Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(218,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.j (of order \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 407.4 | ||
Character | \(\chi\) | \(=\) | 525.407 |
Dual form | 525.2.j.c.218.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27211 | + | 1.27211i | −0.899520 | + | 0.899520i | −0.995394 | − | 0.0958737i | \(-0.969435\pi\) |
0.0958737 | + | 0.995394i | \(0.469435\pi\) | |||||||
\(3\) | −0.774907 | − | 1.54904i | −0.447393 | − | 0.894338i | ||||
\(4\) | − | 1.23654i | − | 0.618272i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.95632 | + | 0.984783i | 1.20691 | + | 0.402036i | ||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | −0.971203 | − | 0.971203i | −0.343372 | − | 0.343372i | ||||
\(9\) | −1.79904 | + | 2.40072i | −0.599680 | + | 0.800240i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.596077i | 0.179724i | 0.995954 | + | 0.0898620i | \(0.0286426\pi\) | ||||
−0.995954 | + | 0.0898620i | \(0.971357\pi\) | |||||||
\(12\) | −1.91545 | + | 0.958205i | −0.552944 | + | 0.276610i | ||||
\(13\) | 0.651688 | − | 0.651688i | 0.180746 | − | 0.180746i | −0.610935 | − | 0.791681i | \(-0.709206\pi\) |
0.791681 | + | 0.610935i | \(0.209206\pi\) | |||||||
\(14\) | 1.79904 | 0.480814 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.94405 | 1.23601 | ||||||||
\(17\) | −2.63250 | + | 2.63250i | −0.638474 | + | 0.638474i | −0.950179 | − | 0.311705i | \(-0.899100\pi\) |
0.311705 | + | 0.950179i | \(0.399100\pi\) | |||||||
\(18\) | −0.765406 | − | 5.34257i | −0.180408 | − | 1.25926i | ||||
\(19\) | 1.16418i | 0.267081i | 0.991043 | + | 0.133540i | \(0.0426345\pi\) | ||||
−0.991043 | + | 0.133540i | \(0.957365\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.547394 | + | 1.64328i | −0.119451 | + | 0.358592i | ||||
\(22\) | −0.758277 | − | 0.758277i | −0.161665 | − | 0.161665i | ||||
\(23\) | 2.83371 | + | 2.83371i | 0.590869 | + | 0.590869i | 0.937866 | − | 0.346997i | \(-0.112799\pi\) |
−0.346997 | + | 0.937866i | \(0.612799\pi\) | |||||||
\(24\) | −0.751839 | + | 2.25702i | −0.153469 | + | 0.460713i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.65804i | 0.325169i | ||||||||
\(27\) | 5.11290 | + | 0.926447i | 0.983977 | + | 0.178295i | ||||
\(28\) | −0.874368 | + | 0.874368i | −0.165240 | + | 0.165240i | ||||
\(29\) | 9.57511 | 1.77805 | 0.889027 | − | 0.457855i | \(-0.151382\pi\) | ||||
0.889027 | + | 0.457855i | \(0.151382\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.54990 | −1.35600 | −0.678001 | − | 0.735061i | \(-0.737154\pi\) | ||||
−0.678001 | + | 0.735061i | \(0.737154\pi\) | |||||||
\(32\) | −4.34698 | + | 4.34698i | −0.768445 | + | 0.768445i | ||||
\(33\) | 0.923346 | − | 0.461904i | 0.160734 | − | 0.0804072i | ||||
\(34\) | − | 6.69767i | − | 1.14864i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.96859 | + | 2.22459i | 0.494766 | + | 0.370765i | ||||
\(37\) | 7.81453 | + | 7.81453i | 1.28470 | + | 1.28470i | 0.937961 | + | 0.346740i | \(0.112711\pi\) |
0.346740 | + | 0.937961i | \(0.387289\pi\) | |||||||
\(38\) | −1.48096 | − | 1.48096i | −0.240244 | − | 0.240244i | ||||
\(39\) | −1.51449 | − | 0.504492i | −0.242512 | − | 0.0807834i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.32646i | 1.30037i | 0.759774 | + | 0.650187i | \(0.225309\pi\) | ||||
−0.759774 | + | 0.650187i | \(0.774691\pi\) | |||||||
\(42\) | −1.39409 | − | 2.78678i | −0.215112 | − | 0.430010i | ||||
\(43\) | −7.71640 | + | 7.71640i | −1.17674 | + | 1.17674i | −0.196171 | + | 0.980570i | \(0.562851\pi\) |
−0.980570 | + | 0.196171i | \(0.937149\pi\) | |||||||
\(44\) | 0.737075 | 0.111118 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.20959 | −1.06300 | ||||||||
\(47\) | −5.33798 | + | 5.33798i | −0.778624 | + | 0.778624i | −0.979597 | − | 0.200972i | \(-0.935590\pi\) |
0.200972 | + | 0.979597i | \(0.435590\pi\) | |||||||
\(48\) | −3.83117 | − | 7.65852i | −0.552982 | − | 1.10541i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.11778 | + | 2.03790i | 0.856660 | + | 0.285363i | ||||
\(52\) | −0.805840 | − | 0.805840i | −0.111750 | − | 0.111750i | ||||
\(53\) | 2.54423 | + | 2.54423i | 0.349476 | + | 0.349476i | 0.859914 | − | 0.510438i | \(-0.170517\pi\) |
−0.510438 | + | 0.859914i | \(0.670517\pi\) | |||||||
\(54\) | −7.68273 | + | 5.32563i | −1.04549 | + | 0.724727i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.37349i | 0.183540i | ||||||||
\(57\) | 1.80335 | − | 0.902128i | 0.238860 | − | 0.119490i | ||||
\(58\) | −12.1806 | + | 12.1806i | −1.59939 | + | 1.59939i | ||||
\(59\) | 4.37549 | 0.569640 | 0.284820 | − | 0.958581i | \(-0.408066\pi\) | ||||
0.284820 | + | 0.958581i | \(0.408066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.0140 | −1.92235 | −0.961173 | − | 0.275946i | \(-0.911009\pi\) | ||||
−0.961173 | + | 0.275946i | \(0.911009\pi\) | |||||||
\(62\) | 9.60433 | − | 9.60433i | 1.21975 | − | 1.21975i | ||||
\(63\) | 2.96968 | − | 0.425452i | 0.374144 | − | 0.0536020i | ||||
\(64\) | − | 1.17161i | − | 0.146451i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.587007 | + | 1.76220i | −0.0722555 | + | 0.216911i | ||||
\(67\) | 1.26066 | + | 1.26066i | 0.154015 | + | 0.154015i | 0.779908 | − | 0.625894i | \(-0.215266\pi\) |
−0.625894 | + | 0.779908i | \(0.715266\pi\) | |||||||
\(68\) | 3.25520 | + | 3.25520i | 0.394751 | + | 0.394751i | ||||
\(69\) | 2.19366 | − | 6.58538i | 0.264086 | − | 0.792786i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.16919i | − | 0.850826i | −0.904999 | − | 0.425413i | \(-0.860129\pi\) | ||
0.904999 | − | 0.425413i | \(-0.139871\pi\) | |||||||
\(72\) | 4.07882 | − | 0.584354i | 0.480694 | − | 0.0688668i | ||||
\(73\) | 5.66151 | − | 5.66151i | 0.662629 | − | 0.662629i | −0.293370 | − | 0.955999i | \(-0.594777\pi\) |
0.955999 | + | 0.293370i | \(0.0947768\pi\) | |||||||
\(74\) | −19.8819 | −2.31123 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.43955 | 0.165128 | ||||||||
\(77\) | 0.421490 | − | 0.421490i | 0.0480333 | − | 0.0480333i | ||||
\(78\) | 2.56837 | − | 1.28483i | 0.290811 | − | 0.145478i | ||||
\(79\) | − | 3.85224i | − | 0.433410i | −0.976237 | − | 0.216705i | \(-0.930469\pi\) | ||
0.976237 | − | 0.216705i | \(-0.0695311\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.52691 | − | 8.63798i | −0.280768 | − | 0.959776i | ||||
\(82\) | −10.5922 | − | 10.5922i | −1.16971 | − | 1.16971i | ||||
\(83\) | 4.70691 | + | 4.70691i | 0.516651 | + | 0.516651i | 0.916556 | − | 0.399905i | \(-0.130957\pi\) |
−0.399905 | + | 0.916556i | \(0.630957\pi\) | |||||||
\(84\) | 2.03198 | + | 0.676876i | 0.221708 | + | 0.0738532i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 19.6323i | − | 2.11700i | ||||||
\(87\) | −7.41982 | − | 14.8322i | −0.795488 | − | 1.59018i | ||||
\(88\) | 0.578912 | − | 0.578912i | 0.0617122 | − | 0.0617122i | ||||
\(89\) | 2.19762 | 0.232947 | 0.116474 | − | 0.993194i | \(-0.462841\pi\) | ||||
0.116474 | + | 0.993194i | \(0.462841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.921626 | −0.0966127 | ||||||||
\(92\) | 3.50400 | − | 3.50400i | 0.365317 | − | 0.365317i | ||||
\(93\) | 5.85047 | + | 11.6951i | 0.606666 | + | 1.21272i | ||||
\(94\) | − | 13.5810i | − | 1.40078i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.1021 | + | 3.36514i | 1.03105 | + | 0.343453i | ||||
\(97\) | 7.69844 | + | 7.69844i | 0.781658 | + | 0.781658i | 0.980111 | − | 0.198452i | \(-0.0635914\pi\) |
−0.198452 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(98\) | −1.27211 | − | 1.27211i | −0.128503 | − | 0.128503i | ||||
\(99\) | −1.43101 | − | 1.07237i | −0.143822 | − | 0.107777i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7638i | 1.27005i | 0.772493 | + | 0.635023i | \(0.219009\pi\) | ||||
−0.772493 | + | 0.635023i | \(0.780991\pi\) | |||||||
\(102\) | −10.3749 | + | 5.19007i | −1.02727 | + | 0.513893i | ||||
\(103\) | 6.78916 | − | 6.78916i | 0.668956 | − | 0.668956i | −0.288518 | − | 0.957474i | \(-0.593163\pi\) |
0.957474 | + | 0.288518i | \(0.0931626\pi\) | |||||||
\(104\) | −1.26584 | −0.124126 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.47309 | −0.628722 | ||||||||
\(107\) | 0.176542 | − | 0.176542i | 0.0170670 | − | 0.0170670i | −0.698522 | − | 0.715589i | \(-0.746158\pi\) |
0.715589 | + | 0.698522i | \(0.246158\pi\) | |||||||
\(108\) | 1.14559 | − | 6.32232i | 0.110235 | − | 0.608365i | ||||
\(109\) | 11.2027i | 1.07303i | 0.843892 | + | 0.536513i | \(0.180259\pi\) | ||||
−0.843892 | + | 0.536513i | \(0.819741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.04948 | − | 18.1605i | 0.574191 | − | 1.72372i | ||||
\(112\) | −3.49597 | − | 3.49597i | −0.330338 | − | 0.330338i | ||||
\(113\) | −0.553500 | − | 0.553500i | −0.0520689 | − | 0.0520689i | 0.680593 | − | 0.732662i | \(-0.261722\pi\) |
−0.732662 | + | 0.680593i | \(0.761722\pi\) | |||||||
\(114\) | −1.14646 | + | 3.44168i | −0.107376 | + | 0.322343i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 11.8400i | − | 1.09932i | ||||||
\(117\) | 0.392108 | + | 2.73693i | 0.0362504 | + | 0.253030i | ||||
\(118\) | −5.56612 | + | 5.56612i | −0.512403 | + | 0.512403i | ||||
\(119\) | 3.72291 | 0.341279 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6447 | 0.967699 | ||||||||
\(122\) | 19.0995 | − | 19.0995i | 1.72919 | − | 1.72919i | ||||
\(123\) | 12.8980 | − | 6.45223i | 1.16297 | − | 0.581778i | ||||
\(124\) | 9.33578i | 0.838378i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.23654 | + | 4.31899i | −0.288334 | + | 0.384766i | ||||
\(127\) | −2.62625 | − | 2.62625i | −0.233042 | − | 0.233042i | 0.580919 | − | 0.813961i | \(-0.302693\pi\) |
−0.813961 | + | 0.580919i | \(0.802693\pi\) | |||||||
\(128\) | −7.20355 | − | 7.20355i | −0.636709 | − | 0.636709i | ||||
\(129\) | 17.9325 | + | 5.97351i | 1.57887 | + | 0.525938i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 16.5281i | − | 1.44406i | −0.691859 | − | 0.722032i | \(-0.743208\pi\) | ||
0.691859 | − | 0.722032i | \(-0.256792\pi\) | |||||||
\(132\) | −0.571164 | − | 1.14176i | −0.0497135 | − | 0.0993772i | ||||
\(133\) | 0.823197 | − | 0.823197i | 0.0713803 | − | 0.0713803i | ||||
\(134\) | −3.20741 | −0.277078 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.11338 | 0.438469 | ||||||||
\(137\) | −11.1583 | + | 11.1583i | −0.953316 | + | 0.953316i | −0.998958 | − | 0.0456415i | \(-0.985467\pi\) |
0.0456415 | + | 0.998958i | \(0.485467\pi\) | |||||||
\(138\) | 5.58676 | + | 11.1679i | 0.475576 | + | 0.950677i | ||||
\(139\) | − | 2.90366i | − | 0.246285i | −0.992389 | − | 0.123142i | \(-0.960703\pi\) | ||
0.992389 | − | 0.123142i | \(-0.0392972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.4052 | + | 4.13230i | 1.04470 | + | 0.348002i | ||||
\(142\) | 9.12001 | + | 9.12001i | 0.765335 | + | 0.765335i | ||||
\(143\) | 0.388456 | + | 0.388456i | 0.0324843 | + | 0.0324843i | ||||
\(144\) | −8.89454 | + | 11.8693i | −0.741211 | + | 0.989106i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.4041i | 1.19210i | ||||||||
\(147\) | 1.54904 | − | 0.774907i | 0.127763 | − | 0.0639132i | ||||
\(148\) | 9.66301 | − | 9.66301i | 0.794294 | − | 0.794294i | ||||
\(149\) | −2.77395 | −0.227251 | −0.113625 | − | 0.993524i | \(-0.536246\pi\) | ||||
−0.113625 | + | 0.993524i | \(0.536246\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.07180 | 0.168600 | 0.0843002 | − | 0.996440i | \(-0.473135\pi\) | ||||
0.0843002 | + | 0.996440i | \(0.473135\pi\) | |||||||
\(152\) | 1.13065 | − | 1.13065i | 0.0917080 | − | 0.0917080i | ||||
\(153\) | −1.58392 | − | 11.0559i | −0.128053 | − | 0.893813i | ||||
\(154\) | 1.07237i | 0.0864137i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.623827 | + | 1.87273i | −0.0499461 | + | 0.149938i | ||||
\(157\) | −9.28263 | − | 9.28263i | −0.740834 | − | 0.740834i | 0.231904 | − | 0.972739i | \(-0.425504\pi\) |
−0.972739 | + | 0.231904i | \(0.925504\pi\) | |||||||
\(158\) | 4.90048 | + | 4.90048i | 0.389861 | + | 0.389861i | ||||
\(159\) | 1.96957 | − | 5.91264i | 0.156197 | − | 0.468903i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.00747i | − | 0.315833i | ||||||
\(162\) | 14.2030 | + | 7.77397i | 1.11589 | + | 0.610781i | ||||
\(163\) | 9.40972 | − | 9.40972i | 0.737026 | − | 0.737026i | −0.234975 | − | 0.972001i | \(-0.575501\pi\) |
0.972001 | + | 0.234975i | \(0.0755009\pi\) | |||||||
\(164\) | 10.2960 | 0.803984 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.9755 | −0.929475 | ||||||||
\(167\) | 10.4473 | − | 10.4473i | 0.808437 | − | 0.808437i | −0.175960 | − | 0.984397i | \(-0.556303\pi\) |
0.984397 | + | 0.175960i | \(0.0563029\pi\) | |||||||
\(168\) | 2.12759 | − | 1.06433i | 0.164147 | − | 0.0821145i | ||||
\(169\) | 12.1506i | 0.934662i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.79486 | − | 2.09440i | −0.213729 | − | 0.160163i | ||||
\(172\) | 9.54166 | + | 9.54166i | 0.727545 | + | 0.727545i | ||||
\(173\) | −18.0363 | − | 18.0363i | −1.37127 | − | 1.37127i | −0.858563 | − | 0.512707i | \(-0.828643\pi\) |
−0.512707 | − | 0.858563i | \(-0.671357\pi\) | |||||||
\(174\) | 28.3071 | + | 9.42941i | 2.14596 | + | 0.714841i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.94703i | 0.222141i | ||||||||
\(177\) | −3.39060 | − | 6.77780i | −0.254853 | − | 0.509451i | ||||
\(178\) | −2.79562 | + | 2.79562i | −0.209540 | + | 0.209540i | ||||
\(179\) | −18.2401 | −1.36333 | −0.681663 | − | 0.731666i | \(-0.738743\pi\) | ||||
−0.681663 | + | 0.731666i | \(0.738743\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.06040 | 0.376137 | 0.188068 | − | 0.982156i | \(-0.439777\pi\) | ||||
0.188068 | + | 0.982156i | \(0.439777\pi\) | |||||||
\(182\) | 1.17241 | − | 1.17241i | 0.0869050 | − | 0.0869050i | ||||
\(183\) | 11.6345 | + | 23.2573i | 0.860043 | + | 1.71923i | ||||
\(184\) | − | 5.50421i | − | 0.405776i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −22.3199 | − | 7.43502i | −1.63658 | − | 0.545162i | ||||
\(187\) | −1.56917 | − | 1.56917i | −0.114749 | − | 0.114749i | ||||
\(188\) | 6.60064 | + | 6.60064i | 0.481401 | + | 0.481401i | ||||
\(189\) | −2.96027 | − | 4.27046i | −0.215328 | − | 0.310630i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.33413i | 0.313607i | 0.987630 | + | 0.156803i | \(0.0501189\pi\) | ||||
−0.987630 | + | 0.156803i | \(0.949881\pi\) | |||||||
\(192\) | −1.81486 | + | 0.907885i | −0.130976 | + | 0.0655210i | ||||
\(193\) | −11.7911 | + | 11.7911i | −0.848741 | + | 0.848741i | −0.989976 | − | 0.141235i | \(-0.954893\pi\) |
0.141235 | + | 0.989976i | \(0.454893\pi\) | |||||||
\(194\) | −19.5866 | −1.40623 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.23654 | 0.0883245 | ||||||||
\(197\) | 5.36265 | − | 5.36265i | 0.382073 | − | 0.382073i | −0.489776 | − | 0.871848i | \(-0.662921\pi\) |
0.871848 | + | 0.489776i | \(0.162921\pi\) | |||||||
\(198\) | 3.18458 | − | 0.456241i | 0.226318 | − | 0.0324236i | ||||
\(199\) | − | 0.778449i | − | 0.0551828i | −0.999619 | − | 0.0275914i | \(-0.991216\pi\) | ||
0.999619 | − | 0.0275914i | \(-0.00878373\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.975920 | − | 2.92971i | 0.0688361 | − | 0.206646i | ||||
\(202\) | −16.2370 | − | 16.2370i | −1.14243 | − | 1.14243i | ||||
\(203\) | −6.77063 | − | 6.77063i | −0.475205 | − | 0.475205i | ||||
\(204\) | 2.51995 | − | 7.56490i | 0.176432 | − | 0.529649i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.2732i | 1.20348i | ||||||||
\(207\) | −11.9009 | + | 1.70499i | −0.827169 | + | 0.118505i | ||||
\(208\) | 3.22198 | − | 3.22198i | 0.223404 | − | 0.223404i | ||||
\(209\) | −0.693939 | −0.0480008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.91922 | 0.269810 | 0.134905 | − | 0.990859i | \(-0.456927\pi\) | ||||
0.134905 | + | 0.990859i | \(0.456927\pi\) | |||||||
\(212\) | 3.14605 | − | 3.14605i | 0.216071 | − | 0.216071i | ||||
\(213\) | −11.1053 | + | 5.55545i | −0.760926 | + | 0.380653i | ||||
\(214\) | 0.449163i | 0.0307042i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.06589 | − | 5.86543i | −0.276649 | − | 0.399092i | ||||
\(217\) | 5.33859 | + | 5.33859i | 0.362407 | + | 0.362407i | ||||
\(218\) | −14.2511 | − | 14.2511i | −0.965209 | − | 0.965209i | ||||
\(219\) | −13.1570 | − | 4.38275i | −0.889069 | − | 0.296159i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.43113i | 0.230803i | ||||||||
\(222\) | 15.4066 | + | 30.7979i | 1.03403 | + | 2.06702i | ||||
\(223\) | −4.95226 | + | 4.95226i | −0.331628 | + | 0.331628i | −0.853204 | − | 0.521577i | \(-0.825344\pi\) |
0.521577 | + | 0.853204i | \(0.325344\pi\) | |||||||
\(224\) | 6.14756 | 0.410751 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.40823 | 0.0936740 | ||||||||
\(227\) | −10.4264 | + | 10.4264i | −0.692027 | + | 0.692027i | −0.962678 | − | 0.270651i | \(-0.912761\pi\) |
0.270651 | + | 0.962678i | \(0.412761\pi\) | |||||||
\(228\) | −1.11552 | − | 2.22993i | −0.0738772 | − | 0.147680i | ||||
\(229\) | − | 18.3432i | − | 1.21215i | −0.795406 | − | 0.606077i | \(-0.792742\pi\) | ||
0.795406 | − | 0.606077i | \(-0.207258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.979520 | − | 0.326289i | −0.0644477 | − | 0.0214682i | ||||
\(232\) | −9.29938 | − | 9.29938i | −0.610534 | − | 0.610534i | ||||
\(233\) | −8.53926 | − | 8.53926i | −0.559426 | − | 0.559426i | 0.369718 | − | 0.929144i | \(-0.379454\pi\) |
−0.929144 | + | 0.369718i | \(0.879454\pi\) | |||||||
\(234\) | −3.98049 | − | 2.98288i | −0.260213 | − | 0.194997i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 5.41048i | − | 0.352192i | ||||||
\(237\) | −5.96726 | + | 2.98512i | −0.387615 | + | 0.193905i | ||||
\(238\) | −4.73597 | + | 4.73597i | −0.306987 | + | 0.306987i | ||||
\(239\) | 5.98239 | 0.386968 | 0.193484 | − | 0.981103i | \(-0.438021\pi\) | ||||
0.193484 | + | 0.981103i | \(0.438021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.05823 | 0.325829 | 0.162914 | − | 0.986640i | \(-0.447911\pi\) | ||||
0.162914 | + | 0.986640i | \(0.447911\pi\) | |||||||
\(242\) | −13.5413 | + | 13.5413i | −0.870465 | + | 0.870465i | ||||
\(243\) | −11.4224 | + | 10.6079i | −0.732750 | + | 0.680498i | ||||
\(244\) | 18.5655i | 1.18853i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.19975 | + | 24.6157i | −0.522797 | + | 1.56944i | ||||
\(247\) | 0.758680 | + | 0.758680i | 0.0482737 | + | 0.0482737i | ||||
\(248\) | 7.33249 | + | 7.33249i | 0.465614 | + | 0.465614i | ||||
\(249\) | 3.64377 | − | 10.9386i | 0.230915 | − | 0.693206i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.3582i | 1.66372i | 0.554989 | + | 0.831858i | \(0.312723\pi\) | ||||
−0.554989 | + | 0.831858i | \(0.687277\pi\) | |||||||
\(252\) | −0.526090 | − | 3.67214i | −0.0331406 | − | 0.231323i | ||||
\(253\) | −1.68911 | + | 1.68911i | −0.106193 | + | 0.106193i | ||||
\(254\) | 6.68178 | 0.419252 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.6707 | 1.29192 | ||||||||
\(257\) | −12.5808 | + | 12.5808i | −0.784766 | + | 0.784766i | −0.980631 | − | 0.195865i | \(-0.937249\pi\) |
0.195865 | + | 0.980631i | \(0.437249\pi\) | |||||||
\(258\) | −30.4111 | + | 15.2132i | −1.89332 | + | 0.947131i | ||||
\(259\) | − | 11.0514i | − | 0.686702i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.2260 | + | 22.9872i | −1.06626 | + | 1.42287i | ||||
\(262\) | 21.0256 | + | 21.0256i | 1.29896 | + | 1.29896i | ||||
\(263\) | 7.32034 | + | 7.32034i | 0.451391 | + | 0.451391i | 0.895816 | − | 0.444425i | \(-0.146592\pi\) |
−0.444425 | + | 0.895816i | \(0.646592\pi\) | |||||||
\(264\) | −1.34536 | − | 0.448154i | −0.0828012 | − | 0.0275820i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.09440i | 0.128416i | ||||||||
\(267\) | −1.70295 | − | 3.40419i | −0.104219 | − | 0.208333i | ||||
\(268\) | 1.55886 | − | 1.55886i | 0.0952228 | − | 0.0952228i | ||||
\(269\) | −7.34074 | −0.447573 | −0.223786 | − | 0.974638i | \(-0.571842\pi\) | ||||
−0.223786 | + | 0.974638i | \(0.571842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.40673 | −0.449927 | −0.224963 | − | 0.974367i | \(-0.572226\pi\) | ||||
−0.224963 | + | 0.974367i | \(0.572226\pi\) | |||||||
\(272\) | −13.0152 | + | 13.0152i | −0.789162 | + | 0.789162i | ||||
\(273\) | 0.714174 | + | 1.42763i | 0.0432238 | + | 0.0864043i | ||||
\(274\) | − | 28.3892i | − | 1.71505i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.14310 | − | 2.71256i | −0.490157 | − | 0.163277i | ||||
\(277\) | 11.1225 | + | 11.1225i | 0.668289 | + | 0.668289i | 0.957320 | − | 0.289031i | \(-0.0933331\pi\) |
−0.289031 | + | 0.957320i | \(0.593333\pi\) | |||||||
\(278\) | 3.69378 | + | 3.69378i | 0.221538 | + | 0.221538i | ||||
\(279\) | 13.5826 | − | 18.1252i | 0.813168 | − | 1.08513i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.1123i | 1.02084i | 0.859927 | + | 0.510418i | \(0.170509\pi\) | ||||
−0.859927 | + | 0.510418i | \(0.829491\pi\) | |||||||
\(282\) | −21.0375 | + | 10.5240i | −1.25277 | + | 0.626697i | ||||
\(283\) | −10.9094 | + | 10.9094i | −0.648494 | + | 0.648494i | −0.952629 | − | 0.304135i | \(-0.901633\pi\) |
0.304135 | + | 0.952629i | \(0.401633\pi\) | |||||||
\(284\) | −8.86501 | −0.526041 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.988321 | −0.0584406 | ||||||||
\(287\) | 5.88769 | − | 5.88769i | 0.347540 | − | 0.347540i | ||||
\(288\) | −2.61549 | − | 18.2563i | −0.154119 | − | 1.07576i | ||||
\(289\) | 3.13992i | 0.184701i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.95961 | − | 17.8908i | 0.349358 | − | 1.04877i | ||||
\(292\) | −7.00070 | − | 7.00070i | −0.409685 | − | 0.409685i | ||||
\(293\) | 15.3592 | + | 15.3592i | 0.897295 | + | 0.897295i | 0.995196 | − | 0.0979008i | \(-0.0312128\pi\) |
−0.0979008 | + | 0.995196i | \(0.531213\pi\) | |||||||
\(294\) | −0.984783 | + | 2.95632i | −0.0574337 | + | 0.172416i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 15.1790i | − | 0.882262i | ||||||
\(297\) | −0.552234 | + | 3.04768i | −0.0320439 | + | 0.176844i | ||||
\(298\) | 3.52878 | − | 3.52878i | 0.204417 | − | 0.204417i | ||||
\(299\) | 3.69338 | 0.213594 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.9126 | 0.628994 | ||||||||
\(302\) | −2.63556 | + | 2.63556i | −0.151659 | + | 0.151659i | ||||
\(303\) | 19.7716 | − | 9.89076i | 1.13585 | − | 0.568209i | ||||
\(304\) | 5.75575i | 0.330115i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.0792 | + | 12.0494i | 0.919188 | + | 0.688817i | ||||
\(307\) | −15.5878 | − | 15.5878i | −0.889641 | − | 0.889641i | 0.104848 | − | 0.994488i | \(-0.466564\pi\) |
−0.994488 | + | 0.104848i | \(0.966564\pi\) | |||||||
\(308\) | −0.521191 | − | 0.521191i | −0.0296976 | − | 0.0296976i | ||||
\(309\) | −15.7776 | − | 5.25571i | −0.897558 | − | 0.298987i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 21.7724i | − | 1.23460i | −0.786729 | − | 0.617299i | \(-0.788227\pi\) | ||
0.786729 | − | 0.617299i | \(-0.211773\pi\) | |||||||
\(312\) | 0.980910 | + | 1.96084i | 0.0555331 | + | 0.111011i | ||||
\(313\) | 16.7825 | − | 16.7825i | 0.948603 | − | 0.948603i | −0.0501392 | − | 0.998742i | \(-0.515966\pi\) |
0.998742 | + | 0.0501392i | \(0.0159665\pi\) | |||||||
\(314\) | 23.6171 | 1.33279 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.76346 | −0.267965 | ||||||||
\(317\) | −19.4564 | + | 19.4564i | −1.09278 | + | 1.09278i | −0.0975486 | + | 0.995231i | \(0.531100\pi\) |
−0.995231 | + | 0.0975486i | \(0.968900\pi\) | |||||||
\(318\) | 5.01604 | + | 10.0271i | 0.281285 | + | 0.562290i | ||||
\(319\) | 5.70750i | 0.319559i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.410274 | − | 0.136667i | −0.0228993 | − | 0.00762800i | ||||
\(322\) | 5.09795 | + | 5.09795i | 0.284098 | + | 0.284098i | ||||
\(323\) | −3.06469 | − | 3.06469i | −0.170524 | − | 0.170524i | ||||
\(324\) | −10.6812 | + | 3.12464i | −0.593402 | + | 0.173591i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.9405i | 1.32594i | ||||||||
\(327\) | 17.3535 | − | 8.68107i | 0.959648 | − | 0.480064i | ||||
\(328\) | 8.08668 | − | 8.08668i | 0.446512 | − | 0.446512i | ||||
\(329\) | 7.54904 | 0.416192 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0430 | −1.10166 | −0.550830 | − | 0.834617i | \(-0.685689\pi\) | ||||
−0.550830 | + | 0.834617i | \(0.685689\pi\) | |||||||
\(332\) | 5.82030 | − | 5.82030i | 0.319431 | − | 0.319431i | ||||
\(333\) | −32.8192 | + | 4.70185i | −1.79848 | + | 0.257660i | ||||
\(334\) | 26.5803i | 1.45441i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.70634 | + | 8.12444i | −0.147643 | + | 0.443225i | ||||
\(337\) | −5.35404 | − | 5.35404i | −0.291653 | − | 0.291653i | 0.546080 | − | 0.837733i | \(-0.316119\pi\) |
−0.837733 | + | 0.546080i | \(0.816119\pi\) | |||||||
\(338\) | −15.4569 | − | 15.4569i | −0.840747 | − | 0.840747i | ||||
\(339\) | −0.428482 | + | 1.28630i | −0.0232720 | + | 0.0698624i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.50033i | − | 0.243706i | ||||||
\(342\) | 6.21970 | − | 0.891068i | 0.336323 | − | 0.0481834i | ||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 14.9884 | 0.808120 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 45.8883 | 2.46697 | ||||||||
\(347\) | 20.2180 | − | 20.2180i | 1.08536 | − | 1.08536i | 0.0893604 | − | 0.995999i | \(-0.471518\pi\) |
0.995999 | − | 0.0893604i | \(-0.0284823\pi\) | |||||||
\(348\) | −18.3407 | + | 9.17492i | −0.983163 | + | 0.491828i | ||||
\(349\) | 14.0744i | 0.753386i | 0.926338 | + | 0.376693i | \(0.122939\pi\) | ||||
−0.926338 | + | 0.376693i | \(0.877061\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.93577 | − | 2.72826i | 0.210076 | − | 0.145624i | ||||
\(352\) | −2.59114 | − | 2.59114i | −0.138108 | − | 0.138108i | ||||
\(353\) | −7.05174 | − | 7.05174i | −0.375326 | − | 0.375326i | 0.494087 | − | 0.869413i | \(-0.335503\pi\) |
−0.869413 | + | 0.494087i | \(0.835503\pi\) | |||||||
\(354\) | 12.9354 | + | 4.30891i | 0.687506 | + | 0.229016i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 2.71745i | − | 0.144025i | ||||||
\(357\) | −2.88491 | − | 5.76694i | −0.152686 | − | 0.305219i | ||||
\(358\) | 23.2034 | − | 23.2034i | 1.22634 | − | 1.22634i | ||||
\(359\) | −15.8072 | −0.834270 | −0.417135 | − | 0.908844i | \(-0.636966\pi\) | ||||
−0.417135 | + | 0.908844i | \(0.636966\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.6447 | 0.928668 | ||||||||
\(362\) | −6.43741 | + | 6.43741i | −0.338343 | + | 0.338343i | ||||
\(363\) | −8.24864 | − | 16.4890i | −0.432941 | − | 0.865450i | ||||
\(364\) | 1.13963i | 0.0597329i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −44.3862 | − | 14.7855i | −2.32010 | − | 0.772853i | ||||
\(367\) | 13.4893 | + | 13.4893i | 0.704138 | + | 0.704138i | 0.965296 | − | 0.261158i | \(-0.0841043\pi\) |
−0.261158 | + | 0.965296i | \(0.584104\pi\) | |||||||
\(368\) | 14.0100 | + | 14.0100i | 0.730321 | + | 0.730321i | ||||
\(369\) | −19.9895 | − | 14.9796i | −1.04061 | − | 0.779808i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.59808i | − | 0.186803i | ||||||
\(372\) | 14.4615 | − | 7.23436i | 0.749793 | − | 0.375084i | ||||
\(373\) | 14.7655 | − | 14.7655i | 0.764527 | − | 0.764527i | −0.212610 | − | 0.977137i | \(-0.568197\pi\) |
0.977137 | + | 0.212610i | \(0.0681965\pi\) | |||||||
\(374\) | 3.99233 | 0.206438 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3685 | 0.534716 | ||||||||
\(377\) | 6.23998 | − | 6.23998i | 0.321376 | − | 0.321376i | ||||
\(378\) | 9.19830 | + | 1.66672i | 0.473110 | + | 0.0857266i | ||||
\(379\) | 31.9071i | 1.63896i | 0.573109 | + | 0.819479i | \(0.305737\pi\) | ||||
−0.573109 | + | 0.819479i | \(0.694263\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.03307 | + | 6.10327i | −0.104157 | + | 0.312680i | ||||
\(382\) | −5.51350 | − | 5.51350i | −0.282095 | − | 0.282095i | ||||
\(383\) | 10.5821 | + | 10.5821i | 0.540720 | + | 0.540720i | 0.923740 | − | 0.383020i | \(-0.125116\pi\) |
−0.383020 | + | 0.923740i | \(0.625116\pi\) | |||||||
\(384\) | −5.57649 | + | 16.7406i | −0.284574 | + | 0.854292i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 29.9992i | − | 1.52692i | ||||||
\(387\) | −4.64281 | − | 32.4070i | −0.236007 | − | 1.64734i | ||||
\(388\) | 9.51946 | − | 9.51946i | 0.483277 | − | 0.483277i | ||||
\(389\) | 22.7753 | 1.15475 | 0.577376 | − | 0.816478i | \(-0.304077\pi\) | ||||
0.577376 | + | 0.816478i | \(0.304077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.9194 | −0.754509 | ||||||||
\(392\) | 0.971203 | − | 0.971203i | 0.0490532 | − | 0.0490532i | ||||
\(393\) | −25.6026 | + | 12.8077i | −1.29148 | + | 0.646064i | ||||
\(394\) | 13.6438i | 0.687364i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.32603 | + | 1.76951i | −0.0666354 | + | 0.0889213i | ||||
\(397\) | 14.8873 | + | 14.8873i | 0.747172 | + | 0.747172i | 0.973947 | − | 0.226775i | \(-0.0728181\pi\) |
−0.226775 | + | 0.973947i | \(0.572818\pi\) | |||||||
\(398\) | 0.990276 | + | 0.990276i | 0.0496380 | + | 0.0496380i | ||||
\(399\) | −1.91307 | − | 0.637263i | −0.0957731 | − | 0.0319031i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0691i | 0.752513i | 0.926515 | + | 0.376257i | \(0.122789\pi\) | ||||
−0.926515 | + | 0.376257i | \(0.877211\pi\) | |||||||
\(402\) | 2.48545 | + | 4.96841i | 0.123963 | + | 0.247802i | ||||
\(403\) | −4.92018 | + | 4.92018i | −0.245092 | + | 0.245092i | ||||
\(404\) | 15.7830 | 0.785233 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.2260 | 0.854912 | ||||||||
\(407\) | −4.65806 | + | 4.65806i | −0.230892 | + | 0.230892i | ||||
\(408\) | −3.96239 | − | 7.92082i | −0.196168 | − | 0.392139i | ||||
\(409\) | 25.3358i | 1.25277i | 0.779512 | + | 0.626387i | \(0.215467\pi\) | ||||
−0.779512 | + | 0.626387i | \(0.784533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.9312 | + | 8.63798i | 1.27909 | + | 0.426080i | ||||
\(412\) | −8.39509 | − | 8.39509i | −0.413596 | − | 0.413596i | ||||
\(413\) | −3.09394 | − | 3.09394i | −0.152243 | − | 0.152243i | ||||
\(414\) | 12.9703 | − | 17.3082i | 0.637457 | − | 0.850652i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.66575i | 0.277786i | ||||||||
\(417\) | −4.49788 | + | 2.25006i | −0.220262 | + | 0.110186i | ||||
\(418\) | 0.882769 | − | 0.882769i | 0.0431776 | − | 0.0431776i | ||||
\(419\) | −19.4078 | −0.948133 | −0.474067 | − | 0.880489i | \(-0.657214\pi\) | ||||
−0.474067 | + | 0.880489i | \(0.657214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.18958 | −0.447872 | −0.223936 | − | 0.974604i | \(-0.571891\pi\) | ||||
−0.223936 | + | 0.974604i | \(0.571891\pi\) | |||||||
\(422\) | −4.98569 | + | 4.98569i | −0.242700 | + | 0.242700i | ||||
\(423\) | −3.21176 | − | 22.4182i | −0.156161 | − | 1.09001i | ||||
\(424\) | − | 4.94192i | − | 0.240001i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.06009 | − | 21.1944i | 0.342063 | − | 1.02687i | ||||
\(427\) | 10.6165 | + | 10.6165i | 0.513769 | + | 0.513769i | ||||
\(428\) | −0.218302 | − | 0.218302i | −0.0105520 | − | 0.0105520i | ||||
\(429\) | 0.300716 | − | 0.902751i | 0.0145187 | − | 0.0435852i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.0854i | − | 0.822972i | −0.911416 | − | 0.411486i | \(-0.865010\pi\) | ||
0.911416 | − | 0.411486i | \(-0.134990\pi\) | |||||||
\(432\) | 25.2784 | + | 4.58040i | 1.21621 | + | 0.220375i | ||||
\(433\) | 20.7996 | − | 20.7996i | 0.999563 | − | 0.999563i | −0.000437230 | − | 1.00000i | \(-0.500139\pi\) |
1.00000 | 0.000437230i | \(0.000139175\pi\) | ||||||||
\(434\) | −13.5826 | −0.651985 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.8527 | 0.663422 | ||||||||
\(437\) | −3.29894 | + | 3.29894i | −0.157809 | + | 0.157809i | ||||
\(438\) | 22.3126 | − | 11.1619i | 1.06614 | − | 0.533335i | ||||
\(439\) | 12.3529i | 0.589572i | 0.955563 | + | 0.294786i | \(0.0952483\pi\) | ||||
−0.955563 | + | 0.294786i | \(0.904752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.40072 | − | 1.79904i | −0.114320 | − | 0.0856685i | ||||
\(442\) | −4.36479 | − | 4.36479i | −0.207612 | − | 0.207612i | ||||
\(443\) | 6.57501 | + | 6.57501i | 0.312388 | + | 0.312388i | 0.845834 | − | 0.533446i | \(-0.179103\pi\) |
−0.533446 | + | 0.845834i | \(0.679103\pi\) | |||||||
\(444\) | −22.4563 | − | 7.48044i | −1.06573 | − | 0.355006i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 12.5997i | − | 0.596611i | ||||||
\(447\) | 2.14955 | + | 4.29696i | 0.101670 | + | 0.203239i | ||||
\(448\) | −0.828450 | + | 0.828450i | −0.0391406 | + | 0.0391406i | ||||
\(449\) | 14.2416 | 0.672104 | 0.336052 | − | 0.941843i | \(-0.390908\pi\) | ||||
0.336052 | + | 0.941843i | \(0.390908\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.96321 | −0.233708 | ||||||||
\(452\) | −0.684427 | + | 0.684427i | −0.0321927 | + | 0.0321927i | ||||
\(453\) | −1.60545 | − | 3.20929i | −0.0754306 | − | 0.150786i | ||||
\(454\) | − | 26.5272i | − | 1.24498i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.62757 | − | 0.875274i | −0.123047 | − | 0.0409885i | ||||
\(457\) | −17.6696 | − | 17.6696i | −0.826550 | − | 0.826550i | 0.160488 | − | 0.987038i | \(-0.448693\pi\) |
−0.987038 | + | 0.160488i | \(0.948693\pi\) | |||||||
\(458\) | 23.3346 | + | 23.3346i | 1.09036 | + | 1.09036i | ||||
\(459\) | −15.8986 | + | 11.0208i | −0.742081 | + | 0.514407i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.7105i | 1.01116i | 0.862780 | + | 0.505580i | \(0.168721\pi\) | ||||
−0.862780 | + | 0.505580i | \(0.831279\pi\) | |||||||
\(462\) | 1.66114 | − | 0.830984i | 0.0772831 | − | 0.0386609i | ||||
\(463\) | −1.05768 | + | 1.05768i | −0.0491547 | + | 0.0491547i | −0.731257 | − | 0.682102i | \(-0.761066\pi\) |
0.682102 | + | 0.731257i | \(0.261066\pi\) | |||||||
\(464\) | 47.3398 | 2.19770 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.7258 | 1.00643 | ||||||||
\(467\) | 26.8566 | − | 26.8566i | 1.24278 | − | 1.24278i | 0.283932 | − | 0.958844i | \(-0.408361\pi\) |
0.958844 | − | 0.283932i | \(-0.0916390\pi\) | |||||||
\(468\) | 3.38434 | − | 0.484858i | 0.156441 | − | 0.0224126i | ||||
\(469\) | − | 1.78285i | − | 0.0823242i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.18597 | + | 21.5723i | −0.331112 | + | 0.994000i | ||||
\(472\) | −4.24949 | − | 4.24949i | −0.195599 | − | 0.195599i | ||||
\(473\) | −4.59957 | − | 4.59957i | −0.211488 | − | 0.211488i | ||||
\(474\) | 3.79362 | − | 11.3884i | 0.174247 | − | 0.523089i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 4.60354i | − | 0.211003i | ||||||
\(477\) | −10.6851 | + | 1.53081i | −0.489239 | + | 0.0700910i | ||||
\(478\) | −7.61027 | + | 7.61027i | −0.348086 | + | 0.348086i | ||||
\(479\) | −2.38823 | −0.109121 | −0.0545605 | − | 0.998510i | \(-0.517376\pi\) | ||||
−0.0545605 | + | 0.998510i | \(0.517376\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.1853 | 0.464409 | ||||||||
\(482\) | −6.43463 | + | 6.43463i | −0.293090 | + | 0.293090i | ||||
\(483\) | −6.20772 | + | 3.10541i | −0.282461 | + | 0.141301i | ||||
\(484\) | − | 13.1626i | − | 0.598301i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.03617 | − | 28.0251i | 0.0470016 | − | 1.27124i | ||||
\(487\) | 15.5114 | + | 15.5114i | 0.702890 | + | 0.702890i | 0.965030 | − | 0.262140i | \(-0.0844281\pi\) |
−0.262140 | + | 0.965030i | \(0.584428\pi\) | |||||||
\(488\) | 14.5817 | + | 14.5817i | 0.660080 | + | 0.660080i | ||||
\(489\) | −21.8677 | − | 7.28436i | −0.988890 | − | 0.329410i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 33.8566i | − | 1.52793i | −0.645259 | − | 0.763964i | \(-0.723251\pi\) | ||
0.645259 | − | 0.763964i | \(-0.276749\pi\) | |||||||
\(492\) | −7.97846 | − | 15.9489i | −0.359697 | − | 0.719033i | ||||
\(493\) | −25.2065 | + | 25.2065i | −1.13524 | + | 1.13524i | ||||
\(494\) | −1.93025 | −0.0868462 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −37.3271 | −1.67604 | ||||||||
\(497\) | −5.06938 | + | 5.06938i | −0.227393 | + | 0.227393i | ||||
\(498\) | 9.27986 | + | 18.5504i | 0.415840 | + | 0.831265i | ||||
\(499\) | − | 3.55804i | − | 0.159280i | −0.996824 | − | 0.0796398i | \(-0.974623\pi\) | ||
0.996824 | − | 0.0796398i | \(-0.0253770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.2790 | − | 8.08760i | −1.08470 | − | 0.361327i | ||||
\(502\) | −33.5306 | − | 33.5306i | −1.49655 | − | 1.49655i | ||||
\(503\) | 8.89336 | + | 8.89336i | 0.396535 | + | 0.396535i | 0.877009 | − | 0.480474i | \(-0.159535\pi\) |
−0.480474 | + | 0.877009i | \(0.659535\pi\) | |||||||
\(504\) | −3.29736 | − | 2.47096i | −0.146876 | − | 0.110065i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 4.29747i | − | 0.191046i | ||||||
\(507\) | 18.8218 | − | 9.41558i | 0.835903 | − | 0.418161i | ||||
\(508\) | −3.24747 | + | 3.24747i | −0.144083 | + | 0.144083i | ||||
\(509\) | −24.4919 | −1.08558 | −0.542791 | − | 0.839868i | \(-0.682633\pi\) | ||||
−0.542791 | + | 0.839868i | \(0.682633\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00658 | −0.354190 | ||||||||
\(512\) | −11.8883 | + | 11.8883i | −0.525395 | + | 0.525395i | ||||
\(513\) | −1.07855 | + | 5.95231i | −0.0476191 | + | 0.262801i | ||||
\(514\) | − | 32.0083i | − | 1.41182i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.38651 | − | 22.1743i | 0.325173 | − | 0.976169i | ||||
\(517\) | −3.18185 | − | 3.18185i | −0.139938 | − | 0.139938i | ||||
\(518\) | 14.0587 | + | 14.0587i | 0.617702 | + | 0.617702i | ||||
\(519\) | −13.9624 | + | 41.9153i | −0.612883 | + | 1.83988i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.4652i | − | 1.24708i | −0.781790 | − | 0.623541i | \(-0.785693\pi\) | ||
0.781790 | − | 0.623541i | \(-0.214307\pi\) | |||||||
\(522\) | −7.32884 | − | 51.1557i | −0.320775 | − | 2.23902i | ||||
\(523\) | −7.00886 | + | 7.00886i | −0.306476 | + | 0.306476i | −0.843541 | − | 0.537065i | \(-0.819533\pi\) |
0.537065 | + | 0.843541i | \(0.319533\pi\) | |||||||
\(524\) | −20.4377 | −0.892824 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.6246 | −0.812071 | ||||||||
\(527\) | 19.8751 | − | 19.8751i | 0.865773 | − | 0.865773i | ||||
\(528\) | 4.56507 | − | 2.28368i | 0.198669 | − | 0.0993842i | ||||
\(529\) | − | 6.94022i | − | 0.301749i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.87168 | + | 10.5043i | −0.341602 | + | 0.455849i | ||||
\(532\) | −1.01792 | − | 1.01792i | −0.0441324 | − | 0.0441324i | ||||
\(533\) | 5.42625 | + | 5.42625i | 0.235037 | + | 0.235037i | ||||
\(534\) | 6.49686 | + | 2.16418i | 0.281147 | + | 0.0936531i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 2.44872i | − | 0.105769i | ||||||
\(537\) | 14.1343 | + | 28.2546i | 0.609942 | + | 1.21927i | ||||
\(538\) | 9.33825 | − | 9.33825i | 0.402600 | − | 0.402600i | ||||
\(539\) | −0.596077 | −0.0256749 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.17756 | −0.222601 | −0.111300 | − | 0.993787i | \(-0.535502\pi\) | ||||
−0.111300 | + | 0.993787i | \(0.535502\pi\) | |||||||
\(542\) | 9.42220 | − | 9.42220i | 0.404718 | − | 0.404718i | ||||
\(543\) | −3.92134 | − | 7.83876i | −0.168281 | − | 0.336393i | ||||
\(544\) | − | 22.8868i | − | 0.981265i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.72462 | − | 0.907602i | −0.116603 | − | 0.0388418i | ||||
\(547\) | −3.24667 | − | 3.24667i | −0.138818 | − | 0.138818i | 0.634283 | − | 0.773101i | \(-0.281295\pi\) |
−0.773101 | + | 0.634283i | \(0.781295\pi\) | |||||||
\(548\) | 13.7977 | + | 13.7977i | 0.589408 | + | 0.589408i | ||||
\(549\) | 27.0108 | − | 36.0444i | 1.15279 | − | 1.53834i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.1471i | 0.474883i | ||||||||
\(552\) | −8.52623 | + | 4.26525i | −0.362901 | + | 0.181541i | ||||
\(553\) | −2.72394 | + | 2.72394i | −0.115834 | + | 0.115834i | ||||
\(554\) | −28.2982 | −1.20228 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.59050 | −0.152271 | ||||||||
\(557\) | 9.93063 | − | 9.93063i | 0.420774 | − | 0.420774i | −0.464696 | − | 0.885470i | \(-0.653836\pi\) |
0.885470 | + | 0.464696i | \(0.153836\pi\) | |||||||
\(558\) | 5.77874 | + | 40.3359i | 0.244634 | + | 1.70755i | ||||
\(559\) | 10.0574i | 0.425382i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.21475 | + | 3.64667i | −0.0512866 | + | 0.153962i | ||||
\(562\) | −21.7688 | − | 21.7688i | −0.918262 | − | 0.918262i | ||||
\(563\) | −11.8553 | − | 11.8553i | −0.499641 | − | 0.499641i | 0.411685 | − | 0.911326i | \(-0.364940\pi\) |
−0.911326 | + | 0.411685i | \(0.864940\pi\) | |||||||
\(564\) | 5.10977 | − | 15.3395i | 0.215160 | − | 0.645911i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 27.7559i | − | 1.16667i | ||||||
\(567\) | −4.32118 | + | 7.89477i | −0.181472 | + | 0.331549i | ||||
\(568\) | −6.96274 | + | 6.96274i | −0.292150 | + | 0.292150i | ||||
\(569\) | −19.3729 | −0.812155 | −0.406077 | − | 0.913839i | \(-0.633104\pi\) | ||||
−0.406077 | + | 0.913839i | \(0.633104\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8864 | −0.455581 | −0.227791 | − | 0.973710i | \(-0.573150\pi\) | ||||
−0.227791 | + | 0.973710i | \(0.573150\pi\) | |||||||
\(572\) | 0.480343 | − | 0.480343i | 0.0200841 | − | 0.0200841i | ||||
\(573\) | 6.71373 | − | 3.35855i | 0.280470 | − | 0.140305i | ||||
\(574\) | 14.9796i | 0.625237i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.81270 | + | 2.10777i | 0.117196 | + | 0.0878235i | ||||
\(577\) | 3.36353 | + | 3.36353i | 0.140025 | + | 0.140025i | 0.773645 | − | 0.633619i | \(-0.218431\pi\) |
−0.633619 | + | 0.773645i | \(0.718431\pi\) | |||||||
\(578\) | −3.99433 | − | 3.99433i | −0.166142 | − | 0.166142i | ||||
\(579\) | 27.4018 | + | 9.12785i | 1.13878 | + | 0.379341i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 6.65658i | − | 0.276162i | ||||||
\(582\) | 15.1778 | + | 30.3404i | 0.629139 | + | 1.25765i | ||||
\(583\) | −1.51655 | + | 1.51655i | −0.0628093 | + | 0.0628093i | ||||
\(584\) | −10.9969 | −0.455057 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.0773 | −1.61427 | ||||||||
\(587\) | 11.6266 | − | 11.6266i | 0.479883 | − | 0.479883i | −0.425211 | − | 0.905094i | \(-0.639800\pi\) |
0.905094 | + | 0.425211i | \(0.139800\pi\) | |||||||
\(588\) | −0.958205 | − | 1.91545i | −0.0395157 | − | 0.0789919i | ||||
\(589\) | − | 8.78942i | − | 0.362162i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4625 | − | 4.15140i | −0.512639 | − | 0.170766i | ||||
\(592\) | 38.6354 | + | 38.6354i | 1.58791 | + | 1.58791i | ||||
\(593\) | −18.7263 | − | 18.7263i | −0.768999 | − | 0.768999i | 0.208932 | − | 0.977930i | \(-0.433001\pi\) |
−0.977930 | + | 0.208932i | \(0.933001\pi\) | |||||||
\(594\) | −3.17449 | − | 4.57950i | −0.130251 | − | 0.187899i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.43011i | 0.140503i | ||||||||
\(597\) | −1.20585 | + | 0.603226i | −0.0493521 | + | 0.0246884i | ||||
\(598\) | −4.69840 | + | 4.69840i | −0.192132 | + | 0.192132i | ||||
\(599\) | 27.9518 | 1.14208 | 0.571041 | − | 0.820922i | \(-0.306540\pi\) | ||||
0.571041 | + | 0.820922i | \(0.306540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.9760 | 0.814837 | 0.407418 | − | 0.913242i | \(-0.366429\pi\) | ||||
0.407418 | + | 0.913242i | \(0.366429\pi\) | |||||||
\(602\) | −13.8821 | + | 13.8821i | −0.565793 | + | 0.565793i | ||||
\(603\) | −5.29448 | + | 0.758517i | −0.215608 | + | 0.0308892i | ||||
\(604\) | − | 2.56187i | − | 0.104241i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.5696 | + | 37.7339i | −0.510604 | + | 1.53283i | ||||
\(607\) | −23.8478 | − | 23.8478i | −0.967953 | − | 0.967953i | 0.0315491 | − | 0.999502i | \(-0.489956\pi\) |
−0.999502 | + | 0.0315491i | \(0.989956\pi\) | |||||||
\(608\) | −5.06065 | − | 5.06065i | −0.205237 | − | 0.205237i | ||||
\(609\) | −5.24136 | + | 15.7346i | −0.212390 | + | 0.637597i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.95740i | 0.281466i | ||||||||
\(612\) | −13.6710 | + | 1.95859i | −0.552619 | + | 0.0791712i | ||||
\(613\) | −11.8807 | + | 11.8807i | −0.479858 | + | 0.479858i | −0.905086 | − | 0.425228i | \(-0.860194\pi\) |
0.425228 | + | 0.905086i | \(0.360194\pi\) | |||||||
\(614\) | 39.6588 | 1.60050 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.818705 | −0.0329866 | ||||||||
\(617\) | 7.72276 | − | 7.72276i | 0.310906 | − | 0.310906i | −0.534354 | − | 0.845261i | \(-0.679445\pi\) |
0.845261 | + | 0.534354i | \(0.179445\pi\) | |||||||
\(618\) | 26.7568 | − | 13.3851i | 1.07632 | − | 0.538427i | ||||
\(619\) | 7.02322i | 0.282287i | 0.989989 | + | 0.141144i | \(0.0450779\pi\) | ||||
−0.989989 | + | 0.141144i | \(0.954922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.8632 | + | 17.1137i | 0.476052 | + | 0.686750i | ||||
\(622\) | 27.6969 | + | 27.6969i | 1.11054 | + | 1.11054i | ||||
\(623\) | −1.55395 | − | 1.55395i | −0.0622577 | − | 0.0622577i | ||||
\(624\) | −7.48770 | − | 2.49423i | −0.299748 | − | 0.0998493i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 42.6985i | 1.70657i | ||||||||
\(627\) | 0.537738 | + | 1.07494i | 0.0214752 | + | 0.0429289i | ||||
\(628\) | −11.4784 | + | 11.4784i | −0.458037 | + | 0.458037i | ||||
\(629\) | −41.1435 | −1.64050 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6907 | −0.943111 | −0.471555 | − | 0.881836i | \(-0.656307\pi\) | ||||
−0.471555 | + | 0.881836i | \(0.656307\pi\) | |||||||
\(632\) | −3.74131 | + | 3.74131i | −0.148821 | + | 0.148821i | ||||
\(633\) | −3.03703 | − | 6.07102i | −0.120711 | − | 0.241301i | ||||
\(634\) | − | 49.5014i | − | 1.96595i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.31124 | − | 2.43545i | −0.289909 | − | 0.0965720i | ||||
\(637\) | 0.651688 | + | 0.651688i | 0.0258208 | + | 0.0258208i | ||||
\(638\) | −7.26059 | − | 7.26059i | −0.287450 | − | 0.287450i | ||||
\(639\) | 17.2112 | + | 12.8976i | 0.680865 | + | 0.510223i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 0.574461i | − | 0.0226898i | −0.999936 | − | 0.0113449i | \(-0.996389\pi\) | ||
0.999936 | − | 0.0113449i | \(-0.00361128\pi\) | |||||||
\(642\) | 0.695771 | − | 0.348059i | 0.0274599 | − | 0.0137368i | ||||
\(643\) | 4.70272 | − | 4.70272i | 0.185457 | − | 0.185457i | −0.608272 | − | 0.793729i | \(-0.708137\pi\) |
0.793729 | + | 0.608272i | \(0.208137\pi\) | |||||||
\(644\) | −4.95540 | −0.195270 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.79727 | 0.306779 | ||||||||
\(647\) | −4.55125 | + | 4.55125i | −0.178928 | + | 0.178928i | −0.790888 | − | 0.611960i | \(-0.790381\pi\) |
0.611960 | + | 0.790888i | \(0.290381\pi\) | |||||||
\(648\) | −5.93509 | + | 10.8434i | −0.233152 | + | 0.425968i | ||||
\(649\) | 2.60813i | 0.102378i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.13277 | − | 12.4066i | 0.161976 | − | 0.486252i | ||||
\(652\) | −11.6355 | − | 11.6355i | −0.455682 | − | 0.455682i | ||||
\(653\) | 18.2705 | + | 18.2705i | 0.714980 | + | 0.714980i | 0.967573 | − | 0.252593i | \(-0.0812833\pi\) |
−0.252593 | + | 0.967573i | \(0.581283\pi\) | |||||||
\(654\) | −11.0323 | + | 33.1189i | −0.431395 | + | 1.29505i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.1664i | 1.60728i | ||||||||
\(657\) | 3.40642 | + | 23.7770i | 0.132897 | + | 0.927628i | ||||
\(658\) | −9.60324 | + | 9.60324i | −0.374373 | + | 0.374373i | ||||
\(659\) | −23.1110 | −0.900276 | −0.450138 | − | 0.892959i | \(-0.648625\pi\) | ||||
−0.450138 | + | 0.892959i | \(0.648625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.9566 | 0.659537 | 0.329768 | − | 0.944062i | \(-0.393029\pi\) | ||||
0.329768 | + | 0.944062i | \(0.393029\pi\) | |||||||
\(662\) | 25.4969 | − | 25.4969i | 0.990965 | − | 0.990965i | ||||
\(663\) | 5.31496 | − | 2.65881i | 0.206416 | − | 0.103260i | ||||
\(664\) | − | 9.14274i | − | 0.354807i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 35.7684 | − | 47.7310i | 1.38600 | − | 1.84954i | ||||
\(667\) | 27.1331 | + | 27.1331i | 1.05060 | + | 1.05060i | ||||
\(668\) | −12.9186 | − | 12.9186i | −0.499834 | − | 0.499834i | ||||
\(669\) | 11.5088 | + | 3.83370i | 0.444955 | + | 0.148219i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.94951i | − | 0.345492i | ||||||
\(672\) | −4.76378 | − | 9.52280i | −0.183767 | − | 0.367350i | ||||
\(673\) | 20.0108 | − | 20.0108i | 0.771359 | − | 0.771359i | −0.206985 | − | 0.978344i | \(-0.566365\pi\) |
0.978344 | + | 0.206985i | \(0.0663653\pi\) | |||||||
\(674\) | 13.6219 | 0.524696 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.0247 | 0.577875 | ||||||||
\(677\) | 9.33392 | − | 9.33392i | 0.358732 | − | 0.358732i | −0.504614 | − | 0.863345i | \(-0.668365\pi\) |
0.863345 | + | 0.504614i | \(0.168365\pi\) | |||||||
\(678\) | −1.09125 | − | 2.18140i | −0.0419091 | − | 0.0837762i | ||||
\(679\) | − | 10.8872i | − | 0.417814i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.2305 | + | 8.07143i | 0.928513 | + | 0.309298i | ||||
\(682\) | 5.72492 | + | 5.72492i | 0.219219 | + | 0.219219i | ||||
\(683\) | −34.9400 | − | 34.9400i | −1.33694 | − | 1.33694i | −0.899005 | − | 0.437939i | \(-0.855709\pi\) |
−0.437939 | − | 0.899005i | \(-0.644291\pi\) | |||||||
\(684\) | −2.58982 | + | 3.45597i | −0.0990241 | + | 0.132142i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.79904i | 0.0686876i | ||||||||
\(687\) | −28.4143 | + | 14.2143i | −1.08407 | + | 0.542308i | ||||
\(688\) | −38.1503 | + | 38.1503i | −1.45447 | + | 1.45447i | ||||
\(689\) | 3.31608 | 0.126333 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.0437 | −1.33313 | −0.666563 | − | 0.745449i | \(-0.732235\pi\) | ||||
−0.666563 | + | 0.745449i | \(0.732235\pi\) | |||||||
\(692\) | −22.3026 | + | 22.3026i | −0.847818 | + | 0.847818i | ||||
\(693\) | 0.253602 | + | 1.77016i | 0.00963356 | + | 0.0672427i | ||||
\(694\) | 51.4392i | 1.95261i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.19895 | + | 21.6112i | −0.272875 | + | 0.819172i | ||||
\(697\) | −21.9194 | − | 21.9194i | −0.830255 | − | 0.830255i | ||||
\(698\) | −17.9042 | − | 17.9042i | −0.677686 | − | 0.677686i | ||||
\(699\) | −6.61051 | + | 19.8448i | −0.250033 | + | 0.750598i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 52.2978i | 1.97526i | 0.156805 | + | 0.987630i | \(0.449881\pi\) | ||||
−0.156805 | + | 0.987630i | \(0.550119\pi\) | |||||||
\(702\) | −1.53609 | + | 8.47739i | −0.0579759 | + | 0.319959i | ||||
\(703\) | −9.09750 | + | 9.09750i | −0.343119 | + | 0.343119i | ||||
\(704\) | 0.698367 | 0.0263207 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.9412 | 0.675227 | ||||||||
\(707\) | 9.02537 | − | 9.02537i | 0.339434 | − | 0.339434i | ||||
\(708\) | −8.38105 | + | 4.19262i | −0.314979 | + | 0.157568i | ||||
\(709\) | 22.2416i | 0.835302i | 0.908608 | + | 0.417651i | \(0.137146\pi\) | ||||
−0.908608 | + | 0.417651i | \(0.862854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.24814 | + | 6.93033i | 0.346832 | + | 0.259908i | ||||
\(712\) | −2.13433 | − | 2.13433i | −0.0799875 | − | 0.0799875i | ||||
\(713\) | −21.3942 | − | 21.3942i | −0.801219 | − | 0.801219i | ||||
\(714\) | 11.0061 | + | 3.66626i | 0.411894 | + | 0.137206i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.5546i | 0.842906i | ||||||||
\(717\) | −4.63579 | − | 9.26695i | −0.173127 | − | 0.346080i | ||||
\(718\) | 20.1085 | − | 20.1085i | 0.750443 | − | 0.750443i | ||||
\(719\) | 40.5531 | 1.51238 | 0.756188 | − | 0.654354i | \(-0.227059\pi\) | ||||
0.756188 | + | 0.654354i | \(0.227059\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.60132 | −0.357572 | ||||||||
\(722\) | −22.4460 | + | 22.4460i | −0.835355 | + | 0.835355i | ||||
\(723\) | −3.91965 | − | 7.83539i | −0.145773 | − | 0.291401i | ||||
\(724\) | − | 6.25741i | − | 0.232555i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 31.4691 | + | 10.4827i | 1.16793 | + | 0.389050i | ||||
\(727\) | 25.9411 | + | 25.9411i | 0.962103 | + | 0.962103i | 0.999308 | − | 0.0372050i | \(-0.0118454\pi\) |
−0.0372050 | + | 0.999308i | \(0.511845\pi\) | |||||||
\(728\) | 0.895086 | + | 0.895086i | 0.0331741 | + | 0.0331741i | ||||
\(729\) | 25.2834 | + | 9.47366i | 0.936422 | + | 0.350876i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 40.6268i | − | 1.50264i | ||||||
\(732\) | 28.7586 | − | 14.3865i | 1.06295 | − | 0.531740i | ||||
\(733\) | 20.5005 | − | 20.5005i | 0.757205 | − | 0.757205i | −0.218608 | − | 0.975813i | \(-0.570152\pi\) |
0.975813 | + | 0.218608i | \(0.0701515\pi\) | |||||||
\(734\) | −34.3199 | −1.26677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.6361 | −0.908100 | ||||||||
\(737\) | −0.751453 | + | 0.751453i | −0.0276801 | + | 0.0276801i | ||||
\(738\) | 44.4847 | − | 6.37312i | 1.63750 | − | 0.234598i | ||||
\(739\) | − | 11.5622i | − | 0.425323i | −0.977126 | − | 0.212661i | \(-0.931787\pi\) | ||
0.977126 | − | 0.212661i | \(-0.0682131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.587318 | − | 1.76313i | 0.0215757 | − | 0.0647702i | ||||
\(742\) | 4.57716 | + | 4.57716i | 0.168033 | + | 0.168033i | ||||
\(743\) | 24.6182 | + | 24.6182i | 0.903153 | + | 0.903153i | 0.995708 | − | 0.0925542i | \(-0.0295031\pi\) |
−0.0925542 | + | 0.995708i | \(0.529503\pi\) | |||||||
\(744\) | 5.67632 | − | 17.0403i | 0.208104 | − | 0.624728i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 37.5667i | 1.37541i | ||||||||
\(747\) | −19.7679 | + | 2.83206i | −0.723270 | + | 0.103620i | ||||
\(748\) | −1.94035 | + | 1.94035i | −0.0709461 | + | 0.0709461i | ||||
\(749\) | −0.249668 | −0.00912268 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.1876 | 1.46647 | 0.733233 | − | 0.679977i | \(-0.238010\pi\) | ||||
0.733233 | + | 0.679977i | \(0.238010\pi\) | |||||||
\(752\) | −26.3912 | + | 26.3912i | −0.962389 | + | 0.962389i | ||||
\(753\) | 40.8299 | − | 20.4252i | 1.48792 | − | 0.744334i | ||||
\(754\) | 15.8759i | 0.578167i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.28061 | + | 3.66050i | −0.192054 | + | 0.133131i | ||||
\(757\) | 4.46261 | + | 4.46261i | 0.162196 | + | 0.162196i | 0.783539 | − | 0.621343i | \(-0.213412\pi\) |
−0.621343 | + | 0.783539i | \(0.713412\pi\) | |||||||
\(758\) | −40.5895 | − | 40.5895i | −1.47428 | − | 1.47428i | ||||
\(759\) | 3.92539 | + | 1.30759i | 0.142483 | + | 0.0474626i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 27.3558i | − | 0.991646i | −0.868424 | − | 0.495823i | \(-0.834867\pi\) | ||
0.868424 | − | 0.495823i | \(-0.165133\pi\) | |||||||
\(762\) | −5.17775 | − | 10.3503i | −0.187570 | − | 0.374953i | ||||
\(763\) | 7.92153 | − | 7.92153i | 0.286779 | − | 0.286779i | ||||
\(764\) | 5.35934 | 0.193894 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.9232 | −0.972776 | ||||||||
\(767\) | 2.85145 | − | 2.85145i | 0.102960 | − | 0.102960i | ||||
\(768\) | −16.0178 | − | 32.0196i | −0.577994 | − | 1.15541i | ||||
\(769\) | − | 10.3542i | − | 0.373382i | −0.982419 | − | 0.186691i | \(-0.940224\pi\) | ||
0.982419 | − | 0.186691i | \(-0.0597762\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.2370 | + | 9.73916i | 1.05294 | + | 0.350747i | ||||
\(772\) | 14.5802 | + | 14.5802i | 0.524752 | + | 0.524752i | ||||
\(773\) | 1.59901 | + | 1.59901i | 0.0575125 | + | 0.0575125i | 0.735278 | − | 0.677766i | \(-0.237052\pi\) |
−0.677766 | + | 0.735278i | \(0.737052\pi\) | |||||||
\(774\) | 47.1316 | + | 35.3192i | 1.69411 | + | 1.26952i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 14.9535i | − | 0.536800i | ||||||
\(777\) | −17.1191 | + | 8.56382i | −0.614143 | + | 0.307225i | ||||
\(778\) | −28.9727 | + | 28.9727i | −1.03872 | + | 1.03872i | ||||
\(779\) | −9.69347 | −0.347305 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.27339 | 0.152914 | ||||||||
\(782\) | 18.9792 | − | 18.9792i | 0.678696 | − | 0.678696i | ||||
\(783\) | 48.9565 | + | 8.87084i | 1.74956 | + | 0.317018i | ||||
\(784\) | 4.94405i | 0.176573i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16.2766 | − | 48.8623i | 0.580566 | − | 1.74286i | ||||
\(787\) | −6.16607 | − | 6.16607i | −0.219797 | − | 0.219797i | 0.588616 | − | 0.808413i | \(-0.299673\pi\) |
−0.808413 | + | 0.588616i | \(0.799673\pi\) | |||||||
\(788\) | −6.63114 | − | 6.63114i | −0.236225 | − | 0.236225i | ||||
\(789\) | 5.66691 | − | 17.0121i | 0.201747 | − | 0.605646i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.782768i | 0.0278320i | ||||||||
\(792\) | 0.348320 | + | 2.43129i | 0.0123770 | + | 0.0863922i | ||||
\(793\) | −9.78445 | + | 9.78445i | −0.347456 | + | 0.347456i | ||||
\(794\) | −37.8767 | −1.34419 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.962586 | −0.0341180 | ||||||||
\(797\) | −24.9323 | + | 24.9323i | −0.883148 | + | 0.883148i | −0.993853 | − | 0.110705i | \(-0.964689\pi\) |
0.110705 | + | 0.993853i | \(0.464689\pi\) | |||||||
\(798\) | 3.24431 | − | 1.62296i | 0.114847 | − | 0.0574523i | ||||
\(799\) | − | 28.1044i | − | 0.994263i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.95360 | + | 5.27587i | −0.139694 | + | 0.186414i | ||||
\(802\) | −19.1696 | − | 19.1696i | −0.676901 | − | 0.676901i | ||||
\(803\) | 3.37469 | + | 3.37469i | 0.119090 | + | 0.119090i | ||||
\(804\) | −3.62272 | − | 1.20677i | −0.127763 | − | 0.0425594i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 12.5181i | − | 0.440930i | ||||||
\(807\) | 5.68839 | + | 11.3711i | 0.200241 | + | 0.400281i | ||||
\(808\) | 12.3962 | − | 12.3962i | 0.436099 | − | 0.436099i | ||||
\(809\) | 21.2421 | 0.746831 | 0.373416 | − | 0.927664i | \(-0.378187\pi\) | ||||
0.373416 | + | 0.927664i | \(0.378187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.9414 | −0.735351 | −0.367675 | − | 0.929954i | \(-0.619846\pi\) | ||||
−0.367675 | + | 0.929954i | \(0.619846\pi\) | |||||||
\(812\) | −8.37217 | + | 8.37217i | −0.293806 | + | 0.293806i | ||||
\(813\) | 5.73952 | + | 11.4733i | 0.201294 | + | 0.402386i | ||||
\(814\) | − | 11.8512i | − | 0.415383i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 30.2466 | + | 10.0755i | 1.05884 | + | 0.352712i | ||||
\(817\) | −8.98326 | − | 8.98326i | −0.314284 | − | 0.314284i | ||||
\(818\) | −32.2300 | − | 32.2300i | −1.12689 | − | 1.12689i | ||||
\(819\) | 1.65804 | − | 2.21257i | 0.0579367 | − | 0.0773133i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 13.9737i | − | 0.487684i | −0.969815 | − | 0.243842i | \(-0.921592\pi\) | ||
0.969815 | − | 0.243842i | \(-0.0784078\pi\) | |||||||
\(822\) | −43.9759 | + | 21.9990i | −1.53384 | + | 0.767302i | ||||
\(823\) | 9.64020 | − | 9.64020i | 0.336036 | − | 0.336036i | −0.518837 | − | 0.854873i | \(-0.673635\pi\) |
0.854873 | + | 0.518837i | \(0.173635\pi\) | |||||||
\(824\) | −13.1873 | −0.459402 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.87168 | 0.273891 | ||||||||
\(827\) | 11.2829 | − | 11.2829i | 0.392345 | − | 0.392345i | −0.483178 | − | 0.875522i | \(-0.660518\pi\) |
0.875522 | + | 0.483178i | \(0.160518\pi\) | |||||||
\(828\) | 2.10829 | + | 14.7160i | 0.0732681 | + | 0.511415i | ||||
\(829\) | 18.8442i | 0.654485i | 0.944940 | + | 0.327242i | \(0.106119\pi\) | ||||
−0.944940 | + | 0.327242i | \(0.893881\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.61031 | − | 25.8482i | 0.298688 | − | 0.896663i | ||||
\(832\) | −0.763521 | − | 0.763521i | −0.0264703 | − | 0.0264703i | ||||
\(833\) | −2.63250 | − | 2.63250i | −0.0912106 | − | 0.0912106i | ||||
\(834\) | 2.85947 | − | 8.58414i | 0.0990154 | − | 0.297244i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.858086i | 0.0296775i | ||||||||
\(837\) | −38.6019 | − | 6.99459i | −1.33428 | − | 0.241768i | ||||
\(838\) | 24.6889 | − | 24.6889i | 0.852865 | − | 0.852865i | ||||
\(839\) | 46.9582 | 1.62118 | 0.810588 | − | 0.585617i | \(-0.199148\pi\) | ||||
0.810588 | + | 0.585617i | \(0.199148\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.6827 | 2.16147 | ||||||||
\(842\) | 11.6902 | − | 11.6902i | 0.402870 | − | 0.402870i | ||||
\(843\) | 26.5076 | − | 13.2605i | 0.912972 | − | 0.456714i | ||||
\(844\) | − | 4.84628i | − | 0.166816i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 32.6042 | + | 24.4328i | 1.12096 | + | 0.840017i | ||||
\(847\) | −7.52693 | − | 7.52693i | −0.258629 | − | 0.258629i | ||||
\(848\) | 12.5788 | + | 12.5788i | 0.431957 | + | 0.431957i | ||||
\(849\) | 25.3527 | + | 8.44528i | 0.870104 | + | 0.289841i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.2882i | 1.51818i | ||||||||
\(852\) | 6.86955 | + | 13.7322i | 0.235347 | + | 0.470459i | ||||
\(853\) | −26.8180 | + | 26.8180i | −0.918232 | + | 0.918232i | −0.996901 | − | 0.0786690i | \(-0.974933\pi\) |
0.0786690 | + | 0.996901i | \(0.474933\pi\) | |||||||
\(854\) | −27.0108 | −0.924290 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.342917 | −0.0117207 | ||||||||
\(857\) | −24.3943 | + | 24.3943i | −0.833293 | + | 0.833293i | −0.987966 | − | 0.154673i | \(-0.950568\pi\) |
0.154673 | + | 0.987966i | \(0.450568\pi\) | |||||||
\(858\) | 0.765856 | + | 1.53095i | 0.0261459 | + | 0.0522657i | ||||
\(859\) | − | 1.97722i | − | 0.0674617i | −0.999431 | − | 0.0337309i | \(-0.989261\pi\) | ||
0.999431 | − | 0.0337309i | \(-0.0107389\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.6827 | − | 4.55785i | −0.466304 | − | 0.155331i | ||||
\(862\) | 21.7345 | + | 21.7345i | 0.740280 | + | 0.740280i | ||||
\(863\) | 17.7690 | + | 17.7690i | 0.604863 | + | 0.604863i | 0.941599 | − | 0.336736i | \(-0.109323\pi\) |
−0.336736 | + | 0.941599i | \(0.609323\pi\) | |||||||
\(864\) | −26.2529 | + | 18.1984i | −0.893142 | + | 0.619122i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 52.9188i | 1.79825i | ||||||||
\(867\) | 4.86385 | − | 2.43314i | 0.165185 | − | 0.0826339i | ||||
\(868\) | 6.60140 | − | 6.60140i | 0.224066 | − | 0.224066i | ||||
\(869\) | 2.29623 | 0.0778943 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.64312 | 0.0556749 | ||||||||
\(872\) | 10.8801 | − | 10.8801i | 0.368448 | − | 0.368448i | ||||
\(873\) | −32.3316 | + | 4.63200i | −1.09426 | + | 0.156770i | ||||
\(874\) | − | 8.39324i | − | 0.283905i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.41946 | + | 16.2692i | −0.183107 | + | 0.549686i | ||||
\(877\) | 30.0684 | + | 30.0684i | 1.01534 | + | 1.01534i | 0.999881 | + | 0.0154576i | \(0.00492051\pi\) |
0.0154576 | + | 0.999881i | \(0.495079\pi\) | |||||||
\(878\) | −15.7143 | − | 15.7143i | −0.530331 | − | 0.530331i | ||||
\(879\) | 11.8901 | − | 35.6940i | 0.401042 | − | 1.20393i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 34.7319i | − | 1.17015i | −0.810980 | − | 0.585074i | \(-0.801066\pi\) | ||
0.810980 | − | 0.585074i | \(-0.198934\pi\) | |||||||
\(882\) | 5.34257 | − | 0.765406i | 0.179894 | − | 0.0257726i | ||||
\(883\) | −0.424655 | + | 0.424655i | −0.0142908 | + | 0.0142908i | −0.714216 | − | 0.699925i | \(-0.753217\pi\) |
0.699925 | + | 0.714216i | \(0.253217\pi\) | |||||||
\(884\) | 4.24274 | 0.142699 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.7283 | −0.561999 | ||||||||
\(887\) | −39.8779 | + | 39.8779i | −1.33897 | + | 1.33897i | −0.441912 | + | 0.897059i | \(0.645700\pi\) |
−0.897059 | + | 0.441912i | \(0.854300\pi\) | |||||||
\(888\) | −23.5129 | + | 11.7623i | −0.789040 | + | 0.394717i | ||||
\(889\) | 3.71408i | 0.124566i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.14890 | − | 1.50624i | 0.172495 | − | 0.0504608i | ||||
\(892\) | 6.12368 | + | 6.12368i | 0.205036 | + | 0.205036i | ||||
\(893\) | −6.21435 | − | 6.21435i | −0.207955 | − | 0.207955i | ||||
\(894\) | −8.20069 | − | 2.73174i | −0.274272 | − | 0.0913630i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10.1874i | 0.340336i | ||||||||
\(897\) | −2.86203 | − | 5.72119i | −0.0955603 | − | 0.191025i | ||||
\(898\) | −18.1170 | + | 18.1170i | −0.604571 | + | 0.604571i | ||||
\(899\) | −72.2912 | −2.41105 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.3953 | −0.446263 | ||||||||
\(902\) | 6.31376 | − | 6.31376i | 0.210225 | − | 0.210225i | ||||
\(903\) | −8.45628 | − | 16.9041i | −0.281407 | − | 0.562533i | ||||
\(904\) | 1.07512i | 0.0357580i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.12490 | + | 2.04027i | 0.203486 | + | 0.0677834i | ||||
\(907\) | −12.8493 | − | 12.8493i | −0.426653 | − | 0.426653i | 0.460834 | − | 0.887487i | \(-0.347550\pi\) |
−0.887487 | + | 0.460834i | \(0.847550\pi\) | |||||||
\(908\) | 12.8927 | + | 12.8927i | 0.427860 | + | 0.427860i | ||||
\(909\) | −30.6423 | − | 22.9626i | −1.01634 | − | 0.761621i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.5488i | 0.515156i | 0.966258 | + | 0.257578i | \(0.0829244\pi\) | ||||
−0.966258 | + | 0.257578i | \(0.917076\pi\) | |||||||
\(912\) | 8.91587 | − | 4.46017i | 0.295234 | − | 0.147691i | ||||
\(913\) | −2.80568 | + | 2.80568i | −0.0928546 | + | 0.0928546i | ||||
\(914\) | 44.9555 | 1.48700 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.6822 | −0.749440 | ||||||||
\(917\) | −11.6871 | + | 11.6871i | −0.385943 | + | 0.385943i | ||||
\(918\) | 6.20504 | − | 34.2445i | 0.204797 | − | 1.13024i | ||||
\(919\) | − | 53.8863i | − | 1.77755i | −0.458348 | − | 0.888773i | \(-0.651559\pi\) | ||
0.458348 | − | 0.888773i | \(-0.348441\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0670 | + | 36.2251i | −0.397621 | + | 1.19366i | ||||
\(922\) | −27.6182 | − | 27.6182i | −0.909558 | − | 0.909558i | ||||
\(923\) | −4.67207 | − | 4.67207i | −0.153783 | − | 0.153783i | ||||
\(924\) | −0.403470 | + | 1.21122i | −0.0132732 | + | 0.0398462i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 2.69098i | − | 0.0884313i | ||||||
\(927\) | 4.08491 | + | 28.5128i | 0.134166 | + | 0.936485i | ||||
\(928\) | −41.6228 | + | 41.6228i | −1.36634 | + | 1.36634i | ||||
\(929\) | −14.9417 | −0.490220 | −0.245110 | − | 0.969495i | \(-0.578824\pi\) | ||||
−0.245110 | + | 0.969495i | \(0.578824\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.16418 | −0.0381544 | ||||||||
\(932\) | −10.5592 | + | 10.5592i | −0.345877 | + | 0.345877i | ||||
\(933\) | −33.7262 | + | 16.8715i | −1.10415 | + | 0.552350i | ||||
\(934\) | 68.3293i | 2.23580i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.27730 | − | 3.03894i | 0.0744359 | − | 0.0993307i | ||||
\(937\) | −13.0089 | − | 13.0089i | −0.424981 | − | 0.424981i | 0.461933 | − | 0.886915i | \(-0.347156\pi\) |
−0.886915 | + | 0.461933i | \(0.847156\pi\) | |||||||
\(938\) | 2.26798 | + | 2.26798i | 0.0740523 | + | 0.0740523i | ||||
\(939\) | −39.0016 | − | 12.9919i | −1.27277 | − | 0.423974i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.15194i | − | 0.102750i | −0.998679 | − | 0.0513751i | \(-0.983640\pi\) | ||
0.998679 | − | 0.0513751i | \(-0.0163604\pi\) | |||||||
\(942\) | −18.3010 | − | 36.5838i | −0.596280 | − | 1.19196i | ||||
\(943\) | −23.5947 | + | 23.5947i | −0.768350 | + | 0.768350i | ||||
\(944\) | 21.6326 | 0.704082 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.7023 | 0.380476 | ||||||||
\(947\) | 14.6574 | − | 14.6574i | 0.476302 | − | 0.476302i | −0.427645 | − | 0.903947i | \(-0.640657\pi\) |
0.903947 | + | 0.427645i | \(0.140657\pi\) | |||||||
\(948\) | 3.69123 | + | 7.37878i | 0.119886 | + | 0.239652i | ||||
\(949\) | − | 7.37907i | − | 0.239535i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.2156 | + | 15.0618i | 1.46622 | + | 0.488412i | ||||
\(952\) | −3.61571 | − | 3.61571i | −0.117186 | − | 0.117186i | ||||
\(953\) | −9.88130 | − | 9.88130i | −0.320087 | − | 0.320087i | 0.528714 | − | 0.848800i | \(-0.322675\pi\) |
−0.848800 | + | 0.528714i | \(0.822675\pi\) | |||||||
\(954\) | 11.6453 | − | 15.5401i | 0.377032 | − | 0.503128i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 7.39748i | − | 0.239252i | ||||||
\(957\) | 8.84114 | − | 4.42278i | 0.285794 | − | 0.142968i | ||||
\(958\) | 3.03810 | − | 3.03810i | 0.0981565 | − | 0.0981565i | ||||
\(959\) | 15.7802 | 0.509569 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.0011 | 0.838744 | ||||||||
\(962\) | −12.9568 | + | 12.9568i | −0.417745 | + | 0.417745i | ||||
\(963\) | 0.106222 | + | 0.741435i | 0.00342296 | + | 0.0238924i | ||||
\(964\) | − | 6.25471i | − | 0.201451i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.94648 | − | 11.8474i | 0.126976 | − | 0.381182i | ||||
\(967\) | −1.97663 | − | 1.97663i | −0.0635642 | − | 0.0635642i | 0.674610 | − | 0.738174i | \(-0.264312\pi\) |
−0.738174 | + | 0.674610i | \(0.764312\pi\) | |||||||
\(968\) | −10.3382 | − | 10.3382i | −0.332281 | − | 0.332281i | ||||
\(969\) | −2.37248 | + | 7.12218i | −0.0762149 | + | 0.228797i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.57758i | 0.114810i | 0.998351 | + | 0.0574051i | \(0.0182827\pi\) | ||||
−0.998351 | + | 0.0574051i | \(0.981717\pi\) | |||||||
\(972\) | 13.1171 | + | 14.1243i | 0.420733 | + | 0.453038i | ||||
\(973\) | −2.05320 | + | 2.05320i | −0.0658224 | + | 0.0658224i | ||||
\(974\) | −39.4646 | −1.26453 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −74.2300 | −2.37604 | ||||||||
\(977\) | 23.9909 | − | 23.9909i | 0.767537 | − | 0.767537i | −0.210135 | − | 0.977672i | \(-0.567390\pi\) |
0.977672 | + | 0.210135i | \(0.0673905\pi\) | |||||||
\(978\) | 37.0847 | − | 18.5516i | 1.18584 | − | 0.593215i | ||||
\(979\) | 1.30995i | 0.0418662i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.8946 | − | 20.1542i | −0.858679 | − | 0.643473i | ||||
\(982\) | 43.0694 | + | 43.0694i | 1.37440 | + | 1.37440i | ||||
\(983\) | 24.6787 | + | 24.6787i | 0.787127 | + | 0.787127i | 0.981022 | − | 0.193895i | \(-0.0621122\pi\) |
−0.193895 | + | 0.981022i | \(0.562112\pi\) | |||||||
\(984\) | −18.7930 | − | 6.26016i | −0.599099 | − | 0.199567i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 64.1309i | − | 2.04234i | ||||||
\(987\) | −5.84980 | − | 11.6938i | −0.186201 | − | 0.372216i | ||||
\(988\) | 0.938141 | − | 0.938141i | 0.0298462 | − | 0.0298462i | ||||
\(989\) | −43.7320 | −1.39060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.6595 | −0.815102 | −0.407551 | − | 0.913182i | \(-0.633617\pi\) | ||||
−0.407551 | + | 0.913182i | \(0.633617\pi\) | |||||||
\(992\) | 32.8193 | − | 32.8193i | 1.04201 | − | 1.04201i | ||||
\(993\) | 15.5314 | + | 31.0473i | 0.492875 | + | 0.985256i | ||||
\(994\) | − | 12.8976i | − | 0.409089i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.5261 | − | 4.50568i | −0.428590 | − | 0.142768i | ||||
\(997\) | −17.2215 | − | 17.2215i | −0.545409 | − | 0.545409i | 0.379701 | − | 0.925109i | \(-0.376027\pi\) |
−0.925109 | + | 0.379701i | \(0.876027\pi\) | |||||||
\(998\) | 4.52623 | + | 4.52623i | 0.143275 | + | 0.143275i | ||||
\(999\) | 32.7151 | + | 47.1946i | 1.03506 | + | 1.49317i |
(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 | 525.2.j.c.407.4 | yes | 32 | |
3.2 | odd | 2 | inner | 525.2.j.c.407.14 | yes | 32 | |
5.2 | odd | 4 | inner | 525.2.j.c.218.3 | ✓ | 32 | |
5.3 | odd | 4 | inner | 525.2.j.c.218.14 | yes | 32 | |
5.4 | even | 2 | inner | 525.2.j.c.407.13 | yes | 32 | |
15.2 | even | 4 | inner | 525.2.j.c.218.13 | yes | 32 | |
15.8 | even | 4 | inner | 525.2.j.c.218.4 | yes | 32 | |
15.14 | odd | 2 | inner | 525.2.j.c.407.3 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.j.c.218.3 | ✓ | 32 | 5.2 | odd | 4 | inner | |
525.2.j.c.218.4 | yes | 32 | 15.8 | even | 4 | inner | |
525.2.j.c.218.13 | yes | 32 | 15.2 | even | 4 | inner | |
525.2.j.c.218.14 | yes | 32 | 5.3 | odd | 4 | inner | |
525.2.j.c.407.3 | yes | 32 | 15.14 | odd | 2 | inner | |
525.2.j.c.407.4 | yes | 32 | 1.1 | even | 1 | trivial | |
525.2.j.c.407.13 | yes | 32 | 5.4 | even | 2 | inner | |
525.2.j.c.407.14 | yes | 32 | 3.2 | odd | 2 | inner |