Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(8,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.n (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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.11 | ||
Character | \(\chi\) | \(=\) | 273.8 |
Dual form | 273.2.n.c.239.11 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.150864 | + | 0.150864i | −0.106677 | + | 0.106677i | −0.758431 | − | 0.651754i | \(-0.774034\pi\) |
0.651754 | + | 0.758431i | \(0.274034\pi\) | |||||||
\(3\) | −1.22804 | − | 1.22144i | −0.709010 | − | 0.705198i | ||||
\(4\) | 1.95448i | 0.977240i | ||||||||
\(5\) | 0.482343 | − | 0.482343i | 0.215710 | − | 0.215710i | −0.590978 | − | 0.806688i | \(-0.701258\pi\) |
0.806688 | + | 0.590978i | \(0.201258\pi\) | |||||||
\(6\) | 0.369539 | 0.000996021i | 0.150864 | 0.000406624i | ||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.596590 | − | 0.596590i | −0.210926 | − | 0.210926i | ||||
\(9\) | 0.0161717 | + | 2.99996i | 0.00539057 | + | 0.999985i | ||||
\(10\) | 0.145537i | 0.0460227i | ||||||||
\(11\) | 2.26572 | + | 2.26572i | 0.683139 | + | 0.683139i | 0.960706 | − | 0.277567i | \(-0.0895282\pi\) |
−0.277567 | + | 0.960706i | \(0.589528\pi\) | |||||||
\(12\) | 2.38728 | − | 2.40018i | 0.689148 | − | 0.692873i | ||||
\(13\) | −0.580602 | + | 3.55850i | −0.161030 | + | 0.986950i | ||||
\(14\) | − | 0.213354i | − | 0.0570214i | ||||||
\(15\) | −1.18149 | + | 0.00318447i | −0.305059 | + | 0.000822227i | ||||
\(16\) | −3.72895 | −0.932238 | ||||||||
\(17\) | 6.99624 | 1.69684 | 0.848419 | − | 0.529325i | \(-0.177555\pi\) | ||||
0.848419 | + | 0.529325i | \(0.177555\pi\) | |||||||
\(18\) | −0.455026 | − | 0.450147i | −0.107251 | − | 0.106101i | ||||
\(19\) | 1.76208 | + | 1.76208i | 0.404248 | + | 0.404248i | 0.879727 | − | 0.475479i | \(-0.157725\pi\) |
−0.475479 | + | 0.879727i | \(0.657725\pi\) | |||||||
\(20\) | 0.942729 | + | 0.942729i | 0.210801 | + | 0.210801i | ||||
\(21\) | 1.73204 | − | 0.00466839i | 0.377963 | − | 0.00101873i | ||||
\(22\) | −0.683631 | −0.145751 | ||||||||
\(23\) | −5.46061 | −1.13862 | −0.569308 | − | 0.822124i | \(-0.692789\pi\) | ||||
−0.569308 | + | 0.822124i | \(0.692789\pi\) | |||||||
\(24\) | 0.00393874 | + | 1.46134i | 0.000803993 | + | 0.298294i | ||||
\(25\) | 4.53469i | 0.906938i | ||||||||
\(26\) | −0.449258 | − | 0.624443i | −0.0881068 | − | 0.122463i | ||||
\(27\) | 3.64441 | − | 3.70382i | 0.701366 | − | 0.712801i | ||||
\(28\) | −1.38203 | − | 1.38203i | −0.261178 | − | 0.261178i | ||||
\(29\) | 2.64935i | 0.491972i | 0.969273 | + | 0.245986i | \(0.0791117\pi\) | ||||
−0.969273 | + | 0.245986i | \(0.920888\pi\) | |||||||
\(30\) | 0.177764 | − | 0.178725i | 0.0324552 | − | 0.0326306i | ||||
\(31\) | 2.48703 | + | 2.48703i | 0.446683 | + | 0.446683i | 0.894250 | − | 0.447567i | \(-0.147709\pi\) |
−0.447567 | + | 0.894250i | \(0.647709\pi\) | |||||||
\(32\) | 1.75575 | − | 1.75575i | 0.310375 | − | 0.310375i | ||||
\(33\) | −0.0149585 | − | 5.54983i | −0.00260393 | − | 0.966101i | ||||
\(34\) | −1.05548 | + | 1.05548i | −0.181014 | + | 0.181014i | ||||
\(35\) | 0.682135i | 0.115302i | ||||||||
\(36\) | −5.86335 | + | 0.0316073i | −0.977226 | + | 0.00526788i | ||||
\(37\) | 0.194897 | − | 0.194897i | 0.0320408 | − | 0.0320408i | −0.690905 | − | 0.722946i | \(-0.742788\pi\) |
0.722946 | + | 0.690905i | \(0.242788\pi\) | |||||||
\(38\) | −0.531670 | −0.0862482 | ||||||||
\(39\) | 5.05949 | − | 3.66081i | 0.810167 | − | 0.586199i | ||||
\(40\) | −0.575522 | −0.0909980 | ||||||||
\(41\) | 2.65812 | − | 2.65812i | 0.415128 | − | 0.415128i | −0.468392 | − | 0.883521i | \(-0.655167\pi\) |
0.883521 | + | 0.468392i | \(0.155167\pi\) | |||||||
\(42\) | −0.260600 | + | 0.262008i | −0.0402114 | + | 0.0404287i | ||||
\(43\) | − | 3.03374i | − | 0.462641i | −0.972878 | − | 0.231320i | \(-0.925695\pi\) | ||
0.972878 | − | 0.231320i | \(-0.0743046\pi\) | |||||||
\(44\) | −4.42829 | + | 4.42829i | −0.667591 | + | 0.667591i | ||||
\(45\) | 1.45481 | + | 1.43921i | 0.216870 | + | 0.214544i | ||||
\(46\) | 0.823811 | − | 0.823811i | 0.121464 | − | 0.121464i | ||||
\(47\) | −7.69758 | − | 7.69758i | −1.12281 | − | 1.12281i | −0.991318 | − | 0.131489i | \(-0.958024\pi\) |
−0.131489 | − | 0.991318i | \(-0.541976\pi\) | |||||||
\(48\) | 4.57931 | + | 4.55469i | 0.660966 | + | 0.657413i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −0.684123 | − | 0.684123i | −0.0967497 | − | 0.0967497i | ||||
\(51\) | −8.59168 | − | 8.54549i | −1.20308 | − | 1.19661i | ||||
\(52\) | −6.95501 | − | 1.13477i | −0.964486 | − | 0.157365i | ||||
\(53\) | − | 6.50740i | − | 0.893860i | −0.894569 | − | 0.446930i | \(-0.852517\pi\) | ||
0.894569 | − | 0.446930i | \(-0.147483\pi\) | |||||||
\(54\) | 0.00896410 | + | 1.10859i | 0.00121986 | + | 0.150859i | ||||
\(55\) | 2.18570 | 0.294720 | ||||||||
\(56\) | 0.843706 | 0.112745 | ||||||||
\(57\) | −0.0116334 | − | 4.31618i | −0.00154088 | − | 0.571691i | ||||
\(58\) | −0.399692 | − | 0.399692i | −0.0524822 | − | 0.0524822i | ||||
\(59\) | −6.12738 | − | 6.12738i | −0.797717 | − | 0.797717i | 0.185018 | − | 0.982735i | \(-0.440766\pi\) |
−0.982735 | + | 0.185018i | \(0.940766\pi\) | |||||||
\(60\) | −0.00622399 | − | 2.30920i | −0.000803513 | − | 0.298116i | ||||
\(61\) | −9.34181 | −1.19610 | −0.598048 | − | 0.801460i | \(-0.704057\pi\) | ||||
−0.598048 | + | 0.801460i | \(0.704057\pi\) | |||||||
\(62\) | −0.750407 | −0.0953018 | ||||||||
\(63\) | −2.13272 | − | 2.10985i | −0.268698 | − | 0.265817i | ||||
\(64\) | − | 6.92814i | − | 0.866018i | ||||||
\(65\) | 1.43637 | + | 1.99646i | 0.178159 | + | 0.247631i | ||||
\(66\) | 0.839528 | + | 0.835014i | 0.103339 | + | 0.102783i | ||||
\(67\) | 5.81479 | + | 5.81479i | 0.710390 | + | 0.710390i | 0.966617 | − | 0.256227i | \(-0.0824794\pi\) |
−0.256227 | + | 0.966617i | \(0.582479\pi\) | |||||||
\(68\) | 13.6740i | 1.65822i | ||||||||
\(69\) | 6.70585 | + | 6.66980i | 0.807290 | + | 0.802950i | ||||
\(70\) | −0.102910 | − | 0.102910i | −0.0123001 | − | 0.0123001i | ||||
\(71\) | −8.10653 | + | 8.10653i | −0.962068 | + | 0.962068i | −0.999306 | − | 0.0372384i | \(-0.988144\pi\) |
0.0372384 | + | 0.999306i | \(0.488144\pi\) | |||||||
\(72\) | 1.78010 | − | 1.79939i | 0.209786 | − | 0.212060i | ||||
\(73\) | 6.20581 | − | 6.20581i | 0.726335 | − | 0.726335i | −0.243553 | − | 0.969888i | \(-0.578313\pi\) |
0.969888 | + | 0.243553i | \(0.0783129\pi\) | |||||||
\(74\) | 0.0588059i | 0.00683605i | ||||||||
\(75\) | 5.53885 | − | 5.56879i | 0.639571 | − | 0.643028i | ||||
\(76\) | −3.44395 | + | 3.44395i | −0.395048 | + | 0.395048i | ||||
\(77\) | −3.20421 | −0.365153 | ||||||||
\(78\) | −0.211011 | + | 1.31558i | −0.0238923 | + | 0.148960i | ||||
\(79\) | 3.96770 | 0.446401 | 0.223201 | − | 0.974773i | \(-0.428349\pi\) | ||||
0.223201 | + | 0.974773i | \(0.428349\pi\) | |||||||
\(80\) | −1.79863 | + | 1.79863i | −0.201093 | + | 0.201093i | ||||
\(81\) | −8.99948 | + | 0.0970288i | −0.999942 | + | 0.0107810i | ||||
\(82\) | 0.802031i | 0.0885695i | ||||||||
\(83\) | 9.36521 | − | 9.36521i | 1.02796 | − | 1.02796i | 0.0283674 | − | 0.999598i | \(-0.490969\pi\) |
0.999598 | − | 0.0283674i | \(-0.00903082\pi\) | |||||||
\(84\) | 0.00912427 | + | 3.38525i | 0.000995539 | + | 0.369361i | ||||
\(85\) | 3.37459 | − | 3.37459i | 0.366025 | − | 0.366025i | ||||
\(86\) | 0.457683 | + | 0.457683i | 0.0493533 | + | 0.0493533i | ||||
\(87\) | 3.23602 | − | 3.25351i | 0.346938 | − | 0.348813i | ||||
\(88\) | − | 2.70341i | − | 0.288184i | ||||||
\(89\) | 8.54508 | + | 8.54508i | 0.905777 | + | 0.905777i | 0.995928 | − | 0.0901515i | \(-0.0287351\pi\) |
−0.0901515 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(90\) | −0.436604 | + | 0.00235358i | −0.0460221 | + | 0.000248089i | ||||
\(91\) | −2.10569 | − | 2.92678i | −0.220736 | − | 0.306810i | ||||
\(92\) | − | 10.6726i | − | 1.11270i | ||||||
\(93\) | −0.0164196 | − | 6.09192i | −0.00170263 | − | 0.631703i | ||||
\(94\) | 2.32258 | 0.239556 | ||||||||
\(95\) | 1.69985 | 0.174401 | ||||||||
\(96\) | −4.30067 | + | 0.0115916i | −0.438935 | + | 0.00118306i | ||||
\(97\) | 7.88241 | + | 7.88241i | 0.800338 | + | 0.800338i | 0.983148 | − | 0.182810i | \(-0.0585195\pi\) |
−0.182810 | + | 0.983148i | \(0.558519\pi\) | |||||||
\(98\) | 0.150864 | + | 0.150864i | 0.0152396 | + | 0.0152396i | ||||
\(99\) | −6.76041 | + | 6.83369i | −0.679446 | + | 0.686811i | ||||
\(100\) | −8.86296 | −0.886296 | ||||||||
\(101\) | 4.29867 | 0.427734 | 0.213867 | − | 0.976863i | \(-0.431394\pi\) | ||||
0.213867 | + | 0.976863i | \(0.431394\pi\) | |||||||
\(102\) | 2.58539 | − | 0.00696841i | 0.255992 | − | 0.000689975i | ||||
\(103\) | − | 2.69298i | − | 0.265348i | −0.991160 | − | 0.132674i | \(-0.957644\pi\) | ||
0.991160 | − | 0.132674i | \(-0.0423563\pi\) | |||||||
\(104\) | 2.46935 | − | 1.77658i | 0.242139 | − | 0.174208i | ||||
\(105\) | 0.833187 | − | 0.837691i | 0.0813107 | − | 0.0817502i | ||||
\(106\) | 0.981734 | + | 0.981734i | 0.0953545 | + | 0.0953545i | ||||
\(107\) | − | 14.6863i | − | 1.41978i | −0.704313 | − | 0.709889i | \(-0.748745\pi\) | ||
0.704313 | − | 0.709889i | \(-0.251255\pi\) | |||||||
\(108\) | 7.23905 | + | 7.12292i | 0.696578 | + | 0.685403i | ||||
\(109\) | 14.5346 | + | 14.5346i | 1.39216 | + | 1.39216i | 0.820464 | + | 0.571699i | \(0.193715\pi\) |
0.571699 | + | 0.820464i | \(0.306285\pi\) | |||||||
\(110\) | −0.329745 | + | 0.329745i | −0.0314399 | + | 0.0314399i | ||||
\(111\) | −0.477396 | + | 0.00128673i | −0.0453124 | + | 0.000122131i | ||||
\(112\) | 2.63677 | − | 2.63677i | 0.249151 | − | 0.249151i | ||||
\(113\) | 12.7034i | 1.19503i | 0.801856 | + | 0.597517i | \(0.203846\pi\) | ||||
−0.801856 | + | 0.597517i | \(0.796154\pi\) | |||||||
\(114\) | 0.652912 | + | 0.649402i | 0.0611508 | + | 0.0608221i | ||||
\(115\) | −2.63388 | + | 2.63388i | −0.245611 | + | 0.245611i | ||||
\(116\) | −5.17810 | −0.480774 | ||||||||
\(117\) | −10.6847 | − | 1.68423i | −0.987803 | − | 0.155707i | ||||
\(118\) | 1.84881 | 0.170197 | ||||||||
\(119\) | −4.94709 | + | 4.94709i | −0.453499 | + | 0.453499i | ||||
\(120\) | 0.706765 | + | 0.702965i | 0.0645185 | + | 0.0641716i | ||||
\(121\) | − | 0.733069i | − | 0.0666427i | ||||||
\(122\) | 1.40935 | − | 1.40935i | 0.127596 | − | 0.127596i | ||||
\(123\) | −6.51101 | + | 0.0175492i | −0.587078 | + | 0.00158235i | ||||
\(124\) | −4.86084 | + | 4.86084i | −0.436517 | + | 0.436517i | ||||
\(125\) | 4.59899 | + | 4.59899i | 0.411346 | + | 0.411346i | ||||
\(126\) | 0.640054 | − | 0.00345031i | 0.0570205 | − | 0.000307378i | ||||
\(127\) | − | 7.09824i | − | 0.629867i | −0.949114 | − | 0.314934i | \(-0.898018\pi\) | ||
0.949114 | − | 0.314934i | \(-0.101982\pi\) | |||||||
\(128\) | 4.55670 | + | 4.55670i | 0.402759 | + | 0.402759i | ||||
\(129\) | −3.70553 | + | 3.72556i | −0.326254 | + | 0.328017i | ||||
\(130\) | −0.517892 | − | 0.0844988i | −0.0454221 | − | 0.00741104i | ||||
\(131\) | − | 0.537316i | − | 0.0469455i | −0.999724 | − | 0.0234728i | \(-0.992528\pi\) | ||
0.999724 | − | 0.0234728i | \(-0.00747230\pi\) | |||||||
\(132\) | 10.8470 | − | 0.0292360i | 0.944112 | − | 0.00254467i | ||||
\(133\) | −2.49195 | −0.216080 | ||||||||
\(134\) | −1.75449 | −0.151565 | ||||||||
\(135\) | −0.0286600 | − | 3.54436i | −0.00246666 | − | 0.305050i | ||||
\(136\) | −4.17389 | − | 4.17389i | −0.357908 | − | 0.357908i | ||||
\(137\) | 0.824478 | + | 0.824478i | 0.0704399 | + | 0.0704399i | 0.741449 | − | 0.671009i | \(-0.234139\pi\) |
−0.671009 | + | 0.741449i | \(0.734139\pi\) | |||||||
\(138\) | −2.01791 | + | 0.00543888i | −0.171776 | + | 0.000462988i | ||||
\(139\) | −11.0135 | −0.934154 | −0.467077 | − | 0.884217i | \(-0.654693\pi\) | ||||
−0.467077 | + | 0.884217i | \(0.654693\pi\) | |||||||
\(140\) | −1.33322 | −0.112678 | ||||||||
\(141\) | 0.0508201 | + | 18.8551i | 0.00427983 | + | 1.58788i | ||||
\(142\) | − | 2.44597i | − | 0.205261i | ||||||
\(143\) | −9.37802 | + | 6.74706i | −0.784229 | + | 0.564218i | ||||
\(144\) | −0.0603035 | − | 11.1867i | −0.00502529 | − | 0.932224i | ||||
\(145\) | 1.27789 | + | 1.27789i | 0.106123 | + | 0.106123i | ||||
\(146\) | 1.87247i | 0.154967i | ||||||||
\(147\) | −1.22144 | + | 1.22804i | −0.100743 | + | 0.101287i | ||||
\(148\) | 0.380922 | + | 0.380922i | 0.0313116 | + | 0.0313116i | ||||
\(149\) | 8.65446 | − | 8.65446i | 0.709001 | − | 0.709001i | −0.257324 | − | 0.966325i | \(-0.582841\pi\) |
0.966325 | + | 0.257324i | \(0.0828409\pi\) | |||||||
\(150\) | 0.00451665 | + | 1.67575i | 0.000368783 | + | 0.136824i | ||||
\(151\) | −1.97985 | + | 1.97985i | −0.161118 | + | 0.161118i | −0.783062 | − | 0.621944i | \(-0.786343\pi\) |
0.621944 | + | 0.783062i | \(0.286343\pi\) | |||||||
\(152\) | − | 2.10248i | − | 0.170533i | ||||||
\(153\) | 0.113141 | + | 20.9884i | 0.00914692 | + | 1.69681i | ||||
\(154\) | 0.483400 | − | 0.483400i | 0.0389535 | − | 0.0389535i | ||||
\(155\) | 2.39920 | 0.192708 | ||||||||
\(156\) | 7.15498 | + | 9.88867i | 0.572857 | + | 0.791728i | ||||
\(157\) | 3.37297 | 0.269192 | 0.134596 | − | 0.990901i | \(-0.457026\pi\) | ||||
0.134596 | + | 0.990901i | \(0.457026\pi\) | |||||||
\(158\) | −0.598585 | + | 0.598585i | −0.0476208 | + | 0.0476208i | ||||
\(159\) | −7.94839 | + | 7.99135i | −0.630348 | + | 0.633755i | ||||
\(160\) | − | 1.69374i | − | 0.133902i | ||||||
\(161\) | 3.86123 | − | 3.86123i | 0.304308 | − | 0.304308i | ||||
\(162\) | 1.34306 | − | 1.37234i | 0.105521 | − | 0.107821i | ||||
\(163\) | 8.94685 | − | 8.94685i | 0.700772 | − | 0.700772i | −0.263805 | − | 0.964576i | \(-0.584977\pi\) |
0.964576 | + | 0.263805i | \(0.0849774\pi\) | |||||||
\(164\) | 5.19524 | + | 5.19524i | 0.405680 | + | 0.405680i | ||||
\(165\) | −2.68413 | − | 2.66970i | −0.208959 | − | 0.207836i | ||||
\(166\) | 2.82575i | 0.219321i | ||||||||
\(167\) | 5.08432 | + | 5.08432i | 0.393436 | + | 0.393436i | 0.875910 | − | 0.482474i | \(-0.160262\pi\) |
−0.482474 | + | 0.875910i | \(0.660262\pi\) | |||||||
\(168\) | −1.03611 | − | 1.03054i | −0.0799373 | − | 0.0795075i | ||||
\(169\) | −12.3258 | − | 4.13214i | −0.948139 | − | 0.317857i | ||||
\(170\) | 1.01821i | 0.0780931i | ||||||||
\(171\) | −5.25766 | + | 5.31465i | −0.402063 | + | 0.406422i | ||||
\(172\) | 5.92938 | 0.452111 | ||||||||
\(173\) | −17.6050 | −1.33849 | −0.669243 | − | 0.743044i | \(-0.733381\pi\) | ||||
−0.669243 | + | 0.743044i | \(0.733381\pi\) | |||||||
\(174\) | 0.00263881 | + | 0.979038i | 0.000200047 | + | 0.0742207i | ||||
\(175\) | −3.20651 | − | 3.20651i | −0.242389 | − | 0.242389i | ||||
\(176\) | −8.44874 | − | 8.44874i | −0.636848 | − | 0.636848i | ||||
\(177\) | 0.0404536 | + | 15.0089i | 0.00304068 | + | 1.12814i | ||||
\(178\) | −2.57830 | −0.193251 | ||||||||
\(179\) | 11.2103 | 0.837895 | 0.418947 | − | 0.908011i | \(-0.362399\pi\) | ||||
0.418947 | + | 0.908011i | \(0.362399\pi\) | |||||||
\(180\) | −2.81290 | + | 2.84339i | −0.209661 | + | 0.211934i | ||||
\(181\) | − | 23.1248i | − | 1.71885i | −0.511258 | − | 0.859427i | \(-0.670820\pi\) | ||
0.511258 | − | 0.859427i | \(-0.329180\pi\) | |||||||
\(182\) | 0.759221 | + | 0.123874i | 0.0562772 | + | 0.00918215i | ||||
\(183\) | 11.4721 | + | 11.4105i | 0.848045 | + | 0.843485i | ||||
\(184\) | 3.25775 | + | 3.25775i | 0.240164 | + | 0.240164i | ||||
\(185\) | − | 0.188014i | − | 0.0138231i | ||||||
\(186\) | 0.921531 | + | 0.916577i | 0.0675700 | + | 0.0672067i | ||||
\(187\) | 15.8515 | + | 15.8515i | 1.15918 | + | 1.15918i | ||||
\(188\) | 15.0448 | − | 15.0448i | 1.09725 | − | 1.09725i | ||||
\(189\) | 0.0420151 | + | 5.19598i | 0.00305615 | + | 0.377952i | ||||
\(190\) | −0.256447 | + | 0.256447i | −0.0186046 | + | 0.0186046i | ||||
\(191\) | 10.1254i | 0.732651i | 0.930487 | + | 0.366326i | \(0.119384\pi\) | ||||
−0.930487 | + | 0.366326i | \(0.880616\pi\) | |||||||
\(192\) | −8.46231 | + | 8.50805i | −0.610714 | + | 0.614015i | ||||
\(193\) | −9.40769 | + | 9.40769i | −0.677180 | + | 0.677180i | −0.959361 | − | 0.282181i | \(-0.908942\pi\) |
0.282181 | + | 0.959361i | \(0.408942\pi\) | |||||||
\(194\) | −2.37835 | −0.170756 | ||||||||
\(195\) | 0.674643 | − | 4.20617i | 0.0483122 | − | 0.301210i | ||||
\(196\) | 1.95448 | 0.139606 | ||||||||
\(197\) | 17.9619 | − | 17.9619i | 1.27973 | − | 1.27973i | 0.338913 | − | 0.940818i | \(-0.389941\pi\) |
0.940818 | − | 0.338913i | \(-0.110059\pi\) | |||||||
\(198\) | −0.0110555 | − | 2.05086i | −0.000785679 | − | 0.145749i | ||||
\(199\) | − | 16.1933i | − | 1.14792i | −0.818885 | − | 0.573958i | \(-0.805407\pi\) | ||
0.818885 | − | 0.573958i | \(-0.194593\pi\) | |||||||
\(200\) | 2.70535 | − | 2.70535i | 0.191297 | − | 0.191297i | ||||
\(201\) | −0.0383898 | − | 14.2432i | −0.00270781 | − | 1.00464i | ||||
\(202\) | −0.648516 | + | 0.648516i | −0.0456294 | + | 0.0456294i | ||||
\(203\) | −1.87337 | − | 1.87337i | −0.131485 | − | 0.131485i | ||||
\(204\) | 16.7020 | − | 16.7923i | 1.16937 | − | 1.17569i | ||||
\(205\) | − | 2.56425i | − | 0.179095i | ||||||
\(206\) | 0.406275 | + | 0.406275i | 0.0283065 | + | 0.0283065i | ||||
\(207\) | −0.0883073 | − | 16.3816i | −0.00613779 | − | 1.13860i | ||||
\(208\) | 2.16504 | − | 13.2695i | 0.150118 | − | 0.920072i | ||||
\(209\) | 7.98473i | 0.552316i | ||||||||
\(210\) | 0.000679421 | 0.252076i | 4.68845e−5 | 0.0173949i | ||||||
\(211\) | −0.155025 | −0.0106723 | −0.00533617 | − | 0.999986i | \(-0.501699\pi\) | ||||
−0.00533617 | + | 0.999986i | \(0.501699\pi\) | |||||||
\(212\) | 12.7186 | 0.873515 | ||||||||
\(213\) | 19.8568 | − | 0.0535201i | 1.36056 | − | 0.00366713i | ||||
\(214\) | 2.21564 | + | 2.21564i | 0.151458 | + | 0.151458i | ||||
\(215\) | −1.46330 | − | 1.46330i | −0.0997964 | − | 0.0997964i | ||||
\(216\) | −4.38388 | + | 0.0354484i | −0.298285 | + | 0.00241196i | ||||
\(217\) | −3.51719 | −0.238762 | ||||||||
\(218\) | −4.38551 | −0.297024 | ||||||||
\(219\) | −15.2010 | + | 0.0409713i | −1.02719 | + | 0.00276859i | ||||
\(220\) | 4.27191i | 0.288012i | ||||||||
\(221\) | −4.06203 | + | 24.8961i | −0.273242 | + | 1.67469i | ||||
\(222\) | 0.0718279 | − | 0.0722161i | 0.00482077 | − | 0.00484683i | ||||
\(223\) | −1.28745 | − | 1.28745i | −0.0862142 | − | 0.0862142i | 0.662685 | − | 0.748899i | \(-0.269417\pi\) |
−0.748899 | + | 0.662685i | \(0.769417\pi\) | |||||||
\(224\) | 2.48300i | 0.165902i | ||||||||
\(225\) | −13.6039 | + | 0.0733337i | −0.906925 | + | 0.00488891i | ||||
\(226\) | −1.91649 | − | 1.91649i | −0.127483 | − | 0.127483i | ||||
\(227\) | −10.2367 | + | 10.2367i | −0.679431 | + | 0.679431i | −0.959871 | − | 0.280440i | \(-0.909520\pi\) |
0.280440 | + | 0.959871i | \(0.409520\pi\) | |||||||
\(228\) | 8.43588 | − | 0.0227373i | 0.558680 | − | 0.00150581i | ||||
\(229\) | 15.8188 | − | 15.8188i | 1.04533 | − | 1.04533i | 0.0464123 | − | 0.998922i | \(-0.485221\pi\) |
0.998922 | − | 0.0464123i | \(-0.0147788\pi\) | |||||||
\(230\) | − | 0.794719i | − | 0.0524022i | ||||||
\(231\) | 3.93490 | + | 3.91374i | 0.258897 | + | 0.257505i | ||||
\(232\) | 1.58057 | − | 1.58057i | 0.103770 | − | 0.103770i | ||||
\(233\) | −26.3871 | −1.72868 | −0.864339 | − | 0.502909i | \(-0.832263\pi\) | ||||
−0.864339 | + | 0.502909i | \(0.832263\pi\) | |||||||
\(234\) | 1.86604 | − | 1.35785i | 0.121987 | − | 0.0887657i | ||||
\(235\) | −7.42574 | −0.484402 | ||||||||
\(236\) | 11.9758 | − | 11.9758i | 0.779561 | − | 0.779561i | ||||
\(237\) | −4.87250 | − | 4.84631i | −0.316503 | − | 0.314801i | ||||
\(238\) | − | 1.49268i | − | 0.0967561i | ||||||
\(239\) | −1.97439 | + | 1.97439i | −0.127713 | + | 0.127713i | −0.768074 | − | 0.640361i | \(-0.778785\pi\) |
0.640361 | + | 0.768074i | \(0.278785\pi\) | |||||||
\(240\) | 4.40572 | − | 0.0118747i | 0.284388 | − | 0.000766511i | ||||
\(241\) | 1.72902 | − | 1.72902i | 0.111376 | − | 0.111376i | −0.649222 | − | 0.760599i | \(-0.724906\pi\) |
0.760599 | + | 0.649222i | \(0.224906\pi\) | |||||||
\(242\) | 0.110594 | + | 0.110594i | 0.00710925 | + | 0.00710925i | ||||
\(243\) | 11.1702 | + | 10.8732i | 0.716572 | + | 0.697514i | ||||
\(244\) | − | 18.2584i | − | 1.16887i | ||||||
\(245\) | −0.482343 | − | 0.482343i | −0.0308157 | − | 0.0308157i | ||||
\(246\) | 0.979632 | − | 0.984927i | 0.0624591 | − | 0.0627967i | ||||
\(247\) | −7.29341 | + | 5.24728i | −0.464069 | + | 0.333877i | ||||
\(248\) | − | 2.96747i | − | 0.188435i | ||||||
\(249\) | −22.9399 | + | 0.0618300i | −1.45376 | + | 0.00391832i | ||||
\(250\) | −1.38765 | −0.0877625 | ||||||||
\(251\) | −26.0371 | −1.64345 | −0.821724 | − | 0.569885i | \(-0.806988\pi\) | ||||
−0.821724 | + | 0.569885i | \(0.806988\pi\) | |||||||
\(252\) | 4.12367 | − | 4.16837i | 0.259767 | − | 0.262582i | ||||
\(253\) | −12.3722 | − | 12.3722i | −0.777833 | − | 0.777833i | ||||
\(254\) | 1.07087 | + | 1.07087i | 0.0671925 | + | 0.0671925i | ||||
\(255\) | −8.26599 | + | 0.0222793i | −0.517636 | + | 0.00139519i | ||||
\(256\) | 12.4814 | 0.780087 | ||||||||
\(257\) | 2.75007 | 0.171545 | 0.0857724 | − | 0.996315i | \(-0.472664\pi\) | ||||
0.0857724 | + | 0.996315i | \(0.472664\pi\) | |||||||
\(258\) | −0.00302167 | − | 1.12109i | −0.000188121 | − | 0.0697958i | ||||
\(259\) | 0.275626i | 0.0171265i | ||||||||
\(260\) | −3.90205 | + | 2.80735i | −0.241995 | + | 0.174104i | ||||
\(261\) | −7.94793 | + | 0.0428445i | −0.491964 | + | 0.00265201i | ||||
\(262\) | 0.0810618 | + | 0.0810618i | 0.00500802 | + | 0.00500802i | ||||
\(263\) | − | 2.53223i | − | 0.156144i | −0.996948 | − | 0.0780720i | \(-0.975124\pi\) | ||
0.996948 | − | 0.0780720i | \(-0.0248764\pi\) | |||||||
\(264\) | −3.30205 | + | 3.31990i | −0.203227 | + | 0.204325i | ||||
\(265\) | −3.13879 | − | 3.13879i | −0.192815 | − | 0.192815i | ||||
\(266\) | 0.375947 | − | 0.375947i | 0.0230508 | − | 0.0230508i | ||||
\(267\) | −0.0564154 | − | 20.9310i | −0.00345257 | − | 1.28096i | ||||
\(268\) | −11.3649 | + | 11.3649i | −0.694221 | + | 0.694221i | ||||
\(269\) | − | 21.4014i | − | 1.30487i | −0.757845 | − | 0.652435i | \(-0.773748\pi\) | ||
0.757845 | − | 0.652435i | \(-0.226252\pi\) | |||||||
\(270\) | 0.539042 | + | 0.530395i | 0.0328051 | + | 0.0322788i | ||||
\(271\) | 1.24920 | − | 1.24920i | 0.0758836 | − | 0.0758836i | −0.668146 | − | 0.744030i | \(-0.732912\pi\) |
0.744030 | + | 0.668146i | \(0.232912\pi\) | |||||||
\(272\) | −26.0887 | −1.58186 | ||||||||
\(273\) | −0.989016 | + | 6.16619i | −0.0598580 | + | 0.373195i | ||||
\(274\) | −0.248769 | −0.0150287 | ||||||||
\(275\) | −10.2743 | + | 10.2743i | −0.619565 | + | 0.619565i | ||||
\(276\) | −13.0360 | + | 13.1065i | −0.784675 | + | 0.788916i | ||||
\(277\) | 13.0013i | 0.781173i | 0.920566 | + | 0.390586i | \(0.127728\pi\) | ||||
−0.920566 | + | 0.390586i | \(0.872272\pi\) | |||||||
\(278\) | 1.66155 | − | 1.66155i | 0.0996530 | − | 0.0996530i | ||||
\(279\) | −7.42075 | + | 7.50119i | −0.444269 | + | 0.449085i | ||||
\(280\) | 0.406955 | − | 0.406955i | 0.0243202 | − | 0.0243202i | ||||
\(281\) | 8.36416 | + | 8.36416i | 0.498964 | + | 0.498964i | 0.911115 | − | 0.412151i | \(-0.135222\pi\) |
−0.412151 | + | 0.911115i | \(0.635222\pi\) | |||||||
\(282\) | −2.85222 | − | 2.83689i | −0.169848 | − | 0.168934i | ||||
\(283\) | − | 9.91078i | − | 0.589135i | −0.955631 | − | 0.294567i | \(-0.904824\pi\) | ||
0.955631 | − | 0.294567i | \(-0.0951755\pi\) | |||||||
\(284\) | −15.8440 | − | 15.8440i | −0.940171 | − | 0.940171i | ||||
\(285\) | −2.08749 | − | 2.07626i | −0.123652 | − | 0.122987i | ||||
\(286\) | 0.396918 | − | 2.43270i | 0.0234702 | − | 0.143849i | ||||
\(287\) | 3.75915i | 0.221895i | ||||||||
\(288\) | 5.29556 | + | 5.23877i | 0.312044 | + | 0.308697i | ||||
\(289\) | 31.9474 | 1.87926 | ||||||||
\(290\) | −0.385577 | −0.0226419 | ||||||||
\(291\) | −0.0520404 | − | 19.3078i | −0.00305066 | − | 1.13184i | ||||
\(292\) | 12.1291 | + | 12.1291i | 0.709804 | + | 0.709804i | ||||
\(293\) | −5.43142 | − | 5.43142i | −0.317307 | − | 0.317307i | 0.530425 | − | 0.847732i | \(-0.322032\pi\) |
−0.847732 | + | 0.530425i | \(0.822032\pi\) | |||||||
\(294\) | −0.000996021 | − | 0.369539i | −5.80891e−5 | − | 0.0215520i | ||||
\(295\) | −5.91100 | −0.344152 | ||||||||
\(296\) | −0.232547 | −0.0135165 | ||||||||
\(297\) | 16.6490 | − | 0.134625i | 0.966073 | − | 0.00781173i | ||||
\(298\) | 2.61130i | 0.151268i | ||||||||
\(299\) | 3.17044 | − | 19.4316i | 0.183351 | − | 1.12376i | ||||
\(300\) | 10.8841 | + | 10.8256i | 0.628393 | + | 0.625015i | ||||
\(301\) | 2.14518 | + | 2.14518i | 0.123646 | + | 0.123646i | ||||
\(302\) | − | 0.597377i | − | 0.0343752i | ||||||
\(303\) | −5.27895 | − | 5.25057i | −0.303268 | − | 0.301637i | ||||
\(304\) | −6.57070 | − | 6.57070i | −0.376856 | − | 0.376856i | ||||
\(305\) | −4.50596 | + | 4.50596i | −0.258010 | + | 0.258010i | ||||
\(306\) | −3.18347 | − | 3.14934i | −0.181987 | − | 0.180036i | ||||
\(307\) | 14.3434 | − | 14.3434i | 0.818619 | − | 0.818619i | −0.167289 | − | 0.985908i | \(-0.553501\pi\) |
0.985908 | + | 0.167289i | \(0.0535013\pi\) | |||||||
\(308\) | − | 6.26255i | − | 0.356842i | ||||||
\(309\) | −3.28932 | + | 3.30710i | −0.187123 | + | 0.188134i | ||||
\(310\) | −0.361954 | + | 0.361954i | −0.0205576 | + | 0.0205576i | ||||
\(311\) | 11.0703 | 0.627742 | 0.313871 | − | 0.949466i | \(-0.398374\pi\) | ||||
0.313871 | + | 0.949466i | \(0.398374\pi\) | |||||||
\(312\) | −5.20245 | − | 0.834438i | −0.294531 | − | 0.0472408i | ||||
\(313\) | 1.23211 | 0.0696430 | 0.0348215 | − | 0.999394i | \(-0.488914\pi\) | ||||
0.0348215 | + | 0.999394i | \(0.488914\pi\) | |||||||
\(314\) | −0.508861 | + | 0.508861i | −0.0287167 | + | 0.0287167i | ||||
\(315\) | −2.04638 | + | 0.0110313i | −0.115300 | + | 0.000621543i | ||||
\(316\) | 7.75479i | 0.436241i | ||||||||
\(317\) | 6.47040 | − | 6.47040i | 0.363414 | − | 0.363414i | −0.501654 | − | 0.865068i | \(-0.667275\pi\) |
0.865068 | + | 0.501654i | \(0.167275\pi\) | |||||||
\(318\) | −0.00648150 | − | 2.40474i | −0.000363465 | − | 0.134851i | ||||
\(319\) | −6.00267 | + | 6.00267i | −0.336085 | + | 0.336085i | ||||
\(320\) | −3.34174 | − | 3.34174i | −0.186809 | − | 0.186809i | ||||
\(321\) | −17.9384 | + | 18.0354i | −1.00123 | + | 1.00664i | ||||
\(322\) | 1.16505i | 0.0649254i | ||||||||
\(323\) | 12.3279 | + | 12.3279i | 0.685944 | + | 0.685944i | ||||
\(324\) | −0.189641 | − | 17.5893i | −0.0105356 | − | 0.977183i | ||||
\(325\) | −16.1367 | − | 2.63285i | −0.895102 | − | 0.146044i | ||||
\(326\) | 2.69952i | 0.149513i | ||||||||
\(327\) | −0.0959588 | − | 35.6022i | −0.00530654 | − | 1.96881i | ||||
\(328\) | −3.17161 | −0.175123 | ||||||||
\(329\) | 10.8860 | 0.600166 | ||||||||
\(330\) | 0.807703 | − | 0.00217700i | 0.0444626 | − | 0.000119840i | ||||
\(331\) | 18.7507 | + | 18.7507i | 1.03063 | + | 1.03063i | 0.999516 | + | 0.0311157i | \(0.00990603\pi\) |
0.0311157 | + | 0.999516i | \(0.490094\pi\) | |||||||
\(332\) | 18.3041 | + | 18.3041i | 1.00457 | + | 1.00457i | ||||
\(333\) | 0.587834 | + | 0.581530i | 0.0322131 | + | 0.0318676i | ||||
\(334\) | −1.53409 | −0.0839414 | ||||||||
\(335\) | 5.60944 | 0.306477 | ||||||||
\(336\) | −6.45871 | + | 0.0174082i | −0.352352 | + | 0.000949694i | ||||
\(337\) | 33.9505i | 1.84940i | 0.380696 | + | 0.924700i | \(0.375684\pi\) | ||||
−0.380696 | + | 0.924700i | \(0.624316\pi\) | |||||||
\(338\) | 2.48292 | − | 1.23613i | 0.135053 | − | 0.0672367i | ||||
\(339\) | 15.5164 | − | 15.6003i | 0.842736 | − | 0.847291i | ||||
\(340\) | 6.59556 | + | 6.59556i | 0.357695 | + | 0.357695i | ||||
\(341\) | 11.2698i | 0.610293i | ||||||||
\(342\) | −0.00859800 | − | 1.59499i | −0.000464927 | − | 0.0862469i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −1.80990 | + | 1.80990i | −0.0975832 | + | 0.0975832i | ||||
\(345\) | 6.45165 | − | 0.0173892i | 0.347345 | − | 0.000936201i | ||||
\(346\) | 2.65597 | − | 2.65597i | 0.142786 | − | 0.142786i | ||||
\(347\) | − | 15.9489i | − | 0.856182i | −0.903736 | − | 0.428091i | \(-0.859186\pi\) | ||
0.903736 | − | 0.428091i | \(-0.140814\pi\) | |||||||
\(348\) | 6.35892 | + | 6.32473i | 0.340874 | + | 0.339041i | ||||
\(349\) | 0.619415 | − | 0.619415i | 0.0331565 | − | 0.0331565i | −0.690334 | − | 0.723491i | \(-0.742536\pi\) |
0.723491 | + | 0.690334i | \(0.242536\pi\) | |||||||
\(350\) | 0.967497 | 0.0517149 | ||||||||
\(351\) | 11.0641 | + | 15.1191i | 0.590558 | + | 0.806995i | ||||
\(352\) | 7.95604 | 0.424058 | ||||||||
\(353\) | 1.55571 | − | 1.55571i | 0.0828023 | − | 0.0828023i | −0.664493 | − | 0.747295i | \(-0.731352\pi\) |
0.747295 | + | 0.664493i | \(0.231352\pi\) | |||||||
\(354\) | −2.27041 | − | 2.25821i | −0.120671 | − | 0.120022i | ||||
\(355\) | 7.82025i | 0.415056i | ||||||||
\(356\) | −16.7012 | + | 16.7012i | −0.885161 | + | 0.885161i | ||||
\(357\) | 12.1178 | − | 0.0326612i | 0.641342 | − | 0.00172861i | ||||
\(358\) | −1.69123 | + | 1.69123i | −0.0893843 | + | 0.0893843i | ||||
\(359\) | 14.1096 | + | 14.1096i | 0.744678 | + | 0.744678i | 0.973474 | − | 0.228796i | \(-0.0734790\pi\) |
−0.228796 | + | 0.973474i | \(0.573479\pi\) | |||||||
\(360\) | −0.00930717 | − | 1.72654i | −0.000490531 | − | 0.0909966i | ||||
\(361\) | − | 12.7902i | − | 0.673166i | ||||||
\(362\) | 3.48871 | + | 3.48871i | 0.183363 | + | 0.183363i | ||||
\(363\) | −0.895400 | + | 0.900240i | −0.0469963 | + | 0.0472503i | ||||
\(364\) | 5.72034 | − | 4.11553i | 0.299827 | − | 0.215712i | ||||
\(365\) | − | 5.98665i | − | 0.313356i | ||||||
\(366\) | −3.45217 | + | 0.00930464i | −0.180448 | + | 0.000486361i | ||||
\(367\) | −5.46456 | −0.285248 | −0.142624 | − | 0.989777i | \(-0.545554\pi\) | ||||
−0.142624 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(368\) | 20.3623 | 1.06146 | ||||||||
\(369\) | 8.01723 | + | 7.93125i | 0.417360 | + | 0.412885i | ||||
\(370\) | 0.0283646 | + | 0.0283646i | 0.00147461 | + | 0.00147461i | ||||
\(371\) | 4.60142 | + | 4.60142i | 0.238894 | + | 0.238894i | ||||
\(372\) | 11.9065 | − | 0.0320918i | 0.617326 | − | 0.00166388i | ||||
\(373\) | −20.5478 | −1.06393 | −0.531963 | − | 0.846767i | \(-0.678546\pi\) | ||||
−0.531963 | + | 0.846767i | \(0.678546\pi\) | |||||||
\(374\) | −4.78285 | −0.247315 | ||||||||
\(375\) | −0.0303630 | − | 11.2651i | −0.00156794 | − | 0.581729i | ||||
\(376\) | 9.18460i | 0.473659i | ||||||||
\(377\) | −9.42770 | − | 1.53822i | −0.485551 | − | 0.0792222i | ||||
\(378\) | −0.790227 | − | 0.777550i | −0.0406449 | − | 0.0399929i | ||||
\(379\) | 17.0497 | + | 17.0497i | 0.875786 | + | 0.875786i | 0.993095 | − | 0.117309i | \(-0.0374269\pi\) |
−0.117309 | + | 0.993095i | \(0.537427\pi\) | |||||||
\(380\) | 3.32232i | 0.170432i | ||||||||
\(381\) | −8.67007 | + | 8.71694i | −0.444181 | + | 0.446582i | ||||
\(382\) | −1.52757 | − | 1.52757i | −0.0781572 | − | 0.0781572i | ||||
\(383\) | 20.0335 | − | 20.0335i | 1.02366 | − | 1.02366i | 0.0239518 | − | 0.999713i | \(-0.492375\pi\) |
0.999713 | − | 0.0239518i | \(-0.00762484\pi\) | |||||||
\(384\) | −0.0300838 | − | 11.1616i | −0.00153521 | − | 0.569586i | ||||
\(385\) | −1.54552 | + | 1.54552i | −0.0787672 | + | 0.0787672i | ||||
\(386\) | − | 2.83857i | − | 0.144479i | ||||||
\(387\) | 9.10109 | − | 0.0490607i | 0.462634 | − | 0.00249390i | ||||
\(388\) | −15.4060 | + | 15.4060i | −0.782122 | + | 0.782122i | ||||
\(389\) | 4.65272 | 0.235902 | 0.117951 | − | 0.993019i | \(-0.462367\pi\) | ||||
0.117951 | + | 0.993019i | \(0.462367\pi\) | |||||||
\(390\) | 0.532782 | + | 0.736341i | 0.0269785 | + | 0.0372861i | ||||
\(391\) | −38.2037 | −1.93205 | ||||||||
\(392\) | −0.596590 | + | 0.596590i | −0.0301324 | + | 0.0301324i | ||||
\(393\) | −0.656299 | + | 0.659846i | −0.0331059 | + | 0.0332848i | ||||
\(394\) | 5.41961i | 0.273036i | ||||||||
\(395\) | 1.91379 | − | 1.91379i | 0.0962933 | − | 0.0962933i | ||||
\(396\) | −13.3563 | − | 13.2131i | −0.671180 | − | 0.663982i | ||||
\(397\) | −18.4669 | + | 18.4669i | −0.926827 | + | 0.926827i | −0.997500 | − | 0.0706727i | \(-0.977485\pi\) |
0.0706727 | + | 0.997500i | \(0.477485\pi\) | |||||||
\(398\) | 2.44300 | + | 2.44300i | 0.122456 | + | 0.122456i | ||||
\(399\) | 3.06022 | + | 3.04377i | 0.153203 | + | 0.152379i | ||||
\(400\) | − | 16.9096i | − | 0.845482i | ||||||
\(401\) | −8.87467 | − | 8.87467i | −0.443180 | − | 0.443180i | 0.449899 | − | 0.893079i | \(-0.351460\pi\) |
−0.893079 | + | 0.449899i | \(0.851460\pi\) | |||||||
\(402\) | 2.15459 | + | 2.14300i | 0.107461 | + | 0.106883i | ||||
\(403\) | −10.2940 | + | 7.40611i | −0.512783 | + | 0.368924i | ||||
\(404\) | 8.40167i | 0.417998i | ||||||||
\(405\) | −4.29403 | + | 4.38763i | −0.213372 | + | 0.218023i | ||||
\(406\) | 0.565250 | 0.0280529 | ||||||||
\(407\) | 0.883161 | 0.0437767 | ||||||||
\(408\) | 0.0275564 | + | 10.2239i | 0.00136425 | + | 0.506157i | ||||
\(409\) | −4.25749 | − | 4.25749i | −0.210519 | − | 0.210519i | 0.593969 | − | 0.804488i | \(-0.297560\pi\) |
−0.804488 | + | 0.593969i | \(0.797560\pi\) | |||||||
\(410\) | 0.386854 | + | 0.386854i | 0.0191053 | + | 0.0191053i | ||||
\(411\) | −0.00544328 | − | 2.01954i | −0.000268497 | − | 0.0996167i | ||||
\(412\) | 5.26338 | 0.259308 | ||||||||
\(413\) | 8.66543 | 0.426398 | ||||||||
\(414\) | 2.48472 | + | 2.45808i | 0.122117 | + | 0.120808i | ||||
\(415\) | − | 9.03448i | − | 0.443485i | ||||||
\(416\) | 5.22843 | + | 7.26721i | 0.256345 | + | 0.356304i | ||||
\(417\) | 13.5251 | + | 13.4523i | 0.662325 | + | 0.658764i | ||||
\(418\) | −1.20461 | − | 1.20461i | −0.0589195 | − | 0.0589195i | ||||
\(419\) | 20.5965i | 1.00620i | 0.864227 | + | 0.503102i | \(0.167808\pi\) | ||||
−0.864227 | + | 0.503102i | \(0.832192\pi\) | |||||||
\(420\) | 1.63725 | + | 1.62845i | 0.0798896 | + | 0.0794601i | ||||
\(421\) | −4.61599 | − | 4.61599i | −0.224970 | − | 0.224970i | 0.585618 | − | 0.810587i | \(-0.300852\pi\) |
−0.810587 | + | 0.585618i | \(0.800852\pi\) | |||||||
\(422\) | 0.0233877 | − | 0.0233877i | 0.00113850 | − | 0.00113850i | ||||
\(423\) | 22.9679 | − | 23.2169i | 1.11674 | − | 1.12884i | ||||
\(424\) | −3.88225 | + | 3.88225i | −0.188539 | + | 0.188539i | ||||
\(425\) | 31.7258i | 1.53893i | ||||||||
\(426\) | −2.98761 | + | 3.00376i | −0.144750 | + | 0.145532i | ||||
\(427\) | 6.60566 | − | 6.60566i | 0.319670 | − | 0.319670i | ||||
\(428\) | 28.7041 | 1.38746 | ||||||||
\(429\) | 19.7577 | + | 3.16901i | 0.953912 | + | 0.153001i | ||||
\(430\) | 0.441520 | 0.0212920 | ||||||||
\(431\) | −22.9077 | + | 22.9077i | −1.10342 | + | 1.10342i | −0.109430 | + | 0.993995i | \(0.534902\pi\) |
−0.993995 | + | 0.109430i | \(0.965098\pi\) | |||||||
\(432\) | −13.5898 | + | 13.8114i | −0.653840 | + | 0.664500i | ||||
\(433\) | − | 14.5183i | − | 0.697703i | −0.937178 | − | 0.348852i | \(-0.886572\pi\) | ||
0.937178 | − | 0.348852i | \(-0.113428\pi\) | |||||||
\(434\) | 0.530618 | − | 0.530618i | 0.0254705 | − | 0.0254705i | ||||
\(435\) | −0.00843677 | − | 3.13018i | −0.000404512 | − | 0.150080i | ||||
\(436\) | −28.4076 | + | 28.4076i | −1.36048 | + | 1.36048i | ||||
\(437\) | −9.62202 | − | 9.62202i | −0.460284 | − | 0.460284i | ||||
\(438\) | 2.28711 | − | 2.29947i | 0.109282 | − | 0.109873i | ||||
\(439\) | 31.6097i | 1.50865i | 0.656502 | + | 0.754324i | \(0.272035\pi\) | ||||
−0.656502 | + | 0.754324i | \(0.727965\pi\) | |||||||
\(440\) | −1.30397 | − | 1.30397i | −0.0621642 | − | 0.0621642i | ||||
\(441\) | 2.99996 | − | 0.0161717i | 0.142855 | − | 0.000770081i | ||||
\(442\) | −3.14312 | − | 4.36875i | −0.149503 | − | 0.207800i | ||||
\(443\) | − | 28.5097i | − | 1.35454i | −0.735737 | − | 0.677268i | \(-0.763164\pi\) | ||
0.735737 | − | 0.677268i | \(-0.236836\pi\) | |||||||
\(444\) | −0.00251488 | − | 0.933061i | −0.000119351 | − | 0.0442811i | ||||
\(445\) | 8.24331 | 0.390770 | ||||||||
\(446\) | 0.388461 | 0.0183942 | ||||||||
\(447\) | −21.1989 | + | 0.0571375i | −1.00267 | + | 0.00270251i | ||||
\(448\) | 4.89894 | + | 4.89894i | 0.231453 | + | 0.231453i | ||||
\(449\) | −23.0757 | − | 23.0757i | −1.08901 | − | 1.08901i | −0.995631 | − | 0.0933780i | \(-0.970233\pi\) |
−0.0933780 | − | 0.995631i | \(-0.529767\pi\) | |||||||
\(450\) | 2.04128 | − | 2.06340i | 0.0962267 | − | 0.0972698i | ||||
\(451\) | 12.0451 | 0.567181 | ||||||||
\(452\) | −24.8285 | −1.16783 | ||||||||
\(453\) | 4.84960 | − | 0.0130711i | 0.227854 | − | 0.000614136i | ||||
\(454\) | − | 3.08870i | − | 0.144960i | ||||||
\(455\) | −2.42738 | − | 0.396049i | −0.113797 | − | 0.0185671i | ||||
\(456\) | −2.56805 | + | 2.58193i | −0.120260 | + | 0.120910i | ||||
\(457\) | 27.8568 | + | 27.8568i | 1.30309 | + | 1.30309i | 0.926300 | + | 0.376787i | \(0.122971\pi\) |
0.376787 | + | 0.926300i | \(0.377029\pi\) | |||||||
\(458\) | 4.77298i | 0.223027i | ||||||||
\(459\) | 25.4971 | − | 25.9129i | 1.19010 | − | 1.20951i | ||||
\(460\) | −5.14787 | − | 5.14787i | −0.240021 | − | 0.240021i | ||||
\(461\) | 3.24146 | − | 3.24146i | 0.150970 | − | 0.150970i | −0.627581 | − | 0.778551i | \(-0.715955\pi\) |
0.778551 | + | 0.627581i | \(0.215955\pi\) | |||||||
\(462\) | −1.18408 | + | 0.00319146i | −0.0550884 | + | 0.000148480i | ||||
\(463\) | −20.4120 | + | 20.4120i | −0.948624 | + | 0.948624i | −0.998743 | − | 0.0501194i | \(-0.984040\pi\) |
0.0501194 | + | 0.998743i | \(0.484040\pi\) | |||||||
\(464\) | − | 9.87929i | − | 0.458635i | ||||||
\(465\) | −2.94631 | − | 2.93047i | −0.136632 | − | 0.135898i | ||||
\(466\) | 3.98088 | − | 3.98088i | 0.184411 | − | 0.184411i | ||||
\(467\) | 22.0340 | 1.01961 | 0.509806 | − | 0.860289i | \(-0.329717\pi\) | ||||
0.509806 | + | 0.860289i | \(0.329717\pi\) | |||||||
\(468\) | 3.29180 | − | 20.8831i | 0.152164 | − | 0.965321i | ||||
\(469\) | −8.22336 | −0.379719 | ||||||||
\(470\) | 1.12028 | − | 1.12028i | 0.0516746 | − | 0.0516746i | ||||
\(471\) | −4.14214 | − | 4.11988i | −0.190860 | − | 0.189834i | ||||
\(472\) | 7.31107i | 0.336519i | ||||||||
\(473\) | 6.87359 | − | 6.87359i | 0.316048 | − | 0.316048i | ||||
\(474\) | 1.46622 | − | 0.00395191i | 0.0673458 | − | 0.000181517i | ||||
\(475\) | −7.99048 | + | 7.99048i | −0.366628 | + | 0.366628i | ||||
\(476\) | −9.66899 | − | 9.66899i | −0.443177 | − | 0.443177i | ||||
\(477\) | 19.5219 | − | 0.105236i | 0.893847 | − | 0.00481841i | ||||
\(478\) | − | 0.595731i | − | 0.0272481i | ||||||
\(479\) | −25.6102 | − | 25.6102i | −1.17016 | − | 1.17016i | −0.982171 | − | 0.187989i | \(-0.939803\pi\) |
−0.187989 | − | 0.982171i | \(-0.560197\pi\) | |||||||
\(480\) | −2.06880 | + | 2.07999i | −0.0944275 | + | 0.0949379i | ||||
\(481\) | 0.580382 | + | 0.806697i | 0.0264631 | + | 0.0367822i | ||||
\(482\) | 0.521696i | 0.0237626i | ||||||||
\(483\) | −9.45802 | + | 0.0254922i | −0.430355 | + | 0.00115994i | ||||
\(484\) | 1.43277 | 0.0651259 | ||||||||
\(485\) | 7.60405 | 0.345282 | ||||||||
\(486\) | −3.32556 | + | 0.0448196i | −0.150851 | + | 0.00203306i | ||||
\(487\) | −4.86196 | − | 4.86196i | −0.220317 | − | 0.220317i | 0.588315 | − | 0.808632i | \(-0.299791\pi\) |
−0.808632 | + | 0.588315i | \(0.799791\pi\) | |||||||
\(488\) | 5.57323 | + | 5.57323i | 0.252288 | + | 0.252288i | ||||
\(489\) | −21.9151 | + | 0.0590680i | −0.991037 | + | 0.00267115i | ||||
\(490\) | 0.145537 | 0.00657468 | ||||||||
\(491\) | 2.14655 | 0.0968722 | 0.0484361 | − | 0.998826i | \(-0.484576\pi\) | ||||
0.0484361 | + | 0.998826i | \(0.484576\pi\) | |||||||
\(492\) | −0.0342995 | − | 12.7256i | −0.00154634 | − | 0.573716i | ||||
\(493\) | 18.5355i | 0.834796i | ||||||||
\(494\) | 0.308688 | − | 1.89194i | 0.0138885 | − | 0.0851226i | ||||
\(495\) | 0.0353465 | + | 6.55701i | 0.00158871 | + | 0.294716i | ||||
\(496\) | −9.27400 | − | 9.27400i | −0.416415 | − | 0.416415i | ||||
\(497\) | − | 11.4644i | − | 0.514247i | ||||||
\(498\) | 3.45148 | − | 3.47014i | 0.154665 | − | 0.155501i | ||||
\(499\) | −8.53774 | − | 8.53774i | −0.382202 | − | 0.382202i | 0.489693 | − | 0.871895i | \(-0.337109\pi\) |
−0.871895 | + | 0.489693i | \(0.837109\pi\) | |||||||
\(500\) | −8.98863 | + | 8.98863i | −0.401984 | + | 0.401984i | ||||
\(501\) | −0.0335672 | − | 12.4539i | −0.00149967 | − | 0.556401i | ||||
\(502\) | 3.92807 | − | 3.92807i | 0.175319 | − | 0.175319i | ||||
\(503\) | 21.0850i | 0.940132i | 0.882631 | + | 0.470066i | \(0.155770\pi\) | ||||
−0.882631 | + | 0.470066i | \(0.844230\pi\) | |||||||
\(504\) | 0.0136442 | + | 2.53108i | 0.000607759 | + | 0.112743i | ||||
\(505\) | 2.07343 | − | 2.07343i | 0.0922665 | − | 0.0922665i | ||||
\(506\) | 3.73304 | 0.165954 | ||||||||
\(507\) | 10.0894 | + | 20.1297i | 0.448088 | + | 0.893990i | ||||
\(508\) | 13.8734 | 0.615531 | ||||||||
\(509\) | −2.38009 | + | 2.38009i | −0.105496 | + | 0.105496i | −0.757884 | − | 0.652389i | \(-0.773767\pi\) |
0.652389 | + | 0.757884i | \(0.273767\pi\) | |||||||
\(510\) | 1.24368 | − | 1.25040i | 0.0550711 | − | 0.0553688i | ||||
\(511\) | 8.77634i | 0.388242i | ||||||||
\(512\) | −10.9964 | + | 10.9964i | −0.485977 | + | 0.485977i | ||||
\(513\) | 12.9482 | − | 0.104700i | 0.571675 | − | 0.00462260i | ||||
\(514\) | −0.414888 | + | 0.414888i | −0.0182999 | + | 0.0182999i | ||||
\(515\) | −1.29894 | − | 1.29894i | −0.0572382 | − | 0.0572382i | ||||
\(516\) | −7.28153 | − | 7.24238i | −0.320551 | − | 0.318828i | ||||
\(517\) | − | 34.8810i | − | 1.53407i | ||||||
\(518\) | −0.0415821 | − | 0.0415821i | −0.00182701 | − | 0.00182701i | ||||
\(519\) | 21.6197 | + | 21.5035i | 0.949000 | + | 0.943898i | ||||
\(520\) | 0.334149 | − | 2.04799i | 0.0146534 | − | 0.0898104i | ||||
\(521\) | − | 0.110256i | − | 0.00483042i | −0.999997 | − | 0.00241521i | \(-0.999231\pi\) | ||
0.999997 | − | 0.00241521i | \(-0.000768787\pi\) | |||||||
\(522\) | 1.19260 | − | 1.20552i | 0.0521985 | − | 0.0527643i | ||||
\(523\) | −0.172813 | −0.00755658 | −0.00377829 | − | 0.999993i | \(-0.501203\pi\) | ||||
−0.00377829 | + | 0.999993i | \(0.501203\pi\) | |||||||
\(524\) | 1.05017 | 0.0458770 | ||||||||
\(525\) | 0.0211697 | + | 7.85429i | 0.000923921 | + | 0.342789i | ||||
\(526\) | 0.382023 | + | 0.382023i | 0.0166570 | + | 0.0166570i | ||||
\(527\) | 17.3998 | + | 17.3998i | 0.757949 | + | 0.757949i | ||||
\(528\) | 0.0557794 | + | 20.6950i | 0.00242749 | + | 0.900636i | ||||
\(529\) | 6.81824 | 0.296445 | ||||||||
\(530\) | 0.947065 | 0.0411379 | ||||||||
\(531\) | 18.2828 | − | 18.4810i | 0.793406 | − | 0.802006i | ||||
\(532\) | − | 4.87047i | − | 0.211162i | ||||||
\(533\) | 7.91560 | + | 11.0022i | 0.342863 | + | 0.476559i | ||||
\(534\) | 3.16625 | + | 3.14923i | 0.137017 | + | 0.136281i | ||||
\(535\) | −7.08383 | − | 7.08383i | −0.306261 | − | 0.306261i | ||||
\(536\) | − | 6.93809i | − | 0.299680i | ||||||
\(537\) | −13.7667 | − | 13.6927i | −0.594076 | − | 0.590882i | ||||
\(538\) | 3.22872 | + | 3.22872i | 0.139200 | + | 0.139200i | ||||
\(539\) | 2.26572 | − | 2.26572i | 0.0975913 | − | 0.0975913i | ||||
\(540\) | 6.92739 | − | 0.0560153i | 0.298107 | − | 0.00241052i | ||||
\(541\) | 19.0795 | − | 19.0795i | 0.820292 | − | 0.820292i | −0.165858 | − | 0.986150i | \(-0.553039\pi\) |
0.986150 | + | 0.165858i | \(0.0530393\pi\) | |||||||
\(542\) | 0.376920i | 0.0161901i | ||||||||
\(543\) | −28.2456 | + | 28.3982i | −1.21213 | + | 1.21869i | ||||
\(544\) | 12.2836 | − | 12.2836i | 0.526656 | − | 0.526656i | ||||
\(545\) | 14.0213 | 0.600607 | ||||||||
\(546\) | −0.781051 | − | 1.07947i | −0.0334259 | − | 0.0461968i | ||||
\(547\) | 6.64711 | 0.284210 | 0.142105 | − | 0.989852i | \(-0.454613\pi\) | ||||
0.142105 | + | 0.989852i | \(0.454613\pi\) | |||||||
\(548\) | −1.61143 | + | 1.61143i | −0.0688367 | + | 0.0688367i | ||||
\(549\) | −0.151073 | − | 28.0250i | −0.00644764 | − | 1.19608i | ||||
\(550\) | − | 3.10006i | − | 0.132187i | ||||||
\(551\) | −4.66836 | + | 4.66836i | −0.198879 | + | 0.198879i | ||||
\(552\) | −0.0215079 | − | 7.97978i | −0.000915439 | − | 0.339642i | ||||
\(553\) | −2.80559 | + | 2.80559i | −0.119306 | + | 0.119306i | ||||
\(554\) | −1.96143 | − | 1.96143i | −0.0833333 | − | 0.0833333i | ||||
\(555\) | −0.229648 | + | 0.230889i | −0.00974800 | + | 0.00980069i | ||||
\(556\) | − | 21.5257i | − | 0.912893i | ||||||
\(557\) | −0.645771 | − | 0.645771i | −0.0273622 | − | 0.0273622i | 0.693293 | − | 0.720656i | \(-0.256159\pi\) |
−0.720656 | + | 0.693293i | \(0.756159\pi\) | |||||||
\(558\) | −0.0121354 | − | 2.25119i | −0.000513731 | − | 0.0953005i | ||||
\(559\) | 10.7956 | + | 1.76139i | 0.456603 | + | 0.0744991i | ||||
\(560\) | − | 2.54365i | − | 0.107489i | ||||||
\(561\) | −0.104653 | − | 38.8279i | −0.00441846 | − | 1.63932i | ||||
\(562\) | −2.52371 | −0.106456 | ||||||||
\(563\) | −1.44022 | −0.0606979 | −0.0303489 | − | 0.999539i | \(-0.509662\pi\) | ||||
−0.0303489 | + | 0.999539i | \(0.509662\pi\) | |||||||
\(564\) | −36.8518 | + | 0.0993269i | −1.55174 | + | 0.00418242i | ||||
\(565\) | 6.12738 | + | 6.12738i | 0.257781 | + | 0.257781i | ||||
\(566\) | 1.49518 | + | 1.49518i | 0.0628473 | + | 0.0628473i | ||||
\(567\) | 6.29498 | − | 6.43220i | 0.264364 | − | 0.270127i | ||||
\(568\) | 9.67255 | 0.405851 | ||||||||
\(569\) | 7.58332 | 0.317909 | 0.158955 | − | 0.987286i | \(-0.449188\pi\) | ||||
0.158955 | + | 0.987286i | \(0.449188\pi\) | |||||||
\(570\) | 0.628162 | − | 0.00169309i | 0.0263108 | − | 7.09156e-5i | ||||
\(571\) | 21.6013i | 0.903987i | 0.892021 | + | 0.451993i | \(0.149287\pi\) | ||||
−0.892021 | + | 0.451993i | \(0.850713\pi\) | |||||||
\(572\) | −13.1870 | − | 18.3291i | −0.551376 | − | 0.766380i | ||||
\(573\) | 12.3676 | − | 12.4345i | 0.516664 | − | 0.519457i | ||||
\(574\) | −0.567121 | − | 0.567121i | −0.0236712 | − | 0.0236712i | ||||
\(575\) | − | 24.7622i | − | 1.03265i | ||||||
\(576\) | 20.7841 | − | 0.112040i | 0.866005 | − | 0.00466833i | ||||
\(577\) | −8.06019 | − | 8.06019i | −0.335550 | − | 0.335550i | 0.519139 | − | 0.854690i | \(-0.326253\pi\) |
−0.854690 | + | 0.519139i | \(0.826253\pi\) | |||||||
\(578\) | −4.81973 | + | 4.81973i | −0.200474 | + | 0.200474i | ||||
\(579\) | 23.0439 | − | 0.0621104i | 0.957674 | − | 0.00258122i | ||||
\(580\) | −2.49762 | + | 2.49762i | −0.103708 | + | 0.103708i | ||||
\(581\) | 13.2444i | 0.549470i | ||||||||
\(582\) | 2.92071 | + | 2.90501i | 0.121067 | + | 0.120417i | ||||
\(583\) | 14.7439 | − | 14.7439i | 0.610630 | − | 0.610630i | ||||
\(584\) | −7.40465 | −0.306407 | ||||||||
\(585\) | −5.96608 | + | 4.34132i | −0.246667 | + | 0.179492i | ||||
\(586\) | 1.63882 | 0.0676989 | ||||||||
\(587\) | −9.37281 | + | 9.37281i | −0.386857 | + | 0.386857i | −0.873565 | − | 0.486708i | \(-0.838198\pi\) |
0.486708 | + | 0.873565i | \(0.338198\pi\) | |||||||
\(588\) | −2.40018 | − | 2.38728i | −0.0989819 | − | 0.0984497i | ||||
\(589\) | 8.76467i | 0.361142i | ||||||||
\(590\) | 0.891759 | − | 0.891759i | 0.0367131 | − | 0.0367131i | ||||
\(591\) | −43.9973 | + | 0.118586i | −1.80981 | + | 0.00487798i | ||||
\(592\) | −0.726760 | + | 0.726760i | −0.0298697 | + | 0.0298697i | ||||
\(593\) | −33.7433 | − | 33.7433i | −1.38567 | − | 1.38567i | −0.834183 | − | 0.551487i | \(-0.814060\pi\) |
−0.551487 | − | 0.834183i | \(-0.685940\pi\) | |||||||
\(594\) | −2.49143 | + | 2.53205i | −0.102225 | + | 0.103891i | ||||
\(595\) | 4.77239i | 0.195649i | ||||||||
\(596\) | 16.9150 | + | 16.9150i | 0.692864 | + | 0.692864i | ||||
\(597\) | −19.7792 | + | 19.8861i | −0.809508 | + | 0.813883i | ||||
\(598\) | 2.45322 | + | 3.40984i | 0.100320 | + | 0.139439i | ||||
\(599\) | 14.5774i | 0.595617i | 0.954626 | + | 0.297809i | \(0.0962557\pi\) | ||||
−0.954626 | + | 0.297809i | \(0.903744\pi\) | |||||||
\(600\) | −6.62671 | + | 0.0178610i | −0.270534 | + | 0.000729172i | ||||
\(601\) | −2.77235 | −0.113087 | −0.0565433 | − | 0.998400i | \(-0.518008\pi\) | ||||
−0.0565433 | + | 0.998400i | \(0.518008\pi\) | |||||||
\(602\) | −0.647262 | −0.0263804 | ||||||||
\(603\) | −17.3501 | + | 17.5382i | −0.706550 | + | 0.714209i | ||||
\(604\) | −3.86957 | − | 3.86957i | −0.157451 | − | 0.157451i | ||||
\(605\) | −0.353591 | − | 0.353591i | −0.0143755 | − | 0.0143755i | ||||
\(606\) | 1.58853 | − | 0.00428157i | 0.0645295 | − | 0.000173927i | ||||
\(607\) | −12.2679 | −0.497940 | −0.248970 | − | 0.968511i | \(-0.580092\pi\) | ||||
−0.248970 | + | 0.968511i | \(0.580092\pi\) | |||||||
\(608\) | 6.18752 | 0.250937 | ||||||||
\(609\) | 0.0123682 | + | 4.58879i | 0.000501184 | + | 0.185947i | ||||
\(610\) | − | 1.35958i | − | 0.0550476i | ||||||
\(611\) | 31.8610 | − | 22.9226i | 1.28896 | − | 0.927348i | ||||
\(612\) | −41.0215 | + | 0.221132i | −1.65819 | + | 0.00893874i | ||||
\(613\) | −10.5026 | − | 10.5026i | −0.424195 | − | 0.424195i | 0.462450 | − | 0.886645i | \(-0.346970\pi\) |
−0.886645 | + | 0.462450i | \(0.846970\pi\) | |||||||
\(614\) | 4.32781i | 0.174656i | ||||||||
\(615\) | −3.13207 | + | 3.14900i | −0.126297 | + | 0.126980i | ||||
\(616\) | 1.91160 | + | 1.91160i | 0.0770204 | + | 0.0770204i | ||||
\(617\) | −27.8456 | + | 27.8456i | −1.12102 | + | 1.12102i | −0.129435 | + | 0.991588i | \(0.541316\pi\) |
−0.991588 | + | 0.129435i | \(0.958684\pi\) | |||||||
\(618\) | −0.00268227 | − | 0.995163i | −0.000107897 | − | 0.0400313i | ||||
\(619\) | 12.4038 | − | 12.4038i | 0.498549 | − | 0.498549i | −0.412437 | − | 0.910986i | \(-0.635322\pi\) |
0.910986 | + | 0.412437i | \(0.135322\pi\) | |||||||
\(620\) | 4.68918i | 0.188322i | ||||||||
\(621\) | −19.9007 | + | 20.2251i | −0.798586 | + | 0.811607i | ||||
\(622\) | −1.67012 | + | 1.67012i | −0.0669658 | + | 0.0669658i | ||||
\(623\) | −12.0846 | −0.484158 | ||||||||
\(624\) | −18.8666 | + | 13.6510i | −0.755268 | + | 0.546477i | ||||
\(625\) | −18.2369 | −0.729475 | ||||||||
\(626\) | −0.185882 | + | 0.185882i | −0.00742932 | + | 0.00742932i | ||||
\(627\) | 9.75287 | − | 9.80558i | 0.389492 | − | 0.391597i | ||||
\(628\) | 6.59240i | 0.263065i | ||||||||
\(629\) | 1.36355 | − | 1.36355i | 0.0543681 | − | 0.0543681i | ||||
\(630\) | 0.307061 | − | 0.310390i | 0.0122336 | − | 0.0123662i | ||||
\(631\) | 18.3687 | − | 18.3687i | 0.731245 | − | 0.731245i | −0.239621 | − | 0.970867i | \(-0.577023\pi\) |
0.970867 | + | 0.239621i | \(0.0770232\pi\) | |||||||
\(632\) | −2.36709 | − | 2.36709i | −0.0941578 | − | 0.0941578i | ||||
\(633\) | 0.190377 | + | 0.189353i | 0.00756680 | + | 0.00752612i | ||||
\(634\) | 1.95231i | 0.0775360i | ||||||||
\(635\) | −3.42379 | − | 3.42379i | −0.135869 | − | 0.135869i | ||||
\(636\) | −15.6189 | − | 15.5350i | −0.619331 | − | 0.616002i | ||||
\(637\) | 3.55850 | + | 0.580602i | 0.140993 | + | 0.0230043i | ||||
\(638\) | − | 1.81118i | − | 0.0717052i | ||||||
\(639\) | −24.4503 | − | 24.1881i | −0.967240 | − | 0.956868i | ||||
\(640\) | 4.39578 | 0.173759 | ||||||||
\(641\) | −2.15928 | −0.0852865 | −0.0426432 | − | 0.999090i | \(-0.513578\pi\) | ||||
−0.0426432 | + | 0.999090i | \(0.513578\pi\) | |||||||
\(642\) | −0.0146279 | − | 5.42717i | −0.000577316 | − | 0.214193i | ||||
\(643\) | 15.1851 | + | 15.1851i | 0.598841 | + | 0.598841i | 0.940004 | − | 0.341163i | \(-0.110821\pi\) |
−0.341163 | + | 0.940004i | \(0.610821\pi\) | |||||||
\(644\) | 7.54670 | + | 7.54670i | 0.297382 | + | 0.297382i | ||||
\(645\) | 0.00966086 | + | 3.58433i | 0.000380396 | + | 0.141133i | ||||
\(646\) | −3.71969 | −0.146349 | ||||||||
\(647\) | −4.76357 | −0.187275 | −0.0936377 | − | 0.995606i | \(-0.529850\pi\) | ||||
−0.0936377 | + | 0.995606i | \(0.529850\pi\) | |||||||
\(648\) | 5.42689 | + | 5.31111i | 0.213188 | + | 0.208640i | ||||
\(649\) | − | 27.7658i | − | 1.08990i | ||||||
\(650\) | 2.83165 | − | 2.03725i | 0.111067 | − | 0.0799074i | ||||
\(651\) | 4.31925 | + | 4.29603i | 0.169285 | + | 0.168375i | ||||
\(652\) | 17.4864 | + | 17.4864i | 0.684822 | + | 0.684822i | ||||
\(653\) | − | 15.2734i | − | 0.597694i | −0.954301 | − | 0.298847i | \(-0.903398\pi\) | ||
0.954301 | − | 0.298847i | \(-0.0966021\pi\) | |||||||
\(654\) | 5.38558 | + | 5.35663i | 0.210593 | + | 0.209461i | ||||
\(655\) | −0.259170 | − | 0.259170i | −0.0101266 | − | 0.0101266i | ||||
\(656\) | −9.91200 | + | 9.91200i | −0.386998 | + | 0.386998i | ||||
\(657\) | 18.7175 | + | 18.5168i | 0.730240 | + | 0.722409i | ||||
\(658\) | −1.64231 | + | 1.64231i | −0.0640240 | + | 0.0640240i | ||||
\(659\) | − | 42.9450i | − | 1.67290i | −0.548043 | − | 0.836450i | \(-0.684627\pi\) | ||
0.548043 | − | 0.836450i | \(-0.315373\pi\) | |||||||
\(660\) | 5.21788 | − | 5.24608i | 0.203106 | − | 0.204204i | ||||
\(661\) | 15.7811 | − | 15.7811i | 0.613815 | − | 0.613815i | −0.330123 | − | 0.943938i | \(-0.607090\pi\) |
0.943938 | + | 0.330123i | \(0.107090\pi\) | |||||||
\(662\) | −5.65762 | −0.219890 | ||||||||
\(663\) | 35.3974 | − | 25.6119i | 1.37472 | − | 0.994685i | ||||
\(664\) | −11.1744 | −0.433650 | ||||||||
\(665\) | −1.20198 | + | 1.20198i | −0.0466106 | + | 0.0466106i | ||||
\(666\) | −0.176415 | 0.000950992i | −0.00683595 | 3.68502e-5i | ||||||
\(667\) | − | 14.4671i | − | 0.560166i | ||||||
\(668\) | −9.93720 | + | 9.93720i | −0.384482 | + | 0.384482i | ||||
\(669\) | 0.00849988 | + | 3.15359i | 0.000328624 | + | 0.121925i | ||||
\(670\) | −0.846265 | + | 0.846265i | −0.0326941 | + | 0.0326941i | ||||
\(671\) | −21.1659 | − | 21.1659i | −0.817100 | − | 0.817100i | ||||
\(672\) | 3.03283 | − | 3.04923i | 0.116994 | − | 0.117626i | ||||
\(673\) | − | 50.2096i | − | 1.93544i | −0.252032 | − | 0.967719i | \(-0.581099\pi\) | ||
0.252032 | − | 0.967719i | \(-0.418901\pi\) | |||||||
\(674\) | −5.12192 | − | 5.12192i | −0.197289 | − | 0.197289i | ||||
\(675\) | 16.7957 | + | 16.5263i | 0.646467 | + | 0.636096i | ||||
\(676\) | 8.07618 | − | 24.0905i | 0.310622 | − | 0.926559i | ||||
\(677\) | 33.4956i | 1.28734i | 0.765303 | + | 0.643671i | \(0.222589\pi\) | ||||
−0.765303 | + | 0.643671i | \(0.777411\pi\) | |||||||
\(678\) | 0.0126528 | + | 4.69440i | 0.000485929 | + | 0.180287i | ||||
\(679\) | −11.1474 | −0.427799 | ||||||||
\(680\) | −4.02649 | −0.154409 | ||||||||
\(681\) | 25.0745 | − | 0.0675834i | 0.960857 | − | 0.00258980i | ||||
\(682\) | −1.70021 | − | 1.70021i | −0.0651044 | − | 0.0651044i | ||||
\(683\) | −1.55629 | − | 1.55629i | −0.0595499 | − | 0.0595499i | 0.676705 | − | 0.736255i | \(-0.263407\pi\) |
−0.736255 | + | 0.676705i | \(0.763407\pi\) | |||||||
\(684\) | −10.3874 | − | 10.2760i | −0.397171 | − | 0.392912i | ||||
\(685\) | 0.795361 | 0.0303892 | ||||||||
\(686\) | −0.213354 | −0.00814591 | ||||||||
\(687\) | −38.7478 | + | 0.104437i | −1.47832 | + | 0.00398452i | ||||
\(688\) | 11.3127i | 0.431291i | ||||||||
\(689\) | 23.1566 | + | 3.77821i | 0.882194 | + | 0.143938i | ||||
\(690\) | −0.970701 | + | 0.975947i | −0.0369539 | + | 0.0371537i | ||||
\(691\) | 14.7515 | + | 14.7515i | 0.561172 | + | 0.561172i | 0.929640 | − | 0.368469i | \(-0.120118\pi\) |
−0.368469 | + | 0.929640i | \(0.620118\pi\) | |||||||
\(692\) | − | 34.4087i | − | 1.30802i | ||||||
\(693\) | −0.0518175 | − | 9.61248i | −0.00196838 | − | 0.365148i | ||||
\(694\) | 2.40612 | + | 2.40612i | 0.0913351 | + | 0.0913351i | ||||
\(695\) | −5.31229 | + | 5.31229i | −0.201507 | + | 0.201507i | ||||
\(696\) | −3.87159 | + | 0.0104351i | −0.146752 | + | 0.000395542i | ||||
\(697\) | 18.5968 | − | 18.5968i | 0.704406 | − | 0.704406i | ||||
\(698\) | 0.186895i | 0.00707409i | ||||||||
\(699\) | 32.4045 | + | 32.2303i | 1.22565 | + | 1.21906i | ||||
\(700\) | 6.26706 | − | 6.26706i | 0.236873 | − | 0.236873i | ||||
\(701\) | 33.6849 | 1.27226 | 0.636130 | − | 0.771582i | \(-0.280534\pi\) | ||||
0.636130 | + | 0.771582i | \(0.280534\pi\) | |||||||
\(702\) | −3.95010 | − | 0.611748i | −0.149087 | − | 0.0230890i | ||||
\(703\) | 0.686846 | 0.0259049 | ||||||||
\(704\) | 15.6972 | − | 15.6972i | 0.591610 | − | 0.591610i | ||||
\(705\) | 9.11912 | + | 9.07009i | 0.343446 | + | 0.341599i | ||||
\(706\) | 0.469403i | 0.0176662i | ||||||||
\(707\) | −3.03962 | + | 3.03962i | −0.114317 | + | 0.114317i | ||||
\(708\) | −29.3346 | + | 0.0790657i | −1.10246 | + | 0.00297147i | ||||
\(709\) | −8.52119 | + | 8.52119i | −0.320020 | + | 0.320020i | −0.848775 | − | 0.528755i | \(-0.822659\pi\) |
0.528755 | + | 0.848775i | \(0.322659\pi\) | |||||||
\(710\) | −1.17980 | − | 1.17980i | −0.0442770 | − | 0.0442770i | ||||
\(711\) | 0.0641645 | + | 11.9029i | 0.00240636 | + | 0.446395i | ||||
\(712\) | − | 10.1958i | − | 0.382105i | ||||||
\(713\) | −13.5807 | − | 13.5807i | −0.508600 | − | 0.508600i | ||||
\(714\) | −1.82322 | + | 1.83307i | −0.0682322 | + | 0.0686010i | ||||
\(715\) | −1.26902 | + | 7.77781i | −0.0474588 | + | 0.290874i | ||||
\(716\) | 21.9102i | 0.818824i | ||||||||
\(717\) | 4.83623 | − | 0.0130351i | 0.180612 | − | 0.000486806i | ||||
\(718\) | −4.25728 | −0.158880 | ||||||||
\(719\) | 6.61231 | 0.246598 | 0.123299 | − | 0.992370i | \(-0.460653\pi\) | ||||
0.123299 | + | 0.992370i | \(0.460653\pi\) | |||||||
\(720\) | −5.42491 | − | 5.36673i | −0.202174 | − | 0.200006i | ||||
\(721\) | 1.90423 | + | 1.90423i | 0.0709171 | + | 0.0709171i | ||||
\(722\) | 1.92958 | + | 1.92958i | 0.0718115 | + | 0.0718115i | ||||
\(723\) | −4.23521 | + | 0.0114152i | −0.157509 | + | 0.000424535i | ||||
\(724\) | 45.1970 | 1.67973 | ||||||||
\(725\) | −12.0140 | −0.446188 | ||||||||
\(726\) | −0.000730152 | − | 0.270898i | −2.70985e−5 | − | 0.0100540i | ||||
\(727\) | 13.3668i | 0.495748i | 0.968792 | + | 0.247874i | \(0.0797319\pi\) | ||||
−0.968792 | + | 0.247874i | \(0.920268\pi\) | |||||||
\(728\) | −0.489857 | + | 3.00232i | −0.0181553 | + | 0.111274i | ||||
\(729\) | −0.436619 | − | 26.9965i | −0.0161711 | − | 0.999869i | ||||
\(730\) | 0.903173 | + | 0.903173i | 0.0334279 | + | 0.0334279i | ||||
\(731\) | − | 21.2248i | − | 0.785027i | ||||||
\(732\) | −22.3015 | + | 22.4221i | −0.824288 | + | 0.828743i | ||||
\(733\) | −35.9949 | − | 35.9949i | −1.32950 | − | 1.32950i | −0.905802 | − | 0.423702i | \(-0.860730\pi\) |
−0.423702 | − | 0.905802i | \(-0.639270\pi\) | |||||||
\(734\) | 0.824407 | − | 0.824407i | 0.0304294 | − | 0.0304294i | ||||
\(735\) | 0.00318447 | + | 1.18149i | 0.000117461 | + | 0.0435799i | ||||
\(736\) | −9.58744 | + | 9.58744i | −0.353398 | + | 0.353398i | ||||
\(737\) | 26.3493i | 0.970590i | ||||||||
\(738\) | −2.40606 | + | 0.0129702i | −0.0885682 | + | 0.000477440i | ||||
\(739\) | −18.9168 | + | 18.9168i | −0.695865 | + | 0.695865i | −0.963516 | − | 0.267651i | \(-0.913753\pi\) |
0.267651 | + | 0.963516i | \(0.413753\pi\) | |||||||
\(740\) | 0.367470 | 0.0135085 | ||||||||
\(741\) | 15.3659 | + | 2.46458i | 0.564479 | + | 0.0905387i | ||||
\(742\) | −1.38838 | −0.0509691 | ||||||||
\(743\) | −10.9283 | + | 10.9283i | −0.400922 | + | 0.400922i | −0.878558 | − | 0.477636i | \(-0.841494\pi\) |
0.477636 | + | 0.878558i | \(0.341494\pi\) | |||||||
\(744\) | −3.62459 | + | 3.64418i | −0.132884 | + | 0.133602i | ||||
\(745\) | − | 8.34883i | − | 0.305877i | ||||||
\(746\) | 3.09994 | − | 3.09994i | 0.113497 | − | 0.113497i | ||||
\(747\) | 28.2467 | + | 27.9438i | 1.03349 | + | 1.02241i | ||||
\(748\) | −30.9814 | + | 30.9814i | −1.13279 | + | 1.13279i | ||||
\(749\) | 10.3848 | + | 10.3848i | 0.379452 | + | 0.379452i | ||||
\(750\) | 1.70409 | + | 1.69493i | 0.0622245 | + | 0.0618900i | ||||
\(751\) | 31.7550i | 1.15876i | 0.815059 | + | 0.579378i | \(0.196704\pi\) | ||||
−0.815059 | + | 0.579378i | \(0.803296\pi\) | |||||||
\(752\) | 28.7039 | + | 28.7039i | 1.04672 | + | 1.04672i | ||||
\(753\) | 31.9747 | + | 31.8028i | 1.16522 | + | 1.15896i | ||||
\(754\) | 1.65437 | − | 1.19024i | 0.0602484 | − | 0.0433460i | ||||
\(755\) | 1.90993i | 0.0695094i | ||||||||
\(756\) | −10.1554 | + | 0.0821176i | −0.369350 | + | 0.00298659i | ||||
\(757\) | 48.8723 | 1.77629 | 0.888147 | − | 0.459559i | \(-0.151993\pi\) | ||||
0.888147 | + | 0.459559i | \(0.151993\pi\) | |||||||
\(758\) | −5.14440 | −0.186853 | ||||||||
\(759\) | 0.0816823 | + | 30.3054i | 0.00296488 | + | 1.10002i | ||||
\(760\) | −1.01411 | − | 1.01411i | −0.0367858 | − | 0.0367858i | ||||
\(761\) | −10.2908 | − | 10.2908i | −0.373041 | − | 0.373041i | 0.495543 | − | 0.868583i | \(-0.334969\pi\) |
−0.868583 | + | 0.495543i | \(0.834969\pi\) | |||||||
\(762\) | −0.00707000 | − | 2.62308i | −0.000256119 | − | 0.0950242i | ||||
\(763\) | −20.5550 | −0.744142 | ||||||||
\(764\) | −19.7900 | −0.715976 | ||||||||
\(765\) | 10.1782 | + | 10.0690i | 0.367993 | + | 0.364047i | ||||
\(766\) | 6.04469i | 0.218403i | ||||||||
\(767\) | 25.3618 | − | 18.2467i | 0.915763 | − | 0.658850i | ||||
\(768\) | −15.3277 | − | 15.2453i | −0.553090 | − | 0.550116i | ||||
\(769\) | −8.68174 | − | 8.68174i | −0.313072 | − | 0.313072i | 0.533027 | − | 0.846098i | \(-0.321054\pi\) |
−0.846098 | + | 0.533027i | \(0.821054\pi\) | |||||||
\(770\) | − | 0.466329i | − | 0.0168053i | ||||||
\(771\) | −3.37720 | − | 3.35905i | −0.121627 | − | 0.120973i | ||||
\(772\) | −18.3871 | − | 18.3871i | −0.661767 | − | 0.661767i | ||||
\(773\) | −1.81881 | + | 1.81881i | −0.0654181 | + | 0.0654181i | −0.739059 | − | 0.673641i | \(-0.764729\pi\) |
0.673641 | + | 0.739059i | \(0.264729\pi\) | |||||||
\(774\) | −1.36563 | + | 1.38043i | −0.0490865 | + | 0.0496186i | ||||
\(775\) | −11.2779 | + | 11.2779i | −0.405114 | + | 0.405114i | ||||
\(776\) | − | 9.40514i | − | 0.337625i | ||||||
\(777\) | 0.336660 | − | 0.338480i | 0.0120776 | − | 0.0121429i | ||||
\(778\) | −0.701930 | + | 0.701930i | −0.0251654 | + | 0.0251654i | ||||
\(779\) | 9.36762 | 0.335630 | ||||||||
\(780\) | 8.22088 | + | 1.31858i | 0.294355 | + | 0.0472126i | ||||
\(781\) | −36.7342 | −1.31445 | ||||||||
\(782\) | 5.76358 | − | 5.76358i | 0.206105 | − | 0.206105i | ||||
\(783\) | 9.81272 | + | 9.65530i | 0.350678 | + | 0.345052i | ||||
\(784\) | 3.72895i | 0.133177i | ||||||||
\(785\) | 1.62693 | − | 1.62693i | 0.0580675 | − | 0.0580675i | ||||
\(786\) | −0.000535178 | − | 0.198559i | −1.90892e−5 | − | 0.00708238i | ||||
\(787\) | −26.0942 | + | 26.0942i | −0.930158 | + | 0.930158i | −0.997715 | − | 0.0675575i | \(-0.978479\pi\) |
0.0675575 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(788\) | 35.1061 | + | 35.1061i | 1.25060 | + | 1.25060i | ||||
\(789\) | −3.09296 | + | 3.10968i | −0.110112 | + | 0.110708i | ||||
\(790\) | 0.577446i | 0.0205446i | ||||||||
\(791\) | −8.98265 | − | 8.98265i | −0.319386 | − | 0.319386i | ||||
\(792\) | 8.11010 | − | 0.0437187i | 0.288180 | − | 0.00155348i | ||||
\(793\) | 5.42387 | − | 33.2428i | 0.192607 | − | 1.18049i | ||||
\(794\) | − | 5.57199i | − | 0.197743i | ||||||
\(795\) | 0.0207226 | + | 7.68842i | 0.000734956 | + | 0.272680i | ||||
\(796\) | 31.6495 | 1.12179 | ||||||||
\(797\) | 19.6614 | 0.696441 | 0.348220 | − | 0.937413i | \(-0.386786\pi\) | ||||
0.348220 | + | 0.937413i | \(0.386786\pi\) | |||||||
\(798\) | −0.920875 | + | 0.00248204i | −0.0325986 | + | 8.78632e-5i | ||||
\(799\) | −53.8541 | − | 53.8541i | −1.90522 | − | 1.90522i | ||||
\(800\) | 7.96177 | + | 7.96177i | 0.281491 | + | 0.281491i | ||||
\(801\) | −25.4967 | + | 25.7731i | −0.900881 | + | 0.910646i | ||||
\(802\) | 2.67774 | 0.0945544 | ||||||||
\(803\) | 28.1212 | 0.992375 | ||||||||
\(804\) | 27.8381 | − | 0.0750321i | 0.981774 | − | 0.00264618i | ||||
\(805\) | − | 3.72487i | − | 0.131285i | ||||||
\(806\) | 0.435688 | − | 2.67032i | 0.0153465 | − | 0.0940581i | ||||
\(807\) | −26.1406 | + | 26.2819i | −0.920192 | + | 0.925165i | ||||
\(808\) | −2.56454 | − | 2.56454i | −0.0902204 | − | 0.0902204i | ||||
\(809\) | 10.3579i | 0.364164i | 0.983283 | + | 0.182082i | \(0.0582837\pi\) | ||||
−0.983283 | + | 0.182082i | \(0.941716\pi\) | |||||||
\(810\) | −0.0141212 | − | 1.30975i | −0.000496170 | − | 0.0460201i | ||||
\(811\) | 35.4816 | + | 35.4816i | 1.24593 | + | 1.24593i | 0.957503 | + | 0.288424i | \(0.0931313\pi\) |
0.288424 | + | 0.957503i | \(0.406869\pi\) | |||||||
\(812\) | 3.66147 | − | 3.66147i | 0.128492 | − | 0.128492i | ||||
\(813\) | −3.05990 | + | 0.00824735i | −0.107315 | + | 0.000289247i | ||||
\(814\) | −0.133238 | + | 0.133238i | −0.00466997 | + | 0.00466997i | ||||
\(815\) | − | 8.63090i | − | 0.302327i | ||||||
\(816\) | 32.0379 | + | 31.8657i | 1.12155 | + | 1.11552i | ||||
\(817\) | 5.34569 | − | 5.34569i | 0.187022 | − | 0.187022i | ||||
\(818\) | 1.28461 | 0.0449152 | ||||||||
\(819\) | 8.74617 | − | 6.36431i | 0.305616 | − | 0.222387i | ||||
\(820\) | 5.01177 | 0.175019 | ||||||||
\(821\) | −16.5284 | + | 16.5284i | −0.576846 | + | 0.576846i | −0.934033 | − | 0.357187i | \(-0.883736\pi\) |
0.357187 | + | 0.934033i | \(0.383736\pi\) | |||||||
\(822\) | 0.305498 | + | 0.303856i | 0.0106555 | + | 0.0105982i | ||||
\(823\) | − | 34.7929i | − | 1.21280i | −0.795159 | − | 0.606401i | \(-0.792613\pi\) | ||
0.795159 | − | 0.606401i | \(-0.207387\pi\) | |||||||
\(824\) | −1.60661 | + | 1.60661i | −0.0559688 | + | 0.0559688i | ||||
\(825\) | 25.1667 | − | 0.0678320i | 0.876194 | − | 0.00236161i | ||||
\(826\) | −1.30730 | + | 1.30730i | −0.0454869 | + | 0.0454869i | ||||
\(827\) | 17.9323 | + | 17.9323i | 0.623566 | + | 0.623566i | 0.946441 | − | 0.322876i | \(-0.104650\pi\) |
−0.322876 | + | 0.946441i | \(0.604650\pi\) | |||||||
\(828\) | 32.0175 | − | 0.172595i | 1.11268 | − | 0.00599809i | ||||
\(829\) | 30.6603i | 1.06488i | 0.846468 | + | 0.532439i | \(0.178724\pi\) | ||||
−0.846468 | + | 0.532439i | \(0.821276\pi\) | |||||||
\(830\) | 1.36298 | + | 1.36298i | 0.0473097 | + | 0.0473097i | ||||
\(831\) | 15.8803 | − | 15.9661i | 0.550882 | − | 0.553859i | ||||
\(832\) | 24.6538 | + | 4.02249i | 0.854716 | + | 0.139455i | ||||
\(833\) | − | 6.99624i | − | 0.242405i | ||||||
\(834\) | −4.06993 | + | 0.0109697i | −0.140930 | + | 0.000379849i | ||||
\(835\) | 4.90477 | 0.169737 | ||||||||
\(836\) | −15.6060 | −0.539745 | ||||||||
\(837\) | 18.2752 | − | 0.147775i | 0.631685 | − | 0.00510785i | ||||
\(838\) | −3.10728 | − | 3.10728i | −0.107339 | − | 0.107339i | ||||
\(839\) | 29.2035 | + | 29.2035i | 1.00822 | + | 1.00822i | 0.999966 | + | 0.00824984i | \(0.00262603\pi\) |
0.00824984 | + | 0.999966i | \(0.497374\pi\) | |||||||
\(840\) | −0.996829 | + | 0.00268676i | −0.0343939 | + | 9.27019e-5i | ||||
\(841\) | 21.9810 | 0.757964 | ||||||||
\(842\) | 1.39278 | 0.0479982 | ||||||||
\(843\) | −0.0552210 | − | 20.4879i | −0.00190191 | − | 0.705639i | ||||
\(844\) | − | 0.302993i | − | 0.0104294i | ||||||
\(845\) | −7.93837 | + | 3.95215i | −0.273088 | + | 0.135958i | ||||
\(846\) | 0.0375601 | + | 6.96764i | 0.00129134 | + | 0.239552i | ||||
\(847\) | 0.518358 | + | 0.518358i | 0.0178110 | + | 0.0178110i | ||||
\(848\) | 24.2658i | 0.833290i | ||||||||
\(849\) | −12.1054 | + | 12.1708i | −0.415457 | + | 0.417702i | ||||
\(850\) | −4.78629 | − | 4.78629i | −0.164169 | − | 0.164169i | ||||
\(851\) | −1.06425 | + | 1.06425i | −0.0364822 | + | 0.0364822i | ||||
\(852\) | 0.104604 | + | 38.8097i | 0.00358367 | + | 1.32960i | ||||
\(853\) | 10.1411 | − | 10.1411i | 0.347224 | − | 0.347224i | −0.511851 | − | 0.859074i | \(-0.671040\pi\) |
0.859074 | + | 0.511851i | \(0.171040\pi\) | |||||||
\(854\) | 1.99312i | 0.0682031i | ||||||||
\(855\) | 0.0274895 | + | 5.09948i | 0.000940120 | + | 0.174398i | ||||
\(856\) | −8.76170 | + | 8.76170i | −0.299469 | + | 0.299469i | ||||
\(857\) | 21.5730 | 0.736921 | 0.368460 | − | 0.929643i | \(-0.379885\pi\) | ||||
0.368460 | + | 0.929643i | \(0.379885\pi\) | |||||||
\(858\) | −3.45883 | + | 2.50265i | −0.118082 | + | 0.0854389i | ||||
\(859\) | −25.1184 | −0.857030 | −0.428515 | − | 0.903535i | \(-0.640963\pi\) | ||||
−0.428515 | + | 0.903535i | \(0.640963\pi\) | |||||||
\(860\) | 2.85999 | − | 2.85999i | 0.0975250 | − | 0.0975250i | ||||
\(861\) | 4.59157 | − | 4.61639i | 0.156480 | − | 0.157326i | ||||
\(862\) | − | 6.91191i | − | 0.235420i | ||||||
\(863\) | −36.9361 | + | 36.9361i | −1.25732 | + | 1.25732i | −0.304950 | + | 0.952368i | \(0.598640\pi\) |
−0.952368 | + | 0.304950i | \(0.901360\pi\) | |||||||
\(864\) | −0.104323 | − | 12.9016i | −0.00354915 | − | 0.438922i | ||||
\(865\) | −8.49166 | + | 8.49166i | −0.288725 | + | 0.288725i | ||||
\(866\) | 2.19029 | + | 2.19029i | 0.0744290 | + | 0.0744290i | ||||
\(867\) | −39.2328 | − | 39.0218i | −1.33241 | − | 1.32525i | ||||
\(868\) | − | 6.87427i | − | 0.233328i | ||||||
\(869\) | 8.98968 | + | 8.98968i | 0.304954 | + | 0.304954i | ||||
\(870\) | 0.473505 | + | 0.470959i | 0.0160533 | + | 0.0159670i | ||||
\(871\) | −24.0680 | + | 17.3158i | −0.815513 | + | 0.586725i | ||||
\(872\) | − | 17.3424i | − | 0.587288i | ||||||
\(873\) | −23.5194 | + | 23.7744i | −0.796012 | + | 0.804640i | ||||
\(874\) | 2.90324 | 0.0982035 | ||||||||
\(875\) | −6.50395 | −0.219874 | ||||||||
\(876\) | −0.0800777 | − | 29.7101i | −0.00270557 | − | 1.00381i | ||||
\(877\) | −9.54564 | − | 9.54564i | −0.322333 | − | 0.322333i | 0.527328 | − | 0.849662i | \(-0.323194\pi\) |
−0.849662 | + | 0.527328i | \(0.823194\pi\) | |||||||
\(878\) | −4.76878 | − | 4.76878i | −0.160938 | − | 0.160938i | ||||
\(879\) | 0.0358588 | + | 13.3042i | 0.00120949 | + | 0.448738i | ||||
\(880\) | −8.15038 | −0.274749 | ||||||||
\(881\) | 26.3627 | 0.888183 | 0.444092 | − | 0.895981i | \(-0.353527\pi\) | ||||
0.444092 | + | 0.895981i | \(0.353527\pi\) | |||||||
\(882\) | −0.450147 | + | 0.455026i | −0.0151572 | + | 0.0153215i | ||||
\(883\) | 41.4709i | 1.39561i | 0.716289 | + | 0.697804i | \(0.245839\pi\) | ||||
−0.716289 | + | 0.697804i | \(0.754161\pi\) | |||||||
\(884\) | −48.6590 | − | 7.93916i | −1.63658 | − | 0.267023i | ||||
\(885\) | 7.25895 | + | 7.21992i | 0.244007 | + | 0.242695i | ||||
\(886\) | 4.30109 | + | 4.30109i | 0.144498 | + | 0.144498i | ||||
\(887\) | 0.0464034i | 0.00155807i | 1.00000 | 0.000779036i | \(0.000247975\pi\) | |||||
−1.00000 | 0.000779036i | \(0.999752\pi\) | ||||||||
\(888\) | 0.285577 | + | 0.284042i | 0.00958335 | + | 0.00953183i | ||||
\(889\) | 5.01922 | + | 5.01922i | 0.168339 | + | 0.168339i | ||||
\(890\) | −1.24362 | + | 1.24362i | −0.0416863 | + | 0.0416863i | ||||
\(891\) | −20.6101 | − | 20.1704i | −0.690464 | − | 0.675734i | ||||
\(892\) | 2.51630 | − | 2.51630i | 0.0842519 | − | 0.0842519i | ||||
\(893\) | − | 27.1275i | − | 0.907786i | ||||||
\(894\) | 3.18954 | − | 3.20678i | 0.106674 | − | 0.107251i | ||||
\(895\) | 5.40719 | − | 5.40719i | 0.180742 | − | 0.180742i | ||||
\(896\) | −6.44415 | −0.215284 | ||||||||
\(897\) | −27.6279 | + | 19.9903i | −0.922469 | + | 0.667455i | ||||
\(898\) | 6.96260 | 0.232345 | ||||||||
\(899\) | −6.58900 | + | 6.58900i | −0.219755 | + | 0.219755i | ||||
\(900\) | −0.143329 | − | 26.5885i | −0.00477764 | − | 0.886283i | ||||
\(901\) | − | 45.5273i | − | 1.51674i | ||||||
\(902\) | −1.81717 | + | 1.81717i | −0.0605053 | + | 0.0605053i | ||||
\(903\) | −0.0141627 | − | 5.25457i | −0.000471304 | − | 0.174861i | ||||
\(904\) | 7.57871 | − | 7.57871i | 0.252064 | − | 0.252064i | ||||
\(905\) | −11.1541 | − | 11.1541i | −0.370774 | − | 0.370774i | ||||
\(906\) | −0.729659 | + | 0.733603i | −0.0242413 | + | 0.0243723i | ||||
\(907\) | − | 43.4181i | − | 1.44167i | −0.693105 | − | 0.720836i | \(-0.743758\pi\) | ||
0.693105 | − | 0.720836i | \(-0.256242\pi\) | |||||||
\(908\) | −20.0074 | − | 20.0074i | −0.663967 | − | 0.663967i | ||||
\(909\) | 0.0695168 | + | 12.8958i | 0.00230573 | + | 0.427727i | ||||
\(910\) | 0.425954 | − | 0.306455i | 0.0141203 | − | 0.0101589i | ||||
\(911\) | 28.1213i | 0.931699i | 0.884864 | + | 0.465850i | \(0.154251\pi\) | ||||
−0.884864 | + | 0.465850i | \(0.845749\pi\) | |||||||
\(912\) | 0.0433804 | + | 16.0948i | 0.00143647 | + | 0.532952i | ||||
\(913\) | 42.4378 | 1.40449 | ||||||||
\(914\) | −8.40520 | −0.278019 | ||||||||
\(915\) | 11.0373 | − | 0.0297487i | 0.364880 | − | 0.000983463i | ||||
\(916\) | 30.9175 | + | 30.9175i | 1.02154 | + | 1.02154i | ||||
\(917\) | 0.379940 | + | 0.379940i | 0.0125467 | + | 0.0125467i | ||||
\(918\) | 0.0627150 | + | 7.75594i | 0.00206990 | + | 0.255984i | ||||
\(919\) | −1.38595 | −0.0457184 | −0.0228592 | − | 0.999739i | \(-0.507277\pi\) | ||||
−0.0228592 | + | 0.999739i | \(0.507277\pi\) | |||||||
\(920\) | 3.14270 | 0.103612 | ||||||||
\(921\) | −35.1338 | + | 0.0946962i | −1.15770 | + | 0.00312035i | ||||
\(922\) | 0.978041i | 0.0322101i | ||||||||
\(923\) | −24.1404 | − | 33.5537i | −0.794591 | − | 1.10443i | ||||
\(924\) | −7.64933 | + | 7.69068i | −0.251645 | + | 0.253005i | ||||
\(925\) | 0.883796 | + | 0.883796i | 0.0290590 | + | 0.0290590i | ||||
\(926\) | − | 6.15887i | − | 0.202393i | ||||||
\(927\) | 8.07883 | − | 0.0435501i | 0.265344 | − | 0.00143037i | ||||
\(928\) | 4.65158 | + | 4.65158i | 0.152696 | + | 0.152696i | ||||
\(929\) | 17.0813 | − | 17.0813i | 0.560420 | − | 0.560420i | −0.369007 | − | 0.929427i | \(-0.620302\pi\) |
0.929427 | + | 0.369007i | \(0.120302\pi\) | |||||||
\(930\) | 0.886598 | − | 0.00238965i | 0.0290727 | − | 7.83598e-5i | ||||
\(931\) | 1.76208 | − | 1.76208i | 0.0577498 | − | 0.0577498i | ||||
\(932\) | − | 51.5731i | − | 1.68933i | ||||||
\(933\) | −13.5948 | − | 13.5218i | −0.445075 | − | 0.442683i | ||||
\(934\) | −3.32415 | + | 3.32415i | −0.108769 | + | 0.108769i | ||||
\(935\) | 15.2917 | 0.500092 | ||||||||
\(936\) | 5.36961 | + | 7.37920i | 0.175511 | + | 0.241197i | ||||
\(937\) | −17.1536 | −0.560384 | −0.280192 | − | 0.959944i | \(-0.590398\pi\) | ||||
−0.280192 | + | 0.959944i | \(0.590398\pi\) | |||||||
\(938\) | 1.24061 | − | 1.24061i | 0.0405074 | − | 0.0405074i | ||||
\(939\) | −1.51308 | − | 1.50495i | −0.0493776 | − | 0.0491121i | ||||
\(940\) | − | 14.5135i | − | 0.473377i | ||||||
\(941\) | 7.59277 | − | 7.59277i | 0.247517 | − | 0.247517i | −0.572434 | − | 0.819951i | \(-0.694001\pi\) |
0.819951 | + | 0.572434i | \(0.194001\pi\) | |||||||
\(942\) | 1.24644 | − | 0.00335955i | 0.0406114 | − | 0.000109460i | ||||
\(943\) | −14.5149 | + | 14.5149i | −0.472672 | + | 0.472672i | ||||
\(944\) | 22.8487 | + | 22.8487i | 0.743662 | + | 0.743662i | ||||
\(945\) | 2.52651 | + | 2.48598i | 0.0821874 | + | 0.0808689i | ||||
\(946\) | 2.07396i | 0.0674303i | ||||||||
\(947\) | −23.1528 | − | 23.1528i | −0.752365 | − | 0.752365i | 0.222555 | − | 0.974920i | \(-0.428560\pi\) |
−0.974920 | + | 0.222555i | \(0.928560\pi\) | |||||||
\(948\) | 9.47201 | − | 9.52321i | 0.307637 | − | 0.309299i | ||||
\(949\) | 18.4803 | + | 25.6865i | 0.599894 | + | 0.833818i | ||||
\(950\) | − | 2.41096i | − | 0.0782218i | ||||||
\(951\) | −15.8491 | + | 0.0427182i | −0.513943 | + | 0.00138523i | ||||
\(952\) | 5.90277 | 0.191310 | ||||||||
\(953\) | −39.1269 | −1.26744 | −0.633722 | − | 0.773561i | \(-0.718474\pi\) | ||||
−0.633722 | + | 0.773561i | \(0.718474\pi\) | |||||||
\(954\) | −2.92928 | + | 2.96104i | −0.0948391 | + | 0.0958671i | ||||
\(955\) | 4.88393 | + | 4.88393i | 0.158040 | + | 0.158040i | ||||
\(956\) | −3.85891 | − | 3.85891i | −0.124806 | − | 0.124806i | ||||
\(957\) | 14.7034 | − | 0.0396302i | 0.475294 | − | 0.00128106i | ||||
\(958\) | 7.72734 | 0.249659 | ||||||||
\(959\) | −1.16599 | −0.0376517 | ||||||||
\(960\) | 0.0220625 | + | 8.18553i | 0.000712063 | + | 0.264187i | ||||
\(961\) | − | 18.6294i | − | 0.600948i | ||||||
\(962\) | −0.209261 | − | 0.0341428i | −0.00674684 | − | 0.00110081i | ||||
\(963\) | 44.0583 | − | 0.237503i | 1.41976 | − | 0.00765341i | ||||
\(964\) | 3.37934 | + | 3.37934i | 0.108841 | + | 0.108841i | ||||
\(965\) | 9.07546i | 0.292149i | ||||||||
\(966\) | 1.42303 | − | 1.43072i | 0.0457853 | − | 0.0460328i | ||||
\(967\) | 2.90975 | + | 2.90975i | 0.0935714 | + | 0.0935714i | 0.752343 | − | 0.658772i | \(-0.228924\pi\) |
−0.658772 | + | 0.752343i | \(0.728924\pi\) | |||||||
\(968\) | −0.437342 | + | 0.437342i | −0.0140567 | + | 0.0140567i | ||||
\(969\) | −0.0813901 | − | 30.1970i | −0.00261463 | − | 0.970068i | ||||
\(970\) | −1.14718 | + | 1.14718i | −0.0368337 | + | 0.0368337i | ||||
\(971\) | 19.5157i | 0.626289i | 0.949706 | + | 0.313144i | \(0.101382\pi\) | ||||
−0.949706 | + | 0.313144i | \(0.898618\pi\) | |||||||
\(972\) | −21.2514 | + | 21.8320i | −0.681638 | + | 0.700262i | ||||
\(973\) | 7.78773 | − | 7.78773i | 0.249663 | − | 0.249663i | ||||
\(974\) | 1.46699 | 0.0470055 | ||||||||
\(975\) | 16.6007 | + | 22.9432i | 0.531646 | + | 0.734771i | ||||
\(976\) | 34.8352 | 1.11505 | ||||||||
\(977\) | 28.9855 | − | 28.9855i | 0.927329 | − | 0.927329i | −0.0702036 | − | 0.997533i | \(-0.522365\pi\) |
0.997533 | + | 0.0702036i | \(0.0223649\pi\) | |||||||
\(978\) | 3.29730 | − | 3.31513i | 0.105436 | − | 0.106006i | ||||
\(979\) | 38.7214i | 1.23754i | ||||||||
\(980\) | 0.942729 | − | 0.942729i | 0.0301144 | − | 0.0301144i | ||||
\(981\) | −43.3681 | + | 43.8382i | −1.38464 | + | 1.39965i | ||||
\(982\) | −0.323837 | + | 0.323837i | −0.0103341 | + | 0.0103341i | ||||
\(983\) | 36.9089 | + | 36.9089i | 1.17721 | + | 1.17721i | 0.980452 | + | 0.196759i | \(0.0630417\pi\) |
0.196759 | + | 0.980452i | \(0.436958\pi\) | |||||||
\(984\) | 3.89487 | + | 3.87394i | 0.124164 | + | 0.123497i | ||||
\(985\) | − | 17.3276i | − | 0.552102i | ||||||
\(986\) | −2.79634 | − | 2.79634i | −0.0890537 | − | 0.0890537i | ||||
\(987\) | −13.3685 | − | 13.2966i | −0.425523 | − | 0.423236i | ||||
\(988\) | −10.2557 | − | 14.2548i | −0.326278 | − | 0.453507i | ||||
\(989\) | 16.5661i | 0.526770i | ||||||||
\(990\) | −0.994552 | − | 0.983887i | −0.0316089 | − | 0.0312700i | ||||
\(991\) | 3.59633 | 0.114241 | 0.0571206 | − | 0.998367i | \(-0.481808\pi\) | ||||
0.0571206 | + | 0.998367i | \(0.481808\pi\) | |||||||
\(992\) | 8.73318 | 0.277279 | ||||||||
\(993\) | −0.123794 | − | 45.9295i | −0.00392848 | − | 1.45753i | ||||
\(994\) | 1.72956 | + | 1.72956i | 0.0548584 | + | 0.0548584i | ||||
\(995\) | −7.81074 | − | 7.81074i | −0.247617 | − | 0.247617i | ||||
\(996\) | −0.120845 | − | 44.8356i | −0.00382913 | − | 1.42067i | ||||
\(997\) | −24.3260 | −0.770413 | −0.385206 | − | 0.922830i | \(-0.625870\pi\) | ||||
−0.385206 | + | 0.922830i | \(0.625870\pi\) | |||||||
\(998\) | 2.57608 | 0.0815444 | ||||||||
\(999\) | −0.0115804 | − | 1.43215i | −0.000366389 | − | 0.0453111i |
(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 | 273.2.n.c.8.11 | ✓ | 48 | |
3.2 | odd | 2 | inner | 273.2.n.c.8.14 | yes | 48 | |
13.5 | odd | 4 | inner | 273.2.n.c.239.14 | yes | 48 | |
39.5 | even | 4 | inner | 273.2.n.c.239.11 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.n.c.8.11 | ✓ | 48 | 1.1 | even | 1 | trivial | |
273.2.n.c.8.14 | yes | 48 | 3.2 | odd | 2 | inner | |
273.2.n.c.239.11 | yes | 48 | 39.5 | even | 4 | inner | |
273.2.n.c.239.14 | yes | 48 | 13.5 | odd | 4 | inner |