Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(16,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.g (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.42514325043\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 61.4 | ||
Character | \(\chi\) | \(=\) | 75.61 |
Dual form | 75.4.g.b.16.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.109191 | − | 0.0793317i | 0.0386048 | − | 0.0280480i | −0.568316 | − | 0.822811i | \(-0.692405\pi\) |
0.606920 | + | 0.794763i | \(0.292405\pi\) | |||||||
\(3\) | 0.927051 | − | 2.85317i | 0.178411 | − | 0.549093i | ||||
\(4\) | −2.46651 | + | 7.59113i | −0.308313 | + | 0.948891i | ||||
\(5\) | −6.22327 | + | 9.28822i | −0.556626 | + | 0.830763i | ||||
\(6\) | −0.125121 | − | 0.385084i | −0.00851344 | − | 0.0262017i | ||||
\(7\) | −17.3099 | −0.934647 | −0.467323 | − | 0.884087i | \(-0.654782\pi\) | ||||
−0.467323 | + | 0.884087i | \(0.654782\pi\) | |||||||
\(8\) | 0.666555 | + | 2.05145i | 0.0294578 | + | 0.0906619i | ||||
\(9\) | −7.28115 | − | 5.29007i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0.0573272 | + | 1.50789i | 0.00181284 | + | 0.0476837i | ||||
\(11\) | −34.1037 | + | 24.7778i | −0.934785 | + | 0.679161i | −0.947160 | − | 0.320762i | \(-0.896061\pi\) |
0.0123744 | + | 0.999923i | \(0.496061\pi\) | |||||||
\(12\) | 19.3722 | + | 14.0747i | 0.466023 | + | 0.338585i | ||||
\(13\) | 68.3813 | + | 49.6819i | 1.45889 | + | 1.05995i | 0.983650 | + | 0.180089i | \(0.0576385\pi\) |
0.475239 | + | 0.879857i | \(0.342361\pi\) | |||||||
\(14\) | −1.89008 | + | 1.37322i | −0.0360818 | + | 0.0262150i | ||||
\(15\) | 20.7316 | + | 26.3667i | 0.356858 | + | 0.453857i | ||||
\(16\) | −51.4237 | − | 37.3615i | −0.803495 | − | 0.583773i | ||||
\(17\) | −13.9374 | − | 42.8949i | −0.198842 | − | 0.611974i | −0.999910 | − | 0.0134002i | \(-0.995734\pi\) |
0.801068 | − | 0.598573i | \(-0.204266\pi\) | |||||||
\(18\) | −1.21471 | −0.0159060 | ||||||||
\(19\) | 25.8534 | + | 79.5686i | 0.312167 | + | 0.960753i | 0.976905 | + | 0.213675i | \(0.0685435\pi\) |
−0.664737 | + | 0.747077i | \(0.731457\pi\) | |||||||
\(20\) | −55.1583 | − | 70.1511i | −0.616689 | − | 0.784313i | ||||
\(21\) | −16.0472 | + | 49.3881i | −0.166751 | + | 0.513208i | ||||
\(22\) | −1.75814 | + | 5.41101i | −0.0170381 | + | 0.0524377i | ||||
\(23\) | −16.9333 | + | 12.3027i | −0.153514 | + | 0.111535i | −0.661891 | − | 0.749600i | \(-0.730246\pi\) |
0.508377 | + | 0.861135i | \(0.330246\pi\) | |||||||
\(24\) | 6.47105 | 0.0550374 | ||||||||
\(25\) | −47.5419 | − | 115.606i | −0.380335 | − | 0.924849i | ||||
\(26\) | 11.4080 | 0.0860495 | ||||||||
\(27\) | −21.8435 | + | 15.8702i | −0.155695 | + | 0.113119i | ||||
\(28\) | 42.6950 | − | 131.402i | 0.288164 | − | 0.886878i | ||||
\(29\) | 68.0039 | − | 209.295i | 0.435449 | − | 1.34017i | −0.457177 | − | 0.889376i | \(-0.651139\pi\) |
0.892626 | − | 0.450798i | \(-0.148861\pi\) | |||||||
\(30\) | 4.35541 | + | 1.23433i | 0.0265062 | + | 0.00751187i | ||||
\(31\) | 49.5106 | + | 152.378i | 0.286850 | + | 0.882834i | 0.985838 | + | 0.167701i | \(0.0536342\pi\) |
−0.698988 | + | 0.715134i | \(0.746366\pi\) | |||||||
\(32\) | −25.8351 | −0.142720 | ||||||||
\(33\) | 39.0793 | + | 120.274i | 0.206147 | + | 0.634454i | ||||
\(34\) | −4.92477 | − | 3.57805i | −0.0248409 | − | 0.0180480i | ||||
\(35\) | 107.724 | − | 160.778i | 0.520248 | − | 0.776470i | ||||
\(36\) | 58.1166 | − | 42.2242i | 0.269058 | − | 0.195482i | ||||
\(37\) | 212.955 | + | 154.721i | 0.946206 | + | 0.687459i | 0.949907 | − | 0.312534i | \(-0.101178\pi\) |
−0.00370013 | + | 0.999993i | \(0.501178\pi\) | |||||||
\(38\) | 9.13527 | + | 6.63716i | 0.0389983 | + | 0.0283340i | ||||
\(39\) | 205.144 | − | 149.046i | 0.842290 | − | 0.611960i | ||||
\(40\) | −23.2024 | − | 6.57558i | −0.0917156 | − | 0.0259923i | ||||
\(41\) | −331.812 | − | 241.075i | −1.26391 | − | 0.918284i | −0.264967 | − | 0.964257i | \(-0.585361\pi\) |
−0.998943 | + | 0.0459734i | \(0.985361\pi\) | |||||||
\(42\) | 2.16584 | + | 6.66577i | 0.00795706 | + | 0.0244893i | ||||
\(43\) | 290.699 | 1.03096 | 0.515479 | − | 0.856902i | \(-0.327614\pi\) | ||||
0.515479 | + | 0.856902i | \(0.327614\pi\) | |||||||
\(44\) | −103.974 | − | 320.000i | −0.356243 | − | 1.09640i | ||||
\(45\) | 94.4478 | − | 34.7074i | 0.312877 | − | 0.114975i | ||||
\(46\) | −0.872959 | + | 2.68669i | −0.00279806 | + | 0.00861154i | ||||
\(47\) | −142.456 | + | 438.434i | −0.442114 | + | 1.36069i | 0.443505 | + | 0.896272i | \(0.353735\pi\) |
−0.885618 | + | 0.464414i | \(0.846265\pi\) | |||||||
\(48\) | −154.271 | + | 112.084i | −0.463898 | + | 0.337042i | ||||
\(49\) | −43.3675 | −0.126436 | ||||||||
\(50\) | −14.3624 | − | 8.85153i | −0.0406229 | − | 0.0250359i | ||||
\(51\) | −135.307 | −0.371506 | ||||||||
\(52\) | −545.805 | + | 396.550i | −1.45557 | + | 1.05753i | ||||
\(53\) | −44.0172 | + | 135.471i | −0.114080 | + | 0.351101i | −0.991754 | − | 0.128156i | \(-0.959094\pi\) |
0.877674 | + | 0.479258i | \(0.159094\pi\) | |||||||
\(54\) | −1.12609 | + | 3.46576i | −0.00283781 | + | 0.00873389i | ||||
\(55\) | −17.9050 | − | 470.961i | −0.0438967 | − | 1.15462i | ||||
\(56\) | −11.5380 | − | 35.5103i | −0.0275327 | − | 0.0847369i | ||||
\(57\) | 250.990 | 0.583236 | ||||||||
\(58\) | −9.17830 | − | 28.2479i | −0.0207788 | − | 0.0639506i | ||||
\(59\) | 382.240 | + | 277.714i | 0.843448 | + | 0.612801i | 0.923332 | − | 0.384003i | \(-0.125455\pi\) |
−0.0798836 | + | 0.996804i | \(0.525455\pi\) | |||||||
\(60\) | −251.287 | + | 92.3424i | −0.540684 | + | 0.198689i | ||||
\(61\) | −43.7180 | + | 31.7630i | −0.0917625 | + | 0.0666694i | −0.632721 | − | 0.774380i | \(-0.718062\pi\) |
0.540958 | + | 0.841050i | \(0.318062\pi\) | |||||||
\(62\) | 17.4945 | + | 12.7105i | 0.0358355 | + | 0.0260360i | ||||
\(63\) | 126.036 | + | 91.5705i | 0.252048 | + | 0.183124i | ||||
\(64\) | 408.568 | − | 296.842i | 0.797985 | − | 0.579770i | ||||
\(65\) | −887.012 | + | 325.957i | −1.69262 | + | 0.621999i | ||||
\(66\) | 13.8086 | + | 10.0326i | 0.0257534 | + | 0.0187109i | ||||
\(67\) | 139.046 | + | 427.938i | 0.253539 | + | 0.780313i | 0.994114 | + | 0.108339i | \(0.0345533\pi\) |
−0.740575 | + | 0.671974i | \(0.765447\pi\) | |||||||
\(68\) | 359.998 | 0.642002 | ||||||||
\(69\) | 19.4038 | + | 59.7188i | 0.0338542 | + | 0.104193i | ||||
\(70\) | −0.992327 | − | 26.1014i | −0.00169437 | − | 0.0445674i | ||||
\(71\) | −193.462 | + | 595.416i | −0.323377 | + | 0.995252i | 0.648791 | + | 0.760967i | \(0.275275\pi\) |
−0.972168 | + | 0.234286i | \(0.924725\pi\) | |||||||
\(72\) | 5.99899 | − | 18.4630i | 0.00981928 | − | 0.0302206i | ||||
\(73\) | −39.4327 | + | 28.6495i | −0.0632226 | + | 0.0459339i | −0.618948 | − | 0.785432i | \(-0.712441\pi\) |
0.555725 | + | 0.831366i | \(0.312441\pi\) | |||||||
\(74\) | 35.5271 | 0.0558099 | ||||||||
\(75\) | −373.918 | + | 28.4724i | −0.575684 | + | 0.0438362i | ||||
\(76\) | −667.783 | −1.00789 | ||||||||
\(77\) | 590.331 | − | 428.900i | 0.873694 | − | 0.634776i | ||||
\(78\) | 10.5758 | − | 32.5489i | 0.0153522 | − | 0.0472491i | ||||
\(79\) | −200.110 | + | 615.877i | −0.284990 | + | 0.877108i | 0.701412 | + | 0.712756i | \(0.252553\pi\) |
−0.986402 | + | 0.164352i | \(0.947447\pi\) | |||||||
\(80\) | 667.045 | − | 245.124i | 0.932223 | − | 0.342571i | ||||
\(81\) | 25.0304 | + | 77.0356i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −55.3557 | −0.0745490 | ||||||||
\(83\) | 206.995 | + | 637.066i | 0.273743 | + | 0.842495i | 0.989549 | + | 0.144196i | \(0.0460595\pi\) |
−0.715806 | + | 0.698299i | \(0.753940\pi\) | |||||||
\(84\) | −335.331 | − | 243.632i | −0.435566 | − | 0.316458i | ||||
\(85\) | 485.154 | + | 137.493i | 0.619086 | + | 0.175449i | ||||
\(86\) | 31.7417 | − | 23.0617i | 0.0397999 | − | 0.0289163i | ||||
\(87\) | −534.110 | − | 388.054i | −0.658191 | − | 0.478204i | ||||
\(88\) | −73.5622 | − | 53.4460i | −0.0891108 | − | 0.0647428i | ||||
\(89\) | 700.638 | − | 509.043i | 0.834466 | − | 0.606275i | −0.0863533 | − | 0.996265i | \(-0.527521\pi\) |
0.920819 | + | 0.389990i | \(0.127521\pi\) | |||||||
\(90\) | 7.55943 | − | 11.2824i | 0.00885371 | − | 0.0132142i | ||||
\(91\) | −1183.67 | − | 859.989i | −1.36355 | − | 0.990674i | ||||
\(92\) | −51.6256 | − | 158.887i | −0.0585038 | − | 0.180056i | ||||
\(93\) | 480.659 | 0.535935 | ||||||||
\(94\) | 19.2269 | + | 59.1743i | 0.0210968 | + | 0.0649294i | ||||
\(95\) | −899.943 | − | 255.045i | −0.971918 | − | 0.275442i | ||||
\(96\) | −23.9504 | + | 73.7119i | −0.0254628 | + | 0.0783665i | ||||
\(97\) | −54.7107 | + | 168.382i | −0.0572683 | + | 0.176254i | −0.975599 | − | 0.219561i | \(-0.929538\pi\) |
0.918331 | + | 0.395814i | \(0.129538\pi\) | |||||||
\(98\) | −4.73533 | + | 3.44042i | −0.00488102 | + | 0.00354627i | ||||
\(99\) | 379.390 | 0.385153 | ||||||||
\(100\) | 994.843 | − | 75.7536i | 0.994843 | − | 0.0757536i | ||||
\(101\) | 810.637 | 0.798628 | 0.399314 | − | 0.916814i | \(-0.369248\pi\) | ||||
0.399314 | + | 0.916814i | \(0.369248\pi\) | |||||||
\(102\) | −14.7743 | + | 10.7342i | −0.0143419 | + | 0.0104200i | ||||
\(103\) | 421.601 | − | 1297.56i | 0.403317 | − | 1.24128i | −0.518976 | − | 0.854789i | \(-0.673687\pi\) |
0.922293 | − | 0.386492i | \(-0.126313\pi\) | |||||||
\(104\) | −56.3399 | + | 173.396i | −0.0531209 | + | 0.163489i | ||||
\(105\) | −358.861 | − | 456.405i | −0.333536 | − | 0.424195i | ||||
\(106\) | 5.94087 | + | 18.2841i | 0.00544367 | + | 0.0167539i | ||||
\(107\) | −1109.53 | −1.00245 | −0.501227 | − | 0.865316i | \(-0.667118\pi\) | ||||
−0.501227 | + | 0.865316i | \(0.667118\pi\) | |||||||
\(108\) | −66.5957 | − | 204.960i | −0.0593349 | − | 0.182614i | ||||
\(109\) | −1022.56 | − | 742.936i | −0.898567 | − | 0.652847i | 0.0395305 | − | 0.999218i | \(-0.487414\pi\) |
−0.938098 | + | 0.346371i | \(0.887414\pi\) | |||||||
\(110\) | −39.3172 | − | 50.0041i | −0.0340795 | − | 0.0433428i | ||||
\(111\) | 638.866 | − | 464.163i | 0.546293 | − | 0.396905i | ||||
\(112\) | 890.138 | + | 646.723i | 0.750984 | + | 0.545622i | ||||
\(113\) | 925.944 | + | 672.737i | 0.770845 | + | 0.560051i | 0.902217 | − | 0.431282i | \(-0.141938\pi\) |
−0.131373 | + | 0.991333i | \(0.541938\pi\) | |||||||
\(114\) | 27.4058 | − | 19.9115i | 0.0225157 | − | 0.0163586i | ||||
\(115\) | −8.89028 | − | 233.843i | −0.00720889 | − | 0.189617i | ||||
\(116\) | 1421.05 | + | 1032.45i | 1.13742 | + | 0.826387i | ||||
\(117\) | −235.074 | − | 723.484i | −0.185749 | − | 0.571676i | ||||
\(118\) | 63.7686 | 0.0497490 | ||||||||
\(119\) | 241.255 | + | 742.507i | 0.185847 | + | 0.571979i | ||||
\(120\) | −40.2711 | + | 60.1045i | −0.0306352 | + | 0.0457231i | ||||
\(121\) | 137.821 | − | 424.168i | 0.103547 | − | 0.318684i | ||||
\(122\) | −2.25379 | + | 6.93645i | −0.00167253 | + | 0.00514751i | ||||
\(123\) | −995.435 | + | 723.226i | −0.729719 | + | 0.530172i | ||||
\(124\) | −1278.84 | −0.926153 | ||||||||
\(125\) | 1369.64 | + | 277.868i | 0.980035 | + | 0.198826i | ||||
\(126\) | 21.0264 | 0.0148665 | ||||||||
\(127\) | 1847.74 | − | 1342.46i | 1.29103 | − | 0.937985i | 0.291200 | − | 0.956662i | \(-0.405946\pi\) |
0.999826 | + | 0.0186776i | \(0.00594562\pi\) | |||||||
\(128\) | 84.9307 | − | 261.390i | 0.0586475 | − | 0.180499i | ||||
\(129\) | 269.493 | − | 829.414i | 0.183934 | − | 0.566092i | ||||
\(130\) | −70.9948 | + | 105.960i | −0.0478974 | + | 0.0714867i | ||||
\(131\) | −62.7937 | − | 193.259i | −0.0418803 | − | 0.128894i | 0.927930 | − | 0.372754i | \(-0.121586\pi\) |
−0.969811 | + | 0.243860i | \(0.921586\pi\) | |||||||
\(132\) | −1009.40 | −0.665585 | ||||||||
\(133\) | −447.520 | − | 1377.32i | −0.291766 | − | 0.897964i | ||||
\(134\) | 49.1316 | + | 35.6962i | 0.0316741 | + | 0.0230125i | ||||
\(135\) | −11.4682 | − | 301.651i | −0.00731131 | − | 0.192311i | ||||
\(136\) | 78.7066 | − | 57.1837i | 0.0496252 | − | 0.0360548i | ||||
\(137\) | −51.4587 | − | 37.3869i | −0.0320906 | − | 0.0233152i | 0.571624 | − | 0.820515i | \(-0.306313\pi\) |
−0.603715 | + | 0.797200i | \(0.706313\pi\) | |||||||
\(138\) | 6.85631 | + | 4.98140i | 0.00422933 | + | 0.00307279i | ||||
\(139\) | −1297.59 | + | 942.758i | −0.791802 | + | 0.575278i | −0.908498 | − | 0.417890i | \(-0.862770\pi\) |
0.116695 | + | 0.993168i | \(0.462770\pi\) | |||||||
\(140\) | 954.785 | + | 1214.31i | 0.576386 | + | 0.733055i | ||||
\(141\) | 1118.86 | + | 812.902i | 0.668265 | + | 0.485523i | ||||
\(142\) | 26.1111 | + | 80.3617i | 0.0154309 | + | 0.0474916i | ||||
\(143\) | −3563.06 | −2.08362 | ||||||||
\(144\) | 176.779 | + | 544.069i | 0.102303 | + | 0.314855i | ||||
\(145\) | 1520.77 | + | 1934.13i | 0.870985 | + | 1.10773i | ||||
\(146\) | −2.03287 | + | 6.25653i | −0.00115234 | + | 0.00354654i | ||||
\(147\) | −40.2039 | + | 123.735i | −0.0225575 | + | 0.0694250i | ||||
\(148\) | −1699.76 | + | 1234.95i | −0.944052 | + | 0.685894i | ||||
\(149\) | −2731.00 | −1.50156 | −0.750780 | − | 0.660552i | \(-0.770322\pi\) | ||||
−0.750780 | + | 0.660552i | \(0.770322\pi\) | |||||||
\(150\) | −38.5696 | + | 32.7725i | −0.0209946 | + | 0.0178391i | ||||
\(151\) | −879.795 | −0.474150 | −0.237075 | − | 0.971491i | \(-0.576189\pi\) | ||||
−0.237075 | + | 0.971491i | \(0.576189\pi\) | |||||||
\(152\) | −145.998 | + | 106.074i | −0.0779079 | + | 0.0566034i | ||||
\(153\) | −125.437 | + | 386.055i | −0.0662808 | + | 0.203991i | ||||
\(154\) | 30.4333 | − | 93.6639i | 0.0159246 | − | 0.0490107i | ||||
\(155\) | −1723.44 | − | 488.423i | −0.893095 | − | 0.253104i | ||||
\(156\) | 625.437 | + | 1924.90i | 0.320994 | + | 0.987917i | ||||
\(157\) | 366.317 | 0.186212 | 0.0931059 | − | 0.995656i | \(-0.470320\pi\) | ||||
0.0931059 | + | 0.995656i | \(0.470320\pi\) | |||||||
\(158\) | 27.0084 | + | 83.1232i | 0.0135992 | + | 0.0418539i | ||||
\(159\) | 345.715 | + | 251.177i | 0.172434 | + | 0.125281i | ||||
\(160\) | 160.779 | − | 239.962i | 0.0794416 | − | 0.118567i | ||||
\(161\) | 293.113 | − | 212.959i | 0.143482 | − | 0.104246i | ||||
\(162\) | 8.84445 | + | 6.42587i | 0.00428942 | + | 0.00311645i | ||||
\(163\) | −682.163 | − | 495.620i | −0.327798 | − | 0.238159i | 0.411697 | − | 0.911321i | \(-0.364936\pi\) |
−0.739496 | + | 0.673161i | \(0.764936\pi\) | |||||||
\(164\) | 2648.45 | − | 1924.21i | 1.26103 | − | 0.916193i | ||||
\(165\) | −1360.33 | − | 385.518i | −0.641827 | − | 0.181894i | ||||
\(166\) | 73.1416 | + | 53.1405i | 0.0341981 | + | 0.0248464i | ||||
\(167\) | −689.135 | − | 2120.94i | −0.319323 | − | 0.982774i | −0.973938 | − | 0.226813i | \(-0.927170\pi\) |
0.654616 | − | 0.755962i | \(-0.272830\pi\) | |||||||
\(168\) | −112.013 | −0.0514405 | ||||||||
\(169\) | 1528.80 | + | 4705.16i | 0.695858 | + | 2.14163i | ||||
\(170\) | 63.8819 | − | 23.4751i | 0.0288207 | − | 0.0105909i | ||||
\(171\) | 232.681 | − | 716.118i | 0.104056 | − | 0.320251i | ||||
\(172\) | −717.011 | + | 2206.73i | −0.317858 | + | 0.978267i | ||||
\(173\) | 2340.93 | − | 1700.78i | 1.02877 | − | 0.747446i | 0.0607090 | − | 0.998156i | \(-0.480664\pi\) |
0.968062 | + | 0.250709i | \(0.0806638\pi\) | |||||||
\(174\) | −89.1048 | −0.0388220 | ||||||||
\(175\) | 822.946 | + | 2001.13i | 0.355479 | + | 0.864407i | ||||
\(176\) | 2679.47 | 1.14757 | ||||||||
\(177\) | 1146.72 | − | 833.141i | 0.486965 | − | 0.353801i | ||||
\(178\) | 36.1199 | − | 111.166i | 0.0152096 | − | 0.0468102i | ||||
\(179\) | −836.156 | + | 2573.42i | −0.349146 | + | 1.07456i | 0.610180 | + | 0.792263i | \(0.291097\pi\) |
−0.959326 | + | 0.282299i | \(0.908903\pi\) | |||||||
\(180\) | 30.5123 | + | 802.572i | 0.0126347 | + | 0.332334i | ||||
\(181\) | −1098.49 | − | 3380.80i | −0.451104 | − | 1.38836i | −0.875648 | − | 0.482949i | \(-0.839566\pi\) |
0.424544 | − | 0.905407i | \(-0.360434\pi\) | |||||||
\(182\) | −197.471 | −0.0804258 | ||||||||
\(183\) | 50.0964 | + | 154.181i | 0.0202362 | + | 0.0622807i | ||||
\(184\) | −36.5254 | − | 26.5372i | −0.0146342 | − | 0.0106323i | ||||
\(185\) | −2762.36 | + | 1015.10i | −1.09780 | + | 0.403416i | ||||
\(186\) | 52.4835 | − | 38.1315i | 0.0206897 | − | 0.0150319i | ||||
\(187\) | 1538.16 | + | 1117.54i | 0.601504 | + | 0.437018i | ||||
\(188\) | −2976.84 | − | 2162.80i | −1.15483 | − | 0.839035i | ||||
\(189\) | 378.108 | − | 274.712i | 0.145520 | − | 0.105727i | ||||
\(190\) | −118.499 | + | 43.5456i | −0.0452463 | + | 0.0166270i | ||||
\(191\) | −139.503 | − | 101.355i | −0.0528486 | − | 0.0383967i | 0.561047 | − | 0.827784i | \(-0.310399\pi\) |
−0.613896 | + | 0.789387i | \(0.710399\pi\) | |||||||
\(192\) | −468.178 | − | 1440.90i | −0.175978 | − | 0.541605i | ||||
\(193\) | 1203.86 | 0.448993 | 0.224496 | − | 0.974475i | \(-0.427926\pi\) | ||||
0.224496 | + | 0.974475i | \(0.427926\pi\) | |||||||
\(194\) | 7.38415 | + | 22.7261i | 0.00273274 | + | 0.00841050i | ||||
\(195\) | 107.704 | + | 2832.97i | 0.0395532 | + | 1.04038i | ||||
\(196\) | 106.966 | − | 329.208i | 0.0389818 | − | 0.119974i | ||||
\(197\) | 1296.62 | − | 3990.60i | 0.468937 | − | 1.44324i | −0.385026 | − | 0.922906i | \(-0.625808\pi\) |
0.853963 | − | 0.520334i | \(-0.174192\pi\) | |||||||
\(198\) | 41.4259 | − | 30.0977i | 0.0148687 | − | 0.0108028i | ||||
\(199\) | −2413.09 | −0.859594 | −0.429797 | − | 0.902926i | \(-0.641415\pi\) | ||||
−0.429797 | + | 0.902926i | \(0.641415\pi\) | |||||||
\(200\) | 205.470 | − | 174.587i | 0.0726447 | − | 0.0617260i | ||||
\(201\) | 1349.88 | 0.473699 | ||||||||
\(202\) | 88.5141 | − | 64.3093i | 0.0308309 | − | 0.0223999i | ||||
\(203\) | −1177.14 | + | 3622.87i | −0.406991 | + | 1.25259i | ||||
\(204\) | 333.736 | − | 1027.13i | 0.114540 | − | 0.352519i | ||||
\(205\) | 4304.11 | − | 1581.66i | 1.46640 | − | 0.538869i | ||||
\(206\) | −56.9024 | − | 175.127i | −0.0192455 | − | 0.0592316i | ||||
\(207\) | 188.376 | 0.0632514 | ||||||||
\(208\) | −1660.23 | − | 5109.65i | −0.553443 | − | 1.70332i | ||||
\(209\) | −2853.23 | − | 2072.99i | −0.944316 | − | 0.686085i | ||||
\(210\) | −75.3917 | − | 21.3661i | −0.0247739 | − | 0.00702095i | ||||
\(211\) | −546.184 | + | 396.826i | −0.178203 | + | 0.129472i | −0.673311 | − | 0.739359i | \(-0.735128\pi\) |
0.495108 | + | 0.868831i | \(0.335128\pi\) | |||||||
\(212\) | −919.808 | − | 668.280i | −0.297984 | − | 0.216498i | ||||
\(213\) | 1519.47 | + | 1103.96i | 0.488792 | + | 0.355128i | ||||
\(214\) | −121.151 | + | 88.0211i | −0.0386995 | + | 0.0281168i | ||||
\(215\) | −1809.10 | + | 2700.08i | −0.573858 | + | 0.856482i | ||||
\(216\) | −47.1167 | − | 34.2323i | −0.0148421 | − | 0.0107834i | ||||
\(217\) | −857.023 | − | 2637.64i | −0.268104 | − | 0.825138i | ||||
\(218\) | −170.593 | −0.0530000 | ||||||||
\(219\) | 45.1859 | + | 139.068i | 0.0139424 | + | 0.0429102i | ||||
\(220\) | 3619.29 | + | 1025.71i | 1.10915 | + | 0.314333i | ||||
\(221\) | 1178.05 | − | 3625.65i | 0.358570 | − | 1.10356i | ||||
\(222\) | 32.9354 | − | 101.365i | 0.00995711 | − | 0.0306448i | ||||
\(223\) | 4643.42 | − | 3373.64i | 1.39438 | − | 1.01307i | 0.399009 | − | 0.916947i | \(-0.369354\pi\) |
0.995369 | − | 0.0961277i | \(-0.0306457\pi\) | |||||||
\(224\) | 447.203 | 0.133393 | ||||||||
\(225\) | −265.404 | + | 1093.25i | −0.0786382 | + | 0.323925i | ||||
\(226\) | 154.474 | 0.0454666 | ||||||||
\(227\) | 2143.69 | − | 1557.48i | 0.626790 | − | 0.455390i | −0.228496 | − | 0.973545i | \(-0.573381\pi\) |
0.855287 | + | 0.518155i | \(0.173381\pi\) | |||||||
\(228\) | −619.069 | + | 1905.30i | −0.179820 | + | 0.553428i | ||||
\(229\) | −1138.94 | + | 3505.30i | −0.328661 | + | 1.01151i | 0.641100 | + | 0.767458i | \(0.278479\pi\) |
−0.969761 | + | 0.244057i | \(0.921521\pi\) | |||||||
\(230\) | −19.5219 | − | 24.8282i | −0.00559668 | − | 0.00711793i | ||||
\(231\) | −676.459 | − | 2081.93i | −0.192674 | − | 0.592990i | ||||
\(232\) | 474.685 | 0.134330 | ||||||||
\(233\) | 788.427 | + | 2426.53i | 0.221680 | + | 0.682262i | 0.998612 | + | 0.0526768i | \(0.0167753\pi\) |
−0.776931 | + | 0.629586i | \(0.783225\pi\) | |||||||
\(234\) | −83.0631 | − | 60.3489i | −0.0232052 | − | 0.0168595i | ||||
\(235\) | −3185.73 | − | 4051.66i | −0.884316 | − | 1.12468i | ||||
\(236\) | −3050.96 | + | 2216.65i | −0.841528 | + | 0.611406i | ||||
\(237\) | 1571.69 | + | 1141.90i | 0.430768 | + | 0.312972i | ||||
\(238\) | 85.2472 | + | 61.9357i | 0.0232175 | + | 0.0168685i | ||||
\(239\) | 5039.96 | − | 3661.74i | 1.36405 | − | 0.991039i | 0.365873 | − | 0.930665i | \(-0.380770\pi\) |
0.998176 | − | 0.0603745i | \(-0.0192295\pi\) | |||||||
\(240\) | −80.9951 | − | 2130.43i | −0.0217842 | − | 0.572995i | ||||
\(241\) | 3304.08 | + | 2400.55i | 0.883130 | + | 0.641631i | 0.934078 | − | 0.357070i | \(-0.116224\pi\) |
−0.0509481 | + | 0.998701i | \(0.516224\pi\) | |||||||
\(242\) | −18.6013 | − | 57.2488i | −0.00494105 | − | 0.0152070i | ||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −133.286 | − | 410.212i | −0.0349704 | − | 0.107628i | ||||
\(245\) | 269.887 | − | 402.806i | 0.0703774 | − | 0.105038i | ||||
\(246\) | −51.3176 | + | 157.939i | −0.0133004 | + | 0.0409343i | ||||
\(247\) | −2185.23 | + | 6725.46i | −0.562927 | + | 1.73251i | ||||
\(248\) | −279.593 | + | 203.136i | −0.0715895 | + | 0.0520128i | ||||
\(249\) | 2009.55 | 0.511447 | ||||||||
\(250\) | 171.596 | − | 78.3154i | 0.0434107 | − | 0.0198124i | ||||
\(251\) | −1158.16 | −0.291245 | −0.145622 | − | 0.989340i | \(-0.546518\pi\) | ||||
−0.145622 | + | 0.989340i | \(0.546518\pi\) | |||||||
\(252\) | −1005.99 | + | 730.896i | −0.251474 | + | 0.182707i | ||||
\(253\) | 272.652 | − | 839.137i | 0.0677529 | − | 0.208522i | ||||
\(254\) | 95.2562 | − | 293.168i | 0.0235311 | − | 0.0724214i | ||||
\(255\) | 842.053 | − | 1256.76i | 0.206790 | − | 0.308634i | ||||
\(256\) | 1237.01 | + | 3807.13i | 0.302005 | + | 0.929475i | ||||
\(257\) | −4275.75 | −1.03780 | −0.518899 | − | 0.854836i | \(-0.673658\pi\) | ||||
−0.518899 | + | 0.854836i | \(0.673658\pi\) | |||||||
\(258\) | −36.3727 | − | 111.944i | −0.00877700 | − | 0.0270128i | ||||
\(259\) | −3686.23 | − | 2678.21i | −0.884369 | − | 0.642531i | ||||
\(260\) | −286.558 | − | 7537.39i | −0.0683521 | − | 1.79788i | ||||
\(261\) | −1602.33 | + | 1164.16i | −0.380007 | + | 0.276091i | ||||
\(262\) | −22.1881 | − | 16.1206i | −0.00523200 | − | 0.00380127i | ||||
\(263\) | 216.683 | + | 157.430i | 0.0508033 | + | 0.0369108i | 0.612897 | − | 0.790163i | \(-0.290004\pi\) |
−0.562094 | + | 0.827073i | \(0.690004\pi\) | |||||||
\(264\) | −220.687 | + | 160.338i | −0.0514482 | + | 0.0373793i | ||||
\(265\) | −984.352 | − | 1251.91i | −0.228182 | − | 0.290205i | ||||
\(266\) | −158.131 | − | 114.889i | −0.0364497 | − | 0.0264822i | ||||
\(267\) | −802.860 | − | 2470.95i | −0.184023 | − | 0.566365i | ||||
\(268\) | −3591.49 | −0.818602 | ||||||||
\(269\) | 1922.62 | + | 5917.22i | 0.435778 | + | 1.34119i | 0.892287 | + | 0.451468i | \(0.149099\pi\) |
−0.456510 | + | 0.889718i | \(0.650901\pi\) | |||||||
\(270\) | −25.1827 | − | 32.0277i | −0.00567620 | − | 0.00721906i | ||||
\(271\) | −459.156 | + | 1413.14i | −0.102922 | + | 0.316760i | −0.989237 | − | 0.146322i | \(-0.953256\pi\) |
0.886315 | + | 0.463082i | \(0.153256\pi\) | |||||||
\(272\) | −885.906 | + | 2726.54i | −0.197485 | + | 0.607796i | ||||
\(273\) | −3551.02 | + | 2579.97i | −0.787244 | + | 0.571966i | ||||
\(274\) | −8.58479 | −0.00189280 | ||||||||
\(275\) | 4485.81 | + | 2764.61i | 0.983653 | + | 0.606226i | ||||
\(276\) | −501.192 | −0.109305 | ||||||||
\(277\) | −910.148 | + | 661.262i | −0.197421 | + | 0.143434i | −0.682104 | − | 0.731255i | \(-0.738935\pi\) |
0.484683 | + | 0.874690i | \(0.338935\pi\) | |||||||
\(278\) | −66.8947 | + | 205.881i | −0.0144319 | + | 0.0444170i | ||||
\(279\) | 445.595 | − | 1371.40i | 0.0956168 | − | 0.294278i | ||||
\(280\) | 401.631 | + | 113.823i | 0.0857217 | + | 0.0242936i | ||||
\(281\) | 1122.23 | + | 3453.87i | 0.238244 | + | 0.733240i | 0.996674 | + | 0.0814859i | \(0.0259665\pi\) |
−0.758430 | + | 0.651754i | \(0.774033\pi\) | |||||||
\(282\) | 186.659 | 0.0394162 | ||||||||
\(283\) | 1626.27 | + | 5005.15i | 0.341596 | + | 1.05133i | 0.963381 | + | 0.268137i | \(0.0864080\pi\) |
−0.621784 | + | 0.783188i | \(0.713592\pi\) | |||||||
\(284\) | −4042.70 | − | 2937.20i | −0.844684 | − | 0.613699i | ||||
\(285\) | −1561.98 | + | 2331.25i | −0.324644 | + | 0.484531i | ||||
\(286\) | −389.053 | + | 282.664i | −0.0804378 | + | 0.0584415i | ||||
\(287\) | 5743.63 | + | 4172.99i | 1.18131 | + | 0.858271i | ||||
\(288\) | 188.109 | + | 136.669i | 0.0384876 | + | 0.0279629i | ||||
\(289\) | 2328.98 | − | 1692.10i | 0.474043 | − | 0.344413i | ||||
\(290\) | 319.492 | + | 90.5442i | 0.0646938 | + | 0.0183343i | ||||
\(291\) | 429.703 | + | 312.198i | 0.0865624 | + | 0.0628912i | ||||
\(292\) | −120.221 | − | 370.003i | −0.0240939 | − | 0.0741534i | ||||
\(293\) | 3619.55 | 0.721693 | 0.360847 | − | 0.932625i | \(-0.382488\pi\) | ||||
0.360847 | + | 0.932625i | \(0.382488\pi\) | |||||||
\(294\) | 5.42620 | + | 16.7001i | 0.00107640 | + | 0.00331283i | ||||
\(295\) | −4958.25 | + | 1822.04i | −0.978578 | + | 0.359605i | ||||
\(296\) | −175.455 | + | 539.996i | −0.0344532 | + | 0.106036i | ||||
\(297\) | 351.714 | − | 1082.46i | 0.0687155 | − | 0.211485i | ||||
\(298\) | −298.200 | + | 216.655i | −0.0579674 | + | 0.0421158i | ||||
\(299\) | −1769.14 | −0.342181 | ||||||||
\(300\) | 706.132 | − | 2908.68i | 0.135895 | − | 0.559776i | ||||
\(301\) | −5031.97 | −0.963581 | ||||||||
\(302\) | −96.0655 | + | 69.7956i | −0.0183045 | + | 0.0132990i | ||||
\(303\) | 751.502 | − | 2312.89i | 0.142484 | − | 0.438521i | ||||
\(304\) | 1643.32 | − | 5057.63i | 0.310037 | − | 0.954195i | ||||
\(305\) | −22.9527 | − | 603.732i | −0.00430908 | − | 0.113343i | ||||
\(306\) | 16.9298 | + | 52.1047i | 0.00316279 | + | 0.00973408i | ||||
\(307\) | −1819.08 | −0.338176 | −0.169088 | − | 0.985601i | \(-0.554082\pi\) | ||||
−0.169088 | + | 0.985601i | \(0.554082\pi\) | |||||||
\(308\) | 1799.78 | + | 5539.16i | 0.332962 | + | 1.02475i | ||||
\(309\) | −3311.30 | − | 2405.80i | −0.609622 | − | 0.442916i | ||||
\(310\) | −226.931 | + | 83.3919i | −0.0415768 | + | 0.0152785i | ||||
\(311\) | −276.570 | + | 200.940i | −0.0504272 | + | 0.0366375i | −0.612713 | − | 0.790305i | \(-0.709922\pi\) |
0.562286 | + | 0.826943i | \(0.309922\pi\) | |||||||
\(312\) | 442.499 | + | 321.494i | 0.0802935 | + | 0.0583366i | ||||
\(313\) | 3165.92 | + | 2300.18i | 0.571721 | + | 0.415379i | 0.835730 | − | 0.549141i | \(-0.185045\pi\) |
−0.264009 | + | 0.964520i | \(0.585045\pi\) | |||||||
\(314\) | 39.9984 | − | 29.0606i | 0.00718867 | − | 0.00522287i | ||||
\(315\) | −1634.88 | + | 600.782i | −0.292429 | + | 0.107461i | ||||
\(316\) | −4181.62 | − | 3038.13i | −0.744414 | − | 0.540848i | ||||
\(317\) | 2032.49 | + | 6255.35i | 0.360113 | + | 1.10831i | 0.952985 | + | 0.303017i | \(0.0979939\pi\) |
−0.592872 | + | 0.805296i | \(0.702006\pi\) | |||||||
\(318\) | 57.6752 | 0.0101706 | ||||||||
\(319\) | 2866.67 | + | 8822.70i | 0.503143 | + | 1.54851i | ||||
\(320\) | 214.506 | + | 5642.20i | 0.0374726 | + | 0.985652i | ||||
\(321\) | −1028.59 | + | 3165.68i | −0.178849 | + | 0.550440i | ||||
\(322\) | 15.1108 | − | 46.5064i | 0.00261520 | − | 0.00804875i | ||||
\(323\) | 3052.76 | − | 2217.96i | 0.525883 | − | 0.382076i | ||||
\(324\) | −646.524 | −0.110858 | ||||||||
\(325\) | 2492.55 | − | 10267.3i | 0.425422 | − | 1.75239i | ||||
\(326\) | −113.804 | −0.0193345 | ||||||||
\(327\) | −3067.69 | + | 2228.81i | −0.518788 | + | 0.376922i | ||||
\(328\) | 273.382 | − | 841.384i | 0.0460213 | − | 0.141639i | ||||
\(329\) | 2465.90 | − | 7589.25i | 0.413220 | − | 1.27176i | ||||
\(330\) | −179.119 | + | 65.8223i | −0.0298794 | + | 0.0109800i | ||||
\(331\) | −2960.46 | − | 9111.36i | −0.491606 | − | 1.51301i | −0.822179 | − | 0.569228i | \(-0.807242\pi\) |
0.330573 | − | 0.943780i | \(-0.392758\pi\) | |||||||
\(332\) | −5346.61 | −0.883835 | ||||||||
\(333\) | −732.075 | − | 2253.10i | −0.120473 | − | 0.370777i | ||||
\(334\) | −243.505 | − | 176.917i | −0.0398922 | − | 0.0289834i | ||||
\(335\) | −4840.10 | − | 1371.69i | −0.789382 | − | 0.223712i | ||||
\(336\) | 2670.41 | − | 1940.17i | 0.433581 | − | 0.315015i | ||||
\(337\) | 1448.85 | + | 1052.65i | 0.234196 | + | 0.170153i | 0.698694 | − | 0.715421i | \(-0.253765\pi\) |
−0.464498 | + | 0.885574i | \(0.653765\pi\) | |||||||
\(338\) | 540.200 | + | 392.478i | 0.0869319 | + | 0.0631597i | ||||
\(339\) | 2777.83 | − | 2018.21i | 0.445047 | − | 0.323346i | ||||
\(340\) | −2240.36 | + | 3343.74i | −0.357355 | + | 0.533352i | ||||
\(341\) | −5464.07 | − | 3969.88i | −0.867731 | − | 0.630443i | ||||
\(342\) | −31.4043 | − | 96.6524i | −0.00496535 | − | 0.0152818i | ||||
\(343\) | 6687.98 | 1.05282 | ||||||||
\(344\) | 193.767 | + | 596.353i | 0.0303698 | + | 0.0934686i | ||||
\(345\) | −675.436 | − | 191.419i | −0.105404 | − | 0.0298715i | ||||
\(346\) | 120.682 | − | 371.420i | 0.0187511 | − | 0.0577100i | ||||
\(347\) | −2806.06 | + | 8636.18i | −0.434114 | + | 1.33606i | 0.459879 | + | 0.887982i | \(0.347893\pi\) |
−0.893992 | + | 0.448083i | \(0.852107\pi\) | |||||||
\(348\) | 4263.15 | − | 3097.36i | 0.656692 | − | 0.477115i | ||||
\(349\) | 1036.94 | 0.159043 | 0.0795216 | − | 0.996833i | \(-0.474661\pi\) | ||||
0.0795216 | + | 0.996833i | \(0.474661\pi\) | |||||||
\(350\) | 248.611 | + | 153.219i | 0.0379681 | + | 0.0233997i | ||||
\(351\) | −2282.15 | −0.347043 | ||||||||
\(352\) | 881.071 | − | 640.135i | 0.133413 | − | 0.0969299i | ||||
\(353\) | 1022.00 | − | 3145.41i | 0.154096 | − | 0.474258i | −0.843972 | − | 0.536387i | \(-0.819789\pi\) |
0.998068 | + | 0.0621285i | \(0.0197889\pi\) | |||||||
\(354\) | 59.1168 | − | 181.943i | 0.00887576 | − | 0.0273168i | ||||
\(355\) | −4326.39 | − | 5502.36i | −0.646819 | − | 0.822633i | ||||
\(356\) | 2136.08 | + | 6574.19i | 0.318012 | + | 0.978740i | ||||
\(357\) | 2342.15 | 0.347227 | ||||||||
\(358\) | 112.854 | + | 347.328i | 0.0166606 | + | 0.0512761i | ||||
\(359\) | 10087.2 | + | 7328.80i | 1.48296 | + | 1.07743i | 0.976587 | + | 0.215121i | \(0.0690147\pi\) |
0.506375 | + | 0.862314i | \(0.330985\pi\) | |||||||
\(360\) | 134.155 | + | 170.620i | 0.0196405 | + | 0.0249791i | ||||
\(361\) | −113.721 | + | 82.6235i | −0.0165799 | + | 0.0120460i | ||||
\(362\) | −388.149 | − | 282.007i | −0.0563554 | − | 0.0409446i | ||||
\(363\) | −1082.46 | − | 786.451i | −0.156513 | − | 0.113713i | ||||
\(364\) | 9447.83 | − | 6864.25i | 1.36044 | − | 0.988419i | ||||
\(365\) | −20.7029 | − | 544.553i | −0.00296887 | − | 0.0780910i | ||||
\(366\) | 17.7015 | + | 12.8609i | 0.00252806 | + | 0.00183675i | ||||
\(367\) | −1531.52 | − | 4713.54i | −0.217833 | − | 0.670421i | −0.998940 | − | 0.0460243i | \(-0.985345\pi\) |
0.781107 | − | 0.624397i | \(-0.214655\pi\) | |||||||
\(368\) | 1330.42 | 0.188459 | ||||||||
\(369\) | 1140.67 | + | 3510.61i | 0.160924 | + | 0.495272i | ||||
\(370\) | −221.094 | + | 329.983i | −0.0310653 | + | 0.0463649i | ||||
\(371\) | 761.933 | − | 2344.99i | 0.106624 | − | 0.328155i | ||||
\(372\) | −1185.55 | + | 3648.74i | −0.165236 | + | 0.508544i | ||||
\(373\) | −2349.06 | + | 1706.69i | −0.326085 | + | 0.236915i | −0.738768 | − | 0.673960i | \(-0.764592\pi\) |
0.412683 | + | 0.910875i | \(0.364592\pi\) | |||||||
\(374\) | 256.609 | 0.0354784 | ||||||||
\(375\) | 2062.53 | − | 3650.22i | 0.284023 | − | 0.502657i | ||||
\(376\) | −994.379 | −0.136386 | ||||||||
\(377\) | 15048.4 | − | 10933.3i | 2.05578 | − | 1.49361i | ||||
\(378\) | 19.4926 | − | 59.9919i | 0.00265235 | − | 0.00816310i | ||||
\(379\) | 1478.37 | − | 4549.97i | 0.200367 | − | 0.616665i | −0.799505 | − | 0.600659i | \(-0.794905\pi\) |
0.999872 | − | 0.0160061i | \(-0.00509511\pi\) | |||||||
\(380\) | 4155.79 | − | 6202.52i | 0.561020 | − | 0.837322i | ||||
\(381\) | −2117.32 | − | 6516.44i | −0.284707 | − | 0.876239i | ||||
\(382\) | −23.2731 | −0.00311716 | ||||||||
\(383\) | 475.165 | + | 1462.41i | 0.0633937 | + | 0.195106i | 0.977737 | − | 0.209834i | \(-0.0672924\pi\) |
−0.914343 | + | 0.404940i | \(0.867292\pi\) | |||||||
\(384\) | −667.054 | − | 484.643i | −0.0886471 | − | 0.0644059i | ||||
\(385\) | 309.935 | + | 8152.28i | 0.0410279 | + | 1.07917i | ||||
\(386\) | 131.450 | − | 95.5042i | 0.0173333 | − | 0.0125934i | ||||
\(387\) | −2116.62 | − | 1537.82i | −0.278021 | − | 0.201994i | ||||
\(388\) | −1143.27 | − | 830.631i | −0.149589 | − | 0.108683i | ||||
\(389\) | 2596.01 | − | 1886.11i | 0.338362 | − | 0.245835i | −0.405608 | − | 0.914047i | \(-0.632940\pi\) |
0.743971 | + | 0.668212i | \(0.232940\pi\) | |||||||
\(390\) | 236.505 | + | 300.790i | 0.0307074 | + | 0.0390541i | ||||
\(391\) | 763.731 | + | 554.883i | 0.0987815 | + | 0.0717689i | ||||
\(392\) | −28.9068 | − | 88.9660i | −0.00372453 | − | 0.0114629i | ||||
\(393\) | −609.614 | −0.0782468 | ||||||||
\(394\) | −175.002 | − | 538.600i | −0.0223768 | − | 0.0688687i | ||||
\(395\) | −4475.05 | − | 5691.43i | −0.570037 | − | 0.724980i | ||||
\(396\) | −935.768 | + | 2880.00i | −0.118748 | + | 0.365468i | ||||
\(397\) | 1924.29 | − | 5922.35i | 0.243268 | − | 0.748701i | −0.752649 | − | 0.658422i | \(-0.771224\pi\) |
0.995917 | − | 0.0902790i | \(-0.0287759\pi\) | |||||||
\(398\) | −263.487 | + | 191.434i | −0.0331844 | + | 0.0241099i | ||||
\(399\) | −4344.62 | −0.545120 | ||||||||
\(400\) | −1874.43 | + | 7721.12i | −0.234304 | + | 0.965141i | ||||
\(401\) | −3174.14 | −0.395284 | −0.197642 | − | 0.980274i | \(-0.563328\pi\) | ||||
−0.197642 | + | 0.980274i | \(0.563328\pi\) | |||||||
\(402\) | 147.395 | − | 107.089i | 0.0182870 | − | 0.0132863i | ||||
\(403\) | −4184.83 | + | 12879.6i | −0.517273 | + | 1.59200i | ||||
\(404\) | −1999.44 | + | 6153.65i | −0.246228 | + | 0.757811i | ||||
\(405\) | −871.294 | − | 246.925i | −0.106901 | − | 0.0302958i | ||||
\(406\) | 158.875 | + | 488.968i | 0.0194208 | + | 0.0597712i | ||||
\(407\) | −11096.2 | −1.35140 | ||||||||
\(408\) | −90.1897 | − | 277.575i | −0.0109438 | − | 0.0336814i | ||||
\(409\) | −8167.81 | − | 5934.26i | −0.987463 | − | 0.717434i | −0.0280987 | − | 0.999605i | \(-0.508945\pi\) |
−0.959364 | + | 0.282172i | \(0.908945\pi\) | |||||||
\(410\) | 344.493 | − | 514.156i | 0.0414959 | − | 0.0619326i | ||||
\(411\) | −154.376 | + | 112.161i | −0.0185275 | + | 0.0134610i | ||||
\(412\) | 8810.03 | + | 6400.86i | 1.05349 | + | 0.765407i | ||||
\(413\) | −6616.54 | − | 4807.20i | −0.788326 | − | 0.572752i | ||||
\(414\) | 20.5689 | − | 14.9442i | 0.00244181 | − | 0.00177408i | ||||
\(415\) | −7205.40 | − | 2042.01i | −0.852287 | − | 0.241539i | ||||
\(416\) | −1766.64 | − | 1283.54i | −0.208213 | − | 0.151275i | ||||
\(417\) | 1486.91 | + | 4576.24i | 0.174615 | + | 0.537409i | ||||
\(418\) | −476.000 | −0.0556984 | ||||||||
\(419\) | −1340.31 | − | 4125.05i | −0.156273 | − | 0.480959i | 0.842014 | − | 0.539455i | \(-0.181370\pi\) |
−0.998288 | + | 0.0584955i | \(0.981370\pi\) | |||||||
\(420\) | 4349.76 | − | 1598.44i | 0.505349 | − | 0.185704i | ||||
\(421\) | −5076.40 | + | 15623.5i | −0.587668 | + | 1.80866i | 0.000611374 | 1.00000i | \(0.499805\pi\) | |
−0.588280 | + | 0.808657i | \(0.700195\pi\) | |||||||
\(422\) | −28.1574 | + | 86.6594i | −0.00324805 | + | 0.00999648i | ||||
\(423\) | 3356.59 | − | 2438.71i | 0.385823 | − | 0.280317i | ||||
\(424\) | −307.251 | −0.0351920 | ||||||||
\(425\) | −4296.31 | + | 3650.56i | −0.490356 | + | 0.416654i | ||||
\(426\) | 253.492 | 0.0288303 | ||||||||
\(427\) | 756.754 | − | 549.814i | 0.0857655 | − | 0.0623123i | ||||
\(428\) | 2736.67 | − | 8422.60i | 0.309070 | − | 0.951219i | ||||
\(429\) | −3303.14 | + | 10166.0i | −0.371741 | + | 1.14410i | ||||
\(430\) | 16.6650 | + | 438.342i | 0.00186897 | + | 0.0491599i | ||||
\(431\) | 431.231 | + | 1327.19i | 0.0481941 | + | 0.148326i | 0.972258 | − | 0.233913i | \(-0.0751531\pi\) |
−0.924063 | + | 0.382239i | \(0.875153\pi\) | |||||||
\(432\) | 1716.20 | 0.191136 | ||||||||
\(433\) | −588.938 | − | 1812.56i | −0.0653638 | − | 0.201169i | 0.913041 | − | 0.407868i | \(-0.133728\pi\) |
−0.978405 | + | 0.206699i | \(0.933728\pi\) | |||||||
\(434\) | −302.828 | − | 220.017i | −0.0334936 | − | 0.0243345i | ||||
\(435\) | 6928.23 | − | 2545.97i | 0.763640 | − | 0.280620i | ||||
\(436\) | 8161.88 | − | 5929.95i | 0.896521 | − | 0.651361i | ||||
\(437\) | −1416.70 | − | 1029.29i | −0.155079 | − | 0.112672i | ||||
\(438\) | 15.9664 | + | 11.6002i | 0.00174179 | + | 0.00126548i | ||||
\(439\) | 6450.52 | − | 4686.58i | 0.701290 | − | 0.509517i | −0.179062 | − | 0.983838i | \(-0.557306\pi\) |
0.880352 | + | 0.474321i | \(0.157306\pi\) | |||||||
\(440\) | 954.215 | − | 350.652i | 0.103387 | − | 0.0379925i | ||||
\(441\) | 315.765 | + | 229.417i | 0.0340962 | + | 0.0247724i | ||||
\(442\) | −158.998 | − | 489.344i | −0.0171103 | − | 0.0526600i | ||||
\(443\) | 2866.93 | 0.307476 | 0.153738 | − | 0.988112i | \(-0.450869\pi\) | ||||
0.153738 | + | 0.988112i | \(0.450869\pi\) | |||||||
\(444\) | 1947.76 | + | 5994.58i | 0.208190 | + | 0.640743i | ||||
\(445\) | 367.848 | + | 9675.59i | 0.0391857 | + | 1.03071i | ||||
\(446\) | 239.382 | − | 736.741i | 0.0254149 | − | 0.0782190i | ||||
\(447\) | −2531.78 | + | 7792.02i | −0.267895 | + | 0.824496i | ||||
\(448\) | −7072.28 | + | 5138.31i | −0.745834 | + | 0.541880i | ||||
\(449\) | −10711.2 | −1.12582 | −0.562908 | − | 0.826520i | \(-0.690317\pi\) | ||||
−0.562908 | + | 0.826520i | \(0.690317\pi\) | |||||||
\(450\) | 57.7494 | + | 140.427i | 0.00604963 | + | 0.0147107i | ||||
\(451\) | 17289.3 | 1.80515 | ||||||||
\(452\) | −7390.68 | + | 5369.64i | −0.769089 | + | 0.558776i | ||||
\(453\) | −815.615 | + | 2510.20i | −0.0845936 | + | 0.260352i | ||||
\(454\) | 110.513 | − | 340.125i | 0.0114243 | − | 0.0351604i | ||||
\(455\) | 15354.1 | − | 5642.28i | 1.58200 | − | 0.581349i | ||||
\(456\) | 167.299 | + | 514.893i | 0.0171809 | + | 0.0528773i | ||||
\(457\) | −5306.67 | −0.543185 | −0.271593 | − | 0.962412i | \(-0.587550\pi\) | ||||
−0.271593 | + | 0.962412i | \(0.587550\pi\) | |||||||
\(458\) | 153.720 | + | 473.101i | 0.0156831 | + | 0.0482676i | ||||
\(459\) | 985.193 | + | 715.784i | 0.100185 | + | 0.0727886i | ||||
\(460\) | 1797.06 | + | 509.288i | 0.182149 | + | 0.0516211i | ||||
\(461\) | 6705.63 | − | 4871.92i | 0.677467 | − | 0.492208i | −0.195050 | − | 0.980793i | \(-0.562487\pi\) |
0.872516 | + | 0.488585i | \(0.162487\pi\) | |||||||
\(462\) | −239.026 | − | 173.662i | −0.0240703 | − | 0.0174881i | ||||
\(463\) | −940.467 | − | 683.290i | −0.0944001 | − | 0.0685857i | 0.539584 | − | 0.841932i | \(-0.318582\pi\) |
−0.633984 | + | 0.773346i | \(0.718582\pi\) | |||||||
\(464\) | −11316.6 | + | 8221.97i | −1.13224 | + | 0.822619i | ||||
\(465\) | −2991.27 | + | 4464.46i | −0.298315 | + | 0.445235i | ||||
\(466\) | 278.590 | + | 202.407i | 0.0276940 | + | 0.0201209i | ||||
\(467\) | 2344.11 | + | 7214.44i | 0.232275 | + | 0.714870i | 0.997471 | + | 0.0710724i | \(0.0226421\pi\) |
−0.765196 | + | 0.643798i | \(0.777358\pi\) | |||||||
\(468\) | 6071.87 | 0.599727 | ||||||||
\(469\) | −2406.87 | − | 7407.57i | −0.236970 | − | 0.729317i | ||||
\(470\) | −669.278 | − | 189.674i | −0.0656840 | − | 0.0186149i | ||||
\(471\) | 339.594 | − | 1045.16i | 0.0332223 | − | 0.102248i | ||||
\(472\) | −314.930 | + | 969.256i | −0.0307115 | + | 0.0945204i | ||||
\(473\) | −9913.90 | + | 7202.87i | −0.963725 | + | 0.700187i | ||||
\(474\) | 262.203 | 0.0254079 | ||||||||
\(475\) | 7969.50 | − | 6771.66i | 0.769822 | − | 0.654116i | ||||
\(476\) | −6231.52 | −0.600045 | ||||||||
\(477\) | 1037.15 | − | 753.531i | 0.0995548 | − | 0.0723308i | ||||
\(478\) | 259.824 | − | 799.657i | 0.0248621 | − | 0.0765177i | ||||
\(479\) | −2298.06 | + | 7072.70i | −0.219209 | + | 0.674655i | 0.779619 | + | 0.626254i | \(0.215413\pi\) |
−0.998828 | + | 0.0484014i | \(0.984587\pi\) | |||||||
\(480\) | −535.602 | − | 681.185i | −0.0509308 | − | 0.0647744i | ||||
\(481\) | 6875.32 | + | 21160.1i | 0.651742 | + | 2.00585i | ||||
\(482\) | 551.214 | 0.0520895 | ||||||||
\(483\) | −335.878 | − | 1033.73i | −0.0316418 | − | 0.0973833i | ||||
\(484\) | 2879.98 | + | 2092.43i | 0.270471 | + | 0.196509i | ||||
\(485\) | −1223.49 | − | 1556.05i | −0.114548 | − | 0.145684i | ||||
\(486\) | 26.5334 | − | 19.2776i | 0.00247650 | − | 0.00179928i | ||||
\(487\) | −17128.3 | − | 12444.4i | −1.59375 | − | 1.15793i | −0.898329 | − | 0.439324i | \(-0.855218\pi\) |
−0.695420 | − | 0.718603i | \(-0.744782\pi\) | |||||||
\(488\) | −94.3005 | − | 68.5133i | −0.00874750 | − | 0.00635543i | ||||
\(489\) | −2046.49 | + | 1486.86i | −0.189254 | + | 0.137501i | ||||
\(490\) | −2.48613 | − | 65.3934i | −0.000229208 | − | 0.00602892i | ||||
\(491\) | −7620.36 | − | 5536.52i | −0.700412 | − | 0.508879i | 0.179655 | − | 0.983730i | \(-0.442502\pi\) |
−0.880066 | + | 0.474851i | \(0.842502\pi\) | |||||||
\(492\) | −3034.85 | − | 9340.32i | −0.278093 | − | 0.855882i | ||||
\(493\) | −9925.48 | −0.906737 | ||||||||
\(494\) | 294.935 | + | 907.716i | 0.0268618 | + | 0.0826722i | ||||
\(495\) | −2361.04 | + | 3523.86i | −0.214386 | + | 0.319971i | ||||
\(496\) | 3147.05 | − | 9685.61i | 0.284892 | − | 0.876808i | ||||
\(497\) | 3348.82 | − | 10306.6i | 0.302243 | − | 0.930209i | ||||
\(498\) | 219.425 | − | 159.421i | 0.0197443 | − | 0.0143451i | ||||
\(499\) | 3295.44 | 0.295640 | 0.147820 | − | 0.989014i | \(-0.452774\pi\) | ||||
0.147820 | + | 0.989014i | \(0.452774\pi\) | |||||||
\(500\) | −5487.56 | + | 9711.75i | −0.490822 | + | 0.868645i | ||||
\(501\) | −6690.27 | −0.596605 | ||||||||
\(502\) | −126.460 | + | 91.8789i | −0.0112434 | + | 0.00816883i | ||||
\(503\) | 1734.00 | − | 5336.71i | 0.153709 | − | 0.473066i | −0.844319 | − | 0.535841i | \(-0.819995\pi\) |
0.998028 | + | 0.0627743i | \(0.0199948\pi\) | |||||||
\(504\) | −103.842 | + | 319.593i | −0.00917756 | + | 0.0282456i | ||||
\(505\) | −5044.81 | + | 7529.38i | −0.444537 | + | 0.663471i | ||||
\(506\) | −36.7991 | − | 113.256i | −0.00323304 | − | 0.00995028i | ||||
\(507\) | 14841.9 | 1.30010 | ||||||||
\(508\) | 5633.33 | + | 17337.6i | 0.492005 | + | 1.51424i | ||||
\(509\) | −16627.4 | − | 12080.5i | −1.44793 | − | 1.05198i | −0.986309 | − | 0.164909i | \(-0.947267\pi\) |
−0.461624 | − | 0.887076i | \(-0.652733\pi\) | |||||||
\(510\) | −7.75678 | − | 204.028i | −0.000673482 | − | 0.0177148i | ||||
\(511\) | 682.576 | − | 495.921i | 0.0590908 | − | 0.0429320i | ||||
\(512\) | 2215.91 | + | 1609.95i | 0.191270 | + | 0.138966i | ||||
\(513\) | −1827.50 | − | 1327.76i | −0.157283 | − | 0.114273i | ||||
\(514\) | −466.873 | + | 339.203i | −0.0400639 | + | 0.0291082i | ||||
\(515\) | 9428.24 | + | 11991.0i | 0.806714 | + | 1.02599i | ||||
\(516\) | 5631.48 | + | 4091.51i | 0.480450 | + | 0.349067i | ||||
\(517\) | −6005.15 | − | 18482.0i | −0.510844 | − | 1.57222i | ||||
\(518\) | −614.970 | −0.0521626 | ||||||||
\(519\) | −2682.46 | − | 8255.78i | −0.226873 | − | 0.698244i | ||||
\(520\) | −1259.92 | − | 1602.39i | −0.106253 | − | 0.135133i | ||||
\(521\) | 167.182 | − | 514.532i | 0.0140583 | − | 0.0432669i | −0.943781 | − | 0.330571i | \(-0.892759\pi\) |
0.957840 | + | 0.287304i | \(0.0927589\pi\) | |||||||
\(522\) | −82.6047 | + | 254.231i | −0.00692627 | + | 0.0213169i | ||||
\(523\) | −1819.27 | + | 1321.77i | −0.152105 | + | 0.110511i | −0.661235 | − | 0.750179i | \(-0.729967\pi\) |
0.509130 | + | 0.860690i | \(0.329967\pi\) | |||||||
\(524\) | 1621.94 | 0.135219 | ||||||||
\(525\) | 6472.47 | − | 492.855i | 0.538061 | − | 0.0409714i | ||||
\(526\) | 36.1490 | 0.00299652 | ||||||||
\(527\) | 5846.19 | − | 4247.51i | 0.483233 | − | 0.351090i | ||||
\(528\) | 2484.00 | − | 7644.98i | 0.204739 | − | 0.630123i | ||||
\(529\) | −3624.43 | + | 11154.9i | −0.297890 | + | 0.916812i | ||||
\(530\) | −206.799 | − | 58.6069i | −0.0169486 | − | 0.00480325i | ||||
\(531\) | −1314.02 | − | 4044.15i | −0.107390 | − | 0.330511i | ||||
\(532\) | 11559.3 | 0.942025 | ||||||||
\(533\) | −10712.6 | − | 32970.1i | −0.870574 | − | 2.67935i | ||||
\(534\) | −283.689 | − | 206.112i | −0.0229896 | − | 0.0167029i | ||||
\(535\) | 6904.91 | − | 10305.6i | 0.557991 | − | 0.832801i | ||||
\(536\) | −785.211 | + | 570.489i | −0.0632760 | + | 0.0459727i | ||||
\(537\) | 6567.25 | + | 4771.39i | 0.527743 | + | 0.383428i | ||||
\(538\) | 679.356 | + | 493.581i | 0.0544407 | + | 0.0395535i | ||||
\(539\) | 1478.99 | − | 1074.55i | 0.118190 | − | 0.0858703i | ||||
\(540\) | 2318.16 | + | 656.968i | 0.184736 | + | 0.0523545i | ||||
\(541\) | 15099.0 | + | 10970.0i | 1.19992 | + | 0.871791i | 0.994277 | − | 0.106837i | \(-0.0340722\pi\) |
0.205641 | + | 0.978628i | \(0.434072\pi\) | |||||||
\(542\) | 61.9711 | + | 190.727i | 0.00491123 | + | 0.0151152i | ||||
\(543\) | −10664.3 | −0.842819 | ||||||||
\(544\) | 360.074 | + | 1108.19i | 0.0283788 | + | 0.0873409i | ||||
\(545\) | 13264.2 | − | 4874.30i | 1.04253 | − | 0.383105i | ||||
\(546\) | −183.065 | + | 563.417i | −0.0143489 | + | 0.0441612i | ||||
\(547\) | 3358.29 | − | 10335.8i | 0.262505 | − | 0.807907i | −0.729753 | − | 0.683711i | \(-0.760365\pi\) |
0.992258 | − | 0.124196i | \(-0.0396352\pi\) | |||||||
\(548\) | 410.732 | − | 298.414i | 0.0320175 | − | 0.0232621i | ||||
\(549\) | 486.346 | 0.0378082 | ||||||||
\(550\) | 709.131 | − | 53.9977i | 0.0549771 | − | 0.00418631i | ||||
\(551\) | 18411.4 | 1.42351 | ||||||||
\(552\) | −109.576 | + | 79.6117i | −0.00844903 | + | 0.00613858i | ||||
\(553\) | 3463.89 | − | 10660.8i | 0.266365 | − | 0.819786i | ||||
\(554\) | −46.9208 | + | 144.407i | −0.00359833 | + | 0.0110745i | ||||
\(555\) | 335.416 | + | 8822.54i | 0.0256534 | + | 0.674767i | ||||
\(556\) | −3956.07 | − | 12175.5i | −0.301753 | − | 0.928700i | ||||
\(557\) | −2740.22 | −0.208450 | −0.104225 | − | 0.994554i | \(-0.533236\pi\) | ||||
−0.104225 | + | 0.994554i | \(0.533236\pi\) | |||||||
\(558\) | −60.1407 | − | 185.094i | −0.00456265 | − | 0.0140424i | ||||
\(559\) | 19878.4 | + | 14442.5i | 1.50405 | + | 1.09276i | ||||
\(560\) | −11546.5 | + | 4243.07i | −0.871299 | + | 0.320183i | ||||
\(561\) | 4614.47 | − | 3352.61i | 0.347278 | − | 0.252312i | ||||
\(562\) | 396.538 | + | 288.102i | 0.0297633 | + | 0.0216243i | ||||
\(563\) | 15525.7 | + | 11280.1i | 1.16222 | + | 0.844405i | 0.990058 | − | 0.140663i | \(-0.0449233\pi\) |
0.172166 | + | 0.985068i | \(0.444923\pi\) | |||||||
\(564\) | −8930.53 | + | 6488.41i | −0.666743 | + | 0.484417i | ||||
\(565\) | −12010.9 | + | 4413.74i | −0.894342 | + | 0.328650i | ||||
\(566\) | 574.641 | + | 417.501i | 0.0426748 | + | 0.0310051i | ||||
\(567\) | −433.273 | − | 1333.48i | −0.0320913 | − | 0.0987669i | ||||
\(568\) | −1350.42 | −0.0997575 | ||||||||
\(569\) | 6247.53 | + | 19227.9i | 0.460299 | + | 1.41665i | 0.864800 | + | 0.502117i | \(0.167445\pi\) |
−0.404501 | + | 0.914538i | \(0.632555\pi\) | |||||||
\(570\) | 14.3886 | + | 378.466i | 0.00105732 | + | 0.0278108i | ||||
\(571\) | 1585.15 | − | 4878.60i | 0.116176 | − | 0.357554i | −0.876014 | − | 0.482285i | \(-0.839807\pi\) |
0.992191 | + | 0.124731i | \(0.0398069\pi\) | |||||||
\(572\) | 8788.31 | − | 27047.6i | 0.642409 | − | 1.97713i | ||||
\(573\) | −418.509 | + | 304.064i | −0.0305121 | + | 0.0221684i | ||||
\(574\) | 958.202 | 0.0696769 | ||||||||
\(575\) | 2227.31 | + | 1372.69i | 0.161540 | + | 0.0995570i | ||||
\(576\) | −4545.16 | −0.328788 | ||||||||
\(577\) | −11377.6 | + | 8266.33i | −0.820896 | + | 0.596416i | −0.916969 | − | 0.398958i | \(-0.869372\pi\) |
0.0960729 | + | 0.995374i | \(0.469372\pi\) | |||||||
\(578\) | 120.065 | − | 369.523i | 0.00864025 | − | 0.0265919i | ||||
\(579\) | 1116.04 | − | 3434.81i | 0.0801053 | − | 0.246539i | ||||
\(580\) | −18433.2 | + | 6773.79i | −1.31965 | + | 0.484942i | ||||
\(581\) | −3583.07 | − | 11027.6i | −0.255853 | − | 0.787435i | ||||
\(582\) | 71.6868 | 0.00510569 | ||||||||
\(583\) | −1855.52 | − | 5710.70i | −0.131814 | − | 0.405683i | ||||
\(584\) | −85.0570 | − | 61.7975i | −0.00602686 | − | 0.00437877i | ||||
\(585\) | 8182.80 | + | 2319.01i | 0.578320 | + | 0.163896i | ||||
\(586\) | 395.221 | − | 287.145i | 0.0278608 | − | 0.0202421i | ||||
\(587\) | 2473.25 | + | 1796.92i | 0.173905 | + | 0.126349i | 0.671333 | − | 0.741156i | \(-0.265722\pi\) |
−0.497428 | + | 0.867505i | \(0.665722\pi\) | |||||||
\(588\) | −840.123 | − | 610.385i | −0.0589219 | − | 0.0428093i | ||||
\(589\) | −10844.5 | + | 7878.98i | −0.758640 | + | 0.551184i | ||||
\(590\) | −396.849 | + | 592.297i | −0.0276916 | + | 0.0413296i | ||||
\(591\) | −10183.8 | − | 7398.97i | −0.708809 | − | 0.514980i | ||||
\(592\) | −5170.33 | − | 15912.7i | −0.358952 | − | 1.10474i | ||||
\(593\) | −13287.5 | −0.920153 | −0.460077 | − | 0.887879i | \(-0.652178\pi\) | ||||
−0.460077 | + | 0.887879i | \(0.652178\pi\) | |||||||
\(594\) | −47.4698 | − | 146.097i | −0.00327897 | − | 0.0100916i | ||||
\(595\) | −8397.96 | − | 2379.99i | −0.578627 | − | 0.163983i | ||||
\(596\) | 6736.04 | − | 20731.4i | 0.462951 | − | 1.42482i | ||||
\(597\) | −2237.05 | + | 6884.94i | −0.153361 | + | 0.471997i | ||||
\(598\) | −193.174 | + | 140.349i | −0.0132098 | + | 0.00959750i | ||||
\(599\) | 12749.7 | 0.869682 | 0.434841 | − | 0.900507i | \(-0.356805\pi\) | ||||
0.434841 | + | 0.900507i | \(0.356805\pi\) | |||||||
\(600\) | −307.646 | − | 748.093i | −0.0209327 | − | 0.0509013i | ||||
\(601\) | 21184.3 | 1.43782 | 0.718908 | − | 0.695106i | \(-0.244642\pi\) | ||||
0.718908 | + | 0.695106i | \(0.244642\pi\) | |||||||
\(602\) | −549.445 | + | 399.195i | −0.0371988 | + | 0.0270265i | ||||
\(603\) | 1251.41 | − | 3851.45i | 0.0845131 | − | 0.260104i | ||||
\(604\) | 2170.02 | − | 6678.63i | 0.146187 | − | 0.449917i | ||||
\(605\) | 3082.07 | + | 3919.82i | 0.207114 | + | 0.263410i | ||||
\(606\) | −101.428 | − | 312.164i | −0.00679907 | − | 0.0209254i | ||||
\(607\) | 2387.17 | 0.159625 | 0.0798124 | − | 0.996810i | \(-0.474568\pi\) | ||||
0.0798124 | + | 0.996810i | \(0.474568\pi\) | |||||||
\(608\) | −667.925 | − | 2055.66i | −0.0445525 | − | 0.137119i | ||||
\(609\) | 9245.39 | + | 6717.17i | 0.615176 | + | 0.446951i | ||||
\(610\) | −50.4013 | − | 64.1010i | −0.00334539 | − | 0.00425471i | ||||
\(611\) | −31523.6 | + | 22903.2i | −2.08725 | + | 1.51647i | ||||
\(612\) | −2621.20 | − | 1904.41i | −0.173130 | − | 0.125786i | ||||
\(613\) | 7662.08 | + | 5566.83i | 0.504843 | + | 0.366790i | 0.810864 | − | 0.585235i | \(-0.198998\pi\) |
−0.306021 | + | 0.952025i | \(0.598998\pi\) | |||||||
\(614\) | −198.626 | + | 144.310i | −0.0130552 | + | 0.00948517i | ||||
\(615\) | −522.622 | − | 13746.6i | −0.0342669 | − | 0.901331i | ||||
\(616\) | 1273.35 | + | 925.145i | 0.0832871 | + | 0.0605116i | ||||
\(617\) | 8487.35 | + | 26121.4i | 0.553789 | + | 1.70439i | 0.699121 | + | 0.715004i | \(0.253575\pi\) |
−0.145332 | + | 0.989383i | \(0.546425\pi\) | |||||||
\(618\) | −552.420 | −0.0359572 | ||||||||
\(619\) | −5942.74 | − | 18289.9i | −0.385879 | − | 1.18761i | −0.935841 | − | 0.352423i | \(-0.885358\pi\) |
0.549962 | − | 0.835190i | \(-0.314642\pi\) | |||||||
\(620\) | 7958.55 | − | 11878.1i | 0.515521 | − | 0.769414i | ||||
\(621\) | 174.634 | − | 537.469i | 0.0112847 | − | 0.0347309i | ||||
\(622\) | −14.2580 | + | 43.8816i | −0.000919122 | + | 0.00282877i | ||||
\(623\) | −12128.0 | + | 8811.49i | −0.779931 | + | 0.566653i | ||||
\(624\) | −16117.8 | −1.03402 | ||||||||
\(625\) | −11104.5 | + | 10992.3i | −0.710690 | + | 0.703505i | ||||
\(626\) | 528.167 | 0.0337217 | ||||||||
\(627\) | −8559.69 | + | 6218.98i | −0.545201 | + | 0.396112i | ||||
\(628\) | −903.523 | + | 2780.76i | −0.0574116 | + | 0.176695i | ||||
\(629\) | 3668.71 | − | 11291.1i | 0.232561 | − | 0.715749i | ||||
\(630\) | −130.853 | + | 195.298i | −0.00827509 | + | 0.0123506i | ||||
\(631\) | −276.428 | − | 850.759i | −0.0174397 | − | 0.0536738i | 0.941958 | − | 0.335731i | \(-0.108983\pi\) |
−0.959398 | + | 0.282057i | \(0.908983\pi\) | |||||||
\(632\) | −1396.82 | −0.0879155 | ||||||||
\(633\) | 625.871 | + | 1926.23i | 0.0392988 | + | 0.120949i | ||||
\(634\) | 718.176 | + | 521.786i | 0.0449881 | + | 0.0326857i | ||||
\(635\) | 970.096 | + | 25516.7i | 0.0606253 | + | 1.59464i | ||||
\(636\) | −2759.42 | + | 2004.84i | −0.172041 | + | 0.124995i | ||||
\(637\) | −2965.53 | − | 2154.58i | −0.184456 | − | 0.134015i | ||||
\(638\) | 1012.93 | + | 735.939i | 0.0628565 | + | 0.0456679i | ||||
\(639\) | 4558.42 | − | 3311.89i | 0.282204 | − | 0.205033i | ||||
\(640\) | 1899.30 | + | 2415.55i | 0.117307 | + | 0.149192i | ||||
\(641\) | 7235.76 | + | 5257.09i | 0.445858 | + | 0.323935i | 0.787958 | − | 0.615728i | \(-0.211138\pi\) |
−0.342100 | + | 0.939664i | \(0.611138\pi\) | |||||||
\(642\) | 138.826 | + | 427.263i | 0.00853432 | + | 0.0262659i | ||||
\(643\) | −4002.17 | −0.245459 | −0.122730 | − | 0.992440i | \(-0.539165\pi\) | ||||
−0.122730 | + | 0.992440i | \(0.539165\pi\) | |||||||
\(644\) | 893.635 | + | 2750.32i | 0.0546803 | + | 0.168289i | ||||
\(645\) | 6026.65 | + | 7664.77i | 0.367906 | + | 0.467907i | ||||
\(646\) | 157.379 | − | 484.362i | 0.00958511 | − | 0.0294999i | ||||
\(647\) | −4114.75 | + | 12663.9i | −0.250027 | + | 0.769504i | 0.744742 | + | 0.667353i | \(0.232573\pi\) |
−0.994769 | + | 0.102151i | \(0.967427\pi\) | |||||||
\(648\) | −141.350 | + | 102.697i | −0.00856907 | + | 0.00622579i | ||||
\(649\) | −19916.9 | −1.20463 | ||||||||
\(650\) | −542.357 | − | 1318.83i | −0.0327277 | − | 0.0795827i | ||||
\(651\) | −8320.15 | −0.500910 | ||||||||
\(652\) | 5444.88 | − | 3955.94i | 0.327052 | − | 0.237617i | ||||
\(653\) | −7105.73 | + | 21869.2i | −0.425833 | + | 1.31058i | 0.476362 | + | 0.879249i | \(0.341955\pi\) |
−0.902195 | + | 0.431329i | \(0.858045\pi\) | |||||||
\(654\) | −158.148 | + | 486.730i | −0.00945579 | + | 0.0291019i | ||||
\(655\) | 2185.82 | + | 619.462i | 0.130392 | + | 0.0369533i | ||||
\(656\) | 8056.05 | + | 24794.0i | 0.479475 | + | 1.47567i | ||||
\(657\) | 438.674 | 0.0260491 | ||||||||
\(658\) | −332.815 | − | 1024.30i | −0.0197181 | − | 0.0606860i | ||||
\(659\) | 3238.14 | + | 2352.65i | 0.191412 | + | 0.139069i | 0.679364 | − | 0.733802i | \(-0.262256\pi\) |
−0.487952 | + | 0.872870i | \(0.662256\pi\) | |||||||
\(660\) | 6281.78 | − | 9375.55i | 0.370482 | − | 0.552944i | ||||
\(661\) | 11026.5 | − | 8011.25i | 0.648839 | − | 0.471409i | −0.214036 | − | 0.976826i | \(-0.568661\pi\) |
0.862876 | + | 0.505416i | \(0.168661\pi\) | |||||||
\(662\) | −1046.08 | − | 760.018i | −0.0614152 | − | 0.0446208i | ||||
\(663\) | −9252.49 | − | 6722.33i | −0.541986 | − | 0.393776i | ||||
\(664\) | −1168.93 | + | 849.279i | −0.0683183 | + | 0.0496362i | ||||
\(665\) | 15577.9 | + | 4414.80i | 0.908400 | + | 0.257441i | ||||
\(666\) | −258.678 | − | 187.940i | −0.0150504 | − | 0.0109348i | ||||
\(667\) | 1423.37 | + | 4380.68i | 0.0826282 | + | 0.254304i | ||||
\(668\) | 17800.1 | 1.03100 | ||||||||
\(669\) | −5320.88 | − | 16376.0i | −0.307500 | − | 0.946386i | ||||
\(670\) | −637.313 | + | 234.198i | −0.0367486 | + | 0.0135043i | ||||
\(671\) | 703.928 | − | 2166.47i | 0.0404990 | − | 0.124643i | ||||
\(672\) | 414.580 | − | 1275.94i | 0.0237987 | − | 0.0732450i | ||||
\(673\) | 20400.2 | − | 14821.6i | 1.16846 | − | 0.848933i | 0.177633 | − | 0.984097i | \(-0.443156\pi\) |
0.990823 | + | 0.135163i | \(0.0431559\pi\) | |||||||
\(674\) | 241.710 | 0.0138135 | ||||||||
\(675\) | 2873.17 | + | 1770.74i | 0.163835 | + | 0.100971i | ||||
\(676\) | −39488.3 | −2.24672 | ||||||||
\(677\) | −428.651 | + | 311.433i | −0.0243344 | + | 0.0176800i | −0.599886 | − | 0.800086i | \(-0.704787\pi\) |
0.575552 | + | 0.817765i | \(0.304787\pi\) | |||||||
\(678\) | 143.205 | − | 440.740i | 0.00811174 | − | 0.0249654i | ||||
\(679\) | 947.036 | − | 2914.68i | 0.0535256 | − | 0.164735i | ||||
\(680\) | 41.3224 | + | 1086.91i | 0.00233036 | + | 0.0612959i | ||||
\(681\) | −2456.45 | − | 7560.16i | −0.138225 | − | 0.425413i | ||||
\(682\) | −911.564 | −0.0511812 | ||||||||
\(683\) | −775.606 | − | 2387.07i | −0.0434520 | − | 0.133732i | 0.926977 | − | 0.375118i | \(-0.122398\pi\) |
−0.970429 | + | 0.241387i | \(0.922398\pi\) | |||||||
\(684\) | 4862.23 | + | 3532.62i | 0.271801 | + | 0.197475i | ||||
\(685\) | 667.499 | − | 245.291i | 0.0372319 | − | 0.0136819i | ||||
\(686\) | 730.266 | − | 530.569i | 0.0406438 | − | 0.0295295i | ||||
\(687\) | 8945.37 | + | 6499.19i | 0.496779 | + | 0.360931i | ||||
\(688\) | −14948.8 | − | 10860.9i | −0.828369 | − | 0.601846i | ||||
\(689\) | −9740.41 | + | 7076.82i | −0.538578 | + | 0.391300i | ||||
\(690\) | −88.9370 | + | 32.6823i | −0.00490692 | + | 0.00180318i | ||||
\(691\) | 20773.0 | + | 15092.5i | 1.14362 | + | 0.830889i | 0.987620 | − | 0.156868i | \(-0.0501398\pi\) |
0.156001 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(692\) | 7136.95 | + | 21965.3i | 0.392061 | + | 1.20664i | ||||
\(693\) | −6567.20 | −0.359982 | ||||||||
\(694\) | 378.727 | + | 1165.60i | 0.0207151 | + | 0.0637545i | ||||
\(695\) | −681.261 | − | 17919.4i | −0.0371823 | − | 0.978015i | ||||
\(696\) | 440.057 | − | 1354.36i | 0.0239660 | − | 0.0737597i | ||||
\(697\) | −5716.32 | + | 17593.0i | −0.310647 | + | 0.956073i | ||||
\(698\) | 113.224 | − | 82.2622i | 0.00613983 | − | 0.00446085i | ||||
\(699\) | 7654.21 | 0.414176 | ||||||||
\(700\) | −17220.6 | + | 1311.29i | −0.929827 | + | 0.0708029i | ||||
\(701\) | 34424.0 | 1.85475 | 0.927373 | − | 0.374139i | \(-0.122062\pi\) | ||||
0.927373 | + | 0.374139i | \(0.122062\pi\) | |||||||
\(702\) | −249.189 | + | 181.047i | −0.0133975 | + | 0.00973386i | ||||
\(703\) | −6805.32 | + | 20944.6i | −0.365103 | + | 1.12367i | ||||
\(704\) | −6578.59 | + | 20246.8i | −0.352187 | + | 1.08392i | ||||
\(705\) | −14513.4 | + | 5333.34i | −0.775328 | + | 0.284915i | ||||
\(706\) | −137.937 | − | 424.527i | −0.00735316 | − | 0.0226307i | ||||
\(707\) | −14032.0 | −0.746435 | ||||||||
\(708\) | 3496.09 | + | 10759.9i | 0.185581 | + | 0.571158i | ||||
\(709\) | 5594.78 | + | 4064.85i | 0.296356 | + | 0.215315i | 0.726020 | − | 0.687674i | \(-0.241368\pi\) |
−0.429664 | + | 0.902989i | \(0.641368\pi\) | |||||||
\(710\) | −908.913 | − | 257.587i | −0.0480435 | − | 0.0136156i | ||||
\(711\) | 4715.06 | − | 3425.69i | 0.248704 | − | 0.180694i | ||||
\(712\) | 1511.29 | + | 1098.01i | 0.0795476 | + | 0.0577947i | ||||
\(713\) | −2713.04 | − | 1971.14i | −0.142502 | − | 0.103534i | ||||
\(714\) | 255.742 | − | 185.807i | 0.0134046 | − | 0.00973902i | ||||
\(715\) | 22173.9 | − | 33094.5i | 1.15980 | − | 1.73100i | ||||
\(716\) | −17472.8 | − | 12694.7i | −0.911996 | − | 0.662604i | ||||
\(717\) | −5775.28 | − | 17774.5i | −0.300811 | − | 0.925802i | ||||
\(718\) | 1682.84 | 0.0874693 | ||||||||
\(719\) | −9251.51 | − | 28473.2i | −0.479865 | − | 1.47687i | −0.839282 | − | 0.543696i | \(-0.817024\pi\) |
0.359417 | − | 0.933177i | \(-0.382976\pi\) | |||||||
\(720\) | −6153.57 | − | 1743.93i | −0.318514 | − | 0.0902672i | ||||
\(721\) | −7297.88 | + | 22460.6i | −0.376959 | + | 1.16016i | ||||
\(722\) | −5.86267 | + | 18.0434i | −0.000302197 | + | 0.000930065i | ||||
\(723\) | 9912.23 | − | 7201.65i | 0.509875 | − | 0.370446i | ||||
\(724\) | 28373.5 | 1.45648 | ||||||||
\(725\) | −27428.8 | + | 2088.60i | −1.40507 | + | 0.106991i | ||||
\(726\) | −180.585 | −0.00923158 | ||||||||
\(727\) | −14000.3 | + | 10171.8i | −0.714226 | + | 0.518916i | −0.884534 | − | 0.466475i | \(-0.845524\pi\) |
0.170308 | + | 0.985391i | \(0.445524\pi\) | |||||||
\(728\) | 975.237 | − | 3001.47i | 0.0496493 | − | 0.152805i | ||||
\(729\) | 225.273 | − | 693.320i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −45.4609 | − | 57.8178i | −0.00230491 | − | 0.00293141i | ||||
\(731\) | −4051.59 | − | 12469.5i | −0.204998 | − | 0.630919i | ||||
\(732\) | −1293.97 | −0.0653367 | ||||||||
\(733\) | 1415.86 | + | 4357.57i | 0.0713451 | + | 0.219578i | 0.980371 | − | 0.197162i | \(-0.0631726\pi\) |
−0.909026 | + | 0.416740i | \(0.863173\pi\) | |||||||
\(734\) | −541.161 | − | 393.176i | −0.0272134 | − | 0.0197717i | ||||
\(735\) | −899.076 | − | 1143.46i | −0.0451196 | − | 0.0573837i | ||||
\(736\) | 437.472 | − | 317.842i | 0.0219096 | − | 0.0159182i | ||||
\(737\) | −15345.3 | − | 11149.0i | −0.766963 | − | 0.557232i | ||||
\(738\) | 403.053 | + | 292.835i | 0.0201038 | + | 0.0146063i | ||||
\(739\) | 1388.20 | − | 1008.59i | 0.0691013 | − | 0.0502050i | −0.552698 | − | 0.833381i | \(-0.686402\pi\) |
0.621800 | + | 0.783176i | \(0.286402\pi\) | |||||||
\(740\) | −892.407 | − | 23473.2i | −0.0443318 | − | 1.16607i | ||||
\(741\) | 17163.0 | + | 12469.7i | 0.850878 | + | 0.618199i | ||||
\(742\) | −102.836 | − | 316.496i | −0.00508790 | − | 0.0156590i | ||||
\(743\) | 12824.6 | 0.633228 | 0.316614 | − | 0.948554i | \(-0.397454\pi\) | ||||
0.316614 | + | 0.948554i | \(0.397454\pi\) | |||||||
\(744\) | 320.385 | + | 986.045i | 0.0157875 | + | 0.0485889i | ||||
\(745\) | 16995.8 | − | 25366.2i | 0.835807 | − | 1.24744i | ||||
\(746\) | −121.101 | + | 372.710i | −0.00594345 | + | 0.0182921i | ||||
\(747\) | 1862.96 | − | 5733.60i | 0.0912478 | − | 0.280832i | ||||
\(748\) | −12277.2 | + | 8919.94i | −0.600134 | + | 0.436023i | ||||
\(749\) | 19205.9 | 0.936939 | ||||||||
\(750\) | −64.3690 | − | 562.194i | −0.00313390 | − | 0.0273712i | ||||
\(751\) | −38918.8 | −1.89103 | −0.945516 | − | 0.325574i | \(-0.894442\pi\) | ||||
−0.945516 | + | 0.325574i | \(0.894442\pi\) | |||||||
\(752\) | 23706.2 | − | 17223.5i | 1.14957 | − | 0.835210i | ||||
\(753\) | −1073.67 | + | 3304.43i | −0.0519613 | + | 0.159920i | ||||
\(754\) | 775.787 | − | 2387.63i | 0.0374701 | − | 0.115321i | ||||
\(755\) | 5475.20 | − | 8171.72i | 0.263924 | − | 0.393907i | ||||
\(756\) | 1152.76 | + | 3547.84i | 0.0554572 | + | 0.170680i | ||||
\(757\) | 22740.4 | 1.09183 | 0.545915 | − | 0.837841i | \(-0.316182\pi\) | ||||
0.545915 | + | 0.837841i | \(0.316182\pi\) | |||||||
\(758\) | −199.532 | − | 614.096i | −0.00956112 | − | 0.0294261i | ||||
\(759\) | −2141.44 | − | 1555.85i | −0.102410 | − | 0.0744053i | ||||
\(760\) | −76.6516 | − | 2016.19i | −0.00365848 | − | 0.0962299i | ||||
\(761\) | −32579.1 | + | 23670.1i | −1.55189 | + | 1.12752i | −0.609611 | + | 0.792701i | \(0.708674\pi\) |
−0.942283 | + | 0.334817i | \(0.891326\pi\) | |||||||
\(762\) | −748.152 | − | 543.564i | −0.0355678 | − | 0.0258415i | ||||
\(763\) | 17700.5 | + | 12860.1i | 0.839843 | + | 0.610181i | ||||
\(764\) | 1113.48 | − | 808.992i | 0.0527282 | − | 0.0383093i | ||||
\(765\) | −2805.13 | − | 3567.60i | −0.132575 | − | 0.168610i | ||||
\(766\) | 167.899 | + | 121.986i | 0.00791962 | + | 0.00575394i | ||||
\(767\) | 12340.7 | + | 37980.9i | 0.580962 | + | 1.78802i | ||||
\(768\) | 12009.2 | 0.564249 | ||||||||
\(769\) | −9475.06 | − | 29161.2i | −0.444317 | − | 1.36747i | −0.883232 | − | 0.468937i | \(-0.844637\pi\) |
0.438915 | − | 0.898529i | \(-0.355363\pi\) | |||||||
\(770\) | 680.577 | + | 865.566i | 0.0318523 | + | 0.0405102i | ||||
\(771\) | −3963.84 | + | 12199.4i | −0.185155 | + | 0.569847i | ||||
\(772\) | −2969.33 | + | 9138.64i | −0.138431 | + | 0.426045i | ||||
\(773\) | 24625.4 | − | 17891.4i | 1.14581 | − | 0.832482i | 0.157894 | − | 0.987456i | \(-0.449529\pi\) |
0.987919 | + | 0.154974i | \(0.0495294\pi\) | |||||||
\(774\) | −353.114 | −0.0163985 | ||||||||
\(775\) | 15262.0 | − | 12968.1i | 0.707389 | − | 0.601066i | ||||
\(776\) | −381.894 | −0.0176665 | ||||||||
\(777\) | −11058.7 | + | 8034.62i | −0.510590 | + | 0.370966i | ||||
\(778\) | 133.832 | − | 411.892i | 0.00616723 | − | 0.0189808i | ||||
\(779\) | 10603.6 | − | 32634.4i | 0.487692 | − | 1.50096i | ||||
\(780\) | −21771.1 | − | 6169.95i | −0.999399 | − | 0.283230i | ||||
\(781\) | −8155.30 | − | 25099.4i | −0.373649 | − | 1.14997i | ||||
\(782\) | 127.412 | 0.00582641 | ||||||||
\(783\) | 1836.11 | + | 5650.95i | 0.0838022 | + | 0.257917i | ||||
\(784\) | 2230.11 | + | 1620.27i | 0.101590 | + | 0.0738098i | ||||
\(785\) | −2279.69 | + | 3402.43i | −0.103650 | + | 0.154698i | ||||
\(786\) | −66.5643 | + | 48.3618i | −0.00302070 | + | 0.00219467i | ||||
\(787\) | −19729.0 | − | 14333.9i | −0.893598 | − | 0.649237i | 0.0432156 | − | 0.999066i | \(-0.486240\pi\) |
−0.936814 | + | 0.349829i | \(0.886240\pi\) | |||||||
\(788\) | 27095.0 | + | 19685.7i | 1.22490 | + | 0.889940i | ||||
\(789\) | 650.050 | − | 472.289i | 0.0293313 | − | 0.0213104i | ||||
\(790\) | −940.146 | − | 266.438i | −0.0423404 | − | 0.0119993i | ||||
\(791\) | −16028.0 | − | 11645.0i | −0.720467 | − | 0.523450i | ||||
\(792\) | 252.884 | + | 778.298i | 0.0113458 | + | 0.0349187i | ||||
\(793\) | −4567.54 | −0.204537 | ||||||||
\(794\) | −259.716 | − | 799.324i | −0.0116083 | − | 0.0357266i | ||||
\(795\) | −4484.46 | + | 1647.94i | −0.200060 | + | 0.0735174i | ||||
\(796\) | 5951.89 | − | 18318.0i | 0.265024 | − | 0.815661i | ||||
\(797\) | 12714.0 | − | 39129.5i | 0.565058 | − | 1.73907i | −0.102721 | − | 0.994710i | \(-0.532755\pi\) |
0.667779 | − | 0.744360i | \(-0.267245\pi\) | |||||||
\(798\) | −474.392 | + | 344.666i | −0.0210442 | + | 0.0152895i | ||||
\(799\) | 20792.1 | 0.920615 | ||||||||
\(800\) | 1228.25 | + | 2986.69i | 0.0542815 | + | 0.131994i | ||||
\(801\) | −7794.32 | −0.343819 | ||||||||
\(802\) | −346.586 | + | 251.810i | −0.0152598 | + | 0.0110869i | ||||
\(803\) | 634.928 | − | 1954.11i | 0.0279030 | − | 0.0858767i | ||||
\(804\) | −3329.50 | + | 10247.1i | −0.146048 | + | 0.449488i | ||||
\(805\) | 153.890 | + | 4047.80i | 0.00673777 | + | 0.177225i | ||||
\(806\) | 564.815 | + | 1738.32i | 0.0246833 | + | 0.0759674i | ||||
\(807\) | 18665.2 | 0.814183 | ||||||||
\(808\) | 540.334 | + | 1662.98i | 0.0235259 | + | 0.0724052i | ||||
\(809\) | 13655.9 | + | 9921.57i | 0.593467 | + | 0.431179i | 0.843554 | − | 0.537044i | \(-0.180459\pi\) |
−0.250087 | + | 0.968223i | \(0.580459\pi\) | |||||||
\(810\) | −114.726 | + | 42.1593i | −0.00497663 | + | 0.00182880i | ||||
\(811\) | −9241.81 | + | 6714.57i | −0.400153 | + | 0.290728i | −0.769603 | − | 0.638522i | \(-0.779546\pi\) |
0.369451 | + | 0.929250i | \(0.379546\pi\) | |||||||
\(812\) | −24598.2 | − | 17871.7i | −1.06309 | − | 0.772380i | ||||
\(813\) | 3606.26 | + | 2620.10i | 0.155568 | + | 0.113027i | ||||
\(814\) | −1211.60 | + | 880.281i | −0.0521703 | + | 0.0379040i | ||||
\(815\) | 8848.71 | − | 3251.70i | 0.380315 | − | 0.139757i | ||||
\(816\) | 6957.99 | + | 5055.28i | 0.298503 | + | 0.216875i | ||||
\(817\) | 7515.57 | + | 23130.5i | 0.321832 | + | 0.990496i | ||||
\(818\) | −1362.62 | −0.0582434 | ||||||||
\(819\) | 4069.11 | + | 12523.4i | 0.173609 | + | 0.534315i | ||||
\(820\) | 1390.48 | + | 36574.3i | 0.0592169 | + | 1.55760i | ||||
\(821\) | −1083.81 | + | 3335.64i | −0.0460723 | + | 0.141796i | −0.971446 | − | 0.237259i | \(-0.923751\pi\) |
0.925374 | + | 0.379055i | \(0.123751\pi\) | |||||||
\(822\) | −7.95853 | + | 24.4939i | −0.000337696 | + | 0.00103932i | ||||
\(823\) | 8474.64 | − | 6157.18i | 0.358940 | − | 0.260785i | −0.393670 | − | 0.919252i | \(-0.628795\pi\) |
0.752610 | + | 0.658467i | \(0.228795\pi\) | |||||||
\(824\) | 2942.88 | 0.124418 | ||||||||
\(825\) | 12046.5 | − | 10235.9i | 0.508369 | − | 0.431960i | ||||
\(826\) | −1103.83 | −0.0464977 | ||||||||
\(827\) | −21487.6 | + | 15611.7i | −0.903505 | + | 0.656434i | −0.939364 | − | 0.342922i | \(-0.888583\pi\) |
0.0358592 | + | 0.999357i | \(0.488583\pi\) | |||||||
\(828\) | −464.631 | + | 1429.99i | −0.0195013 | + | 0.0600187i | ||||
\(829\) | 2254.81 | − | 6939.60i | 0.0944667 | − | 0.290739i | −0.892648 | − | 0.450755i | \(-0.851155\pi\) |
0.987114 | + | 0.160017i | \(0.0511548\pi\) | |||||||
\(830\) | −948.759 | + | 348.647i | −0.0396770 | + | 0.0145804i | ||||
\(831\) | 1042.94 | + | 3209.83i | 0.0435368 | + | 0.133993i | ||||
\(832\) | 42686.1 | 1.77870 | ||||||||
\(833\) | 604.430 | + | 1860.25i | 0.0251408 | + | 0.0773754i | ||||
\(834\) | 525.398 | + | 381.724i | 0.0218142 | + | 0.0158490i | ||||
\(835\) | 23988.4 | + | 6798.34i | 0.994196 | + | 0.281756i | ||||
\(836\) | 22773.9 | − | 16546.2i | 0.942165 | − | 0.684523i | ||||
\(837\) | −3499.75 | − | 2542.72i | −0.144527 | − | 0.105005i | ||||
\(838\) | −473.597 | − | 344.089i | −0.0195228 | − | 0.0141842i | ||||
\(839\) | −38021.7 | + | 27624.4i | −1.56455 | + | 1.13671i | −0.632396 | + | 0.774646i | \(0.717928\pi\) |
−0.932153 | + | 0.362065i | \(0.882072\pi\) | |||||||
\(840\) | 697.088 | − | 1040.40i | 0.0286331 | − | 0.0427349i | ||||
\(841\) | −19448.6 | − | 14130.2i | −0.797433 | − | 0.579369i | ||||
\(842\) | 685.147 | + | 2108.67i | 0.0280424 | + | 0.0863057i | ||||
\(843\) | 10894.8 | 0.445122 | ||||||||
\(844\) | −1665.19 | − | 5124.92i | −0.0679125 | − | 0.209013i | ||||
\(845\) | −53216.7 | − | 15081.7i | −2.16652 | − | 0.613994i | ||||
\(846\) | 173.042 | − | 532.568i | 0.00703228 | − | 0.0216431i | ||||
\(847\) | −2385.66 | + | 7342.31i | −0.0967795 | + | 0.297857i | ||||
\(848\) | 7324.92 | − | 5321.86i | 0.296626 | − | 0.215511i | ||||
\(849\) | 15788.2 | 0.638220 | ||||||||
\(850\) | −179.512 | + | 739.441i | −0.00724377 | + | 0.0298384i | ||||
\(851\) | −5509.52 | −0.221932 | ||||||||
\(852\) | −12128.1 | + | 8811.59i | −0.487679 | + | 0.354319i | ||||
\(853\) | 9452.49 | − | 29091.8i | 0.379422 | − | 1.16774i | −0.561024 | − | 0.827800i | \(-0.689592\pi\) |
0.940446 | − | 0.339942i | \(-0.110408\pi\) | |||||||
\(854\) | 39.0129 | − | 120.069i | 0.00156322 | − | 0.00481111i | ||||
\(855\) | 5203.42 | + | 6617.78i | 0.208133 | + | 0.264706i | ||||
\(856\) | −739.564 | − | 2276.14i | −0.0295301 | − | 0.0908843i | ||||
\(857\) | −39552.7 | −1.57654 | −0.788271 | − | 0.615329i | \(-0.789023\pi\) | ||||
−0.788271 | + | 0.615329i | \(0.789023\pi\) | |||||||
\(858\) | 445.815 | + | 1372.08i | 0.0177388 | + | 0.0545944i | ||||
\(859\) | −12039.3 | − | 8747.05i | −0.478201 | − | 0.347434i | 0.322428 | − | 0.946594i | \(-0.395501\pi\) |
−0.800629 | + | 0.599161i | \(0.795501\pi\) | |||||||
\(860\) | −16034.5 | − | 20392.8i | −0.635780 | − | 0.808593i | ||||
\(861\) | 17230.9 | − | 12519.0i | 0.682029 | − | 0.495523i | ||||
\(862\) | 152.375 | + | 110.707i | 0.00602078 | + | 0.00437435i | ||||
\(863\) | −5111.82 | − | 3713.96i | −0.201632 | − | 0.146494i | 0.482387 | − | 0.875958i | \(-0.339770\pi\) |
−0.684020 | + | 0.729464i | \(0.739770\pi\) | |||||||
\(864\) | 564.327 | − | 410.008i | 0.0222208 | − | 0.0161444i | ||||
\(865\) | 1229.03 | + | 32327.5i | 0.0483101 | + | 1.27071i | ||||
\(866\) | −208.100 | − | 151.194i | −0.00816575 | − | 0.00593276i | ||||
\(867\) | −2668.77 | − | 8213.62i | −0.104540 | − | 0.321741i | ||||
\(868\) | 22136.6 | 0.865626 | ||||||||
\(869\) | −8435.54 | − | 25961.9i | −0.329294 | − | 1.01346i | ||||
\(870\) | 554.523 | − | 827.625i | 0.0216093 | − | 0.0322519i | ||||
\(871\) | −11752.7 | + | 36171.0i | −0.457204 | + | 1.40713i | ||||
\(872\) | 842.497 | − | 2592.94i | 0.0327185 | − | 0.100697i | ||||
\(873\) | 1289.11 | − | 936.593i | 0.0499768 | − | 0.0363103i | ||||
\(874\) | −236.345 | −0.00914703 | ||||||||
\(875\) | −23708.3 | − | 4809.86i | −0.915986 | − | 0.185832i | ||||
\(876\) | −1167.13 | −0.0450157 | ||||||||
\(877\) | −20377.7 | + | 14805.3i | −0.784613 | + | 0.570055i | −0.906360 | − | 0.422506i | \(-0.861150\pi\) |
0.121747 | + | 0.992561i | \(0.461150\pi\) | |||||||
\(878\) | 332.543 | − | 1023.46i | 0.0127822 | − | 0.0393396i | ||||
\(879\) | 3355.50 | − | 10327.2i | 0.128758 | − | 0.396277i | ||||
\(880\) | −16675.0 | + | 24887.5i | −0.638768 | + | 0.953360i | ||||
\(881\) | −373.744 | − | 1150.27i | −0.0142926 | − | 0.0439881i | 0.943656 | − | 0.330928i | \(-0.107362\pi\) |
−0.957948 | + | 0.286940i | \(0.907362\pi\) | |||||||
\(882\) | 52.6787 | 0.00201109 | ||||||||
\(883\) | 1932.48 | + | 5947.55i | 0.0736501 | + | 0.226672i | 0.981104 | − | 0.193479i | \(-0.0619772\pi\) |
−0.907454 | + | 0.420151i | \(0.861977\pi\) | |||||||
\(884\) | 24617.1 | + | 17885.4i | 0.936610 | + | 0.680487i | ||||
\(885\) | 602.049 | + | 15835.8i | 0.0228674 | + | 0.601487i | ||||
\(886\) | 313.042 | − | 227.438i | 0.0118700 | − | 0.00862408i | ||||
\(887\) | 16399.9 | + | 11915.3i | 0.620808 | + | 0.451043i | 0.853204 | − | 0.521578i | \(-0.174656\pi\) |
−0.232396 | + | 0.972621i | \(0.574656\pi\) | |||||||
\(888\) | 1378.04 | + | 1001.21i | 0.0520768 | + | 0.0378360i | ||||
\(889\) | −31984.1 | + | 23237.8i | −1.20665 | + | 0.876684i | ||||
\(890\) | 807.747 | + | 1027.30i | 0.0304222 | + | 0.0386913i | ||||
\(891\) | −2762.40 | − | 2007.00i | −0.103865 | − | 0.0754624i | ||||
\(892\) | 14156.7 | + | 43569.9i | 0.531392 | + | 1.63546i | ||||
\(893\) | −38568.6 | −1.44530 | ||||||||
\(894\) | 341.707 | + | 1051.67i | 0.0127834 | + | 0.0393434i | ||||
\(895\) | −18698.9 | − | 23781.5i | −0.698363 | − | 0.888187i | ||||
\(896\) | −1470.14 | + | 4524.63i | −0.0548147 | + | 0.168702i | ||||
\(897\) | −1640.09 | + | 5047.67i | −0.0610489 | + | 0.187889i | ||||
\(898\) | −1169.56 | + | 849.735i | −0.0434618 | + | 0.0315769i | ||||
\(899\) | 35258.8 | 1.30806 | ||||||||
\(900\) | −7644.35 | − | 4711.21i | −0.283124 | − | 0.174489i | ||||
\(901\) | 6424.50 | 0.237548 | ||||||||
\(902\) | 1887.83 | − | 1371.59i | 0.0696873 | − | 0.0506308i | ||||
\(903\) | −4664.89 | + | 14357.1i | −0.171914 | + | 0.529096i | ||||
\(904\) | −762.892 | + | 2347.94i | −0.0280679 | + | 0.0863842i | ||||
\(905\) | 38237.7 | + | 10836.6i | 1.40449 | + | 0.398034i | ||||
\(906\) | 110.081 | + | 338.795i | 0.00403665 | + | 0.0124235i | ||||
\(907\) | 20161.0 | 0.738077 | 0.369039 | − | 0.929414i | \(-0.379687\pi\) | ||||
0.369039 | + | 0.929414i | \(0.379687\pi\) | |||||||
\(908\) | 6535.61 | + | 20114.5i | 0.238868 | + | 0.735159i | ||||
\(909\) | −5902.37 | − | 4288.33i | −0.215368 | − | 0.156474i | ||||
\(910\) | 1228.91 | − | 1834.15i | 0.0447671 | − | 0.0668148i | ||||
\(911\) | −10332.1 | + | 7506.74i | −0.375762 | + | 0.273007i | −0.759596 | − | 0.650395i | \(-0.774603\pi\) |
0.383834 | + | 0.923402i | \(0.374603\pi\) | |||||||
\(912\) | −12906.8 | − | 9377.37i | −0.468627 | − | 0.340478i | ||||
\(913\) | −22844.4 | − | 16597.4i | −0.828081 | − | 0.601636i | ||||
\(914\) | −579.440 | + | 420.988i | −0.0209695 | + | 0.0152353i | ||||
\(915\) | −1743.83 | − | 494.202i | −0.0630045 | − | 0.0178555i | ||||
\(916\) | −23800.0 | − | 17291.7i | −0.858487 | − | 0.623727i | ||||
\(917\) | 1086.95 | + | 3345.30i | 0.0391432 | + | 0.120471i | ||||
\(918\) | 164.358 | 0.00590919 | ||||||||
\(919\) | 7101.13 | + | 21855.0i | 0.254891 | + | 0.784473i | 0.993851 | + | 0.110724i | \(0.0353171\pi\) |
−0.738960 | + | 0.673749i | \(0.764683\pi\) | |||||||
\(920\) | 473.790 | − | 174.107i | 0.0169787 | − | 0.00623929i | ||||
\(921\) | −1686.38 | + | 5190.13i | −0.0603344 | + | 0.185690i | ||||
\(922\) | 345.694 | − | 1063.94i | 0.0123480 | − | 0.0380032i | ||||
\(923\) | −42810.7 | + | 31103.8i | −1.52668 | + | 1.10920i | ||||
\(924\) | 17472.7 | 0.622087 | ||||||||
\(925\) | 7762.39 | − | 31974.7i | 0.275920 | − | 1.13656i | ||||
\(926\) | −156.897 | −0.00556798 | ||||||||
\(927\) | −9933.90 | + | 7217.40i | −0.351966 | + | 0.255718i | ||||
\(928\) | −1756.89 | + | 5407.14i | −0.0621472 | + | 0.191270i | ||||
\(929\) | 9582.59 | − | 29492.2i | 0.338423 | − | 1.04156i | −0.626589 | − | 0.779350i | \(-0.715549\pi\) |
0.965011 | − | 0.262208i | \(-0.0844506\pi\) | |||||||
\(930\) | 27.5548 | + | 724.780i | 0.000971567 | + | 0.0255554i | ||||
\(931\) | −1121.20 | − | 3450.69i | −0.0394691 | − | 0.121473i | ||||
\(932\) | −20364.7 | −0.715740 | ||||||||
\(933\) | 316.921 | + | 975.384i | 0.0111206 | + | 0.0342258i | ||||
\(934\) | 828.289 | + | 601.787i | 0.0290176 | + | 0.0210825i | ||||
\(935\) | −19952.3 | + | 7332.01i | −0.697871 | + | 0.256452i | ||||
\(936\) | 1327.50 | − | 964.483i | 0.0463575 | − | 0.0336807i | ||||
\(937\) | 30089.9 | + | 21861.6i | 1.04909 | + | 0.762205i | 0.972038 | − | 0.234822i | \(-0.0754507\pi\) |
0.0770474 | + | 0.997027i | \(0.475451\pi\) | |||||||
\(938\) | −850.463 | − | 617.897i | −0.0296040 | − | 0.0215086i | ||||
\(939\) | 9497.77 | − | 6900.54i | 0.330083 | − | 0.239819i | ||||
\(940\) | 38614.3 | − | 14189.9i | 1.33985 | − | 0.492364i | ||||
\(941\) | 1747.06 | + | 1269.31i | 0.0605233 | + | 0.0439728i | 0.617636 | − | 0.786464i | \(-0.288091\pi\) |
−0.557112 | + | 0.830437i | \(0.688091\pi\) | |||||||
\(942\) | −45.8341 | − | 141.063i | −0.00158530 | − | 0.00487906i | ||||
\(943\) | 8584.55 | 0.296449 | ||||||||
\(944\) | −9280.40 | − | 28562.1i | −0.319969 | − | 0.984765i | ||||
\(945\) | 198.514 | + | 5221.55i | 0.00683349 | + | 0.179743i | ||||
\(946\) | −511.090 | + | 1572.97i | −0.0175655 | + | 0.0540611i | ||||
\(947\) | 2924.07 | − | 8999.35i | 0.100337 | − | 0.308806i | −0.888271 | − | 0.459320i | \(-0.848093\pi\) |
0.988608 | + | 0.150514i | \(0.0480930\pi\) | |||||||
\(948\) | −12544.9 | + | 9114.38i | −0.429787 | + | 0.312259i | ||||
\(949\) | −4119.83 | −0.140922 | ||||||||
\(950\) | 332.988 | − | 1371.64i | 0.0113722 | − | 0.0468440i | ||||
\(951\) | 19731.8 | 0.672815 | ||||||||
\(952\) | −1362.40 | + | 989.843i | −0.0463821 | + | 0.0336985i | ||||
\(953\) | −3621.07 | + | 11144.5i | −0.123083 | + | 0.378810i | −0.993547 | − | 0.113422i | \(-0.963819\pi\) |
0.870464 | + | 0.492232i | \(0.163819\pi\) | |||||||
\(954\) | 53.4679 | − | 164.557i | 0.00181456 | − | 0.00558463i | ||||
\(955\) | 1809.57 | − | 664.975i | 0.0613155 | − | 0.0225320i | ||||
\(956\) | 15365.7 | + | 47290.7i | 0.519834 | + | 1.59988i | ||||
\(957\) | 27830.2 | 0.940044 | ||||||||
\(958\) | 310.163 | + | 954.583i | 0.0104602 | + | 0.0321933i | ||||
\(959\) | 890.745 | + | 647.164i | 0.0299934 | + | 0.0217915i | ||||
\(960\) | 16297.0 | + | 4618.59i | 0.547900 | + | 0.155275i | ||||
\(961\) | 3333.71 | − | 2422.08i | 0.111903 | − | 0.0813026i | ||||
\(962\) | 2429.39 | + | 1765.05i | 0.0814206 | + | 0.0591555i | ||||
\(963\) | 8078.67 | + | 5869.50i | 0.270334 | + | 0.196409i | ||||
\(964\) | −26372.4 | + | 19160.7i | −0.881119 | + | 0.640170i | ||||
\(965\) | −7491.93 | + | 11181.7i | −0.249921 | + | 0.373007i | ||||
\(966\) | −118.682 | − | 86.2275i | −0.00395293 | − | 0.00287197i | ||||
\(967\) | −12544.0 | − | 38606.3i | −0.417153 | − | 1.28386i | −0.910311 | − | 0.413924i | \(-0.864158\pi\) |
0.493159 | − | 0.869939i | \(-0.335842\pi\) | |||||||
\(968\) | 962.022 | 0.0319427 | ||||||||
\(969\) | −3498.15 | − | 10766.2i | −0.115972 | − | 0.356925i | ||||
\(970\) | −257.038 | − | 72.8448i | −0.00850825 | − | 0.00241124i | ||||
\(971\) | 15870.8 | − | 48845.4i | 0.524530 | − | 1.61434i | −0.240712 | − | 0.970596i | \(-0.577381\pi\) |
0.765243 | − | 0.643742i | \(-0.222619\pi\) | |||||||
\(972\) | −599.361 | + | 1844.64i | −0.0197783 | + | 0.0608714i | ||||
\(973\) | 22461.2 | − | 16319.0i | 0.740055 | − | 0.537682i | ||||
\(974\) | −2857.49 | −0.0940039 | ||||||||
\(975\) | −26983.5 | − | 16630.0i | −0.886323 | − | 0.546241i | ||||
\(976\) | 3434.85 | 0.112651 | ||||||||
\(977\) | 36990.2 | − | 26874.9i | 1.21128 | − | 0.880047i | 0.215934 | − | 0.976408i | \(-0.430720\pi\) |
0.995346 | + | 0.0963612i | \(0.0307204\pi\) | |||||||
\(978\) | −105.502 | + | 324.703i | −0.00344948 | + | 0.0106164i | ||||
\(979\) | −11281.4 | + | 34720.5i | −0.368288 | + | 1.13347i | ||||
\(980\) | 2392.08 | + | 3042.27i | 0.0779715 | + | 0.0991652i | ||||
\(981\) | 3515.26 | + | 10818.9i | 0.114407 | + | 0.352110i | ||||
\(982\) | −1271.29 | −0.0413123 | ||||||||
\(983\) | 3996.75 | + | 12300.7i | 0.129681 | + | 0.399118i | 0.994725 | − | 0.102579i | \(-0.0327094\pi\) |
−0.865044 | + | 0.501696i | \(0.832709\pi\) | |||||||
\(984\) | −2147.17 | − | 1560.01i | −0.0695623 | − | 0.0505400i | ||||
\(985\) | 28996.3 | + | 36877.8i | 0.937968 | + | 1.19292i | ||||
\(986\) | −1083.77 | + | 787.406i | −0.0350044 | + | 0.0254322i | ||||
\(987\) | −19367.4 | − | 14071.3i | −0.624591 | − | 0.453792i | ||||
\(988\) | −45663.9 | − | 33176.8i | −1.47041 | − | 1.06831i | ||||
\(989\) | −4922.49 | + | 3576.40i | −0.158267 | + | 0.114988i | ||||
\(990\) | 21.7494 | + | 572.078i | 0.000698222 | + | 0.0183655i | ||||
\(991\) | −10986.6 | − | 7982.27i | −0.352172 | − | 0.255868i | 0.397608 | − | 0.917556i | \(-0.369841\pi\) |
−0.749780 | + | 0.661688i | \(0.769841\pi\) | |||||||
\(992\) | −1279.11 | − | 3936.69i | −0.0409393 | − | 0.125998i | ||||
\(993\) | −28740.8 | −0.918490 | ||||||||
\(994\) | −451.980 | − | 1391.05i | −0.0144225 | − | 0.0443878i | ||||
\(995\) | 15017.3 | − | 22413.3i | 0.478472 | − | 0.714119i | ||||
\(996\) | −4956.58 | + | 15254.8i | −0.157686 | + | 0.485307i | ||||
\(997\) | 5948.50 | − | 18307.6i | 0.188958 | − | 0.581552i | −0.811036 | − | 0.584996i | \(-0.801096\pi\) |
0.999994 | + | 0.00344351i | \(0.00109610\pi\) | |||||||
\(998\) | 359.832 | − | 261.433i | 0.0114131 | − | 0.00829211i | ||||
\(999\) | −7107.14 | −0.225085 |
(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 | 75.4.g.b.61.4 | yes | 28 | |
3.2 | odd | 2 | 225.4.h.a.136.4 | 28 | |||
25.4 | even | 10 | 1875.4.a.f.1.7 | 14 | |||
25.16 | even | 5 | inner | 75.4.g.b.16.4 | ✓ | 28 | |
25.21 | even | 5 | 1875.4.a.g.1.8 | 14 | |||
75.41 | odd | 10 | 225.4.h.a.91.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.16.4 | ✓ | 28 | 25.16 | even | 5 | inner | |
75.4.g.b.61.4 | yes | 28 | 1.1 | even | 1 | trivial | |
225.4.h.a.91.4 | 28 | 75.41 | odd | 10 | |||
225.4.h.a.136.4 | 28 | 3.2 | odd | 2 | |||
1875.4.a.f.1.7 | 14 | 25.4 | even | 10 | |||
1875.4.a.g.1.8 | 14 | 25.21 | even | 5 |