Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,2,Mod(22,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.34947179416\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 146.2 | ||
Root | \(0.900969 + 1.56052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.146 |
Dual form | 169.2.c.b.22.2 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.277479 | − | 0.480608i | −0.196207 | − | 0.339841i | 0.751088 | − | 0.660202i | \(-0.229529\pi\) |
−0.947296 | + | 0.320361i | \(0.896196\pi\) | |||||||
\(3\) | −0.400969 | − | 0.694498i | −0.231499 | − | 0.400969i | 0.726750 | − | 0.686902i | \(-0.241030\pi\) |
−0.958250 | + | 0.285933i | \(0.907696\pi\) | |||||||
\(4\) | 0.846011 | − | 1.46533i | 0.423005 | − | 0.732667i | ||||
\(5\) | 2.80194 | 1.25306 | 0.626532 | − | 0.779395i | \(-0.284474\pi\) | ||||
0.626532 | + | 0.779395i | \(0.284474\pi\) | |||||||
\(6\) | −0.222521 | + | 0.385418i | −0.0908438 | + | 0.157346i | ||||
\(7\) | −1.34601 | + | 2.33136i | −0.508744 | + | 0.881171i | 0.491204 | + | 0.871044i | \(0.336557\pi\) |
−0.999949 | + | 0.0101266i | \(0.996777\pi\) | |||||||
\(8\) | −2.04892 | −0.724402 | ||||||||
\(9\) | 1.17845 | − | 2.04113i | 0.392816 | − | 0.680377i | ||||
\(10\) | −0.777479 | − | 1.34663i | −0.245860 | − | 0.425843i | ||||
\(11\) | −0.599031 | − | 1.03755i | −0.180615 | − | 0.312834i | 0.761475 | − | 0.648194i | \(-0.224475\pi\) |
−0.942090 | + | 0.335360i | \(0.891142\pi\) | |||||||
\(12\) | −1.35690 | −0.391702 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.49396 | 0.399277 | ||||||||
\(15\) | −1.12349 | − | 1.94594i | −0.290084 | − | 0.502440i | ||||
\(16\) | −1.12349 | − | 1.94594i | −0.280872 | − | 0.486485i | ||||
\(17\) | −0.568532 | + | 0.984726i | −0.137889 | + | 0.238831i | −0.926697 | − | 0.375808i | \(-0.877365\pi\) |
0.788808 | + | 0.614639i | \(0.210698\pi\) | |||||||
\(18\) | −1.30798 | −0.308293 | ||||||||
\(19\) | 0.969501 | − | 1.67922i | 0.222419 | − | 0.385240i | −0.733123 | − | 0.680096i | \(-0.761938\pi\) |
0.955542 | + | 0.294855i | \(0.0952715\pi\) | |||||||
\(20\) | 2.37047 | − | 4.10577i | 0.530053 | − | 0.918079i | ||||
\(21\) | 2.15883 | 0.471096 | ||||||||
\(22\) | −0.332437 | + | 0.575798i | −0.0708758 | + | 0.122761i | ||||
\(23\) | 2.30194 | + | 3.98707i | 0.479987 | + | 0.831362i | 0.999736 | − | 0.0229566i | \(-0.00730797\pi\) |
−0.519749 | + | 0.854319i | \(0.673975\pi\) | |||||||
\(24\) | 0.821552 | + | 1.42297i | 0.167699 | + | 0.290463i | ||||
\(25\) | 2.85086 | 0.570171 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.29590 | −0.826746 | ||||||||
\(28\) | 2.27748 | + | 3.94471i | 0.430403 | + | 0.745480i | ||||
\(29\) | 3.94989 | + | 6.84140i | 0.733475 | + | 1.27042i | 0.955389 | + | 0.295350i | \(0.0954364\pi\) |
−0.221914 | + | 0.975066i | \(0.571230\pi\) | |||||||
\(30\) | −0.623490 | + | 1.07992i | −0.113833 | + | 0.197165i | ||||
\(31\) | −5.89977 | −1.05963 | −0.529815 | − | 0.848113i | \(-0.677739\pi\) | ||||
−0.529815 | + | 0.848113i | \(0.677739\pi\) | |||||||
\(32\) | −2.67241 | + | 4.62874i | −0.472419 | + | 0.818254i | ||||
\(33\) | −0.480386 | + | 0.832052i | −0.0836244 | + | 0.144842i | ||||
\(34\) | 0.631023 | 0.108219 | ||||||||
\(35\) | −3.77144 | + | 6.53232i | −0.637489 | + | 1.10416i | ||||
\(36\) | −1.99396 | − | 3.45364i | −0.332327 | − | 0.575606i | ||||
\(37\) | 0.475541 | + | 0.823662i | 0.0781785 | + | 0.135409i | 0.902464 | − | 0.430765i | \(-0.141756\pi\) |
−0.824286 | + | 0.566174i | \(0.808423\pi\) | |||||||
\(38\) | −1.07606 | −0.174561 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.74094 | −0.907722 | ||||||||
\(41\) | 1.65883 | + | 2.87318i | 0.259066 | + | 0.448716i | 0.965992 | − | 0.258572i | \(-0.0832519\pi\) |
−0.706926 | + | 0.707288i | \(0.749919\pi\) | |||||||
\(42\) | −0.599031 | − | 1.03755i | −0.0924325 | − | 0.160098i | ||||
\(43\) | −3.57942 | + | 6.19973i | −0.545856 | + | 0.945450i | 0.452697 | + | 0.891665i | \(0.350462\pi\) |
−0.998553 | + | 0.0537856i | \(0.982871\pi\) | |||||||
\(44\) | −2.02715 | −0.305604 | ||||||||
\(45\) | 3.30194 | − | 5.71912i | 0.492224 | − | 0.852557i | ||||
\(46\) | 1.27748 | − | 2.21266i | 0.188354 | − | 0.326239i | ||||
\(47\) | 7.69202 | 1.12200 | 0.560998 | − | 0.827817i | \(-0.310417\pi\) | ||||
0.560998 | + | 0.827817i | \(0.310417\pi\) | |||||||
\(48\) | −0.900969 | + | 1.56052i | −0.130044 | + | 0.225242i | ||||
\(49\) | −0.123490 | − | 0.213891i | −0.0176414 | − | 0.0305558i | ||||
\(50\) | −0.791053 | − | 1.37014i | −0.111872 | − | 0.193768i | ||||
\(51\) | 0.911854 | 0.127685 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.87263 | 0.806667 | 0.403334 | − | 0.915053i | \(-0.367851\pi\) | ||||
0.403334 | + | 0.915053i | \(0.367851\pi\) | |||||||
\(54\) | 1.19202 | + | 2.06464i | 0.162214 | + | 0.280962i | ||||
\(55\) | −1.67845 | − | 2.90716i | −0.226322 | − | 0.392001i | ||||
\(56\) | 2.75786 | − | 4.77676i | 0.368535 | − | 0.638322i | ||||
\(57\) | −1.55496 | −0.205959 | ||||||||
\(58\) | 2.19202 | − | 3.79669i | 0.287827 | − | 0.498530i | ||||
\(59\) | −0.00604079 | + | 0.0104630i | −0.000786444 | + | 0.00136216i | −0.866418 | − | 0.499319i | \(-0.833584\pi\) |
0.865632 | + | 0.500681i | \(0.166917\pi\) | |||||||
\(60\) | −3.80194 | −0.490828 | ||||||||
\(61\) | 4.01842 | − | 6.96010i | 0.514506 | − | 0.891150i | −0.485353 | − | 0.874318i | \(-0.661309\pi\) |
0.999858 | − | 0.0168315i | \(-0.00535789\pi\) | |||||||
\(62\) | 1.63706 | + | 2.83548i | 0.207907 | + | 0.360106i | ||||
\(63\) | 3.17241 | + | 5.49477i | 0.399686 | + | 0.692276i | ||||
\(64\) | −1.52781 | −0.190976 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.533188 | 0.0656309 | ||||||||
\(67\) | −4.62833 | − | 8.01651i | −0.565441 | − | 0.979373i | −0.997009 | − | 0.0772919i | \(-0.975373\pi\) |
0.431567 | − | 0.902081i | \(-0.357961\pi\) | |||||||
\(68\) | 0.961968 | + | 1.66618i | 0.116656 | + | 0.202054i | ||||
\(69\) | 1.84601 | − | 3.19738i | 0.222234 | − | 0.384920i | ||||
\(70\) | 4.18598 | 0.500320 | ||||||||
\(71\) | −6.87047 | + | 11.9000i | −0.815375 | + | 1.41227i | 0.0936838 | + | 0.995602i | \(0.470136\pi\) |
−0.909059 | + | 0.416668i | \(0.863198\pi\) | |||||||
\(72\) | −2.41454 | + | 4.18211i | −0.284557 | + | 0.492866i | ||||
\(73\) | −12.8170 | −1.50012 | −0.750058 | − | 0.661372i | \(-0.769975\pi\) | ||||
−0.750058 | + | 0.661372i | \(0.769975\pi\) | |||||||
\(74\) | 0.263906 | − | 0.457098i | 0.0306784 | − | 0.0531365i | ||||
\(75\) | −1.14310 | − | 1.97991i | −0.131994 | − | 0.228621i | ||||
\(76\) | −1.64042 | − | 2.84128i | −0.188169 | − | 0.325918i | ||||
\(77\) | 3.22521 | 0.367547 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.807315 | 0.0908300 | 0.0454150 | − | 0.998968i | \(-0.485539\pi\) | ||||
0.0454150 | + | 0.998968i | \(0.485539\pi\) | |||||||
\(80\) | −3.14795 | − | 5.45241i | −0.351951 | − | 0.609598i | ||||
\(81\) | −1.81282 | − | 3.13990i | −0.201425 | − | 0.348878i | ||||
\(82\) | 0.920583 | − | 1.59450i | 0.101661 | − | 0.176083i | ||||
\(83\) | 16.3327 | 1.79275 | 0.896375 | − | 0.443296i | \(-0.146191\pi\) | ||||
0.896375 | + | 0.443296i | \(0.146191\pi\) | |||||||
\(84\) | 1.82640 | − | 3.16341i | 0.199276 | − | 0.345156i | ||||
\(85\) | −1.59299 | + | 2.75914i | −0.172784 | + | 0.299271i | ||||
\(86\) | 3.97285 | 0.428404 | ||||||||
\(87\) | 3.16756 | − | 5.48638i | 0.339598 | − | 0.588202i | ||||
\(88\) | 1.22737 | + | 2.12586i | 0.130838 | + | 0.226617i | ||||
\(89\) | −7.36443 | − | 12.7556i | −0.780628 | − | 1.35209i | −0.931576 | − | 0.363546i | \(-0.881566\pi\) |
0.150949 | − | 0.988542i | \(-0.451767\pi\) | |||||||
\(90\) | −3.66487 | −0.386312 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.78986 | 0.812149 | ||||||||
\(93\) | 2.36563 | + | 4.09738i | 0.245304 | + | 0.424879i | ||||
\(94\) | −2.13437 | − | 3.69685i | −0.220144 | − | 0.381301i | ||||
\(95\) | 2.71648 | − | 4.70508i | 0.278705 | − | 0.482731i | ||||
\(96\) | 4.28621 | 0.437459 | ||||||||
\(97\) | 1.56584 | − | 2.71212i | 0.158987 | − | 0.275374i | −0.775516 | − | 0.631327i | \(-0.782510\pi\) |
0.934504 | + | 0.355953i | \(0.115844\pi\) | |||||||
\(98\) | −0.0685317 | + | 0.118700i | −0.00692274 | + | 0.0119905i | ||||
\(99\) | −2.82371 | −0.283793 | ||||||||
\(100\) | 2.41185 | − | 4.17745i | 0.241185 | − | 0.417745i | ||||
\(101\) | −2.64526 | − | 4.58172i | −0.263213 | − | 0.455899i | 0.703881 | − | 0.710318i | \(-0.251449\pi\) |
−0.967094 | + | 0.254420i | \(0.918116\pi\) | |||||||
\(102\) | −0.253020 | − | 0.438244i | −0.0250528 | − | 0.0433926i | ||||
\(103\) | −13.5308 | −1.33323 | −0.666614 | − | 0.745403i | \(-0.732257\pi\) | ||||
−0.666614 | + | 0.745403i | \(0.732257\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.04892 | 0.590314 | ||||||||
\(106\) | −1.62953 | − | 2.82243i | −0.158274 | − | 0.274139i | ||||
\(107\) | −2.81551 | − | 4.87661i | −0.272186 | − | 0.471440i | 0.697236 | − | 0.716842i | \(-0.254413\pi\) |
−0.969421 | + | 0.245403i | \(0.921080\pi\) | |||||||
\(108\) | −3.63437 | + | 6.29492i | −0.349718 | + | 0.605729i | ||||
\(109\) | −4.17629 | −0.400016 | −0.200008 | − | 0.979794i | \(-0.564097\pi\) | ||||
−0.200008 | + | 0.979794i | \(0.564097\pi\) | |||||||
\(110\) | −0.931468 | + | 1.61335i | −0.0888120 | + | 0.153827i | ||||
\(111\) | 0.381355 | − | 0.660525i | 0.0361966 | − | 0.0626943i | ||||
\(112\) | 6.04892 | 0.571569 | ||||||||
\(113\) | −3.82155 | + | 6.61912i | −0.359501 | + | 0.622675i | −0.987878 | − | 0.155235i | \(-0.950387\pi\) |
0.628376 | + | 0.777910i | \(0.283720\pi\) | |||||||
\(114\) | 0.431468 | + | 0.747325i | 0.0404107 | + | 0.0699934i | ||||
\(115\) | 6.44989 | + | 11.1715i | 0.601455 | + | 1.04175i | ||||
\(116\) | 13.3666 | 1.24106 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.00670477 | 0.000617224 | ||||||||
\(119\) | −1.53050 | − | 2.65090i | −0.140301 | − | 0.243008i | ||||
\(120\) | 2.30194 | + | 3.98707i | 0.210137 | + | 0.363968i | ||||
\(121\) | 4.78232 | − | 8.28323i | 0.434757 | − | 0.753021i | ||||
\(122\) | −4.46011 | −0.403799 | ||||||||
\(123\) | 1.33028 | − | 2.30411i | 0.119947 | − | 0.207755i | ||||
\(124\) | −4.99127 | + | 8.64513i | −0.448229 | + | 0.776356i | ||||
\(125\) | −6.02177 | −0.538604 | ||||||||
\(126\) | 1.76055 | − | 3.04937i | 0.156843 | − | 0.271659i | ||||
\(127\) | −3.38889 | − | 5.86972i | −0.300715 | − | 0.520854i | 0.675583 | − | 0.737284i | \(-0.263892\pi\) |
−0.976298 | + | 0.216430i | \(0.930559\pi\) | |||||||
\(128\) | 5.76875 | + | 9.99177i | 0.509890 | + | 0.883156i | ||||
\(129\) | 5.74094 | 0.505461 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.6799 | −1.19522 | −0.597611 | − | 0.801786i | \(-0.703883\pi\) | ||||
−0.597611 | + | 0.801786i | \(0.703883\pi\) | |||||||
\(132\) | 0.812823 | + | 1.40785i | 0.0707471 | + | 0.122538i | ||||
\(133\) | 2.60992 | + | 4.52051i | 0.226308 | + | 0.391978i | ||||
\(134\) | −2.56853 | + | 4.44883i | −0.221887 | + | 0.384320i | ||||
\(135\) | −12.0368 | −1.03597 | ||||||||
\(136\) | 1.16487 | − | 2.01762i | 0.0998872 | − | 0.173010i | ||||
\(137\) | 6.49396 | − | 11.2479i | 0.554816 | − | 0.960970i | −0.443101 | − | 0.896471i | \(-0.646122\pi\) |
0.997918 | − | 0.0644987i | \(-0.0205448\pi\) | |||||||
\(138\) | −2.04892 | −0.174415 | ||||||||
\(139\) | −6.02326 | + | 10.4326i | −0.510886 | + | 0.884881i | 0.489034 | + | 0.872265i | \(0.337349\pi\) |
−0.999920 | + | 0.0126165i | \(0.995984\pi\) | |||||||
\(140\) | 6.38135 | + | 11.0528i | 0.539323 | + | 0.934135i | ||||
\(141\) | −3.08426 | − | 5.34210i | −0.259742 | − | 0.449886i | ||||
\(142\) | 7.62565 | 0.639930 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.29590 | −0.441325 | ||||||||
\(145\) | 11.0673 | + | 19.1692i | 0.919092 | + | 1.59191i | ||||
\(146\) | 3.55645 | + | 6.15995i | 0.294334 | + | 0.509801i | ||||
\(147\) | −0.0990311 | + | 0.171527i | −0.00816795 | + | 0.0141473i | ||||
\(148\) | 1.60925 | 0.132280 | ||||||||
\(149\) | −0.370469 | + | 0.641672i | −0.0303500 | + | 0.0525678i | −0.880801 | − | 0.473486i | \(-0.842996\pi\) |
0.850451 | + | 0.526054i | \(0.176329\pi\) | |||||||
\(150\) | −0.634375 | + | 1.09877i | −0.0517965 | + | 0.0897142i | ||||
\(151\) | 19.0737 | 1.55219 | 0.776097 | − | 0.630614i | \(-0.217197\pi\) | ||||
0.776097 | + | 0.630614i | \(0.217197\pi\) | |||||||
\(152\) | −1.98643 | + | 3.44059i | −0.161120 | + | 0.279069i | ||||
\(153\) | 1.33997 | + | 2.32090i | 0.108330 | + | 0.187633i | ||||
\(154\) | −0.894928 | − | 1.55006i | −0.0721154 | − | 0.124907i | ||||
\(155\) | −16.5308 | −1.32779 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.02177 | −0.320972 | −0.160486 | − | 0.987038i | \(-0.551306\pi\) | ||||
−0.160486 | + | 0.987038i | \(0.551306\pi\) | |||||||
\(158\) | −0.224013 | − | 0.388002i | −0.0178215 | − | 0.0308678i | ||||
\(159\) | −2.35474 | − | 4.07853i | −0.186743 | − | 0.323448i | ||||
\(160\) | −7.48792 | + | 12.9695i | −0.591972 | + | 1.02533i | ||||
\(161\) | −12.3937 | −0.976763 | ||||||||
\(162\) | −1.00604 | + | 1.74251i | −0.0790420 | + | 0.136905i | ||||
\(163\) | 7.56853 | − | 13.1091i | 0.592813 | − | 1.02678i | −0.401038 | − | 0.916061i | \(-0.631351\pi\) |
0.993852 | − | 0.110721i | \(-0.0353161\pi\) | |||||||
\(164\) | 5.61356 | 0.438346 | ||||||||
\(165\) | −1.34601 | + | 2.33136i | −0.104787 | + | 0.181496i | ||||
\(166\) | −4.53199 | − | 7.84964i | −0.351751 | − | 0.609250i | ||||
\(167\) | −3.13169 | − | 5.42424i | −0.242337 | − | 0.419740i | 0.719042 | − | 0.694966i | \(-0.244581\pi\) |
−0.961380 | + | 0.275226i | \(0.911247\pi\) | |||||||
\(168\) | −4.42327 | −0.341263 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.76809 | 0.135606 | ||||||||
\(171\) | −2.28501 | − | 3.95776i | −0.174739 | − | 0.302657i | ||||
\(172\) | 6.05645 | + | 10.4901i | 0.461800 | + | 0.799861i | ||||
\(173\) | −8.19567 | + | 14.1953i | −0.623105 | + | 1.07925i | 0.365799 | + | 0.930694i | \(0.380796\pi\) |
−0.988904 | + | 0.148556i | \(0.952538\pi\) | |||||||
\(174\) | −3.51573 | −0.266527 | ||||||||
\(175\) | −3.83728 | + | 6.64637i | −0.290071 | + | 0.502418i | ||||
\(176\) | −1.34601 | + | 2.33136i | −0.101459 | + | 0.175733i | ||||
\(177\) | 0.00968868 | 0.000728246 | ||||||||
\(178\) | −4.08695 | + | 7.07880i | −0.306330 | + | 0.530579i | ||||
\(179\) | 1.22737 | + | 2.12586i | 0.0917376 | + | 0.158894i | 0.908242 | − | 0.418445i | \(-0.137425\pi\) |
−0.816505 | + | 0.577339i | \(0.804091\pi\) | |||||||
\(180\) | −5.58695 | − | 9.67688i | −0.416427 | − | 0.721272i | ||||
\(181\) | 11.8073 | 0.877631 | 0.438815 | − | 0.898577i | \(-0.355398\pi\) | ||||
0.438815 | + | 0.898577i | \(0.355398\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.44504 | −0.476431 | ||||||||
\(184\) | −4.71648 | − | 8.16918i | −0.347704 | − | 0.602240i | ||||
\(185\) | 1.33244 | + | 2.30785i | 0.0979627 | + | 0.169676i | ||||
\(186\) | 1.31282 | − | 2.27388i | 0.0962608 | − | 0.166729i | ||||
\(187\) | 1.36227 | 0.0996192 | ||||||||
\(188\) | 6.50753 | − | 11.2714i | 0.474611 | − | 0.822050i | ||||
\(189\) | 5.78232 | − | 10.0153i | 0.420602 | − | 0.728504i | ||||
\(190\) | −3.01507 | −0.218736 | ||||||||
\(191\) | 4.49665 | − | 7.78842i | 0.325366 | − | 0.563550i | −0.656220 | − | 0.754569i | \(-0.727846\pi\) |
0.981586 | + | 0.191019i | \(0.0611792\pi\) | |||||||
\(192\) | 0.612605 | + | 1.06106i | 0.0442109 | + | 0.0765756i | ||||
\(193\) | 6.76271 | + | 11.7134i | 0.486790 | + | 0.843146i | 0.999885 | − | 0.0151865i | \(-0.00483420\pi\) |
−0.513094 | + | 0.858332i | \(0.671501\pi\) | |||||||
\(194\) | −1.73795 | −0.124778 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.417895 | −0.0298496 | ||||||||
\(197\) | 6.48792 | + | 11.2374i | 0.462245 | + | 0.800632i | 0.999072 | − | 0.0430602i | \(-0.0137107\pi\) |
−0.536827 | + | 0.843692i | \(0.680377\pi\) | |||||||
\(198\) | 0.783520 | + | 1.35710i | 0.0556823 | + | 0.0964446i | ||||
\(199\) | 6.79321 | − | 11.7662i | 0.481558 | − | 0.834083i | −0.518218 | − | 0.855248i | \(-0.673404\pi\) |
0.999776 | + | 0.0211659i | \(0.00673782\pi\) | |||||||
\(200\) | −5.84117 | −0.413033 | ||||||||
\(201\) | −3.71164 | + | 6.42874i | −0.261799 | + | 0.453448i | ||||
\(202\) | −1.46801 | + | 2.54267i | −0.103289 | + | 0.178901i | ||||
\(203\) | −21.2664 | −1.49261 | ||||||||
\(204\) | 0.771438 | − | 1.33617i | 0.0540115 | − | 0.0935506i | ||||
\(205\) | 4.64795 | + | 8.05048i | 0.324627 | + | 0.562270i | ||||
\(206\) | 3.75451 | + | 6.50301i | 0.261589 | + | 0.453086i | ||||
\(207\) | 10.8509 | 0.754187 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.32304 | −0.160688 | ||||||||
\(210\) | −1.67845 | − | 2.90716i | −0.115824 | − | 0.200613i | ||||
\(211\) | −5.23005 | − | 9.05872i | −0.360052 | − | 0.623628i | 0.627917 | − | 0.778280i | \(-0.283908\pi\) |
−0.987969 | + | 0.154652i | \(0.950574\pi\) | |||||||
\(212\) | 4.96830 | − | 8.60536i | 0.341225 | − | 0.591018i | ||||
\(213\) | 11.0194 | 0.755035 | ||||||||
\(214\) | −1.56249 | + | 2.70631i | −0.106810 | + | 0.185000i | ||||
\(215\) | −10.0293 | + | 17.3713i | −0.683993 | + | 1.18471i | ||||
\(216\) | 8.80194 | 0.598896 | ||||||||
\(217\) | 7.94116 | − | 13.7545i | 0.539081 | − | 0.933715i | ||||
\(218\) | 1.15883 | + | 2.00716i | 0.0784861 | + | 0.135942i | ||||
\(219\) | 5.13922 | + | 8.90139i | 0.347276 | + | 0.601500i | ||||
\(220\) | −5.67994 | −0.382941 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.423272 | −0.0284081 | ||||||||
\(223\) | −5.70291 | − | 9.87772i | −0.381895 | − | 0.661461i | 0.609438 | − | 0.792834i | \(-0.291395\pi\) |
−0.991333 | + | 0.131372i | \(0.958062\pi\) | |||||||
\(224\) | −7.19418 | − | 12.4607i | −0.480681 | − | 0.832564i | ||||
\(225\) | 3.35958 | − | 5.81897i | 0.223972 | − | 0.387931i | ||||
\(226\) | 4.24160 | 0.282147 | ||||||||
\(227\) | 5.32036 | − | 9.21513i | 0.353124 | − | 0.611629i | −0.633671 | − | 0.773603i | \(-0.718453\pi\) |
0.986795 | + | 0.161973i | \(0.0517859\pi\) | |||||||
\(228\) | −1.31551 | + | 2.27853i | −0.0871219 | + | 0.150899i | ||||
\(229\) | 1.13946 | 0.0752974 | 0.0376487 | − | 0.999291i | \(-0.488013\pi\) | ||||
0.0376487 | + | 0.999291i | \(0.488013\pi\) | |||||||
\(230\) | 3.57942 | − | 6.19973i | 0.236020 | − | 0.408798i | ||||
\(231\) | −1.29321 | − | 2.23990i | −0.0850869 | − | 0.147375i | ||||
\(232\) | −8.09299 | − | 14.0175i | −0.531331 | − | 0.920292i | ||||
\(233\) | −10.8509 | −0.710863 | −0.355432 | − | 0.934702i | \(-0.615666\pi\) | ||||
−0.355432 | + | 0.934702i | \(0.615666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.5526 | 1.40593 | ||||||||
\(236\) | 0.0102212 | + | 0.0177036i | 0.000665340 | + | 0.00115240i | ||||
\(237\) | −0.323708 | − | 0.560679i | −0.0210271 | − | 0.0364200i | ||||
\(238\) | −0.849363 | + | 1.47114i | −0.0550560 | + | 0.0953598i | ||||
\(239\) | 11.9293 | 0.771643 | 0.385822 | − | 0.922573i | \(-0.373918\pi\) | ||||
0.385822 | + | 0.922573i | \(0.373918\pi\) | |||||||
\(240\) | −2.52446 | + | 4.37249i | −0.162953 | + | 0.282243i | ||||
\(241\) | −1.82424 | + | 3.15968i | −0.117510 | + | 0.203533i | −0.918780 | − | 0.394770i | \(-0.870824\pi\) |
0.801271 | + | 0.598302i | \(0.204158\pi\) | |||||||
\(242\) | −5.30798 | −0.341210 | ||||||||
\(243\) | −7.89762 | + | 13.6791i | −0.506632 | + | 0.877513i | ||||
\(244\) | −6.79925 | − | 11.7766i | −0.435277 | − | 0.753922i | ||||
\(245\) | −0.346011 | − | 0.599308i | −0.0221058 | − | 0.0382884i | ||||
\(246\) | −1.47650 | −0.0941383 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12.0881 | 0.767598 | ||||||||
\(249\) | −6.54892 | − | 11.3431i | −0.415021 | − | 0.718837i | ||||
\(250\) | 1.67092 | + | 2.89411i | 0.105678 | + | 0.183040i | ||||
\(251\) | −0.686645 | + | 1.18930i | −0.0433406 | + | 0.0750682i | −0.886882 | − | 0.461996i | \(-0.847133\pi\) |
0.843541 | + | 0.537064i | \(0.180467\pi\) | |||||||
\(252\) | 10.7356 | 0.676277 | ||||||||
\(253\) | 2.75786 | − | 4.77676i | 0.173385 | − | 0.300312i | ||||
\(254\) | −1.88069 | + | 3.25745i | −0.118005 | + | 0.204391i | ||||
\(255\) | 2.55496 | 0.159998 | ||||||||
\(256\) | 1.67360 | − | 2.89877i | 0.104600 | − | 0.181173i | ||||
\(257\) | −14.7180 | − | 25.4923i | −0.918082 | − | 1.59016i | −0.802325 | − | 0.596887i | \(-0.796404\pi\) |
−0.115756 | − | 0.993278i | \(-0.536929\pi\) | |||||||
\(258\) | −1.59299 | − | 2.75914i | −0.0991752 | − | 0.171777i | ||||
\(259\) | −2.56033 | −0.159091 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.6189 | 1.15248 | ||||||||
\(262\) | 3.79590 | + | 6.57469i | 0.234511 | + | 0.406185i | ||||
\(263\) | −5.34817 | − | 9.26330i | −0.329782 | − | 0.571199i | 0.652686 | − | 0.757628i | \(-0.273642\pi\) |
−0.982468 | + | 0.186429i | \(0.940309\pi\) | |||||||
\(264\) | 0.984271 | − | 1.70481i | 0.0605777 | − | 0.104924i | ||||
\(265\) | 16.4547 | 1.01081 | ||||||||
\(266\) | 1.44839 | − | 2.50869i | 0.0888067 | − | 0.153818i | ||||
\(267\) | −5.90581 | + | 10.2292i | −0.361430 | + | 0.626015i | ||||
\(268\) | −15.6625 | −0.956738 | ||||||||
\(269\) | 5.09299 | − | 8.82132i | 0.310525 | − | 0.537845i | −0.667951 | − | 0.744205i | \(-0.732828\pi\) |
0.978476 | + | 0.206360i | \(0.0661618\pi\) | |||||||
\(270\) | 3.33997 | + | 5.78500i | 0.203264 | + | 0.352064i | ||||
\(271\) | −14.7262 | − | 25.5065i | −0.894551 | − | 1.54941i | −0.834359 | − | 0.551221i | \(-0.814162\pi\) |
−0.0601918 | − | 0.998187i | \(-0.519171\pi\) | |||||||
\(272\) | 2.55496 | 0.154917 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.20775 | −0.435436 | ||||||||
\(275\) | −1.70775 | − | 2.95791i | −0.102981 | − | 0.178369i | ||||
\(276\) | −3.12349 | − | 5.41004i | −0.188012 | − | 0.325646i | ||||
\(277\) | 5.12229 | − | 8.87207i | 0.307769 | − | 0.533071i | −0.670105 | − | 0.742266i | \(-0.733751\pi\) |
0.977874 | + | 0.209195i | \(0.0670843\pi\) | |||||||
\(278\) | 6.68532 | 0.400959 | ||||||||
\(279\) | −6.95257 | + | 12.0422i | −0.416240 | + | 0.720948i | ||||
\(280\) | 7.72737 | − | 13.3842i | 0.461798 | − | 0.799858i | ||||
\(281\) | 11.5646 | 0.689889 | 0.344944 | − | 0.938623i | \(-0.387898\pi\) | ||||
0.344944 | + | 0.938623i | \(0.387898\pi\) | |||||||
\(282\) | −1.71164 | + | 2.96464i | −0.101926 | + | 0.176542i | ||||
\(283\) | 15.3545 | + | 26.5948i | 0.912730 | + | 1.58090i | 0.810191 | + | 0.586167i | \(0.199364\pi\) |
0.102540 | + | 0.994729i | \(0.467303\pi\) | |||||||
\(284\) | 11.6250 | + | 20.1351i | 0.689816 | + | 1.19480i | ||||
\(285\) | −4.35690 | −0.258080 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.93123 | −0.527194 | ||||||||
\(288\) | 6.29859 | + | 10.9095i | 0.371148 | + | 0.642847i | ||||
\(289\) | 7.85354 | + | 13.6027i | 0.461973 | + | 0.800161i | ||||
\(290\) | 6.14191 | − | 10.6381i | 0.360665 | − | 0.624691i | ||||
\(291\) | −2.51142 | −0.147222 | ||||||||
\(292\) | −10.8433 | + | 18.7812i | −0.634557 | + | 1.09909i | ||||
\(293\) | −9.30409 | + | 16.1152i | −0.543551 | + | 0.941458i | 0.455146 | + | 0.890417i | \(0.349587\pi\) |
−0.998697 | + | 0.0510409i | \(0.983746\pi\) | |||||||
\(294\) | 0.109916 | 0.00641045 | ||||||||
\(295\) | −0.0169259 | + | 0.0293166i | −0.000985465 | + | 0.00170688i | ||||
\(296\) | −0.974345 | − | 1.68761i | −0.0566326 | − | 0.0980906i | ||||
\(297\) | 2.57338 | + | 4.45722i | 0.149322 | + | 0.258634i | ||||
\(298\) | 0.411190 | 0.0238196 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.86831 | −0.223337 | ||||||||
\(301\) | −9.63587 | − | 16.6898i | −0.555402 | − | 0.961985i | ||||
\(302\) | −5.29254 | − | 9.16696i | −0.304552 | − | 0.527499i | ||||
\(303\) | −2.12133 | + | 3.67426i | −0.121867 | + | 0.211081i | ||||
\(304\) | −4.35690 | −0.249885 | ||||||||
\(305\) | 11.2594 | − | 19.5018i | 0.644709 | − | 1.11667i | ||||
\(306\) | 0.743627 | − | 1.28800i | 0.0425103 | − | 0.0736301i | ||||
\(307\) | −8.94438 | −0.510483 | −0.255241 | − | 0.966877i | \(-0.582155\pi\) | ||||
−0.255241 | + | 0.966877i | \(0.582155\pi\) | |||||||
\(308\) | 2.72856 | − | 4.72601i | 0.155474 | − | 0.269289i | ||||
\(309\) | 5.42543 | + | 9.39712i | 0.308642 | + | 0.534583i | ||||
\(310\) | 4.58695 | + | 7.94483i | 0.260521 | + | 0.451236i | ||||
\(311\) | 21.0398 | 1.19306 | 0.596529 | − | 0.802591i | \(-0.296546\pi\) | ||||
0.596529 | + | 0.802591i | \(0.296546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.12737 | −0.402863 | −0.201432 | − | 0.979503i | \(-0.564559\pi\) | ||||
−0.201432 | + | 0.979503i | \(0.564559\pi\) | |||||||
\(314\) | 1.11596 | + | 1.93289i | 0.0629771 | + | 0.109080i | ||||
\(315\) | 8.88889 | + | 15.3960i | 0.500832 | + | 0.867467i | ||||
\(316\) | 0.682997 | − | 1.18299i | 0.0384216 | − | 0.0665481i | ||||
\(317\) | −23.9651 | −1.34601 | −0.673007 | − | 0.739636i | \(-0.734997\pi\) | ||||
−0.673007 | + | 0.739636i | \(0.734997\pi\) | |||||||
\(318\) | −1.30678 | + | 2.26341i | −0.0732807 | + | 0.126926i | ||||
\(319\) | 4.73221 | − | 8.19643i | 0.264953 | − | 0.458912i | ||||
\(320\) | −4.28083 | −0.239306 | ||||||||
\(321\) | −2.25786 | + | 3.91074i | −0.126022 | + | 0.218276i | ||||
\(322\) | 3.43900 | + | 5.95652i | 0.191648 | + | 0.331944i | ||||
\(323\) | 1.10238 | + | 1.90938i | 0.0613383 | + | 0.106241i | ||||
\(324\) | −6.13467 | −0.340815 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.40044 | −0.465257 | ||||||||
\(327\) | 1.67456 | + | 2.90043i | 0.0926035 | + | 0.160394i | ||||
\(328\) | −3.39881 | − | 5.88692i | −0.187668 | − | 0.325051i | ||||
\(329\) | −10.3535 | + | 17.9329i | −0.570809 | + | 0.988671i | ||||
\(330\) | 1.49396 | 0.0822397 | ||||||||
\(331\) | 1.44773 | − | 2.50754i | 0.0795745 | − | 0.137827i | −0.823492 | − | 0.567328i | \(-0.807977\pi\) |
0.903066 | + | 0.429501i | \(0.141311\pi\) | |||||||
\(332\) | 13.8177 | − | 23.9329i | 0.758343 | − | 1.31349i | ||||
\(333\) | 2.24160 | 0.122839 | ||||||||
\(334\) | −1.73795 | + | 3.01023i | −0.0950967 | + | 0.164712i | ||||
\(335\) | −12.9683 | − | 22.4618i | −0.708534 | − | 1.22722i | ||||
\(336\) | −2.42543 | − | 4.20096i | −0.132318 | − | 0.229181i | ||||
\(337\) | −3.10560 | −0.169173 | −0.0845865 | − | 0.996416i | \(-0.526957\pi\) | ||||
−0.0845865 | + | 0.996416i | \(0.526957\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.12929 | 0.332898 | ||||||||
\(340\) | 2.69537 | + | 4.66852i | 0.146177 | + | 0.253186i | ||||
\(341\) | 3.53415 | + | 6.12132i | 0.191385 | + | 0.331488i | ||||
\(342\) | −1.26809 | + | 2.19639i | −0.0685702 | + | 0.118767i | ||||
\(343\) | −18.1793 | −0.981589 | ||||||||
\(344\) | 7.33393 | − | 12.7027i | 0.395419 | − | 0.684886i | ||||
\(345\) | 5.17241 | − | 8.95887i | 0.278473 | − | 0.482329i | ||||
\(346\) | 9.09651 | 0.489031 | ||||||||
\(347\) | 5.68933 | − | 9.85421i | 0.305419 | − | 0.529002i | −0.671935 | − | 0.740610i | \(-0.734537\pi\) |
0.977355 | + | 0.211608i | \(0.0678700\pi\) | |||||||
\(348\) | −5.35958 | − | 9.28307i | −0.287304 | − | 0.497625i | ||||
\(349\) | −1.67360 | − | 2.89877i | −0.0895859 | − | 0.155167i | 0.817750 | − | 0.575573i | \(-0.195221\pi\) |
−0.907336 | + | 0.420406i | \(0.861888\pi\) | |||||||
\(350\) | 4.25906 | 0.227656 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.40342 | 0.341303 | ||||||||
\(353\) | 0.318864 | + | 0.552288i | 0.0169714 | + | 0.0293953i | 0.874386 | − | 0.485230i | \(-0.161264\pi\) |
−0.857415 | + | 0.514626i | \(0.827931\pi\) | |||||||
\(354\) | −0.00268841 | − | 0.00465646i | −0.000142887 | − | 0.000247488i | ||||
\(355\) | −19.2506 | + | 33.3431i | −1.02172 | + | 1.76967i | ||||
\(356\) | −24.9215 | −1.32084 | ||||||||
\(357\) | −1.22737 | + | 2.12586i | −0.0649591 | + | 0.112512i | ||||
\(358\) | 0.681136 | − | 1.17976i | 0.0359992 | − | 0.0623524i | ||||
\(359\) | 21.4590 | 1.13256 | 0.566282 | − | 0.824211i | \(-0.308381\pi\) | ||||
0.566282 | + | 0.824211i | \(0.308381\pi\) | |||||||
\(360\) | −6.76540 | + | 11.7180i | −0.356568 | + | 0.617593i | ||||
\(361\) | 7.62014 | + | 13.1985i | 0.401060 | + | 0.694656i | ||||
\(362\) | −3.27628 | − | 5.67469i | −0.172198 | − | 0.298255i | ||||
\(363\) | −7.67025 | −0.402584 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.9124 | −1.87974 | ||||||||
\(366\) | 1.78836 | + | 3.09754i | 0.0934793 | + | 0.161911i | ||||
\(367\) | 4.69351 | + | 8.12940i | 0.244999 | + | 0.424351i | 0.962131 | − | 0.272586i | \(-0.0878789\pi\) |
−0.717132 | + | 0.696937i | \(0.754546\pi\) | |||||||
\(368\) | 5.17241 | − | 8.95887i | 0.269630 | − | 0.467013i | ||||
\(369\) | 7.81940 | 0.407062 | ||||||||
\(370\) | 0.739447 | − | 1.28076i | 0.0384420 | − | 0.0665835i | ||||
\(371\) | −7.90462 | + | 13.6912i | −0.410387 | + | 0.710812i | ||||
\(372\) | 8.00538 | 0.415059 | ||||||||
\(373\) | −13.8632 | + | 24.0118i | −0.717811 | + | 1.24329i | 0.244054 | + | 0.969762i | \(0.421522\pi\) |
−0.961865 | + | 0.273523i | \(0.911811\pi\) | |||||||
\(374\) | −0.378002 | − | 0.654719i | −0.0195460 | − | 0.0338547i | ||||
\(375\) | 2.41454 | + | 4.18211i | 0.124686 | + | 0.215963i | ||||
\(376\) | −15.7603 | −0.812776 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −6.41789 | −0.330101 | ||||||||
\(379\) | 17.9351 | + | 31.0645i | 0.921265 | + | 1.59568i | 0.797460 | + | 0.603371i | \(0.206176\pi\) |
0.123805 | + | 0.992307i | \(0.460490\pi\) | |||||||
\(380\) | −4.59634 | − | 7.96110i | −0.235787 | − | 0.408396i | ||||
\(381\) | −2.71768 | + | 4.70715i | −0.139231 | + | 0.241155i | ||||
\(382\) | −4.99090 | −0.255357 | ||||||||
\(383\) | 2.42758 | − | 4.20470i | 0.124044 | − | 0.214850i | −0.797315 | − | 0.603563i | \(-0.793747\pi\) |
0.921359 | + | 0.388713i | \(0.127080\pi\) | |||||||
\(384\) | 4.62618 | − | 8.01278i | 0.236079 | − | 0.408900i | ||||
\(385\) | 9.03684 | 0.460560 | ||||||||
\(386\) | 3.75302 | − | 6.50042i | 0.191024 | − | 0.330863i | ||||
\(387\) | 8.43631 | + | 14.6121i | 0.428842 | + | 0.742776i | ||||
\(388\) | −2.64944 | − | 4.58897i | −0.134505 | − | 0.232969i | ||||
\(389\) | 2.38537 | 0.120943 | 0.0604716 | − | 0.998170i | \(-0.480740\pi\) | ||||
0.0604716 | + | 0.998170i | \(0.480740\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.23490 | −0.264740 | ||||||||
\(392\) | 0.253020 | + | 0.438244i | 0.0127795 | + | 0.0221347i | ||||
\(393\) | 5.48523 | + | 9.50070i | 0.276693 | + | 0.479247i | ||||
\(394\) | 3.60052 | − | 6.23629i | 0.181392 | − | 0.314180i | ||||
\(395\) | 2.26205 | 0.113816 | ||||||||
\(396\) | −2.38889 | + | 4.13767i | −0.120046 | + | 0.207926i | ||||
\(397\) | −7.63318 | + | 13.2211i | −0.383098 | + | 0.663546i | −0.991503 | − | 0.130081i | \(-0.958476\pi\) |
0.608405 | + | 0.793627i | \(0.291810\pi\) | |||||||
\(398\) | −7.53989 | −0.377941 | ||||||||
\(399\) | 2.09299 | − | 3.62517i | 0.104781 | − | 0.181485i | ||||
\(400\) | −3.20291 | − | 5.54760i | −0.160145 | − | 0.277380i | ||||
\(401\) | 6.37920 | + | 11.0491i | 0.318562 | + | 0.551766i | 0.980188 | − | 0.198068i | \(-0.0634668\pi\) |
−0.661626 | + | 0.749834i | \(0.730133\pi\) | |||||||
\(402\) | 4.11960 | 0.205467 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.95167 | −0.445362 | ||||||||
\(405\) | −5.07942 | − | 8.79781i | −0.252398 | − | 0.437167i | ||||
\(406\) | 5.90097 | + | 10.2208i | 0.292860 | + | 0.507249i | ||||
\(407\) | 0.569728 | − | 0.986798i | 0.0282404 | − | 0.0489138i | ||||
\(408\) | −1.86831 | −0.0924953 | ||||||||
\(409\) | −12.6794 | + | 21.9614i | −0.626956 | + | 1.08592i | 0.361203 | + | 0.932487i | \(0.382366\pi\) |
−0.988159 | + | 0.153433i | \(0.950967\pi\) | |||||||
\(410\) | 2.57942 | − | 4.46768i | 0.127388 | − | 0.220643i | ||||
\(411\) | −10.4155 | −0.513759 | ||||||||
\(412\) | −11.4472 | + | 19.8271i | −0.563963 | + | 0.976812i | ||||
\(413\) | −0.0162619 | − | 0.0281665i | −0.000800198 | − | 0.00138598i | ||||
\(414\) | −3.01089 | − | 5.21501i | −0.147977 | − | 0.256304i | ||||
\(415\) | 45.7633 | 2.24643 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.66056 | 0.473080 | ||||||||
\(418\) | 0.644596 | + | 1.11647i | 0.0315282 | + | 0.0546085i | ||||
\(419\) | 5.83363 | + | 10.1041i | 0.284992 | + | 0.493620i | 0.972607 | − | 0.232455i | \(-0.0746758\pi\) |
−0.687616 | + | 0.726075i | \(0.741343\pi\) | |||||||
\(420\) | 5.11745 | − | 8.86368i | 0.249706 | − | 0.432503i | ||||
\(421\) | 8.29291 | 0.404172 | 0.202086 | − | 0.979368i | \(-0.435228\pi\) | ||||
0.202086 | + | 0.979368i | \(0.435228\pi\) | |||||||
\(422\) | −2.90246 | + | 5.02721i | −0.141290 | + | 0.244721i | ||||
\(423\) | 9.06465 | − | 15.7004i | 0.440738 | − | 0.763381i | ||||
\(424\) | −12.0325 | −0.584351 | ||||||||
\(425\) | −1.62080 | + | 2.80731i | −0.0786204 | + | 0.136175i | ||||
\(426\) | −3.05765 | − | 5.29600i | −0.148143 | − | 0.256592i | ||||
\(427\) | 10.8177 | + | 18.7367i | 0.523504 | + | 0.906735i | ||||
\(428\) | −9.52781 | −0.460544 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.1317 | 0.536818 | ||||||||
\(431\) | 0.466148 | + | 0.807392i | 0.0224536 | + | 0.0388907i | 0.877034 | − | 0.480429i | \(-0.159519\pi\) |
−0.854580 | + | 0.519319i | \(0.826186\pi\) | |||||||
\(432\) | 4.82640 | + | 8.35956i | 0.232210 | + | 0.402200i | ||||
\(433\) | 6.67510 | − | 11.5616i | 0.320785 | − | 0.555615i | −0.659866 | − | 0.751384i | \(-0.729387\pi\) |
0.980650 | + | 0.195768i | \(0.0627201\pi\) | |||||||
\(434\) | −8.81402 | −0.423086 | ||||||||
\(435\) | 8.87531 | − | 15.3725i | 0.425539 | − | 0.737055i | ||||
\(436\) | −3.53319 | + | 6.11966i | −0.169209 | + | 0.293079i | ||||
\(437\) | 8.92692 | 0.427032 | ||||||||
\(438\) | 2.85205 | − | 4.93990i | 0.136276 | − | 0.236037i | ||||
\(439\) | −6.99612 | − | 12.1176i | −0.333906 | − | 0.578343i | 0.649368 | − | 0.760475i | \(-0.275034\pi\) |
−0.983274 | + | 0.182132i | \(0.941700\pi\) | |||||||
\(440\) | 3.43900 | + | 5.95652i | 0.163948 | + | 0.283966i | ||||
\(441\) | −0.582105 | −0.0277193 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.7017 | 1.12610 | 0.563051 | − | 0.826422i | \(-0.309627\pi\) | ||||
0.563051 | + | 0.826422i | \(0.309627\pi\) | |||||||
\(444\) | −0.645260 | − | 1.11762i | −0.0306227 | − | 0.0530401i | ||||
\(445\) | −20.6347 | − | 35.7403i | −0.978177 | − | 1.69425i | ||||
\(446\) | −3.16487 | + | 5.48172i | −0.149861 | + | 0.259567i | ||||
\(447\) | 0.594187 | 0.0281041 | ||||||||
\(448\) | 2.05645 | − | 3.56188i | 0.0971581 | − | 0.168283i | ||||
\(449\) | −6.29321 | + | 10.9002i | −0.296995 | + | 0.514410i | −0.975447 | − | 0.220234i | \(-0.929318\pi\) |
0.678452 | + | 0.734645i | \(0.262651\pi\) | |||||||
\(450\) | −3.72886 | −0.175780 | ||||||||
\(451\) | 1.98739 | − | 3.44225i | 0.0935823 | − | 0.162089i | ||||
\(452\) | 6.46615 | + | 11.1997i | 0.304142 | + | 0.526789i | ||||
\(453\) | −7.64795 | − | 13.2466i | −0.359332 | − | 0.622381i | ||||
\(454\) | −5.90515 | −0.277142 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.18598 | 0.149197 | ||||||||
\(457\) | −16.8192 | − | 29.1316i | −0.786767 | − | 1.36272i | −0.927938 | − | 0.372735i | \(-0.878420\pi\) |
0.141171 | − | 0.989985i | \(-0.454913\pi\) | |||||||
\(458\) | −0.316175 | − | 0.547632i | −0.0147739 | − | 0.0255891i | ||||
\(459\) | 2.44235 | − | 4.23028i | 0.113999 | − | 0.197453i | ||||
\(460\) | 21.8267 | 1.01767 | ||||||||
\(461\) | −0.701415 | + | 1.21489i | −0.0326681 | + | 0.0565829i | −0.881897 | − | 0.471442i | \(-0.843734\pi\) |
0.849229 | + | 0.528025i | \(0.177067\pi\) | |||||||
\(462\) | −0.717677 | + | 1.24305i | −0.0333893 | + | 0.0578320i | ||||
\(463\) | 15.2010 | 0.706453 | 0.353226 | − | 0.935538i | \(-0.385085\pi\) | ||||
0.353226 | + | 0.935538i | \(0.385085\pi\) | |||||||
\(464\) | 8.87531 | − | 15.3725i | 0.412026 | − | 0.713650i | ||||
\(465\) | 6.62833 | + | 11.4806i | 0.307382 | + | 0.532401i | ||||
\(466\) | 3.01089 | + | 5.21501i | 0.139477 | + | 0.241580i | ||||
\(467\) | −39.3414 | −1.82050 | −0.910250 | − | 0.414058i | \(-0.864111\pi\) | ||||
−0.910250 | + | 0.414058i | \(0.864111\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.9191 | 1.15066 | ||||||||
\(470\) | −5.98039 | − | 10.3583i | −0.275855 | − | 0.477794i | ||||
\(471\) | 1.61260 | + | 2.79311i | 0.0743049 | + | 0.128700i | ||||
\(472\) | 0.0123771 | − | 0.0214377i | 0.000569701 | − | 0.000986752i | ||||
\(473\) | 8.57673 | 0.394358 | ||||||||
\(474\) | −0.179644 | + | 0.311153i | −0.00825134 | + | 0.0142917i | ||||
\(475\) | 2.76391 | − | 4.78722i | 0.126817 | − | 0.219653i | ||||
\(476\) | −5.17928 | −0.237392 | ||||||||
\(477\) | 6.92058 | − | 11.9868i | 0.316872 | − | 0.548838i | ||||
\(478\) | −3.31013 | − | 5.73332i | −0.151402 | − | 0.262236i | ||||
\(479\) | −11.1845 | − | 19.3721i | −0.511032 | − | 0.885134i | −0.999918 | − | 0.0127862i | \(-0.995930\pi\) |
0.488886 | − | 0.872348i | \(-0.337403\pi\) | |||||||
\(480\) | 12.0097 | 0.548165 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.02475 | 0.0922250 | ||||||||
\(483\) | 4.96950 | + | 8.60743i | 0.226120 | + | 0.391652i | ||||
\(484\) | −8.09179 | − | 14.0154i | −0.367809 | − | 0.637064i | ||||
\(485\) | 4.38740 | − | 7.59919i | 0.199221 | − | 0.345062i | ||||
\(486\) | 8.76569 | 0.397620 | ||||||||
\(487\) | 11.4602 | − | 19.8497i | 0.519313 | − | 0.899476i | −0.480435 | − | 0.877030i | \(-0.659521\pi\) |
0.999748 | − | 0.0224462i | \(-0.00714544\pi\) | |||||||
\(488\) | −8.23341 | + | 14.2607i | −0.372709 | + | 0.645551i | ||||
\(489\) | −12.1390 | −0.548944 | ||||||||
\(490\) | −0.192021 | + | 0.332591i | −0.00867465 | + | 0.0150249i | ||||
\(491\) | −0.921780 | − | 1.59657i | −0.0415993 | − | 0.0720522i | 0.844476 | − | 0.535593i | \(-0.179912\pi\) |
−0.886075 | + | 0.463541i | \(0.846579\pi\) | |||||||
\(492\) | −2.25086 | − | 3.89861i | −0.101477 | − | 0.175763i | ||||
\(493\) | −8.98254 | −0.404553 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.91185 | −0.355611 | ||||||||
\(496\) | 6.62833 | + | 11.4806i | 0.297621 | + | 0.515495i | ||||
\(497\) | −18.4955 | − | 32.0351i | −0.829634 | − | 1.43697i | ||||
\(498\) | −3.63437 | + | 6.29492i | −0.162860 | + | 0.282082i | ||||
\(499\) | 12.0344 | 0.538736 | 0.269368 | − | 0.963037i | \(-0.413185\pi\) | ||||
0.269368 | + | 0.963037i | \(0.413185\pi\) | |||||||
\(500\) | −5.09448 | + | 8.82390i | −0.227832 | + | 0.394617i | ||||
\(501\) | −2.51142 | + | 4.34990i | −0.112202 | + | 0.194339i | ||||
\(502\) | 0.762118 | 0.0340150 | ||||||||
\(503\) | 15.2528 | − | 26.4186i | 0.680088 | − | 1.17795i | −0.294866 | − | 0.955539i | \(-0.595275\pi\) |
0.974954 | − | 0.222408i | \(-0.0713918\pi\) | |||||||
\(504\) | −6.50000 | − | 11.2583i | −0.289533 | − | 0.501486i | ||||
\(505\) | −7.41185 | − | 12.8377i | −0.329823 | − | 0.571270i | ||||
\(506\) | −3.06100 | −0.136078 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.4681 | −0.508816 | ||||||||
\(509\) | −0.755709 | − | 1.30893i | −0.0334962 | − | 0.0580171i | 0.848791 | − | 0.528728i | \(-0.177331\pi\) |
−0.882288 | + | 0.470711i | \(0.843998\pi\) | |||||||
\(510\) | −0.708947 | − | 1.22793i | −0.0313927 | − | 0.0543738i | ||||
\(511\) | 17.2518 | − | 29.8810i | 0.763176 | − | 1.32186i | ||||
\(512\) | 21.2174 | 0.937687 | ||||||||
\(513\) | −4.16487 | + | 7.21377i | −0.183884 | + | 0.318496i | ||||
\(514\) | −8.16786 | + | 14.1471i | −0.360269 | + | 0.624004i | ||||
\(515\) | −37.9124 | −1.67062 | ||||||||
\(516\) | 4.85690 | − | 8.41239i | 0.213813 | − | 0.370335i | ||||
\(517\) | −4.60776 | − | 7.98088i | −0.202649 | − | 0.350998i | ||||
\(518\) | 0.710439 | + | 1.23052i | 0.0312149 | + | 0.0540658i | ||||
\(519\) | 13.1448 | 0.576994 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.64012 | −0.247098 | −0.123549 | − | 0.992338i | \(-0.539428\pi\) | ||||
−0.123549 | + | 0.992338i | \(0.539428\pi\) | |||||||
\(522\) | −5.16637 | − | 8.94841i | −0.226126 | − | 0.391661i | ||||
\(523\) | 15.8753 | + | 27.4968i | 0.694179 | + | 1.20235i | 0.970457 | + | 0.241275i | \(0.0775657\pi\) |
−0.276278 | + | 0.961078i | \(0.589101\pi\) | |||||||
\(524\) | −11.5734 | + | 20.0457i | −0.505585 | + | 0.875699i | ||||
\(525\) | 6.15452 | 0.268605 | ||||||||
\(526\) | −2.96801 | + | 5.14074i | −0.129411 | + | 0.224147i | ||||
\(527\) | 3.35421 | − | 5.80966i | 0.146112 | − | 0.253073i | ||||
\(528\) | 2.15883 | 0.0939512 | ||||||||
\(529\) | 0.902165 | − | 1.56260i | 0.0392246 | − | 0.0679390i | ||||
\(530\) | −4.56584 | − | 7.90827i | −0.198328 | − | 0.343513i | ||||
\(531\) | 0.0142375 | + | 0.0246601i | 0.000617856 | + | 0.00107016i | ||||
\(532\) | 8.83207 | 0.382919 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.55496 | 0.283661 | ||||||||
\(535\) | −7.88889 | − | 13.6640i | −0.341066 | − | 0.590744i | ||||
\(536\) | 9.48307 | + | 16.4252i | 0.409606 | + | 0.709459i | ||||
\(537\) | 0.984271 | − | 1.70481i | 0.0424744 | − | 0.0735678i | ||||
\(538\) | −5.65279 | −0.243709 | ||||||||
\(539\) | −0.147948 | + | 0.256254i | −0.00637259 | + | 0.0110377i | ||||
\(540\) | −10.1833 | + | 17.6380i | −0.438219 | + | 0.759018i | ||||
\(541\) | −24.3297 | −1.04602 | −0.523009 | − | 0.852327i | \(-0.675191\pi\) | ||||
−0.523009 | + | 0.852327i | \(0.675191\pi\) | |||||||
\(542\) | −8.17241 | + | 14.1550i | −0.351035 | + | 0.608010i | ||||
\(543\) | −4.73437 | − | 8.20016i | −0.203171 | − | 0.351903i | ||||
\(544\) | −3.03870 | − | 5.26318i | −0.130283 | − | 0.225657i | ||||
\(545\) | −11.7017 | −0.501246 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.18896 | −0.350135 | −0.175067 | − | 0.984556i | \(-0.556014\pi\) | ||||
−0.175067 | + | 0.984556i | \(0.556014\pi\) | |||||||
\(548\) | −10.9879 | − | 19.0316i | −0.469381 | − | 0.812991i | ||||
\(549\) | −9.47099 | − | 16.4042i | −0.404212 | − | 0.700116i | ||||
\(550\) | −0.947730 | + | 1.64152i | −0.0404114 | + | 0.0699945i | ||||
\(551\) | 15.3177 | 0.652555 | ||||||||
\(552\) | −3.78232 | + | 6.55118i | −0.160986 | + | 0.278837i | ||||
\(553\) | −1.08665 | + | 1.88214i | −0.0462092 | + | 0.0800367i | ||||
\(554\) | −5.68532 | −0.241546 | ||||||||
\(555\) | 1.06853 | − | 1.85075i | 0.0453566 | − | 0.0785600i | ||||
\(556\) | 10.1915 | + | 17.6522i | 0.432215 | + | 0.748619i | ||||
\(557\) | 12.6664 | + | 21.9388i | 0.536691 | + | 0.929576i | 0.999079 | + | 0.0428988i | \(0.0136593\pi\) |
−0.462388 | + | 0.886678i | \(0.653007\pi\) | |||||||
\(558\) | 7.71678 | 0.326677 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 16.9487 | 0.716213 | ||||||||
\(561\) | −0.546229 | − | 0.946096i | −0.0230618 | − | 0.0399442i | ||||
\(562\) | −3.20895 | − | 5.55806i | −0.135361 | − | 0.234453i | ||||
\(563\) | 12.6969 | − | 21.9916i | 0.535109 | − | 0.926836i | −0.464049 | − | 0.885810i | \(-0.653604\pi\) |
0.999158 | − | 0.0410266i | \(-0.0130628\pi\) | |||||||
\(564\) | −10.4373 | −0.439488 | ||||||||
\(565\) | −10.7078 | + | 18.5464i | −0.450478 | + | 0.780252i | ||||
\(566\) | 8.52111 | − | 14.7590i | 0.358169 | − | 0.620367i | ||||
\(567\) | 9.76032 | 0.409895 | ||||||||
\(568\) | 14.0770 | − | 24.3821i | 0.590659 | − | 1.02305i | ||||
\(569\) | 15.5673 | + | 26.9634i | 0.652617 | + | 1.13037i | 0.982486 | + | 0.186338i | \(0.0596621\pi\) |
−0.329869 | + | 0.944027i | \(0.607005\pi\) | |||||||
\(570\) | 1.20895 | + | 2.09396i | 0.0506372 | + | 0.0877063i | ||||
\(571\) | −20.5090 | −0.858276 | −0.429138 | − | 0.903239i | \(-0.641183\pi\) | ||||
−0.429138 | + | 0.903239i | \(0.641183\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.21206 | −0.301288 | ||||||||
\(574\) | 2.47823 | + | 4.29242i | 0.103439 | + | 0.179162i | ||||
\(575\) | 6.56249 | + | 11.3666i | 0.273675 | + | 0.474019i | ||||
\(576\) | −1.80045 | + | 3.11846i | −0.0750186 | + | 0.129936i | ||||
\(577\) | −15.6890 | −0.653143 | −0.326572 | − | 0.945172i | \(-0.605893\pi\) | ||||
−0.326572 | + | 0.945172i | \(0.605893\pi\) | |||||||
\(578\) | 4.35839 | − | 7.54895i | 0.181285 | − | 0.313995i | ||||
\(579\) | 5.42327 | − | 9.39338i | 0.225383 | − | 0.390376i | ||||
\(580\) | 37.4523 | 1.55512 | ||||||||
\(581\) | −21.9840 | + | 38.0775i | −0.912051 | + | 1.57972i | ||||
\(582\) | 0.696866 | + | 1.20701i | 0.0288860 | + | 0.0500320i | ||||
\(583\) | −3.51789 | − | 6.09316i | −0.145696 | − | 0.252353i | ||||
\(584\) | 26.2610 | 1.08669 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.3268 | 0.426595 | ||||||||
\(587\) | 15.2843 | + | 26.4733i | 0.630853 | + | 1.09267i | 0.987378 | + | 0.158383i | \(0.0506281\pi\) |
−0.356525 | + | 0.934286i | \(0.616039\pi\) | |||||||
\(588\) | 0.167563 | + | 0.290227i | 0.00691017 | + | 0.0119688i | ||||
\(589\) | −5.71983 | + | 9.90704i | −0.235682 | + | 0.408212i | ||||
\(590\) | 0.0187864 | 0.000773422 | ||||||||
\(591\) | 5.20291 | − | 9.01170i | 0.214019 | − | 0.370692i | ||||
\(592\) | 1.06853 | − | 1.85075i | 0.0439164 | − | 0.0760654i | ||||
\(593\) | 29.6883 | 1.21915 | 0.609576 | − | 0.792727i | \(-0.291340\pi\) | ||||
0.609576 | + | 0.792727i | \(0.291340\pi\) | |||||||
\(594\) | 1.42812 | − | 2.47357i | 0.0585963 | − | 0.101492i | ||||
\(595\) | −4.28836 | − | 7.42766i | −0.175806 | − | 0.304505i | ||||
\(596\) | 0.626842 | + | 1.08572i | 0.0256765 | + | 0.0444729i | ||||
\(597\) | −10.8955 | −0.445922 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.2325 | 0.990113 | 0.495057 | − | 0.868861i | \(-0.335147\pi\) | ||||
0.495057 | + | 0.868861i | \(0.335147\pi\) | |||||||
\(600\) | 2.34213 | + | 4.05668i | 0.0956169 | + | 0.165613i | ||||
\(601\) | −8.24094 | − | 14.2737i | −0.336155 | − | 0.582237i | 0.647551 | − | 0.762022i | \(-0.275793\pi\) |
−0.983706 | + | 0.179785i | \(0.942460\pi\) | |||||||
\(602\) | −5.34750 | + | 9.26215i | −0.217948 | + | 0.377497i | ||||
\(603\) | −21.8170 | −0.888457 | ||||||||
\(604\) | 16.1365 | − | 27.9493i | 0.656586 | − | 1.13724i | ||||
\(605\) | 13.3998 | − | 23.2091i | 0.544778 | − | 0.943584i | ||||
\(606\) | 2.35450 | 0.0956451 | ||||||||
\(607\) | −0.715948 | + | 1.24006i | −0.0290594 | + | 0.0503324i | −0.880189 | − | 0.474623i | \(-0.842585\pi\) |
0.851130 | + | 0.524955i | \(0.175918\pi\) | |||||||
\(608\) | 5.18180 | + | 8.97514i | 0.210150 | + | 0.363990i | ||||
\(609\) | 8.52715 | + | 14.7695i | 0.345537 | + | 0.598488i | ||||
\(610\) | −12.4969 | −0.505986 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.53452 | 0.183297 | ||||||||
\(613\) | 1.92423 | + | 3.33287i | 0.0777190 | + | 0.134613i | 0.902265 | − | 0.431181i | \(-0.141903\pi\) |
−0.824546 | + | 0.565794i | \(0.808570\pi\) | |||||||
\(614\) | 2.48188 | + | 4.29874i | 0.100160 | + | 0.173483i | ||||
\(615\) | 3.72737 | − | 6.45599i | 0.150302 | − | 0.260330i | ||||
\(616\) | −6.60819 | −0.266251 | ||||||||
\(617\) | −7.51938 | + | 13.0239i | −0.302719 | + | 0.524324i | −0.976751 | − | 0.214378i | \(-0.931228\pi\) |
0.674032 | + | 0.738702i | \(0.264561\pi\) | |||||||
\(618\) | 3.01089 | − | 5.21501i | 0.121116 | − | 0.209778i | ||||
\(619\) | −12.8170 | −0.515159 | −0.257579 | − | 0.966257i | \(-0.582925\pi\) | ||||
−0.257579 | + | 0.966257i | \(0.582925\pi\) | |||||||
\(620\) | −13.9852 | + | 24.2231i | −0.561660 | + | 0.972824i | ||||
\(621\) | −9.88889 | − | 17.1281i | −0.396827 | − | 0.687325i | ||||
\(622\) | −5.83811 | − | 10.1119i | −0.234087 | − | 0.405450i | ||||
\(623\) | 39.6504 | 1.58856 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1269 | −1.24508 | ||||||||
\(626\) | 1.97770 | + | 3.42547i | 0.0790447 | + | 0.136909i | ||||
\(627\) | 0.931468 | + | 1.61335i | 0.0371993 | + | 0.0644310i | ||||
\(628\) | −3.40246 | + | 5.89324i | −0.135773 | + | 0.235166i | ||||
\(629\) | −1.08144 | −0.0431199 | ||||||||
\(630\) | 4.93296 | − | 8.54414i | 0.196534 | − | 0.340407i | ||||
\(631\) | 12.8758 | − | 22.3016i | 0.512579 | − | 0.887813i | −0.487314 | − | 0.873227i | \(-0.662023\pi\) |
0.999894 | − | 0.0145868i | \(-0.00464329\pi\) | |||||||
\(632\) | −1.65412 | −0.0657974 | ||||||||
\(633\) | −4.19418 | + | 7.26453i | −0.166704 | + | 0.288739i | ||||
\(634\) | 6.64981 | + | 11.5178i | 0.264098 | + | 0.457431i | ||||
\(635\) | −9.49545 | − | 16.4466i | −0.376815 | − | 0.652664i | ||||
\(636\) | −7.96854 | −0.315973 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.25236 | −0.207943 | ||||||||
\(639\) | 16.1930 | + | 28.0471i | 0.640584 | + | 1.10952i | ||||
\(640\) | 16.1637 | + | 27.9963i | 0.638925 | + | 1.10665i | ||||
\(641\) | −12.2286 | + | 21.1805i | −0.482999 | + | 0.836579i | −0.999809 | − | 0.0195209i | \(-0.993786\pi\) |
0.516810 | + | 0.856100i | \(0.327119\pi\) | |||||||
\(642\) | 2.50604 | 0.0989055 | ||||||||
\(643\) | −4.98672 | + | 8.63726i | −0.196657 | + | 0.340620i | −0.947442 | − | 0.319926i | \(-0.896342\pi\) |
0.750785 | + | 0.660546i | \(0.229675\pi\) | |||||||
\(644\) | −10.4852 | + | 18.1610i | −0.413176 | + | 0.715642i | ||||
\(645\) | 16.0858 | 0.633376 | ||||||||
\(646\) | 0.611777 | − | 1.05963i | 0.0240700 | − | 0.0416905i | ||||
\(647\) | −5.92154 | − | 10.2564i | −0.232800 | − | 0.403221i | 0.725831 | − | 0.687873i | \(-0.241455\pi\) |
−0.958631 | + | 0.284652i | \(0.908122\pi\) | |||||||
\(648\) | 3.71432 | + | 6.43340i | 0.145912 | + | 0.252728i | ||||
\(649\) | 0.0144745 | 0.000568173 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.7366 | −0.499188 | ||||||||
\(652\) | −12.8061 | − | 22.1808i | −0.501526 | − | 0.868669i | ||||
\(653\) | 3.73705 | + | 6.47277i | 0.146242 | + | 0.253299i | 0.929836 | − | 0.367975i | \(-0.119949\pi\) |
−0.783593 | + | 0.621274i | \(0.786615\pi\) | |||||||
\(654\) | 0.929312 | − | 1.60962i | 0.0363390 | − | 0.0629410i | ||||
\(655\) | −38.3303 | −1.49769 | ||||||||
\(656\) | 3.72737 | − | 6.45599i | 0.145529 | − | 0.252064i | ||||
\(657\) | −15.1042 | + | 26.1612i | −0.589270 | + | 1.02065i | ||||
\(658\) | 11.4916 | 0.447988 | ||||||||
\(659\) | −17.0869 | + | 29.5955i | −0.665613 | + | 1.15288i | 0.313506 | + | 0.949586i | \(0.398497\pi\) |
−0.979119 | + | 0.203289i | \(0.934837\pi\) | |||||||
\(660\) | 2.27748 | + | 3.94471i | 0.0886508 | + | 0.153548i | ||||
\(661\) | 16.8044 | + | 29.1061i | 0.653615 | + | 1.13209i | 0.982239 | + | 0.187634i | \(0.0600817\pi\) |
−0.328624 | + | 0.944461i | \(0.606585\pi\) | |||||||
\(662\) | −1.60686 | −0.0624524 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33.4644 | −1.29867 | ||||||||
\(665\) | 7.31282 | + | 12.6662i | 0.283579 | + | 0.491173i | ||||
\(666\) | −0.621998 | − | 1.07733i | −0.0241019 | − | 0.0417458i | ||||
\(667\) | −18.1848 | + | 31.4970i | −0.704118 | + | 1.21957i | ||||
\(668\) | −10.5978 | −0.410040 | ||||||||
\(669\) | −4.57338 | + | 7.92132i | −0.176817 | + | 0.306256i | ||||
\(670\) | −7.19687 | + | 12.4653i | −0.278039 | + | 0.481578i | ||||
\(671\) | −9.62863 | −0.371709 | ||||||||
\(672\) | −5.76928 | + | 9.99269i | −0.222555 | + | 0.385476i | ||||
\(673\) | −24.0160 | − | 41.5970i | −0.925750 | − | 1.60345i | −0.790351 | − | 0.612654i | \(-0.790102\pi\) |
−0.135399 | − | 0.990791i | \(-0.543232\pi\) | |||||||
\(674\) | 0.861740 | + | 1.49258i | 0.0331930 | + | 0.0574919i | ||||
\(675\) | −12.2470 | −0.471386 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.6582 | −1.29359 | −0.646794 | − | 0.762665i | \(-0.723891\pi\) | ||||
−0.646794 | + | 0.762665i | \(0.723891\pi\) | |||||||
\(678\) | −1.70075 | − | 2.94579i | −0.0653169 | − | 0.113132i | ||||
\(679\) | 4.21528 | + | 7.30109i | 0.161768 | + | 0.280190i | ||||
\(680\) | 3.26391 | − | 5.65325i | 0.125165 | − | 0.216792i | ||||
\(681\) | −8.53319 | −0.326992 | ||||||||
\(682\) | 1.96130 | − | 3.39708i | 0.0751022 | − | 0.130081i | ||||
\(683\) | 7.95204 | − | 13.7733i | 0.304276 | − | 0.527022i | −0.672824 | − | 0.739803i | \(-0.734919\pi\) |
0.977100 | + | 0.212781i | \(0.0682520\pi\) | |||||||
\(684\) | −7.73258 | −0.295663 | ||||||||
\(685\) | 18.1957 | − | 31.5158i | 0.695221 | − | 1.20416i | ||||
\(686\) | 5.04437 | + | 8.73710i | 0.192595 | + | 0.333584i | ||||
\(687\) | −0.456886 | − | 0.791351i | −0.0174313 | − | 0.0301919i | ||||
\(688\) | 16.0858 | 0.613264 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.74094 | −0.218554 | ||||||||
\(691\) | 16.5951 | + | 28.7436i | 0.631309 | + | 1.09346i | 0.987284 | + | 0.158964i | \(0.0508154\pi\) |
−0.355975 | + | 0.934495i | \(0.615851\pi\) | |||||||
\(692\) | 13.8672 | + | 24.0188i | 0.527154 | + | 0.913057i | ||||
\(693\) | 3.80074 | − | 6.58308i | 0.144378 | − | 0.250070i | ||||
\(694\) | −6.31468 | −0.239702 | ||||||||
\(695\) | −16.8768 | + | 29.2315i | −0.640174 | + | 1.10881i | ||||
\(696\) | −6.49007 | + | 11.2411i | −0.246006 | + | 0.426094i | ||||
\(697\) | −3.77240 | −0.142890 | ||||||||
\(698\) | −0.928780 | + | 1.60869i | −0.0351548 | + | 0.0608900i | ||||
\(699\) | 4.35086 | + | 7.53590i | 0.164564 | + | 0.285034i | ||||
\(700\) | 6.49276 | + | 11.2458i | 0.245403 | + | 0.425051i | ||||
\(701\) | −14.9129 | −0.563253 | −0.281627 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281627 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.84415 | 0.0695534 | ||||||||
\(704\) | 0.915206 | + | 1.58518i | 0.0344931 | + | 0.0597439i | ||||
\(705\) | −8.64191 | − | 14.9682i | −0.325473 | − | 0.563736i | ||||
\(706\) | 0.176956 | − | 0.306497i | 0.00665983 | − | 0.0115352i | ||||
\(707\) | 14.2422 | 0.535633 | ||||||||
\(708\) | 0.00819673 | − | 0.0141971i | 0.000308052 | − | 0.000533561i | ||||
\(709\) | 19.2156 | − | 33.2824i | 0.721656 | − | 1.24995i | −0.238679 | − | 0.971098i | \(-0.576714\pi\) |
0.960336 | − | 0.278847i | \(-0.0899522\pi\) | |||||||
\(710\) | 21.3666 | 0.801874 | ||||||||
\(711\) | 0.951378 | − | 1.64784i | 0.0356795 | − | 0.0617987i | ||||
\(712\) | 15.0891 | + | 26.1351i | 0.565488 | + | 0.979454i | ||||
\(713\) | −13.5809 | − | 23.5228i | −0.508609 | − | 0.880937i | ||||
\(714\) | 1.36227 | 0.0509818 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.15346 | 0.155222 | ||||||||
\(717\) | −4.78328 | − | 8.28489i | −0.178635 | − | 0.309405i | ||||
\(718\) | −5.95444 | − | 10.3134i | −0.222218 | − | 0.384892i | ||||
\(719\) | 5.71864 | − | 9.90497i | 0.213269 | − | 0.369393i | −0.739467 | − | 0.673193i | \(-0.764922\pi\) |
0.952736 | + | 0.303800i | \(0.0982555\pi\) | |||||||
\(720\) | −14.8388 | −0.553008 | ||||||||
\(721\) | 18.2126 | − | 31.5451i | 0.678272 | − | 1.17480i | ||||
\(722\) | 4.22886 | − | 7.32460i | 0.157382 | − | 0.272593i | ||||
\(723\) | 2.92585 | 0.108814 | ||||||||
\(724\) | 9.98911 | − | 17.3017i | 0.371243 | − | 0.643011i | ||||
\(725\) | 11.2606 | + | 19.5039i | 0.418206 | + | 0.724355i | ||||
\(726\) | 2.12833 | + | 3.68638i | 0.0789899 | + | 0.136815i | ||||
\(727\) | 3.63640 | 0.134867 | 0.0674333 | − | 0.997724i | \(-0.478519\pi\) | ||||
0.0674333 | + | 0.997724i | \(0.478519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.78986 | 0.0662910 | ||||||||
\(730\) | 9.96495 | + | 17.2598i | 0.368819 | + | 0.638814i | ||||
\(731\) | −4.07002 | − | 7.04949i | −0.150535 | − | 0.260735i | ||||
\(732\) | −5.45257 | + | 9.44414i | −0.201533 | + | 0.349065i | ||||
\(733\) | 3.52217 | 0.130094 | 0.0650472 | − | 0.997882i | \(-0.479280\pi\) | ||||
0.0650472 | + | 0.997882i | \(0.479280\pi\) | |||||||
\(734\) | 2.60470 | − | 4.51148i | 0.0961414 | − | 0.166522i | ||||
\(735\) | −0.277479 | + | 0.480608i | −0.0102350 | + | 0.0177275i | ||||
\(736\) | −24.6069 | −0.907021 | ||||||||
\(737\) | −5.54503 | + | 9.60428i | −0.204254 | + | 0.353778i | ||||
\(738\) | −2.16972 | − | 3.75806i | −0.0798685 | − | 0.138336i | ||||
\(739\) | 0.210144 | + | 0.363980i | 0.00773027 | + | 0.0133892i | 0.869865 | − | 0.493290i | \(-0.164206\pi\) |
−0.862134 | + | 0.506680i | \(0.830873\pi\) | |||||||
\(740\) | 4.50902 | 0.165755 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.77346 | 0.322084 | ||||||||
\(743\) | −12.6811 | − | 21.9644i | −0.465226 | − | 0.805795i | 0.533986 | − | 0.845493i | \(-0.320694\pi\) |
−0.999212 | + | 0.0396987i | \(0.987360\pi\) | |||||||
\(744\) | −4.84697 | − | 8.39520i | −0.177699 | − | 0.307783i | ||||
\(745\) | −1.03803 | + | 1.79792i | −0.0380306 | + | 0.0658709i | ||||
\(746\) | 15.3870 | 0.563359 | ||||||||
\(747\) | 19.2473 | − | 33.3373i | 0.704221 | − | 1.21975i | ||||
\(748\) | 1.15250 | − | 1.99618i | 0.0421395 | − | 0.0729877i | ||||
\(749\) | 15.1588 | 0.553892 | ||||||||
\(750\) | 1.33997 | − | 2.32090i | 0.0489288 | − | 0.0847471i | ||||
\(751\) | −0.325437 | − | 0.563673i | −0.0118754 | − | 0.0205687i | 0.860027 | − | 0.510249i | \(-0.170447\pi\) |
−0.871902 | + | 0.489680i | \(0.837113\pi\) | |||||||
\(752\) | −8.64191 | − | 14.9682i | −0.315138 | − | 0.545835i | ||||
\(753\) | 1.10129 | 0.0401333 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 53.4432 | 1.94500 | ||||||||
\(756\) | −9.78382 | − | 16.9461i | −0.355834 | − | 0.616322i | ||||
\(757\) | 8.39546 | + | 14.5414i | 0.305138 | + | 0.528515i | 0.977292 | − | 0.211897i | \(-0.0679640\pi\) |
−0.672154 | + | 0.740411i | \(0.734631\pi\) | |||||||
\(758\) | 9.95324 | − | 17.2395i | 0.361518 | − | 0.626167i | ||||
\(759\) | −4.42327 | −0.160555 | ||||||||
\(760\) | −5.56584 | + | 9.64032i | −0.201894 | + | 0.349691i | ||||
\(761\) | 15.4611 | − | 26.7794i | 0.560463 | − | 0.970751i | −0.436993 | − | 0.899465i | \(-0.643956\pi\) |
0.997456 | − | 0.0712857i | \(-0.0227102\pi\) | |||||||
\(762\) | 3.01639 | 0.109272 | ||||||||
\(763\) | 5.62133 | − | 9.73644i | 0.203506 | − | 0.352483i | ||||
\(764\) | −7.60842 | − | 13.1782i | −0.275263 | − | 0.476770i | ||||
\(765\) | 3.75451 | + | 6.50301i | 0.135745 | + | 0.235117i | ||||
\(766\) | −2.69441 | −0.0973531 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.68425 | −0.0968596 | ||||||||
\(769\) | −21.8845 | − | 37.9050i | −0.789174 | − | 1.36689i | −0.926473 | − | 0.376360i | \(-0.877176\pi\) |
0.137299 | − | 0.990530i | \(-0.456158\pi\) | |||||||
\(770\) | −2.50753 | − | 4.34317i | −0.0903652 | − | 0.156517i | ||||
\(771\) | −11.8029 | + | 20.4432i | −0.425071 | + | 0.736245i | ||||
\(772\) | 22.8853 | 0.823660 | ||||||||
\(773\) | −21.2104 | + | 36.7376i | −0.762886 | + | 1.32136i | 0.178470 | + | 0.983945i | \(0.442885\pi\) |
−0.941357 | + | 0.337413i | \(0.890448\pi\) | |||||||
\(774\) | 4.68180 | − | 8.10912i | 0.168284 | − | 0.291476i | ||||
\(775\) | −16.8194 | −0.604171 | ||||||||
\(776\) | −3.20828 | + | 5.55691i | −0.115171 | + | 0.199481i | ||||
\(777\) | 1.02661 | + | 1.77815i | 0.0368296 | + | 0.0637907i | ||||
\(778\) | −0.661890 | − | 1.14643i | −0.0237299 | − | 0.0411014i | ||||
\(779\) | 6.43296 | 0.230485 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.4625 | 0.589075 | ||||||||
\(782\) | 1.45257 | + | 2.51593i | 0.0519440 | + | 0.0899696i | ||||
\(783\) | −16.9683 | − | 29.3900i | −0.606398 | − | 1.05031i | ||||
\(784\) | −0.277479 | + | 0.480608i | −0.00990997 | + | 0.0171646i | ||||
\(785\) | −11.2687 | −0.402199 | ||||||||
\(786\) | 3.04407 | − | 5.27249i | 0.108578 | − | 0.188063i | ||||
\(787\) | −18.0058 | + | 31.1870i | −0.641838 | + | 1.11170i | 0.343185 | + | 0.939268i | \(0.388494\pi\) |
−0.985022 | + | 0.172427i | \(0.944839\pi\) | |||||||
\(788\) | 21.9554 | 0.782129 | ||||||||
\(789\) | −4.28890 | + | 7.42859i | −0.152689 | + | 0.264465i | ||||
\(790\) | −0.627670 | − | 1.08716i | −0.0223315 | − | 0.0386793i | ||||
\(791\) | −10.2877 | − | 17.8188i | −0.365789 | − | 0.633564i | ||||
\(792\) | 5.78554 | 0.205580 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.47219 | 0.300667 | ||||||||
\(795\) | −6.59783 | − | 11.4278i | −0.234001 | − | 0.405302i | ||||
\(796\) | −11.4943 | − | 19.9086i | −0.407403 | − | 0.705643i | ||||
\(797\) | 15.8550 | − | 27.4617i | 0.561614 | − | 0.972744i | −0.435742 | − | 0.900072i | \(-0.643514\pi\) |
0.997356 | − | 0.0726725i | \(-0.0231528\pi\) | |||||||
\(798\) | −2.32304 | −0.0822349 | ||||||||
\(799\) | −4.37316 | + | 7.57453i | −0.154711 | + | 0.267968i | ||||
\(800\) | −7.61865 | + | 13.1959i | −0.269360 | + | 0.466545i | ||||
\(801\) | −34.7144 | −1.22657 | ||||||||
\(802\) | 3.54019 | − | 6.13179i | 0.125008 | − | 0.216521i | ||||
\(803\) | 7.67778 | + | 13.2983i | 0.270943 | + | 0.469287i | ||||
\(804\) | 6.28017 | + | 10.8776i | 0.221484 | + | 0.383622i | ||||
\(805\) | −34.7265 | −1.22395 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.16852 | −0.287546 | ||||||||
\(808\) | 5.41992 | + | 9.38758i | 0.190672 | + | 0.330254i | ||||
\(809\) | 22.6407 | + | 39.2149i | 0.796005 | + | 1.37872i | 0.922199 | + | 0.386716i | \(0.126390\pi\) |
−0.126194 | + | 0.992006i | \(0.540276\pi\) | |||||||
\(810\) | −2.81886 | + | 4.88242i | −0.0990448 | + | 0.171551i | ||||
\(811\) | 42.8635 | 1.50514 | 0.752571 | − | 0.658511i | \(-0.228813\pi\) | ||||
0.752571 | + | 0.658511i | \(0.228813\pi\) | |||||||
\(812\) | −17.9916 | + | 31.1623i | −0.631380 | + | 1.09358i | ||||
\(813\) | −11.8095 | + | 20.4546i | −0.414176 | + | 0.717374i | ||||
\(814\) | −0.632351 | −0.0221639 | ||||||||
\(815\) | 21.2066 | − | 36.7308i | 0.742833 | − | 1.28662i | ||||
\(816\) | −1.02446 | − | 1.77441i | −0.0358632 | − | 0.0621169i | ||||
\(817\) | 6.94049 | + | 12.0213i | 0.242817 | + | 0.420572i | ||||
\(818\) | 14.0731 | 0.492054 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.7289 | 0.549276 | ||||||||
\(821\) | −3.91388 | − | 6.77904i | −0.136595 | − | 0.236590i | 0.789610 | − | 0.613608i | \(-0.210283\pi\) |
−0.926206 | + | 0.377018i | \(0.876949\pi\) | |||||||
\(822\) | 2.89008 | + | 5.00577i | 0.100803 | + | 0.174596i | ||||
\(823\) | 18.3877 | − | 31.8484i | 0.640955 | − | 1.11017i | −0.344265 | − | 0.938872i | \(-0.611872\pi\) |
0.985220 | − | 0.171294i | \(-0.0547947\pi\) | |||||||
\(824\) | 27.7235 | 0.965793 | ||||||||
\(825\) | −1.36951 | + | 2.37206i | −0.0476802 | + | 0.0825846i | ||||
\(826\) | −0.00902470 | + | 0.0156312i | −0.000314009 | + | 0.000543880i | ||||
\(827\) | −47.3293 | −1.64580 | −0.822900 | − | 0.568186i | \(-0.807645\pi\) | ||||
−0.822900 | + | 0.568186i | \(0.807645\pi\) | |||||||
\(828\) | 9.17994 | − | 15.9001i | 0.319025 | − | 0.552567i | ||||
\(829\) | −12.6344 | − | 21.8834i | −0.438810 | − | 0.760041i | 0.558788 | − | 0.829311i | \(-0.311267\pi\) |
−0.997598 | + | 0.0692694i | \(0.977933\pi\) | |||||||
\(830\) | −12.6984 | − | 21.9942i | −0.440766 | − | 0.763430i | ||||
\(831\) | −8.21552 | −0.284993 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.280831 | 0.00973023 | ||||||||
\(834\) | −2.68060 | − | 4.64294i | −0.0928217 | − | 0.160772i | ||||
\(835\) | −8.77479 | − | 15.1984i | −0.303664 | − | 0.525962i | ||||
\(836\) | −1.96532 | + | 3.40403i | −0.0679720 | + | 0.117731i | ||||
\(837\) | 25.3448 | 0.876045 | ||||||||
\(838\) | 3.23742 | − | 5.60738i | 0.111835 | − | 0.193704i | ||||
\(839\) | −18.8442 | + | 32.6390i | −0.650572 | + | 1.12682i | 0.332412 | + | 0.943134i | \(0.392138\pi\) |
−0.982984 | + | 0.183690i | \(0.941196\pi\) | |||||||
\(840\) | −12.3937 | −0.427624 | ||||||||
\(841\) | −16.7032 | + | 28.9308i | −0.575972 | + | 0.997614i | ||||
\(842\) | −2.30111 | − | 3.98564i | −0.0793015 | − | 0.137354i | ||||
\(843\) | −4.63706 | − | 8.03163i | −0.159709 | − | 0.276624i | ||||
\(844\) | −17.6987 | −0.609215 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.0610 | −0.345904 | ||||||||
\(847\) | 12.8741 | + | 22.2986i | 0.442360 | + | 0.766190i | ||||
\(848\) | −6.59783 | − | 11.4278i | −0.226571 | − | 0.392432i | ||||
\(849\) | 12.3134 | − | 21.3274i | 0.422593 | − | 0.731953i | ||||
\(850\) | 1.79895 | 0.0617036 | ||||||||
\(851\) | −2.18933 | + | 3.79204i | −0.0750494 | + | 0.129989i | ||||
\(852\) | 9.32251 | − | 16.1471i | 0.319384 | − | 0.553189i | ||||
\(853\) | 31.0121 | 1.06183 | 0.530917 | − | 0.847424i | \(-0.321848\pi\) | ||||
0.530917 | + | 0.847424i | \(0.321848\pi\) | |||||||
\(854\) | 6.00335 | − | 10.3981i | 0.205430 | − | 0.355816i | ||||
\(855\) | −6.40246 | − | 11.0894i | −0.218960 | − | 0.379249i | ||||
\(856\) | 5.76875 | + | 9.99177i | 0.197172 | + | 0.341512i | ||||
\(857\) | 12.4692 | 0.425940 | 0.212970 | − | 0.977059i | \(-0.431686\pi\) | ||||
0.212970 | + | 0.977059i | \(0.431686\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.3163 | −0.590826 | −0.295413 | − | 0.955370i | \(-0.595457\pi\) | ||||
−0.295413 | + | 0.955370i | \(0.595457\pi\) | |||||||
\(860\) | 16.9698 | + | 29.3925i | 0.578665 | + | 1.00228i | ||||
\(861\) | 3.58115 | + | 6.20273i | 0.122045 | + | 0.211388i | ||||
\(862\) | 0.258693 | − | 0.448069i | 0.00881111 | − | 0.0152613i | ||||
\(863\) | 3.46383 | 0.117910 | 0.0589550 | − | 0.998261i | \(-0.481223\pi\) | ||||
0.0589550 | + | 0.998261i | \(0.481223\pi\) | |||||||
\(864\) | 11.4804 | − | 19.8846i | 0.390571 | − | 0.676488i | ||||
\(865\) | −22.9638 | + | 39.7744i | −0.780791 | + | 1.35237i | ||||
\(866\) | −7.40880 | −0.251761 | ||||||||
\(867\) | 6.29805 | − | 10.9085i | 0.213893 | − | 0.370474i | ||||
\(868\) | −13.4366 | − | 23.2729i | −0.456068 | − | 0.789933i | ||||
\(869\) | −0.483607 | − | 0.837631i | −0.0164052 | − | 0.0284147i | ||||
\(870\) | −9.85086 | −0.333975 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.55688 | 0.289772 | ||||||||
\(873\) | −3.69053 | − | 6.39218i | −0.124905 | − | 0.216343i | ||||
\(874\) | −2.47703 | − | 4.29035i | −0.0837869 | − | 0.145123i | ||||
\(875\) | 8.10537 | − | 14.0389i | 0.274011 | − | 0.474602i | ||||
\(876\) | 17.3913 | 0.587599 | ||||||||
\(877\) | 28.6274 | − | 49.5842i | 0.966680 | − | 1.67434i | 0.261647 | − | 0.965164i | \(-0.415734\pi\) |
0.705033 | − | 0.709175i | \(-0.250932\pi\) | |||||||
\(878\) | −3.88255 | + | 6.72478i | −0.131030 | + | 0.226950i | ||||
\(879\) | 14.9226 | 0.503327 | ||||||||
\(880\) | −3.77144 | + | 6.53232i | −0.127135 | + | 0.220205i | ||||
\(881\) | 21.5891 | + | 37.3934i | 0.727355 | + | 1.25982i | 0.957997 | + | 0.286778i | \(0.0925842\pi\) |
−0.230642 | + | 0.973039i | \(0.574083\pi\) | |||||||
\(882\) | 0.161522 | + | 0.279764i | 0.00543873 | + | 0.00942015i | ||||
\(883\) | 49.9560 | 1.68115 | 0.840576 | − | 0.541693i | \(-0.182216\pi\) | ||||
0.840576 | + | 0.541693i | \(0.182216\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0271471 | 0.000912539 | ||||||||
\(886\) | −6.57673 | − | 11.3912i | −0.220950 | − | 0.382696i | ||||
\(887\) | −8.83728 | − | 15.3066i | −0.296727 | − | 0.513946i | 0.678658 | − | 0.734454i | \(-0.262562\pi\) |
−0.975385 | + | 0.220508i | \(0.929228\pi\) | |||||||
\(888\) | −0.781364 | + | 1.35336i | −0.0262209 | + | 0.0454159i | ||||
\(889\) | 18.2459 | 0.611948 | ||||||||
\(890\) | −11.4514 | + | 19.8344i | −0.383851 | + | 0.664850i | ||||
\(891\) | −2.17187 | + | 3.76180i | −0.0727605 | + | 0.126025i | ||||
\(892\) | −19.2989 | −0.646174 | ||||||||
\(893\) | 7.45742 | − | 12.9166i | 0.249553 | − | 0.432238i | ||||
\(894\) | −0.164874 | − | 0.285571i | −0.00551422 | − | 0.00955092i | ||||
\(895\) | 3.43900 | + | 5.95652i | 0.114953 | + | 0.199105i | ||||
\(896\) | −31.0592 | −1.03761 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.98493 | 0.233090 | ||||||||
\(899\) | −23.3034 | − | 40.3627i | −0.777213 | − | 1.34617i | ||||
\(900\) | −5.68449 | − | 9.84582i | −0.189483 | − | 0.328194i | ||||
\(901\) | −3.33877 | + | 5.78293i | −0.111231 | + | 0.192657i | ||||
\(902\) | −2.20583 | −0.0734462 | ||||||||
\(903\) | −7.72737 | + | 13.3842i | −0.257151 | + | 0.445398i | ||||
\(904\) | 7.83004 | − | 13.5620i | 0.260423 | − | 0.451067i | ||||
\(905\) | 33.0834 | 1.09973 | ||||||||
\(906\) | −4.24429 | + | 7.35133i | −0.141007 | + | 0.244232i | ||||
\(907\) | −3.86712 | − | 6.69804i | −0.128406 | − | 0.222405i | 0.794653 | − | 0.607063i | \(-0.207653\pi\) |
−0.923059 | + | 0.384658i | \(0.874319\pi\) | |||||||
\(908\) | −9.00216 | − | 15.5922i | −0.298747 | − | 0.517445i | ||||
\(909\) | −12.4692 | −0.413577 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.6179 | 1.31260 | 0.656299 | − | 0.754501i | \(-0.272121\pi\) | ||||
0.656299 | + | 0.754501i | \(0.272121\pi\) | |||||||
\(912\) | 1.74698 | + | 3.02586i | 0.0578483 | + | 0.100196i | ||||
\(913\) | −9.78382 | − | 16.9461i | −0.323797 | − | 0.560833i | ||||
\(914\) | −9.33393 | + | 16.1668i | −0.308739 | + | 0.534752i | ||||
\(915\) | −18.0586 | −0.596999 | ||||||||
\(916\) | 0.963992 | − | 1.66968i | 0.0318512 | − | 0.0551679i | ||||
\(917\) | 18.4133 | − | 31.8929i | 0.608062 | − | 1.05319i | ||||
\(918\) | −2.71081 | −0.0894700 | ||||||||
\(919\) | −7.31067 | + | 12.6624i | −0.241157 | + | 0.417696i | −0.961044 | − | 0.276395i | \(-0.910860\pi\) |
0.719887 | + | 0.694091i | \(0.244193\pi\) | |||||||
\(920\) | −13.2153 | − | 22.8895i | −0.435695 | − | 0.754646i | ||||
\(921\) | 3.58642 | + | 6.21186i | 0.118176 | + | 0.204688i | ||||
\(922\) | 0.778512 | 0.0256389 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4.37627 | −0.143969 | ||||||||
\(925\) | 1.35570 | + | 2.34814i | 0.0445751 | + | 0.0772064i | ||||
\(926\) | −4.21797 | − | 7.30574i | −0.138611 | − | 0.240082i | ||||
\(927\) | −15.9453 | + | 27.6181i | −0.523714 | + | 0.907099i | ||||
\(928\) | −42.2228 | −1.38603 | ||||||||
\(929\) | 1.77868 | − | 3.08076i | 0.0583565 | − | 0.101076i | −0.835371 | − | 0.549686i | \(-0.814747\pi\) |
0.893728 | + | 0.448610i | \(0.148081\pi\) | |||||||
\(930\) | 3.67845 | − | 6.37126i | 0.120621 | − | 0.208922i | ||||
\(931\) | −0.478894 | −0.0156951 | ||||||||
\(932\) | −9.17994 | + | 15.9001i | −0.300699 | + | 0.520826i | ||||
\(933\) | −8.43631 | − | 14.6121i | −0.276192 | − | 0.478379i | ||||
\(934\) | 10.9164 | + | 18.9078i | 0.357196 | + | 0.618681i | ||||
\(935\) | 3.81700 | 0.124829 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.5526 | 1.12878 | 0.564392 | − | 0.825507i | \(-0.309111\pi\) | ||||
0.564392 | + | 0.825507i | \(0.309111\pi\) | |||||||
\(938\) | −6.91454 | − | 11.9763i | −0.225768 | − | 0.391041i | ||||
\(939\) | 2.85786 | + | 4.94995i | 0.0932626 | + | 0.161536i | ||||
\(940\) | 18.2337 | − | 31.5817i | 0.594718 | − | 1.03008i | ||||
\(941\) | −20.6233 | −0.672299 | −0.336149 | − | 0.941809i | \(-0.609125\pi\) | ||||
−0.336149 | + | 0.941809i | \(0.609125\pi\) | |||||||
\(942\) | 0.894928 | − | 1.55006i | 0.0291583 | − | 0.0505037i | ||||
\(943\) | −7.63706 | + | 13.2278i | −0.248697 | + | 0.430756i | ||||
\(944\) | 0.0271471 | 0.000883562 | ||||||||
\(945\) | 16.2017 | − | 28.0622i | 0.527042 | − | 0.912863i | ||||
\(946\) | −2.37986 | − | 4.12204i | −0.0773760 | − | 0.134019i | ||||
\(947\) | 14.7500 | + | 25.5477i | 0.479309 | + | 0.830188i | 0.999718 | − | 0.0237289i | \(-0.00755384\pi\) |
−0.520409 | + | 0.853917i | \(0.674221\pi\) | |||||||
\(948\) | −1.09544 | −0.0355783 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.06770 | −0.0995295 | ||||||||
\(951\) | 9.60925 | + | 16.6437i | 0.311601 | + | 0.539709i | ||||
\(952\) | 3.13587 | + | 5.43148i | 0.101634 | + | 0.176035i | ||||
\(953\) | −13.1195 | + | 22.7236i | −0.424981 | + | 0.736089i | −0.996419 | − | 0.0845563i | \(-0.973053\pi\) |
0.571437 | + | 0.820646i | \(0.306386\pi\) | |||||||
\(954\) | −7.68127 | −0.248690 | ||||||||
\(955\) | 12.5993 | − | 21.8227i | 0.407705 | − | 0.706165i | ||||
\(956\) | 10.0923 | − | 17.4804i | 0.326409 | − | 0.565357i | ||||
\(957\) | −7.58987 | −0.245346 | ||||||||
\(958\) | −6.20692 | + | 10.7507i | −0.200537 | + | 0.347340i | ||||
\(959\) | 17.4819 | + | 30.2795i | 0.564519 | + | 0.977776i | ||||
\(960\) | 1.71648 | + | 2.97303i | 0.0553992 | + | 0.0959542i | ||||
\(961\) | 3.80731 | 0.122817 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.2717 | −0.427676 | ||||||||
\(964\) | 3.08665 | + | 5.34624i | 0.0994144 | + | 0.172191i | ||||
\(965\) | 18.9487 | + | 32.8201i | 0.609980 | + | 1.05652i | ||||
\(966\) | 2.75786 | − | 4.77676i | 0.0887328 | − | 0.153690i | ||||
\(967\) | −17.5176 | −0.563330 | −0.281665 | − | 0.959513i | \(-0.590887\pi\) | ||||
−0.281665 | + | 0.959513i | \(0.590887\pi\) | |||||||
\(968\) | −9.79859 | + | 16.9716i | −0.314938 | + | 0.545489i | ||||
\(969\) | 0.884043 | − | 1.53121i | 0.0283996 | − | 0.0491895i | ||||
\(970\) | −4.86964 | −0.156355 | ||||||||
\(971\) | −10.2560 | + | 17.7639i | −0.329131 | + | 0.570071i | −0.982340 | − | 0.187106i | \(-0.940089\pi\) |
0.653209 | + | 0.757178i | \(0.273422\pi\) | |||||||
\(972\) | 13.3629 | + | 23.1453i | 0.428616 | + | 0.742385i | ||||
\(973\) | −16.2148 | − | 28.0848i | −0.519821 | − | 0.900356i | ||||
\(974\) | −12.7199 | −0.407572 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.0586 | −0.578042 | ||||||||
\(977\) | 12.7225 | + | 22.0361i | 0.407030 | + | 0.704996i | 0.994555 | − | 0.104210i | \(-0.0332313\pi\) |
−0.587526 | + | 0.809205i | \(0.699898\pi\) | |||||||
\(978\) | 3.36831 | + | 5.83409i | 0.107707 | + | 0.186554i | ||||
\(979\) | −8.82304 | + | 15.2820i | −0.281986 | + | 0.488414i | ||||
\(980\) | −1.17092 | −0.0374035 | ||||||||
\(981\) | −4.92154 | + | 8.52436i | −0.157133 | + | 0.272162i | ||||
\(982\) | −0.511549 | + | 0.886029i | −0.0163242 | + | 0.0282743i | ||||
\(983\) | 39.5244 | 1.26063 | 0.630316 | − | 0.776339i | \(-0.282926\pi\) | ||||
0.630316 | + | 0.776339i | \(0.282926\pi\) | |||||||
\(984\) | −2.72564 | + | 4.72094i | −0.0868901 | + | 0.150498i | ||||
\(985\) | 18.1787 | + | 31.4865i | 0.579223 | + | 1.00324i | ||||
\(986\) | 2.49247 | + | 4.31708i | 0.0793763 | + | 0.137484i | ||||
\(987\) | 16.6058 | 0.528568 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32.9584 | −1.04802 | ||||||||
\(990\) | 2.19537 | + | 3.80250i | 0.0697736 | + | 0.120851i | ||||
\(991\) | 14.9189 | + | 25.8402i | 0.473913 | + | 0.820841i | 0.999554 | − | 0.0298651i | \(-0.00950777\pi\) |
−0.525641 | + | 0.850707i | \(0.676174\pi\) | |||||||
\(992\) | 15.7666 | − | 27.3085i | 0.500590 | − | 0.867047i | ||||
\(993\) | −2.32198 | −0.0736858 | ||||||||
\(994\) | −10.2642 | + | 17.7781i | −0.325561 | + | 0.563888i | ||||
\(995\) | 19.0341 | − | 32.9681i | 0.603423 | − | 1.04516i | ||||
\(996\) | −22.1618 | −0.702224 | ||||||||
\(997\) | 2.46562 | − | 4.27057i | 0.0780868 | − | 0.135250i | −0.824338 | − | 0.566098i | \(-0.808452\pi\) |
0.902424 | + | 0.430848i | \(0.141786\pi\) | |||||||
\(998\) | −3.33931 | − | 5.78385i | −0.105704 | − | 0.183084i | ||||
\(999\) | −2.04288 | − | 3.53837i | −0.0646338 | − | 0.111949i |
(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 | 169.2.c.b.146.2 | 6 | ||
13.2 | odd | 12 | 169.2.b.b.168.3 | 6 | |||
13.3 | even | 3 | 169.2.a.c.1.2 | yes | 3 | ||
13.4 | even | 6 | 169.2.c.c.22.2 | 6 | |||
13.5 | odd | 4 | 169.2.e.b.23.3 | 12 | |||
13.6 | odd | 12 | 169.2.e.b.147.4 | 12 | |||
13.7 | odd | 12 | 169.2.e.b.147.3 | 12 | |||
13.8 | odd | 4 | 169.2.e.b.23.4 | 12 | |||
13.9 | even | 3 | inner | 169.2.c.b.22.2 | 6 | ||
13.10 | even | 6 | 169.2.a.b.1.2 | ✓ | 3 | ||
13.11 | odd | 12 | 169.2.b.b.168.4 | 6 | |||
13.12 | even | 2 | 169.2.c.c.146.2 | 6 | |||
39.2 | even | 12 | 1521.2.b.l.1351.4 | 6 | |||
39.11 | even | 12 | 1521.2.b.l.1351.3 | 6 | |||
39.23 | odd | 6 | 1521.2.a.r.1.2 | 3 | |||
39.29 | odd | 6 | 1521.2.a.o.1.2 | 3 | |||
52.3 | odd | 6 | 2704.2.a.ba.1.1 | 3 | |||
52.11 | even | 12 | 2704.2.f.o.337.2 | 6 | |||
52.15 | even | 12 | 2704.2.f.o.337.1 | 6 | |||
52.23 | odd | 6 | 2704.2.a.z.1.1 | 3 | |||
65.29 | even | 6 | 4225.2.a.bb.1.2 | 3 | |||
65.49 | even | 6 | 4225.2.a.bg.1.2 | 3 | |||
91.55 | odd | 6 | 8281.2.a.bj.1.2 | 3 | |||
91.62 | odd | 6 | 8281.2.a.bf.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.2.a.b.1.2 | ✓ | 3 | 13.10 | even | 6 | ||
169.2.a.c.1.2 | yes | 3 | 13.3 | even | 3 | ||
169.2.b.b.168.3 | 6 | 13.2 | odd | 12 | |||
169.2.b.b.168.4 | 6 | 13.11 | odd | 12 | |||
169.2.c.b.22.2 | 6 | 13.9 | even | 3 | inner | ||
169.2.c.b.146.2 | 6 | 1.1 | even | 1 | trivial | ||
169.2.c.c.22.2 | 6 | 13.4 | even | 6 | |||
169.2.c.c.146.2 | 6 | 13.12 | even | 2 | |||
169.2.e.b.23.3 | 12 | 13.5 | odd | 4 | |||
169.2.e.b.23.4 | 12 | 13.8 | odd | 4 | |||
169.2.e.b.147.3 | 12 | 13.7 | odd | 12 | |||
169.2.e.b.147.4 | 12 | 13.6 | odd | 12 | |||
1521.2.a.o.1.2 | 3 | 39.29 | odd | 6 | |||
1521.2.a.r.1.2 | 3 | 39.23 | odd | 6 | |||
1521.2.b.l.1351.3 | 6 | 39.11 | even | 12 | |||
1521.2.b.l.1351.4 | 6 | 39.2 | even | 12 | |||
2704.2.a.z.1.1 | 3 | 52.23 | odd | 6 | |||
2704.2.a.ba.1.1 | 3 | 52.3 | odd | 6 | |||
2704.2.f.o.337.1 | 6 | 52.15 | even | 12 | |||
2704.2.f.o.337.2 | 6 | 52.11 | even | 12 | |||
4225.2.a.bb.1.2 | 3 | 65.29 | even | 6 | |||
4225.2.a.bg.1.2 | 3 | 65.49 | even | 6 | |||
8281.2.a.bf.1.2 | 3 | 91.62 | odd | 6 | |||
8281.2.a.bj.1.2 | 3 | 91.55 | odd | 6 |