Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(218,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 407.5 | ||
Character | \(\chi\) | \(=\) | 525.407 |
Dual form | 525.2.j.b.218.5 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.347054 | + | 0.347054i | −0.245404 | + | 0.245404i | −0.819081 | − | 0.573677i | \(-0.805516\pi\) |
0.573677 | + | 0.819081i | \(0.305516\pi\) | |||||||
\(3\) | −0.176396 | + | 1.72305i | −0.101842 | + | 0.994801i | ||||
\(4\) | 1.75911i | 0.879554i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.536770 | − | 0.659208i | −0.219135 | − | 0.269120i | ||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | −1.30461 | − | 1.30461i | −0.461250 | − | 0.461250i | ||||
\(9\) | −2.93777 | − | 0.607876i | −0.979256 | − | 0.202625i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.67137i | 0.805448i | 0.915322 | + | 0.402724i | \(0.131936\pi\) | ||||
−0.915322 | + | 0.402724i | \(0.868064\pi\) | |||||||
\(12\) | −3.03102 | − | 0.310299i | −0.874981 | − | 0.0895757i | ||||
\(13\) | −2.14945 | + | 2.14945i | −0.596149 | + | 0.596149i | −0.939285 | − | 0.343137i | \(-0.888511\pi\) |
0.343137 | + | 0.939285i | \(0.388511\pi\) | |||||||
\(14\) | −0.490808 | −0.131174 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.61267 | −0.653169 | ||||||||
\(17\) | 3.26719 | − | 3.26719i | 0.792410 | − | 0.792410i | −0.189475 | − | 0.981886i | \(-0.560679\pi\) |
0.981886 | + | 0.189475i | \(0.0606787\pi\) | |||||||
\(18\) | 1.23053 | − | 0.808598i | 0.290038 | − | 0.190588i | ||||
\(19\) | 5.24329i | 1.20289i | 0.798913 | + | 0.601446i | \(0.205409\pi\) | ||||
−0.798913 | + | 0.601446i | \(0.794591\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34311 | + | 1.09365i | −0.293090 | + | 0.238653i | ||||
\(22\) | −0.927108 | − | 0.927108i | −0.197660 | − | 0.197660i | ||||
\(23\) | −2.54815 | − | 2.54815i | −0.531326 | − | 0.531326i | 0.389641 | − | 0.920967i | \(-0.372599\pi\) |
−0.920967 | + | 0.389641i | \(0.872599\pi\) | |||||||
\(24\) | 2.47803 | − | 2.01778i | 0.505826 | − | 0.411877i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1.49195i | − | 0.292595i | ||||||
\(27\) | 1.56561 | − | 4.95468i | 0.301301 | − | 0.953529i | ||||
\(28\) | −1.24388 | + | 1.24388i | −0.235071 | + | 0.235071i | ||||
\(29\) | 2.86924 | 0.532804 | 0.266402 | − | 0.963862i | \(-0.414165\pi\) | ||||
0.266402 | + | 0.963862i | \(0.414165\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.28599 | −0.949391 | −0.474696 | − | 0.880150i | \(-0.657442\pi\) | ||||
−0.474696 | + | 0.880150i | \(0.657442\pi\) | |||||||
\(32\) | 3.51596 | − | 3.51596i | 0.621540 | − | 0.621540i | ||||
\(33\) | −4.60289 | − | 0.471218i | −0.801260 | − | 0.0820286i | ||||
\(34\) | 2.26778i | 0.388921i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.06932 | − | 5.16785i | 0.178220 | − | 0.861309i | ||||
\(37\) | 2.14286 | + | 2.14286i | 0.352284 | + | 0.352284i | 0.860959 | − | 0.508675i | \(-0.169864\pi\) |
−0.508675 | + | 0.860959i | \(0.669864\pi\) | |||||||
\(38\) | −1.81970 | − | 1.81970i | −0.295195 | − | 0.295195i | ||||
\(39\) | −3.32444 | − | 4.08274i | −0.532336 | − | 0.653762i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.5768i | − | 1.80800i | −0.427537 | − | 0.903998i | \(-0.640619\pi\) | ||
0.427537 | − | 0.903998i | \(-0.359381\pi\) | |||||||
\(42\) | 0.0865765 | − | 0.845684i | 0.0133590 | − | 0.130492i | ||||
\(43\) | −0.759108 | + | 0.759108i | −0.115763 | + | 0.115763i | −0.762615 | − | 0.646852i | \(-0.776085\pi\) |
0.646852 | + | 0.762615i | \(0.276085\pi\) | |||||||
\(44\) | −4.69922 | −0.708434 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76869 | 0.260779 | ||||||||
\(47\) | −7.66034 | + | 7.66034i | −1.11738 | + | 1.11738i | −0.125250 | + | 0.992125i | \(0.539973\pi\) |
−0.992125 | + | 0.125250i | \(0.960027\pi\) | |||||||
\(48\) | 0.460865 | − | 4.50176i | 0.0665201 | − | 0.649773i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.05320 | + | 6.20584i | 0.707589 | + | 0.868991i | ||||
\(52\) | −3.78111 | − | 3.78111i | −0.524345 | − | 0.524345i | ||||
\(53\) | 4.43577 | + | 4.43577i | 0.609300 | + | 0.609300i | 0.942763 | − | 0.333463i | \(-0.108217\pi\) |
−0.333463 | + | 0.942763i | \(0.608217\pi\) | |||||||
\(54\) | 1.17619 | + | 2.26289i | 0.160059 | + | 0.307940i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.84500i | − | 0.246548i | ||||||
\(57\) | −9.03442 | − | 0.924894i | −1.19664 | − | 0.122505i | ||||
\(58\) | −0.995779 | + | 0.995779i | −0.130752 | + | 0.130752i | ||||
\(59\) | −0.159437 | −0.0207569 | −0.0103785 | − | 0.999946i | \(-0.503304\pi\) | ||||
−0.0103785 | + | 0.999946i | \(0.503304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.72534 | 0.605018 | 0.302509 | − | 0.953147i | \(-0.402176\pi\) | ||||
0.302509 | + | 0.953147i | \(0.402176\pi\) | |||||||
\(62\) | 1.83452 | − | 1.83452i | 0.232984 | − | 0.232984i | ||||
\(63\) | −1.64748 | − | 2.50715i | −0.207563 | − | 0.315871i | ||||
\(64\) | − | 2.78490i | − | 0.348112i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.76099 | − | 1.43391i | 0.216762 | − | 0.176502i | ||||
\(67\) | 5.41156 | + | 5.41156i | 0.661127 | + | 0.661127i | 0.955646 | − | 0.294519i | \(-0.0951594\pi\) |
−0.294519 | + | 0.955646i | \(0.595159\pi\) | |||||||
\(68\) | 5.74734 | + | 5.74734i | 0.696967 | + | 0.696967i | ||||
\(69\) | 4.84006 | − | 3.94109i | 0.582675 | − | 0.474452i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5880i | 1.61260i | 0.591508 | + | 0.806299i | \(0.298533\pi\) | ||||
−0.591508 | + | 0.806299i | \(0.701467\pi\) | |||||||
\(72\) | 3.03961 | + | 4.62569i | 0.358221 | + | 0.545143i | ||||
\(73\) | −4.16486 | + | 4.16486i | −0.487460 | + | 0.487460i | −0.907504 | − | 0.420044i | \(-0.862015\pi\) |
0.420044 | + | 0.907504i | \(0.362015\pi\) | |||||||
\(74\) | −1.48737 | −0.172904 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.22351 | −1.05801 | ||||||||
\(77\) | −1.88894 | + | 1.88894i | −0.215265 | + | 0.215265i | ||||
\(78\) | 2.57069 | + | 0.263173i | 0.291073 | + | 0.0297985i | ||||
\(79\) | 3.89710i | 0.438458i | 0.975673 | + | 0.219229i | \(0.0703542\pi\) | ||||
−0.975673 | + | 0.219229i | \(0.929646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.26097 | + | 3.57160i | 0.917886 | + | 0.396844i | ||||
\(82\) | 4.01778 | + | 4.01778i | 0.443689 | + | 0.443689i | ||||
\(83\) | 4.03778 | + | 4.03778i | 0.443204 | + | 0.443204i | 0.893087 | − | 0.449883i | \(-0.148534\pi\) |
−0.449883 | + | 0.893087i | \(0.648534\pi\) | |||||||
\(84\) | −1.92384 | − | 2.36267i | −0.209908 | − | 0.257789i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 0.526902i | − | 0.0568173i | ||||||
\(87\) | −0.506122 | + | 4.94383i | −0.0542619 | + | 0.530034i | ||||
\(88\) | 3.48510 | − | 3.48510i | 0.371513 | − | 0.371513i | ||||
\(89\) | −3.95125 | −0.418832 | −0.209416 | − | 0.977827i | \(-0.567156\pi\) | ||||
−0.209416 | + | 0.977827i | \(0.567156\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.03977 | −0.318655 | ||||||||
\(92\) | 4.48247 | − | 4.48247i | 0.467330 | − | 0.467330i | ||||
\(93\) | 0.932426 | − | 9.10800i | 0.0966881 | − | 0.944455i | ||||
\(94\) | − | 5.31710i | − | 0.548417i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.43796 | + | 6.67836i | 0.555009 | + | 0.681607i | ||||
\(97\) | 1.86878 | + | 1.86878i | 0.189746 | + | 0.189746i | 0.795586 | − | 0.605840i | \(-0.207163\pi\) |
−0.605840 | + | 0.795586i | \(0.707163\pi\) | |||||||
\(98\) | −0.347054 | − | 0.347054i | −0.0350577 | − | 0.0350577i | ||||
\(99\) | 1.62386 | − | 7.84786i | 0.163204 | − | 0.788740i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.76115i | − | 0.374249i | −0.982336 | − | 0.187124i | \(-0.940083\pi\) | ||
0.982336 | − | 0.187124i | \(-0.0599167\pi\) | |||||||
\(102\) | −3.90749 | − | 0.400027i | −0.386899 | − | 0.0396086i | ||||
\(103\) | 8.85701 | − | 8.85701i | 0.872707 | − | 0.872707i | −0.120060 | − | 0.992767i | \(-0.538309\pi\) |
0.992767 | + | 0.120060i | \(0.0383086\pi\) | |||||||
\(104\) | 5.60838 | 0.549947 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.07890 | −0.299049 | ||||||||
\(107\) | −0.710397 | + | 0.710397i | −0.0686766 | + | 0.0686766i | −0.740611 | − | 0.671934i | \(-0.765464\pi\) |
0.671934 | + | 0.740611i | \(0.265464\pi\) | |||||||
\(108\) | 8.71582 | + | 2.75407i | 0.838680 | + | 0.265011i | ||||
\(109\) | 19.0144i | 1.82125i | 0.413237 | + | 0.910623i | \(0.364398\pi\) | ||||
−0.413237 | + | 0.910623i | \(0.635602\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.07024 | + | 3.31425i | −0.386330 | + | 0.314575i | ||||
\(112\) | −1.84744 | − | 1.84744i | −0.174567 | − | 0.174567i | ||||
\(113\) | −5.69132 | − | 5.69132i | −0.535394 | − | 0.535394i | 0.386779 | − | 0.922173i | \(-0.373588\pi\) |
−0.922173 | + | 0.386779i | \(0.873588\pi\) | |||||||
\(114\) | 3.45642 | − | 2.81444i | 0.323723 | − | 0.263597i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.04730i | 0.468630i | ||||||||
\(117\) | 7.62117 | − | 5.00798i | 0.704577 | − | 0.462988i | ||||
\(118\) | 0.0553332 | − | 0.0553332i | 0.00509383 | − | 0.00509383i | ||||
\(119\) | 4.62051 | 0.423561 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.86380 | 0.351254 | ||||||||
\(122\) | −1.63995 | + | 1.63995i | −0.148474 | + | 0.148474i | ||||
\(123\) | 19.9474 | + | 2.04210i | 1.79859 | + | 0.184130i | ||||
\(124\) | − | 9.29862i | − | 0.835041i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.44188 | + | 0.298350i | 0.128453 | + | 0.0265792i | ||||
\(127\) | 12.1366 | + | 12.1366i | 1.07695 | + | 1.07695i | 0.996781 | + | 0.0801668i | \(0.0255453\pi\) |
0.0801668 | + | 0.996781i | \(0.474455\pi\) | |||||||
\(128\) | 7.99843 | + | 7.99843i | 0.706968 | + | 0.706968i | ||||
\(129\) | −1.17407 | − | 1.44188i | −0.103371 | − | 0.126950i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.94280i | 0.868706i | 0.900743 | + | 0.434353i | \(0.143023\pi\) | ||||
−0.900743 | + | 0.434353i | \(0.856977\pi\) | |||||||
\(132\) | 0.828923 | − | 8.09697i | 0.0721485 | − | 0.704751i | ||||
\(133\) | −3.70756 | + | 3.70756i | −0.321487 | + | 0.321487i | ||||
\(134\) | −3.75620 | −0.324486 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.52483 | −0.730998 | ||||||||
\(137\) | −13.6645 | + | 13.6645i | −1.16744 | + | 1.16744i | −0.184630 | + | 0.982808i | \(0.559109\pi\) |
−0.982808 | + | 0.184630i | \(0.940891\pi\) | |||||||
\(138\) | −0.311989 | + | 3.04753i | −0.0265583 | + | 0.259423i | ||||
\(139\) | − | 16.7933i | − | 1.42439i | −0.701982 | − | 0.712195i | \(-0.747701\pi\) | ||
0.701982 | − | 0.712195i | \(-0.252299\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8479 | − | 14.5504i | −0.997770 | − | 1.22536i | ||||
\(142\) | −4.71576 | − | 4.71576i | −0.395738 | − | 0.395738i | ||||
\(143\) | −5.74196 | − | 5.74196i | −0.480167 | − | 0.480167i | ||||
\(144\) | 7.67544 | + | 1.58818i | 0.639620 | + | 0.132349i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 2.89086i | − | 0.239249i | ||||||
\(147\) | −1.72305 | − | 0.176396i | −0.142114 | − | 0.0145489i | ||||
\(148\) | −3.76952 | + | 3.76952i | −0.309853 | + | 0.309853i | ||||
\(149\) | 9.31256 | 0.762915 | 0.381458 | − | 0.924386i | \(-0.375422\pi\) | ||||
0.381458 | + | 0.924386i | \(0.375422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.3868 | 1.65905 | 0.829527 | − | 0.558466i | \(-0.188610\pi\) | ||||
0.829527 | + | 0.558466i | \(0.188610\pi\) | |||||||
\(152\) | 6.84046 | − | 6.84046i | 0.554834 | − | 0.554834i | ||||
\(153\) | −11.5843 | + | 7.61221i | −0.936535 | + | 0.615410i | ||||
\(154\) | − | 1.31113i | − | 0.105654i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.18199 | − | 5.84804i | 0.575019 | − | 0.468218i | ||||
\(157\) | −6.32887 | − | 6.32887i | −0.505098 | − | 0.505098i | 0.407919 | − | 0.913018i | \(-0.366254\pi\) |
−0.913018 | + | 0.407919i | \(0.866254\pi\) | |||||||
\(158\) | −1.35250 | − | 1.35250i | −0.107599 | − | 0.107599i | ||||
\(159\) | −8.42549 | + | 6.86058i | −0.668185 | + | 0.544080i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.60363i | − | 0.284006i | ||||||
\(162\) | −4.10654 | + | 1.62746i | −0.322640 | + | 0.127866i | ||||
\(163\) | 6.45638 | − | 6.45638i | 0.505703 | − | 0.505703i | −0.407502 | − | 0.913205i | \(-0.633600\pi\) |
0.913205 | + | 0.407502i | \(0.133600\pi\) | |||||||
\(164\) | 20.3649 | 1.59023 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.80266 | −0.217528 | ||||||||
\(167\) | −1.58004 | + | 1.58004i | −0.122268 | + | 0.122268i | −0.765593 | − | 0.643325i | \(-0.777554\pi\) |
0.643325 | + | 0.765593i | \(0.277554\pi\) | |||||||
\(168\) | 3.17902 | + | 0.325450i | 0.245267 | + | 0.0251090i | ||||
\(169\) | 3.75977i | 0.289213i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.18727 | − | 15.4036i | 0.243737 | − | 1.17794i | ||||
\(172\) | −1.33535 | − | 1.33535i | −0.101820 | − | 0.101820i | ||||
\(173\) | 1.69970 | + | 1.69970i | 0.129226 | + | 0.129226i | 0.768761 | − | 0.639536i | \(-0.220873\pi\) |
−0.639536 | + | 0.768761i | \(0.720873\pi\) | |||||||
\(174\) | −1.54012 | − | 1.89142i | −0.116756 | − | 0.143388i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 6.97941i | − | 0.526093i | ||||||
\(177\) | 0.0281240 | − | 0.274717i | 0.00211393 | − | 0.0206490i | ||||
\(178\) | 1.37130 | − | 1.37130i | 0.102783 | − | 0.102783i | ||||
\(179\) | −8.44380 | −0.631119 | −0.315560 | − | 0.948906i | \(-0.602192\pi\) | ||||
−0.315560 | + | 0.948906i | \(0.602192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.51483 | 0.409914 | 0.204957 | − | 0.978771i | \(-0.434295\pi\) | ||||
0.204957 | + | 0.978771i | \(0.434295\pi\) | |||||||
\(182\) | 1.05496 | − | 1.05496i | 0.0781992 | − | 0.0781992i | ||||
\(183\) | −0.833531 | + | 8.14198i | −0.0616164 | + | 0.601872i | ||||
\(184\) | 6.64869i | 0.490148i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.83736 | + | 3.48456i | 0.208045 | + | 0.255501i | ||||
\(187\) | 8.72787 | + | 8.72787i | 0.638245 | + | 0.638245i | ||||
\(188\) | −13.4754 | − | 13.4754i | −0.982792 | − | 0.982792i | ||||
\(189\) | 4.61054 | − | 2.39644i | 0.335368 | − | 0.174315i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.559524i | 0.0404858i | 0.999795 | + | 0.0202429i | \(0.00644395\pi\) | ||||
−0.999795 | + | 0.0202429i | \(0.993556\pi\) | |||||||
\(192\) | 4.79850 | + | 0.491244i | 0.346302 | + | 0.0354525i | ||||
\(193\) | −7.05199 | + | 7.05199i | −0.507613 | + | 0.507613i | −0.913793 | − | 0.406180i | \(-0.866861\pi\) |
0.406180 | + | 0.913793i | \(0.366861\pi\) | |||||||
\(194\) | −1.29713 | −0.0931287 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.75911 | −0.125651 | ||||||||
\(197\) | 10.1505 | − | 10.1505i | 0.723190 | − | 0.723190i | −0.246064 | − | 0.969254i | \(-0.579137\pi\) |
0.969254 | + | 0.246064i | \(0.0791372\pi\) | |||||||
\(198\) | 2.16006 | + | 3.28719i | 0.153509 | + | 0.233611i | ||||
\(199\) | 11.6748i | 0.827604i | 0.910367 | + | 0.413802i | \(0.135799\pi\) | ||||
−0.910367 | + | 0.413802i | \(0.864201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.2789 | + | 8.36978i | −0.725020 | + | 0.590359i | ||||
\(202\) | 1.30532 | + | 1.30532i | 0.0918421 | + | 0.0918421i | ||||
\(203\) | 2.02886 | + | 2.02886i | 0.142398 | + | 0.142398i | ||||
\(204\) | −10.9167 | + | 8.88912i | −0.764324 | + | 0.622363i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.14771i | 0.428332i | ||||||||
\(207\) | 5.93692 | + | 9.03483i | 0.412644 | + | 0.627964i | ||||
\(208\) | 5.61580 | − | 5.61580i | 0.389386 | − | 0.389386i | ||||
\(209\) | −14.0067 | −0.968867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.777102 | −0.0534979 | −0.0267490 | − | 0.999642i | \(-0.508515\pi\) | ||||
−0.0267490 | + | 0.999642i | \(0.508515\pi\) | |||||||
\(212\) | −7.80300 | + | 7.80300i | −0.535912 | + | 0.535912i | ||||
\(213\) | −23.4127 | − | 2.39687i | −1.60421 | − | 0.164231i | ||||
\(214\) | − | 0.493091i | − | 0.0337070i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.50645 | + | 4.42142i | −0.578790 | + | 0.300840i | ||||
\(217\) | −3.73776 | − | 3.73776i | −0.253736 | − | 0.253736i | ||||
\(218\) | −6.59901 | − | 6.59901i | −0.446941 | − | 0.446941i | ||||
\(219\) | −6.44157 | − | 7.91090i | −0.435281 | − | 0.534569i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.0453i | 0.944789i | ||||||||
\(222\) | 0.262367 | − | 2.56281i | 0.0176089 | − | 0.172005i | ||||
\(223\) | 3.33811 | − | 3.33811i | 0.223536 | − | 0.223536i | −0.586450 | − | 0.809986i | \(-0.699475\pi\) |
0.809986 | + | 0.586450i | \(0.199475\pi\) | |||||||
\(224\) | 4.97232 | 0.332227 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.95038 | 0.262776 | ||||||||
\(227\) | −0.242326 | + | 0.242326i | −0.0160838 | + | 0.0160838i | −0.715103 | − | 0.699019i | \(-0.753620\pi\) |
0.699019 | + | 0.715103i | \(0.253620\pi\) | |||||||
\(228\) | 1.62699 | − | 15.8925i | 0.107750 | − | 1.05251i | ||||
\(229\) | − | 13.4793i | − | 0.890735i | −0.895348 | − | 0.445368i | \(-0.853073\pi\) | ||
0.895348 | − | 0.445368i | \(-0.146927\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.92153 | − | 3.58793i | −0.192223 | − | 0.236069i | ||||
\(232\) | −3.74324 | − | 3.74324i | −0.245756 | − | 0.245756i | ||||
\(233\) | −1.19260 | − | 1.19260i | −0.0781301 | − | 0.0781301i | 0.666962 | − | 0.745092i | \(-0.267594\pi\) |
−0.745092 | + | 0.666962i | \(0.767594\pi\) | |||||||
\(234\) | −0.906918 | + | 4.38299i | −0.0592871 | + | 0.286525i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 0.280467i | − | 0.0182568i | ||||||
\(237\) | −6.71488 | − | 0.687432i | −0.436178 | − | 0.0446535i | ||||
\(238\) | −1.60356 | + | 1.60356i | −0.103944 | + | 0.103944i | ||||
\(239\) | 5.15325 | 0.333336 | 0.166668 | − | 0.986013i | \(-0.446699\pi\) | ||||
0.166668 | + | 0.986013i | \(0.446699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9174 | −0.960914 | −0.480457 | − | 0.877018i | \(-0.659529\pi\) | ||||
−0.480457 | + | 0.877018i | \(0.659529\pi\) | |||||||
\(242\) | −1.34094 | + | 1.34094i | −0.0861992 | + | 0.0861992i | ||||
\(243\) | −7.61123 | + | 13.6040i | −0.488261 | + | 0.872698i | ||||
\(244\) | 8.31238i | 0.532146i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.63153 | + | 6.21409i | −0.486569 | + | 0.396196i | ||||
\(247\) | −11.2702 | − | 11.2702i | −0.717103 | − | 0.717103i | ||||
\(248\) | 6.89616 | + | 6.89616i | 0.437907 | + | 0.437907i | ||||
\(249\) | −7.66953 | + | 6.24504i | −0.486037 | + | 0.395763i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.30303i | 0.271605i | 0.990736 | + | 0.135802i | \(0.0433613\pi\) | ||||
−0.990736 | + | 0.135802i | \(0.956639\pi\) | |||||||
\(252\) | 4.41035 | − | 2.89810i | 0.277826 | − | 0.182563i | ||||
\(253\) | 6.80704 | − | 6.80704i | 0.427955 | − | 0.427955i | ||||
\(254\) | −8.42409 | −0.528575 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.0180230 | 0.00112644 | ||||||||
\(257\) | 5.82885 | − | 5.82885i | 0.363594 | − | 0.363594i | −0.501540 | − | 0.865134i | \(-0.667233\pi\) |
0.865134 | + | 0.501540i | \(0.167233\pi\) | |||||||
\(258\) | 0.907876 | + | 0.0929433i | 0.0565219 | + | 0.00578640i | ||||
\(259\) | 3.03046i | 0.188304i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.42916 | − | 1.74414i | −0.521752 | − | 0.107960i | ||||
\(262\) | −3.45068 | − | 3.45068i | −0.213184 | − | 0.213184i | ||||
\(263\) | 0.0624909 | + | 0.0624909i | 0.00385335 | + | 0.00385335i | 0.709031 | − | 0.705177i | \(-0.249133\pi\) |
−0.705177 | + | 0.709031i | \(0.749133\pi\) | |||||||
\(264\) | 5.39022 | + | 6.61974i | 0.331745 | + | 0.407417i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 2.57345i | − | 0.157788i | ||||||
\(267\) | 0.696985 | − | 6.80819i | 0.0426548 | − | 0.416654i | ||||
\(268\) | −9.51951 | + | 9.51951i | −0.581497 | + | 0.581497i | ||||
\(269\) | −29.6699 | −1.80901 | −0.904504 | − | 0.426465i | \(-0.859759\pi\) | ||||
−0.904504 | + | 0.426465i | \(0.859759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.6377 | 1.37514 | 0.687571 | − | 0.726117i | \(-0.258677\pi\) | ||||
0.687571 | + | 0.726117i | \(0.258677\pi\) | |||||||
\(272\) | −8.53611 | + | 8.53611i | −0.517578 | + | 0.517578i | ||||
\(273\) | 0.536204 | − | 5.23767i | 0.0324525 | − | 0.316998i | ||||
\(274\) | − | 9.48463i | − | 0.572988i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.93281 | + | 8.51419i | 0.417306 | + | 0.512494i | ||||
\(277\) | −4.21136 | − | 4.21136i | −0.253036 | − | 0.253036i | 0.569178 | − | 0.822214i | \(-0.307262\pi\) |
−0.822214 | + | 0.569178i | \(0.807262\pi\) | |||||||
\(278\) | 5.82817 | + | 5.82817i | 0.349551 | + | 0.349551i | ||||
\(279\) | 15.5290 | + | 3.21323i | 0.929698 | + | 0.192371i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.0093i | − | 1.31297i | −0.754341 | − | 0.656483i | \(-0.772043\pi\) | ||
0.754341 | − | 0.656483i | \(-0.227957\pi\) | |||||||
\(282\) | 9.16160 | + | 0.937914i | 0.545565 | + | 0.0558520i | ||||
\(283\) | −9.59899 | + | 9.59899i | −0.570601 | + | 0.570601i | −0.932296 | − | 0.361695i | \(-0.882198\pi\) |
0.361695 | + | 0.932296i | \(0.382198\pi\) | |||||||
\(284\) | −23.9027 | −1.41837 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.98553 | 0.235670 | ||||||||
\(287\) | 8.18605 | − | 8.18605i | 0.483207 | − | 0.483207i | ||||
\(288\) | −12.4664 | + | 8.19181i | −0.734587 | + | 0.482707i | ||||
\(289\) | − | 4.34908i | − | 0.255828i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.54963 | + | 2.89034i | −0.208083 | + | 0.169435i | ||||
\(292\) | −7.32643 | − | 7.32643i | −0.428747 | − | 0.428747i | ||||
\(293\) | −3.56359 | − | 3.56359i | −0.208187 | − | 0.208187i | 0.595309 | − | 0.803497i | \(-0.297030\pi\) |
−0.803497 | + | 0.595309i | \(0.797030\pi\) | |||||||
\(294\) | 0.659208 | − | 0.536770i | 0.0384458 | − | 0.0313051i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 5.59120i | − | 0.324982i | ||||||
\(297\) | 13.2358 | + | 4.18231i | 0.768018 | + | 0.242683i | ||||
\(298\) | −3.23196 | + | 3.23196i | −0.187222 | + | 0.187222i | ||||
\(299\) | 10.9542 | 0.633499 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07354 | −0.0618778 | ||||||||
\(302\) | −7.07531 | + | 7.07531i | −0.407139 | + | 0.407139i | ||||
\(303\) | 6.48063 | + | 0.663452i | 0.372303 | + | 0.0381143i | ||||
\(304\) | − | 13.6990i | − | 0.785692i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.37853 | − | 6.66222i | 0.0788053 | − | 0.380854i | ||||
\(307\) | −10.4746 | − | 10.4746i | −0.597814 | − | 0.597814i | 0.341916 | − | 0.939730i | \(-0.388924\pi\) |
−0.939730 | + | 0.341916i | \(0.888924\pi\) | |||||||
\(308\) | −3.32285 | − | 3.32285i | −0.189337 | − | 0.189337i | ||||
\(309\) | 13.6987 | + | 16.8234i | 0.779291 | + | 0.957048i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.4344i | − | 1.15873i | −0.815068 | − | 0.579365i | \(-0.803301\pi\) | ||
0.815068 | − | 0.579365i | \(-0.196699\pi\) | |||||||
\(312\) | −0.989296 | + | 9.66350i | −0.0560078 | + | 0.547088i | ||||
\(313\) | 16.4829 | − | 16.4829i | 0.931670 | − | 0.931670i | −0.0661408 | − | 0.997810i | \(-0.521069\pi\) |
0.997810 | + | 0.0661408i | \(0.0210686\pi\) | |||||||
\(314\) | 4.39291 | 0.247906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.85542 | −0.385647 | ||||||||
\(317\) | 22.9540 | − | 22.9540i | 1.28922 | − | 1.28922i | 0.353965 | − | 0.935259i | \(-0.384833\pi\) |
0.935259 | − | 0.353965i | \(-0.115167\pi\) | |||||||
\(318\) | 0.543105 | − | 5.30509i | 0.0304558 | − | 0.297494i | ||||
\(319\) | 7.66479i | 0.429146i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.09873 | − | 1.34936i | −0.0613254 | − | 0.0753137i | ||||
\(322\) | 1.25065 | + | 1.25065i | 0.0696961 | + | 0.0696961i | ||||
\(323\) | 17.1308 | + | 17.1308i | 0.953185 | + | 0.953185i | ||||
\(324\) | −6.28283 | + | 14.5319i | −0.349046 | + | 0.807330i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.48142i | 0.248203i | ||||||||
\(327\) | −32.7626 | − | 3.35406i | −1.81178 | − | 0.185480i | ||||
\(328\) | −15.1033 | + | 15.1033i | −0.833938 | + | 0.833938i | ||||
\(329\) | −10.8334 | −0.597262 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.21461 | −0.121726 | −0.0608631 | − | 0.998146i | \(-0.519385\pi\) | ||||
−0.0608631 | + | 0.998146i | \(0.519385\pi\) | |||||||
\(332\) | −7.10290 | + | 7.10290i | −0.389822 | + | 0.389822i | ||||
\(333\) | −4.99263 | − | 7.59782i | −0.273595 | − | 0.416358i | ||||
\(334\) | − | 1.09672i | − | 0.0600099i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.50910 | − | 2.85734i | 0.191437 | − | 0.155881i | ||||
\(337\) | −10.8541 | − | 10.8541i | −0.591263 | − | 0.591263i | 0.346710 | − | 0.937972i | \(-0.387299\pi\) |
−0.937972 | + | 0.346710i | \(0.887299\pi\) | |||||||
\(338\) | −1.30484 | − | 1.30484i | −0.0709741 | − | 0.0709741i | ||||
\(339\) | 10.8103 | − | 8.80247i | 0.587136 | − | 0.478085i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 14.1208i | − | 0.764685i | ||||||
\(342\) | 4.23971 | + | 6.45202i | 0.229257 | + | 0.348885i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 1.98068 | 0.106791 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.17977 | −0.0634251 | ||||||||
\(347\) | 5.06341 | − | 5.06341i | 0.271818 | − | 0.271818i | −0.558014 | − | 0.829832i | \(-0.688436\pi\) |
0.829832 | + | 0.558014i | \(0.188436\pi\) | |||||||
\(348\) | −8.69672 | − | 0.890323i | −0.466193 | − | 0.0477263i | ||||
\(349\) | − | 7.42733i | − | 0.397576i | −0.980043 | − | 0.198788i | \(-0.936300\pi\) | ||
0.980043 | − | 0.198788i | \(-0.0637005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.28463 | + | 14.0150i | 0.388825 | + | 0.748066i | ||||
\(352\) | 9.39243 | + | 9.39243i | 0.500618 | + | 0.500618i | ||||
\(353\) | −9.09032 | − | 9.09032i | −0.483829 | − | 0.483829i | 0.422523 | − | 0.906352i | \(-0.361144\pi\) |
−0.906352 | + | 0.422523i | \(0.861144\pi\) | |||||||
\(354\) | 0.0855810 | + | 0.105102i | 0.00454858 | + | 0.00558611i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.95068i | − | 0.368385i | ||||||
\(357\) | −0.815038 | + | 7.96134i | −0.0431364 | + | 0.421359i | ||||
\(358\) | 2.93045 | − | 2.93045i | 0.154879 | − | 0.154879i | ||||
\(359\) | 25.2640 | 1.33338 | 0.666692 | − | 0.745333i | \(-0.267710\pi\) | ||||
0.666692 | + | 0.745333i | \(0.267710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.49208 | −0.446951 | ||||||||
\(362\) | −1.91394 | + | 1.91394i | −0.100594 | + | 0.100594i | ||||
\(363\) | −0.681558 | + | 6.65750i | −0.0357725 | + | 0.349428i | ||||
\(364\) | − | 5.34729i | − | 0.280274i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.53642 | − | 3.11498i | −0.132581 | − | 0.162823i | ||||
\(367\) | −1.61189 | − | 1.61189i | −0.0841399 | − | 0.0841399i | 0.663784 | − | 0.747924i | \(-0.268949\pi\) |
−0.747924 | + | 0.663784i | \(0.768949\pi\) | |||||||
\(368\) | 6.65749 | + | 6.65749i | 0.347045 | + | 0.347045i | ||||
\(369\) | −7.03727 | + | 34.0100i | −0.366346 | + | 1.77049i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.27313i | 0.325685i | ||||||||
\(372\) | 16.0219 | + | 1.64024i | 0.830699 | + | 0.0850424i | ||||
\(373\) | −13.0455 | + | 13.0455i | −0.675469 | + | 0.675469i | −0.958972 | − | 0.283502i | \(-0.908504\pi\) |
0.283502 | + | 0.958972i | \(0.408504\pi\) | |||||||
\(374\) | −6.05808 | −0.313256 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.9875 | 1.03078 | ||||||||
\(377\) | −6.16727 | + | 6.16727i | −0.317630 | + | 0.317630i | ||||
\(378\) | −0.768413 | + | 2.43180i | −0.0395229 | + | 0.125078i | ||||
\(379\) | − | 19.0635i | − | 0.979228i | −0.871939 | − | 0.489614i | \(-0.837138\pi\) | ||
0.871939 | − | 0.489614i | \(-0.162862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.0527 | + | 18.7710i | −1.18103 | + | 0.961670i | ||||
\(382\) | −0.194185 | − | 0.194185i | −0.00993537 | − | 0.00993537i | ||||
\(383\) | −17.7244 | − | 17.7244i | −0.905673 | − | 0.905673i | 0.0902463 | − | 0.995919i | \(-0.471235\pi\) |
−0.995919 | + | 0.0902463i | \(0.971235\pi\) | |||||||
\(384\) | −15.1925 | + | 12.3708i | −0.775291 | + | 0.631293i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4.89484i | − | 0.249141i | ||||||
\(387\) | 2.69153 | − | 1.76864i | 0.136818 | − | 0.0899050i | ||||
\(388\) | −3.28738 | + | 3.28738i | −0.166892 | + | 0.166892i | ||||
\(389\) | 18.3513 | 0.930446 | 0.465223 | − | 0.885193i | \(-0.345974\pi\) | ||||
0.465223 | + | 0.885193i | \(0.345974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.6506 | −0.842056 | ||||||||
\(392\) | 1.30461 | − | 1.30461i | 0.0658928 | − | 0.0658928i | ||||
\(393\) | −17.1319 | − | 1.75387i | −0.864189 | − | 0.0884710i | ||||
\(394\) | 7.04550i | 0.354947i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 13.8052 | + | 2.85655i | 0.693739 | + | 0.143547i | ||||
\(397\) | 10.9124 | + | 10.9124i | 0.547679 | + | 0.547679i | 0.925769 | − | 0.378090i | \(-0.123419\pi\) |
−0.378090 | + | 0.925769i | \(0.623419\pi\) | |||||||
\(398\) | −4.05178 | − | 4.05178i | −0.203097 | − | 0.203097i | ||||
\(399\) | −5.73430 | − | 7.04230i | −0.287074 | − | 0.352556i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.4243i | 1.71907i | 0.511079 | + | 0.859534i | \(0.329246\pi\) | ||||
−0.511079 | + | 0.859534i | \(0.670754\pi\) | |||||||
\(402\) | 0.662578 | − | 6.47210i | 0.0330464 | − | 0.322799i | ||||
\(403\) | 11.3619 | − | 11.3619i | 0.565979 | − | 0.565979i | ||||
\(404\) | 6.61627 | 0.329172 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.40824 | −0.0698900 | ||||||||
\(407\) | −5.72437 | + | 5.72437i | −0.283746 | + | 0.283746i | ||||
\(408\) | 1.50375 | − | 14.6887i | 0.0744465 | − | 0.727198i | ||||
\(409\) | − | 7.59254i | − | 0.375427i | −0.982224 | − | 0.187714i | \(-0.939892\pi\) | ||
0.982224 | − | 0.187714i | \(-0.0601077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.1342 | − | 25.9549i | −1.04247 | − | 1.28026i | ||||
\(412\) | 15.5804 | + | 15.5804i | 0.767593 | + | 0.767593i | ||||
\(413\) | −0.112739 | − | 0.112739i | −0.00554752 | − | 0.00554752i | ||||
\(414\) | −5.19600 | − | 1.07514i | −0.255369 | − | 0.0528404i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.1147i | 0.741061i | ||||||||
\(417\) | 28.9356 | + | 2.96227i | 1.41698 | + | 0.145063i | ||||
\(418\) | 4.86109 | − | 4.86109i | 0.237764 | − | 0.237764i | ||||
\(419\) | 6.20644 | 0.303204 | 0.151602 | − | 0.988442i | \(-0.451557\pi\) | ||||
0.151602 | + | 0.988442i | \(0.451557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.1339 | 1.22495 | 0.612474 | − | 0.790490i | \(-0.290174\pi\) | ||||
0.612474 | + | 0.790490i | \(0.290174\pi\) | |||||||
\(422\) | 0.269696 | − | 0.269696i | 0.0131286 | − | 0.0131286i | ||||
\(423\) | 27.1608 | − | 17.8478i | 1.32061 | − | 0.867788i | ||||
\(424\) | − | 11.5739i | − | 0.562079i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.95731 | − | 7.29363i | 0.433983 | − | 0.353377i | ||||
\(427\) | 3.34132 | + | 3.34132i | 0.161698 | + | 0.161698i | ||||
\(428\) | −1.24966 | − | 1.24966i | −0.0604048 | − | 0.0604048i | ||||
\(429\) | 10.9065 | − | 8.88079i | 0.526571 | − | 0.428769i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.43225i | − | 0.406167i | −0.979161 | − | 0.203084i | \(-0.934904\pi\) | ||
0.979161 | − | 0.203084i | \(-0.0650963\pi\) | |||||||
\(432\) | −4.09043 | + | 12.9450i | −0.196801 | + | 0.622815i | ||||
\(433\) | 18.8277 | − | 18.8277i | 0.904802 | − | 0.904802i | −0.0910444 | − | 0.995847i | \(-0.529021\pi\) |
0.995847 | + | 0.0910444i | \(0.0290205\pi\) | |||||||
\(434\) | 2.59440 | 0.124535 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −33.4483 | −1.60188 | ||||||||
\(437\) | 13.3607 | − | 13.3607i | 0.639128 | − | 0.639128i | ||||
\(438\) | 4.98108 | + | 0.509935i | 0.238005 | + | 0.0243657i | ||||
\(439\) | − | 4.88270i | − | 0.233039i | −0.993188 | − | 0.116519i | \(-0.962826\pi\) | ||
0.993188 | − | 0.116519i | \(-0.0371737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.607876 | − | 2.93777i | 0.0289465 | − | 0.139894i | ||||
\(442\) | −4.87447 | − | 4.87447i | −0.231855 | − | 0.231855i | ||||
\(443\) | 23.8960 | + | 23.8960i | 1.13534 | + | 1.13534i | 0.989276 | + | 0.146059i | \(0.0466590\pi\) |
0.146059 | + | 0.989276i | \(0.453341\pi\) | |||||||
\(444\) | −5.83013 | − | 7.15998i | −0.276686 | − | 0.339798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.31700i | 0.109713i | ||||||||
\(447\) | −1.64270 | + | 16.0460i | −0.0776970 | + | 0.758948i | ||||
\(448\) | 1.96922 | − | 1.96922i | 0.0930368 | − | 0.0930368i | ||||
\(449\) | 23.6736 | 1.11723 | 0.558613 | − | 0.829428i | \(-0.311334\pi\) | ||||
0.558613 | + | 0.829428i | \(0.311334\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.9259 | 1.45625 | ||||||||
\(452\) | 10.0116 | − | 10.0116i | 0.470908 | − | 0.470908i | ||||
\(453\) | −3.59615 | + | 35.1274i | −0.168962 | + | 1.65043i | ||||
\(454\) | − | 0.168200i | − | 0.00789404i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.5798 | + | 12.9930i | 0.495444 | + | 0.608455i | ||||
\(457\) | −10.2580 | − | 10.2580i | −0.479849 | − | 0.479849i | 0.425234 | − | 0.905083i | \(-0.360192\pi\) |
−0.905083 | + | 0.425234i | \(0.860192\pi\) | |||||||
\(458\) | 4.67803 | + | 4.67803i | 0.218590 | + | 0.218590i | ||||
\(459\) | −11.0728 | − | 21.3030i | −0.516832 | − | 0.994341i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3153i | 1.08590i | 0.839764 | + | 0.542951i | \(0.182693\pi\) | ||||
−0.839764 | + | 0.542951i | \(0.817307\pi\) | |||||||
\(462\) | 2.25913 | + | 0.231278i | 0.105104 | + | 0.0107600i | ||||
\(463\) | 17.0563 | − | 17.0563i | 0.792672 | − | 0.792672i | −0.189256 | − | 0.981928i | \(-0.560608\pi\) |
0.981928 | + | 0.189256i | \(0.0606077\pi\) | |||||||
\(464\) | −7.49639 | −0.348011 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.827796 | 0.0383469 | ||||||||
\(467\) | −8.00621 | + | 8.00621i | −0.370483 | + | 0.370483i | −0.867653 | − | 0.497170i | \(-0.834373\pi\) |
0.497170 | + | 0.867653i | \(0.334373\pi\) | |||||||
\(468\) | 8.80957 | + | 13.4065i | 0.407223 | + | 0.619714i | ||||
\(469\) | 7.65310i | 0.353387i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0213 | − | 9.78854i | 0.553913 | − | 0.451032i | ||||
\(472\) | 0.208003 | + | 0.208003i | 0.00957413 | + | 0.00957413i | ||||
\(473\) | −2.02786 | − | 2.02786i | −0.0932409 | − | 0.0932409i | ||||
\(474\) | 2.56900 | − | 2.09185i | 0.117998 | − | 0.0960817i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.12797i | 0.372545i | ||||||||
\(477\) | −10.3349 | − | 15.7277i | −0.473201 | − | 0.720121i | ||||
\(478\) | −1.78845 | + | 1.78845i | −0.0818019 | + | 0.0818019i | ||||
\(479\) | 20.1199 | 0.919304 | 0.459652 | − | 0.888099i | \(-0.347974\pi\) | ||||
0.459652 | + | 0.888099i | \(0.347974\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.21192 | −0.420027 | ||||||||
\(482\) | 5.17713 | − | 5.17713i | 0.235812 | − | 0.235812i | ||||
\(483\) | 6.20921 | + | 0.635665i | 0.282529 | + | 0.0289238i | ||||
\(484\) | 6.79683i | 0.308947i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.07982 | − | 7.36283i | −0.0943425 | − | 0.333985i | ||||
\(487\) | −7.77959 | − | 7.77959i | −0.352527 | − | 0.352527i | 0.508522 | − | 0.861049i | \(-0.330192\pi\) |
−0.861049 | + | 0.508522i | \(0.830192\pi\) | |||||||
\(488\) | −6.16474 | − | 6.16474i | −0.279064 | − | 0.279064i | ||||
\(489\) | 9.98576 | + | 12.2635i | 0.451572 | + | 0.554576i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.29546i | − | 0.103593i | −0.998658 | − | 0.0517963i | \(-0.983505\pi\) | ||
0.998658 | − | 0.0517963i | \(-0.0164947\pi\) | |||||||
\(492\) | −3.59228 | + | 35.0896i | −0.161952 | + | 1.58196i | ||||
\(493\) | 9.37435 | − | 9.37435i | 0.422199 | − | 0.422199i | ||||
\(494\) | 7.82270 | 0.351960 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.8106 | 0.620113 | ||||||||
\(497\) | −9.60816 | + | 9.60816i | −0.430985 | + | 0.430985i | ||||
\(498\) | 0.494377 | − | 4.82910i | 0.0221536 | − | 0.216397i | ||||
\(499\) | − | 12.3264i | − | 0.551806i | −0.961185 | − | 0.275903i | \(-0.911023\pi\) | ||
0.961185 | − | 0.275903i | \(-0.0889769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.44378 | − | 3.00120i | −0.109180 | − | 0.134084i | ||||
\(502\) | −1.49338 | − | 1.49338i | −0.0666529 | − | 0.0666529i | ||||
\(503\) | 4.62523 | + | 4.62523i | 0.206229 | + | 0.206229i | 0.802662 | − | 0.596434i | \(-0.203416\pi\) |
−0.596434 | + | 0.802662i | \(0.703416\pi\) | |||||||
\(504\) | −1.12153 | + | 5.42018i | −0.0499570 | + | 0.241434i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.72482i | 0.210044i | ||||||||
\(507\) | −6.47826 | − | 0.663208i | −0.287709 | − | 0.0294541i | ||||
\(508\) | −21.3496 | + | 21.3496i | −0.947234 | + | 0.947234i | ||||
\(509\) | −13.6161 | −0.603525 | −0.301762 | − | 0.953383i | \(-0.597575\pi\) | ||||
−0.301762 | + | 0.953383i | \(0.597575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.89000 | −0.260558 | ||||||||
\(512\) | −16.0031 | + | 16.0031i | −0.707245 | + | 0.707245i | ||||
\(513\) | 25.9788 | + | 8.20894i | 1.14699 | + | 0.362433i | ||||
\(514\) | 4.04585i | 0.178455i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.53642 | − | 2.06532i | 0.111660 | − | 0.0909207i | ||||
\(517\) | −20.4636 | − | 20.4636i | −0.899987 | − | 0.899987i | ||||
\(518\) | −1.05173 | − | 1.05173i | −0.0462105 | − | 0.0462105i | ||||
\(519\) | −3.22848 | + | 2.62884i | −0.141715 | + | 0.115393i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18.3870i | − | 0.805550i | −0.915299 | − | 0.402775i | \(-0.868046\pi\) | ||
0.915299 | − | 0.402775i | \(-0.131954\pi\) | |||||||
\(522\) | 3.53068 | − | 2.32006i | 0.154534 | − | 0.101546i | ||||
\(523\) | 8.91043 | − | 8.91043i | 0.389626 | − | 0.389626i | −0.484928 | − | 0.874554i | \(-0.661154\pi\) |
0.874554 | + | 0.484928i | \(0.161154\pi\) | |||||||
\(524\) | −17.4905 | −0.764074 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0433754 | −0.00189126 | ||||||||
\(527\) | −17.2703 | + | 17.2703i | −0.752308 | + | 0.752308i | ||||
\(528\) | 12.0258 | + | 1.23114i | 0.523358 | + | 0.0535785i | ||||
\(529\) | − | 10.0139i | − | 0.435385i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.468389 | + | 0.0969179i | 0.0203264 | + | 0.00420588i | ||||
\(532\) | −6.52201 | − | 6.52201i | −0.282765 | − | 0.282765i | ||||
\(533\) | 24.8837 | + | 24.8837i | 1.07783 | + | 1.07783i | ||||
\(534\) | 2.12091 | + | 2.60470i | 0.0917810 | + | 0.112716i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 14.1200i | − | 0.609889i | ||||||
\(537\) | 1.48945 | − | 14.5491i | 0.0642746 | − | 0.627838i | ||||
\(538\) | 10.2971 | − | 10.2971i | 0.443938 | − | 0.443938i | ||||
\(539\) | −2.67137 | −0.115064 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.8258 | 1.19632 | 0.598162 | − | 0.801375i | \(-0.295898\pi\) | ||||
0.598162 | + | 0.801375i | \(0.295898\pi\) | |||||||
\(542\) | −7.85649 | + | 7.85649i | −0.337465 | + | 0.337465i | ||||
\(543\) | −0.972793 | + | 9.50229i | −0.0417465 | + | 0.407783i | ||||
\(544\) | − | 22.9746i | − | 0.985030i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.63166 | + | 2.00384i | 0.0698286 | + | 0.0857566i | ||||
\(547\) | 13.2773 | + | 13.2773i | 0.567695 | + | 0.567695i | 0.931482 | − | 0.363787i | \(-0.118517\pi\) |
−0.363787 | + | 0.931482i | \(0.618517\pi\) | |||||||
\(548\) | −24.0373 | − | 24.0373i | −1.02682 | − | 1.02682i | ||||
\(549\) | −13.8820 | − | 2.87242i | −0.592468 | − | 0.122592i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0442i | 0.640906i | ||||||||
\(552\) | −11.4560 | − | 1.17280i | −0.487600 | − | 0.0499178i | ||||
\(553\) | −2.75566 | + | 2.75566i | −0.117183 | + | 0.117183i | ||||
\(554\) | 2.92314 | 0.124192 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 29.5412 | 1.25283 | ||||||||
\(557\) | −10.4002 | + | 10.4002i | −0.440672 | + | 0.440672i | −0.892238 | − | 0.451566i | \(-0.850866\pi\) |
0.451566 | + | 0.892238i | \(0.350866\pi\) | |||||||
\(558\) | −6.50456 | + | 4.27424i | −0.275360 | + | 0.180943i | ||||
\(559\) | − | 3.26332i | − | 0.138024i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.5781 | + | 13.4990i | −0.699927 | + | 0.569926i | ||||
\(562\) | 7.63842 | + | 7.63842i | 0.322207 | + | 0.322207i | ||||
\(563\) | 10.1623 | + | 10.1623i | 0.428291 | + | 0.428291i | 0.888046 | − | 0.459755i | \(-0.152063\pi\) |
−0.459755 | + | 0.888046i | \(0.652063\pi\) | |||||||
\(564\) | 25.5957 | − | 20.8417i | 1.07777 | − | 0.877592i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 6.66273i | − | 0.280055i | ||||||
\(567\) | 3.31589 | + | 8.36689i | 0.139254 | + | 0.351376i | ||||
\(568\) | 17.7271 | − | 17.7271i | 0.743811 | − | 0.743811i | ||||
\(569\) | −39.8275 | −1.66965 | −0.834827 | − | 0.550512i | \(-0.814433\pi\) | ||||
−0.834827 | + | 0.550512i | \(0.814433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.8314 | −1.83429 | −0.917143 | − | 0.398558i | \(-0.869511\pi\) | ||||
−0.917143 | + | 0.398558i | \(0.869511\pi\) | |||||||
\(572\) | 10.1007 | − | 10.1007i | 0.422332 | − | 0.422332i | ||||
\(573\) | −0.964086 | − | 0.0986978i | −0.0402753 | − | 0.00412316i | ||||
\(574\) | 5.68199i | 0.237162i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.69287 | + | 8.18138i | −0.0705363 | + | 0.340891i | ||||
\(577\) | 27.8182 | + | 27.8182i | 1.15809 | + | 1.15809i | 0.984886 | + | 0.173202i | \(0.0554114\pi\) |
0.173202 | + | 0.984886i | \(0.444589\pi\) | |||||||
\(578\) | 1.50936 | + | 1.50936i | 0.0627812 | + | 0.0627812i | ||||
\(579\) | −10.9070 | − | 13.3948i | −0.453278 | − | 0.556670i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.71029i | 0.236903i | ||||||||
\(582\) | 0.228809 | − | 2.23502i | 0.00948443 | − | 0.0926445i | ||||
\(583\) | −11.8496 | + | 11.8496i | −0.490759 | + | 0.490759i | ||||
\(584\) | 10.8670 | 0.449681 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.47352 | 0.102180 | ||||||||
\(587\) | 27.2778 | − | 27.2778i | 1.12588 | − | 1.12588i | 0.135034 | − | 0.990841i | \(-0.456886\pi\) |
0.990841 | − | 0.135034i | \(-0.0431144\pi\) | |||||||
\(588\) | 0.310299 | − | 3.03102i | 0.0127965 | − | 0.124997i | ||||
\(589\) | − | 27.7160i | − | 1.14202i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.6992 | + | 19.2802i | 0.645779 | + | 0.793081i | ||||
\(592\) | −5.59860 | − | 5.59860i | −0.230101 | − | 0.230101i | ||||
\(593\) | −1.21000 | − | 1.21000i | −0.0496886 | − | 0.0496886i | 0.681826 | − | 0.731515i | \(-0.261186\pi\) |
−0.731515 | + | 0.681826i | \(0.761186\pi\) | |||||||
\(594\) | −6.04501 | + | 3.14204i | −0.248030 | + | 0.128919i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.3818i | 0.671025i | ||||||||
\(597\) | −20.1162 | − | 2.05939i | −0.823301 | − | 0.0842850i | ||||
\(598\) | −3.80170 | + | 3.80170i | −0.155463 | + | 0.155463i | ||||
\(599\) | 15.6005 | 0.637421 | 0.318710 | − | 0.947852i | \(-0.396750\pi\) | ||||
0.318710 | + | 0.947852i | \(0.396750\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.2954 | 0.583122 | 0.291561 | − | 0.956552i | \(-0.405825\pi\) | ||||
0.291561 | + | 0.956552i | \(0.405825\pi\) | |||||||
\(602\) | 0.372576 | − | 0.372576i | 0.0151851 | − | 0.0151851i | ||||
\(603\) | −12.6083 | − | 19.1875i | −0.513452 | − | 0.781374i | ||||
\(604\) | 35.8626i | 1.45923i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.47938 | + | 2.01887i | −0.100718 | + | 0.0820111i | ||||
\(607\) | 26.8784 | + | 26.8784i | 1.09096 | + | 1.09096i | 0.995426 | + | 0.0955365i | \(0.0304567\pi\) |
0.0955365 | + | 0.995426i | \(0.469543\pi\) | |||||||
\(608\) | 18.4352 | + | 18.4352i | 0.747646 | + | 0.747646i | ||||
\(609\) | −3.85369 | + | 3.13793i | −0.156160 | + | 0.127155i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 32.9310i | − | 1.33224i | ||||||
\(612\) | −13.3907 | − | 20.3780i | −0.541287 | − | 0.823733i | ||||
\(613\) | −2.77744 | + | 2.77744i | −0.112180 | + | 0.112180i | −0.760969 | − | 0.648789i | \(-0.775276\pi\) |
0.648789 | + | 0.760969i | \(0.275276\pi\) | |||||||
\(614\) | 7.27046 | 0.293412 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.92867 | 0.198582 | ||||||||
\(617\) | −3.21465 | + | 3.21465i | −0.129417 | + | 0.129417i | −0.768848 | − | 0.639431i | \(-0.779170\pi\) |
0.639431 | + | 0.768848i | \(0.279170\pi\) | |||||||
\(618\) | −10.5928 | − | 1.08443i | −0.426104 | − | 0.0436222i | ||||
\(619\) | 48.7011i | 1.95746i | 0.205146 | + | 0.978731i | \(0.434233\pi\) | ||||
−0.205146 | + | 0.978731i | \(0.565767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.6147 | + | 8.63587i | −0.666724 | + | 0.346545i | ||||
\(622\) | 7.09184 | + | 7.09184i | 0.284357 | + | 0.284357i | ||||
\(623\) | −2.79396 | − | 2.79396i | −0.111938 | − | 0.111938i | ||||
\(624\) | 8.68567 | + | 10.6669i | 0.347705 | + | 0.427017i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.4409i | 0.457271i | ||||||||
\(627\) | 2.47073 | − | 24.1343i | 0.0986716 | − | 0.963830i | ||||
\(628\) | 11.1332 | − | 11.1332i | 0.444261 | − | 0.444261i | ||||
\(629\) | 14.0023 | 0.558307 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0588 | 0.599480 | 0.299740 | − | 0.954021i | \(-0.403100\pi\) | ||||
0.299740 | + | 0.954021i | \(0.403100\pi\) | |||||||
\(632\) | 5.08420 | − | 5.08420i | 0.202239 | − | 0.202239i | ||||
\(633\) | 0.137078 | − | 1.33898i | 0.00544834 | − | 0.0532197i | ||||
\(634\) | 15.9325i | 0.632761i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.0685 | − | 14.8213i | −0.478547 | − | 0.587704i | ||||
\(637\) | −2.14945 | − | 2.14945i | −0.0851641 | − | 0.0851641i | ||||
\(638\) | −2.66009 | − | 2.66009i | −0.105314 | − | 0.105314i | ||||
\(639\) | 8.25981 | − | 39.9184i | 0.326753 | − | 1.57915i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 45.9720i | − | 1.81578i | −0.419204 | − | 0.907892i | \(-0.637691\pi\) | ||
0.419204 | − | 0.907892i | \(-0.362309\pi\) | |||||||
\(642\) | 0.849619 | + | 0.0869793i | 0.0335318 | + | 0.00343280i | ||||
\(643\) | 5.91991 | − | 5.91991i | 0.233458 | − | 0.233458i | −0.580676 | − | 0.814135i | \(-0.697212\pi\) |
0.814135 | + | 0.580676i | \(0.197212\pi\) | |||||||
\(644\) | 6.33917 | 0.249798 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.8906 | −0.467831 | ||||||||
\(647\) | −11.1176 | + | 11.1176i | −0.437079 | + | 0.437079i | −0.891028 | − | 0.453949i | \(-0.850015\pi\) |
0.453949 | + | 0.891028i | \(0.350015\pi\) | |||||||
\(648\) | −6.11781 | − | 15.4369i | −0.240330 | − | 0.606419i | ||||
\(649\) | − | 0.425915i | − | 0.0167186i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.09965 | − | 5.78100i | 0.278257 | − | 0.226575i | ||||
\(652\) | 11.3575 | + | 11.3575i | 0.444793 | + | 0.444793i | ||||
\(653\) | −30.6500 | − | 30.6500i | −1.19943 | − | 1.19943i | −0.974339 | − | 0.225088i | \(-0.927733\pi\) |
−0.225088 | − | 0.974339i | \(-0.572267\pi\) | |||||||
\(654\) | 12.5344 | − | 10.2063i | 0.490135 | − | 0.399100i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 30.2465i | 1.18093i | ||||||||
\(657\) | 14.7671 | − | 9.70367i | 0.576120 | − | 0.378576i | ||||
\(658\) | 3.75976 | − | 3.75976i | 0.146571 | − | 0.146571i | ||||
\(659\) | −50.9397 | −1.98433 | −0.992165 | − | 0.124933i | \(-0.960129\pi\) | ||||
−0.992165 | + | 0.124933i | \(0.960129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5394 | −0.798889 | −0.399445 | − | 0.916757i | \(-0.630797\pi\) | ||||
−0.399445 | + | 0.916757i | \(0.630797\pi\) | |||||||
\(662\) | 0.768589 | − | 0.768589i | 0.0298721 | − | 0.0298721i | ||||
\(663\) | −24.2007 | − | 2.47753i | −0.939877 | − | 0.0962194i | ||||
\(664\) | − | 10.5355i | − | 0.408856i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.36956 | + | 0.904139i | 0.169317 | + | 0.0350347i | ||||
\(667\) | −7.31125 | − | 7.31125i | −0.283093 | − | 0.283093i | ||||
\(668\) | −2.77947 | − | 2.77947i | −0.107541 | − | 0.107541i | ||||
\(669\) | 5.16288 | + | 6.34054i | 0.199609 | + | 0.245139i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.6231i | 0.487310i | ||||||||
\(672\) | −0.877097 | + | 8.56753i | −0.0338347 | + | 0.330500i | ||||
\(673\) | −25.4635 | + | 25.4635i | −0.981544 | + | 0.981544i | −0.999833 | − | 0.0182887i | \(-0.994178\pi\) |
0.0182887 | + | 0.999833i | \(0.494178\pi\) | |||||||
\(674\) | 7.53394 | 0.290196 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.61384 | −0.254379 | ||||||||
\(677\) | 8.67613 | − | 8.67613i | 0.333451 | − | 0.333451i | −0.520445 | − | 0.853895i | \(-0.674234\pi\) |
0.853895 | + | 0.520445i | \(0.174234\pi\) | |||||||
\(678\) | −0.696831 | + | 6.80669i | −0.0267616 | + | 0.261409i | ||||
\(679\) | 2.64285i | 0.101423i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.374794 | − | 0.460284i | −0.0143621 | − | 0.0176381i | ||||
\(682\) | 4.90068 | + | 4.90068i | 0.187657 | + | 0.187657i | ||||
\(683\) | −24.0010 | − | 24.0010i | −0.918373 | − | 0.918373i | 0.0785378 | − | 0.996911i | \(-0.474975\pi\) |
−0.996911 | + | 0.0785378i | \(0.974975\pi\) | |||||||
\(684\) | 27.0965 | + | 5.60675i | 1.03606 | + | 0.214379i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 0.490808i | − | 0.0187391i | ||||||
\(687\) | 23.2254 | + | 2.37769i | 0.886104 | + | 0.0907145i | ||||
\(688\) | 1.98330 | − | 1.98330i | 0.0756127 | − | 0.0756127i | ||||
\(689\) | −19.0689 | −0.726467 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.5680 | −1.23894 | −0.619472 | − | 0.785019i | \(-0.712653\pi\) | ||||
−0.619472 | + | 0.785019i | \(0.712653\pi\) | |||||||
\(692\) | −2.98996 | + | 2.98996i | −0.113661 | + | 0.113661i | ||||
\(693\) | 6.69752 | − | 4.40103i | 0.254418 | − | 0.167181i | ||||
\(694\) | 3.51455i | 0.133410i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.11007 | − | 5.78948i | 0.269506 | − | 0.219450i | ||||
\(697\) | −37.8237 | − | 37.8237i | −1.43267 | − | 1.43267i | ||||
\(698\) | 2.57768 | + | 2.57768i | 0.0975667 | + | 0.0975667i | ||||
\(699\) | 2.26528 | − | 1.84454i | 0.0856808 | − | 0.0697670i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.43359i | 0.0919155i | 0.998943 | + | 0.0459577i | \(0.0146340\pi\) | ||||
−0.998943 | + | 0.0459577i | \(0.985366\pi\) | |||||||
\(702\) | −7.39211 | − | 2.33580i | −0.278997 | − | 0.0881592i | ||||
\(703\) | −11.2356 | + | 11.2356i | −0.423760 | + | 0.423760i | ||||
\(704\) | 7.43948 | 0.280386 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.30965 | 0.237467 | ||||||||
\(707\) | 2.65954 | − | 2.65954i | 0.100022 | − | 0.100022i | ||||
\(708\) | 0.483257 | + | 0.0494732i | 0.0181619 | + | 0.00185932i | ||||
\(709\) | 12.3477i | 0.463728i | 0.972748 | + | 0.231864i | \(0.0744825\pi\) | ||||
−0.972748 | + | 0.231864i | \(0.925518\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.36895 | − | 11.4488i | 0.0888427 | − | 0.429363i | ||||
\(712\) | 5.15485 | + | 5.15485i | 0.193186 | + | 0.193186i | ||||
\(713\) | 13.4695 | + | 13.4695i | 0.504436 | + | 0.504436i | ||||
\(714\) | −2.48015 | − | 3.04587i | −0.0928173 | − | 0.113989i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 14.8536i | − | 0.555103i | ||||||
\(717\) | −0.909011 | + | 8.87927i | −0.0339476 | + | 0.331603i | ||||
\(718\) | −8.76797 | + | 8.76797i | −0.327218 | + | 0.327218i | ||||
\(719\) | −24.2165 | −0.903125 | −0.451562 | − | 0.892240i | \(-0.649133\pi\) | ||||
−0.451562 | + | 0.892240i | \(0.649133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.5257 | 0.466482 | ||||||||
\(722\) | 2.94721 | − | 2.94721i | 0.109684 | − | 0.109684i | ||||
\(723\) | 2.63137 | − | 25.7033i | 0.0978616 | − | 0.955917i | ||||
\(724\) | 9.70117i | 0.360541i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.07397 | − | 2.54704i | −0.0769723 | − | 0.0945297i | ||||
\(727\) | 25.8923 | + | 25.8923i | 0.960293 | + | 0.960293i | 0.999241 | − | 0.0389483i | \(-0.0124008\pi\) |
−0.0389483 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(728\) | 3.96573 | + | 3.96573i | 0.146980 | + | 0.146980i | ||||
\(729\) | −22.0977 | − | 15.5142i | −0.818435 | − | 0.574599i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.96030i | 0.183463i | ||||||||
\(732\) | −14.3226 | − | 1.46627i | −0.529379 | − | 0.0541949i | ||||
\(733\) | −13.4535 | + | 13.4535i | −0.496918 | + | 0.496918i | −0.910477 | − | 0.413559i | \(-0.864285\pi\) |
0.413559 | + | 0.910477i | \(0.364285\pi\) | |||||||
\(734\) | 1.11882 | 0.0412965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.9184 | −0.660481 | ||||||||
\(737\) | −14.4563 | + | 14.4563i | −0.532503 | + | 0.532503i | ||||
\(738\) | −9.36099 | − | 14.2456i | −0.344583 | − | 0.524388i | ||||
\(739\) | 1.96813i | 0.0723987i | 0.999345 | + | 0.0361994i | \(0.0115251\pi\) | ||||
−0.999345 | + | 0.0361994i | \(0.988475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.4070 | − | 17.4310i | 0.786406 | − | 0.640343i | ||||
\(742\) | −2.17711 | − | 2.17711i | −0.0799243 | − | 0.0799243i | ||||
\(743\) | −4.54680 | − | 4.54680i | −0.166806 | − | 0.166806i | 0.618768 | − | 0.785574i | \(-0.287632\pi\) |
−0.785574 | + | 0.618768i | \(0.787632\pi\) | |||||||
\(744\) | −13.0989 | + | 10.6659i | −0.480227 | + | 0.391032i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 9.05496i | − | 0.331526i | ||||||
\(747\) | −9.40761 | − | 14.3166i | −0.344206 | − | 0.523815i | ||||
\(748\) | −15.3533 | + | 15.3533i | −0.561371 | + | 0.561371i | ||||
\(749\) | −1.00465 | −0.0367092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.491718 | −0.0179430 | −0.00897152 | − | 0.999960i | \(-0.502856\pi\) | ||||
−0.00897152 | + | 0.999960i | \(0.502856\pi\) | |||||||
\(752\) | 20.0140 | − | 20.0140i | 0.729835 | − | 0.729835i | ||||
\(753\) | −7.41432 | − | 0.759037i | −0.270193 | − | 0.0276609i | ||||
\(754\) | − | 4.28075i | − | 0.155896i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.21559 | + | 8.11044i | 0.153320 | + | 0.294974i | ||||
\(757\) | −3.50957 | − | 3.50957i | −0.127558 | − | 0.127558i | 0.640446 | − | 0.768003i | \(-0.278750\pi\) |
−0.768003 | + | 0.640446i | \(0.778750\pi\) | |||||||
\(758\) | 6.61607 | + | 6.61607i | 0.240306 | + | 0.240306i | ||||
\(759\) | 10.5281 | + | 12.9296i | 0.382146 | + | 0.469314i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26.9220i | − | 0.975922i | −0.872865 | − | 0.487961i | \(-0.837741\pi\) | ||
0.872865 | − | 0.487961i | \(-0.162259\pi\) | |||||||
\(762\) | 1.48598 | − | 14.5151i | 0.0538312 | − | 0.525826i | ||||
\(763\) | −13.4452 | + | 13.4452i | −0.486749 | + | 0.486749i | ||||
\(764\) | −0.984264 | −0.0356094 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.3026 | 0.444512 | ||||||||
\(767\) | 0.342701 | − | 0.342701i | 0.0123742 | − | 0.0123742i | ||||
\(768\) | −0.00317918 | + | 0.0310544i | −0.000114719 | + | 0.00112058i | ||||
\(769\) | 31.3935i | 1.13208i | 0.824378 | + | 0.566040i | \(0.191525\pi\) | ||||
−0.824378 | + | 0.566040i | \(0.808475\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.01519 | + | 11.0716i | 0.324674 | + | 0.398733i | ||||
\(772\) | −12.4052 | − | 12.4052i | −0.446473 | − | 0.446473i | ||||
\(773\) | 13.3925 | + | 13.3925i | 0.481693 | + | 0.481693i | 0.905672 | − | 0.423979i | \(-0.139367\pi\) |
−0.423979 | + | 0.905672i | \(0.639367\pi\) | |||||||
\(774\) | −0.320291 | + | 1.54792i | −0.0115126 | + | 0.0556387i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 4.87606i | − | 0.175040i | ||||||
\(777\) | −5.22162 | − | 0.534561i | −0.187325 | − | 0.0191773i | ||||
\(778\) | −6.36887 | + | 6.36887i | −0.228335 | + | 0.228335i | ||||
\(779\) | 60.7006 | 2.17482 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.2985 | −1.29886 | ||||||||
\(782\) | 5.77865 | − | 5.77865i | 0.206644 | − | 0.206644i | ||||
\(783\) | 4.49210 | − | 14.2162i | 0.160535 | − | 0.508044i | ||||
\(784\) | − | 2.61267i | − | 0.0933098i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.55437 | − | 5.33700i | 0.233787 | − | 0.190364i | ||||
\(787\) | −22.4712 | − | 22.4712i | −0.801011 | − | 0.801011i | 0.182243 | − | 0.983254i | \(-0.441664\pi\) |
−0.983254 | + | 0.182243i | \(0.941664\pi\) | |||||||
\(788\) | 17.8557 | + | 17.8557i | 0.636085 | + | 0.636085i | ||||
\(789\) | −0.118698 | + | 0.0966515i | −0.00422575 | + | 0.00344088i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.04874i | − | 0.286180i | ||||||
\(792\) | −12.3569 | + | 8.11990i | −0.439084 | + | 0.288528i | ||||
\(793\) | −10.1569 | + | 10.1569i | −0.360681 | + | 0.360681i | ||||
\(794\) | −7.57440 | −0.268805 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.5372 | −0.727922 | ||||||||
\(797\) | 7.83907 | − | 7.83907i | 0.277674 | − | 0.277674i | −0.554506 | − | 0.832180i | \(-0.687093\pi\) |
0.832180 | + | 0.554506i | \(0.187093\pi\) | |||||||
\(798\) | 4.43417 | + | 0.453945i | 0.156968 | + | 0.0160695i | ||||
\(799\) | 50.0556i | 1.77084i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.6079 | + | 2.40187i | 0.410144 | + | 0.0848660i | ||||
\(802\) | −11.9471 | − | 11.9471i | −0.421866 | − | 0.421866i | ||||
\(803\) | −11.1259 | − | 11.1259i | −0.392623 | − | 0.392623i | ||||
\(804\) | −14.7233 | − | 18.0817i | −0.519252 | − | 0.637694i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.88640i | 0.277787i | ||||||||
\(807\) | 5.23366 | − | 51.1227i | 0.184233 | − | 1.79960i | ||||
\(808\) | −4.90684 | + | 4.90684i | −0.172622 | + | 0.172622i | ||||
\(809\) | 6.27026 | 0.220451 | 0.110225 | − | 0.993907i | \(-0.464843\pi\) | ||||
0.110225 | + | 0.993907i | \(0.464843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.90138 | −0.312570 | −0.156285 | − | 0.987712i | \(-0.549952\pi\) | ||||
−0.156285 | + | 0.987712i | \(0.549952\pi\) | |||||||
\(812\) | −3.56898 | + | 3.56898i | −0.125247 | + | 0.125247i | ||||
\(813\) | −3.99320 | + | 39.0058i | −0.140048 | + | 1.36799i | ||||
\(814\) | − | 3.97332i | − | 0.139265i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.2024 | − | 16.2138i | −0.462175 | − | 0.567598i | ||||
\(817\) | −3.98022 | − | 3.98022i | −0.139250 | − | 0.139250i | ||||
\(818\) | 2.63502 | + | 2.63502i | 0.0921313 | + | 0.0921313i | ||||
\(819\) | 8.93015 | + | 1.84781i | 0.312045 | + | 0.0645676i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.8442i | 0.587867i | 0.955826 | + | 0.293934i | \(0.0949645\pi\) | ||||
−0.955826 | + | 0.293934i | \(0.905036\pi\) | |||||||
\(822\) | 16.3425 | + | 1.67305i | 0.570008 | + | 0.0583543i | ||||
\(823\) | −32.4880 | + | 32.4880i | −1.13246 | + | 1.13246i | −0.142695 | + | 0.989767i | \(0.545577\pi\) |
−0.989767 | + | 0.142695i | \(0.954423\pi\) | |||||||
\(824\) | −23.1099 | −0.805072 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.0782529 | 0.00272277 | ||||||||
\(827\) | −4.87454 | + | 4.87454i | −0.169504 | + | 0.169504i | −0.786762 | − | 0.617257i | \(-0.788244\pi\) |
0.617257 | + | 0.786762i | \(0.288244\pi\) | |||||||
\(828\) | −15.8932 | + | 10.4437i | −0.552329 | + | 0.362943i | ||||
\(829\) | 9.82522i | 0.341244i | 0.985337 | + | 0.170622i | \(0.0545777\pi\) | ||||
−0.985337 | + | 0.170622i | \(0.945422\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.99924 | − | 6.51350i | 0.277490 | − | 0.225951i | ||||
\(832\) | 5.98598 | + | 5.98598i | 0.207527 | + | 0.207527i | ||||
\(833\) | 3.26719 | + | 3.26719i | 0.113201 | + | 0.113201i | ||||
\(834\) | −11.0703 | + | 9.01414i | −0.383332 | + | 0.312134i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 24.6394i | − | 0.852171i | ||||||
\(837\) | −8.27579 | + | 26.1904i | −0.286053 | + | 0.905272i | ||||
\(838\) | −2.15397 | + | 2.15397i | −0.0744075 | + | 0.0744075i | ||||
\(839\) | −13.0314 | −0.449893 | −0.224947 | − | 0.974371i | \(-0.572221\pi\) | ||||
−0.224947 | + | 0.974371i | \(0.572221\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7675 | −0.716120 | ||||||||
\(842\) | −8.72279 | + | 8.72279i | −0.300607 | + | 0.300607i | ||||
\(843\) | 37.9231 | + | 3.88235i | 1.30614 | + | 0.133715i | ||||
\(844\) | − | 1.36701i | − | 0.0470543i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.23214 | + | 15.6204i | −0.111123 | + | 0.537041i | ||||
\(847\) | 2.73212 | + | 2.73212i | 0.0938766 | + | 0.0938766i | ||||
\(848\) | −11.5892 | − | 11.5892i | −0.397976 | − | 0.397976i | ||||
\(849\) | −14.8463 | − | 18.2327i | −0.509523 | − | 0.625745i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 10.9207i | − | 0.374355i | ||||||
\(852\) | 4.21634 | − | 41.1855i | 0.144450 | − | 1.41099i | ||||
\(853\) | 36.7177 | − | 36.7177i | 1.25719 | − | 1.25719i | 0.304761 | − | 0.952429i | \(-0.401424\pi\) |
0.952429 | − | 0.304761i | \(-0.0985765\pi\) | |||||||
\(854\) | −2.31923 | −0.0793626 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.85358 | 0.0633542 | ||||||||
\(857\) | −25.5867 | + | 25.5867i | −0.874024 | + | 0.874024i | −0.992908 | − | 0.118884i | \(-0.962068\pi\) |
0.118884 | + | 0.992908i | \(0.462068\pi\) | |||||||
\(858\) | −0.703032 | + | 6.86725i | −0.0240011 | + | 0.234444i | ||||
\(859\) | − | 15.7133i | − | 0.536132i | −0.963401 | − | 0.268066i | \(-0.913615\pi\) | ||
0.963401 | − | 0.268066i | \(-0.0863845\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.6609 | + | 15.5489i | 0.431484 | + | 0.529906i | ||||
\(862\) | 2.92644 | + | 2.92644i | 0.0996751 | + | 0.0996751i | ||||
\(863\) | 11.1088 | + | 11.1088i | 0.378147 | + | 0.378147i | 0.870433 | − | 0.492286i | \(-0.163839\pi\) |
−0.492286 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(864\) | −11.9159 | − | 22.9251i | −0.405386 | − | 0.779927i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.0685i | 0.444084i | ||||||||
\(867\) | 7.49366 | + | 0.767159i | 0.254498 | + | 0.0260541i | ||||
\(868\) | 6.57512 | − | 6.57512i | 0.223174 | − | 0.223174i | ||||
\(869\) | −10.4106 | −0.353155 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.2637 | −0.788260 | ||||||||
\(872\) | 24.8064 | − | 24.8064i | 0.840050 | − | 0.840050i | ||||
\(873\) | −4.35405 | − | 6.62602i | −0.147362 | − | 0.224257i | ||||
\(874\) | 9.27375i | 0.313689i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.9161 | − | 11.3314i | 0.470182 | − | 0.382853i | ||||
\(877\) | 20.7301 | + | 20.7301i | 0.700006 | + | 0.700006i | 0.964412 | − | 0.264405i | \(-0.0851757\pi\) |
−0.264405 | + | 0.964412i | \(0.585176\pi\) | |||||||
\(878\) | 1.69456 | + | 1.69456i | 0.0571886 | + | 0.0571886i | ||||
\(879\) | 6.76884 | − | 5.51163i | 0.228307 | − | 0.185903i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.4774i | 0.892045i | 0.895022 | + | 0.446023i | \(0.147160\pi\) | ||||
−0.895022 | + | 0.446023i | \(0.852840\pi\) | |||||||
\(882\) | 0.808598 | + | 1.23053i | 0.0272269 | + | 0.0414341i | ||||
\(883\) | 26.9720 | − | 26.9720i | 0.907681 | − | 0.907681i | −0.0884037 | − | 0.996085i | \(-0.528177\pi\) |
0.996085 | + | 0.0884037i | \(0.0281766\pi\) | |||||||
\(884\) | −24.7072 | −0.830993 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.5864 | −0.557231 | ||||||||
\(887\) | −1.34997 | + | 1.34997i | −0.0453275 | + | 0.0453275i | −0.729407 | − | 0.684080i | \(-0.760204\pi\) |
0.684080 | + | 0.729407i | \(0.260204\pi\) | |||||||
\(888\) | 9.63389 | + | 0.986265i | 0.323292 | + | 0.0330969i | ||||
\(889\) | 17.1637i | 0.575653i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.54105 | + | 22.0681i | −0.319637 | + | 0.739309i | ||||
\(892\) | 5.87209 | + | 5.87209i | 0.196612 | + | 0.196612i | ||||
\(893\) | −40.1654 | − | 40.1654i | −1.34408 | − | 1.34408i | ||||
\(894\) | −4.99871 | − | 6.13892i | −0.167182 | − | 0.205316i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.3115i | 0.377890i | ||||||||
\(897\) | −1.93228 | + | 18.8746i | −0.0645169 | + | 0.630205i | ||||
\(898\) | −8.21601 | + | 8.21601i | −0.274172 | + | 0.274172i | ||||
\(899\) | −15.1668 | −0.505840 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.9850 | 0.965631 | ||||||||
\(902\) | −10.7330 | + | 10.7330i | −0.357368 | + | 0.357368i | ||||
\(903\) | 0.189368 | − | 1.84976i | 0.00630178 | − | 0.0615561i | ||||
\(904\) | 14.8499i | 0.493901i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.9430 | − | 13.4391i | −0.363558 | − | 0.446486i | ||||
\(907\) | 28.6846 | + | 28.6846i | 0.952456 | + | 0.952456i | 0.998920 | − | 0.0464640i | \(-0.0147953\pi\) |
−0.0464640 | + | 0.998920i | \(0.514795\pi\) | |||||||
\(908\) | −0.426278 | − | 0.426278i | −0.0141465 | − | 0.0141465i | ||||
\(909\) | −2.28631 | + | 11.0494i | −0.0758322 | + | 0.366485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0874i | 1.12937i | 0.825307 | + | 0.564684i | \(0.191002\pi\) | ||||
−0.825307 | + | 0.564684i | \(0.808998\pi\) | |||||||
\(912\) | 23.6040 | + | 2.41645i | 0.781607 | + | 0.0800166i | ||||
\(913\) | −10.7864 | + | 10.7864i | −0.356978 | + | 0.356978i | ||||
\(914\) | 7.12016 | 0.235514 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.7115 | 0.783450 | ||||||||
\(917\) | −7.03062 | + | 7.03062i | −0.232172 | + | 0.232172i | ||||
\(918\) | 11.2361 | + | 3.55046i | 0.370848 | + | 0.117183i | ||||
\(919\) | 2.19661i | 0.0724593i | 0.999343 | + | 0.0362297i | \(0.0115348\pi\) | ||||
−0.999343 | + | 0.0362297i | \(0.988465\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.8958 | − | 16.2005i | 0.655589 | − | 0.533823i | ||||
\(922\) | −8.09166 | − | 8.09166i | −0.266485 | − | 0.266485i | ||||
\(923\) | −29.2066 | − | 29.2066i | −0.961348 | − | 0.961348i | ||||
\(924\) | 6.31156 | − | 5.13929i | 0.207635 | − | 0.169070i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.8389i | 0.389049i | ||||||||
\(927\) | −31.4038 | + | 20.6359i | −1.03144 | + | 0.677771i | ||||
\(928\) | 10.0881 | − | 10.0881i | 0.331159 | − | 0.331159i | ||||
\(929\) | 51.2981 | 1.68304 | 0.841518 | − | 0.540230i | \(-0.181663\pi\) | ||||
0.841518 | + | 0.540230i | \(0.181663\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.24329 | −0.171842 | ||||||||
\(932\) | 2.09792 | − | 2.09792i | 0.0687197 | − | 0.0687197i | ||||
\(933\) | 35.2094 | + | 3.60455i | 1.15271 | + | 0.118008i | ||||
\(934\) | − | 5.55717i | − | 0.181836i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.4761 | − | 3.40920i | −0.538539 | − | 0.111433i | ||||
\(937\) | −16.4279 | − | 16.4279i | −0.536675 | − | 0.536675i | 0.385876 | − | 0.922551i | \(-0.373899\pi\) |
−0.922551 | + | 0.385876i | \(0.873899\pi\) | |||||||
\(938\) | −2.65603 | − | 2.65603i | −0.0867226 | − | 0.0867226i | ||||
\(939\) | 25.4933 | + | 31.3083i | 0.831942 | + | 1.02171i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.2870i | 1.86750i | 0.357922 | + | 0.933752i | \(0.383485\pi\) | ||||
−0.357922 | + | 0.933752i | \(0.616515\pi\) | |||||||
\(942\) | −0.774891 | + | 7.56918i | −0.0252473 | + | 0.246617i | ||||
\(943\) | −29.4995 | + | 29.4995i | −0.960635 | + | 0.960635i | ||||
\(944\) | 0.416557 | 0.0135578 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.40755 | 0.0457634 | ||||||||
\(947\) | 35.8300 | − | 35.8300i | 1.16432 | − | 1.16432i | 0.180799 | − | 0.983520i | \(-0.442132\pi\) |
0.983520 | − | 0.180799i | \(-0.0578684\pi\) | |||||||
\(948\) | 1.20927 | − | 11.8122i | 0.0392752 | − | 0.383642i | ||||
\(949\) | − | 17.9043i | − | 0.581197i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.5017 | + | 43.5997i | 1.15122 | + | 1.41382i | ||||
\(952\) | −6.02797 | − | 6.02797i | −0.195368 | − | 0.195368i | ||||
\(953\) | −35.4764 | − | 35.4764i | −1.14919 | − | 1.14919i | −0.986712 | − | 0.162481i | \(-0.948050\pi\) |
−0.162481 | − | 0.986712i | \(-0.551950\pi\) | |||||||
\(954\) | 9.04510 | + | 1.87159i | 0.292846 | + | 0.0605950i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.06511i | 0.293187i | ||||||||
\(957\) | −13.2068 | − | 1.35204i | −0.426914 | − | 0.0437051i | ||||
\(958\) | −6.98270 | + | 6.98270i | −0.225601 | + | 0.225601i | ||||
\(959\) | −19.3245 | −0.624022 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.05833 | −0.0986558 | ||||||||
\(962\) | 3.19703 | − | 3.19703i | 0.103076 | − | 0.103076i | ||||
\(963\) | 2.51881 | − | 1.65515i | 0.0811677 | − | 0.0533364i | ||||
\(964\) | − | 26.2413i | − | 0.845175i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.37554 | + | 1.93432i | −0.0764317 | + | 0.0622357i | ||||
\(967\) | 21.0372 | + | 21.0372i | 0.676511 | + | 0.676511i | 0.959209 | − | 0.282698i | \(-0.0912293\pi\) |
−0.282698 | + | 0.959209i | \(0.591229\pi\) | |||||||
\(968\) | −5.04075 | − | 5.04075i | −0.162016 | − | 0.162016i | ||||
\(969\) | −32.5390 | + | 26.4954i | −1.04530 | + | 0.851154i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 23.4561i | − | 0.752742i | −0.926469 | − | 0.376371i | \(-0.877172\pi\) | ||
0.926469 | − | 0.376371i | \(-0.122828\pi\) | |||||||
\(972\) | −23.9309 | − | 13.3890i | −0.767585 | − | 0.429451i | ||||
\(973\) | 11.8747 | − | 11.8747i | 0.380684 | − | 0.380684i | ||||
\(974\) | 5.39987 | 0.173023 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.3458 | −0.395179 | ||||||||
\(977\) | 9.03422 | − | 9.03422i | 0.289030 | − | 0.289030i | −0.547666 | − | 0.836697i | \(-0.684484\pi\) |
0.836697 | + | 0.547666i | \(0.184484\pi\) | |||||||
\(978\) | −7.72169 | − | 0.790504i | −0.246913 | − | 0.0252775i | ||||
\(979\) | − | 10.5552i | − | 0.337347i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5584 | − | 55.8598i | 0.369031 | − | 1.78347i | ||||
\(982\) | 0.796647 | + | 0.796647i | 0.0254220 | + | 0.0254220i | ||||
\(983\) | −3.13374 | − | 3.13374i | −0.0999509 | − | 0.0999509i | 0.655363 | − | 0.755314i | \(-0.272516\pi\) |
−0.755314 | + | 0.655363i | \(0.772516\pi\) | |||||||
\(984\) | −23.3594 | − | 28.6877i | −0.744672 | − | 0.914532i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.50680i | 0.207219i | ||||||||
\(987\) | 1.91096 | − | 18.6664i | 0.0608265 | − | 0.594157i | ||||
\(988\) | 19.8254 | − | 19.8254i | 0.630731 | − | 0.630731i | ||||
\(989\) | 3.86864 | 0.123016 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.2283 | −0.928467 | −0.464233 | − | 0.885713i | \(-0.653670\pi\) | ||||
−0.464233 | + | 0.885713i | \(0.653670\pi\) | |||||||
\(992\) | −18.5853 | + | 18.5853i | −0.590085 | + | 0.590085i | ||||
\(993\) | 0.390649 | − | 3.81588i | 0.0123969 | − | 0.121093i | ||||
\(994\) | − | 6.66909i | − | 0.211531i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.9857 | − | 13.4915i | −0.348095 | − | 0.427496i | ||||
\(997\) | 4.57510 | + | 4.57510i | 0.144895 | + | 0.144895i | 0.775833 | − | 0.630938i | \(-0.217330\pi\) |
−0.630938 | + | 0.775833i | \(0.717330\pi\) | |||||||
\(998\) | 4.27793 | + | 4.27793i | 0.135415 | + | 0.135415i | ||||
\(999\) | 13.9721 | − | 7.26231i | 0.442057 | − | 0.229769i |
(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 | 525.2.j.b.407.5 | 24 | ||
3.2 | odd | 2 | inner | 525.2.j.b.407.8 | 24 | ||
5.2 | odd | 4 | 105.2.j.a.8.5 | ✓ | 24 | ||
5.3 | odd | 4 | inner | 525.2.j.b.218.8 | 24 | ||
5.4 | even | 2 | 105.2.j.a.92.8 | yes | 24 | ||
15.2 | even | 4 | 105.2.j.a.8.8 | yes | 24 | ||
15.8 | even | 4 | inner | 525.2.j.b.218.5 | 24 | ||
15.14 | odd | 2 | 105.2.j.a.92.5 | yes | 24 | ||
35.2 | odd | 12 | 735.2.y.j.263.5 | 48 | |||
35.4 | even | 6 | 735.2.y.j.422.8 | 48 | |||
35.9 | even | 6 | 735.2.y.j.557.5 | 48 | |||
35.12 | even | 12 | 735.2.y.g.263.5 | 48 | |||
35.17 | even | 12 | 735.2.y.g.128.8 | 48 | |||
35.19 | odd | 6 | 735.2.y.g.557.5 | 48 | |||
35.24 | odd | 6 | 735.2.y.g.422.8 | 48 | |||
35.27 | even | 4 | 735.2.j.h.638.5 | 24 | |||
35.32 | odd | 12 | 735.2.y.j.128.8 | 48 | |||
35.34 | odd | 2 | 735.2.j.h.197.8 | 24 | |||
105.2 | even | 12 | 735.2.y.j.263.8 | 48 | |||
105.17 | odd | 12 | 735.2.y.g.128.5 | 48 | |||
105.32 | even | 12 | 735.2.y.j.128.5 | 48 | |||
105.44 | odd | 6 | 735.2.y.j.557.8 | 48 | |||
105.47 | odd | 12 | 735.2.y.g.263.8 | 48 | |||
105.59 | even | 6 | 735.2.y.g.422.5 | 48 | |||
105.62 | odd | 4 | 735.2.j.h.638.8 | 24 | |||
105.74 | odd | 6 | 735.2.y.j.422.5 | 48 | |||
105.89 | even | 6 | 735.2.y.g.557.8 | 48 | |||
105.104 | even | 2 | 735.2.j.h.197.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.5 | ✓ | 24 | 5.2 | odd | 4 | ||
105.2.j.a.8.8 | yes | 24 | 15.2 | even | 4 | ||
105.2.j.a.92.5 | yes | 24 | 15.14 | odd | 2 | ||
105.2.j.a.92.8 | yes | 24 | 5.4 | even | 2 | ||
525.2.j.b.218.5 | 24 | 15.8 | even | 4 | inner | ||
525.2.j.b.218.8 | 24 | 5.3 | odd | 4 | inner | ||
525.2.j.b.407.5 | 24 | 1.1 | even | 1 | trivial | ||
525.2.j.b.407.8 | 24 | 3.2 | odd | 2 | inner | ||
735.2.j.h.197.5 | 24 | 105.104 | even | 2 | |||
735.2.j.h.197.8 | 24 | 35.34 | odd | 2 | |||
735.2.j.h.638.5 | 24 | 35.27 | even | 4 | |||
735.2.j.h.638.8 | 24 | 105.62 | odd | 4 | |||
735.2.y.g.128.5 | 48 | 105.17 | odd | 12 | |||
735.2.y.g.128.8 | 48 | 35.17 | even | 12 | |||
735.2.y.g.263.5 | 48 | 35.12 | even | 12 | |||
735.2.y.g.263.8 | 48 | 105.47 | odd | 12 | |||
735.2.y.g.422.5 | 48 | 105.59 | even | 6 | |||
735.2.y.g.422.8 | 48 | 35.24 | odd | 6 | |||
735.2.y.g.557.5 | 48 | 35.19 | odd | 6 | |||
735.2.y.g.557.8 | 48 | 105.89 | even | 6 | |||
735.2.y.j.128.5 | 48 | 105.32 | even | 12 | |||
735.2.y.j.128.8 | 48 | 35.32 | odd | 12 | |||
735.2.y.j.263.5 | 48 | 35.2 | odd | 12 | |||
735.2.y.j.263.8 | 48 | 105.2 | even | 12 | |||
735.2.y.j.422.5 | 48 | 105.74 | odd | 6 | |||
735.2.y.j.422.8 | 48 | 35.4 | even | 6 | |||
735.2.y.j.557.5 | 48 | 35.9 | even | 6 | |||
735.2.y.j.557.8 | 48 | 105.44 | odd | 6 |