Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
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, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
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.bc (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
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 | 901.4 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.901 |
Dual form | 1950.2.bc.e.751.4 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | + | 0.500000i | −0.353553 | + | 0.204124i | ||||
\(7\) | 0.807007 | − | 0.465926i | 0.305020 | − | 0.176103i | −0.339676 | − | 0.940543i | \(-0.610317\pi\) |
0.644696 | + | 0.764439i | \(0.276984\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.45680 | + | 0.841081i | 0.439240 | + | 0.253596i | 0.703275 | − | 0.710918i | \(-0.251720\pi\) |
−0.264035 | + | 0.964513i | \(0.585053\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.86250 | − | 3.08725i | 0.516565 | − | 0.856248i | ||||
\(14\) | 0.931852 | 0.249048 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.27646 | + | 2.21089i | 0.309586 | + | 0.536219i | 0.978272 | − | 0.207326i | \(-0.0664761\pi\) |
−0.668686 | + | 0.743545i | \(0.733143\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 2.27646 | − | 1.31431i | 0.522255 | − | 0.301524i | −0.215602 | − | 0.976481i | \(-0.569171\pi\) |
0.737857 | + | 0.674957i | \(0.235838\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.931852i | 0.203347i | ||||||||
\(22\) | 0.841081 | + | 1.45680i | 0.179319 | + | 0.310590i | ||||
\(23\) | 3.22853 | − | 5.59197i | 0.673194 | − | 1.16601i | −0.303799 | − | 0.952736i | \(-0.598255\pi\) |
0.976993 | − | 0.213271i | \(-0.0684116\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.15660 | − | 1.74238i | 0.619060 | − | 0.341709i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.807007 | + | 0.465926i | 0.152510 | + | 0.0880517i | ||||
\(29\) | 1.69419 | − | 2.93443i | 0.314604 | − | 0.544910i | −0.664749 | − | 0.747067i | \(-0.731462\pi\) |
0.979353 | + | 0.202156i | \(0.0647949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.29493i | 1.66942i | 0.550690 | + | 0.834710i | \(0.314365\pi\) | ||||
−0.550690 | + | 0.834710i | \(0.685635\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −1.45680 | + | 0.841081i | −0.253596 | + | 0.146413i | ||||
\(34\) | 2.55291i | 0.437821i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 7.93269 | + | 4.57994i | 1.30413 | + | 0.752938i | 0.981109 | − | 0.193456i | \(-0.0619695\pi\) |
0.323017 | + | 0.946393i | \(0.395303\pi\) | |||||||
\(38\) | 2.62863 | 0.426419 | ||||||||
\(39\) | 1.74238 | + | 3.15660i | 0.279005 | + | 0.505460i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.01714 | + | 0.587246i | 0.158851 | + | 0.0917124i | 0.577318 | − | 0.816519i | \(-0.304099\pi\) |
−0.418467 | + | 0.908232i | \(0.637433\pi\) | |||||||
\(42\) | −0.465926 | + | 0.807007i | −0.0718939 | + | 0.124524i | ||||
\(43\) | −1.47626 | − | 2.55695i | −0.225127 | − | 0.389932i | 0.731230 | − | 0.682131i | \(-0.238946\pi\) |
−0.956358 | + | 0.292199i | \(0.905613\pi\) | |||||||
\(44\) | 1.68216i | 0.253596i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.59197 | − | 3.22853i | 0.824491 | − | 0.476020i | ||||
\(47\) | − | 3.97934i | − | 0.580446i | −0.956959 | − | 0.290223i | \(-0.906271\pi\) | ||
0.956959 | − | 0.290223i | \(-0.0937294\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −3.06583 | + | 5.31017i | −0.437975 | + | 0.758595i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.55291 | −0.357480 | ||||||||
\(52\) | 3.60488 | + | 0.0693504i | 0.499908 | + | 0.00961716i | ||||
\(53\) | −5.36068 | −0.736346 | −0.368173 | − | 0.929757i | \(-0.620017\pi\) | ||||
−0.368173 | + | 0.929757i | \(0.620017\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.465926 | + | 0.807007i | 0.0622620 | + | 0.107841i | ||||
\(57\) | 2.62863i | 0.348170i | ||||||||
\(58\) | 2.93443 | − | 1.69419i | 0.385310 | − | 0.222459i | ||||
\(59\) | −3.44174 | + | 1.98709i | −0.448076 | + | 0.258697i | −0.707017 | − | 0.707196i | \(-0.749960\pi\) |
0.258941 | + | 0.965893i | \(0.416626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.36188 | + | 7.55500i | 0.558481 | + | 0.967318i | 0.997624 | + | 0.0689005i | \(0.0219491\pi\) |
−0.439142 | + | 0.898418i | \(0.644718\pi\) | |||||||
\(62\) | −4.64747 | + | 8.04965i | −0.590229 | + | 1.02231i | ||||
\(63\) | −0.807007 | − | 0.465926i | −0.101673 | − | 0.0587011i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.68216 | −0.207060 | ||||||||
\(67\) | 4.49598 | + | 2.59575i | 0.549271 | + | 0.317122i | 0.748828 | − | 0.662764i | \(-0.230617\pi\) |
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(68\) | −1.27646 | + | 2.21089i | −0.154793 | + | 0.268110i | ||||
\(69\) | 3.22853 | + | 5.59197i | 0.388669 | + | 0.673194i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.40803 | − | 1.96763i | 0.404458 | − | 0.233514i | −0.283947 | − | 0.958840i | \(-0.591644\pi\) |
0.688406 | + | 0.725326i | \(0.258311\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | − | 7.26330i | − | 0.850106i | −0.905169 | − | 0.425053i | \(-0.860256\pi\) | ||
0.905169 | − | 0.425053i | \(-0.139744\pi\) | |||||||
\(74\) | 4.57994 | + | 7.93269i | 0.532407 | + | 0.922156i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.27646 | + | 1.31431i | 0.261128 | + | 0.150762i | ||||
\(77\) | 1.56753 | 0.178636 | ||||||||
\(78\) | −0.0693504 | + | 3.60488i | −0.00785238 | + | 0.408173i | ||||
\(79\) | −3.68973 | −0.415127 | −0.207563 | − | 0.978222i | \(-0.566553\pi\) | ||||
−0.207563 | + | 0.978222i | \(0.566553\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.587246 | + | 1.01714i | 0.0648505 | + | 0.112324i | ||||
\(83\) | − | 3.84909i | − | 0.422493i | −0.977433 | − | 0.211246i | \(-0.932248\pi\) | ||
0.977433 | − | 0.211246i | \(-0.0677522\pi\) | |||||||
\(84\) | −0.807007 | + | 0.465926i | −0.0880517 | + | 0.0508367i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 2.95252i | − | 0.318378i | ||||||
\(87\) | 1.69419 | + | 2.93443i | 0.181637 | + | 0.314604i | ||||
\(88\) | −0.841081 | + | 1.45680i | −0.0896596 | + | 0.155295i | ||||
\(89\) | 11.6628 | + | 6.73351i | 1.23625 | + | 0.713751i | 0.968326 | − | 0.249689i | \(-0.0803283\pi\) |
0.267926 | + | 0.963439i | \(0.413662\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0646242 | − | 3.35922i | 0.00677446 | − | 0.352142i | ||||
\(92\) | 6.45705 | 0.673194 | ||||||||
\(93\) | −8.04965 | − | 4.64747i | −0.834710 | − | 0.481920i | ||||
\(94\) | 1.98967 | − | 3.44621i | 0.205219 | − | 0.355449i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 12.1945 | − | 7.04052i | 1.23817 | − | 0.714856i | 0.269448 | − | 0.963015i | \(-0.413159\pi\) |
0.968719 | + | 0.248159i | \(0.0798254\pi\) | |||||||
\(98\) | −5.31017 | + | 3.06583i | −0.536408 | + | 0.309695i | ||||
\(99\) | − | 1.68216i | − | 0.169064i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.65892 | + | 9.80153i | −0.563083 | + | 0.975289i | 0.434142 | + | 0.900845i | \(0.357052\pi\) |
−0.997225 | + | 0.0744445i | \(0.976282\pi\) | |||||||
\(102\) | −2.21089 | − | 1.27646i | −0.218911 | − | 0.126388i | ||||
\(103\) | −0.725003 | −0.0714366 | −0.0357183 | − | 0.999362i | \(-0.511372\pi\) | ||||
−0.0357183 | + | 0.999362i | \(0.511372\pi\) | |||||||
\(104\) | 3.08725 | + | 1.86250i | 0.302729 | + | 0.182633i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.64248 | − | 2.68034i | −0.450918 | − | 0.260337i | ||||
\(107\) | −8.60867 | + | 14.9106i | −0.832231 | + | 1.44147i | 0.0640338 | + | 0.997948i | \(0.479603\pi\) |
−0.896265 | + | 0.443519i | \(0.853730\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 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 | ||||
\(112\) | 0.931852i | 0.0880517i | ||||||||
\(113\) | −4.82843 | − | 8.36308i | −0.454220 | − | 0.786732i | 0.544423 | − | 0.838811i | \(-0.316749\pi\) |
−0.998643 | + | 0.0520785i | \(0.983415\pi\) | |||||||
\(114\) | −1.31431 | + | 2.27646i | −0.123097 | + | 0.213210i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.38839 | 0.314604 | ||||||||
\(117\) | −3.60488 | − | 0.0693504i | −0.333272 | − | 0.00641144i | ||||
\(118\) | −3.97418 | −0.365853 | ||||||||
\(119\) | 2.06022 | + | 1.18947i | 0.188860 | + | 0.109038i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.08516 | − | 7.07571i | −0.371379 | − | 0.643247i | ||||
\(122\) | 8.72376i | 0.789812i | ||||||||
\(123\) | −1.01714 | + | 0.587246i | −0.0917124 | + | 0.0529502i | ||||
\(124\) | −8.04965 | + | 4.64747i | −0.722880 | + | 0.417355i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.465926 | − | 0.807007i | −0.0415080 | − | 0.0718939i | ||||
\(127\) | 0.338502 | − | 0.586302i | 0.0300372 | − | 0.0520259i | −0.850616 | − | 0.525787i | \(-0.823771\pi\) |
0.880653 | + | 0.473761i | \(0.157104\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 2.95252 | 0.259955 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.86710 | 0.163130 | 0.0815648 | − | 0.996668i | \(-0.474008\pi\) | ||||
0.0815648 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(132\) | −1.45680 | − | 0.841081i | −0.126798 | − | 0.0732067i | ||||
\(133\) | 1.22474 | − | 2.12132i | 0.106199 | − | 0.183942i | ||||
\(134\) | 2.59575 | + | 4.49598i | 0.224239 | + | 0.388393i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.21089 | + | 1.27646i | −0.189582 | + | 0.109455i | ||||
\(137\) | −6.31212 | + | 3.64431i | −0.539281 | + | 0.311354i | −0.744788 | − | 0.667302i | \(-0.767449\pi\) |
0.205506 | + | 0.978656i | \(0.434116\pi\) | |||||||
\(138\) | 6.45705i | 0.549661i | ||||||||
\(139\) | −2.35569 | − | 4.08018i | −0.199807 | − | 0.346076i | 0.748659 | − | 0.662956i | \(-0.230698\pi\) |
−0.948466 | + | 0.316879i | \(0.897365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.44621 | + | 1.98967i | 0.290223 | + | 0.167560i | ||||
\(142\) | 3.93525 | 0.330239 | ||||||||
\(143\) | 5.30991 | − | 2.93097i | 0.444037 | − | 0.245100i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.63165 | − | 6.29021i | 0.300558 | − | 0.520581i | ||||
\(147\) | −3.06583 | − | 5.31017i | −0.252865 | − | 0.437975i | ||||
\(148\) | 9.15988i | 0.752938i | ||||||||
\(149\) | −2.60016 | + | 1.50120i | −0.213013 | + | 0.122983i | −0.602711 | − | 0.797960i | \(-0.705913\pi\) |
0.389698 | + | 0.920943i | \(0.372579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4200i | 1.01073i | 0.862907 | + | 0.505363i | \(0.168642\pi\) | ||||
−0.862907 | + | 0.505363i | \(0.831358\pi\) | |||||||
\(152\) | 1.31431 | + | 2.27646i | 0.106605 | + | 0.184645i | ||||
\(153\) | 1.27646 | − | 2.21089i | 0.103195 | − | 0.178740i | ||||
\(154\) | 1.35752 | + | 0.783763i | 0.109392 | + | 0.0631574i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.86250 | + | 3.08725i | −0.149119 | + | 0.247178i | ||||
\(157\) | 22.5217 | 1.79743 | 0.898714 | − | 0.438535i | \(-0.144502\pi\) | ||||
0.898714 | + | 0.438535i | \(0.144502\pi\) | |||||||
\(158\) | −3.19540 | − | 1.84486i | −0.254212 | − | 0.146769i | ||||
\(159\) | 2.68034 | − | 4.64248i | 0.212565 | − | 0.368173i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.01702i | − | 0.474207i | ||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | 2.40313 | − | 1.38745i | 0.188227 | − | 0.108673i | −0.402925 | − | 0.915233i | \(-0.632006\pi\) |
0.591152 | + | 0.806560i | \(0.298673\pi\) | |||||||
\(164\) | 1.17449i | 0.0917124i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.92455 | − | 3.33341i | 0.149374 | − | 0.258723i | ||||
\(167\) | −19.2296 | − | 11.1022i | −1.48803 | − | 0.859114i | −0.488122 | − | 0.872775i | \(-0.662318\pi\) |
−0.999907 | + | 0.0136615i | \(0.995651\pi\) | |||||||
\(168\) | −0.931852 | −0.0718939 | ||||||||
\(169\) | −6.06218 | − | 11.5000i | −0.466321 | − | 0.884615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.27646 | − | 1.31431i | −0.174085 | − | 0.100508i | ||||
\(172\) | 1.47626 | − | 2.55695i | 0.112564 | − | 0.194966i | ||||
\(173\) | −0.475314 | − | 0.823267i | −0.0361374 | − | 0.0625919i | 0.847391 | − | 0.530969i | \(-0.178172\pi\) |
−0.883528 | + | 0.468377i | \(0.844839\pi\) | |||||||
\(174\) | 3.38839i | 0.256873i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.45680 | + | 0.841081i | −0.109810 | + | 0.0633989i | ||||
\(177\) | − | 3.97418i | − | 0.298717i | ||||||
\(178\) | 6.73351 | + | 11.6628i | 0.504698 | + | 0.874162i | ||||
\(179\) | 4.94156 | − | 8.55904i | 0.369350 | − | 0.639732i | −0.620114 | − | 0.784511i | \(-0.712914\pi\) |
0.989464 | + | 0.144779i | \(0.0462471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.3015 | 1.06302 | 0.531511 | − | 0.847051i | \(-0.321624\pi\) | ||||
0.531511 | + | 0.847051i | \(0.321624\pi\) | |||||||
\(182\) | 1.73557 | − | 2.87686i | 0.128649 | − | 0.213247i | ||||
\(183\) | −8.72376 | −0.644879 | ||||||||
\(184\) | 5.59197 | + | 3.22853i | 0.412246 | + | 0.238010i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.64747 | − | 8.04965i | −0.340769 | − | 0.590229i | ||||
\(187\) | 4.29442i | 0.314039i | ||||||||
\(188\) | 3.44621 | − | 1.98967i | 0.251340 | − | 0.145111i | ||||
\(189\) | 0.807007 | − | 0.465926i | 0.0587011 | − | 0.0338911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0573183 | + | 0.0992782i | 0.00414741 | + | 0.00718352i | 0.868092 | − | 0.496404i | \(-0.165347\pi\) |
−0.863944 | + | 0.503587i | \(0.832013\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −7.49706 | − | 4.32843i | −0.539650 | − | 0.311567i | 0.205287 | − | 0.978702i | \(-0.434187\pi\) |
−0.744937 | + | 0.667135i | \(0.767521\pi\) | |||||||
\(194\) | 14.0810 | 1.01096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.13165 | −0.437975 | ||||||||
\(197\) | −17.7363 | − | 10.2401i | −1.26366 | − | 0.729574i | −0.289879 | − | 0.957063i | \(-0.593615\pi\) |
−0.973781 | + | 0.227489i | \(0.926948\pi\) | |||||||
\(198\) | 0.841081 | − | 1.45680i | 0.0597731 | − | 0.103530i | ||||
\(199\) | 0.955336 | + | 1.65469i | 0.0677220 | + | 0.117298i | 0.897898 | − | 0.440203i | \(-0.145094\pi\) |
−0.830176 | + | 0.557501i | \(0.811760\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.49598 | + | 2.59575i | −0.317122 | + | 0.183090i | ||||
\(202\) | −9.80153 | + | 5.65892i | −0.689634 | + | 0.398160i | ||||
\(203\) | − | 3.15748i | − | 0.221611i | ||||||
\(204\) | −1.27646 | − | 2.21089i | −0.0893699 | − | 0.154793i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.627871 | − | 0.362501i | −0.0437458 | − | 0.0252567i | ||||
\(207\) | −6.45705 | −0.448796 | ||||||||
\(208\) | 1.74238 | + | 3.15660i | 0.120813 | + | 0.218871i | ||||
\(209\) | 4.42178 | 0.305861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.620118 | + | 1.07408i | −0.0426907 | + | 0.0739425i | −0.886581 | − | 0.462573i | \(-0.846926\pi\) |
0.843891 | + | 0.536515i | \(0.180260\pi\) | |||||||
\(212\) | −2.68034 | − | 4.64248i | −0.184086 | − | 0.318847i | ||||
\(213\) | 3.93525i | 0.269639i | ||||||||
\(214\) | −14.9106 | + | 8.60867i | −1.01927 | + | 0.588476i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 4.33075 | + | 7.50108i | 0.293990 | + | 0.509206i | ||||
\(218\) | −5.14078 | + | 8.90410i | −0.348178 | + | 0.603062i | ||||
\(219\) | 6.29021 | + | 3.63165i | 0.425053 | + | 0.245404i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.20296 | + | 0.177046i | 0.619058 | + | 0.0119094i | ||||
\(222\) | −9.15988 | −0.614771 | ||||||||
\(223\) | −12.7984 | − | 7.38915i | −0.857043 | − | 0.494814i | 0.00597823 | − | 0.999982i | \(-0.498097\pi\) |
−0.863021 | + | 0.505168i | \(0.831430\pi\) | |||||||
\(224\) | −0.465926 | + | 0.807007i | −0.0311310 | + | 0.0539204i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 9.65685i | − | 0.642364i | ||||||
\(227\) | −8.28423 | + | 4.78290i | −0.549843 | + | 0.317452i | −0.749059 | − | 0.662503i | \(-0.769494\pi\) |
0.199215 | + | 0.979956i | \(0.436161\pi\) | |||||||
\(228\) | −2.27646 | + | 1.31431i | −0.150762 | + | 0.0870425i | ||||
\(229\) | 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 | ||||
\(232\) | 2.93443 | + | 1.69419i | 0.192655 | + | 0.111229i | ||||
\(233\) | 18.7413 | 1.22778 | 0.613891 | − | 0.789391i | \(-0.289603\pi\) | ||||
0.613891 | + | 0.789391i | \(0.289603\pi\) | |||||||
\(234\) | −3.08725 | − | 1.86250i | −0.201820 | − | 0.121756i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.44174 | − | 1.98709i | −0.224038 | − | 0.129348i | ||||
\(237\) | 1.84486 | − | 3.19540i | 0.119837 | − | 0.207563i | ||||
\(238\) | 1.18947 | + | 2.06022i | 0.0771018 | + | 0.133544i | ||||
\(239\) | 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 | 0.0787915 | − | 0.996891i | \(-0.474894\pi\) |
0.902729 | + | 0.430210i | \(0.141561\pi\) | |||||||
\(242\) | − | 8.17033i | − | 0.525209i | ||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −4.36188 | + | 7.55500i | −0.279241 | + | 0.483659i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.17449 | −0.0748829 | ||||||||
\(247\) | 0.182296 | − | 9.47589i | 0.0115992 | − | 0.602937i | ||||
\(248\) | −9.29493 | −0.590229 | ||||||||
\(249\) | 3.33341 | + | 1.92455i | 0.211246 | + | 0.121963i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.2599 | − | 22.9668i | −0.836958 | − | 1.44965i | −0.892426 | − | 0.451194i | \(-0.850998\pi\) |
0.0554676 | − | 0.998460i | \(-0.482335\pi\) | |||||||
\(252\) | − | 0.931852i | − | 0.0587011i | ||||||
\(253\) | 9.40661 | − | 5.43091i | 0.591388 | − | 0.341438i | ||||
\(254\) | 0.586302 | − | 0.338502i | 0.0367879 | − | 0.0212395i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −0.912132 | + | 1.57986i | −0.0568972 | + | 0.0985489i | −0.893071 | − | 0.449916i | \(-0.851454\pi\) |
0.836174 | + | 0.548464i | \(0.184787\pi\) | |||||||
\(258\) | 2.55695 | + | 1.47626i | 0.159189 | + | 0.0919078i | ||||
\(259\) | 8.53565 | 0.530379 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.38839 | −0.209736 | ||||||||
\(262\) | 1.61696 | + | 0.933552i | 0.0998960 | + | 0.0576750i | ||||
\(263\) | −6.06828 | + | 10.5106i | −0.374186 | + | 0.648110i | −0.990205 | − | 0.139622i | \(-0.955411\pi\) |
0.616019 | + | 0.787732i | \(0.288745\pi\) | |||||||
\(264\) | −0.841081 | − | 1.45680i | −0.0517650 | − | 0.0896596i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.12132 | − | 1.22474i | 0.130066 | − | 0.0750939i | ||||
\(267\) | −11.6628 | + | 6.73351i | −0.713751 | + | 0.412084i | ||||
\(268\) | 5.19151i | 0.317122i | ||||||||
\(269\) | −11.7655 | − | 20.3784i | −0.717355 | − | 1.24250i | −0.962044 | − | 0.272894i | \(-0.912019\pi\) |
0.244689 | − | 0.969602i | \(-0.421314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9872 | + | 6.34349i | 0.667427 | + | 0.385339i | 0.795101 | − | 0.606477i | \(-0.207418\pi\) |
−0.127674 | + | 0.991816i | \(0.540751\pi\) | |||||||
\(272\) | −2.55291 | −0.154793 | ||||||||
\(273\) | 2.87686 | + | 1.73557i | 0.174115 | + | 0.105042i | ||||
\(274\) | −7.28861 | −0.440321 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.22853 | + | 5.59197i | −0.194334 | + | 0.336597i | ||||
\(277\) | −6.41177 | − | 11.1055i | −0.385246 | − | 0.667265i | 0.606558 | − | 0.795040i | \(-0.292550\pi\) |
−0.991803 | + | 0.127774i | \(0.959217\pi\) | |||||||
\(278\) | − | 4.71139i | − | 0.282570i | ||||||
\(279\) | 8.04965 | − | 4.64747i | 0.481920 | − | 0.278237i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.16720i | 0.308249i | 0.988051 | + | 0.154125i | \(0.0492557\pi\) | ||||
−0.988051 | + | 0.154125i | \(0.950744\pi\) | |||||||
\(282\) | 1.98967 | + | 3.44621i | 0.118483 | + | 0.205219i | ||||
\(283\) | 6.48124 | − | 11.2258i | 0.385270 | − | 0.667307i | −0.606537 | − | 0.795055i | \(-0.707442\pi\) |
0.991807 | + | 0.127749i | \(0.0407750\pi\) | |||||||
\(284\) | 3.40803 | + | 1.96763i | 0.202229 | + | 0.116757i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.06400 | + | 0.116659i | 0.358572 | + | 0.00689817i | ||||
\(287\) | 1.09445 | 0.0646035 | ||||||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | 5.24131 | − | 9.07822i | 0.308313 | − | 0.534013i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0810i | 0.825445i | ||||||||
\(292\) | 6.29021 | − | 3.63165i | 0.368107 | − | 0.212526i | ||||
\(293\) | 11.6657 | − | 6.73521i | 0.681519 | − | 0.393475i | −0.118908 | − | 0.992905i | \(-0.537939\pi\) |
0.800427 | + | 0.599430i | \(0.204606\pi\) | |||||||
\(294\) | − | 6.13165i | − | 0.357605i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.57994 | + | 7.93269i | −0.266204 | + | 0.461078i | ||||
\(297\) | 1.45680 | + | 0.841081i | 0.0845319 | + | 0.0488045i | ||||
\(298\) | −3.00240 | −0.173925 | ||||||||
\(299\) | −11.2507 | − | 20.3823i | −0.650642 | − | 1.17874i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.38270 | − | 1.37565i | −0.137337 | − | 0.0792913i | ||||
\(302\) | −6.21001 | + | 10.7561i | −0.357346 | + | 0.618941i | ||||
\(303\) | −5.65892 | − | 9.80153i | −0.325096 | − | 0.563083i | ||||
\(304\) | 2.62863i | 0.150762i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.21089 | − | 1.27646i | 0.126388 | − | 0.0729702i | ||||
\(307\) | − | 21.4620i | − | 1.22490i | −0.790510 | − | 0.612450i | \(-0.790184\pi\) | ||
0.790510 | − | 0.612450i | \(-0.209816\pi\) | |||||||
\(308\) | 0.783763 | + | 1.35752i | 0.0446590 | + | 0.0773517i | ||||
\(309\) | 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 | \(0.637399\pi\) | |||||||
\(312\) | −3.15660 | + | 1.74238i | −0.178707 | + | 0.0986430i | ||||
\(313\) | 1.40441 | 0.0793819 | 0.0396910 | − | 0.999212i | \(-0.487363\pi\) | ||||
0.0396910 | + | 0.999212i | \(0.487363\pi\) | |||||||
\(314\) | 19.5044 | + | 11.2609i | 1.10070 | + | 0.635487i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.84486 | − | 3.19540i | −0.103782 | − | 0.179755i | ||||
\(317\) | − | 33.1421i | − | 1.86144i | −0.365729 | − | 0.930722i | \(-0.619180\pi\) | ||
0.365729 | − | 0.930722i | \(-0.380820\pi\) | |||||||
\(318\) | 4.64248 | − | 2.68034i | 0.260337 | − | 0.150306i | ||||
\(319\) | 4.93619 | − | 2.84991i | 0.276374 | − | 0.159564i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.60867 | − | 14.9106i | −0.480489 | − | 0.832231i | ||||
\(322\) | 3.00851 | − | 5.21089i | 0.167658 | − | 0.290391i | ||||
\(323\) | 5.81160 | + | 3.35533i | 0.323366 | + | 0.186695i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.77489 | 0.153687 | ||||||||
\(327\) | −8.90410 | − | 5.14078i | −0.492398 | − | 0.284286i | ||||
\(328\) | −0.587246 | + | 1.01714i | −0.0324252 | + | 0.0561622i | ||||
\(329\) | −1.85408 | − | 3.21135i | −0.102218 | − | 0.177048i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.05268 | + | 3.49452i | −0.332686 | + | 0.192076i | −0.657033 | − | 0.753862i | \(-0.728189\pi\) |
0.324347 | + | 0.945938i | \(0.394855\pi\) | |||||||
\(332\) | 3.33341 | − | 1.92455i | 0.182945 | − | 0.105623i | ||||
\(333\) | − | 9.15988i | − | 0.501958i | ||||||
\(334\) | −11.1022 | − | 19.2296i | −0.607485 | − | 1.05220i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.807007 | − | 0.465926i | −0.0440259 | − | 0.0254183i | ||||
\(337\) | 35.3229 | 1.92416 | 0.962082 | − | 0.272761i | \(-0.0879369\pi\) | ||||
0.962082 | + | 0.272761i | \(0.0879369\pi\) | |||||||
\(338\) | 0.500000 | − | 12.9904i | 0.0271964 | − | 0.706584i | ||||
\(339\) | 9.65685 | 0.524488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.81779 | + | 13.5408i | −0.423357 | + | 0.733276i | ||||
\(342\) | −1.31431 | − | 2.27646i | −0.0710699 | − | 0.123097i | ||||
\(343\) | 12.2368i | 0.660723i | ||||||||
\(344\) | 2.55695 | − | 1.47626i | 0.137862 | − | 0.0795945i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 0.950627i | − | 0.0511060i | ||||||
\(347\) | 1.80920 | + | 3.13363i | 0.0971232 | + | 0.168222i | 0.910493 | − | 0.413525i | \(-0.135703\pi\) |
−0.813370 | + | 0.581747i | \(0.802369\pi\) | |||||||
\(348\) | −1.69419 | + | 2.93443i | −0.0908184 | + | 0.157302i | ||||
\(349\) | −25.1956 | − | 14.5467i | −1.34869 | − | 0.778667i | −0.360627 | − | 0.932710i | \(-0.617437\pi\) |
−0.988064 | + | 0.154043i | \(0.950771\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.86250 | − | 3.08725i | 0.0994130 | − | 0.164785i | ||||
\(352\) | −1.68216 | −0.0896596 | ||||||||
\(353\) | 8.30867 | + | 4.79701i | 0.442226 | + | 0.255319i | 0.704541 | − | 0.709663i | \(-0.251153\pi\) |
−0.262315 | + | 0.964982i | \(0.584486\pi\) | |||||||
\(354\) | 1.98709 | − | 3.44174i | 0.105613 | − | 0.182926i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.4670i | 0.713751i | ||||||||
\(357\) | −2.06022 | + | 1.18947i | −0.109038 | + | 0.0629534i | ||||
\(358\) | 8.55904 | − | 4.94156i | 0.452359 | − | 0.261170i | ||||
\(359\) | − | 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 | ||||
\(362\) | 12.3855 | + | 7.15075i | 0.650965 | + | 0.375835i | ||||
\(363\) | 8.17033 | 0.428831 | ||||||||
\(364\) | 2.94148 | − | 1.62364i | 0.154175 | − | 0.0851020i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.55500 | − | 4.36188i | −0.394906 | − | 0.227999i | ||||
\(367\) | −17.4472 | + | 30.2194i | −0.910735 | + | 1.57744i | −0.0977071 | + | 0.995215i | \(0.531151\pi\) |
−0.813028 | + | 0.582224i | \(0.802182\pi\) | |||||||
\(368\) | 3.22853 | + | 5.59197i | 0.168299 | + | 0.291502i | ||||
\(369\) | − | 1.17449i | − | 0.0611416i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.32611 | + | 2.49768i | −0.224600 | + | 0.129673i | ||||
\(372\) | − | 9.29493i | − | 0.481920i | ||||||
\(373\) | 2.40608 | + | 4.16745i | 0.124582 | + | 0.215782i | 0.921569 | − | 0.388213i | \(-0.126908\pi\) |
−0.796987 | + | 0.603996i | \(0.793574\pi\) | |||||||
\(374\) | −2.14721 | + | 3.71907i | −0.111030 | + | 0.192309i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.97934 | 0.205219 | ||||||||
\(377\) | −5.90387 | − | 10.6958i | −0.304065 | − | 0.550861i | ||||
\(378\) | 0.931852 | 0.0479293 | ||||||||
\(379\) | −24.0847 | − | 13.9053i | −1.23715 | − | 0.714267i | −0.268637 | − | 0.963241i | \(-0.586573\pi\) |
−0.968510 | + | 0.248974i | \(0.919907\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.338502 | + | 0.586302i | 0.0173420 | + | 0.0300372i | ||||
\(382\) | 0.114637i | 0.00586532i | ||||||||
\(383\) | 0.697788 | − | 0.402868i | 0.0356553 | − | 0.0205856i | −0.482066 | − | 0.876135i | \(-0.660114\pi\) |
0.517722 | + | 0.855549i | \(0.326780\pi\) | |||||||
\(384\) | 0.866025 | − | 0.500000i | 0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.32843 | − | 7.49706i | −0.220311 | − | 0.381590i | ||||
\(387\) | −1.47626 | + | 2.55695i | −0.0750424 | + | 0.129977i | ||||
\(388\) | 12.1945 | + | 7.04052i | 0.619084 | + | 0.357428i | ||||
\(389\) | −27.5013 | −1.39437 | −0.697186 | − | 0.716891i | \(-0.745565\pi\) | ||||
−0.697186 | + | 0.716891i | \(0.745565\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.4843 | 0.833647 | ||||||||
\(392\) | −5.31017 | − | 3.06583i | −0.268204 | − | 0.154848i | ||||
\(393\) | −0.933552 | + | 1.61696i | −0.0470914 | + | 0.0815648i | ||||
\(394\) | −10.2401 | − | 17.7363i | −0.515887 | − | 0.893542i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.45680 | − | 0.841081i | 0.0732067 | − | 0.0422659i | ||||
\(397\) | 0.994360 | − | 0.574094i | 0.0499055 | − | 0.0288130i | −0.474840 | − | 0.880072i | \(-0.657494\pi\) |
0.524745 | + | 0.851259i | \(0.324161\pi\) | |||||||
\(398\) | 1.91067i | 0.0957733i | ||||||||
\(399\) | 1.22474 | + | 2.12132i | 0.0613139 | + | 0.106199i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8647 | + | 6.85009i | 0.592495 | + | 0.342077i | 0.766083 | − | 0.642741i | \(-0.222203\pi\) |
−0.173589 | + | 0.984818i | \(0.555536\pi\) | |||||||
\(402\) | −5.19151 | −0.258929 | ||||||||
\(403\) | 28.6957 | + | 17.3118i | 1.42944 | + | 0.862363i | ||||
\(404\) | −11.3178 | −0.563083 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.57874 | − | 2.73445i | 0.0783515 | − | 0.135709i | ||||
\(407\) | 7.70420 | + | 13.3441i | 0.381883 | + | 0.661441i | ||||
\(408\) | − | 2.55291i | − | 0.126388i | ||||||
\(409\) | −6.63613 | + | 3.83137i | −0.328136 | + | 0.189449i | −0.655013 | − | 0.755618i | \(-0.727337\pi\) |
0.326878 | + | 0.945067i | \(0.394004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7.28861i | − | 0.359521i | ||||||
\(412\) | −0.362501 | − | 0.627871i | −0.0178592 | − | 0.0309330i | ||||
\(413\) | −1.85167 | + | 3.20719i | −0.0911148 | + | 0.157815i | ||||
\(414\) | −5.59197 | − | 3.22853i | −0.274830 | − | 0.158673i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0693504 | + | 3.60488i | −0.00340018 | + | 0.176744i | ||||
\(417\) | 4.71139 | 0.230718 | ||||||||
\(418\) | 3.82937 | + | 2.21089i | 0.187301 | + | 0.108138i | ||||
\(419\) | 19.5013 | − | 33.7773i | 0.952701 | − | 1.65013i | 0.213159 | − | 0.977018i | \(-0.431625\pi\) |
0.739543 | − | 0.673110i | \(-0.235042\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 32.7923i | − | 1.59820i | −0.601198 | − | 0.799100i | \(-0.705310\pi\) | ||
0.601198 | − | 0.799100i | \(-0.294690\pi\) | |||||||
\(422\) | −1.07408 | + | 0.620118i | −0.0522852 | + | 0.0301869i | ||||
\(423\) | −3.44621 | + | 1.98967i | −0.167560 | + | 0.0967410i | ||||
\(424\) | − | 5.36068i | − | 0.260337i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.96763 | + | 3.40803i | −0.0953318 | + | 0.165119i | ||||
\(427\) | 7.04014 | + | 4.06462i | 0.340696 | + | 0.196701i | ||||
\(428\) | −17.2173 | −0.832231 | ||||||||
\(429\) | −0.116659 | + | 6.06400i | −0.00563233 | + | 0.292773i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.6031 | − | 16.5140i | −1.37776 | − | 0.795452i | −0.385873 | − | 0.922552i | \(-0.626100\pi\) |
−0.991890 | + | 0.127100i | \(0.959433\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 4.49706 | + | 7.78913i | 0.216115 | + | 0.374322i | 0.953617 | − | 0.301023i | \(-0.0973282\pi\) |
−0.737502 | + | 0.675345i | \(0.763995\pi\) | |||||||
\(434\) | 8.66150i | 0.415765i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.90410 | + | 5.14078i | −0.426429 | + | 0.246199i | ||||
\(437\) | − | 16.9732i | − | 0.811937i | ||||||
\(438\) | 3.63165 | + | 6.29021i | 0.173527 | + | 0.300558i | ||||
\(439\) | 3.65685 | − | 6.33386i | 0.174532 | − | 0.302299i | −0.765467 | − | 0.643475i | \(-0.777492\pi\) |
0.939999 | + | 0.341176i | \(0.110825\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.13165 | 0.291983 | ||||||||
\(442\) | 7.88147 | + | 4.75481i | 0.374884 | + | 0.226163i | ||||
\(443\) | −27.5200 | −1.30752 | −0.653758 | − | 0.756703i | \(-0.726809\pi\) | ||||
−0.653758 | + | 0.756703i | \(0.726809\pi\) | |||||||
\(444\) | −7.93269 | − | 4.57994i | −0.376469 | − | 0.217354i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.38915 | − | 12.7984i | −0.349886 | − | 0.606021i | ||||
\(447\) | − | 3.00240i | − | 0.142009i | ||||||
\(448\) | −0.807007 | + | 0.465926i | −0.0381275 | + | 0.0220129i | ||||
\(449\) | 8.88390 | − | 5.12912i | 0.419257 | − | 0.242058i | −0.275502 | − | 0.961300i | \(-0.588844\pi\) |
0.694760 | + | 0.719242i | \(0.255511\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.987844 | + | 1.71100i | 0.0465157 | + | 0.0805676i | ||||
\(452\) | 4.82843 | − | 8.36308i | 0.227110 | − | 0.393366i | ||||
\(453\) | −10.7561 | − | 6.21001i | −0.505363 | − | 0.291772i | ||||
\(454\) | −9.56580 | −0.448945 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.62863 | −0.123097 | ||||||||
\(457\) | −12.7653 | − | 7.37005i | −0.597135 | − | 0.344756i | 0.170778 | − | 0.985309i | \(-0.445372\pi\) |
−0.767914 | + | 0.640553i | \(0.778705\pi\) | |||||||
\(458\) | −7.57389 | + | 13.1184i | −0.353905 | + | 0.612981i | ||||
\(459\) | 1.27646 | + | 2.21089i | 0.0595799 | + | 0.103195i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.1993 | − | 9.93003i | 0.801052 | − | 0.462487i | −0.0427870 | − | 0.999084i | \(-0.513624\pi\) |
0.843839 | + | 0.536597i | \(0.180290\pi\) | |||||||
\(462\) | −1.35752 | + | 0.783763i | −0.0631574 | + | 0.0364640i | ||||
\(463\) | 32.1533i | 1.49429i | 0.664662 | + | 0.747144i | \(0.268576\pi\) | ||||
−0.664662 | + | 0.747144i | \(0.731424\pi\) | |||||||
\(464\) | 1.69419 | + | 2.93443i | 0.0786510 | + | 0.136228i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.2304 | + | 9.37064i | 0.751860 | + | 0.434087i | ||||
\(467\) | −22.2754 | −1.03078 | −0.515392 | − | 0.856955i | \(-0.672354\pi\) | ||||
−0.515392 | + | 0.856955i | \(0.672354\pi\) | |||||||
\(468\) | −1.74238 | − | 3.15660i | −0.0805417 | − | 0.145914i | ||||
\(469\) | 4.83772 | 0.223385 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.2609 | + | 19.5044i | −0.518873 | + | 0.898714i | ||||
\(472\) | −1.98709 | − | 3.44174i | −0.0914631 | − | 0.158419i | ||||
\(473\) | − | 4.96661i | − | 0.228365i | ||||||
\(474\) | 3.19540 | − | 1.84486i | 0.146769 | − | 0.0847374i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.37894i | 0.109038i | ||||||||
\(477\) | 2.68034 | + | 4.64248i | 0.122724 | + | 0.212565i | ||||
\(478\) | −2.31165 | + | 4.00390i | −0.105732 | + | 0.183134i | ||||
\(479\) | −19.0007 | − | 10.9700i | −0.868163 | − | 0.501234i | −0.00142578 | − | 0.999999i | \(-0.500454\pi\) |
−0.866737 | + | 0.498765i | \(0.833787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.9140 | − | 15.9600i | 1.31837 | − | 0.727714i | ||||
\(482\) | 17.5945 | 0.801408 | ||||||||
\(483\) | 5.21089 | + | 3.00851i | 0.237104 | + | 0.136892i | ||||
\(484\) | 4.08516 | − | 7.07571i | 0.185689 | − | 0.321623i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 7.84015 | − | 4.52651i | 0.355271 | − | 0.205116i | −0.311733 | − | 0.950170i | \(-0.600910\pi\) |
0.667004 | + | 0.745054i | \(0.267576\pi\) | |||||||
\(488\) | −7.55500 | + | 4.36188i | −0.341999 | + | 0.197453i | ||||
\(489\) | 2.77489i | 0.125485i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.1000 | + | 26.1540i | −0.681455 | + | 1.18031i | 0.293082 | + | 0.956087i | \(0.405319\pi\) |
−0.974537 | + | 0.224227i | \(0.928014\pi\) | |||||||
\(492\) | −1.01714 | − | 0.587246i | −0.0458562 | − | 0.0264751i | ||||
\(493\) | 8.65027 | 0.389588 | ||||||||
\(494\) | 4.89582 | − | 8.11522i | 0.220273 | − | 0.365121i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.04965 | − | 4.64747i | −0.361440 | − | 0.208677i | ||||
\(497\) | 1.83354 | − | 3.17578i | 0.0822453 | − | 0.142453i | ||||
\(498\) | 1.92455 | + | 3.33341i | 0.0862410 | + | 0.149374i | ||||
\(499\) | 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 | ||||
\(502\) | − | 26.5198i | − | 1.18364i | ||||||
\(503\) | 15.5446 | + | 26.9241i | 0.693101 | + | 1.20049i | 0.970817 | + | 0.239823i | \(0.0770894\pi\) |
−0.277715 | + | 0.960663i | \(0.589577\pi\) | |||||||
\(504\) | 0.465926 | − | 0.807007i | 0.0207540 | − | 0.0359470i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.8618 | 0.482867 | ||||||||
\(507\) | 12.9904 | + | 0.500000i | 0.576923 | + | 0.0222058i | ||||
\(508\) | 0.677003 | 0.0300372 | ||||||||
\(509\) | −22.5466 | − | 13.0173i | −0.999361 | − | 0.576981i | −0.0913018 | − | 0.995823i | \(-0.529103\pi\) |
−0.908059 | + | 0.418842i | \(0.862436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.38416 | − | 5.86154i | −0.149706 | − | 0.259299i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.27646 | − | 1.31431i | 0.100508 | − | 0.0580283i | ||||
\(514\) | −1.57986 | + | 0.912132i | −0.0696846 | + | 0.0402324i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.47626 | + | 2.55695i | 0.0649886 | + | 0.112564i | ||||
\(517\) | 3.34695 | − | 5.79708i | 0.147198 | − | 0.254955i | ||||
\(518\) | 7.39209 | + | 4.26782i | 0.324790 | + | 0.187517i | ||||
\(519\) | 0.950627 | 0.0417279 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.8332 | −1.08796 | −0.543982 | − | 0.839097i | \(-0.683084\pi\) | ||||
−0.543982 | + | 0.839097i | \(0.683084\pi\) | |||||||
\(522\) | −2.93443 | − | 1.69419i | −0.128437 | − | 0.0741529i | ||||
\(523\) | 4.20445 | − | 7.28231i | 0.183848 | − | 0.318433i | −0.759340 | − | 0.650694i | \(-0.774478\pi\) |
0.943188 | + | 0.332261i | \(0.107811\pi\) | |||||||
\(524\) | 0.933552 | + | 1.61696i | 0.0407824 | + | 0.0706372i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.5106 | + | 6.06828i | −0.458283 | + | 0.264590i | ||||
\(527\) | −20.5501 | + | 11.8646i | −0.895175 | + | 0.516829i | ||||
\(528\) | − | 1.68216i | − | 0.0732067i | ||||||
\(529\) | −9.34677 | − | 16.1891i | −0.406381 | − | 0.703873i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.44174 | + | 1.98709i | 0.149359 | + | 0.0862323i | ||||
\(532\) | 2.44949 | 0.106199 | ||||||||
\(533\) | 3.70740 | − | 2.04642i | 0.160585 | − | 0.0886401i | ||||
\(534\) | −13.4670 | −0.582775 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.59575 | + | 4.49598i | −0.112120 | + | 0.194197i | ||||
\(537\) | 4.94156 | + | 8.55904i | 0.213244 | + | 0.369350i | ||||
\(538\) | − | 23.5310i | − | 1.01449i | ||||||
\(539\) | −8.93256 | + | 5.15722i | −0.384753 | + | 0.222137i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7195i | 0.675833i | 0.941176 | + | 0.337916i | \(0.109722\pi\) | ||||
−0.941176 | + | 0.337916i | \(0.890278\pi\) | |||||||
\(542\) | 6.34349 | + | 10.9872i | 0.272476 | + | 0.471942i | ||||
\(543\) | −7.15075 | + | 12.3855i | −0.306868 | + | 0.531511i | ||||
\(544\) | −2.21089 | − | 1.27646i | −0.0947911 | − | 0.0547276i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.62364 | + | 2.94148i | 0.0694855 | + | 0.125884i | ||||
\(547\) | 23.0313 | 0.984745 | 0.492373 | − | 0.870385i | \(-0.336130\pi\) | ||||
0.492373 | + | 0.870385i | \(0.336130\pi\) | |||||||
\(548\) | −6.31212 | − | 3.64431i | −0.269641 | − | 0.155677i | ||||
\(549\) | 4.36188 | − | 7.55500i | 0.186160 | − | 0.322439i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.90681i | − | 0.379443i | ||||||
\(552\) | −5.59197 | + | 3.22853i | −0.238010 | + | 0.137415i | ||||
\(553\) | −2.97764 | + | 1.71914i | −0.126622 | + | 0.0731052i | ||||
\(554\) | − | 12.8235i | − | 0.544820i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.35569 | − | 4.08018i | 0.0999036 | − | 0.173038i | ||||
\(557\) | 35.2097 | + | 20.3283i | 1.49188 | + | 0.861339i | 0.999957 | − | 0.00929877i | \(-0.00295993\pi\) |
0.491925 | + | 0.870637i | \(0.336293\pi\) | |||||||
\(558\) | 9.29493 | 0.393486 | ||||||||
\(559\) | −10.6435 | − | 0.204758i | −0.450171 | − | 0.00866034i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.71907 | − | 2.14721i | −0.157019 | − | 0.0906552i | ||||
\(562\) | −2.58360 | + | 4.47492i | −0.108982 | + | 0.188763i | ||||
\(563\) | 1.71770 | + | 2.97514i | 0.0723923 | + | 0.125387i | 0.899949 | − | 0.435995i | \(-0.143603\pi\) |
−0.827557 | + | 0.561382i | \(0.810270\pi\) | |||||||
\(564\) | 3.97934i | 0.167560i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.2258 | − | 6.48124i | 0.471857 | − | 0.272427i | ||||
\(567\) | 0.931852i | 0.0391341i | ||||||||
\(568\) | 1.96763 | + | 3.40803i | 0.0825597 | + | 0.142998i | ||||
\(569\) | −11.0320 | + | 19.1079i | −0.462484 | + | 0.801046i | −0.999084 | − | 0.0427908i | \(-0.986375\pi\) |
0.536600 | + | 0.843837i | \(0.319708\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.56829 | 0.191177 | 0.0955885 | − | 0.995421i | \(-0.469527\pi\) | ||||
0.0955885 | + | 0.995421i | \(0.469527\pi\) | |||||||
\(572\) | 5.19325 | + | 3.13303i | 0.217141 | + | 0.130999i | ||||
\(573\) | −0.114637 | −0.00478901 | ||||||||
\(574\) | 0.947824 | + | 0.547226i | 0.0395614 | + | 0.0228408i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 4.42655i | − | 0.184280i | −0.995746 | − | 0.0921398i | \(-0.970629\pi\) | ||
0.995746 | − | 0.0921398i | \(-0.0293707\pi\) | |||||||
\(578\) | 9.07822 | − | 5.24131i | 0.377604 | − | 0.218010i | ||||
\(579\) | 7.49706 | − | 4.32843i | 0.311567 | − | 0.179883i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.79339 | − | 3.10624i | −0.0744024 | − | 0.128869i | ||||
\(582\) | −7.04052 | + | 12.1945i | −0.291839 | + | 0.505480i | ||||
\(583\) | −7.80941 | − | 4.50877i | −0.323433 | − | 0.186734i | ||||
\(584\) | 7.26330 | 0.300558 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.4704 | 0.556458 | ||||||||
\(587\) | −37.3725 | − | 21.5770i | −1.54253 | − | 0.890580i | −0.998678 | − | 0.0513987i | \(-0.983632\pi\) |
−0.543852 | − | 0.839181i | \(-0.683035\pi\) | |||||||
\(588\) | 3.06583 | − | 5.31017i | 0.126433 | − | 0.218988i | ||||
\(589\) | 12.2165 | + | 21.1595i | 0.503370 | + | 0.871863i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.7363 | − | 10.2401i | 0.729574 | − | 0.421220i | ||||
\(592\) | −7.93269 | + | 4.57994i | −0.326032 | + | 0.188234i | ||||
\(593\) | 28.8372i | 1.18420i | 0.805864 | + | 0.592101i | \(0.201701\pi\) | ||||
−0.805864 | + | 0.592101i | \(0.798299\pi\) | |||||||
\(594\) | 0.841081 | + | 1.45680i | 0.0345100 | + | 0.0597731i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.60016 | − | 1.50120i | −0.106507 | − | 0.0614916i | ||||
\(597\) | −1.91067 | −0.0781986 | ||||||||
\(598\) | 0.447799 | − | 23.2769i | 0.0183119 | − | 0.951864i | ||||
\(599\) | −28.1704 | −1.15101 | −0.575505 | − | 0.817798i | \(-0.695194\pi\) | ||||
−0.575505 | + | 0.817798i | \(0.695194\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.31925 | − | 12.6773i | 0.298558 | − | 0.517118i | −0.677248 | − | 0.735755i | \(-0.736828\pi\) |
0.975806 | + | 0.218637i | \(0.0701610\pi\) | |||||||
\(602\) | −1.37565 | − | 2.38270i | −0.0560674 | − | 0.0971117i | ||||
\(603\) | − | 5.19151i | − | 0.211415i | ||||||
\(604\) | −10.7561 | + | 6.21001i | −0.437657 | + | 0.252682i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 11.3178i | − | 0.459756i | ||||||
\(607\) | 6.50853 | + | 11.2731i | 0.264173 | + | 0.457561i | 0.967347 | − | 0.253457i | \(-0.0815677\pi\) |
−0.703174 | + | 0.711018i | \(0.748234\pi\) | |||||||
\(608\) | −1.31431 | + | 2.27646i | −0.0533024 | + | 0.0923225i | ||||
\(609\) | 2.73445 | + | 1.57874i | 0.110806 | + | 0.0639737i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2852 | − | 7.41152i | −0.497006 | − | 0.299838i | ||||
\(612\) | 2.55291 | 0.103195 | ||||||||
\(613\) | −23.5813 | − | 13.6146i | −0.952438 | − | 0.549890i | −0.0586006 | − | 0.998282i | \(-0.518664\pi\) |
−0.893837 | + | 0.448391i | \(0.851997\pi\) | |||||||
\(614\) | 10.7310 | − | 18.5866i | 0.433067 | − | 0.750094i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.56753i | 0.0631574i | ||||||||
\(617\) | 20.3825 | − | 11.7678i | 0.820569 | − | 0.473755i | −0.0300439 | − | 0.999549i | \(-0.509565\pi\) |
0.850613 | + | 0.525793i | \(0.176231\pi\) | |||||||
\(618\) | 0.627871 | − | 0.362501i | 0.0252567 | − | 0.0145819i | ||||
\(619\) | 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 | ||||
\(622\) | −12.7792 | − | 7.37808i | −0.512399 | − | 0.295834i | ||||
\(623\) | 12.5493 | 0.502776 | ||||||||
\(624\) | −3.60488 | − | 0.0693504i | −0.144311 | − | 0.00277624i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.21625 | + | 0.702205i | 0.0486113 | + | 0.0280658i | ||||
\(627\) | −2.21089 | + | 3.82937i | −0.0882944 | + | 0.152930i | ||||
\(628\) | 11.2609 | + | 19.5044i | 0.449357 | + | 0.778309i | ||||
\(629\) | 23.3844i | 0.932397i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.3378 | + | 8.27792i | −0.570778 | + | 0.329539i | −0.757460 | − | 0.652882i | \(-0.773560\pi\) |
0.186682 | + | 0.982420i | \(0.440227\pi\) | |||||||
\(632\) | − | 3.68973i | − | 0.146769i | ||||||
\(633\) | −0.620118 | − | 1.07408i | −0.0246475 | − | 0.0426907i | ||||
\(634\) | 16.5710 | − | 28.7019i | 0.658119 | − | 1.13990i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.36068 | 0.212565 | ||||||||
\(637\) | 10.6837 | + | 19.3552i | 0.423303 | + | 0.766879i | ||||
\(638\) | 5.69982 | 0.225658 | ||||||||
\(639\) | −3.40803 | − | 1.96763i | −0.134819 | − | 0.0778381i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.390454 | − | 0.676286i | −0.0154220 | − | 0.0267117i | 0.858211 | − | 0.513296i | \(-0.171576\pi\) |
−0.873633 | + | 0.486585i | \(0.838243\pi\) | |||||||
\(642\) | − | 17.2173i | − | 0.679514i | ||||||
\(643\) | −21.2597 | + | 12.2743i | −0.838399 | + | 0.484050i | −0.856720 | − | 0.515782i | \(-0.827501\pi\) |
0.0183207 | + | 0.999832i | \(0.494168\pi\) | |||||||
\(644\) | 5.21089 | − | 3.00851i | 0.205338 | − | 0.118552i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.35533 | + | 5.81160i | 0.132014 | + | 0.228654i | ||||
\(647\) | 1.58200 | − | 2.74011i | 0.0621950 | − | 0.107725i | −0.833251 | − | 0.552894i | \(-0.813523\pi\) |
0.895446 | + | 0.445170i | \(0.146857\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | −6.68521 | −0.262417 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.66150 | −0.339471 | ||||||||
\(652\) | 2.40313 | + | 1.38745i | 0.0941137 | + | 0.0543366i | ||||
\(653\) | −16.1443 | + | 27.9627i | −0.631774 | + | 1.09426i | 0.355415 | + | 0.934709i | \(0.384340\pi\) |
−0.987189 | + | 0.159556i | \(0.948994\pi\) | |||||||
\(654\) | −5.14078 | − | 8.90410i | −0.201021 | − | 0.348178i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.01714 | + | 0.587246i | −0.0397127 | + | 0.0229281i | ||||
\(657\) | −6.29021 | + | 3.63165i | −0.245404 | + | 0.141684i | ||||
\(658\) | − | 3.70815i | − | 0.144559i | ||||||
\(659\) | −17.6775 | − | 30.6184i | −0.688619 | − | 1.19272i | −0.972285 | − | 0.233799i | \(-0.924884\pi\) |
0.283666 | − | 0.958923i | \(-0.408449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.9243 | + | 9.77124i | 0.658279 | + | 0.380057i | 0.791621 | − | 0.611013i | \(-0.209238\pi\) |
−0.133342 | + | 0.991070i | \(0.542571\pi\) | |||||||
\(662\) | −6.98904 | −0.271637 | ||||||||
\(663\) | −4.75481 | + | 7.88147i | −0.184661 | + | 0.306091i | ||||
\(664\) | 3.84909 | 0.149374 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.57994 | − | 7.93269i | 0.177469 | − | 0.307385i | ||||
\(667\) | −10.9395 | − | 18.9478i | −0.423579 | − | 0.733661i | ||||
\(668\) | − | 22.2044i | − | 0.859114i | ||||||
\(669\) | 12.7984 | − | 7.38915i | 0.494814 | − | 0.285681i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.6748i | 0.566514i | ||||||||
\(672\) | −0.465926 | − | 0.807007i | −0.0179735 | − | 0.0311310i | ||||
\(673\) | −1.25806 | + | 2.17903i | −0.0484948 | + | 0.0839954i | −0.889254 | − | 0.457414i | \(-0.848776\pi\) |
0.840759 | + | 0.541409i | \(0.182109\pi\) | |||||||
\(674\) | 30.5906 | + | 17.6615i | 1.17830 | + | 0.680295i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.92820 | − | 11.0000i | 0.266469 | − | 0.423077i | ||||
\(677\) | 41.0114 | 1.57620 | 0.788098 | − | 0.615550i | \(-0.211066\pi\) | ||||
0.788098 | + | 0.615550i | \(0.211066\pi\) | |||||||
\(678\) | 8.36308 | + | 4.82843i | 0.321182 | + | 0.185435i | ||||
\(679\) | 6.56072 | − | 11.3635i | 0.251777 | − | 0.436091i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 9.56580i | − | 0.366562i | ||||||
\(682\) | −13.5408 | + | 7.81779i | −0.518505 | + | 0.299359i | ||||
\(683\) | −20.9177 | + | 12.0769i | −0.800395 | + | 0.462108i | −0.843609 | − | 0.536958i | \(-0.819574\pi\) |
0.0432142 | + | 0.999066i | \(0.486240\pi\) | |||||||
\(684\) | − | 2.62863i | − | 0.100508i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.11838 | + | 10.5973i | −0.233601 | + | 0.404608i | ||||
\(687\) | −13.1184 | − | 7.57389i | −0.500497 | − | 0.288962i | ||||
\(688\) | 2.95252 | 0.112564 | ||||||||
\(689\) | −9.98427 | + | 16.5497i | −0.380370 | + | 0.630494i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.7340 | − | 20.6310i | −1.35939 | − | 0.784841i | −0.369844 | − | 0.929094i | \(-0.620589\pi\) |
−0.989541 | + | 0.144252i | \(0.953922\pi\) | |||||||
\(692\) | 0.475314 | − | 0.823267i | 0.0180687 | − | 0.0312959i | ||||
\(693\) | −0.783763 | − | 1.35752i | −0.0297727 | − | 0.0515678i | ||||
\(694\) | 3.61841i | 0.137353i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.93443 | + | 1.69419i | −0.111229 | + | 0.0642183i | ||||
\(697\) | 2.99838i | 0.113572i | ||||||||
\(698\) | −14.5467 | − | 25.1956i | −0.550601 | − | 0.953669i | ||||
\(699\) | −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 | \(0.327671\pi\) | |||||||
\(702\) | 3.15660 | − | 1.74238i | 0.119138 | − | 0.0657620i | ||||
\(703\) | 24.0779 | 0.908115 | ||||||||
\(704\) | −1.45680 | − | 0.841081i | −0.0549051 | − | 0.0316994i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.79701 | + | 8.30867i | 0.180538 | + | 0.312701i | ||||
\(707\) | 10.5465i | 0.396644i | ||||||||
\(708\) | 3.44174 | − | 1.98709i | 0.129348 | − | 0.0746793i | ||||
\(709\) | 2.18928 | − | 1.26398i | 0.0822200 | − | 0.0474697i | −0.458326 | − | 0.888784i | \(-0.651551\pi\) |
0.540546 | + | 0.841314i | \(0.318218\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.84486 | + | 3.19540i | 0.0691878 | + | 0.119837i | ||||
\(712\) | −6.73351 | + | 11.6628i | −0.252349 | + | 0.437081i | ||||
\(713\) | 51.9770 | + | 30.0089i | 1.94655 | + | 1.12384i | ||||
\(714\) | −2.37894 | −0.0890295 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.88312 | 0.369350 | ||||||||
\(717\) | −4.00390 | − | 2.31165i | −0.149528 | − | 0.0863302i | ||||
\(718\) | 3.15748 | − | 5.46891i | 0.117836 | − | 0.204098i | ||||
\(719\) | 26.6943 | + | 46.2359i | 0.995530 | + | 1.72431i | 0.579562 | + | 0.814928i | \(0.303224\pi\) |
0.415968 | + | 0.909379i | \(0.363443\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.585082 | + | 0.337797i | −0.0217896 | + | 0.0125802i | ||||
\(722\) | −10.4705 | + | 6.04516i | −0.389673 | + | 0.224978i | ||||
\(723\) | 17.5945i | 0.654347i | ||||||||
\(724\) | 7.15075 | + | 12.3855i | 0.265756 | + | 0.460302i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.07571 | + | 4.08516i | 0.262604 | + | 0.151615i | ||||
\(727\) | −2.09614 | −0.0777417 | −0.0388709 | − | 0.999244i | \(-0.512376\pi\) | ||||
−0.0388709 | + | 0.999244i | \(0.512376\pi\) | |||||||
\(728\) | 3.35922 | + | 0.0646242i | 0.124501 | + | 0.00239513i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.76876 | − | 6.52768i | 0.139393 | − | 0.241435i | ||||
\(732\) | −4.36188 | − | 7.55500i | −0.161220 | − | 0.279241i | ||||
\(733\) | − | 16.7827i | − | 0.619883i | −0.950756 | − | 0.309942i | \(-0.899690\pi\) | ||
0.950756 | − | 0.309942i | \(-0.100310\pi\) | |||||||
\(734\) | −30.2194 | + | 17.4472i | −1.11542 | + | 0.643987i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.45705i | 0.238010i | ||||||||
\(737\) | 4.36648 | + | 7.56297i | 0.160841 | + | 0.278585i | ||||
\(738\) | 0.587246 | − | 1.01714i | 0.0216168 | − | 0.0374414i | ||||
\(739\) | 8.24563 | + | 4.76062i | 0.303321 | + | 0.175122i | 0.643934 | − | 0.765081i | \(-0.277301\pi\) |
−0.340613 | + | 0.940204i | \(0.610635\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.11522 | + | 4.89582i | 0.298120 | + | 0.179852i | ||||
\(742\) | −4.99536 | −0.183385 | ||||||||
\(743\) | −28.2034 | − | 16.2832i | −1.03468 | − | 0.597374i | −0.116360 | − | 0.993207i | \(-0.537123\pi\) |
−0.918323 | + | 0.395833i | \(0.870456\pi\) | |||||||
\(744\) | 4.64747 | − | 8.04965i | 0.170384 | − | 0.295114i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.81216i | 0.176186i | ||||||||
\(747\) | −3.33341 | + | 1.92455i | −0.121963 | + | 0.0704154i | ||||
\(748\) | −3.71907 | + | 2.14721i | −0.135983 | + | 0.0785097i | ||||
\(749\) | 16.0440i | 0.586235i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.38117 | + | 12.7846i | −0.269343 | + | 0.466515i | −0.968692 | − | 0.248265i | \(-0.920140\pi\) |
0.699350 | + | 0.714780i | \(0.253473\pi\) | |||||||
\(752\) | 3.44621 | + | 1.98967i | 0.125670 | + | 0.0725557i | ||||
\(753\) | 26.5198 | 0.966436 | ||||||||
\(754\) | 0.234986 | − | 12.2148i | 0.00855769 | − | 0.444835i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.807007 | + | 0.465926i | 0.0293506 | + | 0.0169456i | ||||
\(757\) | −17.5781 | + | 30.4462i | −0.638888 | + | 1.10659i | 0.346789 | + | 0.937943i | \(0.387272\pi\) |
−0.985677 | + | 0.168643i | \(0.946061\pi\) | |||||||
\(758\) | −13.9053 | − | 24.0847i | −0.505063 | − | 0.874795i | ||||
\(759\) | 10.8618i | 0.394259i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.2215 | + | 20.9125i | −1.31303 | + | 0.758076i | −0.982596 | − | 0.185754i | \(-0.940527\pi\) |
−0.330431 | + | 0.943830i | \(0.607194\pi\) | |||||||
\(762\) | 0.677003i | 0.0245252i | ||||||||
\(763\) | 4.79045 | + | 8.29730i | 0.173426 | + | 0.300382i | ||||
\(764\) | −0.0573183 | + | 0.0992782i | −0.00207370 | + | 0.00359176i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.805736 | 0.0291124 | ||||||||
\(767\) | −0.275611 | + | 14.3264i | −0.00995172 | + | 0.517298i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 39.4957 | + | 22.8028i | 1.42425 | + | 0.822291i | 0.996659 | − | 0.0816812i | \(-0.0260289\pi\) |
0.427591 | + | 0.903972i | \(0.359362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.912132 | − | 1.57986i | −0.0328496 | − | 0.0568972i | ||||
\(772\) | − | 8.65685i | − | 0.311567i | ||||||
\(773\) | −10.9424 | + | 6.31759i | −0.393570 | + | 0.227228i | −0.683706 | − | 0.729758i | \(-0.739633\pi\) |
0.290136 | + | 0.956986i | \(0.406300\pi\) | |||||||
\(774\) | −2.55695 | + | 1.47626i | −0.0919078 | + | 0.0530630i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.04052 | + | 12.1945i | 0.252740 | + | 0.437758i | ||||
\(777\) | −4.26782 | + | 7.39209i | −0.153107 | + | 0.265190i | ||||
\(778\) | −23.8168 | − | 13.7507i | −0.853875 | − | 0.492985i | ||||
\(779\) | 3.08730 | 0.110614 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.61973 | 0.236873 | ||||||||
\(782\) | 14.2758 | + | 8.24215i | 0.510502 | + | 0.294739i | ||||
\(783\) | 1.69419 | − | 2.93443i | 0.0605456 | − | 0.104868i | ||||
\(784\) | −3.06583 | − | 5.31017i | −0.109494 | − | 0.189649i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.61696 | + | 0.933552i | −0.0576750 | + | 0.0332987i | ||||
\(787\) | −45.1559 | + | 26.0708i | −1.60963 | + | 0.929323i | −0.620182 | + | 0.784458i | \(0.712941\pi\) |
−0.989451 | + | 0.144865i | \(0.953725\pi\) | |||||||
\(788\) | − | 20.4801i | − | 0.729574i | ||||||
\(789\) | −6.06828 | − | 10.5106i | −0.216037 | − | 0.374186i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.79315 | − | 4.49938i | −0.277093 | − | 0.159979i | ||||
\(792\) | 1.68216 | 0.0597731 | ||||||||
\(793\) | 31.4481 | + | 0.604996i | 1.11676 | + | 0.0214840i | ||||
\(794\) | 1.14819 | 0.0407477 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.955336 | + | 1.65469i | −0.0338610 | + | 0.0586489i | ||||
\(797\) | −21.3956 | − | 37.0582i | −0.757870 | − | 1.31267i | −0.943935 | − | 0.330132i | \(-0.892907\pi\) |
0.186065 | − | 0.982537i | \(-0.440426\pi\) | |||||||
\(798\) | 2.44949i | 0.0867110i | ||||||||
\(799\) | 8.79787 | − | 5.07945i | 0.311246 | − | 0.179698i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13.4670i | − | 0.475834i | ||||||
\(802\) | 6.85009 | + | 11.8647i | 0.241885 | + | 0.418957i | ||||
\(803\) | 6.10903 | − | 10.5812i | 0.215583 | − | 0.373401i | ||||
\(804\) | −4.49598 | − | 2.59575i | −0.158561 | − | 0.0915452i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.1953 | + | 29.3404i | 0.570456 | + | 1.03347i | ||||
\(807\) | 23.5310 | 0.828331 | ||||||||
\(808\) | −9.80153 | − | 5.65892i | −0.344817 | − | 0.199080i | ||||
\(809\) | −24.3918 | + | 42.2478i | −0.857569 | + | 1.48535i | 0.0166719 | + | 0.999861i | \(0.494693\pi\) |
−0.874241 | + | 0.485492i | \(0.838640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.87402i | − | 0.276494i | −0.990398 | − | 0.138247i | \(-0.955853\pi\) | ||
0.990398 | − | 0.138247i | \(-0.0441468\pi\) | |||||||
\(812\) | 2.73445 | − | 1.57874i | 0.0959606 | − | 0.0554029i | ||||
\(813\) | −10.9872 | + | 6.34349i | −0.385339 | + | 0.222476i | ||||
\(814\) | 15.4084i | 0.540064i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.27646 | − | 2.21089i | 0.0446849 | − | 0.0773966i | ||||
\(817\) | −6.72128 | − | 3.88053i | −0.235148 | − | 0.135763i | ||||
\(818\) | −7.66274 | −0.267922 | ||||||||
\(819\) | −2.94148 | + | 1.62364i | −0.102784 | + | 0.0567347i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.6790 | − | 14.2484i | −0.861304 | − | 0.497274i | 0.00314470 | − | 0.999995i | \(-0.498999\pi\) |
−0.864449 | + | 0.502721i | \(0.832332\pi\) | |||||||
\(822\) | 3.64431 | − | 6.31212i | 0.127110 | − | 0.220161i | ||||
\(823\) | −23.1164 | − | 40.0387i | −0.805786 | − | 1.39566i | −0.915759 | − | 0.401728i | \(-0.868410\pi\) |
0.109973 | − | 0.993935i | \(-0.464924\pi\) | |||||||
\(824\) | − | 0.725003i | − | 0.0252567i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.20719 | + | 1.85167i | −0.111592 | + | 0.0644279i | ||||
\(827\) | − | 9.53716i | − | 0.331640i | −0.986156 | − | 0.165820i | \(-0.946973\pi\) | ||
0.986156 | − | 0.165820i | \(-0.0530270\pi\) | |||||||
\(828\) | −3.22853 | − | 5.59197i | −0.112199 | − | 0.194334i | ||||
\(829\) | 6.64904 | − | 11.5165i | 0.230931 | − | 0.399984i | −0.727152 | − | 0.686477i | \(-0.759156\pi\) |
0.958082 | + | 0.286493i | \(0.0924896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.8235 | 0.444843 | ||||||||
\(832\) | −1.86250 | + | 3.08725i | −0.0645706 | + | 0.107031i | ||||
\(833\) | −15.6536 | −0.542365 | ||||||||
\(834\) | 4.08018 | + | 2.35569i | 0.141285 | + | 0.0815710i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.21089 | + | 3.82937i | 0.0764652 | + | 0.132442i | ||||
\(837\) | 9.29493i | 0.321280i | ||||||||
\(838\) | 33.7773 | − | 19.5013i | 1.16682 | − | 0.673662i | ||||
\(839\) | 42.8848 | − | 24.7595i | 1.48055 | − | 0.854794i | 0.480790 | − | 0.876836i | \(-0.340350\pi\) |
0.999757 | + | 0.0220420i | \(0.00701677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.75941 | + | 15.1717i | 0.302049 | + | 0.523163i | ||||
\(842\) | 16.3962 | − | 28.3990i | 0.565049 | − | 0.978694i | ||||
\(843\) | −4.47492 | − | 2.58360i | −0.154125 | − | 0.0889838i | ||||
\(844\) | −1.24024 | −0.0426907 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.97934 | −0.136812 | ||||||||
\(847\) | −6.59351 | − | 3.80677i | −0.226556 | − | 0.130802i | ||||
\(848\) | 2.68034 | − | 4.64248i | 0.0920432 | − | 0.159424i | ||||
\(849\) | 6.48124 | + | 11.2258i | 0.222436 | + | 0.385270i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.2218 | − | 29.5729i | 1.75586 | − | 1.01375i | ||||
\(852\) | −3.40803 | + | 1.96763i | −0.116757 | + | 0.0674097i | ||||
\(853\) | 6.87904i | 0.235534i | 0.993041 | + | 0.117767i | \(0.0375736\pi\) | ||||
−0.993041 | + | 0.117767i | \(0.962426\pi\) | |||||||
\(854\) | 4.06462 | + | 7.04014i | 0.139089 | + | 0.240908i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.9106 | − | 8.60867i | −0.509635 | − | 0.294238i | ||||
\(857\) | 25.1526 | 0.859198 | 0.429599 | − | 0.903020i | \(-0.358655\pi\) | ||||
0.429599 | + | 0.903020i | \(0.358655\pi\) | |||||||
\(858\) | −3.13303 | + | 5.19325i | −0.106960 | + | 0.177295i | ||||
\(859\) | 52.3171 | 1.78504 | 0.892518 | − | 0.451012i | \(-0.148937\pi\) | ||||
0.892518 | + | 0.451012i | \(0.148937\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.547226 | + | 0.947824i | −0.0186494 | + | 0.0323017i | ||||
\(862\) | −16.5140 | − | 28.6031i | −0.562469 | − | 0.974225i | ||||
\(863\) | 29.9308i | 1.01886i | 0.860513 | + | 0.509428i | \(0.170143\pi\) | ||||
−0.860513 | + | 0.509428i | \(0.829857\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.99411i | 0.305632i | ||||||||
\(867\) | 5.24131 | + | 9.07822i | 0.178004 | + | 0.308313i | ||||
\(868\) | −4.33075 | + | 7.50108i | −0.146995 | + | 0.254603i | ||||
\(869\) | −5.37518 | − | 3.10336i | −0.182340 | − | 0.105274i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.3875 | − | 9.04560i | 0.555269 | − | 0.306498i | ||||
\(872\) | −10.2816 | −0.348178 | ||||||||
\(873\) | −12.1945 | − | 7.04052i | −0.412722 | − | 0.238285i | ||||
\(874\) | 8.48659 | − | 14.6992i | 0.287063 | − | 0.497208i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.26330i | 0.245404i | ||||||||
\(877\) | 13.6363 | − | 7.87295i | 0.460467 | − | 0.265851i | −0.251774 | − | 0.967786i | \(-0.581014\pi\) |
0.712240 | + | 0.701936i | \(0.247681\pi\) | |||||||
\(878\) | 6.33386 | − | 3.65685i | 0.213757 | − | 0.123413i | ||||
\(879\) | 13.4704i | 0.454346i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.56434 | − | 13.1018i | 0.254849 | − | 0.441412i | −0.710005 | − | 0.704196i | \(-0.751308\pi\) |
0.964855 | + | 0.262785i | \(0.0846409\pi\) | |||||||
\(882\) | 5.31017 | + | 3.06583i | 0.178803 | + | 0.103232i | ||||
\(883\) | −54.8263 | −1.84505 | −0.922525 | − | 0.385936i | \(-0.873878\pi\) | ||||
−0.922525 | + | 0.385936i | \(0.873878\pi\) | |||||||
\(884\) | 4.44815 | + | 8.05852i | 0.149608 | + | 0.271037i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.8331 | − | 13.7600i | −0.800687 | − | 0.462277i | ||||
\(887\) | −23.3928 | + | 40.5176i | −0.785454 | + | 1.36045i | 0.143273 | + | 0.989683i | \(0.454237\pi\) |
−0.928727 | + | 0.370763i | \(0.879096\pi\) | |||||||
\(888\) | −4.57994 | − | 7.93269i | −0.153693 | − | 0.266204i | ||||
\(889\) | − | 0.630866i | − | 0.0211586i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.45680 | + | 0.841081i | −0.0488045 | + | 0.0281773i | ||||
\(892\) | − | 14.7783i | − | 0.494814i | ||||||
\(893\) | −5.23009 | − | 9.05879i | −0.175018 | − | 0.303141i | ||||
\(894\) | 1.50120 | − | 2.60016i | 0.0502077 | − | 0.0869623i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.931852 | −0.0311310 | ||||||||
\(897\) | 23.2769 | + | 0.447799i | 0.777194 | + | 0.0149516i | ||||
\(898\) | 10.2582 | 0.342322 | ||||||||
\(899\) | 27.2753 | + | 15.7474i | 0.909684 | + | 0.525206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.84267 | − | 11.8519i | −0.227963 | − | 0.394843i | ||||
\(902\) | 1.97569i | 0.0657832i | ||||||||
\(903\) | 2.38270 | − | 1.37565i | 0.0792913 | − | 0.0457789i | ||||
\(904\) | 8.36308 | − | 4.82843i | 0.278152 | − | 0.160591i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.21001 | − | 10.7561i | −0.206314 | − | 0.357346i | ||||
\(907\) | −14.5536 | + | 25.2077i | −0.483246 | + | 0.837006i | −0.999815 | − | 0.0192392i | \(-0.993876\pi\) |
0.516569 | + | 0.856246i | \(0.327209\pi\) | |||||||
\(908\) | −8.28423 | − | 4.78290i | −0.274922 | − | 0.158726i | ||||
\(909\) | 11.3178 | 0.375389 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.59919 | −0.218641 | −0.109320 | − | 0.994007i | \(-0.534867\pi\) | ||||
−0.109320 | + | 0.994007i | \(0.534867\pi\) | |||||||
\(912\) | −2.27646 | − | 1.31431i | −0.0753810 | − | 0.0435213i | ||||
\(913\) | 3.23740 | − | 5.60734i | 0.107142 | − | 0.185576i | ||||
\(914\) | −7.37005 | − | 12.7653i | −0.243780 | − | 0.422238i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.1184 | + | 7.57389i | −0.433443 | + | 0.250248i | ||||
\(917\) | 1.50677 | − | 0.869932i | 0.0497578 | − | 0.0287277i | ||||
\(918\) | 2.55291i | 0.0842587i | ||||||||
\(919\) | 16.9793 | + | 29.4089i | 0.560094 | + | 0.970111i | 0.997488 | + | 0.0708412i | \(0.0225684\pi\) |
−0.437394 | + | 0.899270i | \(0.644098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.5866 | + | 10.7310i | 0.612450 | + | 0.353598i | ||||
\(922\) | 19.8601 | 0.654056 | ||||||||
\(923\) | 0.272911 | − | 14.1861i | 0.00898298 | − | 0.466942i | ||||
\(924\) | −1.56753 | −0.0515678 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.0766 | + | 27.8455i | −0.528311 | + | 0.915061i | ||||
\(927\) | 0.362501 | + | 0.627871i | 0.0119061 | + | 0.0206220i | ||||
\(928\) | 3.38839i | 0.111229i | ||||||||
\(929\) | 0.599403 | − | 0.346065i | 0.0196658 | − | 0.0113540i | −0.490135 | − | 0.871647i | \(-0.663052\pi\) |
0.509801 | + | 0.860293i | \(0.329719\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.1178i | 0.528240i | ||||||||
\(932\) | 9.37064 | + | 16.2304i | 0.306946 | + | 0.531646i | ||||
\(933\) | 7.37808 | − | 12.7792i | 0.241547 | − | 0.418372i | ||||
\(934\) | −19.2911 | − | 11.1377i | −0.631224 | − | 0.364437i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.0693504 | − | 3.60488i | 0.00226679 | − | 0.117829i | ||||
\(937\) | 22.0269 | 0.719589 | 0.359795 | − | 0.933032i | \(-0.382847\pi\) | ||||
0.359795 | + | 0.933032i | \(0.382847\pi\) | |||||||
\(938\) | 4.18958 | + | 2.41886i | 0.136795 | + | 0.0789785i | ||||
\(939\) | −0.702205 | + | 1.21625i | −0.0229156 | + | 0.0396910i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.7015i | 0.511855i | 0.966696 | + | 0.255928i | \(0.0823809\pi\) | ||||
−0.966696 | + | 0.255928i | \(0.917619\pi\) | |||||||
\(942\) | −19.5044 | + | 11.2609i | −0.635487 | + | 0.366899i | ||||
\(943\) | 6.56773 | − | 3.79188i | 0.213875 | − | 0.123481i | ||||
\(944\) | − | 3.97418i | − | 0.129348i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.48331 | − | 4.30121i | 0.0807392 | − | 0.139844i | ||||
\(947\) | 22.6839 | + | 13.0966i | 0.737129 | + | 0.425581i | 0.821024 | − | 0.570893i | \(-0.193403\pi\) |
−0.0838957 | + | 0.996475i | \(0.526736\pi\) | |||||||
\(948\) | 3.68973 | 0.119837 | ||||||||
\(949\) | −22.4236 | − | 13.5279i | −0.727901 | − | 0.439135i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.7019 | + | 16.5710i | 0.930722 | + | 0.537352i | ||||
\(952\) | −1.18947 | + | 2.06022i | −0.0385509 | + | 0.0667721i | ||||
\(953\) | 11.2248 | + | 19.4420i | 0.363608 | + | 0.629788i | 0.988552 | − | 0.150882i | \(-0.0482113\pi\) |
−0.624943 | + | 0.780670i | \(0.714878\pi\) | |||||||
\(954\) | 5.36068i | 0.173558i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.00390 | + | 2.31165i | −0.129495 | + | 0.0747641i | ||||
\(957\) | 5.69982i | 0.184249i | ||||||||
\(958\) | −10.9700 | − | 19.0007i | −0.354426 | − | 0.613884i | ||||
\(959\) | −3.39595 | + | 5.88196i | −0.109661 | + | 0.189939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −55.3958 | −1.78696 | ||||||||
\(962\) | 33.0203 | + | 0.635241i | 1.06462 | + | 0.0204810i | ||||
\(963\) | 17.2173 | 0.554821 | ||||||||
\(964\) | 15.2373 | + | 8.79725i | 0.490760 | + | 0.283341i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.00851 | + | 5.21089i | 0.0967972 | + | 0.167658i | ||||
\(967\) | − | 36.7073i | − | 1.18043i | −0.807248 | − | 0.590213i | \(-0.799044\pi\) | ||
0.807248 | − | 0.590213i | \(-0.200956\pi\) | |||||||
\(968\) | 7.07571 | − | 4.08516i | 0.227422 | − | 0.131302i | ||||
\(969\) | −5.81160 | + | 3.35533i | −0.186695 | + | 0.107789i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.8673 | − | 22.2869i | −0.412932 | − | 0.715219i | 0.582277 | − | 0.812991i | \(-0.302162\pi\) |
−0.995209 | + | 0.0977711i | \(0.968829\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −3.80212 | − | 2.19516i | −0.121890 | − | 0.0703735i | ||||
\(974\) | 9.05302 | 0.290078 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.72376 | −0.279241 | ||||||||
\(977\) | −26.5140 | − | 15.3079i | −0.848258 | − | 0.489742i | 0.0118045 | − | 0.999930i | \(-0.496242\pi\) |
−0.860063 | + | 0.510188i | \(0.829576\pi\) | |||||||
\(978\) | −1.38745 | + | 2.40313i | −0.0443656 | + | 0.0768435i | ||||
\(979\) | 11.3269 | + | 19.6187i | 0.362008 | + | 0.627016i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.90410 | − | 5.14078i | 0.284286 | − | 0.164133i | ||||
\(982\) | −26.1540 | + | 15.1000i | −0.834609 | + | 0.481861i | ||||
\(983\) | − | 61.1797i | − | 1.95133i | −0.219266 | − | 0.975665i | \(-0.570366\pi\) | ||
0.219266 | − | 0.975665i | \(-0.429634\pi\) | |||||||
\(984\) | −0.587246 | − | 1.01714i | −0.0187207 | − | 0.0324252i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.49135 | + | 4.32513i | 0.238573 | + | 0.137740i | ||||
\(987\) | 3.70815 | 0.118032 | ||||||||
\(988\) | 8.29751 | − | 4.58007i | 0.263979 | − | 0.145712i | ||||
\(989\) | −19.0646 | −0.606218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.3797 | + | 43.9589i | −0.806212 | + | 1.39640i | 0.109258 | + | 0.994013i | \(0.465153\pi\) |
−0.915470 | + | 0.402387i | \(0.868181\pi\) | |||||||
\(992\) | −4.64747 | − | 8.04965i | −0.147557 | − | 0.255577i | ||||
\(993\) | − | 6.98904i | − | 0.221790i | ||||||
\(994\) | 3.17578 | − | 1.83354i | 0.100730 | − | 0.0581562i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.84909i | 0.121963i | ||||||||
\(997\) | −24.6109 | − | 42.6273i | −0.779434 | − | 1.35002i | −0.932268 | − | 0.361768i | \(-0.882173\pi\) |
0.152834 | − | 0.988252i | \(-0.451160\pi\) | |||||||
\(998\) | −4.52168 | + | 7.83178i | −0.143131 | + | 0.247911i | ||||
\(999\) | 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.bc.e.901.4 | yes | 8 | |
5.2 | odd | 4 | 1950.2.y.i.199.4 | 8 | |||
5.3 | odd | 4 | 1950.2.y.l.199.1 | 8 | |||
5.4 | even | 2 | 1950.2.bc.f.901.1 | yes | 8 | ||
13.10 | even | 6 | inner | 1950.2.bc.e.751.4 | ✓ | 8 | |
65.23 | odd | 12 | 1950.2.y.i.49.4 | 8 | |||
65.49 | even | 6 | 1950.2.bc.f.751.1 | yes | 8 | ||
65.62 | odd | 12 | 1950.2.y.l.49.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.i.49.4 | 8 | 65.23 | odd | 12 | |||
1950.2.y.i.199.4 | 8 | 5.2 | odd | 4 | |||
1950.2.y.l.49.1 | 8 | 65.62 | odd | 12 | |||
1950.2.y.l.199.1 | 8 | 5.3 | odd | 4 | |||
1950.2.bc.e.751.4 | ✓ | 8 | 13.10 | even | 6 | inner | |
1950.2.bc.e.901.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1950.2.bc.f.751.1 | yes | 8 | 65.49 | even | 6 | ||
1950.2.bc.f.901.1 | yes | 8 | 5.4 | even | 2 |