||
\(953\) | 11.1962 | + | 6.46410i | 0.362679 | + | 0.209393i | 0.670255 | − | 0.742131i | \(-0.266185\pi\) |
−0.307576 | + | 0.951523i | \(0.599518\pi\) | |||||||
\(954\) | −25.1769 | −0.815133 | ||||||||
\(955\) | −36.0526 | + | 23.8038i | −1.16663 | + | 0.770274i | ||||
\(956\) | −14.5885 | −0.471824 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.19615 | − | 1.26795i | 0.0709545 | − | 0.0409656i | ||||
\(959\) | −2.36603 | − | 4.09808i | −0.0764029 | − | 0.132334i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.6795 | 0.892887 | ||||||||
\(962\) | −3.80385 | + | 8.05256i | −0.122641 | + | 0.259625i | ||||
\(963\) | − | 18.5885i | − | 0.599005i | ||||||
\(964\) | −8.73205 | + | 15.1244i | −0.281240 | + | 0.487123i | ||||
\(965\) | 20.5263 | + | 31.0885i | 0.660764 | + | 1.00077i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.1436 | − | 5.85641i | 0.326196 | − | 0.188329i | −0.327955 | − | 0.944693i | \(-0.606359\pi\) |
0.654151 | + | 0.756364i | \(0.273026\pi\) | |||||||
\(968\) | 9.39230i | 0.301880i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.964102 | − | 16.0622i | −0.0309554 | − | 0.515725i | ||||
\(971\) | 13.3205 | − | 23.0718i | 0.427475 | − | 0.740409i | −0.569173 | − | 0.822218i | \(-0.692736\pi\) |
0.996648 | + | 0.0818089i | \(0.0260697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 29.8564i | − | 0.957152i | ||||||
\(974\) | −16.7321 | + | 28.9808i | −0.536129 | + | 0.928604i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.73205 | 0.247497 | ||||||||
\(977\) | 24.3731 | + | 14.0718i | 0.779763 | + | 0.450197i | 0.836346 | − | 0.548201i | \(-0.184687\pi\) |
−0.0565830 | + | 0.998398i | \(0.518021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.09808 | + | 7.09808i | −0.130975 | + | 0.226855i | ||||
\(980\) | 0.866025 | − | 0.571797i | 0.0276642 | − | 0.0182654i | ||||
\(981\) | −4.20577 | − | 7.28461i | −0.134280 | − | 0.232580i | ||||
\(982\) | 25.6865 | + | 14.8301i | 0.819690 | + | 0.473248i | ||||
\(983\) | 32.3660 | + | 18.6865i | 1.03232 | + | 0.596008i | 0.917647 | − | 0.397396i | \(-0.130086\pi\) |
0.114669 | + | 0.993404i | \(0.463419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.5526 | − | 0.813467i | 0.431820 | − | 0.0259192i | ||||
\(986\) | 1.50000 | + | 2.59808i | 0.0477697 | + | 0.0827396i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.85641i | 0.0590602i | ||||||||
\(989\) | 12.7846 | 0.406527 | ||||||||
\(990\) | 3.80385 | − | 7.60770i | 0.120894 | − | 0.241788i | ||||
\(991\) | 19.2679 | 0.612067 | 0.306033 | − | 0.952021i | \(-0.400998\pi\) | ||||
0.306033 | + | 0.952021i | \(0.400998\pi\) | |||||||
\(992\) | 6.63397 | − | 3.83013i | 0.210629 | − | 0.121607i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.4641 | − | 21.5885i | −0.395337 | − | 0.684744i | ||||
\(995\) | −3.36603 | + | 2.22243i | −0.106710 | + | 0.0704558i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.7321 | + | 6.19615i | 0.339887 | + | 0.196234i | 0.660222 | − | 0.751070i | \(-0.270462\pi\) |
−0.320335 | + | 0.947304i | \(0.603795\pi\) | |||||||
\(998\) | 7.51666i | 0.237936i | ||||||||
\(999\) | 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 | 370.2.n.c.269.1 | yes | 4 | |
5.4 | even | 2 | 370.2.n.a.269.2 | ✓ | 4 | ||
37.26 | even | 3 | 370.2.n.a.359.2 | yes | 4 | ||
185.174 | even | 6 | inner | 370.2.n.c.359.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.n.a.269.2 | ✓ | 4 | 5.4 | even | 2 | ||
370.2.n.a.359.2 | yes | 4 | 37.26 | even | 3 | ||
370.2.n.c.269.1 | yes | 4 | 1.1 | even | 1 | trivial | |
370.2.n.c.359.1 | yes | 4 | 185.174 | even | 6 | inner |