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 | 22.2 | ||
Root | \(-0.623490 + 1.07992i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.22 |
Dual form | 169.2.c.c.146.2 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 | \(-0.770471\pi\) |
0.947296 | + | 0.320361i | \(0.103804\pi\) | |||||||
\(3\) | −0.400969 | + | 0.694498i | −0.231499 | + | 0.400969i | −0.958250 | − | 0.285933i | \(-0.907696\pi\) |
0.726750 | + | 0.686902i | \(0.241030\pi\) | |||||||
\(4\) | 0.846011 | + | 1.46533i | 0.423005 | + | 0.732667i | ||||
\(5\) | −2.80194 | −1.25306 | −0.626532 | − | 0.779395i | \(-0.715526\pi\) | ||||
−0.626532 | + | 0.779395i | \(0.715526\pi\) | |||||||
\(6\) | 0.222521 | + | 0.385418i | 0.0908438 | + | 0.157346i | ||||
\(7\) | 1.34601 | + | 2.33136i | 0.508744 | + | 0.881171i | 0.999949 | + | 0.0101266i | \(0.00322345\pi\) |
−0.491204 | + | 0.871044i | \(0.663443\pi\) | |||||||
\(8\) | 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 | \(-0.775525\pi\) |
0.942090 | + | 0.335360i | \(0.108858\pi\) | |||||||
\(12\) | −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 | 0.788808 | − | 0.614639i | \(-0.210698\pi\) |
−0.926697 | + | 0.375808i | \(0.877365\pi\) | |||||||
\(18\) | 1.30798 | 0.308293 | ||||||||
\(19\) | −0.969501 | − | 1.67922i | −0.222419 | − | 0.385240i | 0.733123 | − | 0.680096i | \(-0.238062\pi\) |
−0.955542 | + | 0.294855i | \(0.904729\pi\) | |||||||
\(20\) | −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 | −0.519749 | − | 0.854319i | \(-0.673975\pi\) |
0.999736 | + | 0.0229566i | \(0.00730797\pi\) | |||||||
\(24\) | −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 | −0.221914 | − | 0.975066i | \(-0.571230\pi\) |
0.955389 | − | 0.295350i | \(-0.0954364\pi\) | |||||||
\(30\) | −0.623490 | − | 1.07992i | −0.113833 | − | 0.197165i | ||||
\(31\) | 5.89977 | 1.05963 | 0.529815 | − | 0.848113i | \(-0.322261\pi\) | ||||
0.529815 | + | 0.848113i | \(0.322261\pi\) | |||||||
\(32\) | 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 | \(-0.858244\pi\) |
0.824286 | + | 0.566174i | \(0.191577\pi\) | |||||||
\(38\) | −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 | \(-0.916748\pi\) |
0.706926 | + | 0.707288i | \(0.250081\pi\) | |||||||
\(42\) | −0.599031 | + | 1.03755i | −0.0924325 | + | 0.160098i | ||||
\(43\) | −3.57942 | − | 6.19973i | −0.545856 | − | 0.945450i | −0.998553 | − | 0.0537856i | \(-0.982871\pi\) |
0.452697 | − | 0.891665i | \(-0.350462\pi\) | |||||||
\(44\) | 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 | \(-0.689583\pi\) | ||||
−0.560998 | + | 0.827817i | \(0.689583\pi\) | |||||||
\(48\) | −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 | \(-0.166416\pi\) |
−0.865632 | + | 0.500681i | \(0.833083\pi\) | |||||||
\(60\) | 3.80194 | 0.490828 | ||||||||
\(61\) | 4.01842 | + | 6.96010i | 0.514506 | + | 0.891150i | 0.999858 | + | 0.0168315i | \(0.00535789\pi\) |
−0.485353 | + | 0.874318i | \(0.661309\pi\) | |||||||
\(62\) | 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 | −0.431567 | − | 0.902081i | \(-0.642039\pi\) |
0.997009 | − | 0.0772919i | \(-0.0246273\pi\) | |||||||
\(68\) | 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 | 0.909059 | + | 0.416668i | \(0.136802\pi\) |
−0.0936838 | + | 0.995602i | \(0.529864\pi\) | |||||||
\(72\) | 2.41454 | + | 4.18211i | 0.284557 | + | 0.492866i | ||||
\(73\) | 12.8170 | 1.50012 | 0.750058 | − | 0.661372i | \(-0.230025\pi\) | ||||
0.750058 | + | 0.661372i | \(0.230025\pi\) | |||||||
\(74\) | 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 | \(-0.853809\pi\) | ||||
−0.896375 | + | 0.443296i | \(0.853809\pi\) | |||||||
\(84\) | −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 | −0.150949 | − | 0.988542i | \(-0.548233\pi\) |
0.931576 | − | 0.363546i | \(-0.118434\pi\) | |||||||
\(90\) | −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 | \(-0.217490\pi\) |
−0.934504 | + | 0.355953i | \(0.884156\pi\) | |||||||
\(98\) | 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 | −0.967094 | − | 0.254420i | \(-0.918116\pi\) |
0.703881 | + | 0.710318i | \(0.251449\pi\) | |||||||
\(102\) | 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 | −0.969421 | − | 0.245403i | \(-0.921080\pi\) |
0.697236 | + | 0.716842i | \(0.254413\pi\) | |||||||
\(108\) | −3.63437 | − | 6.29492i | −0.349718 | − | 0.605729i | ||||
\(109\) | 4.17629 | 0.400016 | 0.200008 | − | 0.979794i | \(-0.435903\pi\) | ||||
0.200008 | + | 0.979794i | \(0.435903\pi\) | |||||||
\(110\) | 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 | 0.628376 | − | 0.777910i | \(-0.283720\pi\) |
−0.987878 | + | 0.155235i | \(0.950387\pi\) | |||||||
\(114\) | 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 | −0.976298 | − | 0.216430i | \(-0.930559\pi\) |
0.675583 | + | 0.737284i | \(0.263892\pi\) | |||||||
\(128\) | −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 | −0.997918 | − | 0.0644987i | \(-0.979455\pi\) |
0.443101 | − | 0.896471i | \(-0.353878\pi\) | |||||||
\(138\) | 2.04892 | 0.174415 | ||||||||
\(139\) | −6.02326 | − | 10.4326i | −0.510886 | − | 0.884881i | −0.999920 | − | 0.0126165i | \(-0.995984\pi\) |
0.489034 | − | 0.872265i | \(-0.337349\pi\) | |||||||
\(140\) | 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 | \(-0.157004\pi\) |
−0.850451 | + | 0.526054i | \(0.823671\pi\) | |||||||
\(150\) | 0.634375 | + | 1.09877i | 0.0517965 | + | 0.0897142i | ||||
\(151\) | −19.0737 | −1.55219 | −0.776097 | − | 0.630614i | \(-0.782803\pi\) | ||||
−0.776097 | + | 0.630614i | \(0.782803\pi\) | |||||||
\(152\) | −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 | −0.993852 | − | 0.110721i | \(-0.964684\pi\) |
0.401038 | − | 0.916061i | \(-0.368649\pi\) | |||||||
\(164\) | −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 | \(-0.755419\pi\) |
0.961380 | + | 0.275226i | \(0.0887526\pi\) | |||||||
\(168\) | −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 | −0.988904 | − | 0.148556i | \(-0.952538\pi\) |
0.365799 | − | 0.930694i | \(-0.380796\pi\) | |||||||
\(174\) | 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 | −0.816505 | − | 0.577339i | \(-0.804091\pi\) |
0.908242 | + | 0.418445i | \(0.137425\pi\) | |||||||
\(180\) | 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 | 0.981586 | − | 0.191019i | \(-0.0611792\pi\) |
−0.656220 | + | 0.754569i | \(0.727846\pi\) | |||||||
\(192\) | 0.612605 | − | 1.06106i | 0.0442109 | − | 0.0765756i | ||||
\(193\) | −6.76271 | + | 11.7134i | −0.486790 | + | 0.843146i | −0.999885 | − | 0.0151865i | \(-0.995166\pi\) |
0.513094 | + | 0.858332i | \(0.328499\pi\) | |||||||
\(194\) | −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 | \(-0.986289\pi\) |
0.536827 | + | 0.843692i | \(0.319623\pi\) | |||||||
\(198\) | 0.783520 | − | 1.35710i | 0.0556823 | − | 0.0964446i | ||||
\(199\) | 6.79321 | + | 11.7662i | 0.481558 | + | 0.834083i | 0.999776 | − | 0.0211659i | \(-0.00673782\pi\) |
−0.518218 | + | 0.855248i | \(0.673404\pi\) | |||||||
\(200\) | 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 | −0.987969 | − | 0.154652i | \(-0.950574\pi\) |
0.627917 | + | 0.778280i | \(0.283908\pi\) | |||||||
\(212\) | 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 | \(-0.708605\pi\) |
0.991333 | + | 0.131372i | \(0.0419383\pi\) | |||||||
\(224\) | −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 | \(-0.281547\pi\) |
−0.986795 | + | 0.161973i | \(0.948214\pi\) | |||||||
\(228\) | 1.31551 | + | 2.27853i | 0.0871219 | + | 0.150899i | ||||
\(229\) | −1.13946 | −0.0752974 | −0.0376487 | − | 0.999291i | \(-0.511987\pi\) | ||||
−0.0376487 | + | 0.999291i | \(0.511987\pi\) | |||||||
\(230\) | 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 | \(-0.626082\pi\) | ||||
−0.385822 | + | 0.922573i | \(0.626082\pi\) | |||||||
\(240\) | 2.52446 | + | 4.37249i | 0.162953 | + | 0.282243i | ||||
\(241\) | 1.82424 | + | 3.15968i | 0.117510 | + | 0.203533i | 0.918780 | − | 0.394770i | \(-0.129176\pi\) |
−0.801271 | + | 0.598302i | \(0.795842\pi\) | |||||||
\(242\) | 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 | 0.843541 | − | 0.537064i | \(-0.180467\pi\) |
−0.886882 | + | 0.461996i | \(0.847133\pi\) | |||||||
\(252\) | −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 | −0.115756 | + | 0.993278i | \(0.536929\pi\) |
−0.802325 | + | 0.596887i | \(0.796404\pi\) | |||||||
\(258\) | 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 | −0.982468 | − | 0.186429i | \(-0.940309\pi\) |
0.652686 | + | 0.757628i | \(0.273642\pi\) | |||||||
\(264\) | 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 | 0.978476 | − | 0.206360i | \(-0.0661618\pi\) |
−0.667951 | + | 0.744205i | \(0.732828\pi\) | |||||||
\(270\) | 3.33997 | − | 5.78500i | 0.203264 | − | 0.352064i | ||||
\(271\) | 14.7262 | − | 25.5065i | 0.894551 | − | 1.54941i | 0.0601918 | − | 0.998187i | \(-0.480829\pi\) |
0.834359 | − | 0.551221i | \(-0.185838\pi\) | |||||||
\(272\) | 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 | 0.977874 | − | 0.209195i | \(-0.0670843\pi\) |
−0.670105 | + | 0.742266i | \(0.733751\pi\) | |||||||
\(278\) | −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 | \(-0.612102\pi\) | ||||
−0.344944 | + | 0.938623i | \(0.612102\pi\) | |||||||
\(282\) | −1.71164 | − | 2.96464i | −0.101926 | − | 0.176542i | ||||
\(283\) | 15.3545 | − | 26.5948i | 0.912730 | − | 1.58090i | 0.102540 | − | 0.994729i | \(-0.467303\pi\) |
0.810191 | − | 0.586167i | \(-0.199364\pi\) | |||||||
\(284\) | −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 | 0.998697 | + | 0.0510409i | \(0.0162539\pi\) |
−0.455146 | + | 0.890417i | \(0.650413\pi\) | |||||||
\(294\) | −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 | \(-0.417845\pi\) | ||||
0.255241 | + | 0.966877i | \(0.417845\pi\) | |||||||
\(308\) | 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 | \(-0.265003\pi\) | ||||
0.673007 | + | 0.739636i | \(0.265003\pi\) | |||||||
\(318\) | 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 | \(-0.192023\pi\) |
−0.903066 | + | 0.429501i | \(0.858689\pi\) | |||||||
\(332\) | −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 | 0.977355 | − | 0.211608i | \(-0.0678700\pi\) |
−0.671935 | + | 0.740610i | \(0.734537\pi\) | |||||||
\(348\) | −5.35958 | + | 9.28307i | −0.287304 | + | 0.497625i | ||||
\(349\) | 1.67360 | − | 2.89877i | 0.0895859 | − | 0.155167i | −0.817750 | − | 0.575573i | \(-0.804779\pi\) |
0.907336 | + | 0.420406i | \(0.138112\pi\) | |||||||
\(350\) | 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 | \(-0.838736\pi\) |
0.857415 | + | 0.514626i | \(0.172069\pi\) | |||||||
\(354\) | −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 | \(-0.691619\pi\) | ||||
−0.566282 | + | 0.824211i | \(0.691619\pi\) | |||||||
\(360\) | −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 | −0.717132 | − | 0.696937i | \(-0.754546\pi\) |
0.962131 | + | 0.272586i | \(0.0878789\pi\) | |||||||
\(368\) | 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 | −0.961865 | − | 0.273523i | \(-0.911811\pi\) |
0.244054 | − | 0.969762i | \(-0.421522\pi\) | |||||||
\(374\) | −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 | −0.123805 | + | 0.992307i | \(0.539510\pi\) |
−0.797460 | + | 0.603371i | \(0.793824\pi\) | |||||||
\(380\) | −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 | \(-0.206253\pi\) |
−0.921359 | + | 0.388713i | \(0.872920\pi\) | |||||||
\(384\) | −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 | \(-0.0415237\pi\) |
−0.608405 | + | 0.793627i | \(0.708190\pi\) | |||||||
\(398\) | 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 | \(-0.936533\pi\) |
0.661626 | + | 0.749834i | \(0.269867\pi\) | |||||||
\(402\) | 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 | 0.988159 | + | 0.153433i | \(0.0490329\pi\) |
−0.361203 | + | 0.932487i | \(0.617634\pi\) | |||||||
\(410\) | −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 | −0.687616 | − | 0.726075i | \(-0.741343\pi\) |
0.972607 | + | 0.232455i | \(0.0746758\pi\) | |||||||
\(420\) | 5.11745 | + | 8.86368i | 0.249706 | + | 0.432503i | ||||
\(421\) | −8.29291 | −0.404172 | −0.202086 | − | 0.979368i | \(-0.564772\pi\) | ||||
−0.202086 | + | 0.979368i | \(0.564772\pi\) | |||||||
\(422\) | 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 | \(-0.840481\pi\) |
0.854580 | + | 0.519319i | \(0.173814\pi\) | |||||||
\(432\) | 4.82640 | − | 8.35956i | 0.232210 | − | 0.402200i | ||||
\(433\) | 6.67510 | + | 11.5616i | 0.320785 | + | 0.555615i | 0.980650 | − | 0.195768i | \(-0.0627201\pi\) |
−0.659866 | + | 0.751384i | \(0.729387\pi\) | |||||||
\(434\) | 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 | −0.983274 | − | 0.182132i | \(-0.941700\pi\) |
0.649368 | + | 0.760475i | \(0.275034\pi\) | |||||||
\(440\) | −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 | \(-0.0706822\pi\) |
−0.678452 | + | 0.734645i | \(0.737349\pi\) | |||||||
\(450\) | 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 | −0.141171 | − | 0.989985i | \(-0.545087\pi\) |
0.927938 | − | 0.372735i | \(-0.121580\pi\) | |||||||
\(458\) | −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 | \(-0.156266\pi\) |
−0.849229 | + | 0.528025i | \(0.822933\pi\) | |||||||
\(462\) | 0.717677 | + | 1.24305i | 0.0333893 | + | 0.0578320i | ||||
\(463\) | −15.2010 | −0.706453 | −0.353226 | − | 0.935538i | \(-0.614915\pi\) | ||||
−0.353226 | + | 0.935538i | \(0.614915\pi\) | |||||||
\(464\) | 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 | −0.488886 | − | 0.872348i | \(-0.662597\pi\) |
0.999918 | − | 0.0127862i | \(-0.00407010\pi\) | |||||||
\(480\) | 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 | −0.999748 | − | 0.0224462i | \(-0.992855\pi\) |
0.480435 | − | 0.877030i | \(-0.340479\pi\) | |||||||
\(488\) | 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 | −0.886075 | − | 0.463541i | \(-0.846579\pi\) |
0.844476 | + | 0.535593i | \(0.179912\pi\) | |||||||
\(492\) | 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 | \(-0.586815\pi\) | ||||
−0.269368 | + | 0.963037i | \(0.586815\pi\) | |||||||
\(500\) | 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 | 0.974954 | + | 0.222408i | \(0.0713918\pi\) |
−0.294866 | + | 0.955539i | \(0.595275\pi\) | |||||||
\(504\) | −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 | \(-0.822669\pi\) |
0.882288 | + | 0.470711i | \(0.156002\pi\) | |||||||
\(510\) | −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 | −0.276278 | − | 0.961078i | \(-0.589101\pi\) |
0.970457 | − | 0.241275i | \(-0.0775657\pi\) | |||||||
\(524\) | −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 | \(-0.324809\pi\) | ||||
0.523009 | + | 0.852327i | \(0.324809\pi\) | |||||||
\(542\) | −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 | 0.462388 | + | 0.886678i | \(0.346993\pi\) |
−0.999079 | + | 0.0428988i | \(0.986341\pi\) | |||||||
\(558\) | 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 | 0.999158 | + | 0.0410266i | \(0.0130628\pi\) |
−0.464049 | + | 0.885810i | \(0.653604\pi\) | |||||||
\(564\) | 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 | −0.329869 | − | 0.944027i | \(-0.607005\pi\) |
0.982486 | − | 0.186338i | \(-0.0596621\pi\) | |||||||
\(570\) | −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 | \(-0.394107\pi\) | ||||
0.326572 | + | 0.945172i | \(0.394107\pi\) | |||||||
\(578\) | −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 | 0.356525 | + | 0.934286i | \(0.383961\pi\) |
−0.987378 | + | 0.158383i | \(0.949372\pi\) | |||||||
\(588\) | 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 | \(-0.708660\pi\) | ||||
−0.609576 | + | 0.792727i | \(0.708660\pi\) | |||||||
\(594\) | 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 | −0.983706 | − | 0.179785i | \(-0.942460\pi\) |
0.647551 | + | 0.762022i | \(0.275793\pi\) | |||||||
\(602\) | −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 | 0.851130 | − | 0.524955i | \(-0.175918\pi\) |
−0.880189 | + | 0.474623i | \(0.842585\pi\) | |||||||
\(608\) | 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 | \(-0.858097\pi\) |
0.824546 | + | 0.565794i | \(0.191430\pi\) | |||||||
\(614\) | 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 | \(-0.0687724\pi\) |
−0.674032 | + | 0.738702i | \(0.735439\pi\) | |||||||
\(618\) | −3.01089 | − | 5.21501i | −0.121116 | − | 0.209778i | ||||
\(619\) | 12.8170 | 0.515159 | 0.257579 | − | 0.966257i | \(-0.417075\pi\) | ||||
0.257579 | + | 0.966257i | \(0.417075\pi\) | |||||||
\(620\) | −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 | −0.999894 | − | 0.0145868i | \(-0.995357\pi\) |
0.487314 | − | 0.873227i | \(-0.337977\pi\) | |||||||
\(632\) | 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 | 0.516810 | − | 0.856100i | \(-0.327119\pi\) |
−0.999809 | + | 0.0195209i | \(0.993786\pi\) | |||||||
\(642\) | −2.50604 | −0.0989055 | ||||||||
\(643\) | 4.98672 | + | 8.63726i | 0.196657 | + | 0.340620i | 0.947442 | − | 0.319926i | \(-0.103658\pi\) |
−0.750785 | + | 0.660546i | \(0.770325\pi\) | |||||||
\(644\) | 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 | −0.958631 | − | 0.284652i | \(-0.908122\pi\) |
0.725831 | + | 0.687873i | \(0.241455\pi\) | |||||||
\(648\) | −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 | −0.783593 | − | 0.621274i | \(-0.786615\pi\) |
0.929836 | + | 0.367975i | \(0.119949\pi\) | |||||||
\(654\) | 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 | −0.979119 | − | 0.203289i | \(-0.934837\pi\) |
0.313506 | − | 0.949586i | \(-0.398497\pi\) | |||||||
\(660\) | 2.27748 | − | 3.94471i | 0.0886508 | − | 0.153548i | ||||
\(661\) | −16.8044 | + | 29.1061i | −0.653615 | + | 1.13209i | 0.328624 | + | 0.944461i | \(0.393415\pi\) |
−0.982239 | + | 0.187634i | \(0.939918\pi\) | |||||||
\(662\) | −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 | −0.135399 | + | 0.990791i | \(0.543232\pi\) |
−0.790351 | + | 0.612654i | \(0.790102\pi\) | |||||||
\(674\) | −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 | \(-0.265081\pi\) |
−0.977100 | + | 0.212781i | \(0.931748\pi\) | |||||||
\(684\) | 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 | 0.355975 | + | 0.934495i | \(0.384149\pi\) |
−0.987284 | + | 0.158964i | \(0.949185\pi\) | |||||||
\(692\) | 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 | −0.960336 | − | 0.278847i | \(-0.910048\pi\) |
0.238679 | − | 0.971098i | \(-0.423286\pi\) | |||||||
\(710\) | −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 | 0.952736 | − | 0.303800i | \(-0.0982555\pi\) |
−0.739467 | + | 0.673193i | \(0.764922\pi\) | |||||||
\(720\) | 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 | \(-0.520720\pi\) | ||||
−0.0650472 | + | 0.997882i | \(0.520720\pi\) | |||||||
\(734\) | −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 | \(-0.835794\pi\) |
0.862134 | + | 0.506680i | \(0.169127\pi\) | |||||||
\(740\) | 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 | \(-0.679306\pi\) |
0.999212 | + | 0.0396987i | \(0.0126398\pi\) | |||||||
\(744\) | −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 | −0.871902 | − | 0.489680i | \(-0.837113\pi\) |
0.860027 | + | 0.510249i | \(0.170447\pi\) | |||||||
\(752\) | 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 | −0.672154 | − | 0.740411i | \(-0.734631\pi\) |
0.977292 | + | 0.211897i | \(0.0679640\pi\) | |||||||
\(758\) | 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 | −0.997456 | − | 0.0712857i | \(-0.977290\pi\) |
0.436993 | − | 0.899465i | \(-0.356044\pi\) | |||||||
\(762\) | −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 | −0.137299 | − | 0.990530i | \(-0.543842\pi\) |
0.926473 | − | 0.376360i | \(-0.122824\pi\) | |||||||
\(770\) | −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 | 0.941357 | + | 0.337413i | \(0.109552\pi\) |
−0.178470 | + | 0.983945i | \(0.557115\pi\) | |||||||
\(774\) | −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 | 0.985022 | + | 0.172427i | \(0.0551610\pi\) |
−0.343185 | + | 0.939268i | \(0.611506\pi\) | |||||||
\(788\) | −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 | 0.997356 | + | 0.0726725i | \(0.0231528\pi\) |
−0.435742 | + | 0.900072i | \(0.643514\pi\) | |||||||
\(798\) | 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 | −0.126194 | − | 0.992006i | \(-0.540276\pi\) |
0.922199 | − | 0.386716i | \(-0.126390\pi\) | |||||||
\(810\) | −2.81886 | − | 4.88242i | −0.0990448 | − | 0.171551i | ||||
\(811\) | −42.8635 | −1.50514 | −0.752571 | − | 0.658511i | \(-0.771187\pi\) | ||||
−0.752571 | + | 0.658511i | \(0.771187\pi\) | |||||||
\(812\) | 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 | \(-0.789717\pi\) |
0.926206 | + | 0.377018i | \(0.123051\pi\) | |||||||
\(822\) | 2.89008 | − | 5.00577i | 0.100803 | − | 0.174596i | ||||
\(823\) | 18.3877 | + | 31.8484i | 0.640955 | + | 1.11017i | 0.985220 | + | 0.171294i | \(0.0547947\pi\) |
−0.344265 | + | 0.938872i | \(0.611872\pi\) | |||||||
\(824\) | −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 | \(-0.192355\pi\) | ||||
0.822900 | + | 0.568186i | \(0.192355\pi\) | |||||||
\(828\) | 9.17994 | + | 15.9001i | 0.319025 | + | 0.552567i | ||||
\(829\) | −12.6344 | + | 21.8834i | −0.438810 | + | 0.760041i | −0.997598 | − | 0.0692694i | \(-0.977933\pi\) |
0.558788 | + | 0.829311i | \(0.311267\pi\) | |||||||
\(830\) | 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 | 0.982984 | + | 0.183690i | \(0.0588043\pi\) |
−0.332412 | + | 0.943134i | \(0.607862\pi\) | |||||||
\(840\) | 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 | \(-0.678152\pi\) | ||||
−0.530917 | + | 0.847424i | \(0.678152\pi\) | |||||||
\(854\) | 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 | \(-0.518777\pi\) | ||||
−0.0589550 | + | 0.998261i | \(0.518777\pi\) | |||||||
\(864\) | −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 | −0.705033 | − | 0.709175i | \(-0.749068\pi\) |
−0.261647 | − | 0.965164i | \(-0.584266\pi\) | |||||||
\(878\) | 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 | −0.230642 | − | 0.973039i | \(-0.574083\pi\) |
0.957997 | − | 0.286778i | \(-0.0925842\pi\) | |||||||
\(882\) | −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 | −0.975385 | − | 0.220508i | \(-0.929228\pi\) |
0.678658 | + | 0.734454i | \(0.262562\pi\) | |||||||
\(888\) | −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 | −0.923059 | − | 0.384658i | \(-0.874319\pi\) |
0.794653 | + | 0.607063i | \(0.207653\pi\) | |||||||
\(908\) | 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 | 0.719887 | − | 0.694091i | \(-0.244193\pi\) |
−0.961044 | + | 0.276395i | \(0.910860\pi\) | |||||||
\(920\) | −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 | \(-0.185253\pi\) |
−0.893728 | + | 0.448610i | \(0.851919\pi\) | |||||||
\(930\) | −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 | \(-0.390875\pi\) | ||||
0.336149 | + | 0.941809i | \(0.390875\pi\) | |||||||
\(942\) | −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 | \(-0.992446\pi\) |
0.520409 | + | 0.853917i | \(0.325779\pi\) | |||||||
\(948\) | −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 | 0.571437 | − | 0.820646i | \(-0.306386\pi\) |
−0.996419 | + | 0.0845563i | \(0.973053\pi\) | |||||||
\(954\) | 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 | \(-0.409113\pi\) | ||||
0.281665 | + | 0.959513i | \(0.409113\pi\) | |||||||
\(968\) | 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 | 0.653209 | − | 0.757178i | \(-0.273422\pi\) |
−0.982340 | + | 0.187106i | \(0.940089\pi\) | |||||||
\(972\) | 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 | \(-0.966769\pi\) |
0.587526 | + | 0.809205i | \(0.300102\pi\) | |||||||
\(978\) | 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 | \(-0.717074\pi\) | ||||
−0.630316 | + | 0.776339i | \(0.717074\pi\) | |||||||
\(984\) | −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 | −0.525641 | − | 0.850707i | \(-0.676174\pi\) |
0.999554 | + | 0.0298651i | \(0.00950777\pi\) | |||||||
\(992\) | 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 | 0.902424 | − | 0.430848i | \(-0.141786\pi\) |
−0.824338 | + | 0.566098i | \(0.808452\pi\) | |||||||
\(998\) | −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.c.22.2 | 6 | ||
13.2 | odd | 12 | 169.2.e.b.23.4 | 12 | |||
13.3 | even | 3 | inner | 169.2.c.c.146.2 | 6 | ||
13.4 | even | 6 | 169.2.a.c.1.2 | yes | 3 | ||
13.5 | odd | 4 | 169.2.e.b.147.3 | 12 | |||
13.6 | odd | 12 | 169.2.b.b.168.4 | 6 | |||
13.7 | odd | 12 | 169.2.b.b.168.3 | 6 | |||
13.8 | odd | 4 | 169.2.e.b.147.4 | 12 | |||
13.9 | even | 3 | 169.2.a.b.1.2 | ✓ | 3 | ||
13.10 | even | 6 | 169.2.c.b.146.2 | 6 | |||
13.11 | odd | 12 | 169.2.e.b.23.3 | 12 | |||
13.12 | even | 2 | 169.2.c.b.22.2 | 6 | |||
39.17 | odd | 6 | 1521.2.a.o.1.2 | 3 | |||
39.20 | even | 12 | 1521.2.b.l.1351.4 | 6 | |||
39.32 | even | 12 | 1521.2.b.l.1351.3 | 6 | |||
39.35 | odd | 6 | 1521.2.a.r.1.2 | 3 | |||
52.7 | even | 12 | 2704.2.f.o.337.1 | 6 | |||
52.19 | even | 12 | 2704.2.f.o.337.2 | 6 | |||
52.35 | odd | 6 | 2704.2.a.z.1.1 | 3 | |||
52.43 | odd | 6 | 2704.2.a.ba.1.1 | 3 | |||
65.4 | even | 6 | 4225.2.a.bb.1.2 | 3 | |||
65.9 | even | 6 | 4225.2.a.bg.1.2 | 3 | |||
91.48 | odd | 6 | 8281.2.a.bf.1.2 | 3 | |||
91.69 | odd | 6 | 8281.2.a.bj.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.2.a.b.1.2 | ✓ | 3 | 13.9 | even | 3 | ||
169.2.a.c.1.2 | yes | 3 | 13.4 | even | 6 | ||
169.2.b.b.168.3 | 6 | 13.7 | odd | 12 | |||
169.2.b.b.168.4 | 6 | 13.6 | odd | 12 | |||
169.2.c.b.22.2 | 6 | 13.12 | even | 2 | |||
169.2.c.b.146.2 | 6 | 13.10 | even | 6 | |||
169.2.c.c.22.2 | 6 | 1.1 | even | 1 | trivial | ||
169.2.c.c.146.2 | 6 | 13.3 | even | 3 | inner | ||
169.2.e.b.23.3 | 12 | 13.11 | odd | 12 | |||
169.2.e.b.23.4 | 12 | 13.2 | odd | 12 | |||
169.2.e.b.147.3 | 12 | 13.5 | odd | 4 | |||
169.2.e.b.147.4 | 12 | 13.8 | odd | 4 | |||
1521.2.a.o.1.2 | 3 | 39.17 | odd | 6 | |||
1521.2.a.r.1.2 | 3 | 39.35 | odd | 6 | |||
1521.2.b.l.1351.3 | 6 | 39.32 | even | 12 | |||
1521.2.b.l.1351.4 | 6 | 39.20 | even | 12 | |||
2704.2.a.z.1.1 | 3 | 52.35 | odd | 6 | |||
2704.2.a.ba.1.1 | 3 | 52.43 | odd | 6 | |||
2704.2.f.o.337.1 | 6 | 52.7 | even | 12 | |||
2704.2.f.o.337.2 | 6 | 52.19 | even | 12 | |||
4225.2.a.bb.1.2 | 3 | 65.4 | even | 6 | |||
4225.2.a.bg.1.2 | 3 | 65.9 | even | 6 | |||
8281.2.a.bf.1.2 | 3 | 91.48 | odd | 6 | |||
8281.2.a.bj.1.2 | 3 | 91.69 | odd | 6 |