Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(62,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.62");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.k (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: | \(2.86104277578\) |
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 | 62.7 | ||
Character | \(\chi\) | \(=\) | 105.62 |
Dual form | 105.3.k.d.83.7 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.67168 | + | 1.67168i | −0.835842 | + | 0.835842i | −0.988309 | − | 0.152466i | \(-0.951278\pi\) |
0.152466 | + | 0.988309i | \(0.451278\pi\) | |||||||
\(3\) | −2.55943 | + | 1.56503i | −0.853143 | + | 0.521678i | ||||
\(4\) | − | 1.58906i | − | 0.397265i | ||||||
\(5\) | 0.529219 | + | 4.97191i | 0.105844 | + | 0.994383i | ||||
\(6\) | 1.66231 | − | 6.89480i | 0.277052 | − | 1.14913i | ||||
\(7\) | −1.73590 | + | 6.78135i | −0.247985 | + | 0.968764i | ||||
\(8\) | −4.03033 | − | 4.03033i | −0.503791 | − | 0.503791i | ||||
\(9\) | 4.10134 | − | 8.01118i | 0.455705 | − | 0.890131i | ||||
\(10\) | −9.19616 | − | 7.42678i | −0.919616 | − | 0.742678i | ||||
\(11\) | − | 4.41779i | − | 0.401617i | −0.979630 | − | 0.200809i | \(-0.935643\pi\) | ||
0.979630 | − | 0.200809i | \(-0.0643570\pi\) | |||||||
\(12\) | 2.48693 | + | 4.06708i | 0.207244 | + | 0.338924i | ||||
\(13\) | −1.62244 | − | 1.62244i | −0.124803 | − | 0.124803i | 0.641946 | − | 0.766750i | \(-0.278127\pi\) |
−0.766750 | + | 0.641946i | \(0.778127\pi\) | |||||||
\(14\) | −8.43440 | − | 14.2381i | −0.602457 | − | 1.01701i | ||||
\(15\) | −9.13571 | − | 11.8970i | −0.609047 | − | 0.793134i | ||||
\(16\) | 19.8311 | 1.23945 | ||||||||
\(17\) | −13.9255 | − | 13.9255i | −0.819145 | − | 0.819145i | 0.166839 | − | 0.985984i | \(-0.446644\pi\) |
−0.985984 | + | 0.166839i | \(0.946644\pi\) | |||||||
\(18\) | 6.53602 | + | 20.2483i | 0.363112 | + | 1.12491i | ||||
\(19\) | 0.694013 | 0.0365270 | 0.0182635 | − | 0.999833i | \(-0.494186\pi\) | ||||
0.0182635 | + | 0.999833i | \(0.494186\pi\) | |||||||
\(20\) | 7.90067 | − | 0.840961i | 0.395034 | − | 0.0420481i | ||||
\(21\) | −6.17013 | − | 20.0731i | −0.293816 | − | 0.955862i | ||||
\(22\) | 7.38515 | + | 7.38515i | 0.335689 | + | 0.335689i | ||||
\(23\) | 23.1818 | + | 23.1818i | 1.00790 | + | 1.00790i | 0.999969 | + | 0.00793606i | \(0.00252615\pi\) |
0.00793606 | + | 0.999969i | \(0.497474\pi\) | |||||||
\(24\) | 16.6229 | + | 4.00774i | 0.692623 | + | 0.166989i | ||||
\(25\) | −24.4399 | + | 5.26247i | −0.977594 | + | 0.210499i | ||||
\(26\) | 5.42443 | 0.208632 | ||||||||
\(27\) | 2.04067 | + | 26.9228i | 0.0755805 | + | 0.997140i | ||||
\(28\) | 10.7760 | + | 2.75844i | 0.384856 | + | 0.0985158i | ||||
\(29\) | −49.1234 | −1.69391 | −0.846956 | − | 0.531663i | \(-0.821567\pi\) | ||||
−0.846956 | + | 0.531663i | \(0.821567\pi\) | |||||||
\(30\) | 35.1601 | + | 4.61602i | 1.17200 | + | 0.153867i | ||||
\(31\) | 33.8768i | 1.09280i | 0.837524 | + | 0.546401i | \(0.184002\pi\) | ||||
−0.837524 | + | 0.546401i | \(0.815998\pi\) | |||||||
\(32\) | −17.0301 | + | 17.0301i | −0.532190 | + | 0.532190i | ||||
\(33\) | 6.91399 | + | 11.3070i | 0.209515 | + | 0.342637i | ||||
\(34\) | 46.5580 | 1.36935 | ||||||||
\(35\) | −34.6349 | − | 5.04191i | −0.989570 | − | 0.144054i | ||||
\(36\) | −12.7302 | − | 6.51728i | −0.353618 | − | 0.181036i | ||||
\(37\) | 2.02579 | + | 2.02579i | 0.0547510 | + | 0.0547510i | 0.733952 | − | 0.679201i | \(-0.237674\pi\) |
−0.679201 | + | 0.733952i | \(0.737674\pi\) | |||||||
\(38\) | −1.16017 | + | 1.16017i | −0.0305308 | + | 0.0305308i | ||||
\(39\) | 6.69171 | + | 1.61335i | 0.171582 | + | 0.0413679i | ||||
\(40\) | 17.9055 | − | 22.1714i | 0.447638 | − | 0.554285i | ||||
\(41\) | 32.5085 | 0.792891 | 0.396446 | − | 0.918058i | \(-0.370244\pi\) | ||||
0.396446 | + | 0.918058i | \(0.370244\pi\) | |||||||
\(42\) | 43.8704 | + | 23.2414i | 1.04453 | + | 0.553366i | ||||
\(43\) | −30.4591 | + | 30.4591i | −0.708351 | + | 0.708351i | −0.966188 | − | 0.257838i | \(-0.916990\pi\) |
0.257838 | + | 0.966188i | \(0.416990\pi\) | |||||||
\(44\) | −7.02014 | −0.159549 | ||||||||
\(45\) | 42.0014 | + | 16.1518i | 0.933365 | + | 0.358930i | ||||
\(46\) | −77.5053 | −1.68490 | ||||||||
\(47\) | −18.7790 | − | 18.7790i | −0.399554 | − | 0.399554i | 0.478522 | − | 0.878076i | \(-0.341173\pi\) |
−0.878076 | + | 0.478522i | \(0.841173\pi\) | |||||||
\(48\) | −50.7563 | + | 31.0364i | −1.05742 | + | 0.646591i | ||||
\(49\) | −42.9733 | − | 23.5434i | −0.877007 | − | 0.480478i | ||||
\(50\) | 32.0585 | − | 49.6529i | 0.641171 | − | 0.993058i | ||||
\(51\) | 57.4350 | + | 13.8474i | 1.12618 | + | 0.271518i | ||||
\(52\) | −2.57816 | + | 2.57816i | −0.0495800 | + | 0.0495800i | ||||
\(53\) | 33.8448 | + | 33.8448i | 0.638581 | + | 0.638581i | 0.950205 | − | 0.311624i | \(-0.100873\pi\) |
−0.311624 | + | 0.950205i | \(0.600873\pi\) | |||||||
\(54\) | −48.4178 | − | 41.5950i | −0.896625 | − | 0.770278i | ||||
\(55\) | 21.9649 | − | 2.33798i | 0.399361 | − | 0.0425087i | ||||
\(56\) | 34.3273 | − | 20.3348i | 0.612988 | − | 0.363122i | ||||
\(57\) | −1.77628 | + | 1.08615i | −0.0311627 | + | 0.0190553i | ||||
\(58\) | 82.1189 | − | 82.1189i | 1.41584 | − | 1.41584i | ||||
\(59\) | − | 23.1041i | − | 0.391596i | −0.980644 | − | 0.195798i | \(-0.937270\pi\) | ||
0.980644 | − | 0.195798i | \(-0.0627296\pi\) | |||||||
\(60\) | −18.9051 | + | 14.5172i | −0.315084 | + | 0.241953i | ||||
\(61\) | − | 12.9880i | − | 0.212919i | −0.994317 | − | 0.106459i | \(-0.966049\pi\) | ||
0.994317 | − | 0.106459i | \(-0.0339514\pi\) | |||||||
\(62\) | −56.6314 | − | 56.6314i | −0.913410 | − | 0.913410i | ||||
\(63\) | 47.2071 | + | 41.7192i | 0.749319 | + | 0.662209i | ||||
\(64\) | 22.3867i | 0.349792i | ||||||||
\(65\) | 7.20802 | − | 8.92528i | 0.110893 | − | 0.137312i | ||||
\(66\) | −30.4598 | − | 7.34376i | −0.461512 | − | 0.111269i | ||||
\(67\) | −56.3395 | − | 56.3395i | −0.840888 | − | 0.840888i | 0.148086 | − | 0.988974i | \(-0.452689\pi\) |
−0.988974 | + | 0.148086i | \(0.952689\pi\) | |||||||
\(68\) | −22.1284 | + | 22.1284i | −0.325418 | + | 0.325418i | ||||
\(69\) | −95.6125 | − | 23.0519i | −1.38569 | − | 0.334085i | ||||
\(70\) | 66.3272 | − | 49.4702i | 0.947531 | − | 0.706718i | ||||
\(71\) | 92.7547i | 1.30640i | 0.757184 | + | 0.653202i | \(0.226575\pi\) | ||||
−0.757184 | + | 0.653202i | \(0.773425\pi\) | |||||||
\(72\) | −48.8175 | + | 15.7579i | −0.678020 | + | 0.218860i | ||||
\(73\) | −95.4460 | − | 95.4460i | −1.30748 | − | 1.30748i | −0.923229 | − | 0.384251i | \(-0.874460\pi\) |
−0.384251 | − | 0.923229i | \(-0.625540\pi\) | |||||||
\(74\) | −6.77295 | −0.0915263 | ||||||||
\(75\) | 54.3161 | − | 51.7181i | 0.724215 | − | 0.689574i | ||||
\(76\) | − | 1.10283i | − | 0.0145109i | ||||||
\(77\) | 29.9586 | + | 7.66883i | 0.389072 | + | 0.0995952i | ||||
\(78\) | −13.8834 | + | 8.48941i | −0.177993 | + | 0.108839i | ||||
\(79\) | 100.280i | 1.26937i | 0.772770 | + | 0.634687i | \(0.218871\pi\) | ||||
−0.772770 | + | 0.634687i | \(0.781129\pi\) | |||||||
\(80\) | 10.4950 | + | 98.5987i | 0.131188 | + | 1.23248i | ||||
\(81\) | −47.3580 | − | 65.7132i | −0.584667 | − | 0.811274i | ||||
\(82\) | −54.3440 | + | 54.3440i | −0.662732 | + | 0.662732i | ||||
\(83\) | 5.62594 | − | 5.62594i | 0.0677824 | − | 0.0677824i | −0.672403 | − | 0.740185i | \(-0.734738\pi\) |
0.740185 | + | 0.672403i | \(0.234738\pi\) | |||||||
\(84\) | −31.8974 | + | 9.80471i | −0.379731 | + | 0.116723i | ||||
\(85\) | 61.8666 | − | 76.6059i | 0.727842 | − | 0.901245i | ||||
\(86\) | − | 101.836i | − | 1.18414i | ||||||
\(87\) | 125.728 | − | 76.8798i | 1.44515 | − | 0.883676i | ||||
\(88\) | −17.8052 | + | 17.8052i | −0.202331 | + | 0.202331i | ||||
\(89\) | 158.669i | 1.78280i | 0.453220 | + | 0.891399i | \(0.350275\pi\) | ||||
−0.453220 | + | 0.891399i | \(0.649725\pi\) | |||||||
\(90\) | −97.2139 | + | 43.2123i | −1.08015 | + | 0.480137i | ||||
\(91\) | 13.8188 | − | 8.18596i | 0.151854 | − | 0.0899556i | ||||
\(92\) | 36.8373 | − | 36.8373i | 0.400405 | − | 0.400405i | ||||
\(93\) | −53.0184 | − | 86.7053i | −0.570090 | − | 0.932315i | ||||
\(94\) | 62.7852 | 0.667928 | ||||||||
\(95\) | 0.367285 | + | 3.45057i | 0.00386616 | + | 0.0363218i | ||||
\(96\) | 16.9346 | − | 70.2399i | 0.176402 | − | 0.731665i | ||||
\(97\) | 37.1038 | − | 37.1038i | 0.382514 | − | 0.382514i | −0.489493 | − | 0.872007i | \(-0.662818\pi\) |
0.872007 | + | 0.489493i | \(0.162818\pi\) | |||||||
\(98\) | 111.195 | − | 32.4807i | 1.13464 | − | 0.331435i | ||||
\(99\) | −35.3917 | − | 18.1189i | −0.357492 | − | 0.183019i | ||||
\(100\) | 8.36238 | + | 38.8364i | 0.0836238 | + | 0.388364i | ||||
\(101\) | −17.6626 | −0.174877 | −0.0874384 | − | 0.996170i | \(-0.527868\pi\) | ||||
−0.0874384 | + | 0.996170i | \(0.527868\pi\) | |||||||
\(102\) | −119.162 | + | 72.8648i | −1.16825 | + | 0.714361i | ||||
\(103\) | 96.5666 | + | 96.5666i | 0.937540 | + | 0.937540i | 0.998161 | − | 0.0606213i | \(-0.0193082\pi\) |
−0.0606213 | + | 0.998161i | \(0.519308\pi\) | |||||||
\(104\) | 13.0780i | 0.125750i | ||||||||
\(105\) | 96.5364 | − | 41.3004i | 0.919394 | − | 0.393338i | ||||
\(106\) | −113.156 | −1.06751 | ||||||||
\(107\) | −7.22790 | + | 7.22790i | −0.0675504 | + | 0.0675504i | −0.740075 | − | 0.672524i | \(-0.765210\pi\) |
0.672524 | + | 0.740075i | \(0.265210\pi\) | |||||||
\(108\) | 42.7819 | − | 3.24275i | 0.396129 | − | 0.0300255i | ||||
\(109\) | 125.106i | 1.14776i | 0.818940 | + | 0.573880i | \(0.194562\pi\) | ||||
−0.818940 | + | 0.573880i | \(0.805438\pi\) | |||||||
\(110\) | −32.8100 | + | 40.6267i | −0.298273 | + | 0.369334i | ||||
\(111\) | −8.35527 | − | 2.01443i | −0.0752727 | − | 0.0181480i | ||||
\(112\) | −34.4248 | + | 134.482i | −0.307364 | + | 1.20073i | ||||
\(113\) | 71.6887 | + | 71.6887i | 0.634414 | + | 0.634414i | 0.949172 | − | 0.314758i | \(-0.101923\pi\) |
−0.314758 | + | 0.949172i | \(0.601923\pi\) | |||||||
\(114\) | 1.15367 | − | 4.78508i | 0.0101199 | − | 0.0419744i | ||||
\(115\) | −102.990 | + | 127.526i | −0.895562 | + | 1.10892i | ||||
\(116\) | 78.0601i | 0.672932i | ||||||||
\(117\) | −19.6519 | + | 6.34349i | −0.167965 | + | 0.0542179i | ||||
\(118\) | 38.6228 | + | 38.6228i | 0.327312 | + | 0.327312i | ||||
\(119\) | 118.607 | − | 70.2603i | 0.996694 | − | 0.590422i | ||||
\(120\) | −11.1290 | + | 84.7688i | −0.0927413 | + | 0.706407i | ||||
\(121\) | 101.483 | 0.838703 | ||||||||
\(122\) | 21.7119 | + | 21.7119i | 0.177966 | + | 0.177966i | ||||
\(123\) | −83.2032 | + | 50.8769i | −0.676449 | + | 0.413634i | ||||
\(124\) | 53.8323 | 0.434132 | ||||||||
\(125\) | −39.0986 | − | 118.728i | −0.312789 | − | 0.949823i | ||||
\(126\) | −148.657 | + | 9.17401i | −1.17982 | + | 0.0728096i | ||||
\(127\) | 4.25412 | + | 4.25412i | 0.0334970 | + | 0.0334970i | 0.723657 | − | 0.690160i | \(-0.242460\pi\) |
−0.690160 | + | 0.723657i | \(0.742460\pi\) | |||||||
\(128\) | −105.544 | − | 105.544i | −0.824561 | − | 0.824561i | ||||
\(129\) | 30.2883 | − | 125.627i | 0.234793 | − | 0.973855i | ||||
\(130\) | 2.87071 | + | 26.9698i | 0.0220824 | + | 0.207460i | ||||
\(131\) | −115.412 | −0.881007 | −0.440504 | − | 0.897751i | \(-0.645200\pi\) | ||||
−0.440504 | + | 0.897751i | \(0.645200\pi\) | |||||||
\(132\) | 17.9675 | − | 10.9867i | 0.136118 | − | 0.0832329i | ||||
\(133\) | −1.20473 | + | 4.70634i | −0.00905815 | + | 0.0353860i | ||||
\(134\) | 188.364 | 1.40570 | ||||||||
\(135\) | −132.778 | + | 24.3941i | −0.983539 | + | 0.180697i | ||||
\(136\) | 112.249i | 0.825357i | ||||||||
\(137\) | 134.388 | − | 134.388i | 0.980935 | − | 0.980935i | −0.0188868 | − | 0.999822i | \(-0.506012\pi\) |
0.999822 | + | 0.0188868i | \(0.00601221\pi\) | |||||||
\(138\) | 198.369 | − | 121.298i | 1.43746 | − | 0.878974i | ||||
\(139\) | 228.384 | 1.64305 | 0.821524 | − | 0.570174i | \(-0.193124\pi\) | ||||
0.821524 | + | 0.570174i | \(0.193124\pi\) | |||||||
\(140\) | −8.01189 | + | 55.0370i | −0.0572278 | + | 0.393121i | ||||
\(141\) | 77.4534 | + | 18.6738i | 0.549315 | + | 0.132438i | ||||
\(142\) | −155.057 | − | 155.057i | −1.09195 | − | 1.09195i | ||||
\(143\) | −7.16762 | + | 7.16762i | −0.0501232 | + | 0.0501232i | ||||
\(144\) | 81.3342 | − | 158.871i | 0.564821 | − | 1.10327i | ||||
\(145\) | −25.9971 | − | 244.237i | −0.179290 | − | 1.68440i | ||||
\(146\) | 319.111 | 2.18569 | ||||||||
\(147\) | 146.833 | − | 6.99698i | 0.998867 | − | 0.0475985i | ||||
\(148\) | 3.21909 | − | 3.21909i | 0.0217506 | − | 0.0217506i | ||||
\(149\) | −67.7175 | −0.454480 | −0.227240 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227240 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(150\) | −4.34307 | + | 177.256i | −0.0289538 | + | 1.18171i | ||||
\(151\) | 108.833 | 0.720749 | 0.360375 | − | 0.932808i | \(-0.382649\pi\) | ||||
0.360375 | + | 0.932808i | \(0.382649\pi\) | |||||||
\(152\) | −2.79710 | − | 2.79710i | −0.0184020 | − | 0.0184020i | ||||
\(153\) | −168.673 | + | 54.4463i | −1.10243 | + | 0.355858i | ||||
\(154\) | −62.9012 | + | 37.2614i | −0.408449 | + | 0.241957i | ||||
\(155\) | −168.433 | + | 17.9283i | −1.08666 | + | 0.115666i | ||||
\(156\) | 2.56371 | − | 10.6335i | 0.0164340 | − | 0.0681636i | ||||
\(157\) | 12.8504 | − | 12.8504i | 0.0818495 | − | 0.0818495i | −0.664997 | − | 0.746846i | \(-0.731567\pi\) |
0.746846 | + | 0.664997i | \(0.231567\pi\) | |||||||
\(158\) | −167.637 | − | 167.637i | −1.06100 | − | 1.06100i | ||||
\(159\) | −139.592 | − | 33.6551i | −0.877935 | − | 0.211667i | ||||
\(160\) | −93.6847 | − | 75.6594i | −0.585529 | − | 0.472871i | ||||
\(161\) | −197.445 | + | 116.963i | −1.22637 | + | 0.726476i | ||||
\(162\) | 189.019 | + | 30.6841i | 1.16679 | + | 0.189408i | ||||
\(163\) | −140.352 | + | 140.352i | −0.861054 | + | 0.861054i | −0.991461 | − | 0.130407i | \(-0.958372\pi\) |
0.130407 | + | 0.991461i | \(0.458372\pi\) | |||||||
\(164\) | − | 51.6580i | − | 0.314988i | ||||||
\(165\) | −52.5585 | + | 40.3597i | −0.318536 | + | 0.244604i | ||||
\(166\) | 18.8096i | 0.113311i | ||||||||
\(167\) | 70.3795 | + | 70.3795i | 0.421434 | + | 0.421434i | 0.885697 | − | 0.464263i | \(-0.153681\pi\) |
−0.464263 | + | 0.885697i | \(0.653681\pi\) | |||||||
\(168\) | −56.0336 | + | 105.769i | −0.333533 | + | 0.629577i | ||||
\(169\) | − | 163.735i | − | 0.968848i | ||||||
\(170\) | 24.6394 | + | 231.482i | 0.144938 | + | 1.36166i | ||||
\(171\) | 2.84638 | − | 5.55986i | 0.0166455 | − | 0.0325138i | ||||
\(172\) | 48.4013 | + | 48.4013i | 0.281403 | + | 0.281403i | ||||
\(173\) | −74.9815 | + | 74.9815i | −0.433419 | + | 0.433419i | −0.889790 | − | 0.456371i | \(-0.849149\pi\) |
0.456371 | + | 0.889790i | \(0.349149\pi\) | |||||||
\(174\) | −81.6586 | + | 338.696i | −0.469302 | + | 1.94653i | ||||
\(175\) | 6.73844 | − | 174.870i | 0.0385054 | − | 0.999258i | ||||
\(176\) | − | 87.6098i | − | 0.497783i | ||||||
\(177\) | 36.1587 | + | 59.1334i | 0.204287 | + | 0.334087i | ||||
\(178\) | −265.245 | − | 265.245i | −1.49014 | − | 1.49014i | ||||
\(179\) | −110.262 | −0.615991 | −0.307996 | − | 0.951388i | \(-0.599658\pi\) | ||||
−0.307996 | + | 0.951388i | \(0.599658\pi\) | |||||||
\(180\) | 25.6663 | − | 66.7428i | 0.142590 | − | 0.370793i | ||||
\(181\) | 58.1797i | 0.321435i | 0.987000 | + | 0.160717i | \(0.0513808\pi\) | ||||
−0.987000 | + | 0.160717i | \(0.948619\pi\) | |||||||
\(182\) | −9.41625 | + | 36.7849i | −0.0517376 | + | 0.202115i | ||||
\(183\) | 20.3267 | + | 33.2420i | 0.111075 | + | 0.181650i | ||||
\(184\) | − | 186.861i | − | 1.01555i | ||||||
\(185\) | −8.99995 | + | 11.1441i | −0.0486484 | + | 0.0602385i | ||||
\(186\) | 233.574 | + | 56.3140i | 1.25577 | + | 0.302763i | ||||
\(187\) | −61.5198 | + | 61.5198i | −0.328983 | + | 0.328983i | ||||
\(188\) | −29.8410 | + | 29.8410i | −0.158729 | + | 0.158729i | ||||
\(189\) | −186.115 | − | 32.8966i | −0.984736 | − | 0.174056i | ||||
\(190\) | −6.38225 | − | 5.15428i | −0.0335908 | − | 0.0271278i | ||||
\(191\) | − | 12.6214i | − | 0.0660807i | −0.999454 | − | 0.0330403i | \(-0.989481\pi\) | ||
0.999454 | − | 0.0330403i | \(-0.0105190\pi\) | |||||||
\(192\) | −35.0359 | − | 57.2971i | −0.182479 | − | 0.298423i | ||||
\(193\) | 211.567 | − | 211.567i | 1.09620 | − | 1.09620i | 0.101353 | − | 0.994851i | \(-0.467683\pi\) |
0.994851 | − | 0.101353i | \(-0.0323171\pi\) | |||||||
\(194\) | 124.052i | 0.639442i | ||||||||
\(195\) | −4.48005 | + | 34.1244i | −0.0229746 | + | 0.174997i | ||||
\(196\) | −37.4119 | + | 68.2872i | −0.190877 | + | 0.348404i | ||||
\(197\) | −102.520 | + | 102.520i | −0.520407 | + | 0.520407i | −0.917694 | − | 0.397288i | \(-0.869952\pi\) |
0.397288 | + | 0.917694i | \(0.369952\pi\) | |||||||
\(198\) | 89.4528 | − | 28.8748i | 0.451782 | − | 0.145832i | ||||
\(199\) | 235.953 | 1.18570 | 0.592848 | − | 0.805314i | \(-0.298004\pi\) | ||||
0.592848 | + | 0.805314i | \(0.298004\pi\) | |||||||
\(200\) | 119.710 | + | 77.2912i | 0.598551 | + | 0.386456i | ||||
\(201\) | 232.370 | + | 56.0237i | 1.15607 | + | 0.278725i | ||||
\(202\) | 29.5262 | − | 29.5262i | 0.146169 | − | 0.146169i | ||||
\(203\) | 85.2732 | − | 333.123i | 0.420065 | − | 1.64100i | ||||
\(204\) | 22.0044 | − | 91.2677i | 0.107865 | − | 0.447391i | ||||
\(205\) | 17.2041 | + | 161.630i | 0.0839227 | + | 0.788437i | ||||
\(206\) | −322.858 | −1.56727 | ||||||||
\(207\) | 280.790 | − | 90.6371i | 1.35647 | − | 0.437860i | ||||
\(208\) | −32.1749 | − | 32.1749i | −0.154687 | − | 0.154687i | ||||
\(209\) | − | 3.06600i | − | 0.0146699i | ||||||
\(210\) | −92.3371 | + | 230.420i | −0.439700 | + | 1.09724i | ||||
\(211\) | −89.6482 | −0.424873 | −0.212437 | − | 0.977175i | \(-0.568140\pi\) | ||||
−0.212437 | + | 0.977175i | \(0.568140\pi\) | |||||||
\(212\) | 53.7814 | − | 53.7814i | 0.253686 | − | 0.253686i | ||||
\(213\) | −145.164 | − | 237.399i | −0.681522 | − | 1.11455i | ||||
\(214\) | − | 24.1655i | − | 0.112923i | ||||||
\(215\) | −167.559 | − | 135.320i | −0.779346 | − | 0.629397i | ||||
\(216\) | 100.283 | − | 116.732i | 0.464274 | − | 0.540427i | ||||
\(217\) | −229.731 | − | 58.8067i | −1.05867 | − | 0.270999i | ||||
\(218\) | −209.137 | − | 209.137i | −0.959346 | − | 0.959346i | ||||
\(219\) | 393.663 | + | 94.9110i | 1.79755 | + | 0.433384i | ||||
\(220\) | −3.71519 | − | 34.9035i | −0.0168872 | − | 0.158652i | ||||
\(221\) | 45.1866i | 0.204464i | ||||||||
\(222\) | 17.3349 | − | 10.5999i | 0.0780850 | − | 0.0477473i | ||||
\(223\) | −85.1659 | − | 85.1659i | −0.381910 | − | 0.381910i | 0.489880 | − | 0.871790i | \(-0.337041\pi\) |
−0.871790 | + | 0.489880i | \(0.837041\pi\) | |||||||
\(224\) | −85.9244 | − | 145.049i | −0.383591 | − | 0.647541i | ||||
\(225\) | −58.0776 | + | 217.375i | −0.258123 | + | 0.966112i | ||||
\(226\) | −239.682 | −1.06054 | ||||||||
\(227\) | 129.989 | + | 129.989i | 0.572639 | + | 0.572639i | 0.932865 | − | 0.360226i | \(-0.117300\pi\) |
−0.360226 | + | 0.932865i | \(0.617300\pi\) | |||||||
\(228\) | 1.72596 | + | 2.82261i | 0.00757001 | + | 0.0123799i | ||||
\(229\) | −109.923 | −0.480011 | −0.240006 | − | 0.970771i | \(-0.577149\pi\) | ||||
−0.240006 | + | 0.970771i | \(0.577149\pi\) | |||||||
\(230\) | −41.0173 | − | 385.350i | −0.178336 | − | 1.67543i | ||||
\(231\) | −88.6788 | + | 27.2584i | −0.383891 | + | 0.118002i | ||||
\(232\) | 197.984 | + | 197.984i | 0.853378 | + | 0.853378i | ||||
\(233\) | 218.319 | + | 218.319i | 0.936990 | + | 0.936990i | 0.998129 | − | 0.0611395i | \(-0.0194735\pi\) |
−0.0611395 | + | 0.998129i | \(0.519473\pi\) | |||||||
\(234\) | 22.2474 | − | 43.4561i | 0.0950745 | − | 0.185710i | ||||
\(235\) | 83.4295 | − | 103.306i | 0.355019 | − | 0.439600i | ||||
\(236\) | −36.7139 | −0.155567 | ||||||||
\(237\) | −156.942 | − | 256.661i | −0.662204 | − | 1.08296i | ||||
\(238\) | −80.8198 | + | 315.726i | −0.339579 | + | 1.32658i | ||||
\(239\) | −20.1742 | −0.0844109 | −0.0422054 | − | 0.999109i | \(-0.513438\pi\) | ||||
−0.0422054 | + | 0.999109i | \(0.513438\pi\) | |||||||
\(240\) | −181.171 | − | 235.931i | −0.754881 | − | 0.983046i | ||||
\(241\) | 257.604i | 1.06890i | 0.845201 | + | 0.534449i | \(0.179481\pi\) | ||||
−0.845201 | + | 0.534449i | \(0.820519\pi\) | |||||||
\(242\) | −169.648 | + | 169.648i | −0.701024 | + | 0.701024i | ||||
\(243\) | 224.053 | + | 94.0713i | 0.922027 | + | 0.387125i | ||||
\(244\) | −20.6388 | −0.0845852 | ||||||||
\(245\) | 94.3136 | − | 226.119i | 0.384953 | − | 0.922936i | ||||
\(246\) | 54.0394 | − | 224.140i | 0.219672 | − | 0.911137i | ||||
\(247\) | −1.12600 | − | 1.12600i | −0.00455869 | − | 0.00455869i | ||||
\(248\) | 136.535 | − | 136.535i | 0.550544 | − | 0.550544i | ||||
\(249\) | −5.59441 | + | 23.2040i | −0.0224675 | + | 0.0931887i | ||||
\(250\) | 263.836 | + | 133.115i | 1.05534 | + | 0.532460i | ||||
\(251\) | 191.569 | 0.763223 | 0.381612 | − | 0.924323i | \(-0.375369\pi\) | ||||
0.381612 | + | 0.924323i | \(0.375369\pi\) | |||||||
\(252\) | 66.2943 | − | 75.0149i | 0.263073 | − | 0.297678i | ||||
\(253\) | 102.412 | − | 102.412i | 0.404792 | − | 0.404792i | ||||
\(254\) | −14.2231 | −0.0559964 | ||||||||
\(255\) | −38.4524 | + | 292.890i | −0.150794 | + | 1.14859i | ||||
\(256\) | 263.325 | 1.02861 | ||||||||
\(257\) | 205.696 | + | 205.696i | 0.800374 | + | 0.800374i | 0.983154 | − | 0.182779i | \(-0.0585094\pi\) |
−0.182779 | + | 0.983154i | \(0.558509\pi\) | |||||||
\(258\) | 159.377 | + | 260.642i | 0.617739 | + | 1.01024i | ||||
\(259\) | −17.2541 | + | 10.2210i | −0.0666182 | + | 0.0394633i | ||||
\(260\) | −14.1828 | − | 11.4540i | −0.0545493 | − | 0.0440538i | ||||
\(261\) | −201.472 | + | 393.537i | −0.771923 | + | 1.50780i | ||||
\(262\) | 192.932 | − | 192.932i | 0.736383 | − | 0.736383i | ||||
\(263\) | 4.82449 | + | 4.82449i | 0.0183441 | + | 0.0183441i | 0.716219 | − | 0.697875i | \(-0.245871\pi\) |
−0.697875 | + | 0.716219i | \(0.745871\pi\) | |||||||
\(264\) | 17.7054 | − | 73.4367i | 0.0670657 | − | 0.278169i | ||||
\(265\) | −150.362 | + | 186.185i | −0.567404 | + | 0.702584i | ||||
\(266\) | −5.85358 | − | 9.88145i | −0.0220059 | − | 0.0371483i | ||||
\(267\) | −248.322 | − | 406.102i | −0.930046 | − | 1.52098i | ||||
\(268\) | −89.5269 | + | 89.5269i | −0.334056 | + | 0.334056i | ||||
\(269\) | − | 106.984i | − | 0.397708i | −0.980029 | − | 0.198854i | \(-0.936278\pi\) | ||
0.980029 | − | 0.198854i | \(-0.0637220\pi\) | |||||||
\(270\) | 181.183 | − | 262.742i | 0.671049 | − | 0.973118i | ||||
\(271\) | − | 187.036i | − | 0.690171i | −0.938571 | − | 0.345085i | \(-0.887850\pi\) | ||
0.938571 | − | 0.345085i | \(-0.112150\pi\) | |||||||
\(272\) | −276.158 | − | 276.158i | −1.01529 | − | 1.01529i | ||||
\(273\) | −22.5568 | + | 42.5782i | −0.0826256 | + | 0.155964i | ||||
\(274\) | 449.309i | 1.63981i | ||||||||
\(275\) | 23.2485 | + | 107.970i | 0.0845399 | + | 0.392619i | ||||
\(276\) | −36.6308 | + | 151.934i | −0.132720 | + | 0.550485i | ||||
\(277\) | 95.7717 | + | 95.7717i | 0.345746 | + | 0.345746i | 0.858522 | − | 0.512776i | \(-0.171383\pi\) |
−0.512776 | + | 0.858522i | \(0.671383\pi\) | |||||||
\(278\) | −381.786 | + | 381.786i | −1.37333 | + | 1.37333i | ||||
\(279\) | 271.393 | + | 138.941i | 0.972736 | + | 0.497995i | ||||
\(280\) | 119.270 | + | 159.911i | 0.425963 | + | 0.571110i | ||||
\(281\) | − | 140.834i | − | 0.501189i | −0.968092 | − | 0.250594i | \(-0.919374\pi\) | ||
0.968092 | − | 0.250594i | \(-0.0806261\pi\) | |||||||
\(282\) | −160.694 | + | 98.2610i | −0.569838 | + | 0.348443i | ||||
\(283\) | 204.752 | + | 204.752i | 0.723504 | + | 0.723504i | 0.969317 | − | 0.245813i | \(-0.0790551\pi\) |
−0.245813 | + | 0.969317i | \(0.579055\pi\) | |||||||
\(284\) | 147.393 | 0.518989 | ||||||||
\(285\) | −6.34030 | − | 8.25667i | −0.0222467 | − | 0.0289708i | ||||
\(286\) | − | 23.9640i | − | 0.0837902i | ||||||
\(287\) | −56.4314 | + | 220.452i | −0.196625 | + | 0.768124i | ||||
\(288\) | 66.5848 | + | 206.277i | 0.231197 | + | 0.716240i | ||||
\(289\) | 98.8373i | 0.341998i | ||||||||
\(290\) | 451.747 | + | 364.829i | 1.55775 | + | 1.25803i | ||||
\(291\) | −36.8958 | + | 153.033i | −0.126790 | + | 0.525888i | ||||
\(292\) | −151.669 | + | 151.669i | −0.519416 | + | 0.519416i | ||||
\(293\) | −158.208 | + | 158.208i | −0.539959 | + | 0.539959i | −0.923517 | − | 0.383558i | \(-0.874699\pi\) |
0.383558 | + | 0.923517i | \(0.374699\pi\) | |||||||
\(294\) | −233.762 | + | 257.156i | −0.795110 | + | 0.874680i | ||||
\(295\) | 114.872 | − | 12.2272i | 0.389396 | − | 0.0414480i | ||||
\(296\) | − | 16.3292i | − | 0.0551661i | ||||||
\(297\) | 118.939 | − | 9.01527i | 0.400469 | − | 0.0303544i | ||||
\(298\) | 113.202 | − | 113.202i | 0.379873 | − | 0.379873i | ||||
\(299\) | − | 75.2224i | − | 0.251580i | ||||||
\(300\) | −82.1832 | − | 86.3116i | −0.273944 | − | 0.287705i | ||||
\(301\) | −153.680 | − | 259.427i | −0.510564 | − | 0.861885i | ||||
\(302\) | −181.935 | + | 181.935i | −0.602433 | + | 0.602433i | ||||
\(303\) | 45.2060 | − | 27.6425i | 0.149195 | − | 0.0912293i | ||||
\(304\) | 13.7631 | 0.0452732 | ||||||||
\(305\) | 64.5754 | − | 6.87352i | 0.211723 | − | 0.0225361i | ||||
\(306\) | 190.950 | − | 372.984i | 0.624020 | − | 1.21890i | ||||
\(307\) | −390.484 | + | 390.484i | −1.27194 | + | 1.27194i | −0.326865 | + | 0.945071i | \(0.605992\pi\) |
−0.945071 | + | 0.326865i | \(0.894008\pi\) | |||||||
\(308\) | 12.1862 | − | 47.6060i | 0.0395657 | − | 0.154565i | ||||
\(309\) | −398.285 | − | 96.0253i | −1.28895 | − | 0.310761i | ||||
\(310\) | 251.596 | − | 311.537i | 0.811600 | − | 1.00496i | ||||
\(311\) | −314.164 | −1.01017 | −0.505087 | − | 0.863068i | \(-0.668540\pi\) | ||||
−0.505087 | + | 0.863068i | \(0.668540\pi\) | |||||||
\(312\) | −20.4675 | − | 33.4721i | −0.0656009 | − | 0.107282i | ||||
\(313\) | 138.521 | + | 138.521i | 0.442558 | + | 0.442558i | 0.892871 | − | 0.450313i | \(-0.148688\pi\) |
−0.450313 | + | 0.892871i | \(0.648688\pi\) | |||||||
\(314\) | 42.9635i | 0.136827i | ||||||||
\(315\) | −182.441 | + | 256.788i | −0.579179 | + | 0.815200i | ||||
\(316\) | 159.352 | 0.504278 | ||||||||
\(317\) | 171.788 | − | 171.788i | 0.541917 | − | 0.541917i | −0.382174 | − | 0.924090i | \(-0.624824\pi\) |
0.924090 | + | 0.382174i | \(0.124824\pi\) | |||||||
\(318\) | 289.614 | − | 177.092i | 0.910736 | − | 0.556895i | ||||
\(319\) | 217.017i | 0.680304i | ||||||||
\(320\) | −111.305 | + | 11.8475i | −0.347827 | + | 0.0370234i | ||||
\(321\) | 7.18738 | − | 29.8112i | 0.0223906 | − | 0.0928697i | ||||
\(322\) | 134.541 | − | 525.591i | 0.417830 | − | 1.63227i | ||||
\(323\) | −9.66445 | − | 9.66445i | −0.0299209 | − | 0.0299209i | ||||
\(324\) | −104.422 | + | 75.2547i | −0.322291 | + | 0.232268i | ||||
\(325\) | 48.1904 | + | 31.1142i | 0.148278 | + | 0.0957361i | ||||
\(326\) | − | 469.248i | − | 1.43941i | ||||||
\(327\) | −195.795 | − | 320.199i | −0.598761 | − | 0.979203i | ||||
\(328\) | −131.020 | − | 131.020i | −0.399452 | − | 0.399452i | ||||
\(329\) | 159.946 | − | 94.7486i | 0.486157 | − | 0.287990i | ||||
\(330\) | 20.3926 | − | 155.330i | 0.0617958 | − | 0.470697i | ||||
\(331\) | −97.1798 | −0.293595 | −0.146797 | − | 0.989167i | \(-0.546897\pi\) | ||||
−0.146797 | + | 0.989167i | \(0.546897\pi\) | |||||||
\(332\) | −8.93996 | − | 8.93996i | −0.0269276 | − | 0.0269276i | ||||
\(333\) | 24.5374 | − | 7.92049i | 0.0736858 | − | 0.0237853i | ||||
\(334\) | −235.305 | −0.704505 | ||||||||
\(335\) | 250.299 | − | 309.931i | 0.747162 | − | 0.925168i | ||||
\(336\) | −122.361 | − | 398.072i | −0.364169 | − | 1.18474i | ||||
\(337\) | −142.405 | − | 142.405i | −0.422566 | − | 0.422566i | 0.463520 | − | 0.886086i | \(-0.346586\pi\) |
−0.886086 | + | 0.463520i | \(0.846586\pi\) | |||||||
\(338\) | 273.714 | + | 273.714i | 0.809804 | + | 0.809804i | ||||
\(339\) | −295.677 | − | 71.2869i | −0.872205 | − | 0.210286i | ||||
\(340\) | −121.731 | − | 98.3097i | −0.358033 | − | 0.289146i | ||||
\(341\) | 149.661 | 0.438888 | ||||||||
\(342\) | 4.53608 | + | 14.0526i | 0.0132634 | + | 0.0410894i | ||||
\(343\) | 234.253 | − | 250.548i | 0.682955 | − | 0.730461i | ||||
\(344\) | 245.520 | 0.713722 | ||||||||
\(345\) | 64.0119 | − | 487.576i | 0.185542 | − | 1.41326i | ||||
\(346\) | − | 250.691i | − | 0.724540i | ||||||
\(347\) | 42.5261 | − | 42.5261i | 0.122554 | − | 0.122554i | −0.643170 | − | 0.765723i | \(-0.722381\pi\) |
0.765723 | + | 0.643170i | \(0.222381\pi\) | |||||||
\(348\) | −122.167 | − | 199.789i | −0.351054 | − | 0.574107i | ||||
\(349\) | −323.576 | −0.927152 | −0.463576 | − | 0.886057i | \(-0.653434\pi\) | ||||
−0.463576 | + | 0.886057i | \(0.653434\pi\) | |||||||
\(350\) | 281.063 | + | 303.592i | 0.803038 | + | 0.867407i | ||||
\(351\) | 40.3698 | − | 46.9916i | 0.115014 | − | 0.133879i | ||||
\(352\) | 75.2353 | + | 75.2353i | 0.213737 | + | 0.213737i | ||||
\(353\) | −121.979 | + | 121.979i | −0.345550 | + | 0.345550i | −0.858449 | − | 0.512899i | \(-0.828572\pi\) |
0.512899 | + | 0.858449i | \(0.328572\pi\) | |||||||
\(354\) | −159.298 | − | 38.4063i | −0.449995 | − | 0.108492i | ||||
\(355\) | −461.168 | + | 49.0876i | −1.29907 | + | 0.138275i | ||||
\(356\) | 252.135 | 0.708243 | ||||||||
\(357\) | −193.605 | + | 365.449i | −0.542312 | + | 1.02367i | ||||
\(358\) | 184.324 | − | 184.324i | 0.514872 | − | 0.514872i | ||||
\(359\) | −456.029 | −1.27028 | −0.635138 | − | 0.772399i | \(-0.719057\pi\) | ||||
−0.635138 | + | 0.772399i | \(0.719057\pi\) | |||||||
\(360\) | −104.182 | − | 234.377i | −0.289395 | − | 0.651047i | ||||
\(361\) | −360.518 | −0.998666 | ||||||||
\(362\) | −97.2581 | − | 97.2581i | −0.268669 | − | 0.268669i | ||||
\(363\) | −259.739 | + | 158.824i | −0.715534 | + | 0.437533i | ||||
\(364\) | −13.0080 | − | 21.9588i | −0.0357362 | − | 0.0603264i | ||||
\(365\) | 424.037 | − | 525.061i | 1.16175 | − | 1.43852i | ||||
\(366\) | −89.5499 | − | 21.5902i | −0.244672 | − | 0.0589896i | ||||
\(367\) | 52.7521 | − | 52.7521i | 0.143739 | − | 0.143739i | −0.631576 | − | 0.775314i | \(-0.717591\pi\) |
0.775314 | + | 0.631576i | \(0.217591\pi\) | |||||||
\(368\) | 459.721 | + | 459.721i | 1.24924 | + | 1.24924i | ||||
\(369\) | 133.329 | − | 260.432i | 0.361324 | − | 0.705777i | ||||
\(370\) | −3.58438 | − | 33.6745i | −0.00968750 | − | 0.0910122i | ||||
\(371\) | −288.264 | + | 170.762i | −0.776993 | + | 0.460276i | ||||
\(372\) | −137.780 | + | 84.2494i | −0.370376 | + | 0.226477i | ||||
\(373\) | −269.362 | + | 269.362i | −0.722150 | + | 0.722150i | −0.969043 | − | 0.246893i | \(-0.920591\pi\) |
0.246893 | + | 0.969043i | \(0.420591\pi\) | |||||||
\(374\) | − | 205.683i | − | 0.549956i | ||||||
\(375\) | 285.883 | + | 242.685i | 0.762355 | + | 0.647159i | ||||
\(376\) | 151.371i | 0.402583i | ||||||||
\(377\) | 79.7000 | + | 79.7000i | 0.211406 | + | 0.211406i | ||||
\(378\) | 366.118 | − | 256.133i | 0.968567 | − | 0.677600i | ||||
\(379\) | − | 253.497i | − | 0.668856i | −0.942421 | − | 0.334428i | \(-0.891457\pi\) | ||
0.942421 | − | 0.334428i | \(-0.108543\pi\) | |||||||
\(380\) | 5.48317 | − | 0.583638i | 0.0144294 | − | 0.00153589i | ||||
\(381\) | −17.5459 | − | 4.23027i | −0.0460523 | − | 0.0111031i | ||||
\(382\) | 21.0990 | + | 21.0990i | 0.0552330 | + | 0.0552330i | ||||
\(383\) | 162.755 | − | 162.755i | 0.424948 | − | 0.424948i | −0.461955 | − | 0.886903i | \(-0.652852\pi\) |
0.886903 | + | 0.461955i | \(0.152852\pi\) | |||||||
\(384\) | 435.311 | + | 104.952i | 1.13362 | + | 0.273313i | ||||
\(385\) | −22.2741 | + | 153.010i | −0.0578548 | + | 0.397428i | ||||
\(386\) | 707.348i | 1.83251i | ||||||||
\(387\) | 119.090 | + | 368.936i | 0.307726 | + | 0.953324i | ||||
\(388\) | −58.9602 | − | 58.9602i | −0.151959 | − | 0.151959i | ||||
\(389\) | −309.463 | −0.795534 | −0.397767 | − | 0.917486i | \(-0.630215\pi\) | ||||
−0.397767 | + | 0.917486i | \(0.630215\pi\) | |||||||
\(390\) | −49.5560 | − | 64.5345i | −0.127067 | − | 0.165473i | ||||
\(391\) | − | 645.635i | − | 1.65124i | ||||||
\(392\) | 78.3089 | + | 268.085i | 0.199768 | + | 0.683889i | ||||
\(393\) | 295.389 | − | 180.624i | 0.751625 | − | 0.459602i | ||||
\(394\) | − | 342.763i | − | 0.869956i | ||||||
\(395\) | −498.586 | + | 53.0704i | −1.26224 | + | 0.134355i | ||||
\(396\) | −28.7920 | + | 56.2396i | −0.0727070 | + | 0.142019i | ||||
\(397\) | 463.385 | − | 463.385i | 1.16722 | − | 1.16722i | 0.184357 | − | 0.982859i | \(-0.440980\pi\) |
0.982859 | − | 0.184357i | \(-0.0590203\pi\) | |||||||
\(398\) | −394.440 | + | 394.440i | −0.991055 | + | 0.991055i | ||||
\(399\) | −4.28215 | − | 13.9310i | −0.0107322 | − | 0.0349148i | ||||
\(400\) | −484.670 | + | 104.361i | −1.21167 | + | 0.260902i | ||||
\(401\) | − | 516.485i | − | 1.28799i | −0.765028 | − | 0.643997i | \(-0.777275\pi\) | ||
0.765028 | − | 0.643997i | \(-0.222725\pi\) | |||||||
\(402\) | −482.104 | + | 294.796i | −1.19926 | + | 0.733323i | ||||
\(403\) | 54.9633 | − | 54.9633i | 0.136385 | − | 0.136385i | ||||
\(404\) | 28.0669i | 0.0694724i | ||||||||
\(405\) | 301.657 | − | 270.237i | 0.744833 | − | 0.667251i | ||||
\(406\) | 414.327 | + | 699.427i | 1.02051 | + | 1.72273i | ||||
\(407\) | 8.94950 | − | 8.94950i | 0.0219889 | − | 0.0219889i | ||||
\(408\) | −175.673 | − | 287.292i | −0.430570 | − | 0.704147i | ||||
\(409\) | −119.076 | −0.291139 | −0.145570 | − | 0.989348i | \(-0.546501\pi\) | ||||
−0.145570 | + | 0.989348i | \(0.546501\pi\) | |||||||
\(410\) | −298.954 | − | 241.434i | −0.729155 | − | 0.588863i | ||||
\(411\) | −133.635 | + | 554.278i | −0.325145 | + | 1.34861i | ||||
\(412\) | 153.450 | − | 153.450i | 0.372452 | − | 0.372452i | ||||
\(413\) | 156.677 | + | 40.1064i | 0.379364 | + | 0.0971099i | ||||
\(414\) | −317.876 | + | 620.909i | −0.767816 | + | 1.49978i | ||||
\(415\) | 30.9491 | + | 24.9943i | 0.0745760 | + | 0.0602273i | ||||
\(416\) | 55.2607 | 0.132838 | ||||||||
\(417\) | −584.532 | + | 357.428i | −1.40175 | + | 0.857142i | ||||
\(418\) | 5.12539 | + | 5.12539i | 0.0122617 | + | 0.0122617i | ||||
\(419\) | 732.322i | 1.74778i | 0.486120 | + | 0.873892i | \(0.338412\pi\) | ||||
−0.486120 | + | 0.873892i | \(0.661588\pi\) | |||||||
\(420\) | −65.6289 | − | 153.402i | −0.156259 | − | 0.365243i | ||||
\(421\) | 307.320 | 0.729976 | 0.364988 | − | 0.931012i | \(-0.381073\pi\) | ||||
0.364988 | + | 0.931012i | \(0.381073\pi\) | |||||||
\(422\) | 149.864 | − | 149.864i | 0.355127 | − | 0.355127i | ||||
\(423\) | −227.461 | + | 73.4229i | −0.537734 | + | 0.173577i | ||||
\(424\) | − | 272.812i | − | 0.643424i | ||||||
\(425\) | 413.619 | + | 267.054i | 0.973220 | + | 0.628363i | ||||
\(426\) | 639.525 | + | 154.187i | 1.50123 | + | 0.361942i | ||||
\(427\) | 88.0764 | + | 22.5459i | 0.206268 | + | 0.0528007i | ||||
\(428\) | 11.4856 | + | 11.4856i | 0.0268354 | + | 0.0268354i | ||||
\(429\) | 7.12744 | − | 29.5626i | 0.0166141 | − | 0.0689104i | ||||
\(430\) | 506.320 | − | 53.8936i | 1.17749 | − | 0.125334i | ||||
\(431\) | − | 205.822i | − | 0.477546i | −0.971075 | − | 0.238773i | \(-0.923255\pi\) | ||
0.971075 | − | 0.238773i | \(-0.0767452\pi\) | |||||||
\(432\) | 40.4689 | + | 533.909i | 0.0936779 | + | 1.23590i | ||||
\(433\) | 291.861 | + | 291.861i | 0.674043 | + | 0.674043i | 0.958646 | − | 0.284603i | \(-0.0918617\pi\) |
−0.284603 | + | 0.958646i | \(0.591862\pi\) | |||||||
\(434\) | 482.343 | − | 285.731i | 1.11139 | − | 0.658366i | ||||
\(435\) | 448.777 | + | 584.422i | 1.03167 | + | 1.34350i | ||||
\(436\) | 198.801 | 0.455965 | ||||||||
\(437\) | 16.0885 | + | 16.0885i | 0.0368157 | + | 0.0368157i | ||||
\(438\) | −816.742 | + | 499.420i | −1.86471 | + | 1.14023i | ||||
\(439\) | 116.671 | 0.265765 | 0.132882 | − | 0.991132i | \(-0.457577\pi\) | ||||
0.132882 | + | 0.991132i | \(0.457577\pi\) | |||||||
\(440\) | −97.9486 | − | 79.1029i | −0.222610 | − | 0.179779i | ||||
\(441\) | −364.859 | + | 247.707i | −0.827345 | + | 0.561695i | ||||
\(442\) | −75.5377 | − | 75.5377i | −0.170900 | − | 0.170900i | ||||
\(443\) | −282.021 | − | 282.021i | −0.636617 | − | 0.636617i | 0.313102 | − | 0.949719i | \(-0.398632\pi\) |
−0.949719 | + | 0.313102i | \(0.898632\pi\) | |||||||
\(444\) | −3.20105 | + | 13.2770i | −0.00720957 | + | 0.0299032i | ||||
\(445\) | −788.888 | + | 83.9707i | −1.77278 | + | 0.188698i | ||||
\(446\) | 284.741 | 0.638433 | ||||||||
\(447\) | 173.318 | − | 105.980i | 0.387736 | − | 0.237092i | ||||
\(448\) | −151.812 | − | 38.8610i | −0.338866 | − | 0.0867433i | ||||
\(449\) | 407.834 | 0.908317 | 0.454158 | − | 0.890921i | \(-0.349940\pi\) | ||||
0.454158 | + | 0.890921i | \(0.349940\pi\) | |||||||
\(450\) | −266.295 | − | 460.470i | −0.591767 | − | 1.02327i | ||||
\(451\) | − | 143.616i | − | 0.318439i | ||||||
\(452\) | 113.918 | − | 113.918i | 0.252030 | − | 0.252030i | ||||
\(453\) | −278.550 | + | 170.327i | −0.614902 | + | 0.375999i | ||||
\(454\) | −434.602 | −0.957272 | ||||||||
\(455\) | 48.0130 | + | 64.3735i | 0.105523 | + | 0.141480i | ||||
\(456\) | 11.5365 | + | 2.78142i | 0.0252994 | + | 0.00609961i | ||||
\(457\) | 461.473 | + | 461.473i | 1.00979 | + | 1.00979i | 0.999952 | + | 0.00983627i | \(0.00313103\pi\) |
0.00983627 | + | 0.999952i | \(0.496869\pi\) | |||||||
\(458\) | 183.756 | − | 183.756i | 0.401214 | − | 0.401214i | ||||
\(459\) | 346.495 | − | 403.330i | 0.754891 | − | 0.878714i | ||||
\(460\) | 202.647 | + | 163.657i | 0.440537 | + | 0.355776i | ||||
\(461\) | 788.797 | 1.71106 | 0.855528 | − | 0.517757i | \(-0.173233\pi\) | ||||
0.855528 | + | 0.517757i | \(0.173233\pi\) | |||||||
\(462\) | 102.676 | − | 193.810i | 0.222242 | − | 0.419503i | ||||
\(463\) | −548.664 | + | 548.664i | −1.18502 | + | 1.18502i | −0.206592 | + | 0.978427i | \(0.566237\pi\) |
−0.978427 | + | 0.206592i | \(0.933763\pi\) | |||||||
\(464\) | −974.173 | −2.09951 | ||||||||
\(465\) | 403.033 | − | 309.489i | 0.866738 | − | 0.665568i | ||||
\(466\) | −729.920 | −1.56635 | ||||||||
\(467\) | −299.104 | − | 299.104i | −0.640480 | − | 0.640480i | 0.310194 | − | 0.950673i | \(-0.399606\pi\) |
−0.950673 | + | 0.310194i | \(0.899606\pi\) | |||||||
\(468\) | 10.0802 | + | 31.2280i | 0.0215389 | + | 0.0667266i | ||||
\(469\) | 479.857 | − | 284.258i | 1.02315 | − | 0.606094i | ||||
\(470\) | 33.2272 | + | 312.163i | 0.0706961 | + | 0.664176i | ||||
\(471\) | −12.7783 | + | 53.0009i | −0.0271302 | + | 0.112528i | ||||
\(472\) | −93.1173 | + | 93.1173i | −0.197283 | + | 0.197283i | ||||
\(473\) | 134.562 | + | 134.562i | 0.284486 | + | 0.284486i | ||||
\(474\) | 691.414 | + | 166.698i | 1.45868 | + | 0.351683i | ||||
\(475\) | −16.9616 | + | 3.65222i | −0.0357086 | + | 0.00768888i | ||||
\(476\) | −111.648 | − | 188.473i | −0.234554 | − | 0.395952i | ||||
\(477\) | 409.946 | − | 132.328i | 0.859426 | − | 0.277417i | ||||
\(478\) | 33.7249 | − | 33.7249i | 0.0705542 | − | 0.0705542i | ||||
\(479\) | − | 568.767i | − | 1.18740i | −0.804685 | − | 0.593702i | \(-0.797666\pi\) | ||
0.804685 | − | 0.593702i | \(-0.202334\pi\) | |||||||
\(480\) | 358.189 | + | 47.0251i | 0.746226 | + | 0.0979690i | ||||
\(481\) | − | 6.57345i | − | 0.0136662i | ||||||
\(482\) | −430.633 | − | 430.633i | −0.893430 | − | 0.893430i | ||||
\(483\) | 322.296 | − | 608.366i | 0.667279 | − | 1.25956i | ||||
\(484\) | − | 161.263i | − | 0.333188i | ||||||
\(485\) | 204.113 | + | 164.841i | 0.420852 | + | 0.339878i | ||||
\(486\) | −531.803 | + | 217.288i | −1.09424 | + | 0.447094i | ||||
\(487\) | 382.818 | + | 382.818i | 0.786073 | + | 0.786073i | 0.980848 | − | 0.194775i | \(-0.0623976\pi\) |
−0.194775 | + | 0.980848i | \(0.562398\pi\) | |||||||
\(488\) | −52.3461 | + | 52.3461i | −0.107267 | + | 0.107267i | ||||
\(489\) | 139.565 | − | 578.875i | 0.285409 | − | 1.18379i | ||||
\(490\) | 220.338 | + | 535.663i | 0.449669 | + | 1.09319i | ||||
\(491\) | − | 1.38553i | − | 0.00282185i | −0.999999 | − | 0.00141093i | \(-0.999551\pi\) | ||
0.999999 | − | 0.00141093i | \(-0.000449112\pi\) | |||||||
\(492\) | 80.8465 | + | 132.215i | 0.164322 | + | 0.268730i | ||||
\(493\) | 684.067 | + | 684.067i | 1.38756 | + | 1.38756i | ||||
\(494\) | 3.76462 | 0.00762070 | ||||||||
\(495\) | 71.3555 | − | 185.553i | 0.144152 | − | 0.374855i | ||||
\(496\) | 671.816i | 1.35447i | ||||||||
\(497\) | −629.002 | − | 161.012i | −1.26560 | − | 0.323969i | ||||
\(498\) | −29.4377 | − | 48.1418i | −0.0591118 | − | 0.0966703i | ||||
\(499\) | − | 356.741i | − | 0.714913i | −0.933930 | − | 0.357456i | \(-0.883644\pi\) | ||
0.933930 | − | 0.357456i | \(-0.116356\pi\) | |||||||
\(500\) | −188.666 | + | 62.1300i | −0.377331 | + | 0.124260i | ||||
\(501\) | −290.277 | − | 69.9849i | −0.579396 | − | 0.139691i | ||||
\(502\) | −320.243 | + | 320.243i | −0.637934 | + | 0.637934i | ||||
\(503\) | 279.707 | − | 279.707i | 0.556078 | − | 0.556078i | −0.372111 | − | 0.928188i | \(-0.621366\pi\) |
0.928188 | + | 0.372111i | \(0.121366\pi\) | |||||||
\(504\) | −22.1180 | − | 358.402i | −0.0438849 | − | 0.711116i | ||||
\(505\) | −9.34737 | − | 87.8167i | −0.0185096 | − | 0.173894i | ||||
\(506\) | 342.402i | 0.676685i | ||||||||
\(507\) | 256.251 | + | 419.069i | 0.505427 | + | 0.826566i | ||||
\(508\) | 6.76005 | − | 6.76005i | 0.0133072 | − | 0.0133072i | ||||
\(509\) | 493.836i | 0.970208i | 0.874457 | + | 0.485104i | \(0.161218\pi\) | ||||
−0.874457 | + | 0.485104i | \(0.838782\pi\) | |||||||
\(510\) | −425.340 | − | 553.901i | −0.834000 | − | 1.08608i | ||||
\(511\) | 812.937 | − | 481.568i | 1.59087 | − | 0.942403i | ||||
\(512\) | −18.0214 | + | 18.0214i | −0.0351981 | + | 0.0351981i | ||||
\(513\) | 1.41625 | + | 18.6847i | 0.00276073 | + | 0.0364225i | ||||
\(514\) | −687.719 | −1.33797 | ||||||||
\(515\) | −429.016 | + | 531.226i | −0.833040 | + | 1.03151i | ||||
\(516\) | −199.629 | − | 48.1300i | −0.386879 | − | 0.0932752i | ||||
\(517\) | −82.9618 | + | 82.9618i | −0.160468 | + | 0.160468i | ||||
\(518\) | 11.7571 | − | 45.9297i | 0.0226972 | − | 0.0886674i | ||||
\(519\) | 74.5612 | − | 309.258i | 0.143663 | − | 0.595873i | ||||
\(520\) | −65.0226 | + | 6.92112i | −0.125043 | + | 0.0133098i | ||||
\(521\) | −16.2593 | −0.0312079 | −0.0156039 | − | 0.999878i | \(-0.504967\pi\) | ||||
−0.0156039 | + | 0.999878i | \(0.504967\pi\) | |||||||
\(522\) | −321.072 | − | 994.667i | −0.615080 | − | 1.90549i | ||||
\(523\) | −629.367 | − | 629.367i | −1.20338 | − | 1.20338i | −0.973132 | − | 0.230246i | \(-0.926047\pi\) |
−0.230246 | − | 0.973132i | \(-0.573953\pi\) | |||||||
\(524\) | 183.397i | 0.349993i | ||||||||
\(525\) | 256.431 | + | 458.114i | 0.488440 | + | 0.872597i | ||||
\(526\) | −16.1301 | −0.0306655 | ||||||||
\(527\) | 471.751 | − | 471.751i | 0.895163 | − | 0.895163i | ||||
\(528\) | 137.112 | + | 224.231i | 0.259682 | + | 0.424680i | ||||
\(529\) | 545.792i | 1.03174i | ||||||||
\(530\) | −59.8842 | − | 562.600i | −0.112989 | − | 1.06151i | ||||
\(531\) | −185.091 | − | 94.7580i | −0.348571 | − | 0.178452i | ||||
\(532\) | 7.47866 | + | 1.91439i | 0.0140576 | + | 0.00359849i | ||||
\(533\) | −52.7433 | − | 52.7433i | −0.0989555 | − | 0.0989555i | ||||
\(534\) | 1093.99 | + | 263.758i | 2.04867 | + | 0.493928i | ||||
\(535\) | −39.7616 | − | 32.1113i | −0.0743208 | − | 0.0600212i | ||||
\(536\) | 454.134i | 0.847265i | ||||||||
\(537\) | 282.209 | − | 172.564i | 0.525528 | − | 0.321349i | ||||
\(538\) | 178.843 | + | 178.843i | 0.332421 | + | 0.332421i | ||||
\(539\) | −104.010 | + | 189.847i | −0.192968 | + | 0.352221i | ||||
\(540\) | 38.7637 | + | 210.992i | 0.0717846 | + | 0.390726i | ||||
\(541\) | 577.099 | 1.06673 | 0.533364 | − | 0.845886i | \(-0.320928\pi\) | ||||
0.533364 | + | 0.845886i | \(0.320928\pi\) | |||||||
\(542\) | 312.666 | + | 312.666i | 0.576874 | + | 0.576874i | ||||
\(543\) | −91.0532 | − | 148.907i | −0.167685 | − | 0.274230i | ||||
\(544\) | 474.303 | 0.871881 | ||||||||
\(545\) | −622.015 | + | 66.2084i | −1.14131 | + | 0.121483i | ||||
\(546\) | −33.4695 | − | 108.885i | −0.0612994 | − | 0.199423i | ||||
\(547\) | −289.511 | − | 289.511i | −0.529270 | − | 0.529270i | 0.391084 | − | 0.920355i | \(-0.372100\pi\) |
−0.920355 | + | 0.391084i | \(0.872100\pi\) | |||||||
\(548\) | −213.551 | − | 213.551i | −0.389691 | − | 0.389691i | ||||
\(549\) | −104.050 | − | 53.2684i | −0.189526 | − | 0.0970280i | ||||
\(550\) | −219.356 | − | 141.628i | −0.398829 | − | 0.257505i | ||||
\(551\) | −34.0923 | −0.0618735 | ||||||||
\(552\) | 292.443 | + | 478.257i | 0.529788 | + | 0.866407i | ||||
\(553\) | −680.037 | − | 174.077i | −1.22972 | − | 0.314786i | ||||
\(554\) | −320.200 | −0.577979 | ||||||||
\(555\) | 5.59380 | − | 42.6078i | 0.0100789 | − | 0.0767708i | ||||
\(556\) | − | 362.915i | − | 0.652726i | ||||||
\(557\) | −12.4652 | + | 12.4652i | −0.0223792 | + | 0.0223792i | −0.718208 | − | 0.695829i | \(-0.755037\pi\) |
0.695829 | + | 0.718208i | \(0.255037\pi\) | |||||||
\(558\) | −685.949 | + | 221.420i | −1.22930 | + | 0.396809i | ||||
\(559\) | 98.8363 | 0.176809 | ||||||||
\(560\) | −686.850 | − | 99.9867i | −1.22652 | − | 0.178548i | ||||
\(561\) | 61.1750 | − | 253.736i | 0.109046 | − | 0.452292i | ||||
\(562\) | 235.430 | + | 235.430i | 0.418915 | + | 0.418915i | ||||
\(563\) | 689.690 | − | 689.690i | 1.22503 | − | 1.22503i | 0.259204 | − | 0.965823i | \(-0.416540\pi\) |
0.965823 | − | 0.259204i | \(-0.0834602\pi\) | |||||||
\(564\) | 29.6737 | − | 123.078i | 0.0526130 | − | 0.218223i | ||||
\(565\) | −318.491 | + | 394.369i | −0.563701 | + | 0.697999i | ||||
\(566\) | −684.560 | −1.20947 | ||||||||
\(567\) | 527.832 | − | 207.080i | 0.930921 | − | 0.365220i | ||||
\(568\) | 373.832 | − | 373.832i | 0.658155 | − | 0.658155i | ||||
\(569\) | −44.3368 | −0.0779205 | −0.0389602 | − | 0.999241i | \(-0.512405\pi\) | ||||
−0.0389602 | + | 0.999241i | \(0.512405\pi\) | |||||||
\(570\) | 24.4015 | + | 3.20358i | 0.0428097 | + | 0.00562031i | ||||
\(571\) | 89.1696 | 0.156164 | 0.0780819 | − | 0.996947i | \(-0.475120\pi\) | ||||
0.0780819 | + | 0.996947i | \(0.475120\pi\) | |||||||
\(572\) | 11.3898 | + | 11.3898i | 0.0199122 | + | 0.0199122i | ||||
\(573\) | 19.7529 | + | 32.3036i | 0.0344728 | + | 0.0563762i | ||||
\(574\) | −274.190 | − | 462.861i | −0.477683 | − | 0.806378i | ||||
\(575\) | −688.553 | − | 444.566i | −1.19748 | − | 0.773159i | ||||
\(576\) | 179.344 | + | 91.8155i | 0.311361 | + | 0.159402i | ||||
\(577\) | −146.556 | + | 146.556i | −0.253997 | + | 0.253997i | −0.822607 | − | 0.568610i | \(-0.807481\pi\) |
0.568610 | + | 0.822607i | \(0.307481\pi\) | |||||||
\(578\) | −165.225 | − | 165.225i | −0.285856 | − | 0.285856i | ||||
\(579\) | −210.381 | + | 872.601i | −0.363353 | + | 1.50708i | ||||
\(580\) | −388.108 | + | 41.3109i | −0.669152 | + | 0.0712257i | ||||
\(581\) | 28.3854 | + | 47.9175i | 0.0488561 | + | 0.0824742i | ||||
\(582\) | −194.145 | − | 317.502i | −0.333583 | − | 0.545535i | ||||
\(583\) | 149.519 | − | 149.519i | 0.256465 | − | 0.256465i | ||||
\(584\) | 769.358i | 1.31739i | ||||||||
\(585\) | −41.9395 | − | 94.3504i | −0.0716914 | − | 0.161283i | ||||
\(586\) | − | 528.948i | − | 0.902642i | ||||||
\(587\) | 85.7254 | + | 85.7254i | 0.146040 | + | 0.146040i | 0.776346 | − | 0.630307i | \(-0.217071\pi\) |
−0.630307 | + | 0.776346i | \(0.717071\pi\) | |||||||
\(588\) | −11.1186 | − | 233.327i | −0.0189092 | − | 0.396815i | ||||
\(589\) | 23.5110i | 0.0399167i | ||||||||
\(590\) | −171.589 | + | 212.469i | −0.290830 | + | 0.360118i | ||||
\(591\) | 101.945 | − | 422.840i | 0.172496 | − | 0.715465i | ||||
\(592\) | 40.1736 | + | 40.1736i | 0.0678608 | + | 0.0678608i | ||||
\(593\) | 607.214 | − | 607.214i | 1.02397 | − | 1.02397i | 0.0242632 | − | 0.999706i | \(-0.492276\pi\) |
0.999706 | − | 0.0242632i | \(-0.00772398\pi\) | |||||||
\(594\) | −183.758 | + | 213.900i | −0.309357 | + | 0.360100i | ||||
\(595\) | 412.097 | + | 552.519i | 0.692600 | + | 0.928603i | ||||
\(596\) | 107.607i | 0.180549i | ||||||||
\(597\) | −603.906 | + | 369.275i | −1.01157 | + | 0.618551i | ||||
\(598\) | 125.748 | + | 125.748i | 0.210281 | + | 0.210281i | ||||
\(599\) | 214.278 | 0.357726 | 0.178863 | − | 0.983874i | \(-0.442758\pi\) | ||||
0.178863 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(600\) | −427.353 | − | 10.4709i | −0.712255 | − | 0.0174515i | ||||
\(601\) | − | 674.896i | − | 1.12296i | −0.827492 | − | 0.561478i | \(-0.810233\pi\) | ||
0.827492 | − | 0.561478i | \(-0.189767\pi\) | |||||||
\(602\) | 690.585 | + | 176.777i | 1.14715 | + | 0.293649i | ||||
\(603\) | −682.414 | + | 220.278i | −1.13170 | + | 0.365304i | ||||
\(604\) | − | 172.942i | − | 0.286328i | ||||||
\(605\) | 53.7068 | + | 504.565i | 0.0887716 | + | 0.833992i | ||||
\(606\) | −29.3607 | + | 121.780i | −0.0484500 | + | 0.200957i | ||||
\(607\) | 428.929 | − | 428.929i | 0.706638 | − | 0.706638i | −0.259189 | − | 0.965827i | \(-0.583455\pi\) |
0.965827 | + | 0.259189i | \(0.0834552\pi\) | |||||||
\(608\) | −11.8191 | + | 11.8191i | −0.0194393 | + | 0.0194393i | ||||
\(609\) | 303.098 | + | 986.060i | 0.497698 | + | 1.61915i | ||||
\(610\) | −96.4594 | + | 119.440i | −0.158130 | + | 0.195803i | ||||
\(611\) | 60.9358i | 0.0997313i | ||||||||
\(612\) | 86.5185 | + | 268.031i | 0.141370 | + | 0.437959i | ||||
\(613\) | −134.802 | + | 134.802i | −0.219905 | + | 0.219905i | −0.808458 | − | 0.588553i | \(-0.799698\pi\) |
0.588553 | + | 0.808458i | \(0.299698\pi\) | |||||||
\(614\) | − | 1305.53i | − | 2.12628i | ||||||
\(615\) | −296.989 | − | 386.754i | −0.482908 | − | 0.628869i | ||||
\(616\) | −89.8351 | − | 151.651i | −0.145836 | − | 0.246187i | ||||
\(617\) | −525.987 | + | 525.987i | −0.852491 | + | 0.852491i | −0.990439 | − | 0.137948i | \(-0.955949\pi\) |
0.137948 | + | 0.990439i | \(0.455949\pi\) | |||||||
\(618\) | 826.331 | − | 505.283i | 1.33711 | − | 0.817610i | ||||
\(619\) | −957.834 | −1.54739 | −0.773695 | − | 0.633558i | \(-0.781594\pi\) | ||||
−0.773695 | + | 0.633558i | \(0.781594\pi\) | |||||||
\(620\) | 28.4891 | + | 267.650i | 0.0459502 | + | 0.431693i | ||||
\(621\) | −576.812 | + | 671.425i | −0.928844 | + | 1.08120i | ||||
\(622\) | 525.184 | − | 525.184i | 0.844347 | − | 0.844347i | ||||
\(623\) | −1075.99 | − | 275.433i | −1.72711 | − | 0.442107i | ||||
\(624\) | 132.704 | + | 31.9945i | 0.212667 | + | 0.0512733i | ||||
\(625\) | 569.613 | − | 257.228i | 0.911381 | − | 0.411564i | ||||
\(626\) | −463.126 | −0.739817 | ||||||||
\(627\) | 4.79840 | + | 7.84721i | 0.00765295 | + | 0.0125155i | ||||
\(628\) | −20.4200 | − | 20.4200i | −0.0325159 | − | 0.0325159i | ||||
\(629\) | − | 56.4200i | − | 0.0896980i | ||||||
\(630\) | −124.284 | − | 734.253i | −0.197277 | − | 1.16548i | ||||
\(631\) | −482.882 | −0.765265 | −0.382633 | − | 0.923901i | \(-0.624983\pi\) | ||||
−0.382633 | + | 0.923901i | \(0.624983\pi\) | |||||||
\(632\) | 404.164 | − | 404.164i | 0.639499 | − | 0.639499i | ||||
\(633\) | 229.448 | − | 140.302i | 0.362477 | − | 0.221647i | ||||
\(634\) | 574.349i | 0.905914i | ||||||||
\(635\) | −18.8997 | + | 23.4025i | −0.0297634 | + | 0.0368543i | ||||
\(636\) | −53.4800 | + | 221.819i | −0.0840880 | + | 0.348773i | ||||
\(637\) | 31.5239 | + | 107.920i | 0.0494881 | + | 0.169419i | ||||
\(638\) | −362.784 | − | 362.784i | −0.568627 | − | 0.568627i | ||||
\(639\) | 743.074 | + | 380.419i | 1.16287 | + | 0.595334i | ||||
\(640\) | 468.899 | − | 580.610i | 0.732654 | − | 0.907204i | ||||
\(641\) | 618.098i | 0.964272i | 0.876096 | + | 0.482136i | \(0.160139\pi\) | ||||
−0.876096 | + | 0.482136i | \(0.839861\pi\) | |||||||
\(642\) | 37.8199 | + | 61.8499i | 0.0589094 | + | 0.0963395i | ||||
\(643\) | 235.650 | + | 235.650i | 0.366485 | + | 0.366485i | 0.866193 | − | 0.499709i | \(-0.166560\pi\) |
−0.499709 | + | 0.866193i | \(0.666560\pi\) | |||||||
\(644\) | 185.861 | + | 313.752i | 0.288604 | + | 0.487193i | ||||
\(645\) | 640.637 | + | 84.1067i | 0.993236 | + | 0.130398i | ||||
\(646\) | 32.3118 | 0.0500183 | ||||||||
\(647\) | −129.060 | − | 129.060i | −0.199474 | − | 0.199474i | 0.600300 | − | 0.799775i | \(-0.295048\pi\) |
−0.799775 | + | 0.600300i | \(0.795048\pi\) | |||||||
\(648\) | −73.9775 | + | 455.714i | −0.114163 | + | 0.703263i | ||||
\(649\) | −102.069 | −0.157272 | ||||||||
\(650\) | −132.572 | + | 28.5459i | −0.203957 | + | 0.0439167i | ||||
\(651\) | 680.013 | − | 209.025i | 1.04457 | − | 0.321082i | ||||
\(652\) | 223.027 | + | 223.027i | 0.342066 | + | 0.342066i | ||||
\(653\) | 607.844 | + | 607.844i | 0.930849 | + | 0.930849i | 0.997759 | − | 0.0669099i | \(-0.0213140\pi\) |
−0.0669099 | + | 0.997759i | \(0.521314\pi\) | |||||||
\(654\) | 862.579 | + | 207.965i | 1.31893 | + | 0.317990i | ||||
\(655\) | −61.0782 | − | 573.818i | −0.0932492 | − | 0.876059i | ||||
\(656\) | 644.681 | 0.982745 | ||||||||
\(657\) | −1156.09 | + | 373.178i | −1.75965 | + | 0.568004i | ||||
\(658\) | −108.989 | + | 425.768i | −0.165636 | + | 0.647064i | ||||
\(659\) | 795.993 | 1.20788 | 0.603940 | − | 0.797030i | \(-0.293597\pi\) | ||||
0.603940 | + | 0.797030i | \(0.293597\pi\) | |||||||
\(660\) | 64.1339 | + | 83.5186i | 0.0971726 | + | 0.126543i | ||||
\(661\) | − | 353.138i | − | 0.534248i | −0.963662 | − | 0.267124i | \(-0.913927\pi\) | ||
0.963662 | − | 0.267124i | \(-0.0860734\pi\) | |||||||
\(662\) | 162.454 | − | 162.454i | 0.245399 | − | 0.245399i | ||||
\(663\) | −70.7185 | − | 115.652i | −0.106664 | − | 0.174437i | ||||
\(664\) | −45.3488 | −0.0682964 | ||||||||
\(665\) | −24.0371 | − | 3.49915i | −0.0361460 | − | 0.00526188i | ||||
\(666\) | −27.7782 | + | 54.2593i | −0.0417090 | + | 0.0814704i | ||||
\(667\) | −1138.77 | − | 1138.77i | −1.70730 | − | 1.70730i | ||||
\(668\) | 111.837 | − | 111.837i | 0.167421 | − | 0.167421i | ||||
\(669\) | 351.263 | + | 84.6885i | 0.525058 | + | 0.126590i | ||||
\(670\) | 99.6858 | + | 936.529i | 0.148785 | + | 1.39780i | ||||
\(671\) | −57.3785 | −0.0855119 | ||||||||
\(672\) | 446.924 | + | 236.769i | 0.665066 | + | 0.352334i | ||||
\(673\) | 45.1352 | − | 45.1352i | 0.0670657 | − | 0.0670657i | −0.672778 | − | 0.739844i | \(-0.734899\pi\) |
0.739844 | + | 0.672778i | \(0.234899\pi\) | |||||||
\(674\) | 476.112 | 0.706398 | ||||||||
\(675\) | −191.554 | − | 647.250i | −0.283784 | − | 0.958888i | ||||
\(676\) | −260.185 | −0.384890 | ||||||||
\(677\) | −812.127 | − | 812.127i | −1.19960 | − | 1.19960i | −0.974287 | − | 0.225309i | \(-0.927661\pi\) |
−0.225309 | − | 0.974287i | \(-0.572339\pi\) | |||||||
\(678\) | 613.449 | − | 375.110i | 0.904791 | − | 0.553260i | ||||
\(679\) | 187.206 | + | 316.022i | 0.275708 | + | 0.465423i | ||||
\(680\) | −558.090 | + | 59.4041i | −0.820720 | + | 0.0873589i | ||||
\(681\) | −536.135 | − | 129.260i | −0.787276 | − | 0.189810i | ||||
\(682\) | −250.186 | + | 250.186i | −0.366841 | + | 0.366841i | ||||
\(683\) | −654.128 | − | 654.128i | −0.957728 | − | 0.957728i | 0.0414145 | − | 0.999142i | \(-0.486814\pi\) |
−0.999142 | + | 0.0414145i | \(0.986814\pi\) | |||||||
\(684\) | −8.83495 | − | 4.52307i | −0.0129166 | − | 0.00661268i | ||||
\(685\) | 739.287 | + | 597.045i | 1.07925 | + | 0.871599i | ||||
\(686\) | 27.2396 | + | 810.435i | 0.0397078 | + | 1.18139i | ||||
\(687\) | 281.339 | − | 172.033i | 0.409518 | − | 0.250411i | ||||
\(688\) | −604.038 | + | 604.038i | −0.877962 | + | 0.877962i | ||||
\(689\) | − | 109.823i | − | 0.159394i | ||||||
\(690\) | 708.066 | + | 922.082i | 1.02618 | + | 1.33635i | ||||
\(691\) | 1308.29i | 1.89333i | 0.322219 | + | 0.946665i | \(0.395571\pi\) | ||||
−0.322219 | + | 0.946665i | \(0.604429\pi\) | |||||||
\(692\) | 119.150 | + | 119.150i | 0.172182 | + | 0.172182i | ||||
\(693\) | 184.307 | − | 208.551i | 0.265955 | − | 0.300939i | ||||
\(694\) | 142.180i | 0.204871i | ||||||||
\(695\) | 120.865 | + | 1135.50i | 0.173907 | + | 1.63382i | ||||
\(696\) | −816.576 | − | 196.874i | −1.17324 | − | 0.282865i | ||||
\(697\) | −452.697 | − | 452.697i | −0.649493 | − | 0.649493i | ||||
\(698\) | 540.917 | − | 540.917i | 0.774953 | − | 0.774953i | ||||
\(699\) | −900.447 | − | 217.095i | −1.28819 | − | 0.310579i | ||||
\(700\) | −277.879 | − | 10.7078i | −0.396970 | − | 0.0152968i | ||||
\(701\) | − | 793.166i | − | 1.13148i | −0.824584 | − | 0.565739i | \(-0.808591\pi\) | ||
0.824584 | − | 0.565739i | \(-0.191409\pi\) | |||||||
\(702\) | 11.0695 | + | 146.041i | 0.0157685 | + | 0.208035i | ||||
\(703\) | 1.40592 | + | 1.40592i | 0.00199989 | + | 0.00199989i | ||||
\(704\) | 98.8997 | 0.140483 | ||||||||
\(705\) | −51.8545 | + | 394.974i | −0.0735525 | + | 0.560247i | ||||
\(706\) | − | 407.822i | − | 0.577651i | ||||||
\(707\) | 30.6604 | − | 119.776i | 0.0433669 | − | 0.169414i | ||||
\(708\) | 93.9665 | − | 57.4584i | 0.132721 | − | 0.0811560i | ||||
\(709\) | − | 283.272i | − | 0.399538i | −0.979843 | − | 0.199769i | \(-0.935981\pi\) | ||
0.979843 | − | 0.199769i | \(-0.0640192\pi\) | |||||||
\(710\) | 688.869 | − | 852.987i | 0.970238 | − | 1.20139i | ||||
\(711\) | 803.365 | + | 411.285i | 1.12991 | + | 0.578459i | ||||
\(712\) | 639.489 | − | 639.489i | 0.898158 | − | 0.898158i | ||||
\(713\) | −785.326 | + | 785.326i | −1.10144 | + | 1.10144i | ||||
\(714\) | −287.269 | − | 934.563i | −0.402337 | − | 1.30891i | ||||
\(715\) | −39.4300 | − | 31.8435i | −0.0551469 | − | 0.0445364i | ||||
\(716\) | 175.214i | 0.244712i | ||||||||
\(717\) | 51.6344 | − | 31.5733i | 0.0720145 | − | 0.0440353i | ||||
\(718\) | 762.337 | − | 762.337i | 1.06175 | − | 1.06175i | ||||
\(719\) | 639.857i | 0.889927i | 0.895549 | + | 0.444963i | \(0.146783\pi\) | ||||
−0.895549 | + | 0.444963i | \(0.853217\pi\) | |||||||
\(720\) | 832.935 | + | 320.309i | 1.15685 | + | 0.444874i | ||||
\(721\) | −822.481 | + | 487.222i | −1.14075 | + | 0.675758i | ||||
\(722\) | 602.673 | − | 602.673i | 0.834727 | − | 0.834727i | ||||
\(723\) | −403.159 | − | 659.320i | −0.557620 | − | 0.911922i | ||||
\(724\) | 92.4510 | 0.127695 | ||||||||
\(725\) | 1200.57 | − | 258.510i | 1.65596 | − | 0.356566i | ||||
\(726\) | 168.697 | − | 699.706i | 0.232365 | − | 0.963782i | ||||
\(727\) | 65.1910 | − | 65.1910i | 0.0896713 | − | 0.0896713i | −0.660848 | − | 0.750520i | \(-0.729803\pi\) |
0.750520 | + | 0.660848i | \(0.229803\pi\) | |||||||
\(728\) | −88.6863 | − | 22.7020i | −0.121822 | − | 0.0311841i | ||||
\(729\) | −720.671 | + | 109.881i | −0.988575 | + | 0.150729i | ||||
\(730\) | 168.880 | + | 1586.59i | 0.231342 | + | 2.17342i | ||||
\(731\) | 848.314 | 1.16048 | ||||||||
\(732\) | 52.8235 | − | 32.3004i | 0.0721632 | − | 0.0441262i | ||||
\(733\) | 631.927 | + | 631.927i | 0.862110 | + | 0.862110i | 0.991583 | − | 0.129473i | \(-0.0413285\pi\) |
−0.129473 | + | 0.991583i | \(0.541329\pi\) | |||||||
\(734\) | 176.370i | 0.240286i | ||||||||
\(735\) | 112.495 | + | 726.340i | 0.153055 | + | 0.988218i | ||||
\(736\) | −789.576 | −1.07279 | ||||||||
\(737\) | −248.896 | + | 248.896i | −0.337715 | + | 0.337715i | ||||
\(738\) | 212.476 | + | 658.243i | 0.287908 | + | 0.891928i | ||||
\(739\) | − | 235.665i | − | 0.318898i | −0.987206 | − | 0.159449i | \(-0.949028\pi\) | ||
0.987206 | − | 0.159449i | \(-0.0509717\pi\) | |||||||
\(740\) | 17.7087 | + | 14.3015i | 0.0239306 | + | 0.0193263i | ||||
\(741\) | 4.64413 | + | 1.11969i | 0.00626738 | + | 0.00151105i | ||||
\(742\) | 196.427 | − | 767.348i | 0.264726 | − | 1.03416i | ||||
\(743\) | 122.316 | + | 122.316i | 0.164625 | + | 0.164625i | 0.784612 | − | 0.619987i | \(-0.212862\pi\) |
−0.619987 | + | 0.784612i | \(0.712862\pi\) | |||||||
\(744\) | −135.770 | + | 563.133i | −0.182486 | + | 0.756899i | ||||
\(745\) | −35.8374 | − | 336.685i | −0.0481039 | − | 0.451927i | ||||
\(746\) | − | 900.577i | − | 1.20721i | ||||||
\(747\) | −21.9965 | − | 68.1443i | −0.0294465 | − | 0.0912240i | ||||
\(748\) | 97.7587 | + | 97.7587i | 0.130693 | + | 0.130693i | ||||
\(749\) | −36.4680 | − | 61.5618i | −0.0486889 | − | 0.0821919i | ||||
\(750\) | −883.599 | + | 72.2138i | −1.17813 | + | 0.0962851i | ||||
\(751\) | 314.517 | 0.418797 | 0.209399 | − | 0.977830i | \(-0.432849\pi\) | ||||
0.209399 | + | 0.977830i | \(0.432849\pi\) | |||||||
\(752\) | −372.409 | − | 372.409i | −0.495225 | − | 0.495225i | ||||
\(753\) | −490.307 | + | 299.812i | −0.651138 | + | 0.398157i | ||||
\(754\) | −266.467 | −0.353404 | ||||||||
\(755\) | 57.5966 | + | 541.109i | 0.0762869 | + | 0.716700i | ||||
\(756\) | −52.2747 | + | 295.748i | −0.0691464 | + | 0.391201i | ||||
\(757\) | 782.579 | + | 782.579i | 1.03379 | + | 1.03379i | 0.999409 | + | 0.0343817i | \(0.0109462\pi\) |
0.0343817 | + | 0.999409i | \(0.489054\pi\) | |||||||
\(758\) | 423.766 | + | 423.766i | 0.559058 | + | 0.559058i | ||||
\(759\) | −101.838 | + | 422.396i | −0.134174 | + | 0.556516i | ||||
\(760\) | 12.4267 | − | 15.3872i | 0.0163509 | − | 0.0202463i | ||||
\(761\) | 78.7855 | 0.103529 | 0.0517644 | − | 0.998659i | \(-0.483515\pi\) | ||||
0.0517644 | + | 0.998659i | \(0.483515\pi\) | |||||||
\(762\) | 36.4029 | − | 22.2596i | 0.0477729 | − | 0.0292121i | ||||
\(763\) | −848.386 | − | 217.171i | −1.11191 | − | 0.284627i | ||||
\(764\) | −20.0562 | −0.0262515 | ||||||||
\(765\) | −359.967 | − | 809.811i | −0.470545 | − | 1.05858i | ||||
\(766\) | 544.150i | 0.710379i | ||||||||
\(767\) | −37.4852 | + | 37.4852i | −0.0488725 | + | 0.0488725i | ||||
\(768\) | −673.962 | + | 412.113i | −0.877554 | + | 0.536605i | ||||
\(769\) | 959.073 | 1.24717 | 0.623584 | − | 0.781756i | \(-0.285676\pi\) | ||||
0.623584 | + | 0.781756i | \(0.285676\pi\) | |||||||
\(770\) | −218.549 | − | 293.020i | −0.283830 | − | 0.380545i | ||||
\(771\) | −848.386 | − | 204.543i | −1.10037 | − | 0.265296i | ||||
\(772\) | −336.193 | − | 336.193i | −0.435483 | − | 0.435483i | ||||
\(773\) | −313.143 | + | 313.143i | −0.405100 | + | 0.405100i | −0.880026 | − | 0.474926i | \(-0.842475\pi\) |
0.474926 | + | 0.880026i | \(0.342475\pi\) | |||||||
\(774\) | −815.826 | − | 417.664i | −1.05404 | − | 0.539618i | ||||
\(775\) | −178.276 | − | 827.945i | −0.230033 | − | 1.06832i | ||||
\(776\) | −299.081 | −0.385414 | ||||||||
\(777\) | 28.1644 | − | 53.1632i | 0.0362477 | − | 0.0684211i | ||||
\(778\) | 517.324 | − | 517.324i | 0.664941 | − | 0.664941i | ||||
\(779\) | 22.5613 | 0.0289619 | ||||||||
\(780\) | 54.2257 | + | 7.11908i | 0.0695202 | + | 0.00912702i | ||||
\(781\) | 409.771 | 0.524674 | ||||||||
\(782\) | 1079.30 | + | 1079.30i | 1.38018 | + | 1.38018i | ||||
\(783\) | −100.245 | − | 1322.54i | −0.128027 | − | 1.68907i | ||||
\(784\) | −852.210 | − | 466.893i | −1.08700 | − | 0.595527i | ||||
\(785\) | 70.6916 | + | 57.0903i | 0.0900530 | + | 0.0727265i | ||||
\(786\) | −191.851 | + | 795.742i | −0.244085 | + | 1.01239i | ||||
\(787\) | −617.290 | + | 617.290i | −0.784358 | + | 0.784358i | −0.980563 | − | 0.196205i | \(-0.937138\pi\) |
0.196205 | + | 0.980563i | \(0.437138\pi\) | |||||||
\(788\) | 162.911 | + | 162.911i | 0.206739 | + | 0.206739i | ||||
\(789\) | −19.8984 | − | 4.79745i | −0.0252198 | − | 0.00608042i | ||||
\(790\) | 744.762 | − | 922.195i | 0.942736 | − | 1.16734i | ||||
\(791\) | −610.590 | + | 361.702i | −0.771922 | + | 0.457272i | ||||
\(792\) | 69.6153 | + | 215.665i | 0.0878981 | + | 0.272305i | ||||
\(793\) | −21.0724 | + | 21.0724i | −0.0265730 | + | 0.0265730i | ||||
\(794\) | 1549.27i | 1.95122i | ||||||||
\(795\) | 93.4557 | − | 711.848i | 0.117554 | − | 0.895407i | ||||
\(796\) | − | 374.944i | − | 0.471035i | ||||||
\(797\) | 843.997 | + | 843.997i | 1.05897 | + | 1.05897i | 0.998149 | + | 0.0608184i | \(0.0193710\pi\) |
0.0608184 | + | 0.998149i | \(0.480629\pi\) | |||||||
\(798\) | 30.4466 | + | 16.1298i | 0.0381537 | + | 0.0202128i | ||||
\(799\) | 523.013i | 0.654585i | ||||||||
\(800\) | 326.592 | − | 505.833i | 0.408240 | − | 0.632291i | ||||
\(801\) | 1271.13 | + | 650.756i | 1.58692 | + | 0.812429i | ||||
\(802\) | 863.401 | + | 863.401i | 1.07656 | + | 1.07656i | ||||
\(803\) | −421.661 | + | 421.661i | −0.525107 | + | 0.525107i | ||||
\(804\) | 89.0251 | − | 369.250i | 0.110728 | − | 0.459266i | ||||
\(805\) | −686.020 | − | 919.781i | −0.852199 | − | 1.14259i | ||||
\(806\) | 183.763i | 0.227993i | ||||||||
\(807\) | 167.433 | + | 273.817i | 0.207476 | + | 0.339302i | ||||
\(808\) | 71.1860 | + | 71.1860i | 0.0881014 | + | 0.0881014i | ||||
\(809\) | −56.0803 | −0.0693205 | −0.0346602 | − | 0.999399i | \(-0.511035\pi\) | ||||
−0.0346602 | + | 0.999399i | \(0.511035\pi\) | |||||||
\(810\) | −52.5259 | + | 956.026i | −0.0648467 | + | 1.18028i | ||||
\(811\) | 882.859i | 1.08861i | 0.838889 | + | 0.544303i | \(0.183206\pi\) | ||||
−0.838889 | + | 0.544303i | \(0.816794\pi\) | |||||||
\(812\) | −529.353 | − | 135.504i | −0.651912 | − | 0.166877i | ||||
\(813\) | 292.718 | + | 478.706i | 0.360047 | + | 0.588814i | ||||
\(814\) | 29.9215i | 0.0367586i | ||||||||
\(815\) | −772.094 | − | 623.540i | −0.947354 | − | 0.765080i | ||||
\(816\) | 1139.00 | + | 274.610i | 1.39584 | + | 0.336532i | ||||
\(817\) | −21.1390 | + | 21.1390i | −0.0258739 | + | 0.0258739i | ||||
\(818\) | 199.057 | − | 199.057i | 0.243346 | − | 0.243346i | ||||
\(819\) | −8.90379 | − | 144.278i | −0.0108715 | − | 0.176164i | ||||
\(820\) | 256.839 | − | 27.3384i | 0.313219 | − | 0.0333395i | ||||
\(821\) | − | 1159.68i | − | 1.41253i | −0.707949 | − | 0.706264i | \(-0.750379\pi\) | ||
0.707949 | − | 0.706264i | \(-0.249621\pi\) | |||||||
\(822\) | −703.184 | − | 1149.97i | −0.855454 | − | 1.39900i | ||||
\(823\) | 704.019 | − | 704.019i | 0.855430 | − | 0.855430i | −0.135366 | − | 0.990796i | \(-0.543221\pi\) |
0.990796 | + | 0.135366i | \(0.0432210\pi\) | |||||||
\(824\) | − | 778.391i | − | 0.944649i | ||||||
\(825\) | −228.480 | − | 239.957i | −0.276945 | − | 0.290857i | ||||
\(826\) | −328.960 | + | 194.870i | −0.398257 | + | 0.235920i | ||||
\(827\) | −572.404 | + | 572.404i | −0.692145 | + | 0.692145i | −0.962704 | − | 0.270558i | \(-0.912792\pi\) |
0.270558 | + | 0.962704i | \(0.412792\pi\) | |||||||
\(828\) | −144.028 | − | 446.192i | −0.173947 | − | 0.538880i | ||||
\(829\) | −463.044 | −0.558557 | −0.279279 | − | 0.960210i | \(-0.590095\pi\) | ||||
−0.279279 | + | 0.960210i | \(0.590095\pi\) | |||||||
\(830\) | −93.5197 | + | 9.95441i | −0.112674 | + | 0.0119933i | ||||
\(831\) | −395.007 | − | 95.2349i | −0.475339 | − | 0.114603i | ||||
\(832\) | 36.3212 | − | 36.3212i | 0.0436552 | − | 0.0436552i | ||||
\(833\) | 270.570 | + | 926.277i | 0.324814 | + | 1.11198i | ||||
\(834\) | 379.646 | − | 1574.66i | 0.455210 | − | 1.88808i | ||||
\(835\) | −312.674 | + | 387.167i | −0.374460 | + | 0.463673i | ||||
\(836\) | −4.87206 | −0.00582783 | ||||||||
\(837\) | −912.059 | + | 69.1316i | −1.08968 | + | 0.0825945i | ||||
\(838\) | −1224.21 | − | 1224.21i | −1.46087 | − | 1.46087i | ||||
\(839\) | − | 401.831i | − | 0.478940i | −0.970904 | − | 0.239470i | \(-0.923026\pi\) | ||
0.970904 | − | 0.239470i | \(-0.0769737\pi\) | |||||||
\(840\) | −555.528 | − | 222.619i | −0.661343 | − | 0.265023i | ||||
\(841\) | 1572.11 | 1.86934 | ||||||||
\(842\) | −513.742 | + | 513.742i | −0.610145 | + | 0.610145i | ||||
\(843\) | 220.410 | + | 360.455i | 0.261459 | + | 0.427586i | ||||
\(844\) | 142.456i | 0.168787i | ||||||||
\(845\) | 814.078 | − | 86.6519i | 0.963406 | − | 0.102547i | ||||
\(846\) | 257.504 | − | 502.984i | 0.304378 | − | 0.594543i | ||||
\(847\) | −176.164 | + | 688.192i | −0.207986 | + | 0.812506i | ||||
\(848\) | 671.181 | + | 671.181i | 0.791487 | + | 0.791487i | ||||
\(849\) | −844.490 | − | 203.604i | −0.994688 | − | 0.239816i | ||||
\(850\) | −1137.87 | + | 245.010i | −1.33867 | + | 0.288247i | ||||
\(851\) | 93.9227i | 0.110367i | ||||||||
\(852\) | −377.241 | + | 230.675i | −0.442771 | + | 0.270745i | ||||
\(853\) | −615.673 | − | 615.673i | −0.721774 | − | 0.721774i | 0.247192 | − | 0.968966i | \(-0.420492\pi\) |
−0.968966 | + | 0.247192i | \(0.920492\pi\) | |||||||
\(854\) | −184.926 | + | 109.546i | −0.216541 | + | 0.128274i | ||||
\(855\) | 29.1495 | + | 11.2096i | 0.0340930 | + | 0.0131106i | ||||
\(856\) | 58.2616 | 0.0680627 | ||||||||
\(857\) | 90.9145 | + | 90.9145i | 0.106085 | + | 0.106085i | 0.758157 | − | 0.652072i | \(-0.226100\pi\) |
−0.652072 | + | 0.758157i | \(0.726100\pi\) | |||||||
\(858\) | 37.5045 | + | 61.3341i | 0.0437115 | + | 0.0714850i | ||||
\(859\) | 974.498 | 1.13446 | 0.567228 | − | 0.823561i | \(-0.308016\pi\) | ||||
0.567228 | + | 0.823561i | \(0.308016\pi\) | |||||||
\(860\) | −215.032 | + | 266.262i | −0.250038 | + | 0.309607i | ||||
\(861\) | −200.582 | − | 652.547i | −0.232964 | − | 0.757895i | ||||
\(862\) | 344.070 | + | 344.070i | 0.399153 | + | 0.399153i | ||||
\(863\) | −341.306 | − | 341.306i | −0.395488 | − | 0.395488i | 0.481150 | − | 0.876638i | \(-0.340219\pi\) |
−0.876638 | + | 0.481150i | \(0.840219\pi\) | |||||||
\(864\) | −493.250 | − | 423.744i | −0.570891 | − | 0.490444i | ||||
\(865\) | −412.483 | − | 333.120i | −0.476859 | − | 0.385110i | ||||
\(866\) | −975.798 | −1.12679 | ||||||||
\(867\) | −154.684 | − | 252.967i | −0.178413 | − | 0.291773i | ||||
\(868\) | −93.4474 | + | 365.056i | −0.107658 | + | 0.420571i | ||||
\(869\) | 443.018 | 0.509802 | ||||||||
\(870\) | −1727.18 | − | 226.755i | −1.98527 | − | 0.260638i | ||||
\(871\) | 182.815i | 0.209891i | ||||||||
\(872\) | 504.218 | − | 504.218i | 0.578232 | − | 0.578232i | ||||
\(873\) | −145.070 | − | 449.421i | −0.166174 | − | 0.514801i | ||||
\(874\) | −53.7897 | −0.0615443 | ||||||||
\(875\) | 873.006 | − | 59.0417i | 0.997721 | − | 0.0674763i | ||||
\(876\) | 150.819 | − | 625.555i | 0.172168 | − | 0.714104i | ||||
\(877\) | −798.731 | − | 798.731i | −0.910754 | − | 0.910754i | 0.0855778 | − | 0.996331i | \(-0.472726\pi\) |
−0.996331 | + | 0.0855778i | \(0.972726\pi\) | |||||||
\(878\) | −195.037 | + | 195.037i | −0.222138 | + | 0.222138i | ||||
\(879\) | 157.321 | − | 652.523i | 0.178978 | − | 0.742347i | ||||
\(880\) | 435.588 | − | 46.3648i | 0.494987 | − | 0.0526873i | ||||
\(881\) | −90.0599 | −0.102225 | −0.0511123 | − | 0.998693i | \(-0.516277\pi\) | ||||
−0.0511123 | + | 0.998693i | \(0.516277\pi\) | |||||||
\(882\) | 195.840 | − | 1024.02i | 0.222041 | − | 1.16102i | ||||
\(883\) | −149.663 | + | 149.663i | −0.169494 | + | 0.169494i | −0.786757 | − | 0.617263i | \(-0.788241\pi\) |
0.617263 | + | 0.786757i | \(0.288241\pi\) | |||||||
\(884\) | 71.8042 | 0.0812265 | ||||||||
\(885\) | −274.870 | + | 211.073i | −0.310588 | + | 0.238500i | ||||
\(886\) | 942.902 | 1.06422 | ||||||||
\(887\) | 449.819 | + | 449.819i | 0.507124 | + | 0.507124i | 0.913643 | − | 0.406518i | \(-0.133257\pi\) |
−0.406518 | + | 0.913643i | \(0.633257\pi\) | |||||||
\(888\) | 25.5557 | + | 41.7933i | 0.0287789 | + | 0.0470646i | ||||
\(889\) | −36.2333 | + | 21.4639i | −0.0407574 | + | 0.0241439i | ||||
\(890\) | 1178.40 | − | 1459.15i | 1.32405 | − | 1.63949i | ||||
\(891\) | −290.307 | + | 209.218i | −0.325822 | + | 0.234812i | ||||
\(892\) | −135.334 | + | 135.334i | −0.151719 | + | 0.151719i | ||||
\(893\) | −13.0329 | − | 13.0329i | −0.0145945 | − | 0.0145945i | ||||
\(894\) | −112.568 | + | 466.898i | −0.125915 | + | 0.522258i | ||||
\(895\) | −58.3530 | − | 548.215i | −0.0651989 | − | 0.612531i | ||||
\(896\) | 898.942 | − | 532.516i | 1.00328 | − | 0.594326i | ||||
\(897\) | 117.726 | + | 192.526i | 0.131244 | + | 0.214633i | ||||
\(898\) | −681.770 | + | 681.770i | −0.759210 | + | 0.759210i | ||||
\(899\) | − | 1664.15i | − | 1.85111i | ||||||
\(900\) | 345.422 | + | 92.2889i | 0.383803 | + | 0.102543i | ||||
\(901\) | − | 942.610i | − | 1.04618i | ||||||
\(902\) | 240.081 | + | 240.081i | 0.266165 | + | 0.266165i | ||||
\(903\) | 799.345 | + | 423.472i | 0.885210 | + | 0.468961i | ||||
\(904\) | − | 577.859i | − | 0.639224i | ||||||
\(905\) | −289.264 | + | 30.7898i | −0.319629 | + | 0.0340219i | ||||
\(906\) | 180.915 | − | 750.382i | 0.199685 | − | 0.828237i | ||||
\(907\) | 1098.67 | + | 1098.67i | 1.21133 | + | 1.21133i | 0.970591 | + | 0.240735i | \(0.0773886\pi\) |
0.240735 | + | 0.970591i | \(0.422611\pi\) | |||||||
\(908\) | 206.561 | − | 206.561i | 0.227490 | − | 0.227490i | ||||
\(909\) | −72.4402 | + | 141.498i | −0.0796922 | + | 0.155663i | ||||
\(910\) | −187.875 | − | 27.3495i | −0.206456 | − | 0.0300544i | ||||
\(911\) | 1217.82i | 1.33680i | 0.743804 | + | 0.668398i | \(0.233020\pi\) | ||||
−0.743804 | + | 0.668398i | \(0.766980\pi\) | |||||||
\(912\) | −35.2255 | + | 21.5396i | −0.0386245 | + | 0.0236180i | ||||
\(913\) | −24.8542 | − | 24.8542i | −0.0272226 | − | 0.0272226i | ||||
\(914\) | −1542.88 | −1.68805 | ||||||||
\(915\) | −154.519 | + | 118.655i | −0.168873 | + | 0.129678i | ||||
\(916\) | 174.674i | 0.190692i | ||||||||
\(917\) | 200.343 | − | 782.649i | 0.218477 | − | 0.853488i | ||||
\(918\) | 95.0097 | + | 1253.47i | 0.103496 | + | 1.36544i | ||||
\(919\) | − | 80.9089i | − | 0.0880401i | −0.999031 | − | 0.0440201i | \(-0.985983\pi\) | ||
0.999031 | − | 0.0440201i | \(-0.0140166\pi\) | |||||||
\(920\) | 929.055 | − | 98.8903i | 1.00984 | − | 0.107489i | ||||
\(921\) | 388.295 | − | 1610.54i | 0.421602 | − | 1.74868i | ||||
\(922\) | −1318.62 | + | 1318.62i | −1.43017 | + | 1.43017i | ||||
\(923\) | 150.489 | − | 150.489i | 0.163044 | − | 0.163044i | ||||
\(924\) | 43.3152 | + | 140.916i | 0.0468779 | + | 0.152506i | ||||
\(925\) | −60.1705 | − | 38.8493i | −0.0650492 | − | 0.0419992i | ||||
\(926\) | − | 1834.39i | − | 1.98098i | ||||||
\(927\) | 1169.66 | − | 377.560i | 1.26177 | − | 0.407292i | ||||
\(928\) | 836.576 | − | 836.576i | 0.901482 | − | 0.901482i | ||||
\(929\) | − | 1204.04i | − | 1.29607i | −0.761612 | − | 0.648033i | \(-0.775592\pi\) | ||
0.761612 | − | 0.648033i | \(-0.224408\pi\) | |||||||
\(930\) | −156.376 | + | 1191.11i | −0.168147 | + | 1.28077i | ||||
\(931\) | −29.8240 | − | 16.3394i | −0.0320344 | − | 0.0175504i | ||||
\(932\) | 346.921 | − | 346.921i | 0.372233 | − | 0.372233i | ||||
\(933\) | 804.081 | − | 491.678i | 0.861823 | − | 0.526986i | ||||
\(934\) | 1000.02 | 1.07068 | ||||||||
\(935\) | −338.429 | − | 273.314i | −0.361956 | − | 0.292314i | ||||
\(936\) | 104.770 | + | 53.6372i | 0.111934 | + | 0.0573048i | ||||
\(937\) | −498.626 | + | 498.626i | −0.532152 | + | 0.532152i | −0.921212 | − | 0.389061i | \(-0.872800\pi\) |
0.389061 | + | 0.921212i | \(0.372800\pi\) | |||||||
\(938\) | −326.980 | + | 1277.36i | −0.348593 | + | 1.36179i | ||||
\(939\) | −571.323 | − | 137.744i | −0.608438 | − | 0.146692i | ||||
\(940\) | −164.159 | − | 132.574i | −0.174638 | − | 0.141037i | ||||
\(941\) | −759.571 | −0.807195 | −0.403598 | − | 0.914937i | \(-0.632240\pi\) | ||||
−0.403598 | + | 0.914937i | \(0.632240\pi\) | |||||||
\(942\) | −67.2394 | − | 109.962i | −0.0713794 | − | 0.116733i | ||||
\(943\) | 753.607 | + | 753.607i | 0.799159 | + | 0.799159i | ||||
\(944\) | − | 458.181i | − | 0.485361i | ||||||
\(945\) | 65.0635 | − | 942.758i | 0.0688502 | − | 0.997627i | ||||
\(946\) | −449.890 | −0.475571 | ||||||||
\(947\) | −911.272 | + | 911.272i | −0.962273 | + | 0.962273i | −0.999314 | − | 0.0370409i | \(-0.988207\pi\) |
0.0370409 | + | 0.999314i | \(0.488207\pi\) | |||||||
\(948\) | −407.849 | + | 249.391i | −0.430221 | + | 0.263070i | ||||
\(949\) | 309.712i | 0.326356i | ||||||||
\(950\) | 22.2490 | − | 34.4598i | 0.0234200 | − | 0.0362734i | ||||
\(951\) | −170.825 | + | 708.531i | −0.179626 | + | 0.745038i | ||||
\(952\) | −761.196 | − | 194.852i | −0.799576 | − | 0.204676i | ||||
\(953\) | 335.606 | + | 335.606i | 0.352158 | + | 0.352158i | 0.860912 | − | 0.508754i | \(-0.169894\pi\) |
−0.508754 | + | 0.860912i | \(0.669894\pi\) | |||||||
\(954\) | −464.090 | + | 906.511i | −0.486468 | + | 0.950221i | ||||
\(955\) | 62.7525 | − | 6.67949i | 0.0657095 | − | 0.00699423i | ||||
\(956\) | 32.0580i | 0.0335335i | ||||||||
\(957\) | −339.639 | − | 555.440i | −0.354900 | − | 0.580397i | ||||
\(958\) | 950.798 | + | 950.798i | 0.992483 | + | 0.992483i | ||||
\(959\) | 678.048 | + | 1144.62i | 0.707037 | + | 1.19355i | ||||
\(960\) | 266.335 | − | 204.518i | 0.277432 | − | 0.213040i | ||||
\(961\) | −186.641 | −0.194215 | ||||||||
\(962\) | 10.9887 | + | 10.9887i | 0.0114228 | + | 0.0114228i | ||||
\(963\) | 28.2599 | + | 87.5481i | 0.0293457 | + | 0.0909118i | ||||
\(964\) | 409.349 | 0.424636 | ||||||||
\(965\) | 1163.86 | + | 939.929i | 1.20607 | + | 0.974019i | ||||
\(966\) | 478.218 | + | 1555.77i | 0.495050 | + | 1.61053i | ||||
\(967\) | −44.4403 | − | 44.4403i | −0.0459568 | − | 0.0459568i | 0.683755 | − | 0.729712i | \(-0.260346\pi\) |
−0.729712 | + | 0.683755i | \(0.760346\pi\) | |||||||
\(968\) | −409.011 | − | 409.011i | −0.422532 | − | 0.422532i | ||||
\(969\) | 39.8607 | + | 9.61028i | 0.0411359 | + | 0.00991773i | ||||
\(970\) | −616.775 | + | 65.6506i | −0.635850 | + | 0.0676810i | ||||
\(971\) | 1113.37 | 1.14663 | 0.573313 | − | 0.819337i | \(-0.305658\pi\) | ||||
0.573313 | + | 0.819337i | \(0.305658\pi\) | |||||||
\(972\) | 149.485 | − | 356.033i | 0.153791 | − | 0.366289i | ||||
\(973\) | −396.450 | + | 1548.75i | −0.407452 | + | 1.59173i | ||||
\(974\) | −1279.90 | −1.31407 | ||||||||
\(975\) | −172.035 | − | 4.21514i | −0.176446 | − | 0.00432322i | ||||
\(976\) | − | 257.567i | − | 0.263901i | ||||||
\(977\) | −537.682 | + | 537.682i | −0.550340 | + | 0.550340i | −0.926539 | − | 0.376199i | \(-0.877231\pi\) |
0.376199 | + | 0.926539i | \(0.377231\pi\) | |||||||
\(978\) | 734.388 | + | 1201.01i | 0.750908 | + | 1.22802i | ||||
\(979\) | 700.966 | 0.716002 | ||||||||
\(980\) | −359.317 | − | 149.870i | −0.366650 | − | 0.152929i | ||||
\(981\) | 1002.25 | + | 513.102i | 1.02166 | + | 0.523039i | ||||
\(982\) | 2.31617 | + | 2.31617i | 0.00235862 | + | 0.00235862i | ||||
\(983\) | −994.643 | + | 994.643i | −1.01184 | + | 1.01184i | −0.0119152 | + | 0.999929i | \(0.503793\pi\) |
−0.999929 | + | 0.0119152i | \(0.996207\pi\) | |||||||
\(984\) | 540.388 | + | 130.286i | 0.549174 | + | 0.132404i | ||||
\(985\) | −563.977 | − | 455.465i | −0.572565 | − | 0.462401i | ||||
\(986\) | −2287.09 | −2.31956 | ||||||||
\(987\) | −261.084 | + | 492.822i | −0.264523 | + | 0.499313i | ||||
\(988\) | −1.78928 | + | 1.78928i | −0.00181101 | + | 0.00181101i | ||||
\(989\) | −1412.19 | −1.42790 | ||||||||
\(990\) | 190.903 | + | 429.471i | 0.192831 | + | 0.433809i | ||||
\(991\) | −717.169 | −0.723682 | −0.361841 | − | 0.932240i | \(-0.617852\pi\) | ||||
−0.361841 | + | 0.932240i | \(0.617852\pi\) | |||||||
\(992\) | −576.925 | − | 576.925i | −0.581578 | − | 0.581578i | ||||
\(993\) | 248.725 | − | 152.090i | 0.250478 | − | 0.153162i | ||||
\(994\) | 1320.65 | − | 782.330i | 1.32863 | − | 0.787052i | ||||
\(995\) | 124.871 | + | 1173.14i | 0.125499 | + | 1.17904i | ||||
\(996\) | 36.8725 | + | 8.88985i | 0.0370206 | + | 0.00892555i | ||||
\(997\) | 572.089 | − | 572.089i | 0.573810 | − | 0.573810i | −0.359381 | − | 0.933191i | \(-0.617012\pi\) |
0.933191 | + | 0.359381i | \(0.117012\pi\) | |||||||
\(998\) | 596.359 | + | 596.359i | 0.597554 | + | 0.597554i | ||||
\(999\) | −50.4058 | + | 58.6737i | −0.0504562 | + | 0.0587325i |
(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 | 105.3.k.d.62.7 | ✓ | 32 | |
3.2 | odd | 2 | inner | 105.3.k.d.62.10 | yes | 32 | |
5.3 | odd | 4 | inner | 105.3.k.d.83.9 | yes | 32 | |
7.6 | odd | 2 | inner | 105.3.k.d.62.8 | yes | 32 | |
15.8 | even | 4 | inner | 105.3.k.d.83.8 | yes | 32 | |
21.20 | even | 2 | inner | 105.3.k.d.62.9 | yes | 32 | |
35.13 | even | 4 | inner | 105.3.k.d.83.10 | yes | 32 | |
105.83 | odd | 4 | inner | 105.3.k.d.83.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.d.62.7 | ✓ | 32 | 1.1 | even | 1 | trivial | |
105.3.k.d.62.8 | yes | 32 | 7.6 | odd | 2 | inner | |
105.3.k.d.62.9 | yes | 32 | 21.20 | even | 2 | inner | |
105.3.k.d.62.10 | yes | 32 | 3.2 | odd | 2 | inner | |
105.3.k.d.83.7 | yes | 32 | 105.83 | odd | 4 | inner | |
105.3.k.d.83.8 | yes | 32 | 15.8 | even | 4 | inner | |
105.3.k.d.83.9 | yes | 32 | 5.3 | odd | 4 | inner | |
105.3.k.d.83.10 | yes | 32 | 35.13 | even | 4 | inner |