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 | 218.14 | ||
Character | \(\chi\) | \(=\) | 525.218 |
Dual form | 525.2.j.c.407.14 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 | \(-0.0305645\pi\) |
−0.0958737 | + | 0.995394i | \(0.530565\pi\) | |||||||
\(3\) | 1.54904 | − | 0.774907i | 0.894338 | − | 0.447393i | ||||
\(4\) | 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 | \(0.971357\pi\) | |||||||
\(12\) | 0.958205 | + | 1.91545i | 0.276610 | + | 0.552944i | ||||
\(13\) | 0.651688 | + | 0.651688i | 0.180746 | + | 0.180746i | 0.791681 | − | 0.610935i | \(-0.209206\pi\) |
−0.610935 | + | 0.791681i | \(0.709206\pi\) | |||||||
\(14\) | −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 | \(-0.100900\pi\) |
−0.311705 | + | 0.950179i | \(0.600900\pi\) | |||||||
\(18\) | 5.34257 | − | 0.765406i | 1.25926 | − | 0.180408i | ||||
\(19\) | − | 1.16418i | − | 0.267081i | −0.991043 | − | 0.133540i | \(-0.957365\pi\) | ||
0.991043 | − | 0.133540i | \(-0.0426345\pi\) | |||||||
\(20\) | 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 | \(-0.887201\pi\) |
0.346997 | + | 0.937866i | \(0.387201\pi\) | |||||||
\(24\) | 0.751839 | − | 2.25702i | 0.153469 | − | 0.460713i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.65804i | 0.325169i | ||||||||
\(27\) | 0.926447 | − | 5.11290i | 0.178295 | − | 0.983977i | ||||
\(28\) | −0.874368 | − | 0.874368i | −0.165240 | − | 0.165240i | ||||
\(29\) | −9.57511 | −1.77805 | −0.889027 | − | 0.457855i | \(-0.848618\pi\) | ||||
−0.889027 | + | 0.457855i | \(0.848618\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | 0.461904 | + | 0.923346i | 0.0804072 | + | 0.160734i | ||||
\(34\) | 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 | 0.346740 | − | 0.937961i | \(-0.387289\pi\) |
0.937961 | − | 0.346740i | \(-0.112711\pi\) | |||||||
\(38\) | 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 | \(0.774691\pi\) | |||||||
\(42\) | −2.78678 | + | 1.39409i | −0.430010 | + | 0.215112i | ||||
\(43\) | −7.71640 | − | 7.71640i | −1.17674 | − | 1.17674i | −0.980570 | − | 0.196171i | \(-0.937149\pi\) |
−0.196171 | − | 0.980570i | \(-0.562851\pi\) | |||||||
\(44\) | −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 | \(-0.0644102\pi\) |
−0.200972 | + | 0.979597i | \(0.564410\pi\) | |||||||
\(48\) | 7.65852 | − | 3.83117i | 1.10541 | − | 0.552982i | ||||
\(49\) | − | 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 | \(-0.829483\pi\) |
0.510438 | + | 0.859914i | \(0.329483\pi\) | |||||||
\(54\) | 7.68273 | − | 5.32563i | 1.04549 | − | 0.724727i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.37349i | 0.183540i | ||||||||
\(57\) | −0.902128 | − | 1.80335i | −0.119490 | − | 0.238860i | ||||
\(58\) | −12.1806 | − | 12.1806i | −1.59939 | − | 1.59939i | ||||
\(59\) | −4.37549 | −0.569640 | −0.284820 | − | 0.958581i | \(-0.591934\pi\) | ||||
−0.284820 | + | 0.958581i | \(0.591934\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | 0.425452 | + | 2.96968i | 0.0536020 | + | 0.374144i | ||||
\(64\) | 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 | −0.625894 | − | 0.779908i | \(-0.715266\pi\) |
0.779908 | + | 0.625894i | \(0.215266\pi\) | |||||||
\(68\) | −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 | \(-0.139871\pi\) | |||||||
\(72\) | −0.584354 | − | 4.07882i | −0.0688668 | − | 0.480694i | ||||
\(73\) | 5.66151 | + | 5.66151i | 0.662629 | + | 0.662629i | 0.955999 | − | 0.293370i | \(-0.0947768\pi\) |
−0.293370 | + | 0.955999i | \(0.594777\pi\) | |||||||
\(74\) | 19.8819 | 2.31123 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.43955 | 0.165128 | ||||||||
\(77\) | −0.421490 | − | 0.421490i | −0.0480333 | − | 0.0480333i | ||||
\(78\) | 1.28483 | + | 2.56837i | 0.145478 | + | 0.290811i | ||||
\(79\) | 3.85224i | 0.433410i | 0.976237 | + | 0.216705i | \(0.0695311\pi\) | ||||
−0.976237 | + | 0.216705i | \(0.930469\pi\) | |||||||
\(80\) | 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 | \(-0.869043\pi\) |
0.399905 | + | 0.916556i | \(0.369043\pi\) | |||||||
\(84\) | −2.03198 | − | 0.676876i | −0.221708 | − | 0.0738532i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 19.6323i | − | 2.11700i | ||||||
\(87\) | −14.8322 | + | 7.41982i | −1.59018 | + | 0.795488i | ||||
\(88\) | 0.578912 | + | 0.578912i | 0.0617122 | + | 0.0617122i | ||||
\(89\) | −2.19762 | −0.232947 | −0.116474 | − | 0.993194i | \(-0.537159\pi\) | ||||
−0.116474 | + | 0.993194i | \(0.537159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.921626 | −0.0966127 | ||||||||
\(92\) | −3.50400 | − | 3.50400i | −0.365317 | − | 0.365317i | ||||
\(93\) | −11.6951 | + | 5.85047i | −1.21272 | + | 0.606666i | ||||
\(94\) | 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 | −0.198452 | − | 0.980111i | \(-0.563591\pi\) |
0.980111 | + | 0.198452i | \(0.0635914\pi\) | |||||||
\(98\) | 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 | \(0.780991\pi\) | |||||||
\(102\) | 5.19007 | + | 10.3749i | 0.513893 | + | 1.02727i | ||||
\(103\) | 6.78916 | + | 6.78916i | 0.668956 | + | 0.668956i | 0.957474 | − | 0.288518i | \(-0.0931626\pi\) |
−0.288518 | + | 0.957474i | \(0.593163\pi\) | |||||||
\(104\) | 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 | \(-0.253842\pi\) |
−0.715589 | + | 0.698522i | \(0.753842\pi\) | |||||||
\(108\) | 6.32232 | + | 1.14559i | 0.608365 | + | 0.110235i | ||||
\(109\) | − | 11.2027i | − | 1.07303i | −0.843892 | − | 0.536513i | \(-0.819741\pi\) | ||
0.843892 | − | 0.536513i | \(-0.180259\pi\) | |||||||
\(110\) | 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 | \(-0.738278\pi\) |
0.732662 | + | 0.680593i | \(0.238278\pi\) | |||||||
\(114\) | 1.14646 | − | 3.44168i | 0.107376 | − | 0.322343i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 11.8400i | − | 1.09932i | ||||||
\(117\) | 2.73693 | − | 0.392108i | 0.253030 | − | 0.0362504i | ||||
\(118\) | −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 | ||||
\(123\) | 6.45223 | + | 12.8980i | 0.581778 | + | 1.16297i | ||||
\(124\) | − | 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 | −0.813961 | − | 0.580919i | \(-0.802693\pi\) |
0.580919 | + | 0.813961i | \(0.302693\pi\) | |||||||
\(128\) | 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 | \(-0.256792\pi\) | |||||||
\(132\) | −1.14176 | + | 0.571164i | −0.0993772 | + | 0.0497135i | ||||
\(133\) | 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 | \(-0.0145332\pi\) |
−0.0456415 | + | 0.998958i | \(0.514533\pi\) | |||||||
\(138\) | −11.1679 | + | 5.58676i | −0.950677 | + | 0.475576i | ||||
\(139\) | 2.90366i | 0.246285i | 0.992389 | + | 0.123142i | \(0.0392972\pi\) | ||||
−0.992389 | + | 0.123142i | \(0.960703\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −0.774907 | − | 1.54904i | −0.0639132 | − | 0.127763i | ||||
\(148\) | 9.66301 | + | 9.66301i | 0.794294 | + | 0.794294i | ||||
\(149\) | 2.77395 | 0.227251 | 0.113625 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113625 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(150\) | 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 | ||||
\(153\) | 11.0559 | − | 1.58392i | 0.893813 | − | 0.128053i | ||||
\(154\) | − | 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 | −0.972739 | − | 0.231904i | \(-0.925504\pi\) |
0.231904 | + | 0.972739i | \(0.425504\pi\) | |||||||
\(158\) | −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 | ||||||
\(162\) | 7.77397 | − | 14.2030i | 0.610781 | − | 1.11589i | ||||
\(163\) | 9.40972 | + | 9.40972i | 0.737026 | + | 0.737026i | 0.972001 | − | 0.234975i | \(-0.0755009\pi\) |
−0.234975 | + | 0.972001i | \(0.575501\pi\) | |||||||
\(164\) | −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 | \(-0.443697\pi\) |
−0.984397 | + | 0.175960i | \(0.943697\pi\) | |||||||
\(168\) | 1.06433 | + | 2.12759i | 0.0821145 | + | 0.164147i | ||||
\(169\) | − | 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 | 0.512707 | − | 0.858563i | \(-0.328643\pi\) |
0.858563 | − | 0.512707i | \(-0.171357\pi\) | |||||||
\(174\) | −28.3071 | − | 9.42941i | −2.14596 | − | 0.714841i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.94703i | 0.222141i | ||||||||
\(177\) | −6.77780 | + | 3.39060i | −0.509451 | + | 0.254853i | ||||
\(178\) | −2.79562 | − | 2.79562i | −0.209540 | − | 0.209540i | ||||
\(179\) | 18.2401 | 1.36333 | 0.681663 | − | 0.731666i | \(-0.261257\pi\) | ||||
0.681663 | + | 0.731666i | \(0.261257\pi\) | |||||||
\(180\) | 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 | ||||
\(183\) | −23.2573 | + | 11.6345i | −1.71923 | + | 0.860043i | ||||
\(184\) | 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 | \(0.949881\pi\) | |||||||
\(192\) | 0.907885 | + | 1.81486i | 0.0655210 | + | 0.130976i | ||||
\(193\) | −11.7911 | − | 11.7911i | −0.848741 | − | 0.848741i | 0.141235 | − | 0.989976i | \(-0.454893\pi\) |
−0.989976 | + | 0.141235i | \(0.954893\pi\) | |||||||
\(194\) | 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 | \(-0.337079\pi\) |
−0.871848 | + | 0.489776i | \(0.837079\pi\) | |||||||
\(198\) | 0.456241 | + | 3.18458i | 0.0324236 | + | 0.226318i | ||||
\(199\) | 0.778449i | 0.0551828i | 0.999619 | + | 0.0275914i | \(0.00878373\pi\) | ||||
−0.999619 | + | 0.0275914i | \(0.991216\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | 1.70499 | + | 11.9009i | 0.118505 | + | 0.827169i | ||||
\(208\) | 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 | ||||
\(213\) | −5.55545 | − | 11.1053i | −0.380653 | − | 0.760926i | ||||
\(214\) | − | 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 | ||||||||
\(222\) | 30.7979 | − | 15.4066i | 2.06702 | − | 1.03403i | ||||
\(223\) | −4.95226 | − | 4.95226i | −0.331628 | − | 0.331628i | 0.521577 | − | 0.853204i | \(-0.325344\pi\) |
−0.853204 | + | 0.521577i | \(0.825344\pi\) | |||||||
\(224\) | −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 | \(-0.0872389\pi\) |
−0.270651 | + | 0.962678i | \(0.587239\pi\) | |||||||
\(228\) | 2.22993 | − | 1.11552i | 0.147680 | − | 0.0738772i | ||||
\(229\) | 18.3432i | 1.21215i | 0.795406 | + | 0.606077i | \(0.207258\pi\) | ||||
−0.795406 | + | 0.606077i | \(0.792742\pi\) | |||||||
\(230\) | 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 | \(-0.620546\pi\) |
0.929144 | + | 0.369718i | \(0.120546\pi\) | |||||||
\(234\) | 3.98049 | + | 2.98288i | 0.260213 | + | 0.194997i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 5.41048i | − | 0.352192i | ||||||
\(237\) | 2.98512 | + | 5.96726i | 0.193905 | + | 0.387615i | ||||
\(238\) | −4.73597 | − | 4.73597i | −0.306987 | − | 0.306987i | ||||
\(239\) | −5.98239 | −0.386968 | −0.193484 | − | 0.981103i | \(-0.561979\pi\) | ||||
−0.193484 | + | 0.981103i | \(0.561979\pi\) | |||||||
\(240\) | 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 | ||||
\(243\) | −10.6079 | − | 11.4224i | −0.680498 | − | 0.732750i | ||||
\(244\) | − | 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 | \(0.687277\pi\) | |||||||
\(252\) | −3.67214 | + | 0.526090i | −0.231323 | + | 0.0331406i | ||||
\(253\) | −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 | \(-0.0627514\pi\) |
−0.195865 | + | 0.980631i | \(0.562751\pi\) | |||||||
\(258\) | −15.2132 | − | 30.4111i | −0.947131 | − | 1.89332i | ||||
\(259\) | 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 | \(-0.853408\pi\) |
0.444425 | + | 0.895816i | \(0.353408\pi\) | |||||||
\(264\) | 1.34536 | + | 0.448154i | 0.0828012 | + | 0.0275820i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.09440i | 0.128416i | ||||||||
\(267\) | −3.40419 | + | 1.70295i | −0.208333 | + | 0.104219i | ||||
\(268\) | 1.55886 | + | 1.55886i | 0.0952228 | + | 0.0952228i | ||||
\(269\) | 7.34074 | 0.447573 | 0.223786 | − | 0.974638i | \(-0.428158\pi\) | ||||
0.223786 | + | 0.974638i | \(0.428158\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | −1.42763 | + | 0.714174i | −0.0864043 | + | 0.0432238i | ||||
\(274\) | 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 | −0.289031 | − | 0.957320i | \(-0.593333\pi\) |
0.957320 | + | 0.289031i | \(0.0933331\pi\) | |||||||
\(278\) | −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 | \(0.829491\pi\) | |||||||
\(282\) | 10.5240 | + | 21.0375i | 0.626697 | + | 1.25277i | ||||
\(283\) | −10.9094 | − | 10.9094i | −0.648494 | − | 0.648494i | 0.304135 | − | 0.952629i | \(-0.401633\pi\) |
−0.952629 | + | 0.304135i | \(0.901633\pi\) | |||||||
\(284\) | 8.86501 | 0.526041 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.988321 | −0.0584406 | ||||||||
\(287\) | −5.88769 | − | 5.88769i | −0.347540 | − | 0.347540i | ||||
\(288\) | 18.2563 | − | 2.61549i | 1.07576 | − | 0.154119i | ||||
\(289\) | − | 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 | \(-0.968787\pi\) |
0.0979008 | + | 0.995196i | \(0.468787\pi\) | |||||||
\(294\) | 0.984783 | − | 2.95632i | 0.0574337 | − | 0.172416i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 15.1790i | − | 0.882262i | ||||||
\(297\) | 3.04768 | + | 0.552234i | 0.176844 | + | 0.0320439i | ||||
\(298\) | 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 | ||||
\(303\) | 9.89076 | + | 19.7716i | 0.568209 | + | 1.13585i | ||||
\(304\) | − | 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 | −0.994488 | − | 0.104848i | \(-0.966564\pi\) |
0.104848 | + | 0.994488i | \(0.466564\pi\) | |||||||
\(308\) | 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 | \(-0.211773\pi\) | |||||||
\(312\) | 1.96084 | − | 0.980910i | 0.111011 | − | 0.0555331i | ||||
\(313\) | 16.7825 | + | 16.7825i | 0.948603 | + | 0.948603i | 0.998742 | − | 0.0501392i | \(-0.0159665\pi\) |
−0.0501392 | + | 0.998742i | \(0.515966\pi\) | |||||||
\(314\) | −23.6171 | −1.33279 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.76346 | −0.267965 | ||||||||
\(317\) | 19.4564 | + | 19.4564i | 1.09278 | + | 1.09278i | 0.995231 | + | 0.0975486i | \(0.0311002\pi\) |
0.0975486 | + | 0.995231i | \(0.468900\pi\) | |||||||
\(318\) | −10.0271 | + | 5.01604i | −0.562290 | + | 0.281285i | ||||
\(319\) | − | 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 | ||||||||
\(327\) | −8.68107 | − | 17.3535i | −0.480064 | − | 0.959648i | ||||
\(328\) | 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 | ||||
\(333\) | −4.70185 | − | 32.8192i | −0.257660 | − | 1.79848i | ||||
\(334\) | − | 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 | −0.837733 | − | 0.546080i | \(-0.816119\pi\) |
0.546080 | + | 0.837733i | \(0.316119\pi\) | |||||||
\(338\) | 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 | ||||||
\(342\) | −0.891068 | − | 6.21970i | −0.0481834 | − | 0.336323i | ||||
\(343\) | 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 | −0.995999 | − | 0.0893604i | \(-0.971518\pi\) |
−0.0893604 | − | 0.995999i | \(-0.528482\pi\) | |||||||
\(348\) | −9.17492 | − | 18.3407i | −0.491828 | − | 0.983163i | ||||
\(349\) | − | 14.0744i | − | 0.753386i | −0.926338 | − | 0.376693i | \(-0.877061\pi\) | ||
0.926338 | − | 0.376693i | \(-0.122939\pi\) | |||||||
\(350\) | 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 | \(-0.664497\pi\) |
0.869413 | + | 0.494087i | \(0.164497\pi\) | |||||||
\(354\) | −12.9354 | − | 4.30891i | −0.687506 | − | 0.229016i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 2.71745i | − | 0.144025i | ||||||
\(357\) | −5.76694 | + | 2.88491i | −0.305219 | + | 0.152686i | ||||
\(358\) | 23.2034 | + | 23.2034i | 1.22634 | + | 1.22634i | ||||
\(359\) | 15.8072 | 0.834270 | 0.417135 | − | 0.908844i | \(-0.363034\pi\) | ||||
0.417135 | + | 0.908844i | \(0.363034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.6447 | 0.928668 | ||||||||
\(362\) | 6.43741 | + | 6.43741i | 0.338343 | + | 0.338343i | ||||
\(363\) | 16.4890 | − | 8.24864i | 0.865450 | − | 0.432941i | ||||
\(364\) | − | 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 | −0.261158 | − | 0.965296i | \(-0.584104\pi\) |
0.965296 | + | 0.261158i | \(0.0841043\pi\) | |||||||
\(368\) | −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 | ||||||
\(372\) | −7.23436 | − | 14.4615i | −0.375084 | − | 0.749793i | ||||
\(373\) | 14.7655 | + | 14.7655i | 0.764527 | + | 0.764527i | 0.977137 | − | 0.212610i | \(-0.0681965\pi\) |
−0.212610 | + | 0.977137i | \(0.568197\pi\) | |||||||
\(374\) | −3.99233 | −0.206438 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3685 | 0.534716 | ||||||||
\(377\) | −6.23998 | − | 6.23998i | −0.321376 | − | 0.321376i | ||||
\(378\) | −1.66672 | + | 9.19830i | −0.0857266 | + | 0.473110i | ||||
\(379\) | − | 31.9071i | − | 1.63896i | −0.573109 | − | 0.819479i | \(-0.694263\pi\) | ||
0.573109 | − | 0.819479i | \(-0.305737\pi\) | |||||||
\(380\) | 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 | \(-0.874884\pi\) |
0.383020 | + | 0.923740i | \(0.374884\pi\) | |||||||
\(384\) | 5.57649 | − | 16.7406i | 0.284574 | − | 0.854292i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 29.9992i | − | 1.52692i | ||||||
\(387\) | −32.4070 | + | 4.64281i | −1.64734 | + | 0.236007i | ||||
\(388\) | 9.51946 | + | 9.51946i | 0.483277 | + | 0.483277i | ||||
\(389\) | −22.7753 | −1.15475 | −0.577376 | − | 0.816478i | \(-0.695923\pi\) | ||||
−0.577376 | + | 0.816478i | \(0.695923\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.9194 | −0.754509 | ||||||||
\(392\) | −0.971203 | − | 0.971203i | −0.0490532 | − | 0.0490532i | ||||
\(393\) | −12.8077 | − | 25.6026i | −0.646064 | − | 1.29148i | ||||
\(394\) | − | 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 | −0.226775 | − | 0.973947i | \(-0.572818\pi\) |
0.973947 | + | 0.226775i | \(0.0728181\pi\) | |||||||
\(398\) | −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 | \(0.877211\pi\) | |||||||
\(402\) | 4.96841 | − | 2.48545i | 0.247802 | − | 0.123963i | ||||
\(403\) | −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 | ||||
\(408\) | 7.92082 | − | 3.96239i | 0.392139 | − | 0.196168i | ||||
\(409\) | − | 25.3358i | − | 1.25277i | −0.779512 | − | 0.626387i | \(-0.784533\pi\) | ||
0.779512 | − | 0.626387i | \(-0.215467\pi\) | |||||||
\(410\) | 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 | ||||||||
\(417\) | 2.25006 | + | 4.49788i | 0.110186 | + | 0.220262i | ||||
\(418\) | 0.882769 | + | 0.882769i | 0.0431776 | + | 0.0431776i | ||||
\(419\) | 19.4078 | 0.948133 | 0.474067 | − | 0.880489i | \(-0.342786\pi\) | ||||
0.474067 | + | 0.880489i | \(0.342786\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | 22.4182 | − | 3.21176i | 1.09001 | − | 0.156161i | ||||
\(424\) | 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 | \(-0.134990\pi\) | |||||||
\(432\) | 4.58040 | − | 25.2784i | 0.220375 | − | 1.21621i | ||||
\(433\) | 20.7996 | + | 20.7996i | 0.999563 | + | 0.999563i | 1.00000 | 0.000437230i | \(-0.000139175\pi\) | |
−0.000437230 | 1.00000i | \(0.500139\pi\) | ||||||||
\(434\) | 13.5826 | 0.651985 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.8527 | 0.663422 | ||||||||
\(437\) | 3.29894 | + | 3.29894i | 0.157809 | + | 0.157809i | ||||
\(438\) | 11.1619 | + | 22.3126i | 0.533335 | + | 1.06614i | ||||
\(439\) | − | 12.3529i | − | 0.589572i | −0.955563 | − | 0.294786i | \(-0.904752\pi\) | ||
0.955563 | − | 0.294786i | \(-0.0952483\pi\) | |||||||
\(440\) | 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 | \(-0.820897\pi\) |
0.533446 | + | 0.845834i | \(0.320897\pi\) | |||||||
\(444\) | 22.4563 | + | 7.48044i | 1.06573 | + | 0.355006i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 12.5997i | − | 0.596611i | ||||||
\(447\) | 4.29696 | − | 2.14955i | 0.203239 | − | 0.101670i | ||||
\(448\) | −0.828450 | − | 0.828450i | −0.0391406 | − | 0.0391406i | ||||
\(449\) | −14.2416 | −0.672104 | −0.336052 | − | 0.941843i | \(-0.609092\pi\) | ||||
−0.336052 | + | 0.941843i | \(0.609092\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.96321 | −0.233708 | ||||||||
\(452\) | 0.684427 | + | 0.684427i | 0.0321927 | + | 0.0321927i | ||||
\(453\) | 3.20929 | − | 1.60545i | 0.150786 | − | 0.0754306i | ||||
\(454\) | 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 | −0.987038 | − | 0.160488i | \(-0.948693\pi\) |
0.160488 | + | 0.987038i | \(0.448693\pi\) | |||||||
\(458\) | −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 | \(0.831279\pi\) | |||||||
\(462\) | −0.830984 | − | 1.66114i | −0.0386609 | − | 0.0772831i | ||||
\(463\) | −1.05768 | − | 1.05768i | −0.0491547 | − | 0.0491547i | 0.682102 | − | 0.731257i | \(-0.261066\pi\) |
−0.731257 | + | 0.682102i | \(0.761066\pi\) | |||||||
\(464\) | −47.3398 | −2.19770 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.7258 | 1.00643 | ||||||||
\(467\) | −26.8566 | − | 26.8566i | −1.24278 | − | 1.24278i | −0.958844 | − | 0.283932i | \(-0.908361\pi\) |
−0.283932 | − | 0.958844i | \(-0.591639\pi\) | |||||||
\(468\) | 0.484858 | + | 3.38434i | 0.0224126 | + | 0.156441i | ||||
\(469\) | 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 | ||||||
\(477\) | 1.53081 | + | 10.6851i | 0.0700910 | + | 0.489239i | ||||
\(478\) | −7.61027 | − | 7.61027i | −0.348086 | − | 0.348086i | ||||
\(479\) | 2.38823 | 0.109121 | 0.0545605 | − | 0.998510i | \(-0.482624\pi\) | ||||
0.0545605 | + | 0.998510i | \(0.482624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.1853 | 0.464409 | ||||||||
\(482\) | 6.43463 | + | 6.43463i | 0.293090 | + | 0.293090i | ||||
\(483\) | −3.10541 | − | 6.20772i | −0.141301 | − | 0.282461i | ||||
\(484\) | 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 | −0.262140 | − | 0.965030i | \(-0.584428\pi\) |
0.965030 | + | 0.262140i | \(0.0844281\pi\) | |||||||
\(488\) | −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 | \(-0.276749\pi\) | |||||||
\(492\) | −15.9489 | + | 7.97846i | −0.719033 | + | 0.359697i | ||||
\(493\) | −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 | ||||
\(498\) | −18.5504 | + | 9.27986i | −0.831265 | + | 0.415840i | ||||
\(499\) | 3.55804i | 0.159280i | 0.996824 | + | 0.0796398i | \(0.0253770\pi\) | ||||
−0.996824 | + | 0.0796398i | \(0.974623\pi\) | |||||||
\(500\) | 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 | \(-0.840465\pi\) |
0.480474 | + | 0.877009i | \(0.340465\pi\) | |||||||
\(504\) | 3.29736 | + | 2.47096i | 0.146876 | + | 0.110065i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 4.29747i | − | 0.191046i | ||||||
\(507\) | −9.41558 | − | 18.8218i | −0.418161 | − | 0.835903i | ||||
\(508\) | −3.24747 | − | 3.24747i | −0.144083 | − | 0.144083i | ||||
\(509\) | 24.4919 | 1.08558 | 0.542791 | − | 0.839868i | \(-0.317367\pi\) | ||||
0.542791 | + | 0.839868i | \(0.317367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00658 | −0.354190 | ||||||||
\(512\) | 11.8883 | + | 11.8883i | 0.525395 | + | 0.525395i | ||||
\(513\) | −5.95231 | − | 1.07855i | −0.262801 | − | 0.0476191i | ||||
\(514\) | 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 | \(-0.214307\pi\) | |||||||
\(522\) | −51.1557 | + | 7.32884i | −2.23902 | + | 0.320775i | ||||
\(523\) | −7.00886 | − | 7.00886i | −0.306476 | − | 0.306476i | 0.537065 | − | 0.843541i | \(-0.319533\pi\) |
−0.843541 | + | 0.537065i | \(0.819533\pi\) | |||||||
\(524\) | 20.4377 | 0.892824 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.6246 | −0.812071 | ||||||||
\(527\) | −19.8751 | − | 19.8751i | −0.865773 | − | 0.865773i | ||||
\(528\) | 2.28368 | + | 4.56507i | 0.0993842 | + | 0.198669i | ||||
\(529\) | 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 | ||||||
\(537\) | 28.2546 | − | 14.1343i | 1.21927 | − | 0.609942i | ||||
\(538\) | 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 | ||||
\(543\) | 7.83876 | − | 3.92134i | 0.336393 | − | 0.168281i | ||||
\(544\) | 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 | −0.773101 | − | 0.634283i | \(-0.781295\pi\) |
0.634283 | + | 0.773101i | \(0.281295\pi\) | |||||||
\(548\) | −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 | ||||||||
\(552\) | 4.26525 | + | 8.52623i | 0.181541 | + | 0.362901i | ||||
\(553\) | −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 | \(-0.346164\pi\) |
−0.885470 | + | 0.464696i | \(0.846164\pi\) | |||||||
\(558\) | −40.3359 | + | 5.77874i | −1.70755 | + | 0.244634i | ||||
\(559\) | − | 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 | \(-0.635060\pi\) |
0.911326 | + | 0.411685i | \(0.135060\pi\) | |||||||
\(564\) | −5.10977 | + | 15.3395i | −0.215160 | + | 0.645911i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 27.7559i | − | 1.16667i | ||||||
\(567\) | 7.89477 | + | 4.32118i | 0.331549 | + | 0.181472i | ||||
\(568\) | −6.96274 | − | 6.96274i | −0.292150 | − | 0.292150i | ||||
\(569\) | 19.3729 | 0.812155 | 0.406077 | − | 0.913839i | \(-0.366896\pi\) | ||||
0.406077 | + | 0.913839i | \(0.366896\pi\) | |||||||
\(570\) | 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 | ||||
\(573\) | 3.35855 | + | 6.71373i | 0.140305 | + | 0.280470i | ||||
\(574\) | − | 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 | −0.633619 | − | 0.773645i | \(-0.718431\pi\) |
0.773645 | + | 0.633619i | \(0.218431\pi\) | |||||||
\(578\) | 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 | ||||||
\(582\) | 30.3404 | − | 15.1778i | 1.25765 | − | 0.629139i | ||||
\(583\) | −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 | \(-0.360200\pi\) |
−0.905094 | + | 0.425211i | \(0.860200\pi\) | |||||||
\(588\) | 1.91545 | − | 0.958205i | 0.0789919 | − | 0.0395157i | ||||
\(589\) | 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 | \(-0.566999\pi\) |
0.977930 | + | 0.208932i | \(0.0669986\pi\) | |||||||
\(594\) | 3.17449 | + | 4.57950i | 0.130251 | + | 0.187899i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.43011i | 0.140503i | ||||||||
\(597\) | 0.603226 | + | 1.20585i | 0.0246884 | + | 0.0493521i | ||||
\(598\) | −4.69840 | − | 4.69840i | −0.192132 | − | 0.192132i | ||||
\(599\) | −27.9518 | −1.14208 | −0.571041 | − | 0.820922i | \(-0.693460\pi\) | ||||
−0.571041 | + | 0.820922i | \(0.693460\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | −0.758517 | − | 5.29448i | −0.0308892 | − | 0.215608i | ||||
\(604\) | 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 | −0.999502 | − | 0.0315491i | \(-0.989956\pi\) |
0.0315491 | + | 0.999502i | \(0.489956\pi\) | |||||||
\(608\) | 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 | ||||||||
\(612\) | 1.95859 | + | 13.6710i | 0.0791712 | + | 0.552619i | ||||
\(613\) | −11.8807 | − | 11.8807i | −0.479858 | − | 0.479858i | 0.425228 | − | 0.905086i | \(-0.360194\pi\) |
−0.905086 | + | 0.425228i | \(0.860194\pi\) | |||||||
\(614\) | −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 | \(-0.320555\pi\) |
−0.845261 | + | 0.534354i | \(0.820555\pi\) | |||||||
\(618\) | 13.3851 | + | 26.7568i | 0.538427 | + | 1.07632i | ||||
\(619\) | − | 7.02322i | − | 0.282287i | −0.989989 | − | 0.141144i | \(-0.954922\pi\) | ||
0.989989 | − | 0.141144i | \(-0.0450779\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | 1.07494 | − | 0.537738i | 0.0429289 | − | 0.0214752i | ||||
\(628\) | −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 | ||||
\(633\) | 6.07102 | − | 3.03703i | 0.241301 | − | 0.120711i | ||||
\(634\) | 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 | \(-0.00361128\pi\) | |||||||
\(642\) | −0.348059 | − | 0.695771i | −0.0137368 | − | 0.0274599i | ||||
\(643\) | 4.70272 | + | 4.70272i | 0.185457 | + | 0.185457i | 0.793729 | − | 0.608272i | \(-0.208137\pi\) |
−0.608272 | + | 0.793729i | \(0.708137\pi\) | |||||||
\(644\) | 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 | \(-0.209619\pi\) |
−0.611960 | + | 0.790888i | \(0.709619\pi\) | |||||||
\(648\) | −10.8434 | − | 5.93509i | −0.425968 | − | 0.233152i | ||||
\(649\) | − | 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 | \(-0.918717\pi\) |
0.252593 | + | 0.967573i | \(0.418717\pi\) | |||||||
\(654\) | 11.0323 | − | 33.1189i | 0.431395 | − | 1.29505i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.1664i | 1.60728i | ||||||||
\(657\) | 23.7770 | − | 3.40642i | 0.927628 | − | 0.132897i | ||||
\(658\) | −9.60324 | − | 9.60324i | −0.374373 | − | 0.374373i | ||||
\(659\) | 23.1110 | 0.900276 | 0.450138 | − | 0.892959i | \(-0.351375\pi\) | ||||
0.450138 | + | 0.892959i | \(0.351375\pi\) | |||||||
\(660\) | 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 | ||||
\(663\) | 2.65881 | + | 5.31496i | 0.103260 | + | 0.206416i | ||||
\(664\) | 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 | ||||||
\(672\) | −9.52280 | + | 4.76378i | −0.367350 | + | 0.183767i | ||||
\(673\) | 20.0108 | + | 20.0108i | 0.771359 | + | 0.771359i | 0.978344 | − | 0.206985i | \(-0.0663653\pi\) |
−0.206985 | + | 0.978344i | \(0.566365\pi\) | |||||||
\(674\) | −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 | \(-0.331635\pi\) |
−0.863345 | + | 0.504614i | \(0.831635\pi\) | |||||||
\(678\) | 2.18140 | − | 1.09125i | 0.0837762 | − | 0.0419091i | ||||
\(679\) | 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 | 0.437939 | − | 0.899005i | \(-0.355709\pi\) |
0.899005 | − | 0.437939i | \(-0.144291\pi\) | |||||||
\(684\) | 2.58982 | − | 3.45597i | 0.0990241 | − | 0.132142i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.79904i | 0.0686876i | ||||||||
\(687\) | 14.2143 | + | 28.4143i | 0.542308 | + | 1.08407i | ||||
\(688\) | −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 | ||||
\(693\) | −1.77016 | + | 0.253602i | −0.0672427 | + | 0.00963356i | ||||
\(694\) | − | 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 | \(0.550119\pi\) | |||||||
\(702\) | 8.47739 | + | 1.53609i | 0.319959 | + | 0.0579759i | ||||
\(703\) | −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 | ||||
\(708\) | −4.19262 | − | 8.38105i | −0.157568 | − | 0.314979i | ||||
\(709\) | − | 22.2416i | − | 0.835302i | −0.908608 | − | 0.417651i | \(-0.862854\pi\) | ||
0.908608 | − | 0.417651i | \(-0.137146\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | −9.26695 | + | 4.63579i | −0.346080 | + | 0.173127i | ||||
\(718\) | 20.1085 | + | 20.1085i | 0.750443 | + | 0.750443i | ||||
\(719\) | −40.5531 | −1.51238 | −0.756188 | − | 0.654354i | \(-0.772941\pi\) | ||||
−0.756188 | + | 0.654354i | \(0.772941\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.60132 | −0.357572 | ||||||||
\(722\) | 22.4460 | + | 22.4460i | 0.835355 | + | 0.835355i | ||||
\(723\) | 7.83539 | − | 3.91965i | 0.291401 | − | 0.145773i | ||||
\(724\) | 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 | −0.0372050 | − | 0.999308i | \(-0.511845\pi\) |
0.999308 | + | 0.0372050i | \(0.0118454\pi\) | |||||||
\(728\) | −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 | ||||||
\(732\) | −14.3865 | − | 28.7586i | −0.531740 | − | 1.06295i | ||||
\(733\) | 20.5005 | + | 20.5005i | 0.757205 | + | 0.757205i | 0.975813 | − | 0.218608i | \(-0.0701515\pi\) |
−0.218608 | + | 0.975813i | \(0.570152\pi\) | |||||||
\(734\) | 34.3199 | 1.26677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.6361 | −0.908100 | ||||||||
\(737\) | 0.751453 | + | 0.751453i | 0.0276801 | + | 0.0276801i | ||||
\(738\) | 6.37312 | + | 44.4847i | 0.234598 | + | 1.63750i | ||||
\(739\) | 11.5622i | 0.425323i | 0.977126 | + | 0.212661i | \(0.0682131\pi\) | ||||
−0.977126 | + | 0.212661i | \(0.931787\pi\) | |||||||
\(740\) | 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 | \(-0.970497\pi\) |
0.0925542 | + | 0.995708i | \(0.470497\pi\) | |||||||
\(744\) | −5.67632 | + | 17.0403i | −0.208104 | + | 0.624728i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 37.5667i | 1.37541i | ||||||||
\(747\) | 2.83206 | + | 19.7679i | 0.103620 | + | 0.723270i | ||||
\(748\) | −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 | ||||
\(753\) | 20.4252 | + | 40.8299i | 0.744334 | + | 1.48792i | ||||
\(754\) | − | 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 | −0.621343 | − | 0.783539i | \(-0.713412\pi\) |
0.783539 | + | 0.621343i | \(0.213412\pi\) | |||||||
\(758\) | 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 | \(-0.165133\pi\) | |||||||
\(762\) | −10.3503 | + | 5.17775i | −0.374953 | + | 0.187570i | ||||
\(763\) | 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 | ||||
\(768\) | 32.0196 | − | 16.0178i | 1.15541 | − | 0.577994i | ||||
\(769\) | 10.3542i | 0.373382i | 0.982419 | + | 0.186691i | \(0.0597762\pi\) | ||||
−0.982419 | + | 0.186691i | \(0.940224\pi\) | |||||||
\(770\) | 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 | \(-0.762948\pi\) |
0.677766 | + | 0.735278i | \(0.262948\pi\) | |||||||
\(774\) | −47.1316 | − | 35.3192i | −1.69411 | − | 1.26952i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 14.9535i | − | 0.536800i | ||||||
\(777\) | 8.56382 | + | 17.1191i | 0.307225 | + | 0.614143i | ||||
\(778\) | −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 | ||||
\(783\) | −8.87084 | + | 48.9565i | −0.317018 | + | 1.74956i | ||||
\(784\) | − | 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 | −0.808413 | − | 0.588616i | \(-0.799673\pi\) |
0.588616 | + | 0.808413i | \(0.299673\pi\) | |||||||
\(788\) | 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 | ||||||||
\(792\) | 2.43129 | − | 0.348320i | 0.0863922 | − | 0.0123770i | ||||
\(793\) | −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 | \(-0.0353109\pi\) |
−0.110705 | + | 0.993853i | \(0.535311\pi\) | |||||||
\(798\) | 1.62296 | + | 3.24431i | 0.0574523 | + | 0.114847i | ||||
\(799\) | 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 | ||||||
\(807\) | 11.3711 | − | 5.68839i | 0.400281 | − | 0.200241i | ||||
\(808\) | 12.3962 | + | 12.3962i | 0.436099 | + | 0.436099i | ||||
\(809\) | −21.2421 | −0.746831 | −0.373416 | − | 0.927664i | \(-0.621813\pi\) | ||||
−0.373416 | + | 0.927664i | \(0.621813\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | −11.4733 | + | 5.73952i | −0.402386 | + | 0.201294i | ||||
\(814\) | 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 | \(-0.0784078\pi\) | |||||||
\(822\) | 21.9990 | + | 43.9759i | 0.767302 | + | 1.53384i | ||||
\(823\) | 9.64020 | + | 9.64020i | 0.336036 | + | 0.336036i | 0.854873 | − | 0.518837i | \(-0.173635\pi\) |
−0.518837 | + | 0.854873i | \(0.673635\pi\) | |||||||
\(824\) | 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 | \(-0.339482\pi\) |
−0.875522 | + | 0.483178i | \(0.839482\pi\) | |||||||
\(828\) | −14.7160 | + | 2.10829i | −0.511415 | + | 0.0732681i | ||||
\(829\) | − | 18.8442i | − | 0.654485i | −0.944940 | − | 0.327242i | \(-0.893881\pi\) | ||
0.944940 | − | 0.327242i | \(-0.106119\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | −6.99459 | + | 38.6019i | −0.241768 | + | 1.33428i | ||||
\(838\) | 24.6889 | + | 24.6889i | 0.852865 | + | 0.852865i | ||||
\(839\) | −46.9582 | −1.62118 | −0.810588 | − | 0.585617i | \(-0.800852\pi\) | ||||
−0.810588 | + | 0.585617i | \(0.800852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.6827 | 2.16147 | ||||||||
\(842\) | −11.6902 | − | 11.6902i | −0.402870 | − | 0.402870i | ||||
\(843\) | 13.2605 | + | 26.5076i | 0.456714 | + | 0.912972i | ||||
\(844\) | 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 | ||||||||
\(852\) | 13.7322 | − | 6.86955i | 0.470459 | − | 0.235347i | ||||
\(853\) | −26.8180 | − | 26.8180i | −0.918232 | − | 0.918232i | 0.0786690 | − | 0.996901i | \(-0.474933\pi\) |
−0.996901 | + | 0.0786690i | \(0.974933\pi\) | |||||||
\(854\) | 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 | \(-0.0494324\pi\) |
−0.154673 | + | 0.987966i | \(0.549432\pi\) | |||||||
\(858\) | −1.53095 | + | 0.765856i | −0.0522657 | + | 0.0261459i | ||||
\(859\) | 1.97722i | 0.0674617i | 0.999431 | + | 0.0337309i | \(0.0107389\pi\) | ||||
−0.999431 | + | 0.0337309i | \(0.989261\pi\) | |||||||
\(860\) | 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 | \(-0.890677\pi\) |
0.336736 | + | 0.941599i | \(0.390677\pi\) | |||||||
\(864\) | 26.2529 | − | 18.1984i | 0.893142 | − | 0.619122i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 52.9188i | 1.79825i | ||||||||
\(867\) | −2.43314 | − | 4.86385i | −0.0826339 | − | 0.165185i | ||||
\(868\) | 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 | ||||
\(873\) | −4.63200 | − | 32.3316i | −0.156770 | − | 1.09426i | ||||
\(874\) | 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 | 0.0154576 | − | 0.999881i | \(-0.495079\pi\) |
0.999881 | − | 0.0154576i | \(-0.00492051\pi\) | |||||||
\(878\) | 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 | \(-0.198934\pi\) | |||||||
\(882\) | −0.765406 | − | 5.34257i | −0.0257726 | − | 0.179894i | ||||
\(883\) | −0.424655 | − | 0.424655i | −0.0142908 | − | 0.0142908i | 0.699925 | − | 0.714216i | \(-0.253217\pi\) |
−0.714216 | + | 0.699925i | \(0.753217\pi\) | |||||||
\(884\) | −4.24274 | −0.142699 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.7283 | −0.561999 | ||||||||
\(887\) | 39.8779 | + | 39.8779i | 1.33897 | + | 1.33897i | 0.897059 | + | 0.441912i | \(0.145700\pi\) |
0.441912 | + | 0.897059i | \(0.354300\pi\) | |||||||
\(888\) | −11.7623 | − | 23.5129i | −0.394717 | − | 0.789040i | ||||
\(889\) | − | 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 | ||||||||
\(897\) | −5.72119 | + | 2.86203i | −0.191025 | + | 0.0955603i | ||||
\(898\) | −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 | ||||
\(903\) | 16.9041 | − | 8.45628i | 0.562533 | − | 0.281407i | ||||
\(904\) | − | 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 | −0.887487 | − | 0.460834i | \(-0.847550\pi\) |
0.460834 | + | 0.887487i | \(0.347550\pi\) | |||||||
\(908\) | −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 | \(0.917076\pi\) | |||||||
\(912\) | −4.46017 | − | 8.91587i | −0.147691 | − | 0.295234i | ||||
\(913\) | −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 | ||||
\(918\) | 34.2445 | + | 6.20504i | 1.13024 | + | 0.204797i | ||||
\(919\) | 53.8863i | 1.77755i | 0.458348 | + | 0.888773i | \(0.348441\pi\) | ||||
−0.458348 | + | 0.888773i | \(0.651559\pi\) | |||||||
\(920\) | 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 | ||||||
\(927\) | 28.5128 | − | 4.08491i | 0.936485 | − | 0.134166i | ||||
\(928\) | −41.6228 | − | 41.6228i | −1.36634 | − | 1.36634i | ||||
\(929\) | 14.9417 | 0.490220 | 0.245110 | − | 0.969495i | \(-0.421176\pi\) | ||||
0.245110 | + | 0.969495i | \(0.421176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.16418 | −0.0381544 | ||||||||
\(932\) | 10.5592 | + | 10.5592i | 0.345877 | + | 0.345877i | ||||
\(933\) | −16.8715 | − | 33.7262i | −0.552350 | − | 1.10415i | ||||
\(934\) | − | 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 | −0.886915 | − | 0.461933i | \(-0.847156\pi\) |
0.461933 | + | 0.886915i | \(0.347156\pi\) | |||||||
\(938\) | −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 | \(-0.0163604\pi\) | |||||||
\(942\) | −36.5838 | + | 18.3010i | −1.19196 | + | 0.596280i | ||||
\(943\) | −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 | \(-0.359343\pi\) |
−0.903947 | + | 0.427645i | \(0.859343\pi\) | |||||||
\(948\) | −7.37878 | + | 3.69123i | −0.239652 | + | 0.119886i | ||||
\(949\) | 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 | \(-0.677325\pi\) |
0.848800 | + | 0.528714i | \(0.177325\pi\) | |||||||
\(954\) | −11.6453 | + | 15.5401i | −0.377032 | + | 0.503128i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 7.39748i | − | 0.239252i | ||||||
\(957\) | −4.42278 | − | 8.84114i | −0.142968 | − | 0.285794i | ||||
\(958\) | 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 | ||||
\(963\) | −0.741435 | + | 0.106222i | −0.0238924 | + | 0.00342296i | ||||
\(964\) | 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 | −0.738174 | − | 0.674610i | \(-0.764312\pi\) |
0.674610 | + | 0.738174i | \(0.264312\pi\) | |||||||
\(968\) | 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 | \(0.981717\pi\) | |||||||
\(972\) | 14.1243 | − | 13.1171i | 0.453038 | − | 0.420733i | ||||
\(973\) | −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 | \(-0.432610\pi\) |
−0.977672 | + | 0.210135i | \(0.932610\pi\) | |||||||
\(978\) | 18.5516 | + | 37.0847i | 0.593215 | + | 1.18584i | ||||
\(979\) | − | 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 | \(-0.937888\pi\) |
0.193895 | + | 0.981022i | \(0.437888\pi\) | |||||||
\(984\) | 18.7930 | + | 6.26016i | 0.599099 | + | 0.199567i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 64.1309i | − | 2.04234i | ||||||
\(987\) | −11.6938 | + | 5.84980i | −0.372216 | + | 0.186201i | ||||
\(988\) | 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 | ||||
\(993\) | −31.0473 | + | 15.5314i | −0.985256 | + | 0.492875i | ||||
\(994\) | 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 | −0.925109 | − | 0.379701i | \(-0.876027\pi\) |
0.379701 | + | 0.925109i | \(0.376027\pi\) | |||||||
\(998\) | −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.218.14 | yes | 32 | |
3.2 | odd | 2 | inner | 525.2.j.c.218.4 | yes | 32 | |
5.2 | odd | 4 | inner | 525.2.j.c.407.4 | yes | 32 | |
5.3 | odd | 4 | inner | 525.2.j.c.407.13 | yes | 32 | |
5.4 | even | 2 | inner | 525.2.j.c.218.3 | ✓ | 32 | |
15.2 | even | 4 | inner | 525.2.j.c.407.14 | yes | 32 | |
15.8 | even | 4 | inner | 525.2.j.c.407.3 | yes | 32 | |
15.14 | odd | 2 | inner | 525.2.j.c.218.13 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.j.c.218.3 | ✓ | 32 | 5.4 | even | 2 | inner | |
525.2.j.c.218.4 | yes | 32 | 3.2 | odd | 2 | inner | |
525.2.j.c.218.13 | yes | 32 | 15.14 | odd | 2 | inner | |
525.2.j.c.218.14 | yes | 32 | 1.1 | even | 1 | trivial | |
525.2.j.c.407.3 | yes | 32 | 15.8 | even | 4 | inner | |
525.2.j.c.407.4 | yes | 32 | 5.2 | odd | 4 | inner | |
525.2.j.c.407.13 | yes | 32 | 5.3 | odd | 4 | inner | |
525.2.j.c.407.14 | yes | 32 | 15.2 | even | 4 | inner |