Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(307,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.w (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: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 2 x^{12} + 4 x^{11} + 112 x^{10} - 208 x^{9} + 200 x^{8} + 392 x^{7} + 1708 x^{6} - 1744 x^{5} + 872 x^{4} - 80 x^{3} + 4 x^{2} - 8 x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.7 | ||
Root | \(2.18338 + 2.18338i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.307 |
Dual form | 1170.2.w.h.343.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.18338 | − | 0.482541i | 0.976438 | − | 0.215799i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.10714 | 0.796425 | 0.398213 | − | 0.917293i | \(-0.369631\pi\) | ||||
0.398213 | + | 0.917293i | \(0.369631\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.482541 | − | 2.18338i | −0.152593 | − | 0.690446i | ||||
\(11\) | 1.24283 | − | 1.24283i | 0.374729 | − | 0.374729i | −0.494467 | − | 0.869196i | \(-0.664637\pi\) |
0.869196 | + | 0.494467i | \(0.164637\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.37977 | − | 1.25584i | −0.937380 | − | 0.348308i | ||||
\(14\) | − | 2.10714i | − | 0.563158i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.54027 | − | 1.54027i | 0.373569 | − | 0.373569i | −0.495206 | − | 0.868775i | \(-0.664907\pi\) |
0.868775 | + | 0.495206i | \(0.164907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.19612 | − | 1.19612i | 0.274410 | − | 0.274410i | −0.556463 | − | 0.830872i | \(-0.687842\pi\) |
0.830872 | + | 0.556463i | \(0.187842\pi\) | |||||||
\(20\) | −2.18338 | + | 0.482541i | −0.488219 | + | 0.107900i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.24283 | − | 1.24283i | −0.264973 | − | 0.264973i | ||||
\(23\) | 2.88018 | + | 2.88018i | 0.600559 | + | 0.600559i | 0.940461 | − | 0.339902i | \(-0.110394\pi\) |
−0.339902 | + | 0.940461i | \(0.610394\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.53431 | − | 2.10714i | 0.906862 | − | 0.421429i | ||||
\(26\) | −1.25584 | + | 3.37977i | −0.246291 | + | 0.662828i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.10714 | −0.398213 | ||||||||
\(29\) | 0.655858i | 0.121790i | 0.998144 | + | 0.0608948i | \(0.0193954\pi\) | ||||
−0.998144 | + | 0.0608948i | \(0.980605\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.01590 | − | 5.01590i | −0.900882 | − | 0.900882i | 0.0946301 | − | 0.995513i | \(-0.469833\pi\) |
−0.995513 | + | 0.0946301i | \(0.969833\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.54027 | − | 1.54027i | −0.264153 | − | 0.264153i | ||||
\(35\) | 4.60070 | − | 1.01678i | 0.777660 | − | 0.171868i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.16468 | 1.01347 | 0.506734 | − | 0.862103i | \(-0.330853\pi\) | ||||
0.506734 | + | 0.862103i | \(0.330853\pi\) | |||||||
\(38\) | −1.19612 | − | 1.19612i | −0.194037 | − | 0.194037i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.482541 | + | 2.18338i | 0.0762965 | + | 0.345223i | ||||
\(41\) | 5.07630 | + | 5.07630i | 0.792785 | + | 0.792785i | 0.981946 | − | 0.189161i | \(-0.0605768\pi\) |
−0.189161 | + | 0.981946i | \(0.560577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.01007 | − | 3.01007i | −0.459031 | − | 0.459031i | 0.439307 | − | 0.898337i | \(-0.355224\pi\) |
−0.898337 | + | 0.439307i | \(0.855224\pi\) | |||||||
\(44\) | −1.24283 | + | 1.24283i | −0.187364 | + | 0.187364i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.88018 | − | 2.88018i | 0.424659 | − | 0.424659i | ||||
\(47\) | 9.52254 | 1.38901 | 0.694503 | − | 0.719490i | \(-0.255624\pi\) | ||||
0.694503 | + | 0.719490i | \(0.255624\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.55995 | −0.365706 | ||||||||
\(50\) | −2.10714 | − | 4.53431i | −0.297995 | − | 0.641248i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.37977 | + | 1.25584i | 0.468690 | + | 0.174154i | ||||
\(53\) | −3.88517 | + | 3.88517i | −0.533669 | + | 0.533669i | −0.921662 | − | 0.387993i | \(-0.873168\pi\) |
0.387993 | + | 0.921662i | \(0.373168\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.11386 | − | 3.31330i | 0.285033 | − | 0.446765i | ||||
\(56\) | 2.10714i | 0.281579i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.655858 | 0.0861183 | ||||||||
\(59\) | 1.87321 | + | 1.87321i | 0.243871 | + | 0.243871i | 0.818449 | − | 0.574579i | \(-0.194834\pi\) |
−0.574579 | + | 0.818449i | \(0.694834\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.35868 | 0.558072 | 0.279036 | − | 0.960281i | \(-0.409985\pi\) | ||||
0.279036 | + | 0.960281i | \(0.409985\pi\) | |||||||
\(62\) | −5.01590 | + | 5.01590i | −0.637020 | + | 0.637020i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −7.98533 | − | 1.11111i | −0.990458 | − | 0.137816i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.11822i | − | 0.869629i | −0.900520 | − | 0.434815i | \(-0.856814\pi\) | ||
0.900520 | − | 0.434815i | \(-0.143186\pi\) | |||||||
\(68\) | −1.54027 | + | 1.54027i | −0.186785 | + | 0.186785i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.01678 | − | 4.60070i | −0.121529 | − | 0.549889i | ||||
\(71\) | −1.46384 | − | 1.46384i | −0.173726 | − | 0.173726i | 0.614888 | − | 0.788614i | \(-0.289201\pi\) |
−0.788614 | + | 0.614888i | \(0.789201\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.7472i | − | 1.72603i | −0.505174 | − | 0.863017i | \(-0.668572\pi\) | ||
0.505174 | − | 0.863017i | \(-0.331428\pi\) | |||||||
\(74\) | − | 6.16468i | − | 0.716630i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.19612 | + | 1.19612i | −0.137205 | + | 0.137205i | ||||
\(77\) | 2.61883 | − | 2.61883i | 0.298444 | − | 0.298444i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.75410i | 0.197352i | 0.995120 | + | 0.0986760i | \(0.0314607\pi\) | ||||
−0.995120 | + | 0.0986760i | \(0.968539\pi\) | |||||||
\(80\) | 2.18338 | − | 0.482541i | 0.244109 | − | 0.0539498i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.07630 | − | 5.07630i | 0.560584 | − | 0.560584i | ||||
\(83\) | −13.9129 | −1.52714 | −0.763569 | − | 0.645726i | \(-0.776555\pi\) | ||||
−0.763569 | + | 0.645726i | \(0.776555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.61975 | − | 4.10623i | 0.284151 | − | 0.445383i | ||||
\(86\) | −3.01007 | + | 3.01007i | −0.324584 | + | 0.324584i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.24283 | + | 1.24283i | 0.132487 | + | 0.132487i | ||||
\(89\) | 1.31506 | + | 1.31506i | 0.139396 | + | 0.139396i | 0.773362 | − | 0.633965i | \(-0.218574\pi\) |
−0.633965 | + | 0.773362i | \(0.718574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.12166 | − | 2.64624i | −0.746553 | − | 0.277402i | ||||
\(92\) | −2.88018 | − | 2.88018i | −0.300279 | − | 0.300279i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 9.52254i | − | 0.982175i | ||||||
\(95\) | 2.03441 | − | 3.18877i | 0.208726 | − | 0.327161i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.58936i | − | 0.669048i | −0.942387 | − | 0.334524i | \(-0.891425\pi\) | ||
0.942387 | − | 0.334524i | \(-0.108575\pi\) | |||||||
\(98\) | 2.55995i | 0.258594i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.53431 | + | 2.10714i | −0.453431 | + | 0.210714i | ||||
\(101\) | − | 1.61904i | − | 0.161101i | −0.996751 | − | 0.0805505i | \(-0.974332\pi\) | ||
0.996751 | − | 0.0805505i | \(-0.0256678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.42044 | − | 5.42044i | −0.534092 | − | 0.534092i | 0.387695 | − | 0.921788i | \(-0.373271\pi\) |
−0.921788 | + | 0.387695i | \(0.873271\pi\) | |||||||
\(104\) | 1.25584 | − | 3.37977i | 0.123146 | − | 0.331414i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.88517 | + | 3.88517i | 0.377361 | + | 0.377361i | ||||
\(107\) | 5.59200 | + | 5.59200i | 0.540599 | + | 0.540599i | 0.923705 | − | 0.383106i | \(-0.125145\pi\) |
−0.383106 | + | 0.923705i | \(0.625145\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.50709 | + | 8.50709i | −0.814832 | + | 0.814832i | −0.985354 | − | 0.170522i | \(-0.945455\pi\) |
0.170522 | + | 0.985354i | \(0.445455\pi\) | |||||||
\(110\) | −3.31330 | − | 2.11386i | −0.315911 | − | 0.201549i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.10714 | 0.199106 | ||||||||
\(113\) | 3.53973 | − | 3.53973i | 0.332990 | − | 0.332990i | −0.520731 | − | 0.853721i | \(-0.674341\pi\) |
0.853721 | + | 0.520731i | \(0.174341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.67833 | + | 4.89872i | 0.716008 | + | 0.456808i | ||||
\(116\) | − | 0.655858i | − | 0.0608948i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.87321 | − | 1.87321i | 0.172443 | − | 0.172443i | ||||
\(119\) | 3.24556 | − | 3.24556i | 0.297520 | − | 0.297520i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.91072i | 0.719157i | ||||||||
\(122\) | − | 4.35868i | − | 0.394616i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.01590 | + | 5.01590i | 0.450441 | + | 0.450441i | ||||
\(125\) | 8.88334 | − | 6.78869i | 0.794550 | − | 0.607199i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.45775 | + | 9.45775i | −0.839240 | + | 0.839240i | −0.988759 | − | 0.149519i | \(-0.952228\pi\) |
0.149519 | + | 0.988759i | \(0.452228\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.11111 | + | 7.98533i | −0.0974504 | + | 0.700359i | ||||
\(131\) | −21.7528 | −1.90055 | −0.950276 | − | 0.311408i | \(-0.899199\pi\) | ||||
−0.950276 | + | 0.311408i | \(0.899199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.52040 | − | 2.52040i | 0.218547 | − | 0.218547i | ||||
\(134\) | −7.11822 | −0.614921 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.54027 | + | 1.54027i | 0.132077 | + | 0.132077i | ||||
\(137\) | 18.4668 | 1.57773 | 0.788864 | − | 0.614568i | \(-0.210669\pi\) | ||||
0.788864 | + | 0.614568i | \(0.210669\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.02338i | 0.0868015i | 0.999058 | + | 0.0434008i | \(0.0138192\pi\) | ||||
−0.999058 | + | 0.0434008i | \(0.986181\pi\) | |||||||
\(140\) | −4.60070 | + | 1.01678i | −0.388830 | + | 0.0859339i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.46384 | + | 1.46384i | −0.122843 | + | 0.122843i | ||||
\(143\) | −5.76130 | + | 2.63969i | −0.481784 | + | 0.220742i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.316478 | + | 1.43199i | 0.0262821 | + | 0.118920i | ||||
\(146\) | −14.7472 | −1.22049 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.16468 | −0.506734 | ||||||||
\(149\) | 6.88021 | − | 6.88021i | 0.563649 | − | 0.563649i | −0.366693 | − | 0.930342i | \(-0.619510\pi\) |
0.930342 | + | 0.366693i | \(0.119510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.76761 | + | 1.76761i | −0.143846 | + | 0.143846i | −0.775363 | − | 0.631516i | \(-0.782433\pi\) |
0.631516 | + | 0.775363i | \(0.282433\pi\) | |||||||
\(152\) | 1.19612 | + | 1.19612i | 0.0970184 | + | 0.0970184i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.61883 | − | 2.61883i | −0.211031 | − | 0.211031i | ||||
\(155\) | −13.3720 | − | 8.53124i | −1.07407 | − | 0.685246i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.73178 | + | 1.73178i | 0.138211 | + | 0.138211i | 0.772827 | − | 0.634616i | \(-0.218842\pi\) |
−0.634616 | + | 0.772827i | \(0.718842\pi\) | |||||||
\(158\) | 1.75410 | 0.139549 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.482541 | − | 2.18338i | −0.0381482 | − | 0.172611i | ||||
\(161\) | 6.06895 | + | 6.06895i | 0.478300 | + | 0.478300i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9324i | 1.24792i | 0.781455 | + | 0.623962i | \(0.214478\pi\) | ||||
−0.781455 | + | 0.623962i | \(0.785522\pi\) | |||||||
\(164\) | −5.07630 | − | 5.07630i | −0.396393 | − | 0.396393i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.9129i | 1.07985i | ||||||||
\(167\) | 22.6158 | 1.75006 | 0.875032 | − | 0.484065i | \(-0.160840\pi\) | ||||
0.875032 | + | 0.484065i | \(0.160840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.84571 | + | 8.48893i | 0.757363 | + | 0.652995i | ||||
\(170\) | −4.10623 | − | 2.61975i | −0.314933 | − | 0.200925i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.01007 | + | 3.01007i | 0.229515 | + | 0.229515i | ||||
\(173\) | 12.8009 | + | 12.8009i | 0.973237 | + | 0.973237i | 0.999651 | − | 0.0264145i | \(-0.00840898\pi\) |
−0.0264145 | + | 0.999651i | \(0.508409\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.55444 | − | 4.44005i | 0.722248 | − | 0.335637i | ||||
\(176\) | 1.24283 | − | 1.24283i | 0.0936822 | − | 0.0936822i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.31506 | − | 1.31506i | 0.0985680 | − | 0.0985680i | ||||
\(179\) | −18.7205 | −1.39923 | −0.699617 | − | 0.714518i | \(-0.746646\pi\) | ||||
−0.699617 | + | 0.714518i | \(0.746646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6965i | 1.24104i | 0.784190 | + | 0.620520i | \(0.213079\pi\) | ||||
−0.784190 | + | 0.620520i | \(0.786921\pi\) | |||||||
\(182\) | −2.64624 | + | 7.12166i | −0.196153 | + | 0.527893i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.88018 | + | 2.88018i | −0.212330 | + | 0.212330i | ||||
\(185\) | 13.4598 | − | 2.97471i | 0.989588 | − | 0.218705i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.82859i | − | 0.279974i | ||||||
\(188\) | −9.52254 | −0.694503 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.18877 | − | 2.03441i | −0.231338 | − | 0.147592i | ||||
\(191\) | −6.58561 | −0.476518 | −0.238259 | − | 0.971202i | \(-0.576577\pi\) | ||||
−0.238259 | + | 0.971202i | \(0.576577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4497i | 0.752185i | 0.926582 | + | 0.376092i | \(0.122732\pi\) | ||||
−0.926582 | + | 0.376092i | \(0.877268\pi\) | |||||||
\(194\) | −6.58936 | −0.473088 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.55995 | 0.182853 | ||||||||
\(197\) | 11.5736i | 0.824583i | 0.911052 | + | 0.412292i | \(0.135271\pi\) | ||||
−0.911052 | + | 0.412292i | \(0.864729\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.7883 | −1.68631 | −0.843155 | − | 0.537671i | \(-0.819304\pi\) | ||||
−0.843155 | + | 0.537671i | \(0.819304\pi\) | |||||||
\(200\) | 2.10714 | + | 4.53431i | 0.148998 | + | 0.320624i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.61904 | −0.113916 | ||||||||
\(203\) | 1.38199i | 0.0969964i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5330 | + | 8.63398i | 0.945188 | + | 0.603023i | ||||
\(206\) | −5.42044 | + | 5.42044i | −0.377660 | + | 0.377660i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.37977 | − | 1.25584i | −0.234345 | − | 0.0870771i | ||||
\(209\) | − | 2.97317i | − | 0.205658i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.22265 | 0.221857 | 0.110928 | − | 0.993828i | \(-0.464618\pi\) | ||||
0.110928 | + | 0.993828i | \(0.464618\pi\) | |||||||
\(212\) | 3.88517 | − | 3.88517i | 0.266835 | − | 0.266835i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.59200 | − | 5.59200i | 0.382261 | − | 0.382261i | ||||
\(215\) | −8.02460 | − | 5.11964i | −0.547273 | − | 0.349156i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.5692 | − | 10.5692i | −0.717486 | − | 0.717486i | ||||
\(218\) | 8.50709 | + | 8.50709i | 0.576173 | + | 0.576173i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.11386 | + | 3.31330i | −0.142517 | + | 0.223383i | ||||
\(221\) | −7.14008 | + | 3.27141i | −0.480294 | + | 0.220059i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.20878 | 0.415771 | 0.207885 | − | 0.978153i | \(-0.433342\pi\) | ||||
0.207885 | + | 0.978153i | \(0.433342\pi\) | |||||||
\(224\) | − | 2.10714i | − | 0.140789i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.53973 | − | 3.53973i | −0.235459 | − | 0.235459i | ||||
\(227\) | 1.01019i | 0.0670489i | 0.999438 | + | 0.0335244i | \(0.0106732\pi\) | ||||
−0.999438 | + | 0.0335244i | \(0.989327\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.16009 | − | 8.16009i | −0.539234 | − | 0.539234i | 0.384070 | − | 0.923304i | \(-0.374522\pi\) |
−0.923304 | + | 0.384070i | \(0.874522\pi\) | |||||||
\(230\) | 4.89872 | − | 7.67833i | 0.323012 | − | 0.506294i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.655858 | −0.0430592 | ||||||||
\(233\) | 8.81549 | + | 8.81549i | 0.577522 | + | 0.577522i | 0.934220 | − | 0.356698i | \(-0.116097\pi\) |
−0.356698 | + | 0.934220i | \(0.616097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.7913 | − | 4.59502i | 1.35628 | − | 0.299746i | ||||
\(236\) | −1.87321 | − | 1.87321i | −0.121935 | − | 0.121935i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.24556 | − | 3.24556i | −0.210379 | − | 0.210379i | ||||
\(239\) | −14.8422 | + | 14.8422i | −0.960061 | + | 0.960061i | −0.999233 | − | 0.0391714i | \(-0.987528\pi\) |
0.0391714 | + | 0.999233i | \(0.487528\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.7506 | + | 16.7506i | −1.07900 | + | 1.07900i | −0.0823985 | + | 0.996599i | \(0.526258\pi\) |
−0.996599 | + | 0.0823985i | \(0.973742\pi\) | |||||||
\(242\) | 7.91072 | 0.508521 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.35868 | −0.279036 | ||||||||
\(245\) | −5.58934 | + | 1.23528i | −0.357090 | + | 0.0789191i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.54477 | + | 2.54048i | −0.352805 | + | 0.161647i | ||||
\(248\) | 5.01590 | − | 5.01590i | 0.318510 | − | 0.318510i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.78869 | − | 8.88334i | −0.429354 | − | 0.561832i | ||||
\(251\) | 12.6899i | 0.800981i | 0.916301 | + | 0.400491i | \(0.131160\pi\) | ||||
−0.916301 | + | 0.400491i | \(0.868840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.15917 | 0.450093 | ||||||||
\(254\) | 9.45775 | + | 9.45775i | 0.593432 | + | 0.593432i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.27952 | − | 6.27952i | 0.391706 | − | 0.391706i | −0.483589 | − | 0.875295i | \(-0.660667\pi\) |
0.875295 | + | 0.483589i | \(0.160667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.9899 | 0.807151 | ||||||||
\(260\) | 7.98533 | + | 1.11111i | 0.495229 | + | 0.0689079i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.7528i | 1.34389i | ||||||||
\(263\) | 1.75042 | − | 1.75042i | 0.107935 | − | 0.107935i | −0.651077 | − | 0.759012i | \(-0.725682\pi\) |
0.759012 | + | 0.651077i | \(0.225682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.60805 | + | 10.3576i | −0.405929 | + | 0.636260i | ||||
\(266\) | −2.52040 | − | 2.52040i | −0.154536 | − | 0.154536i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.11822i | 0.434815i | ||||||||
\(269\) | − | 22.0044i | − | 1.34163i | −0.741623 | − | 0.670817i | \(-0.765944\pi\) | ||
0.741623 | − | 0.670817i | \(-0.234056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.44668 | + | 6.44668i | −0.391608 | + | 0.391608i | −0.875260 | − | 0.483652i | \(-0.839310\pi\) |
0.483652 | + | 0.875260i | \(0.339310\pi\) | |||||||
\(272\) | 1.54027 | − | 1.54027i | 0.0933923 | − | 0.0933923i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 18.4668i | − | 1.11562i | ||||||
\(275\) | 3.01656 | − | 8.25423i | 0.181906 | − | 0.497749i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.610861 | + | 0.610861i | −0.0367031 | + | 0.0367031i | −0.725220 | − | 0.688517i | \(-0.758262\pi\) |
0.688517 | + | 0.725220i | \(0.258262\pi\) | |||||||
\(278\) | 1.02338 | 0.0613780 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.01678 | + | 4.60070i | 0.0607645 | + | 0.274944i | ||||
\(281\) | 2.98812 | − | 2.98812i | 0.178256 | − | 0.178256i | −0.612339 | − | 0.790595i | \(-0.709771\pi\) |
0.790595 | + | 0.612339i | \(0.209771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.2284 | + | 19.2284i | 1.14301 | + | 1.14301i | 0.987896 | + | 0.155116i | \(0.0495752\pi\) |
0.155116 | + | 0.987896i | \(0.450425\pi\) | |||||||
\(284\) | 1.46384 | + | 1.46384i | 0.0868630 | + | 0.0868630i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.63969 | + | 5.76130i | 0.156088 | + | 0.340673i | ||||
\(287\) | 10.6965 | + | 10.6965i | 0.631394 | + | 0.631394i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.2552i | 0.720892i | ||||||||
\(290\) | 1.43199 | − | 0.316478i | 0.0840892 | − | 0.0185843i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.7472i | 0.863017i | ||||||||
\(293\) | 22.2931i | 1.30238i | 0.758916 | + | 0.651188i | \(0.225729\pi\) | ||||
−0.758916 | + | 0.651188i | \(0.774271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.99383 | + | 3.18603i | 0.290752 | + | 0.185498i | ||||
\(296\) | 6.16468i | 0.358315i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.88021 | − | 6.88021i | −0.398560 | − | 0.398560i | ||||
\(299\) | −6.11729 | − | 13.3514i | −0.353772 | − | 0.772132i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.34264 | − | 6.34264i | −0.365584 | − | 0.365584i | ||||
\(302\) | 1.76761 | + | 1.76761i | 0.101715 | + | 0.101715i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.19612 | − | 1.19612i | 0.0686024 | − | 0.0686024i | ||||
\(305\) | 9.51666 | − | 2.10324i | 0.544922 | − | 0.120431i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.0008 | −1.08444 | −0.542218 | − | 0.840238i | \(-0.682415\pi\) | ||||
−0.542218 | + | 0.840238i | \(0.682415\pi\) | |||||||
\(308\) | −2.61883 | + | 2.61883i | −0.149222 | + | 0.149222i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.53124 | + | 13.3720i | −0.484542 | + | 0.759479i | ||||
\(311\) | − | 7.95375i | − | 0.451016i | −0.974241 | − | 0.225508i | \(-0.927596\pi\) | ||
0.974241 | − | 0.225508i | \(-0.0724042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.4521 | − | 21.4521i | 1.21254 | − | 1.21254i | 0.242358 | − | 0.970187i | \(-0.422079\pi\) |
0.970187 | − | 0.242358i | \(-0.0779209\pi\) | |||||||
\(314\) | 1.73178 | − | 1.73178i | 0.0977300 | − | 0.0977300i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 1.75410i | − | 0.0986760i | ||||||
\(317\) | 9.21536i | 0.517586i | 0.965933 | + | 0.258793i | \(0.0833248\pi\) | ||||
−0.965933 | + | 0.258793i | \(0.916675\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.815122 | + | 0.815122i | 0.0456381 | + | 0.0456381i | ||||
\(320\) | −2.18338 | + | 0.482541i | −0.122055 | + | 0.0269749i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.06895 | − | 6.06895i | 0.338209 | − | 0.338209i | ||||
\(323\) | − | 3.68470i | − | 0.205022i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.9712 | + | 1.42728i | −0.996861 | + | 0.0791714i | ||||
\(326\) | 15.9324 | 0.882416 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.07630 | + | 5.07630i | −0.280292 | + | 0.280292i | ||||
\(329\) | 20.0654 | 1.10624 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.58330 | + | 6.58330i | 0.361851 | + | 0.361851i | 0.864494 | − | 0.502643i | \(-0.167639\pi\) |
−0.502643 | + | 0.864494i | \(0.667639\pi\) | |||||||
\(332\) | 13.9129 | 0.763569 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 22.6158i | − | 1.23748i | ||||||
\(335\) | −3.43484 | − | 15.5418i | −0.187665 | − | 0.849139i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.4607 | − | 10.4607i | 0.569832 | − | 0.569832i | −0.362249 | − | 0.932081i | \(-0.617991\pi\) |
0.932081 | + | 0.362249i | \(0.117991\pi\) | |||||||
\(338\) | 8.48893 | − | 9.84571i | 0.461737 | − | 0.535536i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.61975 | + | 4.10623i | −0.142076 | + | 0.222692i | ||||
\(341\) | −12.4679 | −0.675173 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1442 | −1.08768 | ||||||||
\(344\) | 3.01007 | − | 3.01007i | 0.162292 | − | 0.162292i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.8009 | − | 12.8009i | 0.688182 | − | 0.688182i | ||||
\(347\) | −12.9575 | − | 12.9575i | −0.695596 | − | 0.695596i | 0.267861 | − | 0.963458i | \(-0.413683\pi\) |
−0.963458 | + | 0.267861i | \(0.913683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4575 | + | 14.4575i | 0.773892 | + | 0.773892i | 0.978784 | − | 0.204893i | \(-0.0656846\pi\) |
−0.204893 | + | 0.978784i | \(0.565685\pi\) | |||||||
\(350\) | −4.44005 | − | 9.55444i | −0.237331 | − | 0.510706i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.24283 | − | 1.24283i | −0.0662433 | − | 0.0662433i | ||||
\(353\) | 28.3107 | 1.50683 | 0.753413 | − | 0.657547i | \(-0.228406\pi\) | ||||
0.753413 | + | 0.657547i | \(0.228406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.90249 | − | 2.48976i | −0.207123 | − | 0.132143i | ||||
\(356\) | −1.31506 | − | 1.31506i | −0.0696981 | − | 0.0696981i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.7205i | 0.989407i | ||||||||
\(359\) | −3.64287 | − | 3.64287i | −0.192263 | − | 0.192263i | 0.604410 | − | 0.796673i | \(-0.293409\pi\) |
−0.796673 | + | 0.604410i | \(0.793409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1386i | 0.849399i | ||||||||
\(362\) | 16.6965 | 0.877548 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.12166 | + | 2.64624i | 0.373277 | + | 0.138701i | ||||
\(365\) | −7.11616 | − | 32.1989i | −0.372477 | − | 1.68537i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.99757 | + | 6.99757i | 0.365270 | + | 0.365270i | 0.865749 | − | 0.500479i | \(-0.166843\pi\) |
−0.500479 | + | 0.865749i | \(0.666843\pi\) | |||||||
\(368\) | 2.88018 | + | 2.88018i | 0.150140 | + | 0.150140i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.97471 | − | 13.4598i | −0.154648 | − | 0.699744i | ||||
\(371\) | −8.18661 | + | 8.18661i | −0.425028 | + | 0.425028i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.34687 | − | 2.34687i | 0.121516 | − | 0.121516i | −0.643733 | − | 0.765250i | \(-0.722615\pi\) |
0.765250 | + | 0.643733i | \(0.222615\pi\) | |||||||
\(374\) | −3.82859 | −0.197972 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.52254i | 0.491088i | ||||||||
\(377\) | 0.823655 | − | 2.21665i | 0.0424204 | − | 0.114163i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.34919 | + | 3.34919i | −0.172037 | + | 0.172037i | −0.787874 | − | 0.615837i | \(-0.788818\pi\) |
0.615837 | + | 0.787874i | \(0.288818\pi\) | |||||||
\(380\) | −2.03441 | + | 3.18877i | −0.104363 | + | 0.163581i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.58561i | 0.336949i | ||||||||
\(383\) | −24.7318 | −1.26373 | −0.631867 | − | 0.775077i | \(-0.717711\pi\) | ||||
−0.631867 | + | 0.775077i | \(0.717711\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.45421 | − | 6.98160i | 0.227008 | − | 0.355815i | ||||
\(386\) | 10.4497 | 0.531875 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.58936i | 0.334524i | ||||||||
\(389\) | 3.36767 | 0.170748 | 0.0853738 | − | 0.996349i | \(-0.472792\pi\) | ||||
0.0853738 | + | 0.996349i | \(0.472792\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.87248 | 0.448701 | ||||||||
\(392\) | − | 2.55995i | − | 0.129297i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.5736 | 0.583068 | ||||||||
\(395\) | 0.846427 | + | 3.82987i | 0.0425884 | + | 0.192702i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.6097 | −0.783427 | −0.391714 | − | 0.920087i | \(-0.628118\pi\) | ||||
−0.391714 | + | 0.920087i | \(0.628118\pi\) | |||||||
\(398\) | 23.7883i | 1.19240i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.53431 | − | 2.10714i | 0.226715 | − | 0.105357i | ||||
\(401\) | −26.3476 | + | 26.3476i | −1.31574 | + | 1.31574i | −0.398620 | + | 0.917116i | \(0.630511\pi\) |
−0.917116 | + | 0.398620i | \(0.869489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.6534 | + | 23.2518i | 0.530684 | + | 1.15825i | ||||
\(404\) | 1.61904i | 0.0805505i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.38199 | 0.0685868 | ||||||||
\(407\) | 7.66168 | − | 7.66168i | 0.379775 | − | 0.379775i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.1408 | + | 21.1408i | −1.04535 | + | 1.04535i | −0.0464256 | + | 0.998922i | \(0.514783\pi\) |
−0.998922 | + | 0.0464256i | \(0.985217\pi\) | |||||||
\(410\) | 8.63398 | − | 13.5330i | 0.426402 | − | 0.668349i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.42044 | + | 5.42044i | 0.267046 | + | 0.267046i | ||||
\(413\) | 3.94712 | + | 3.94712i | 0.194225 | + | 0.194225i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.3772 | + | 6.71355i | −1.49116 | + | 0.329555i | ||||
\(416\) | −1.25584 | + | 3.37977i | −0.0615728 | + | 0.165707i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.97317 | −0.145422 | ||||||||
\(419\) | 14.7707i | 0.721595i | 0.932644 | + | 0.360797i | \(0.117495\pi\) | ||||
−0.932644 | + | 0.360797i | \(0.882505\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.9707 | − | 21.9707i | −1.07079 | − | 1.07079i | −0.997296 | − | 0.0734913i | \(-0.976586\pi\) |
−0.0734913 | − | 0.997296i | \(-0.523414\pi\) | |||||||
\(422\) | − | 3.22265i | − | 0.156876i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.88517 | − | 3.88517i | −0.188680 | − | 0.188680i | ||||
\(425\) | 3.73848 | − | 10.2296i | 0.181343 | − | 0.496209i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.18436 | 0.444462 | ||||||||
\(428\) | −5.59200 | − | 5.59200i | −0.270299 | − | 0.270299i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.11964 | + | 8.02460i | −0.246891 | + | 0.386981i | ||||
\(431\) | −1.95159 | − | 1.95159i | −0.0940049 | − | 0.0940049i | 0.658540 | − | 0.752545i | \(-0.271174\pi\) |
−0.752545 | + | 0.658540i | \(0.771174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.1334 | − | 23.1334i | −1.11172 | − | 1.11172i | −0.992918 | − | 0.118804i | \(-0.962094\pi\) |
−0.118804 | − | 0.992918i | \(-0.537906\pi\) | |||||||
\(434\) | −10.5692 | + | 10.5692i | −0.507339 | + | 0.507339i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.50709 | − | 8.50709i | 0.407416 | − | 0.407416i | ||||
\(437\) | 6.89010 | 0.329598 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.1398 | 1.67713 | 0.838566 | − | 0.544800i | \(-0.183395\pi\) | ||||
0.838566 | + | 0.544800i | \(0.183395\pi\) | |||||||
\(440\) | 3.31330 | + | 2.11386i | 0.157955 | + | 0.100774i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.27141 | + | 7.14008i | 0.155605 | + | 0.339619i | ||||
\(443\) | −3.49624 | + | 3.49624i | −0.166111 | + | 0.166111i | −0.785268 | − | 0.619156i | \(-0.787475\pi\) |
0.619156 | + | 0.785268i | \(0.287475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.50585 | + | 2.23671i | 0.166193 | + | 0.106030i | ||||
\(446\) | − | 6.20878i | − | 0.293994i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.10714 | −0.0995532 | ||||||||
\(449\) | −7.86444 | − | 7.86444i | −0.371146 | − | 0.371146i | 0.496749 | − | 0.867894i | \(-0.334527\pi\) |
−0.867894 | + | 0.496749i | \(0.834527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.6180 | 0.594159 | ||||||||
\(452\) | −3.53973 | + | 3.53973i | −0.166495 | + | 0.166495i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.01019 | 0.0474107 | ||||||||
\(455\) | −16.8262 | − | 2.34126i | −0.788826 | − | 0.109760i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.00799i | − | 0.281042i | −0.990078 | − | 0.140521i | \(-0.955122\pi\) | ||
0.990078 | − | 0.140521i | \(-0.0448778\pi\) | |||||||
\(458\) | −8.16009 | + | 8.16009i | −0.381296 | + | 0.381296i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.67833 | − | 4.89872i | −0.358004 | − | 0.228404i | ||||
\(461\) | 26.1391 | + | 26.1391i | 1.21742 | + | 1.21742i | 0.968532 | + | 0.248889i | \(0.0800656\pi\) |
0.248889 | + | 0.968532i | \(0.419934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.7752i | − | 1.43024i | −0.698999 | − | 0.715122i | \(-0.746371\pi\) | ||
0.698999 | − | 0.715122i | \(-0.253629\pi\) | |||||||
\(464\) | 0.655858i | 0.0304474i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.81549 | − | 8.81549i | 0.408370 | − | 0.408370i | ||||
\(467\) | −27.6301 | + | 27.6301i | −1.27857 | + | 1.27857i | −0.337096 | + | 0.941470i | \(0.609445\pi\) |
−0.941470 | + | 0.337096i | \(0.890555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14.9991i | − | 0.692595i | ||||||
\(470\) | −4.59502 | − | 20.7913i | −0.211953 | − | 0.959033i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.87321 | + | 1.87321i | −0.0862214 | + | 0.0862214i | ||||
\(473\) | −7.48203 | −0.344024 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.90319 | − | 7.94399i | 0.133207 | − | 0.364495i | ||||
\(476\) | −3.24556 | + | 3.24556i | −0.148760 | + | 0.148760i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.8422 | + | 14.8422i | 0.678866 | + | 0.678866i | ||||
\(479\) | −11.7482 | − | 11.7482i | −0.536787 | − | 0.536787i | 0.385797 | − | 0.922584i | \(-0.373927\pi\) |
−0.922584 | + | 0.385797i | \(0.873927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.8352 | − | 7.74188i | −0.950004 | − | 0.352999i | ||||
\(482\) | 16.7506 | + | 16.7506i | 0.762967 | + | 0.762967i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 7.91072i | − | 0.359578i | ||||||
\(485\) | −3.17964 | − | 14.3871i | −0.144380 | − | 0.653283i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.8941i | − | 0.493657i | −0.969059 | − | 0.246829i | \(-0.920612\pi\) | ||
0.969059 | − | 0.246829i | \(-0.0793884\pi\) | |||||||
\(488\) | 4.35868i | 0.197308i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.23528 | + | 5.58934i | 0.0558042 | + | 0.252500i | ||||
\(491\) | − | 19.7178i | − | 0.889854i | −0.895567 | − | 0.444927i | \(-0.853230\pi\) | ||
0.895567 | − | 0.444927i | \(-0.146770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.01019 | + | 1.01019i | 0.0454969 | + | 0.0454969i | ||||
\(494\) | 2.54048 | + | 5.54477i | 0.114302 | + | 0.249471i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.01590 | − | 5.01590i | −0.225221 | − | 0.225221i | ||||
\(497\) | −3.08452 | − | 3.08452i | −0.138360 | − | 0.138360i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.8969 | + | 25.8969i | −1.15930 | + | 1.15930i | −0.174678 | + | 0.984626i | \(0.555888\pi\) |
−0.984626 | + | 0.174678i | \(0.944112\pi\) | |||||||
\(500\) | −8.88334 | + | 6.78869i | −0.397275 | + | 0.303599i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.6899 | 0.566379 | ||||||||
\(503\) | −18.7885 | + | 18.7885i | −0.837737 | + | 0.837737i | −0.988561 | − | 0.150824i | \(-0.951807\pi\) |
0.150824 | + | 0.988561i | \(0.451807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.781256 | − | 3.53499i | −0.0347654 | − | 0.157305i | ||||
\(506\) | − | 7.15917i | − | 0.318264i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.45775 | − | 9.45775i | 0.419620 | − | 0.419620i | ||||
\(509\) | −9.87855 | + | 9.87855i | −0.437859 | + | 0.437859i | −0.891291 | − | 0.453432i | \(-0.850200\pi\) |
0.453432 | + | 0.891291i | \(0.350200\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 31.0746i | − | 1.37466i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.27952 | − | 6.27952i | −0.276978 | − | 0.276978i | ||||
\(515\) | −14.4505 | − | 9.21931i | −0.636765 | − | 0.406251i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.8349 | − | 11.8349i | 0.520500 | − | 0.520500i | ||||
\(518\) | − | 12.9899i | − | 0.570742i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.11111 | − | 7.98533i | 0.0487252 | − | 0.350180i | ||||
\(521\) | 23.5852 | 1.03329 | 0.516643 | − | 0.856201i | \(-0.327182\pi\) | ||||
0.516643 | + | 0.856201i | \(0.327182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.1997 | − | 13.1997i | 0.577184 | − | 0.577184i | −0.356943 | − | 0.934126i | \(-0.616181\pi\) |
0.934126 | + | 0.356943i | \(0.116181\pi\) | |||||||
\(524\) | 21.7528 | 0.950276 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.75042 | − | 1.75042i | −0.0763217 | − | 0.0763217i | ||||
\(527\) | −15.4516 | −0.673084 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 6.40914i | − | 0.278658i | ||||||
\(530\) | 10.3576 | + | 6.60805i | 0.449904 | + | 0.287035i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.52040 | + | 2.52040i | −0.109273 | + | 0.109273i | ||||
\(533\) | −10.7817 | − | 23.5318i | −0.467007 | − | 1.01927i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.9078 | + | 9.51109i | 0.644522 | + | 0.411200i | ||||
\(536\) | 7.11822 | 0.307460 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.0044 | −0.948679 | ||||||||
\(539\) | −3.18159 | + | 3.18159i | −0.137041 | + | 0.137041i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.0817 | − | 24.0817i | 1.03535 | − | 1.03535i | 0.0360013 | − | 0.999352i | \(-0.488538\pi\) |
0.999352 | − | 0.0360013i | \(-0.0114620\pi\) | |||||||
\(542\) | 6.44668 | + | 6.44668i | 0.276908 | + | 0.276908i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.54027 | − | 1.54027i | −0.0660384 | − | 0.0660384i | ||||
\(545\) | −14.4692 | + | 22.6793i | −0.619793 | + | 0.971473i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5594 | − | 13.5594i | −0.579760 | − | 0.579760i | 0.355077 | − | 0.934837i | \(-0.384455\pi\) |
−0.934837 | + | 0.355077i | \(0.884455\pi\) | |||||||
\(548\) | −18.4668 | −0.788864 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.25423 | − | 3.01656i | −0.351961 | − | 0.128627i | ||||
\(551\) | 0.784486 | + | 0.784486i | 0.0334202 | + | 0.0334202i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.69615i | 0.157176i | ||||||||
\(554\) | 0.610861 | + | 0.610861i | 0.0259530 | + | 0.0259530i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 1.02338i | − | 0.0434008i | ||||||
\(557\) | 10.4636 | 0.443359 | 0.221679 | − | 0.975120i | \(-0.428846\pi\) | ||||
0.221679 | + | 0.975120i | \(0.428846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.39316 | + | 13.9535i | 0.270402 | + | 0.590170i | ||||
\(560\) | 4.60070 | − | 1.01678i | 0.194415 | − | 0.0429670i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.98812 | − | 2.98812i | −0.126046 | − | 0.126046i | ||||
\(563\) | −11.8657 | − | 11.8657i | −0.500078 | − | 0.500078i | 0.411384 | − | 0.911462i | \(-0.365045\pi\) |
−0.911462 | + | 0.411384i | \(0.865045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.02052 | − | 9.43665i | 0.253285 | − | 0.397003i | ||||
\(566\) | 19.2284 | − | 19.2284i | 0.808232 | − | 0.808232i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.46384 | − | 1.46384i | 0.0614214 | − | 0.0614214i | ||||
\(569\) | −31.9702 | −1.34026 | −0.670129 | − | 0.742244i | \(-0.733761\pi\) | ||||
−0.670129 | + | 0.742244i | \(0.733761\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 40.3412i | − | 1.68823i | −0.536165 | − | 0.844113i | \(-0.680127\pi\) | ||
0.536165 | − | 0.844113i | \(-0.319873\pi\) | |||||||
\(572\) | 5.76130 | − | 2.63969i | 0.240892 | − | 0.110371i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.6965 | − | 10.6965i | 0.446463 | − | 0.446463i | ||||
\(575\) | 19.1286 | + | 6.99067i | 0.797716 | + | 0.291531i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6.68207i | − | 0.278178i | −0.990280 | − | 0.139089i | \(-0.955583\pi\) | ||
0.990280 | − | 0.139089i | \(-0.0444175\pi\) | |||||||
\(578\) | 12.2552 | 0.509748 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.316478 | − | 1.43199i | −0.0131411 | − | 0.0594600i | ||||
\(581\) | −29.3165 | −1.21625 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.65725i | 0.399962i | ||||||||
\(584\) | 14.7472 | 0.610245 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.2931 | 0.920919 | ||||||||
\(587\) | − | 27.0614i | − | 1.11694i | −0.829524 | − | 0.558472i | \(-0.811388\pi\) | ||
0.829524 | − | 0.558472i | \(-0.188612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.9993 | −0.494421 | ||||||||
\(590\) | 3.18603 | − | 4.99383i | 0.131167 | − | 0.205593i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.16468 | 0.253367 | ||||||||
\(593\) | 24.5808i | 1.00941i | 0.863292 | + | 0.504705i | \(0.168399\pi\) | ||||
−0.863292 | + | 0.504705i | \(0.831601\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52018 | − | 8.65242i | 0.226305 | − | 0.354714i | ||||
\(596\) | −6.88021 | + | 6.88021i | −0.281824 | + | 0.281824i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.3514 | + | 6.11729i | −0.545979 | + | 0.250155i | ||||
\(599\) | 27.0675i | 1.10595i | 0.833199 | + | 0.552974i | \(0.186507\pi\) | ||||
−0.833199 | + | 0.552974i | \(0.813493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.64287 | 0.270968 | 0.135484 | − | 0.990780i | \(-0.456741\pi\) | ||||
0.135484 | + | 0.990780i | \(0.456741\pi\) | |||||||
\(602\) | −6.34264 | + | 6.34264i | −0.258507 | + | 0.258507i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.76761 | − | 1.76761i | 0.0719231 | − | 0.0719231i | ||||
\(605\) | 3.81725 | + | 17.2721i | 0.155193 | + | 0.702212i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.3366 | − | 12.3366i | −0.500728 | − | 0.500728i | 0.410936 | − | 0.911664i | \(-0.365202\pi\) |
−0.911664 | + | 0.410936i | \(0.865202\pi\) | |||||||
\(608\) | −1.19612 | − | 1.19612i | −0.0485092 | − | 0.0485092i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.10324 | − | 9.51666i | −0.0851578 | − | 0.385318i | ||||
\(611\) | −32.1840 | − | 11.9588i | −1.30203 | − | 0.483802i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.4995 | −1.75693 | −0.878464 | − | 0.477808i | \(-0.841432\pi\) | ||||
−0.878464 | + | 0.477808i | \(0.841432\pi\) | |||||||
\(614\) | 19.0008i | 0.766812i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.61883 | + | 2.61883i | 0.105516 | + | 0.105516i | ||||
\(617\) | 6.19626i | 0.249452i | 0.992191 | + | 0.124726i | \(0.0398052\pi\) | ||||
−0.992191 | + | 0.124726i | \(0.960195\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.3512 | + | 23.3512i | 0.938565 | + | 0.938565i | 0.998219 | − | 0.0596543i | \(-0.0189998\pi\) |
−0.0596543 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(620\) | 13.3720 | + | 8.53124i | 0.537033 | + | 0.342623i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.95375 | −0.318916 | ||||||||
\(623\) | 2.77102 | + | 2.77102i | 0.111019 | + | 0.111019i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.1199 | − | 19.1089i | 0.644796 | − | 0.764355i | ||||
\(626\) | −21.4521 | − | 21.4521i | −0.857399 | − | 0.857399i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.73178 | − | 1.73178i | −0.0691055 | − | 0.0691055i | ||||
\(629\) | 9.49525 | − | 9.49525i | 0.378600 | − | 0.378600i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.4170 | − | 17.4170i | 0.693360 | − | 0.693360i | −0.269610 | − | 0.962970i | \(-0.586895\pi\) |
0.962970 | + | 0.269610i | \(0.0868948\pi\) | |||||||
\(632\) | −1.75410 | −0.0697744 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.21536 | 0.365989 | ||||||||
\(635\) | −16.0861 | + | 25.2136i | −0.638358 | + | 1.00057i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.65203 | + | 3.21489i | 0.342806 | + | 0.127379i | ||||
\(638\) | 0.815122 | − | 0.815122i | 0.0322710 | − | 0.0322710i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.482541 | + | 2.18338i | 0.0190741 | + | 0.0863057i | ||||
\(641\) | − | 5.10269i | − | 0.201544i | −0.994910 | − | 0.100772i | \(-0.967869\pi\) | ||
0.994910 | − | 0.100772i | \(-0.0321313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.9867 | 1.85297 | 0.926487 | − | 0.376327i | \(-0.122813\pi\) | ||||
0.926487 | + | 0.376327i | \(0.122813\pi\) | |||||||
\(644\) | −6.06895 | − | 6.06895i | −0.239150 | − | 0.239150i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.68470 | −0.144972 | ||||||||
\(647\) | 19.2898 | − | 19.2898i | 0.758358 | − | 0.758358i | −0.217665 | − | 0.976024i | \(-0.569844\pi\) |
0.976024 | + | 0.217665i | \(0.0698441\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.65618 | 0.182771 | ||||||||
\(650\) | 1.42728 | + | 17.9712i | 0.0559826 | + | 0.704887i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 15.9324i | − | 0.623962i | ||||||
\(653\) | 22.6253 | − | 22.6253i | 0.885395 | − | 0.885395i | −0.108682 | − | 0.994077i | \(-0.534663\pi\) |
0.994077 | + | 0.108682i | \(0.0346629\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.4947 | + | 10.4966i | −1.85577 | + | 0.410137i | ||||
\(656\) | 5.07630 | + | 5.07630i | 0.198196 | + | 0.198196i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 20.0654i | − | 0.782230i | ||||||
\(659\) | − | 45.2569i | − | 1.76296i | −0.472222 | − | 0.881480i | \(-0.656548\pi\) | ||
0.472222 | − | 0.881480i | \(-0.343452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2218 | + | 23.2218i | −0.903222 | + | 0.903222i | −0.995713 | − | 0.0924919i | \(-0.970517\pi\) |
0.0924919 | + | 0.995713i | \(0.470517\pi\) | |||||||
\(662\) | 6.58330 | − | 6.58330i | 0.255867 | − | 0.255867i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 13.9129i | − | 0.539925i | ||||||
\(665\) | 4.28680 | − | 6.71920i | 0.166235 | − | 0.260559i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.88899 | + | 1.88899i | −0.0731419 | + | 0.0731419i | ||||
\(668\) | −22.6158 | −0.875032 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −15.5418 | + | 3.43484i | −0.600432 | + | 0.132699i | ||||
\(671\) | 5.41712 | − | 5.41712i | 0.209125 | − | 0.209125i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3770 | + | 26.3770i | 1.01676 | + | 1.01676i | 0.999857 | + | 0.0169012i | \(0.00538009\pi\) |
0.0169012 | + | 0.999857i | \(0.494620\pi\) | |||||||
\(674\) | −10.4607 | − | 10.4607i | −0.402932 | − | 0.402932i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.84571 | − | 8.48893i | −0.378681 | − | 0.326497i | ||||
\(677\) | −10.0002 | − | 10.0002i | −0.384340 | − | 0.384340i | 0.488323 | − | 0.872663i | \(-0.337609\pi\) |
−0.872663 | + | 0.488323i | \(0.837609\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.8847i | − | 0.532847i | ||||||
\(680\) | 4.10623 | + | 2.61975i | 0.157467 | + | 0.100463i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.4679i | 0.477419i | ||||||||
\(683\) | 28.2136i | 1.07956i | 0.841805 | + | 0.539782i | \(0.181493\pi\) | ||||
−0.841805 | + | 0.539782i | \(0.818507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.3201 | − | 8.91101i | 1.54055 | − | 0.340472i | ||||
\(686\) | 20.1442i | 0.769108i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.01007 | − | 3.01007i | −0.114758 | − | 0.114758i | ||||
\(689\) | 18.0101 | − | 8.25182i | 0.686132 | − | 0.314369i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2102 | − | 18.2102i | −0.692747 | − | 0.692747i | 0.270089 | − | 0.962835i | \(-0.412947\pi\) |
−0.962835 | + | 0.270089i | \(0.912947\pi\) | |||||||
\(692\) | −12.8009 | − | 12.8009i | −0.486618 | − | 0.486618i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.9575 | + | 12.9575i | −0.491861 | + | 0.491861i | ||||
\(695\) | 0.493821 | + | 2.23442i | 0.0187317 | + | 0.0847563i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.6377 | 0.592321 | ||||||||
\(698\) | 14.4575 | − | 14.4575i | 0.547224 | − | 0.547224i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.55444 | + | 4.44005i | −0.361124 | + | 0.167818i | ||||
\(701\) | − | 5.82154i | − | 0.219876i | −0.993938 | − | 0.109938i | \(-0.964935\pi\) | ||
0.993938 | − | 0.109938i | \(-0.0350653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.37372 | − | 7.37372i | 0.278105 | − | 0.278105i | ||||
\(704\) | −1.24283 | + | 1.24283i | −0.0468411 | + | 0.0468411i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 28.3107i | − | 1.06549i | ||||||
\(707\) | − | 3.41156i | − | 0.128305i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.34798 | + | 9.34798i | 0.351071 | + | 0.351071i | 0.860508 | − | 0.509437i | \(-0.170146\pi\) |
−0.509437 | + | 0.860508i | \(0.670146\pi\) | |||||||
\(710\) | −2.48976 | + | 3.90249i | −0.0934390 | + | 0.146458i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.31506 | + | 1.31506i | −0.0492840 | + | 0.0492840i | ||||
\(713\) | − | 28.8934i | − | 1.08207i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.3054 | + | 8.54352i | −0.422797 | + | 0.319510i | ||||
\(716\) | 18.7205 | 0.699617 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.64287 | + | 3.64287i | −0.135951 | + | 0.135951i | ||||
\(719\) | −19.9476 | −0.743920 | −0.371960 | − | 0.928249i | \(-0.621314\pi\) | ||||
−0.371960 | + | 0.928249i | \(0.621314\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.4217 | − | 11.4217i | −0.425365 | − | 0.425365i | ||||
\(722\) | 16.1386 | 0.600616 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 16.6965i | − | 0.620520i | ||||||
\(725\) | 1.38199 | + | 2.97386i | 0.0513257 | + | 0.110446i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.61314 | − | 6.61314i | 0.245268 | − | 0.245268i | −0.573757 | − | 0.819025i | \(-0.694515\pi\) |
0.819025 | + | 0.573757i | \(0.194515\pi\) | |||||||
\(728\) | 2.64624 | − | 7.12166i | 0.0980763 | − | 0.263946i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32.1989 | + | 7.11616i | −1.19173 | + | 0.263381i | ||||
\(731\) | −9.27260 | −0.342960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.105862 | 0.00391011 | 0.00195506 | − | 0.999998i | \(-0.499378\pi\) | ||||
0.00195506 | + | 0.999998i | \(0.499378\pi\) | |||||||
\(734\) | 6.99757 | − | 6.99757i | 0.258285 | − | 0.258285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.88018 | − | 2.88018i | 0.106165 | − | 0.106165i | ||||
\(737\) | −8.84677 | − | 8.84677i | −0.325875 | − | 0.325875i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.2967 | + | 13.2967i | 0.489128 | + | 0.489128i | 0.908031 | − | 0.418903i | \(-0.137585\pi\) |
−0.418903 | + | 0.908031i | \(0.637585\pi\) | |||||||
\(740\) | −13.4598 | + | 2.97471i | −0.494794 | + | 0.109353i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.18661 | + | 8.18661i | 0.300540 | + | 0.300540i | ||||
\(743\) | 10.0152 | 0.367421 | 0.183710 | − | 0.982980i | \(-0.441189\pi\) | ||||
0.183710 | + | 0.982980i | \(0.441189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7021 | − | 18.3421i | 0.428733 | − | 0.672003i | ||||
\(746\) | −2.34687 | − | 2.34687i | −0.0859250 | − | 0.0859250i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.82859i | 0.139987i | ||||||||
\(749\) | 11.7831 | + | 11.7831i | 0.430547 | + | 0.430547i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 17.0923i | − | 0.623708i | −0.950130 | − | 0.311854i | \(-0.899050\pi\) | ||
0.950130 | − | 0.311854i | \(-0.100950\pi\) | |||||||
\(752\) | 9.52254 | 0.347251 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.21665 | − | 0.823655i | −0.0807256 | − | 0.0299957i | ||||
\(755\) | −3.00642 | + | 4.71231i | −0.109415 | + | 0.171499i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.13441 | − | 8.13441i | −0.295650 | − | 0.295650i | 0.543657 | − | 0.839307i | \(-0.317039\pi\) |
−0.839307 | + | 0.543657i | \(0.817039\pi\) | |||||||
\(758\) | 3.34919 | + | 3.34919i | 0.121648 | + | 0.121648i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.18877 | + | 2.03441i | 0.115669 | + | 0.0737960i | ||||
\(761\) | −12.7947 | + | 12.7947i | −0.463806 | + | 0.463806i | −0.899901 | − | 0.436095i | \(-0.856361\pi\) |
0.436095 | + | 0.899901i | \(0.356361\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.9257 | + | 17.9257i | −0.648953 | + | 0.648953i | ||||
\(764\) | 6.58561 | 0.238259 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.7318i | 0.893595i | ||||||||
\(767\) | −3.97856 | − | 8.68347i | −0.143657 | − | 0.313542i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.446059 | − | 0.446059i | 0.0160853 | − | 0.0160853i | −0.699018 | − | 0.715104i | \(-0.746379\pi\) |
0.715104 | + | 0.699018i | \(0.246379\pi\) | |||||||
\(770\) | −6.98160 | − | 4.45421i | −0.251599 | − | 0.160519i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 10.4497i | − | 0.376092i | ||||||
\(773\) | 12.4535 | 0.447920 | 0.223960 | − | 0.974598i | \(-0.428102\pi\) | ||||
0.223960 | + | 0.974598i | \(0.428102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.3129 | − | 12.1744i | −1.19663 | − | 0.437318i | ||||
\(776\) | 6.58936 | 0.236544 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 3.36767i | − | 0.120737i | ||||||
\(779\) | 12.1438 | 0.435096 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.63862 | −0.130200 | ||||||||
\(782\) | − | 8.87248i | − | 0.317279i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.55995 | −0.0914266 | ||||||||
\(785\) | 4.61679 | + | 2.94548i | 0.164780 | + | 0.105129i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.6968 | −0.809053 | −0.404527 | − | 0.914526i | \(-0.632564\pi\) | ||||
−0.404527 | + | 0.914526i | \(0.632564\pi\) | |||||||
\(788\) | − | 11.5736i | − | 0.412292i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.82987 | − | 0.846427i | 0.136261 | − | 0.0301145i | ||||
\(791\) | 7.45872 | − | 7.45872i | 0.265202 | − | 0.265202i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7313 | − | 5.47382i | −0.523125 | − | 0.194381i | ||||
\(794\) | 15.6097i | 0.553967i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.7883 | 0.843155 | ||||||||
\(797\) | 4.98891 | − | 4.98891i | 0.176716 | − | 0.176716i | −0.613206 | − | 0.789923i | \(-0.710121\pi\) |
0.789923 | + | 0.613206i | \(0.210121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.6672 | − | 14.6672i | 0.518890 | − | 0.518890i | ||||
\(800\) | −2.10714 | − | 4.53431i | −0.0744988 | − | 0.160312i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.3476 | + | 26.3476i | 0.930366 | + | 0.930366i | ||||
\(803\) | −18.3284 | − | 18.3284i | −0.646795 | − | 0.646795i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.1794 | + | 10.3223i | 0.570247 | + | 0.363814i | ||||
\(806\) | 23.2518 | − | 10.6534i | 0.819009 | − | 0.375250i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.61904 | 0.0569578 | ||||||||
\(809\) | − | 19.9396i | − | 0.701040i | −0.936555 | − | 0.350520i | \(-0.886005\pi\) | ||
0.936555 | − | 0.350520i | \(-0.113995\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.3132 | − | 31.3132i | −1.09955 | − | 1.09955i | −0.994462 | − | 0.105092i | \(-0.966486\pi\) |
−0.105092 | − | 0.994462i | \(-0.533514\pi\) | |||||||
\(812\) | − | 1.38199i | − | 0.0484982i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.66168 | − | 7.66168i | −0.268542 | − | 0.268542i | ||||
\(815\) | 7.68806 | + | 34.7866i | 0.269301 | + | 1.21852i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.20082 | −0.251925 | ||||||||
\(818\) | 21.1408 | + | 21.1408i | 0.739172 | + | 0.739172i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.5330 | − | 8.63398i | −0.472594 | − | 0.301512i | ||||
\(821\) | 16.2309 | + | 16.2309i | 0.566463 | + | 0.566463i | 0.931136 | − | 0.364673i | \(-0.118819\pi\) |
−0.364673 | + | 0.931136i | \(0.618819\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.00377 | + | 6.00377i | 0.209278 | + | 0.209278i | 0.803961 | − | 0.594683i | \(-0.202722\pi\) |
−0.594683 | + | 0.803961i | \(0.702722\pi\) | |||||||
\(824\) | 5.42044 | − | 5.42044i | 0.188830 | − | 0.188830i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.94712 | − | 3.94712i | 0.137338 | − | 0.137338i | ||||
\(827\) | −45.4835 | −1.58162 | −0.790808 | − | 0.612064i | \(-0.790339\pi\) | ||||
−0.790808 | + | 0.612064i | \(0.790339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.9896 | 0.451148 | 0.225574 | − | 0.974226i | \(-0.427574\pi\) | ||||
0.225574 | + | 0.974226i | \(0.427574\pi\) | |||||||
\(830\) | 6.71355 | + | 30.3772i | 0.233031 | + | 1.05441i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.37977 | + | 1.25584i | 0.117173 | + | 0.0435385i | ||||
\(833\) | −3.94300 | + | 3.94300i | −0.136617 | + | 0.136617i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.3789 | − | 10.9131i | 1.70883 | − | 0.377662i | ||||
\(836\) | 2.97317i | 0.102829i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.7707 | 0.510244 | ||||||||
\(839\) | 29.4940 | + | 29.4940i | 1.01824 | + | 1.01824i | 0.999830 | + | 0.0184141i | \(0.00586173\pi\) |
0.0184141 | + | 0.999830i | \(0.494138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5699 | 0.985167 | ||||||||
\(842\) | −21.9707 | + | 21.9707i | −0.757161 | + | 0.757161i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.22265 | −0.110928 | ||||||||
\(845\) | 25.5932 | + | 13.7836i | 0.880433 | + | 0.474171i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.6690i | 0.572755i | ||||||||
\(848\) | −3.88517 | + | 3.88517i | −0.133417 | + | 0.133417i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.2296 | − | 3.73848i | −0.350872 | − | 0.128229i | ||||
\(851\) | 17.7554 | + | 17.7554i | 0.608647 | + | 0.608647i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 46.2016i | − | 1.58191i | −0.611873 | − | 0.790956i | \(-0.709584\pi\) | ||
0.611873 | − | 0.790956i | \(-0.290416\pi\) | |||||||
\(854\) | − | 9.18436i | − | 0.314282i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.59200 | + | 5.59200i | −0.191131 | + | 0.191131i | ||||
\(857\) | −28.5928 | + | 28.5928i | −0.976711 | + | 0.976711i | −0.999735 | − | 0.0230243i | \(-0.992670\pi\) |
0.0230243 | + | 0.999735i | \(0.492670\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.1464i | − | 1.06270i | −0.847152 | − | 0.531351i | \(-0.821685\pi\) | ||
0.847152 | − | 0.531351i | \(-0.178315\pi\) | |||||||
\(860\) | 8.02460 | + | 5.11964i | 0.273637 | + | 0.174578i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.95159 | + | 1.95159i | −0.0664715 | + | 0.0664715i | ||||
\(863\) | 13.1379 | 0.447221 | 0.223610 | − | 0.974679i | \(-0.428216\pi\) | ||||
0.223610 | + | 0.974679i | \(0.428216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.1263 | + | 21.7723i | 1.16033 | + | 0.740281i | ||||
\(866\) | −23.1334 | + | 23.1334i | −0.786106 | + | 0.786106i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.5692 | + | 10.5692i | 0.358743 | + | 0.358743i | ||||
\(869\) | 2.18006 | + | 2.18006i | 0.0739534 | + | 0.0739534i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.93937 | + | 24.0580i | −0.302899 | + | 0.815173i | ||||
\(872\) | −8.50709 | − | 8.50709i | −0.288087 | − | 0.288087i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 6.89010i | − | 0.233061i | ||||||
\(875\) | 18.7185 | − | 14.3047i | 0.632800 | − | 0.483589i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.9786i | 1.72143i | 0.509091 | + | 0.860713i | \(0.329982\pi\) | ||||
−0.509091 | + | 0.860713i | \(0.670018\pi\) | |||||||
\(878\) | − | 35.1398i | − | 1.18591i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.11386 | − | 3.31330i | 0.0712583 | − | 0.111691i | ||||
\(881\) | − | 55.2917i | − | 1.86282i | −0.363968 | − | 0.931412i | \(-0.618578\pi\) | ||
0.363968 | − | 0.931412i | \(-0.381422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.18223 | − | 5.18223i | −0.174396 | − | 0.174396i | 0.614512 | − | 0.788908i | \(-0.289353\pi\) |
−0.788908 | + | 0.614512i | \(0.789353\pi\) | |||||||
\(884\) | 7.14008 | − | 3.27141i | 0.240147 | − | 0.110030i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.49624 | + | 3.49624i | 0.117458 | + | 0.117458i | ||||
\(887\) | 33.3749 | + | 33.3749i | 1.12062 | + | 1.12062i | 0.991649 | + | 0.128969i | \(0.0411669\pi\) |
0.128969 | + | 0.991649i | \(0.458833\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.9288 | + | 19.9288i | −0.668392 | + | 0.668392i | ||||
\(890\) | 2.23671 | − | 3.50585i | 0.0749746 | − | 0.117516i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.20878 | −0.207885 | ||||||||
\(893\) | 11.3901 | − | 11.3901i | 0.381156 | − | 0.381156i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.8739 | + | 9.03340i | −1.36626 | + | 0.301953i | ||||
\(896\) | 2.10714i | 0.0703947i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.86444 | + | 7.86444i | −0.262440 | + | 0.262440i | ||||
\(899\) | 3.28972 | − | 3.28972i | 0.109718 | − | 0.109718i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.9684i | 0.398725i | ||||||||
\(902\) | − | 12.6180i | − | 0.420134i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.53973 | + | 3.53973i | 0.117730 | + | 0.117730i | ||||
\(905\) | 8.05675 | + | 36.4548i | 0.267816 | + | 1.21180i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9601 | + | 20.9601i | −0.695969 | + | 0.695969i | −0.963539 | − | 0.267569i | \(-0.913780\pi\) |
0.267569 | + | 0.963539i | \(0.413780\pi\) | |||||||
\(908\) | − | 1.01019i | − | 0.0335244i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.34126 | + | 16.8262i | −0.0776120 | + | 0.557784i | ||||
\(911\) | 41.4685 | 1.37391 | 0.686956 | − | 0.726699i | \(-0.258947\pi\) | ||||
0.686956 | + | 0.726699i | \(0.258947\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.2914 | + | 17.2914i | −0.572263 | + | 0.572263i | ||||
\(914\) | −6.00799 | −0.198727 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.16009 | + | 8.16009i | 0.269617 | + | 0.269617i | ||||
\(917\) | −45.8363 | −1.51365 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0132i | 1.12199i | 0.827818 | + | 0.560996i | \(0.189582\pi\) | ||||
−0.827818 | + | 0.560996i | \(0.810418\pi\) | |||||||
\(920\) | −4.89872 | + | 7.67833i | −0.161506 | + | 0.253147i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.1391 | − | 26.1391i | 0.860847 | − | 0.860847i | ||||
\(923\) | 3.10909 | + | 6.78580i | 0.102337 | + | 0.223357i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.9526 | − | 12.9899i | 0.919075 | − | 0.427104i | ||||
\(926\) | −30.7752 | −1.01134 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.655858 | 0.0215296 | ||||||||
\(929\) | 15.6158 | − | 15.6158i | 0.512338 | − | 0.512338i | −0.402904 | − | 0.915242i | \(-0.631999\pi\) |
0.915242 | + | 0.402904i | \(0.131999\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.06201 | + | 3.06201i | −0.100353 | + | 0.100353i | ||||
\(932\) | −8.81549 | − | 8.81549i | −0.288761 | − | 0.288761i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.6301 | + | 27.6301i | 0.904083 | + | 0.904083i | ||||
\(935\) | −1.84745 | − | 8.35927i | −0.0604182 | − | 0.273378i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.35972 | + | 5.35972i | 0.175094 | + | 0.175094i | 0.789213 | − | 0.614119i | \(-0.210489\pi\) |
−0.614119 | + | 0.789213i | \(0.710489\pi\) | |||||||
\(938\) | −14.9991 | −0.489739 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −20.7913 | + | 4.59502i | −0.678139 | + | 0.149873i | ||||
\(941\) | 34.8653 | + | 34.8653i | 1.13658 | + | 1.13658i | 0.989059 | + | 0.147518i | \(0.0471286\pi\) |
0.147518 | + | 0.989059i | \(0.452871\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.2413i | 0.952228i | ||||||||
\(944\) | 1.87321 | + | 1.87321i | 0.0609677 | + | 0.0609677i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.48203i | 0.243262i | ||||||||
\(947\) | 12.1066 | 0.393411 | 0.196706 | − | 0.980463i | \(-0.436976\pi\) | ||||
0.196706 | + | 0.980463i | \(0.436976\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.5202 | + | 49.8423i | −0.601192 | + | 1.61795i | ||||
\(950\) | −7.94399 | − | 2.90319i | −0.257737 | − | 0.0941918i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.24556 | + | 3.24556i | 0.105189 | + | 0.105189i | ||||
\(953\) | −25.0126 | − | 25.0126i | −0.810237 | − | 0.810237i | 0.174432 | − | 0.984669i | \(-0.444191\pi\) |
−0.984669 | + | 0.174432i | \(0.944191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.3789 | + | 3.17783i | −0.465290 | + | 0.102832i | ||||
\(956\) | 14.8422 | − | 14.8422i | 0.480031 | − | 0.480031i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.7482 | + | 11.7482i | −0.379566 | + | 0.379566i | ||||
\(959\) | 38.9123 | 1.25654 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.3185i | 0.623178i | ||||||||
\(962\) | −7.74188 | + | 20.8352i | −0.249608 | + | 0.671754i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.7506 | − | 16.7506i | 0.539499 | − | 0.539499i | ||||
\(965\) | 5.04241 | + | 22.8156i | 0.162321 | + | 0.734462i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.24404i | − | 0.0400056i | −0.999800 | − | 0.0200028i | \(-0.993632\pi\) | ||
0.999800 | − | 0.0200028i | \(-0.00636751\pi\) | |||||||
\(968\) | −7.91072 | −0.254260 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.3871 | + | 3.17964i | −0.461941 | + | 0.102092i | ||||
\(971\) | −5.03837 | −0.161689 | −0.0808445 | − | 0.996727i | \(-0.525762\pi\) | ||||
−0.0808445 | + | 0.996727i | \(0.525762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.15640i | 0.0691310i | ||||||||
\(974\) | −10.8941 | −0.349068 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.35868 | 0.139518 | ||||||||
\(977\) | 28.7753i | 0.920604i | 0.887762 | + | 0.460302i | \(0.152259\pi\) | ||||
−0.887762 | + | 0.460302i | \(0.847741\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.26881 | 0.104472 | ||||||||
\(980\) | 5.58934 | − | 1.23528i | 0.178545 | − | 0.0394596i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.7178 | −0.629222 | ||||||||
\(983\) | − | 47.1354i | − | 1.50338i | −0.659514 | − | 0.751692i | \(-0.729238\pi\) | ||
0.659514 | − | 0.751692i | \(-0.270762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.58473 | + | 25.2695i | 0.177944 | + | 0.805154i | ||||
\(986\) | 1.01019 | − | 1.01019i | 0.0321712 | − | 0.0321712i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.54477 | − | 2.54048i | 0.176403 | − | 0.0808234i | ||||
\(989\) | − | 17.3391i | − | 0.551350i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.72707 | −0.277225 | −0.138612 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138612 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(992\) | −5.01590 | + | 5.01590i | −0.159255 | + | 0.159255i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.08452 | + | 3.08452i | −0.0978352 | + | 0.0978352i | ||||
\(995\) | −51.9390 | + | 11.4789i | −1.64658 | + | 0.363904i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.6404 | − | 18.6404i | −0.590347 | − | 0.590347i | 0.347378 | − | 0.937725i | \(-0.387072\pi\) |
−0.937725 | + | 0.347378i | \(0.887072\pi\) | |||||||
\(998\) | 25.8969 | + | 25.8969i | 0.819751 | + | 0.819751i | ||||
\(999\) | 0 | 0 |
(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 | 1170.2.w.h.307.7 | yes | 14 | |
3.2 | odd | 2 | 1170.2.w.g.307.1 | yes | 14 | ||
5.3 | odd | 4 | 1170.2.m.g.73.3 | ✓ | 14 | ||
13.5 | odd | 4 | 1170.2.m.g.577.3 | yes | 14 | ||
15.8 | even | 4 | 1170.2.m.h.73.5 | yes | 14 | ||
39.5 | even | 4 | 1170.2.m.h.577.5 | yes | 14 | ||
65.18 | even | 4 | inner | 1170.2.w.h.343.7 | yes | 14 | |
195.83 | odd | 4 | 1170.2.w.g.343.1 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.m.g.73.3 | ✓ | 14 | 5.3 | odd | 4 | ||
1170.2.m.g.577.3 | yes | 14 | 13.5 | odd | 4 | ||
1170.2.m.h.73.5 | yes | 14 | 15.8 | even | 4 | ||
1170.2.m.h.577.5 | yes | 14 | 39.5 | even | 4 | ||
1170.2.w.g.307.1 | yes | 14 | 3.2 | odd | 2 | ||
1170.2.w.g.343.1 | yes | 14 | 195.83 | odd | 4 | ||
1170.2.w.h.307.7 | yes | 14 | 1.1 | even | 1 | trivial | |
1170.2.w.h.343.7 | yes | 14 | 65.18 | even | 4 | inner |