Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), degree \(2\), not 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.i.199.4 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | 0.465926 | − | 0.807007i | 0.176103 | − | 0.305020i | −0.764439 | − | 0.644696i | \(-0.776984\pi\) |
0.940543 | + | 0.339676i | \(0.110317\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.45680 | − | 0.841081i | 0.439240 | − | 0.253596i | −0.264035 | − | 0.964513i | \(-0.585053\pi\) |
0.703275 | + | 0.710918i | \(0.251720\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −3.08725 | + | 1.86250i | −0.856248 | + | 0.516565i | ||||
\(14\) | −0.931852 | −0.249048 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.21089 | − | 1.27646i | −0.536219 | − | 0.309586i | 0.207326 | − | 0.978272i | \(-0.433524\pi\) |
−0.743545 | + | 0.668686i | \(0.766857\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.27646 | − | 1.31431i | −0.522255 | − | 0.301524i | 0.215602 | − | 0.976481i | \(-0.430829\pi\) |
−0.737857 | + | 0.674957i | \(0.764162\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.931852i | − | 0.203347i | ||||||
\(22\) | −1.45680 | − | 0.841081i | −0.310590 | − | 0.179319i | ||||
\(23\) | −5.59197 | + | 3.22853i | −1.16601 | + | 0.673194i | −0.952736 | − | 0.303799i | \(-0.901745\pi\) |
−0.213271 | + | 0.976993i | \(0.568412\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.15660 | + | 1.74238i | 0.619060 | + | 0.341709i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.465926 | + | 0.807007i | 0.0880517 | + | 0.152510i | ||||
\(29\) | −1.69419 | − | 2.93443i | −0.314604 | − | 0.544910i | 0.664749 | − | 0.747067i | \(-0.268538\pi\) |
−0.979353 | + | 0.202156i | \(0.935205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.29493i | − | 1.66942i | −0.550690 | − | 0.834710i | \(-0.685635\pi\) | ||
0.550690 | − | 0.834710i | \(-0.314365\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0.841081 | − | 1.45680i | 0.146413 | − | 0.253596i | ||||
\(34\) | 2.55291i | 0.437821i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −4.57994 | − | 7.93269i | −0.752938 | − | 1.30413i | −0.946393 | − | 0.323017i | \(-0.895303\pi\) |
0.193456 | − | 0.981109i | \(-0.438030\pi\) | |||||||
\(38\) | 2.62863i | 0.426419i | ||||||||
\(39\) | −1.74238 | + | 3.15660i | −0.279005 | + | 0.505460i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.01714 | − | 0.587246i | 0.158851 | − | 0.0917124i | −0.418467 | − | 0.908232i | \(-0.637433\pi\) |
0.577318 | + | 0.816519i | \(0.304099\pi\) | |||||||
\(42\) | −0.807007 | + | 0.465926i | −0.124524 | + | 0.0718939i | ||||
\(43\) | −2.55695 | − | 1.47626i | −0.389932 | − | 0.225127i | 0.292199 | − | 0.956358i | \(-0.405613\pi\) |
−0.682131 | + | 0.731230i | \(0.738946\pi\) | |||||||
\(44\) | 1.68216i | 0.253596i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.59197 | + | 3.22853i | 0.824491 | + | 0.476020i | ||||
\(47\) | 3.97934 | 0.580446 | 0.290223 | − | 0.956959i | \(-0.406271\pi\) | ||||
0.290223 | + | 0.956959i | \(0.406271\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 3.06583 | + | 5.31017i | 0.437975 | + | 0.758595i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.55291 | −0.357480 | ||||||||
\(52\) | −0.0693504 | − | 3.60488i | −0.00961716 | − | 0.499908i | ||||
\(53\) | − | 5.36068i | − | 0.736346i | −0.929757 | − | 0.368173i | \(-0.879983\pi\) | ||
0.929757 | − | 0.368173i | \(-0.120017\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.465926 | − | 0.807007i | 0.0622620 | − | 0.107841i | ||||
\(57\) | −2.62863 | −0.348170 | ||||||||
\(58\) | −1.69419 | + | 2.93443i | −0.222459 | + | 0.385310i | ||||
\(59\) | 3.44174 | + | 1.98709i | 0.448076 | + | 0.258697i | 0.707017 | − | 0.707196i | \(-0.250040\pi\) |
−0.258941 | + | 0.965893i | \(0.583374\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.36188 | − | 7.55500i | 0.558481 | − | 0.967318i | −0.439142 | − | 0.898418i | \(-0.644718\pi\) |
0.997624 | − | 0.0689005i | \(-0.0219491\pi\) | |||||||
\(62\) | −8.04965 | + | 4.64747i | −1.02231 | + | 0.590229i | ||||
\(63\) | −0.465926 | − | 0.807007i | −0.0587011 | − | 0.101673i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.68216 | −0.207060 | ||||||||
\(67\) | −2.59575 | − | 4.49598i | −0.317122 | − | 0.549271i | 0.662764 | − | 0.748828i | \(-0.269383\pi\) |
−0.979886 | + | 0.199557i | \(0.936050\pi\) | |||||||
\(68\) | 2.21089 | − | 1.27646i | 0.268110 | − | 0.154793i | ||||
\(69\) | −3.22853 | + | 5.59197i | −0.388669 | + | 0.673194i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.40803 | + | 1.96763i | 0.404458 | + | 0.233514i | 0.688406 | − | 0.725326i | \(-0.258311\pi\) |
−0.283947 | + | 0.958840i | \(0.591644\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −7.26330 | −0.850106 | −0.425053 | − | 0.905169i | \(-0.639744\pi\) | ||||
−0.425053 | + | 0.905169i | \(0.639744\pi\) | |||||||
\(74\) | −4.57994 | + | 7.93269i | −0.532407 | + | 0.922156i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.27646 | − | 1.31431i | 0.261128 | − | 0.150762i | ||||
\(77\) | − | 1.56753i | − | 0.178636i | ||||||
\(78\) | 3.60488 | − | 0.0693504i | 0.408173 | − | 0.00785238i | ||||
\(79\) | 3.68973 | 0.415127 | 0.207563 | − | 0.978222i | \(-0.433447\pi\) | ||||
0.207563 | + | 0.978222i | \(0.433447\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.01714 | − | 0.587246i | −0.112324 | − | 0.0648505i | ||||
\(83\) | −3.84909 | −0.422493 | −0.211246 | − | 0.977433i | \(-0.567752\pi\) | ||||
−0.211246 | + | 0.977433i | \(0.567752\pi\) | |||||||
\(84\) | 0.807007 | + | 0.465926i | 0.0880517 | + | 0.0508367i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.95252i | 0.318378i | ||||||||
\(87\) | −2.93443 | − | 1.69419i | −0.314604 | − | 0.181637i | ||||
\(88\) | 1.45680 | − | 0.841081i | 0.155295 | − | 0.0896596i | ||||
\(89\) | −11.6628 | + | 6.73351i | −1.23625 | + | 0.713751i | −0.968326 | − | 0.249689i | \(-0.919672\pi\) |
−0.267926 | + | 0.963439i | \(0.586338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0646242 | + | 3.35922i | 0.00677446 | + | 0.352142i | ||||
\(92\) | − | 6.45705i | − | 0.673194i | ||||||
\(93\) | −4.64747 | − | 8.04965i | −0.481920 | − | 0.834710i | ||||
\(94\) | −1.98967 | − | 3.44621i | −0.205219 | − | 0.355449i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 7.04052 | − | 12.1945i | 0.714856 | − | 1.23817i | −0.248159 | − | 0.968719i | \(-0.579825\pi\) |
0.963015 | − | 0.269448i | \(-0.0868412\pi\) | |||||||
\(98\) | 3.06583 | − | 5.31017i | 0.309695 | − | 0.536408i | ||||
\(99\) | − | 1.68216i | − | 0.169064i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.65892 | − | 9.80153i | −0.563083 | − | 0.975289i | −0.997225 | − | 0.0744445i | \(-0.976282\pi\) |
0.434142 | − | 0.900845i | \(-0.357052\pi\) | |||||||
\(102\) | 1.27646 | + | 2.21089i | 0.126388 | + | 0.218911i | ||||
\(103\) | − | 0.725003i | − | 0.0714366i | −0.999362 | − | 0.0357183i | \(-0.988628\pi\) | ||
0.999362 | − | 0.0357183i | \(-0.0113719\pi\) | |||||||
\(104\) | −3.08725 | + | 1.86250i | −0.302729 | + | 0.182633i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.64248 | + | 2.68034i | −0.450918 | + | 0.260337i | ||||
\(107\) | −14.9106 | + | 8.60867i | −1.44147 | + | 0.832231i | −0.997948 | − | 0.0640338i | \(-0.979603\pi\) |
−0.443519 | + | 0.896265i | \(0.646270\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 10.2816i | 0.984795i | 0.870370 | + | 0.492398i | \(0.163879\pi\) | ||||
−0.870370 | + | 0.492398i | \(0.836121\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.93269 | − | 4.57994i | −0.752938 | − | 0.434709i | ||||
\(112\) | −0.931852 | −0.0880517 | ||||||||
\(113\) | −8.36308 | − | 4.82843i | −0.786732 | − | 0.454220i | 0.0520785 | − | 0.998643i | \(-0.483415\pi\) |
−0.838811 | + | 0.544423i | \(0.816749\pi\) | |||||||
\(114\) | 1.31431 | + | 2.27646i | 0.123097 | + | 0.213210i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.38839 | 0.314604 | ||||||||
\(117\) | 0.0693504 | + | 3.60488i | 0.00641144 | + | 0.333272i | ||||
\(118\) | − | 3.97418i | − | 0.365853i | ||||||
\(119\) | −2.06022 | + | 1.18947i | −0.188860 | + | 0.109038i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.08516 | + | 7.07571i | −0.371379 | + | 0.643247i | ||||
\(122\) | −8.72376 | −0.789812 | ||||||||
\(123\) | 0.587246 | − | 1.01714i | 0.0529502 | − | 0.0917124i | ||||
\(124\) | 8.04965 | + | 4.64747i | 0.722880 | + | 0.417355i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.465926 | + | 0.807007i | −0.0415080 | + | 0.0718939i | ||||
\(127\) | 0.586302 | − | 0.338502i | 0.0520259 | − | 0.0300372i | −0.473761 | − | 0.880653i | \(-0.657104\pi\) |
0.525787 | + | 0.850616i | \(0.323771\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.95252 | −0.259955 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.86710 | 0.163130 | 0.0815648 | − | 0.996668i | \(-0.474008\pi\) | ||||
0.0815648 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(132\) | 0.841081 | + | 1.45680i | 0.0732067 | + | 0.126798i | ||||
\(133\) | −2.12132 | + | 1.22474i | −0.183942 | + | 0.106199i | ||||
\(134\) | −2.59575 | + | 4.49598i | −0.224239 | + | 0.388393i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.21089 | − | 1.27646i | −0.189582 | − | 0.109455i | ||||
\(137\) | −3.64431 | + | 6.31212i | −0.311354 | + | 0.539281i | −0.978656 | − | 0.205506i | \(-0.934116\pi\) |
0.667302 | + | 0.744788i | \(0.267449\pi\) | |||||||
\(138\) | 6.45705 | 0.549661 | ||||||||
\(139\) | 2.35569 | − | 4.08018i | 0.199807 | − | 0.346076i | −0.748659 | − | 0.662956i | \(-0.769302\pi\) |
0.948466 | + | 0.316879i | \(0.102635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.44621 | − | 1.98967i | 0.290223 | − | 0.167560i | ||||
\(142\) | − | 3.93525i | − | 0.330239i | ||||||
\(143\) | −2.93097 | + | 5.30991i | −0.245100 | + | 0.444037i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.63165 | + | 6.29021i | 0.300558 | + | 0.520581i | ||||
\(147\) | 5.31017 | + | 3.06583i | 0.437975 | + | 0.252865i | ||||
\(148\) | 9.15988 | 0.752938 | ||||||||
\(149\) | 2.60016 | + | 1.50120i | 0.213013 | + | 0.122983i | 0.602711 | − | 0.797960i | \(-0.294087\pi\) |
−0.389698 | + | 0.920943i | \(0.627421\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.4200i | − | 1.01073i | −0.862907 | − | 0.505363i | \(-0.831358\pi\) | ||
0.862907 | − | 0.505363i | \(-0.168642\pi\) | |||||||
\(152\) | −2.27646 | − | 1.31431i | −0.184645 | − | 0.106605i | ||||
\(153\) | −2.21089 | + | 1.27646i | −0.178740 | + | 0.103195i | ||||
\(154\) | −1.35752 | + | 0.783763i | −0.109392 | + | 0.0631574i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.86250 | − | 3.08725i | −0.149119 | − | 0.247178i | ||||
\(157\) | − | 22.5217i | − | 1.79743i | −0.438535 | − | 0.898714i | \(-0.644502\pi\) | ||
0.438535 | − | 0.898714i | \(-0.355498\pi\) | |||||||
\(158\) | −1.84486 | − | 3.19540i | −0.146769 | − | 0.254212i | ||||
\(159\) | −2.68034 | − | 4.64248i | −0.212565 | − | 0.368173i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.01702i | 0.474207i | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −1.38745 | + | 2.40313i | −0.108673 | + | 0.188227i | −0.915233 | − | 0.402925i | \(-0.867994\pi\) |
0.806560 | + | 0.591152i | \(0.201327\pi\) | |||||||
\(164\) | 1.17449i | 0.0917124i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.92455 | + | 3.33341i | 0.149374 | + | 0.258723i | ||||
\(167\) | 11.1022 | + | 19.2296i | 0.859114 | + | 1.48803i | 0.872775 | + | 0.488122i | \(0.162318\pi\) |
−0.0136615 | + | 0.999907i | \(0.504349\pi\) | |||||||
\(168\) | − | 0.931852i | − | 0.0718939i | ||||||
\(169\) | 6.06218 | − | 11.5000i | 0.466321 | − | 0.884615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.27646 | + | 1.31431i | −0.174085 | + | 0.100508i | ||||
\(172\) | 2.55695 | − | 1.47626i | 0.194966 | − | 0.112564i | ||||
\(173\) | −0.823267 | − | 0.475314i | −0.0625919 | − | 0.0361374i | 0.468377 | − | 0.883528i | \(-0.344839\pi\) |
−0.530969 | + | 0.847391i | \(0.678172\pi\) | |||||||
\(174\) | 3.38839i | 0.256873i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.45680 | − | 0.841081i | −0.109810 | − | 0.0633989i | ||||
\(177\) | 3.97418 | 0.298717 | ||||||||
\(178\) | 11.6628 | + | 6.73351i | 0.874162 | + | 0.504698i | ||||
\(179\) | −4.94156 | − | 8.55904i | −0.369350 | − | 0.639732i | 0.620114 | − | 0.784511i | \(-0.287086\pi\) |
−0.989464 | + | 0.144779i | \(0.953753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.3015 | 1.06302 | 0.531511 | − | 0.847051i | \(-0.321624\pi\) | ||||
0.531511 | + | 0.847051i | \(0.321624\pi\) | |||||||
\(182\) | 2.87686 | − | 1.73557i | 0.213247 | − | 0.128649i | ||||
\(183\) | − | 8.72376i | − | 0.644879i | ||||||
\(184\) | −5.59197 | + | 3.22853i | −0.412246 | + | 0.238010i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.64747 | + | 8.04965i | −0.340769 | + | 0.590229i | ||||
\(187\) | −4.29442 | −0.314039 | ||||||||
\(188\) | −1.98967 | + | 3.44621i | −0.145111 | + | 0.251340i | ||||
\(189\) | −0.807007 | − | 0.465926i | −0.0587011 | − | 0.0338911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0573183 | − | 0.0992782i | 0.00414741 | − | 0.00718352i | −0.863944 | − | 0.503587i | \(-0.832013\pi\) |
0.868092 | + | 0.496404i | \(0.165347\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −4.32843 | − | 7.49706i | −0.311567 | − | 0.539650i | 0.667135 | − | 0.744937i | \(-0.267521\pi\) |
−0.978702 | + | 0.205287i | \(0.934187\pi\) | |||||||
\(194\) | −14.0810 | −1.01096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.13165 | −0.437975 | ||||||||
\(197\) | 10.2401 | + | 17.7363i | 0.729574 | + | 1.26366i | 0.957063 | + | 0.289879i | \(0.0936150\pi\) |
−0.227489 | + | 0.973781i | \(0.573052\pi\) | |||||||
\(198\) | −1.45680 | + | 0.841081i | −0.103530 | + | 0.0597731i | ||||
\(199\) | −0.955336 | + | 1.65469i | −0.0677220 | + | 0.117298i | −0.897898 | − | 0.440203i | \(-0.854906\pi\) |
0.830176 | + | 0.557501i | \(0.188240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.49598 | − | 2.59575i | −0.317122 | − | 0.183090i | ||||
\(202\) | −5.65892 | + | 9.80153i | −0.398160 | + | 0.689634i | ||||
\(203\) | −3.15748 | −0.221611 | ||||||||
\(204\) | 1.27646 | − | 2.21089i | 0.0893699 | − | 0.154793i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.627871 | + | 0.362501i | −0.0437458 | + | 0.0252567i | ||||
\(207\) | 6.45705i | 0.448796i | ||||||||
\(208\) | 3.15660 | + | 1.74238i | 0.218871 | + | 0.120813i | ||||
\(209\) | −4.42178 | −0.305861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.620118 | − | 1.07408i | −0.0426907 | − | 0.0739425i | 0.843891 | − | 0.536515i | \(-0.180260\pi\) |
−0.886581 | + | 0.462573i | \(0.846926\pi\) | |||||||
\(212\) | 4.64248 | + | 2.68034i | 0.318847 | + | 0.184086i | ||||
\(213\) | 3.93525 | 0.269639 | ||||||||
\(214\) | 14.9106 | + | 8.60867i | 1.01927 | + | 0.588476i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −7.50108 | − | 4.33075i | −0.509206 | − | 0.293990i | ||||
\(218\) | 8.90410 | − | 5.14078i | 0.603062 | − | 0.348178i | ||||
\(219\) | −6.29021 | + | 3.63165i | −0.425053 | + | 0.245404i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.20296 | − | 0.177046i | 0.619058 | − | 0.0119094i | ||||
\(222\) | 9.15988i | 0.614771i | ||||||||
\(223\) | −7.38915 | − | 12.7984i | −0.494814 | − | 0.857043i | 0.505168 | − | 0.863021i | \(-0.331430\pi\) |
−0.999982 | + | 0.00597823i | \(0.998097\pi\) | |||||||
\(224\) | 0.465926 | + | 0.807007i | 0.0311310 | + | 0.0539204i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.65685i | 0.642364i | ||||||||
\(227\) | −4.78290 | + | 8.28423i | −0.317452 | + | 0.549843i | −0.979956 | − | 0.199215i | \(-0.936161\pi\) |
0.662503 | + | 0.749059i | \(0.269494\pi\) | |||||||
\(228\) | 1.31431 | − | 2.27646i | 0.0870425 | − | 0.150762i | ||||
\(229\) | 15.1478i | 1.00099i | 0.865739 | + | 0.500497i | \(0.166849\pi\) | ||||
−0.865739 | + | 0.500497i | \(0.833151\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.783763 | − | 1.35752i | −0.0515678 | − | 0.0893181i | ||||
\(232\) | −1.69419 | − | 2.93443i | −0.111229 | − | 0.192655i | ||||
\(233\) | 18.7413i | 1.22778i | 0.789391 | + | 0.613891i | \(0.210397\pi\) | ||||
−0.789391 | + | 0.613891i | \(0.789603\pi\) | |||||||
\(234\) | 3.08725 | − | 1.86250i | 0.201820 | − | 0.121756i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.44174 | + | 1.98709i | −0.224038 | + | 0.129348i | ||||
\(237\) | 3.19540 | − | 1.84486i | 0.207563 | − | 0.119837i | ||||
\(238\) | 2.06022 | + | 1.18947i | 0.133544 | + | 0.0771018i | ||||
\(239\) | 4.62330i | 0.299057i | 0.988757 | + | 0.149528i | \(0.0477755\pi\) | ||||
−0.988757 | + | 0.149528i | \(0.952224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2373 | + | 8.79725i | 0.981520 | + | 0.566681i | 0.902729 | − | 0.430210i | \(-0.141561\pi\) |
0.0787915 | + | 0.996891i | \(0.474894\pi\) | |||||||
\(242\) | 8.17033 | 0.525209 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 4.36188 | + | 7.55500i | 0.279241 | + | 0.483659i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.17449 | −0.0748829 | ||||||||
\(247\) | 9.47589 | − | 0.182296i | 0.602937 | − | 0.0115992i | ||||
\(248\) | − | 9.29493i | − | 0.590229i | ||||||
\(249\) | −3.33341 | + | 1.92455i | −0.211246 | + | 0.121963i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.2599 | + | 22.9668i | −0.836958 | + | 1.44965i | 0.0554676 | + | 0.998460i | \(0.482335\pi\) |
−0.892426 | + | 0.451194i | \(0.850998\pi\) | |||||||
\(252\) | 0.931852 | 0.0587011 | ||||||||
\(253\) | −5.43091 | + | 9.40661i | −0.341438 | + | 0.591388i | ||||
\(254\) | −0.586302 | − | 0.338502i | −0.0367879 | − | 0.0212395i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.57986 | + | 0.912132i | −0.0985489 | + | 0.0568972i | −0.548464 | − | 0.836174i | \(-0.684787\pi\) |
0.449916 | + | 0.893071i | \(0.351454\pi\) | |||||||
\(258\) | 1.47626 | + | 2.55695i | 0.0919078 | + | 0.159189i | ||||
\(259\) | −8.53565 | −0.530379 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.38839 | −0.209736 | ||||||||
\(262\) | −0.933552 | − | 1.61696i | −0.0576750 | − | 0.0998960i | ||||
\(263\) | 10.5106 | − | 6.06828i | 0.648110 | − | 0.374186i | −0.139622 | − | 0.990205i | \(-0.544589\pi\) |
0.787732 | + | 0.616019i | \(0.211255\pi\) | |||||||
\(264\) | 0.841081 | − | 1.45680i | 0.0517650 | − | 0.0896596i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.12132 | + | 1.22474i | 0.130066 | + | 0.0750939i | ||||
\(267\) | −6.73351 | + | 11.6628i | −0.412084 | + | 0.713751i | ||||
\(268\) | 5.19151 | 0.317122 | ||||||||
\(269\) | 11.7655 | − | 20.3784i | 0.717355 | − | 1.24250i | −0.244689 | − | 0.969602i | \(-0.578686\pi\) |
0.962044 | − | 0.272894i | \(-0.0879809\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9872 | − | 6.34349i | 0.667427 | − | 0.385339i | −0.127674 | − | 0.991816i | \(-0.540751\pi\) |
0.795101 | + | 0.606477i | \(0.207418\pi\) | |||||||
\(272\) | 2.55291i | 0.154793i | ||||||||
\(273\) | 1.73557 | + | 2.87686i | 0.105042 | + | 0.174115i | ||||
\(274\) | 7.28861 | 0.440321 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.22853 | − | 5.59197i | −0.194334 | − | 0.336597i | ||||
\(277\) | 11.1055 | + | 6.41177i | 0.667265 | + | 0.385246i | 0.795040 | − | 0.606558i | \(-0.207450\pi\) |
−0.127774 | + | 0.991803i | \(0.540783\pi\) | |||||||
\(278\) | −4.71139 | −0.282570 | ||||||||
\(279\) | −8.04965 | − | 4.64747i | −0.481920 | − | 0.278237i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.16720i | − | 0.308249i | −0.988051 | − | 0.154125i | \(-0.950744\pi\) | ||
0.988051 | − | 0.154125i | \(-0.0492557\pi\) | |||||||
\(282\) | −3.44621 | − | 1.98967i | −0.205219 | − | 0.118483i | ||||
\(283\) | −11.2258 | + | 6.48124i | −0.667307 | + | 0.385270i | −0.795055 | − | 0.606537i | \(-0.792558\pi\) |
0.127749 | + | 0.991807i | \(0.459225\pi\) | |||||||
\(284\) | −3.40803 | + | 1.96763i | −0.202229 | + | 0.116757i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.06400 | − | 0.116659i | 0.358572 | − | 0.00689817i | ||||
\(287\) | − | 1.09445i | − | 0.0646035i | ||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | −5.24131 | − | 9.07822i | −0.308313 | − | 0.534013i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 14.0810i | − | 0.825445i | ||||||
\(292\) | 3.63165 | − | 6.29021i | 0.212526 | − | 0.368107i | ||||
\(293\) | −6.73521 | + | 11.6657i | −0.393475 | + | 0.681519i | −0.992905 | − | 0.118908i | \(-0.962061\pi\) |
0.599430 | + | 0.800427i | \(0.295394\pi\) | |||||||
\(294\) | − | 6.13165i | − | 0.357605i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.57994 | − | 7.93269i | −0.266204 | − | 0.461078i | ||||
\(297\) | −0.841081 | − | 1.45680i | −0.0488045 | − | 0.0845319i | ||||
\(298\) | − | 3.00240i | − | 0.173925i | ||||||
\(299\) | 11.2507 | − | 20.3823i | 0.650642 | − | 1.17874i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.38270 | + | 1.37565i | −0.137337 | + | 0.0792913i | ||||
\(302\) | −10.7561 | + | 6.21001i | −0.618941 | + | 0.357346i | ||||
\(303\) | −9.80153 | − | 5.65892i | −0.563083 | − | 0.325096i | ||||
\(304\) | 2.62863i | 0.150762i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.21089 | + | 1.27646i | 0.126388 | + | 0.0729702i | ||||
\(307\) | 21.4620 | 1.22490 | 0.612450 | − | 0.790510i | \(-0.290184\pi\) | ||||
0.612450 | + | 0.790510i | \(0.290184\pi\) | |||||||
\(308\) | 1.35752 | + | 0.783763i | 0.0773517 | + | 0.0446590i | ||||
\(309\) | −0.362501 | − | 0.627871i | −0.0206220 | − | 0.0357183i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.7562 | −0.836745 | −0.418372 | − | 0.908276i | \(-0.637399\pi\) | ||||
−0.418372 | + | 0.908276i | \(0.637399\pi\) | |||||||
\(312\) | −1.74238 | + | 3.15660i | −0.0986430 | + | 0.178707i | ||||
\(313\) | 1.40441i | 0.0793819i | 0.999212 | + | 0.0396910i | \(0.0126373\pi\) | ||||
−0.999212 | + | 0.0396910i | \(0.987363\pi\) | |||||||
\(314\) | −19.5044 | + | 11.2609i | −1.10070 | + | 0.635487i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.84486 | + | 3.19540i | −0.103782 | + | 0.179755i | ||||
\(317\) | 33.1421 | 1.86144 | 0.930722 | − | 0.365729i | \(-0.119180\pi\) | ||||
0.930722 | + | 0.365729i | \(0.119180\pi\) | |||||||
\(318\) | −2.68034 | + | 4.64248i | −0.150306 | + | 0.260337i | ||||
\(319\) | −4.93619 | − | 2.84991i | −0.276374 | − | 0.159564i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.60867 | + | 14.9106i | −0.480489 | + | 0.832231i | ||||
\(322\) | 5.21089 | − | 3.00851i | 0.290391 | − | 0.167658i | ||||
\(323\) | 3.35533 | + | 5.81160i | 0.186695 | + | 0.323366i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.77489 | 0.153687 | ||||||||
\(327\) | 5.14078 | + | 8.90410i | 0.284286 | + | 0.492398i | ||||
\(328\) | 1.01714 | − | 0.587246i | 0.0561622 | − | 0.0324252i | ||||
\(329\) | 1.85408 | − | 3.21135i | 0.102218 | − | 0.177048i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.05268 | − | 3.49452i | −0.332686 | − | 0.192076i | 0.324347 | − | 0.945938i | \(-0.394855\pi\) |
−0.657033 | + | 0.753862i | \(0.728189\pi\) | |||||||
\(332\) | 1.92455 | − | 3.33341i | 0.105623 | − | 0.182945i | ||||
\(333\) | −9.15988 | −0.501958 | ||||||||
\(334\) | 11.1022 | − | 19.2296i | 0.607485 | − | 1.05220i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.807007 | + | 0.465926i | −0.0440259 | + | 0.0254183i | ||||
\(337\) | − | 35.3229i | − | 1.92416i | −0.272761 | − | 0.962082i | \(-0.587937\pi\) | ||
0.272761 | − | 0.962082i | \(-0.412063\pi\) | |||||||
\(338\) | −12.9904 | + | 0.500000i | −0.706584 | + | 0.0271964i | ||||
\(339\) | −9.65685 | −0.524488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.81779 | − | 13.5408i | −0.423357 | − | 0.733276i | ||||
\(342\) | 2.27646 | + | 1.31431i | 0.123097 | + | 0.0710699i | ||||
\(343\) | 12.2368 | 0.660723 | ||||||||
\(344\) | −2.55695 | − | 1.47626i | −0.137862 | − | 0.0795945i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.950627i | 0.0511060i | ||||||||
\(347\) | −3.13363 | − | 1.80920i | −0.168222 | − | 0.0971232i | 0.413525 | − | 0.910493i | \(-0.364297\pi\) |
−0.581747 | + | 0.813370i | \(0.697631\pi\) | |||||||
\(348\) | 2.93443 | − | 1.69419i | 0.157302 | − | 0.0908184i | ||||
\(349\) | 25.1956 | − | 14.5467i | 1.34869 | − | 0.778667i | 0.360627 | − | 0.932710i | \(-0.382563\pi\) |
0.988064 | + | 0.154043i | \(0.0492294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.86250 | + | 3.08725i | 0.0994130 | + | 0.164785i | ||||
\(352\) | 1.68216i | 0.0896596i | ||||||||
\(353\) | 4.79701 | + | 8.30867i | 0.255319 | + | 0.442226i | 0.964982 | − | 0.262315i | \(-0.0844861\pi\) |
−0.709663 | + | 0.704541i | \(0.751153\pi\) | |||||||
\(354\) | −1.98709 | − | 3.44174i | −0.105613 | − | 0.182926i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 13.4670i | − | 0.713751i | ||||||
\(357\) | −1.18947 | + | 2.06022i | −0.0629534 | + | 0.109038i | ||||
\(358\) | −4.94156 | + | 8.55904i | −0.261170 | + | 0.452359i | ||||
\(359\) | − | 6.31495i | − | 0.333290i | −0.986017 | − | 0.166645i | \(-0.946707\pi\) | ||
0.986017 | − | 0.166645i | \(-0.0532935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.04516 | − | 10.4705i | −0.318166 | − | 0.551080i | ||||
\(362\) | −7.15075 | − | 12.3855i | −0.375835 | − | 0.650965i | ||||
\(363\) | 8.17033i | 0.428831i | ||||||||
\(364\) | −2.94148 | − | 1.62364i | −0.154175 | − | 0.0851020i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.55500 | + | 4.36188i | −0.394906 | + | 0.227999i | ||||
\(367\) | −30.2194 | + | 17.4472i | −1.57744 | + | 0.910735i | −0.582224 | + | 0.813028i | \(0.697818\pi\) |
−0.995215 | + | 0.0977071i | \(0.968849\pi\) | |||||||
\(368\) | 5.59197 | + | 3.22853i | 0.291502 | + | 0.168299i | ||||
\(369\) | − | 1.17449i | − | 0.0611416i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.32611 | − | 2.49768i | −0.224600 | − | 0.129673i | ||||
\(372\) | 9.29493 | 0.481920 | ||||||||
\(373\) | 4.16745 | + | 2.40608i | 0.215782 | + | 0.124582i | 0.603996 | − | 0.796987i | \(-0.293574\pi\) |
−0.388213 | + | 0.921569i | \(0.626908\pi\) | |||||||
\(374\) | 2.14721 | + | 3.71907i | 0.111030 | + | 0.192309i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.97934 | 0.205219 | ||||||||
\(377\) | 10.6958 | + | 5.90387i | 0.550861 | + | 0.304065i | ||||
\(378\) | 0.931852i | 0.0479293i | ||||||||
\(379\) | 24.0847 | − | 13.9053i | 1.23715 | − | 0.714267i | 0.268637 | − | 0.963241i | \(-0.413427\pi\) |
0.968510 | + | 0.248974i | \(0.0800935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.338502 | − | 0.586302i | 0.0173420 | − | 0.0300372i | ||||
\(382\) | −0.114637 | −0.00586532 | ||||||||
\(383\) | −0.402868 | + | 0.697788i | −0.0205856 | + | 0.0356553i | −0.876135 | − | 0.482066i | \(-0.839886\pi\) |
0.855549 | + | 0.517722i | \(0.173220\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.32843 | + | 7.49706i | −0.220311 | + | 0.381590i | ||||
\(387\) | −2.55695 | + | 1.47626i | −0.129977 | + | 0.0750424i | ||||
\(388\) | 7.04052 | + | 12.1945i | 0.357428 | + | 0.619084i | ||||
\(389\) | 27.5013 | 1.39437 | 0.697186 | − | 0.716891i | \(-0.254435\pi\) | ||||
0.697186 | + | 0.716891i | \(0.254435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.4843 | 0.833647 | ||||||||
\(392\) | 3.06583 | + | 5.31017i | 0.154848 | + | 0.268204i | ||||
\(393\) | 1.61696 | − | 0.933552i | 0.0815648 | − | 0.0470914i | ||||
\(394\) | 10.2401 | − | 17.7363i | 0.515887 | − | 0.893542i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.45680 | + | 0.841081i | 0.0732067 | + | 0.0422659i | ||||
\(397\) | 0.574094 | − | 0.994360i | 0.0288130 | − | 0.0499055i | −0.851259 | − | 0.524745i | \(-0.824161\pi\) |
0.880072 | + | 0.474840i | \(0.157494\pi\) | |||||||
\(398\) | 1.91067 | 0.0957733 | ||||||||
\(399\) | −1.22474 | + | 2.12132i | −0.0613139 | + | 0.106199i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8647 | − | 6.85009i | 0.592495 | − | 0.342077i | −0.173589 | − | 0.984818i | \(-0.555536\pi\) |
0.766083 | + | 0.642741i | \(0.222203\pi\) | |||||||
\(402\) | 5.19151i | 0.258929i | ||||||||
\(403\) | 17.3118 | + | 28.6957i | 0.862363 | + | 1.42944i | ||||
\(404\) | 11.3178 | 0.563083 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.57874 | + | 2.73445i | 0.0783515 | + | 0.135709i | ||||
\(407\) | −13.3441 | − | 7.70420i | −0.661441 | − | 0.381883i | ||||
\(408\) | −2.55291 | −0.126388 | ||||||||
\(409\) | 6.63613 | + | 3.83137i | 0.328136 | + | 0.189449i | 0.655013 | − | 0.755618i | \(-0.272663\pi\) |
−0.326878 | + | 0.945067i | \(0.605996\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.28861i | 0.359521i | ||||||||
\(412\) | 0.627871 | + | 0.362501i | 0.0309330 | + | 0.0178592i | ||||
\(413\) | 3.20719 | − | 1.85167i | 0.157815 | − | 0.0911148i | ||||
\(414\) | 5.59197 | − | 3.22853i | 0.274830 | − | 0.158673i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0693504 | − | 3.60488i | −0.00340018 | − | 0.176744i | ||||
\(417\) | − | 4.71139i | − | 0.230718i | ||||||
\(418\) | 2.21089 | + | 3.82937i | 0.108138 | + | 0.187301i | ||||
\(419\) | −19.5013 | − | 33.7773i | −0.952701 | − | 1.65013i | −0.739543 | − | 0.673110i | \(-0.764958\pi\) |
−0.213159 | − | 0.977018i | \(-0.568375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.7923i | 1.59820i | 0.601198 | + | 0.799100i | \(0.294690\pi\) | ||||
−0.601198 | + | 0.799100i | \(0.705310\pi\) | |||||||
\(422\) | −0.620118 | + | 1.07408i | −0.0301869 | + | 0.0522852i | ||||
\(423\) | 1.98967 | − | 3.44621i | 0.0967410 | − | 0.167560i | ||||
\(424\) | − | 5.36068i | − | 0.260337i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.96763 | − | 3.40803i | −0.0953318 | − | 0.165119i | ||||
\(427\) | −4.06462 | − | 7.04014i | −0.196701 | − | 0.340696i | ||||
\(428\) | − | 17.2173i | − | 0.832231i | ||||||
\(429\) | 0.116659 | + | 6.06400i | 0.00563233 | + | 0.292773i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.6031 | + | 16.5140i | −1.37776 | + | 0.795452i | −0.991890 | − | 0.127100i | \(-0.959433\pi\) |
−0.385873 | + | 0.922552i | \(0.626100\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 7.78913 | + | 4.49706i | 0.374322 | + | 0.216115i | 0.675345 | − | 0.737502i | \(-0.263995\pi\) |
−0.301023 | + | 0.953617i | \(0.597328\pi\) | |||||||
\(434\) | 8.66150i | 0.415765i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.90410 | − | 5.14078i | −0.426429 | − | 0.246199i | ||||
\(437\) | 16.9732 | 0.811937 | ||||||||
\(438\) | 6.29021 | + | 3.63165i | 0.300558 | + | 0.173527i | ||||
\(439\) | −3.65685 | − | 6.33386i | −0.174532 | − | 0.302299i | 0.765467 | − | 0.643475i | \(-0.222508\pi\) |
−0.939999 | + | 0.341176i | \(0.889175\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.13165 | 0.291983 | ||||||||
\(442\) | −4.75481 | − | 7.88147i | −0.226163 | − | 0.374884i | ||||
\(443\) | − | 27.5200i | − | 1.30752i | −0.756703 | − | 0.653758i | \(-0.773191\pi\) | ||
0.756703 | − | 0.653758i | \(-0.226809\pi\) | |||||||
\(444\) | 7.93269 | − | 4.57994i | 0.376469 | − | 0.217354i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.38915 | + | 12.7984i | −0.349886 | + | 0.606021i | ||||
\(447\) | 3.00240 | 0.142009 | ||||||||
\(448\) | 0.465926 | − | 0.807007i | 0.0220129 | − | 0.0381275i | ||||
\(449\) | −8.88390 | − | 5.12912i | −0.419257 | − | 0.242058i | 0.275502 | − | 0.961300i | \(-0.411156\pi\) |
−0.694760 | + | 0.719242i | \(0.744489\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.987844 | − | 1.71100i | 0.0465157 | − | 0.0805676i | ||||
\(452\) | 8.36308 | − | 4.82843i | 0.393366 | − | 0.227110i | ||||
\(453\) | −6.21001 | − | 10.7561i | −0.291772 | − | 0.505363i | ||||
\(454\) | 9.56580 | 0.448945 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.62863 | −0.123097 | ||||||||
\(457\) | 7.37005 | + | 12.7653i | 0.344756 | + | 0.597135i | 0.985309 | − | 0.170778i | \(-0.0546282\pi\) |
−0.640553 | + | 0.767914i | \(0.721295\pi\) | |||||||
\(458\) | 13.1184 | − | 7.57389i | 0.612981 | − | 0.353905i | ||||
\(459\) | −1.27646 | + | 2.21089i | −0.0595799 | + | 0.103195i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.1993 | + | 9.93003i | 0.801052 | + | 0.462487i | 0.843839 | − | 0.536597i | \(-0.180290\pi\) |
−0.0427870 | + | 0.999084i | \(0.513624\pi\) | |||||||
\(462\) | −0.783763 | + | 1.35752i | −0.0364640 | + | 0.0631574i | ||||
\(463\) | 32.1533 | 1.49429 | 0.747144 | − | 0.664662i | \(-0.231424\pi\) | ||||
0.747144 | + | 0.664662i | \(0.231424\pi\) | |||||||
\(464\) | −1.69419 | + | 2.93443i | −0.0786510 | + | 0.136228i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.2304 | − | 9.37064i | 0.751860 | − | 0.434087i | ||||
\(467\) | 22.2754i | 1.03078i | 0.856955 | + | 0.515392i | \(0.172354\pi\) | ||||
−0.856955 | + | 0.515392i | \(0.827646\pi\) | |||||||
\(468\) | −3.15660 | − | 1.74238i | −0.145914 | − | 0.0805417i | ||||
\(469\) | −4.83772 | −0.223385 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.2609 | − | 19.5044i | −0.518873 | − | 0.898714i | ||||
\(472\) | 3.44174 | + | 1.98709i | 0.158419 | + | 0.0914631i | ||||
\(473\) | −4.96661 | −0.228365 | ||||||||
\(474\) | −3.19540 | − | 1.84486i | −0.146769 | − | 0.0847374i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 2.37894i | − | 0.109038i | ||||||
\(477\) | −4.64248 | − | 2.68034i | −0.212565 | − | 0.122724i | ||||
\(478\) | 4.00390 | − | 2.31165i | 0.183134 | − | 0.105732i | ||||
\(479\) | 19.0007 | − | 10.9700i | 0.868163 | − | 0.501234i | 0.00142578 | − | 0.999999i | \(-0.499546\pi\) |
0.866737 | + | 0.498765i | \(0.166213\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.9140 | + | 15.9600i | 1.31837 | + | 0.727714i | ||||
\(482\) | − | 17.5945i | − | 0.801408i | ||||||
\(483\) | 3.00851 | + | 5.21089i | 0.136892 | + | 0.237104i | ||||
\(484\) | −4.08516 | − | 7.07571i | −0.185689 | − | 0.321623i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 4.52651 | − | 7.84015i | 0.205116 | − | 0.355271i | −0.745054 | − | 0.667004i | \(-0.767576\pi\) |
0.950170 | + | 0.311733i | \(0.100910\pi\) | |||||||
\(488\) | 4.36188 | − | 7.55500i | 0.197453 | − | 0.341999i | ||||
\(489\) | 2.77489i | 0.125485i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.1000 | − | 26.1540i | −0.681455 | − | 1.18031i | −0.974537 | − | 0.224227i | \(-0.928014\pi\) |
0.293082 | − | 0.956087i | \(-0.405319\pi\) | |||||||
\(492\) | 0.587246 | + | 1.01714i | 0.0264751 | + | 0.0458562i | ||||
\(493\) | 8.65027i | 0.389588i | ||||||||
\(494\) | −4.89582 | − | 8.11522i | −0.220273 | − | 0.365121i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.04965 | + | 4.64747i | −0.361440 | + | 0.208677i | ||||
\(497\) | 3.17578 | − | 1.83354i | 0.142453 | − | 0.0822453i | ||||
\(498\) | 3.33341 | + | 1.92455i | 0.149374 | + | 0.0862410i | ||||
\(499\) | 9.04336i | 0.404836i | 0.979299 | + | 0.202418i | \(0.0648800\pi\) | ||||
−0.979299 | + | 0.202418i | \(0.935120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.2296 | + | 11.1022i | 0.859114 | + | 0.496010i | ||||
\(502\) | 26.5198 | 1.18364 | ||||||||
\(503\) | 26.9241 | + | 15.5446i | 1.20049 | + | 0.693101i | 0.960663 | − | 0.277715i | \(-0.0895772\pi\) |
0.239823 | + | 0.970817i | \(0.422911\pi\) | |||||||
\(504\) | −0.465926 | − | 0.807007i | −0.0207540 | − | 0.0359470i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.8618 | 0.482867 | ||||||||
\(507\) | −0.500000 | − | 12.9904i | −0.0222058 | − | 0.576923i | ||||
\(508\) | 0.677003i | 0.0300372i | ||||||||
\(509\) | 22.5466 | − | 13.0173i | 0.999361 | − | 0.576981i | 0.0913018 | − | 0.995823i | \(-0.470897\pi\) |
0.908059 | + | 0.418842i | \(0.137564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.38416 | + | 5.86154i | −0.149706 | + | 0.259299i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.31431 | + | 2.27646i | −0.0580283 | + | 0.100508i | ||||
\(514\) | 1.57986 | + | 0.912132i | 0.0696846 | + | 0.0402324i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.47626 | − | 2.55695i | 0.0649886 | − | 0.112564i | ||||
\(517\) | 5.79708 | − | 3.34695i | 0.254955 | − | 0.147198i | ||||
\(518\) | 4.26782 | + | 7.39209i | 0.187517 | + | 0.324790i | ||||
\(519\) | −0.950627 | −0.0417279 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.8332 | −1.08796 | −0.543982 | − | 0.839097i | \(-0.683084\pi\) | ||||
−0.543982 | + | 0.839097i | \(0.683084\pi\) | |||||||
\(522\) | 1.69419 | + | 2.93443i | 0.0741529 | + | 0.128437i | ||||
\(523\) | −7.28231 | + | 4.20445i | −0.318433 | + | 0.183848i | −0.650694 | − | 0.759340i | \(-0.725522\pi\) |
0.332261 | + | 0.943188i | \(0.392189\pi\) | |||||||
\(524\) | −0.933552 | + | 1.61696i | −0.0407824 | + | 0.0706372i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.5106 | − | 6.06828i | −0.458283 | − | 0.264590i | ||||
\(527\) | −11.8646 | + | 20.5501i | −0.516829 | + | 0.895175i | ||||
\(528\) | −1.68216 | −0.0732067 | ||||||||
\(529\) | 9.34677 | − | 16.1891i | 0.406381 | − | 0.703873i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.44174 | − | 1.98709i | 0.149359 | − | 0.0862323i | ||||
\(532\) | − | 2.44949i | − | 0.106199i | ||||||
\(533\) | −2.04642 | + | 3.70740i | −0.0886401 | + | 0.160585i | ||||
\(534\) | 13.4670 | 0.582775 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.59575 | − | 4.49598i | −0.112120 | − | 0.194197i | ||||
\(537\) | −8.55904 | − | 4.94156i | −0.369350 | − | 0.213244i | ||||
\(538\) | −23.5310 | −1.01449 | ||||||||
\(539\) | 8.93256 | + | 5.15722i | 0.384753 | + | 0.222137i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15.7195i | − | 0.675833i | −0.941176 | − | 0.337916i | \(-0.890278\pi\) | ||
0.941176 | − | 0.337916i | \(-0.109722\pi\) | |||||||
\(542\) | −10.9872 | − | 6.34349i | −0.471942 | − | 0.272476i | ||||
\(543\) | 12.3855 | − | 7.15075i | 0.531511 | − | 0.306868i | ||||
\(544\) | 2.21089 | − | 1.27646i | 0.0947911 | − | 0.0547276i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.62364 | − | 2.94148i | 0.0694855 | − | 0.125884i | ||||
\(547\) | − | 23.0313i | − | 0.984745i | −0.870385 | − | 0.492373i | \(-0.836130\pi\) | ||
0.870385 | − | 0.492373i | \(-0.163870\pi\) | |||||||
\(548\) | −3.64431 | − | 6.31212i | −0.155677 | − | 0.269641i | ||||
\(549\) | −4.36188 | − | 7.55500i | −0.186160 | − | 0.322439i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.90681i | 0.379443i | ||||||||
\(552\) | −3.22853 | + | 5.59197i | −0.137415 | + | 0.238010i | ||||
\(553\) | 1.71914 | − | 2.97764i | 0.0731052 | − | 0.126622i | ||||
\(554\) | − | 12.8235i | − | 0.544820i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.35569 | + | 4.08018i | 0.0999036 | + | 0.173038i | ||||
\(557\) | −20.3283 | − | 35.2097i | −0.861339 | − | 1.49188i | −0.870637 | − | 0.491925i | \(-0.836293\pi\) |
0.00929877 | − | 0.999957i | \(-0.497040\pi\) | |||||||
\(558\) | 9.29493i | 0.393486i | ||||||||
\(559\) | 10.6435 | − | 0.204758i | 0.450171 | − | 0.00866034i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.71907 | + | 2.14721i | −0.157019 | + | 0.0906552i | ||||
\(562\) | −4.47492 | + | 2.58360i | −0.188763 | + | 0.108982i | ||||
\(563\) | 2.97514 | + | 1.71770i | 0.125387 | + | 0.0723923i | 0.561382 | − | 0.827557i | \(-0.310270\pi\) |
−0.435995 | + | 0.899949i | \(0.643603\pi\) | |||||||
\(564\) | 3.97934i | 0.167560i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.2258 | + | 6.48124i | 0.471857 | + | 0.272427i | ||||
\(567\) | −0.931852 | −0.0391341 | ||||||||
\(568\) | 3.40803 | + | 1.96763i | 0.142998 | + | 0.0825597i | ||||
\(569\) | 11.0320 | + | 19.1079i | 0.462484 | + | 0.801046i | 0.999084 | − | 0.0427908i | \(-0.0136249\pi\) |
−0.536600 | + | 0.843837i | \(0.680292\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.56829 | 0.191177 | 0.0955885 | − | 0.995421i | \(-0.469527\pi\) | ||||
0.0955885 | + | 0.995421i | \(0.469527\pi\) | |||||||
\(572\) | −3.13303 | − | 5.19325i | −0.130999 | − | 0.217141i | ||||
\(573\) | − | 0.114637i | − | 0.00478901i | ||||||
\(574\) | −0.947824 | + | 0.547226i | −0.0395614 | + | 0.0228408i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 4.42655 | 0.184280 | 0.0921398 | − | 0.995746i | \(-0.470629\pi\) | ||||
0.0921398 | + | 0.995746i | \(0.470629\pi\) | |||||||
\(578\) | −5.24131 | + | 9.07822i | −0.218010 | + | 0.377604i | ||||
\(579\) | −7.49706 | − | 4.32843i | −0.311567 | − | 0.179883i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.79339 | + | 3.10624i | −0.0744024 | + | 0.128869i | ||||
\(582\) | −12.1945 | + | 7.04052i | −0.505480 | + | 0.291839i | ||||
\(583\) | −4.50877 | − | 7.80941i | −0.186734 | − | 0.323433i | ||||
\(584\) | −7.26330 | −0.300558 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.4704 | 0.556458 | ||||||||
\(587\) | 21.5770 | + | 37.3725i | 0.890580 | + | 1.54253i | 0.839181 | + | 0.543852i | \(0.183035\pi\) |
0.0513987 | + | 0.998678i | \(0.483632\pi\) | |||||||
\(588\) | −5.31017 | + | 3.06583i | −0.218988 | + | 0.126433i | ||||
\(589\) | −12.2165 | + | 21.1595i | −0.503370 | + | 0.871863i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.7363 | + | 10.2401i | 0.729574 | + | 0.421220i | ||||
\(592\) | −4.57994 | + | 7.93269i | −0.188234 | + | 0.326032i | ||||
\(593\) | 28.8372 | 1.18420 | 0.592101 | − | 0.805864i | \(-0.298299\pi\) | ||||
0.592101 | + | 0.805864i | \(0.298299\pi\) | |||||||
\(594\) | −0.841081 | + | 1.45680i | −0.0345100 | + | 0.0597731i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.60016 | + | 1.50120i | −0.106507 | + | 0.0614916i | ||||
\(597\) | 1.91067i | 0.0781986i | ||||||||
\(598\) | −23.2769 | + | 0.447799i | −0.951864 | + | 0.0183119i | ||||
\(599\) | 28.1704 | 1.15101 | 0.575505 | − | 0.817798i | \(-0.304806\pi\) | ||||
0.575505 | + | 0.817798i | \(0.304806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.31925 | + | 12.6773i | 0.298558 | + | 0.517118i | 0.975806 | − | 0.218637i | \(-0.0701610\pi\) |
−0.677248 | + | 0.735755i | \(0.736828\pi\) | |||||||
\(602\) | 2.38270 | + | 1.37565i | 0.0971117 | + | 0.0560674i | ||||
\(603\) | −5.19151 | −0.211415 | ||||||||
\(604\) | 10.7561 | + | 6.21001i | 0.437657 | + | 0.252682i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.3178i | 0.459756i | ||||||||
\(607\) | −11.2731 | − | 6.50853i | −0.457561 | − | 0.264173i | 0.253457 | − | 0.967347i | \(-0.418432\pi\) |
−0.711018 | + | 0.703174i | \(0.751766\pi\) | |||||||
\(608\) | 2.27646 | − | 1.31431i | 0.0923225 | − | 0.0533024i | ||||
\(609\) | −2.73445 | + | 1.57874i | −0.110806 | + | 0.0639737i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2852 | + | 7.41152i | −0.497006 | + | 0.299838i | ||||
\(612\) | − | 2.55291i | − | 0.103195i | ||||||
\(613\) | −13.6146 | − | 23.5813i | −0.549890 | − | 0.952438i | −0.998282 | − | 0.0586006i | \(-0.981336\pi\) |
0.448391 | − | 0.893837i | \(-0.351997\pi\) | |||||||
\(614\) | −10.7310 | − | 18.5866i | −0.433067 | − | 0.750094i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1.56753i | − | 0.0631574i | ||||||
\(617\) | 11.7678 | − | 20.3825i | 0.473755 | − | 0.820569i | −0.525793 | − | 0.850613i | \(-0.676231\pi\) |
0.999549 | + | 0.0300439i | \(0.00956471\pi\) | |||||||
\(618\) | −0.362501 | + | 0.627871i | −0.0145819 | + | 0.0252567i | ||||
\(619\) | 23.0280i | 0.925573i | 0.886470 | + | 0.462786i | \(0.153150\pi\) | ||||
−0.886470 | + | 0.462786i | \(0.846850\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.22853 | + | 5.59197i | 0.129556 | + | 0.224398i | ||||
\(622\) | 7.37808 | + | 12.7792i | 0.295834 | + | 0.512399i | ||||
\(623\) | 12.5493i | 0.502776i | ||||||||
\(624\) | 3.60488 | − | 0.0693504i | 0.144311 | − | 0.00277624i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.21625 | − | 0.702205i | 0.0486113 | − | 0.0280658i | ||||
\(627\) | −3.82937 | + | 2.21089i | −0.152930 | + | 0.0882944i | ||||
\(628\) | 19.5044 | + | 11.2609i | 0.778309 | + | 0.449357i | ||||
\(629\) | 23.3844i | 0.932397i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.3378 | − | 8.27792i | −0.570778 | − | 0.329539i | 0.186682 | − | 0.982420i | \(-0.440227\pi\) |
−0.757460 | + | 0.652882i | \(0.773560\pi\) | |||||||
\(632\) | 3.68973 | 0.146769 | ||||||||
\(633\) | −1.07408 | − | 0.620118i | −0.0426907 | − | 0.0246475i | ||||
\(634\) | −16.5710 | − | 28.7019i | −0.658119 | − | 1.13990i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.36068 | 0.212565 | ||||||||
\(637\) | −19.3552 | − | 10.6837i | −0.766879 | − | 0.423303i | ||||
\(638\) | 5.69982i | 0.225658i | ||||||||
\(639\) | 3.40803 | − | 1.96763i | 0.134819 | − | 0.0778381i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.390454 | + | 0.676286i | −0.0154220 | + | 0.0267117i | −0.873633 | − | 0.486585i | \(-0.838243\pi\) |
0.858211 | + | 0.513296i | \(0.171576\pi\) | |||||||
\(642\) | 17.2173 | 0.679514 | ||||||||
\(643\) | 12.2743 | − | 21.2597i | 0.484050 | − | 0.838399i | −0.515782 | − | 0.856720i | \(-0.672499\pi\) |
0.999832 | + | 0.0183207i | \(0.00583198\pi\) | |||||||
\(644\) | −5.21089 | − | 3.00851i | −0.205338 | − | 0.118552i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.35533 | − | 5.81160i | 0.132014 | − | 0.228654i | ||||
\(647\) | 2.74011 | − | 1.58200i | 0.107725 | − | 0.0621950i | −0.445170 | − | 0.895446i | \(-0.646857\pi\) |
0.552894 | + | 0.833251i | \(0.313523\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 6.68521 | 0.262417 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.66150 | −0.339471 | ||||||||
\(652\) | −1.38745 | − | 2.40313i | −0.0543366 | − | 0.0941137i | ||||
\(653\) | 27.9627 | − | 16.1443i | 1.09426 | − | 0.631774i | 0.159556 | − | 0.987189i | \(-0.448994\pi\) |
0.934709 | + | 0.355415i | \(0.115660\pi\) | |||||||
\(654\) | 5.14078 | − | 8.90410i | 0.201021 | − | 0.348178i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.01714 | − | 0.587246i | −0.0397127 | − | 0.0229281i | ||||
\(657\) | −3.63165 | + | 6.29021i | −0.141684 | + | 0.245404i | ||||
\(658\) | −3.70815 | −0.144559 | ||||||||
\(659\) | 17.6775 | − | 30.6184i | 0.688619 | − | 1.19272i | −0.283666 | − | 0.958923i | \(-0.591551\pi\) |
0.972285 | − | 0.233799i | \(-0.0751159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.9243 | − | 9.77124i | 0.658279 | − | 0.380057i | −0.133342 | − | 0.991070i | \(-0.542571\pi\) |
0.791621 | + | 0.611013i | \(0.209238\pi\) | |||||||
\(662\) | 6.98904i | 0.271637i | ||||||||
\(663\) | 7.88147 | − | 4.75481i | 0.306091 | − | 0.184661i | ||||
\(664\) | −3.84909 | −0.149374 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.57994 | + | 7.93269i | 0.177469 | + | 0.307385i | ||||
\(667\) | 18.9478 | + | 10.9395i | 0.733661 | + | 0.423579i | ||||
\(668\) | −22.2044 | −0.859114 | ||||||||
\(669\) | −12.7984 | − | 7.38915i | −0.494814 | − | 0.285681i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 14.6748i | − | 0.566514i | ||||||
\(672\) | 0.807007 | + | 0.465926i | 0.0311310 | + | 0.0179735i | ||||
\(673\) | 2.17903 | − | 1.25806i | 0.0839954 | − | 0.0484948i | −0.457414 | − | 0.889254i | \(-0.651224\pi\) |
0.541409 | + | 0.840759i | \(0.317891\pi\) | |||||||
\(674\) | −30.5906 | + | 17.6615i | −1.17830 | + | 0.680295i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.92820 | + | 11.0000i | 0.266469 | + | 0.423077i | ||||
\(677\) | − | 41.0114i | − | 1.57620i | −0.615550 | − | 0.788098i | \(-0.711066\pi\) | ||
0.615550 | − | 0.788098i | \(-0.288934\pi\) | |||||||
\(678\) | 4.82843 | + | 8.36308i | 0.185435 | + | 0.321182i | ||||
\(679\) | −6.56072 | − | 11.3635i | −0.251777 | − | 0.436091i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.56580i | 0.366562i | ||||||||
\(682\) | −7.81779 | + | 13.5408i | −0.299359 | + | 0.518505i | ||||
\(683\) | 12.0769 | − | 20.9177i | 0.462108 | − | 0.800395i | −0.536958 | − | 0.843609i | \(-0.680426\pi\) |
0.999066 | + | 0.0432142i | \(0.0137598\pi\) | |||||||
\(684\) | − | 2.62863i | − | 0.100508i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.11838 | − | 10.5973i | −0.233601 | − | 0.404608i | ||||
\(687\) | 7.57389 | + | 13.1184i | 0.288962 | + | 0.500497i | ||||
\(688\) | 2.95252i | 0.112564i | ||||||||
\(689\) | 9.98427 | + | 16.5497i | 0.380370 | + | 0.630494i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.7340 | + | 20.6310i | −1.35939 | + | 0.784841i | −0.989541 | − | 0.144252i | \(-0.953922\pi\) |
−0.369844 | + | 0.929094i | \(0.620589\pi\) | |||||||
\(692\) | 0.823267 | − | 0.475314i | 0.0312959 | − | 0.0180687i | ||||
\(693\) | −1.35752 | − | 0.783763i | −0.0515678 | − | 0.0297727i | ||||
\(694\) | 3.61841i | 0.137353i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.93443 | − | 1.69419i | −0.111229 | − | 0.0642183i | ||||
\(697\) | −2.99838 | −0.113572 | ||||||||
\(698\) | −25.1956 | − | 14.5467i | −0.953669 | − | 0.550601i | ||||
\(699\) | 9.37064 | + | 16.2304i | 0.354430 | + | 0.613891i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.2880 | 1.03065 | 0.515327 | − | 0.856994i | \(-0.327671\pi\) | ||||
0.515327 | + | 0.856994i | \(0.327671\pi\) | |||||||
\(702\) | 1.74238 | − | 3.15660i | 0.0657620 | − | 0.119138i | ||||
\(703\) | 24.0779i | 0.908115i | ||||||||
\(704\) | 1.45680 | − | 0.841081i | 0.0549051 | − | 0.0316994i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.79701 | − | 8.30867i | 0.180538 | − | 0.312701i | ||||
\(707\) | −10.5465 | −0.396644 | ||||||||
\(708\) | −1.98709 | + | 3.44174i | −0.0746793 | + | 0.129348i | ||||
\(709\) | −2.18928 | − | 1.26398i | −0.0822200 | − | 0.0474697i | 0.458326 | − | 0.888784i | \(-0.348449\pi\) |
−0.540546 | + | 0.841314i | \(0.681782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.84486 | − | 3.19540i | 0.0691878 | − | 0.119837i | ||||
\(712\) | −11.6628 | + | 6.73351i | −0.437081 | + | 0.252349i | ||||
\(713\) | 30.0089 | + | 51.9770i | 1.12384 | + | 1.94655i | ||||
\(714\) | 2.37894 | 0.0890295 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.88312 | 0.369350 | ||||||||
\(717\) | 2.31165 | + | 4.00390i | 0.0863302 | + | 0.149528i | ||||
\(718\) | −5.46891 | + | 3.15748i | −0.204098 | + | 0.117836i | ||||
\(719\) | −26.6943 | + | 46.2359i | −0.995530 | + | 1.72431i | −0.415968 | + | 0.909379i | \(0.636557\pi\) |
−0.579562 | + | 0.814928i | \(0.696776\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.585082 | − | 0.337797i | −0.0217896 | − | 0.0125802i | ||||
\(722\) | −6.04516 | + | 10.4705i | −0.224978 | + | 0.389673i | ||||
\(723\) | 17.5945 | 0.654347 | ||||||||
\(724\) | −7.15075 | + | 12.3855i | −0.265756 | + | 0.460302i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.07571 | − | 4.08516i | 0.262604 | − | 0.151615i | ||||
\(727\) | 2.09614i | 0.0777417i | 0.999244 | + | 0.0388709i | \(0.0123761\pi\) | ||||
−0.999244 | + | 0.0388709i | \(0.987624\pi\) | |||||||
\(728\) | 0.0646242 | + | 3.35922i | 0.00239513 | + | 0.124501i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.76876 | + | 6.52768i | 0.139393 | + | 0.241435i | ||||
\(732\) | 7.55500 | + | 4.36188i | 0.279241 | + | 0.161220i | ||||
\(733\) | −16.7827 | −0.619883 | −0.309942 | − | 0.950756i | \(-0.600310\pi\) | ||||
−0.309942 | + | 0.950756i | \(0.600310\pi\) | |||||||
\(734\) | 30.2194 | + | 17.4472i | 1.11542 | + | 0.643987i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.45705i | − | 0.238010i | ||||||
\(737\) | −7.56297 | − | 4.36648i | −0.278585 | − | 0.160841i | ||||
\(738\) | −1.01714 | + | 0.587246i | −0.0374414 | + | 0.0216168i | ||||
\(739\) | −8.24563 | + | 4.76062i | −0.303321 | + | 0.175122i | −0.643934 | − | 0.765081i | \(-0.722699\pi\) |
0.340613 | + | 0.940204i | \(0.389365\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.11522 | − | 4.89582i | 0.298120 | − | 0.179852i | ||||
\(742\) | 4.99536i | 0.183385i | ||||||||
\(743\) | −16.2832 | − | 28.2034i | −0.597374 | − | 1.03468i | −0.993207 | − | 0.116360i | \(-0.962877\pi\) |
0.395833 | − | 0.918323i | \(-0.370456\pi\) | |||||||
\(744\) | −4.64747 | − | 8.04965i | −0.170384 | − | 0.295114i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 4.81216i | − | 0.176186i | ||||||
\(747\) | −1.92455 | + | 3.33341i | −0.0704154 | + | 0.121963i | ||||
\(748\) | 2.14721 | − | 3.71907i | 0.0785097 | − | 0.135983i | ||||
\(749\) | 16.0440i | 0.586235i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.38117 | − | 12.7846i | −0.269343 | − | 0.466515i | 0.699350 | − | 0.714780i | \(-0.253473\pi\) |
−0.968692 | + | 0.248265i | \(0.920140\pi\) | |||||||
\(752\) | −1.98967 | − | 3.44621i | −0.0725557 | − | 0.125670i | ||||
\(753\) | 26.5198i | 0.966436i | ||||||||
\(754\) | −0.234986 | − | 12.2148i | −0.00855769 | − | 0.444835i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.807007 | − | 0.465926i | 0.0293506 | − | 0.0169456i | ||||
\(757\) | −30.4462 | + | 17.5781i | −1.10659 | + | 0.638888i | −0.937943 | − | 0.346789i | \(-0.887272\pi\) |
−0.168643 | + | 0.985677i | \(0.553939\pi\) | |||||||
\(758\) | −24.0847 | − | 13.9053i | −0.874795 | − | 0.505063i | ||||
\(759\) | 10.8618i | 0.394259i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.2215 | − | 20.9125i | −1.31303 | − | 0.758076i | −0.330431 | − | 0.943830i | \(-0.607194\pi\) |
−0.982596 | + | 0.185754i | \(0.940527\pi\) | |||||||
\(762\) | −0.677003 | −0.0245252 | ||||||||
\(763\) | 8.29730 | + | 4.79045i | 0.300382 | + | 0.173426i | ||||
\(764\) | 0.0573183 | + | 0.0992782i | 0.00207370 | + | 0.00359176i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.805736 | 0.0291124 | ||||||||
\(767\) | −14.3264 | + | 0.275611i | −0.517298 | + | 0.00995172i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −39.4957 | + | 22.8028i | −1.42425 | + | 0.822291i | −0.996659 | − | 0.0816812i | \(-0.973971\pi\) |
−0.427591 | + | 0.903972i | \(0.640638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.912132 | + | 1.57986i | −0.0328496 | + | 0.0568972i | ||||
\(772\) | 8.65685 | 0.311567 | ||||||||
\(773\) | 6.31759 | − | 10.9424i | 0.227228 | − | 0.393570i | −0.729758 | − | 0.683706i | \(-0.760367\pi\) |
0.956986 | + | 0.290136i | \(0.0937004\pi\) | |||||||
\(774\) | 2.55695 | + | 1.47626i | 0.0919078 | + | 0.0530630i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.04052 | − | 12.1945i | 0.252740 | − | 0.437758i | ||||
\(777\) | −7.39209 | + | 4.26782i | −0.265190 | + | 0.153107i | ||||
\(778\) | −13.7507 | − | 23.8168i | −0.492985 | − | 0.853875i | ||||
\(779\) | −3.08730 | −0.110614 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.61973 | 0.236873 | ||||||||
\(782\) | −8.24215 | − | 14.2758i | −0.294739 | − | 0.510502i | ||||
\(783\) | −2.93443 | + | 1.69419i | −0.104868 | + | 0.0605456i | ||||
\(784\) | 3.06583 | − | 5.31017i | 0.109494 | − | 0.189649i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.61696 | − | 0.933552i | −0.0576750 | − | 0.0332987i | ||||
\(787\) | −26.0708 | + | 45.1559i | −0.929323 | + | 1.60963i | −0.144865 | + | 0.989451i | \(0.546275\pi\) |
−0.784458 | + | 0.620182i | \(0.787059\pi\) | |||||||
\(788\) | −20.4801 | −0.729574 | ||||||||
\(789\) | 6.06828 | − | 10.5106i | 0.216037 | − | 0.374186i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.79315 | + | 4.49938i | −0.277093 | + | 0.159979i | ||||
\(792\) | − | 1.68216i | − | 0.0597731i | ||||||
\(793\) | 0.604996 | + | 31.4481i | 0.0214840 | + | 1.11676i | ||||
\(794\) | −1.14819 | −0.0407477 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.955336 | − | 1.65469i | −0.0338610 | − | 0.0586489i | ||||
\(797\) | 37.0582 | + | 21.3956i | 1.31267 | + | 0.757870i | 0.982537 | − | 0.186065i | \(-0.0595736\pi\) |
0.330132 | + | 0.943935i | \(0.392907\pi\) | |||||||
\(798\) | 2.44949 | 0.0867110 | ||||||||
\(799\) | −8.79787 | − | 5.07945i | −0.311246 | − | 0.179698i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.4670i | 0.475834i | ||||||||
\(802\) | −11.8647 | − | 6.85009i | −0.418957 | − | 0.241885i | ||||
\(803\) | −10.5812 | + | 6.10903i | −0.373401 | + | 0.215583i | ||||
\(804\) | 4.49598 | − | 2.59575i | 0.158561 | − | 0.0915452i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.1953 | − | 29.3404i | 0.570456 | − | 1.03347i | ||||
\(807\) | − | 23.5310i | − | 0.828331i | ||||||
\(808\) | −5.65892 | − | 9.80153i | −0.199080 | − | 0.344817i | ||||
\(809\) | 24.3918 | + | 42.2478i | 0.857569 | + | 1.48535i | 0.874241 | + | 0.485492i | \(0.161360\pi\) |
−0.0166719 | + | 0.999861i | \(0.505307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.87402i | 0.276494i | 0.990398 | + | 0.138247i | \(0.0441468\pi\) | ||||
−0.990398 | + | 0.138247i | \(0.955853\pi\) | |||||||
\(812\) | 1.57874 | − | 2.73445i | 0.0554029 | − | 0.0959606i | ||||
\(813\) | 6.34349 | − | 10.9872i | 0.222476 | − | 0.385339i | ||||
\(814\) | 15.4084i | 0.540064i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.27646 | + | 2.21089i | 0.0446849 | + | 0.0773966i | ||||
\(817\) | 3.88053 | + | 6.72128i | 0.135763 | + | 0.235148i | ||||
\(818\) | − | 7.66274i | − | 0.267922i | ||||||
\(819\) | 2.94148 | + | 1.62364i | 0.102784 | + | 0.0567347i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.6790 | + | 14.2484i | −0.861304 | + | 0.497274i | −0.864449 | − | 0.502721i | \(-0.832332\pi\) |
0.00314470 | + | 0.999995i | \(0.498999\pi\) | |||||||
\(822\) | 6.31212 | − | 3.64431i | 0.220161 | − | 0.127110i | ||||
\(823\) | −40.0387 | − | 23.1164i | −1.39566 | − | 0.805786i | −0.401728 | − | 0.915759i | \(-0.631590\pi\) |
−0.993935 | + | 0.109973i | \(0.964924\pi\) | |||||||
\(824\) | − | 0.725003i | − | 0.0252567i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.20719 | − | 1.85167i | −0.111592 | − | 0.0644279i | ||||
\(827\) | 9.53716 | 0.331640 | 0.165820 | − | 0.986156i | \(-0.446973\pi\) | ||||
0.165820 | + | 0.986156i | \(0.446973\pi\) | |||||||
\(828\) | −5.59197 | − | 3.22853i | −0.194334 | − | 0.112199i | ||||
\(829\) | −6.64904 | − | 11.5165i | −0.230931 | − | 0.399984i | 0.727152 | − | 0.686477i | \(-0.240844\pi\) |
−0.958082 | + | 0.286493i | \(0.907510\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.8235 | 0.444843 | ||||||||
\(832\) | −3.08725 | + | 1.86250i | −0.107031 | + | 0.0645706i | ||||
\(833\) | − | 15.6536i | − | 0.542365i | ||||||
\(834\) | −4.08018 | + | 2.35569i | −0.141285 | + | 0.0815710i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.21089 | − | 3.82937i | 0.0764652 | − | 0.132442i | ||||
\(837\) | −9.29493 | −0.321280 | ||||||||
\(838\) | −19.5013 | + | 33.7773i | −0.673662 | + | 1.16682i | ||||
\(839\) | −42.8848 | − | 24.7595i | −1.48055 | − | 0.854794i | −0.480790 | − | 0.876836i | \(-0.659650\pi\) |
−0.999757 | + | 0.0220420i | \(0.992983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.75941 | − | 15.1717i | 0.302049 | − | 0.523163i | ||||
\(842\) | 28.3990 | − | 16.3962i | 0.978694 | − | 0.565049i | ||||
\(843\) | −2.58360 | − | 4.47492i | −0.0889838 | − | 0.154125i | ||||
\(844\) | 1.24024 | 0.0426907 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.97934 | −0.136812 | ||||||||
\(847\) | 3.80677 | + | 6.59351i | 0.130802 | + | 0.226556i | ||||
\(848\) | −4.64248 | + | 2.68034i | −0.159424 | + | 0.0920432i | ||||
\(849\) | −6.48124 | + | 11.2258i | −0.222436 | + | 0.385270i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.2218 | + | 29.5729i | 1.75586 | + | 1.01375i | ||||
\(852\) | −1.96763 | + | 3.40803i | −0.0674097 | + | 0.116757i | ||||
\(853\) | 6.87904 | 0.235534 | 0.117767 | − | 0.993041i | \(-0.462426\pi\) | ||||
0.117767 | + | 0.993041i | \(0.462426\pi\) | |||||||
\(854\) | −4.06462 | + | 7.04014i | −0.139089 | + | 0.240908i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.9106 | + | 8.60867i | −0.509635 | + | 0.294238i | ||||
\(857\) | − | 25.1526i | − | 0.859198i | −0.903020 | − | 0.429599i | \(-0.858655\pi\) | ||
0.903020 | − | 0.429599i | \(-0.141345\pi\) | |||||||
\(858\) | 5.19325 | − | 3.13303i | 0.177295 | − | 0.106960i | ||||
\(859\) | −52.3171 | −1.78504 | −0.892518 | − | 0.451012i | \(-0.851063\pi\) | ||||
−0.892518 | + | 0.451012i | \(0.851063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.547226 | − | 0.947824i | −0.0186494 | − | 0.0323017i | ||||
\(862\) | 28.6031 | + | 16.5140i | 0.974225 | + | 0.562469i | ||||
\(863\) | 29.9308 | 1.01886 | 0.509428 | − | 0.860513i | \(-0.329857\pi\) | ||||
0.509428 | + | 0.860513i | \(0.329857\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 8.99411i | − | 0.305632i | ||||||
\(867\) | −9.07822 | − | 5.24131i | −0.308313 | − | 0.178004i | ||||
\(868\) | 7.50108 | − | 4.33075i | 0.254603 | − | 0.146995i | ||||
\(869\) | 5.37518 | − | 3.10336i | 0.182340 | − | 0.105274i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.3875 | + | 9.04560i | 0.555269 | + | 0.306498i | ||||
\(872\) | 10.2816i | 0.348178i | ||||||||
\(873\) | −7.04052 | − | 12.1945i | −0.238285 | − | 0.412722i | ||||
\(874\) | −8.48659 | − | 14.6992i | −0.287063 | − | 0.497208i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 7.26330i | − | 0.245404i | ||||||
\(877\) | 7.87295 | − | 13.6363i | 0.265851 | − | 0.460467i | −0.701936 | − | 0.712240i | \(-0.747681\pi\) |
0.967786 | + | 0.251774i | \(0.0810139\pi\) | |||||||
\(878\) | −3.65685 | + | 6.33386i | −0.123413 | + | 0.213757i | ||||
\(879\) | 13.4704i | 0.454346i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.56434 | + | 13.1018i | 0.254849 | + | 0.441412i | 0.964855 | − | 0.262785i | \(-0.0846409\pi\) |
−0.710005 | + | 0.704196i | \(0.751308\pi\) | |||||||
\(882\) | −3.06583 | − | 5.31017i | −0.103232 | − | 0.178803i | ||||
\(883\) | − | 54.8263i | − | 1.84505i | −0.385936 | − | 0.922525i | \(-0.626122\pi\) | ||
0.385936 | − | 0.922525i | \(-0.373878\pi\) | |||||||
\(884\) | −4.44815 | + | 8.05852i | −0.149608 | + | 0.271037i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.8331 | + | 13.7600i | −0.800687 | + | 0.462277i | ||||
\(887\) | −40.5176 | + | 23.3928i | −1.36045 | + | 0.785454i | −0.989683 | − | 0.143273i | \(-0.954237\pi\) |
−0.370763 | + | 0.928727i | \(0.620904\pi\) | |||||||
\(888\) | −7.93269 | − | 4.57994i | −0.266204 | − | 0.153693i | ||||
\(889\) | − | 0.630866i | − | 0.0211586i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.45680 | − | 0.841081i | −0.0488045 | − | 0.0281773i | ||||
\(892\) | 14.7783 | 0.494814 | ||||||||
\(893\) | −9.05879 | − | 5.23009i | −0.303141 | − | 0.175018i | ||||
\(894\) | −1.50120 | − | 2.60016i | −0.0502077 | − | 0.0869623i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.931852 | −0.0311310 | ||||||||
\(897\) | −0.447799 | − | 23.2769i | −0.0149516 | − | 0.777194i | ||||
\(898\) | 10.2582i | 0.342322i | ||||||||
\(899\) | −27.2753 | + | 15.7474i | −0.909684 | + | 0.525206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.84267 | + | 11.8519i | −0.227963 | + | 0.394843i | ||||
\(902\) | −1.97569 | −0.0657832 | ||||||||
\(903\) | −1.37565 | + | 2.38270i | −0.0457789 | + | 0.0792913i | ||||
\(904\) | −8.36308 | − | 4.82843i | −0.278152 | − | 0.160591i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.21001 | + | 10.7561i | −0.206314 | + | 0.357346i | ||||
\(907\) | −25.2077 | + | 14.5536i | −0.837006 | + | 0.483246i | −0.856246 | − | 0.516569i | \(-0.827209\pi\) |
0.0192392 | + | 0.999815i | \(0.493876\pi\) | |||||||
\(908\) | −4.78290 | − | 8.28423i | −0.158726 | − | 0.274922i | ||||
\(909\) | −11.3178 | −0.375389 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.59919 | −0.218641 | −0.109320 | − | 0.994007i | \(-0.534867\pi\) | ||||
−0.109320 | + | 0.994007i | \(0.534867\pi\) | |||||||
\(912\) | 1.31431 | + | 2.27646i | 0.0435213 | + | 0.0753810i | ||||
\(913\) | −5.60734 | + | 3.23740i | −0.185576 | + | 0.107142i | ||||
\(914\) | 7.37005 | − | 12.7653i | 0.243780 | − | 0.422238i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.1184 | − | 7.57389i | −0.433443 | − | 0.250248i | ||||
\(917\) | 0.869932 | − | 1.50677i | 0.0287277 | − | 0.0497578i | ||||
\(918\) | 2.55291 | 0.0842587 | ||||||||
\(919\) | −16.9793 | + | 29.4089i | −0.560094 | + | 0.970111i | 0.437394 | + | 0.899270i | \(0.355902\pi\) |
−0.997488 | + | 0.0708412i | \(0.977432\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.5866 | − | 10.7310i | 0.612450 | − | 0.353598i | ||||
\(922\) | − | 19.8601i | − | 0.654056i | ||||||
\(923\) | −14.1861 | + | 0.272911i | −0.466942 | + | 0.00898298i | ||||
\(924\) | 1.56753 | 0.0515678 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.0766 | − | 27.8455i | −0.528311 | − | 0.915061i | ||||
\(927\) | −0.627871 | − | 0.362501i | −0.0206220 | − | 0.0119061i | ||||
\(928\) | 3.38839 | 0.111229 | ||||||||
\(929\) | −0.599403 | − | 0.346065i | −0.0196658 | − | 0.0113540i | 0.490135 | − | 0.871647i | \(-0.336948\pi\) |
−0.509801 | + | 0.860293i | \(0.670281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 16.1178i | − | 0.528240i | ||||||
\(932\) | −16.2304 | − | 9.37064i | −0.531646 | − | 0.306946i | ||||
\(933\) | −12.7792 | + | 7.37808i | −0.418372 | + | 0.241547i | ||||
\(934\) | 19.2911 | − | 11.1377i | 0.631224 | − | 0.364437i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.0693504 | + | 3.60488i | 0.00226679 | + | 0.117829i | ||||
\(937\) | − | 22.0269i | − | 0.719589i | −0.933032 | − | 0.359795i | \(-0.882847\pi\) | ||
0.933032 | − | 0.359795i | \(-0.117153\pi\) | |||||||
\(938\) | 2.41886 | + | 4.18958i | 0.0789785 | + | 0.136795i | ||||
\(939\) | 0.702205 | + | 1.21625i | 0.0229156 | + | 0.0396910i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 15.7015i | − | 0.511855i | −0.966696 | − | 0.255928i | \(-0.917619\pi\) | ||
0.966696 | − | 0.255928i | \(-0.0823809\pi\) | |||||||
\(942\) | −11.2609 | + | 19.5044i | −0.366899 | + | 0.635487i | ||||
\(943\) | −3.79188 | + | 6.56773i | −0.123481 | + | 0.213875i | ||||
\(944\) | − | 3.97418i | − | 0.129348i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.48331 | + | 4.30121i | 0.0807392 | + | 0.139844i | ||||
\(947\) | −13.0966 | − | 22.6839i | −0.425581 | − | 0.737129i | 0.570893 | − | 0.821024i | \(-0.306597\pi\) |
−0.996475 | + | 0.0838957i | \(0.973264\pi\) | |||||||
\(948\) | 3.68973i | 0.119837i | ||||||||
\(949\) | 22.4236 | − | 13.5279i | 0.727901 | − | 0.439135i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.7019 | − | 16.5710i | 0.930722 | − | 0.537352i | ||||
\(952\) | −2.06022 | + | 1.18947i | −0.0667721 | + | 0.0385509i | ||||
\(953\) | 19.4420 | + | 11.2248i | 0.629788 | + | 0.363608i | 0.780670 | − | 0.624943i | \(-0.214878\pi\) |
−0.150882 | + | 0.988552i | \(0.548211\pi\) | |||||||
\(954\) | 5.36068i | 0.173558i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.00390 | − | 2.31165i | −0.129495 | − | 0.0747641i | ||||
\(957\) | −5.69982 | −0.184249 | ||||||||
\(958\) | −19.0007 | − | 10.9700i | −0.613884 | − | 0.354426i | ||||
\(959\) | 3.39595 | + | 5.88196i | 0.109661 | + | 0.189939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −55.3958 | −1.78696 | ||||||||
\(962\) | −0.635241 | − | 33.0203i | −0.0204810 | − | 1.06462i | ||||
\(963\) | 17.2173i | 0.554821i | ||||||||
\(964\) | −15.2373 | + | 8.79725i | −0.490760 | + | 0.283341i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.00851 | − | 5.21089i | 0.0967972 | − | 0.167658i | ||||
\(967\) | 36.7073 | 1.18043 | 0.590213 | − | 0.807248i | \(-0.299044\pi\) | ||||
0.590213 | + | 0.807248i | \(0.299044\pi\) | |||||||
\(968\) | −4.08516 | + | 7.07571i | −0.131302 | + | 0.227422i | ||||
\(969\) | 5.81160 | + | 3.35533i | 0.186695 | + | 0.107789i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.8673 | + | 22.2869i | −0.412932 | + | 0.715219i | −0.995209 | − | 0.0977711i | \(-0.968829\pi\) |
0.582277 | + | 0.812991i | \(0.302162\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −2.19516 | − | 3.80212i | −0.0703735 | − | 0.121890i | ||||
\(974\) | −9.05302 | −0.290078 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.72376 | −0.279241 | ||||||||
\(977\) | 15.3079 | + | 26.5140i | 0.489742 | + | 0.848258i | 0.999930 | − | 0.0118045i | \(-0.00375759\pi\) |
−0.510188 | + | 0.860063i | \(0.670424\pi\) | |||||||
\(978\) | 2.40313 | − | 1.38745i | 0.0768435 | − | 0.0443656i | ||||
\(979\) | −11.3269 | + | 19.6187i | −0.362008 | + | 0.627016i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.90410 | + | 5.14078i | 0.284286 | + | 0.164133i | ||||
\(982\) | −15.1000 | + | 26.1540i | −0.481861 | + | 0.834609i | ||||
\(983\) | −61.1797 | −1.95133 | −0.975665 | − | 0.219266i | \(-0.929634\pi\) | ||||
−0.975665 | + | 0.219266i | \(0.929634\pi\) | |||||||
\(984\) | 0.587246 | − | 1.01714i | 0.0187207 | − | 0.0324252i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.49135 | − | 4.32513i | 0.238573 | − | 0.137740i | ||||
\(987\) | − | 3.70815i | − | 0.118032i | ||||||
\(988\) | −4.58007 | + | 8.29751i | −0.145712 | + | 0.263979i | ||||
\(989\) | 19.0646 | 0.606218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.3797 | − | 43.9589i | −0.806212 | − | 1.39640i | −0.915470 | − | 0.402387i | \(-0.868181\pi\) |
0.109258 | − | 0.994013i | \(-0.465153\pi\) | |||||||
\(992\) | 8.04965 | + | 4.64747i | 0.255577 | + | 0.147557i | ||||
\(993\) | −6.98904 | −0.221790 | ||||||||
\(994\) | −3.17578 | − | 1.83354i | −0.100730 | − | 0.0581562i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 3.84909i | − | 0.121963i | ||||||
\(997\) | 42.6273 | + | 24.6109i | 1.35002 | + | 0.779434i | 0.988252 | − | 0.152834i | \(-0.0488399\pi\) |
0.361768 | + | 0.932268i | \(0.382173\pi\) | |||||||
\(998\) | 7.83178 | − | 4.52168i | 0.247911 | − | 0.143131i | ||||
\(999\) | −7.93269 | + | 4.57994i | −0.250979 | + | 0.144903i |
(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 | 1950.2.y.i.49.4 | 8 | ||
5.2 | odd | 4 | 1950.2.bc.e.751.4 | ✓ | 8 | ||
5.3 | odd | 4 | 1950.2.bc.f.751.1 | yes | 8 | ||
5.4 | even | 2 | 1950.2.y.l.49.1 | 8 | |||
13.4 | even | 6 | 1950.2.y.l.199.1 | 8 | |||
65.4 | even | 6 | inner | 1950.2.y.i.199.4 | 8 | ||
65.17 | odd | 12 | 1950.2.bc.e.901.4 | yes | 8 | ||
65.43 | odd | 12 | 1950.2.bc.f.901.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.i.49.4 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.y.i.199.4 | 8 | 65.4 | even | 6 | inner | ||
1950.2.y.l.49.1 | 8 | 5.4 | even | 2 | |||
1950.2.y.l.199.1 | 8 | 13.4 | even | 6 | |||
1950.2.bc.e.751.4 | ✓ | 8 | 5.2 | odd | 4 | ||
1950.2.bc.e.901.4 | yes | 8 | 65.17 | odd | 12 | ||
1950.2.bc.f.751.1 | yes | 8 | 5.3 | odd | 4 | ||
1950.2.bc.f.901.1 | yes | 8 | 65.43 | odd | 12 |