Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(413,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.413");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 413.10 | ||
Character | \(\chi\) | \(=\) | 552.413 |
Dual form | 552.2.b.c.413.11 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32616 | − | 0.491215i | −0.937739 | − | 0.347342i | ||||
\(3\) | 1.50954 | + | 0.849295i | 0.871531 | + | 0.490341i | ||||
\(4\) | 1.51742 | + | 1.30286i | 0.758708 | + | 0.651431i | ||||
\(5\) | 3.96539i | 1.77338i | 0.462368 | + | 0.886688i | \(0.347000\pi\) | ||||
−0.462368 | + | 0.886688i | \(0.653000\pi\) | |||||||
\(6\) | −1.58470 | − | 1.86781i | −0.646952 | − | 0.762530i | ||||
\(7\) | 0.287329i | 0.108600i | 0.998525 | + | 0.0543001i | \(0.0172928\pi\) | ||||
−0.998525 | + | 0.0543001i | \(0.982707\pi\) | |||||||
\(8\) | −1.37235 | − | 2.47319i | −0.485200 | − | 0.874403i | ||||
\(9\) | 1.55740 | + | 2.56408i | 0.519132 | + | 0.854694i | ||||
\(10\) | 1.94786 | − | 5.25875i | 0.615967 | − | 1.66296i | ||||
\(11\) | 2.51457i | 0.758171i | 0.925362 | + | 0.379086i | \(0.123761\pi\) | ||||
−0.925362 | + | 0.379086i | \(0.876239\pi\) | |||||||
\(12\) | 1.18408 | + | 3.25545i | 0.341814 | + | 0.939768i | ||||
\(13\) | − | 4.58211i | − | 1.27085i | −0.772163 | − | 0.635425i | \(-0.780825\pi\) | ||
0.772163 | − | 0.635425i | \(-0.219175\pi\) | |||||||
\(14\) | 0.141140 | − | 0.381045i | 0.0377214 | − | 0.101839i | ||||
\(15\) | −3.36779 | + | 5.98590i | −0.869559 | + | 1.54555i | ||||
\(16\) | 0.605098 | + | 3.95397i | 0.151275 | + | 0.988492i | ||||
\(17\) | 3.13989 | 0.761535 | 0.380767 | − | 0.924671i | \(-0.375660\pi\) | ||||
0.380767 | + | 0.924671i | \(0.375660\pi\) | |||||||
\(18\) | −0.805843 | − | 4.16541i | −0.189939 | − | 0.981796i | ||||
\(19\) | 5.13304 | 1.17760 | 0.588800 | − | 0.808279i | \(-0.299600\pi\) | ||||
0.588800 | + | 0.808279i | \(0.299600\pi\) | |||||||
\(20\) | −5.16636 | + | 6.01714i | −1.15523 | + | 1.34547i | ||||
\(21\) | −0.244027 | + | 0.433734i | −0.0532511 | + | 0.0946485i | ||||
\(22\) | 1.23519 | − | 3.33473i | 0.263344 | − | 0.710966i | ||||
\(23\) | −4.77034 | + | 0.493825i | −0.994685 | + | 0.102970i | ||||
\(24\) | 0.0288475 | − | 4.89889i | 0.00588846 | − | 0.999983i | ||||
\(25\) | −10.7243 | −2.14486 | ||||||||
\(26\) | −2.25080 | + | 6.07663i | −0.441419 | + | 1.19172i | ||||
\(27\) | 0.173281 | + | 5.19326i | 0.0333479 | + | 0.999444i | ||||
\(28\) | −0.374351 | + | 0.435998i | −0.0707456 | + | 0.0823958i | ||||
\(29\) | −4.88646 | −0.907392 | −0.453696 | − | 0.891156i | \(-0.649895\pi\) | ||||
−0.453696 | + | 0.891156i | \(0.649895\pi\) | |||||||
\(30\) | 7.40660 | − | 6.28397i | 1.35225 | − | 1.14729i | ||||
\(31\) | 2.61622 | 0.469887 | 0.234944 | − | 0.972009i | \(-0.424509\pi\) | ||||
0.234944 | + | 0.972009i | \(0.424509\pi\) | |||||||
\(32\) | 1.13979 | − | 5.54084i | 0.201488 | − | 0.979491i | ||||
\(33\) | −2.13561 | + | 3.79583i | −0.371762 | + | 0.660769i | ||||
\(34\) | −4.16400 | − | 1.54236i | −0.714121 | − | 0.264513i | ||||
\(35\) | −1.13937 | −0.192589 | ||||||||
\(36\) | −0.977432 | + | 5.91985i | −0.162905 | + | 0.986642i | ||||
\(37\) | −3.22198 | −0.529691 | −0.264845 | − | 0.964291i | \(-0.585321\pi\) | ||||
−0.264845 | + | 0.964291i | \(0.585321\pi\) | |||||||
\(38\) | −6.80725 | − | 2.52143i | −1.10428 | − | 0.409030i | ||||
\(39\) | 3.89157 | − | 6.91686i | 0.623149 | − | 1.10758i | ||||
\(40\) | 9.80714 | − | 5.44192i | 1.55065 | − | 0.860443i | ||||
\(41\) | − | 5.33846i | − | 0.833727i | −0.908969 | − | 0.416864i | \(-0.863129\pi\) | ||
0.908969 | − | 0.416864i | \(-0.136871\pi\) | |||||||
\(42\) | 0.536677 | − | 0.455332i | 0.0828110 | − | 0.0702592i | ||||
\(43\) | −9.45753 | −1.44226 | −0.721130 | − | 0.692800i | \(-0.756377\pi\) | ||||
−0.721130 | + | 0.692800i | \(0.756377\pi\) | |||||||
\(44\) | −3.27614 | + | 3.81565i | −0.493896 | + | 0.575230i | ||||
\(45\) | −10.1676 | + | 6.17568i | −1.51569 | + | 0.920616i | ||||
\(46\) | 6.56882 | + | 1.68837i | 0.968520 | + | 0.248937i | ||||
\(47\) | 4.95291i | 0.722456i | 0.932478 | + | 0.361228i | \(0.117642\pi\) | ||||
−0.932478 | + | 0.361228i | \(0.882358\pi\) | |||||||
\(48\) | −2.44467 | + | 6.48256i | −0.352857 | + | 0.935677i | ||||
\(49\) | 6.91744 | 0.988206 | ||||||||
\(50\) | 14.2222 | + | 5.26795i | 2.01132 | + | 0.745000i | ||||
\(51\) | 4.73977 | + | 2.66669i | 0.663701 | + | 0.373412i | ||||
\(52\) | 5.96986 | − | 6.95297i | 0.827871 | − | 0.964203i | ||||
\(53\) | − | 1.01064i | − | 0.138822i | −0.997588 | − | 0.0694112i | \(-0.977888\pi\) | ||
0.997588 | − | 0.0694112i | \(-0.0221121\pi\) | |||||||
\(54\) | 2.32121 | − | 6.97223i | 0.315877 | − | 0.948800i | ||||
\(55\) | −9.97125 | −1.34452 | ||||||||
\(56\) | 0.710618 | − | 0.394317i | 0.0949604 | − | 0.0526929i | ||||
\(57\) | 7.74851 | + | 4.35947i | 1.02631 | + | 0.577426i | ||||
\(58\) | 6.48024 | + | 2.40030i | 0.850897 | + | 0.315175i | ||||
\(59\) | 7.08582 | 0.922495 | 0.461247 | − | 0.887272i | \(-0.347402\pi\) | ||||
0.461247 | + | 0.887272i | \(0.347402\pi\) | |||||||
\(60\) | −12.9091 | + | 4.69533i | −1.66656 | + | 0.606164i | ||||
\(61\) | 7.14363 | 0.914648 | 0.457324 | − | 0.889300i | \(-0.348808\pi\) | ||||
0.457324 | + | 0.889300i | \(0.348808\pi\) | |||||||
\(62\) | −3.46954 | − | 1.28513i | −0.440632 | − | 0.163211i | ||||
\(63\) | −0.736736 | + | 0.447485i | −0.0928200 | + | 0.0563778i | ||||
\(64\) | −4.23329 | + | 6.78817i | −0.529161 | + | 0.848521i | ||||
\(65\) | 18.1699 | 2.25369 | ||||||||
\(66\) | 4.69674 | − | 3.98485i | 0.578128 | − | 0.490501i | ||||
\(67\) | −4.13224 | −0.504834 | −0.252417 | − | 0.967619i | \(-0.581225\pi\) | ||||
−0.252417 | + | 0.967619i | \(0.581225\pi\) | |||||||
\(68\) | 4.76451 | + | 4.09084i | 0.577782 | + | 0.496088i | ||||
\(69\) | −7.62040 | − | 3.30598i | −0.917388 | − | 0.397993i | ||||
\(70\) | 1.51099 | + | 0.559677i | 0.180598 | + | 0.0668942i | ||||
\(71\) | − | 7.87281i | − | 0.934331i | −0.884170 | − | 0.467165i | \(-0.845275\pi\) | ||
0.884170 | − | 0.467165i | \(-0.154725\pi\) | |||||||
\(72\) | 4.20415 | − | 7.37056i | 0.495464 | − | 0.868628i | ||||
\(73\) | 9.35254 | 1.09463 | 0.547316 | − | 0.836926i | \(-0.315650\pi\) | ||||
0.547316 | + | 0.836926i | \(0.315650\pi\) | |||||||
\(74\) | 4.27287 | + | 1.58269i | 0.496712 | + | 0.183984i | ||||
\(75\) | −16.1887 | − | 9.10811i | −1.86931 | − | 1.05171i | ||||
\(76\) | 7.78895 | + | 6.68765i | 0.893454 | + | 0.767126i | ||||
\(77\) | −0.722509 | −0.0823376 | ||||||||
\(78\) | −8.55852 | + | 7.26129i | −0.969061 | + | 0.822179i | ||||
\(79\) | 13.9945i | 1.57450i | 0.616632 | + | 0.787252i | \(0.288497\pi\) | ||||
−0.616632 | + | 0.787252i | \(0.711503\pi\) | |||||||
\(80\) | −15.6790 | + | 2.39945i | −1.75297 | + | 0.268267i | ||||
\(81\) | −4.14904 | + | 7.98658i | −0.461004 | + | 0.887398i | ||||
\(82\) | −2.62233 | + | 7.07967i | −0.289588 | + | 0.781818i | ||||
\(83\) | 6.51283i | 0.714876i | 0.933937 | + | 0.357438i | \(0.116350\pi\) | ||||
−0.933937 | + | 0.357438i | \(0.883650\pi\) | |||||||
\(84\) | −0.935386 | + | 0.340220i | −0.102059 | + | 0.0371211i | ||||
\(85\) | 12.4509i | 1.35049i | ||||||||
\(86\) | 12.5422 | + | 4.64568i | 1.35246 | + | 0.500957i | ||||
\(87\) | −7.37628 | − | 4.15005i | −0.790820 | − | 0.444932i | ||||
\(88\) | 6.21899 | − | 3.45088i | 0.662947 | − | 0.367865i | ||||
\(89\) | 4.88399 | 0.517702 | 0.258851 | − | 0.965917i | \(-0.416656\pi\) | ||||
0.258851 | + | 0.965917i | \(0.416656\pi\) | |||||||
\(90\) | 16.5175 | − | 3.19548i | 1.74109 | − | 0.336834i | ||||
\(91\) | 1.31658 | 0.138015 | ||||||||
\(92\) | −7.88197 | − | 5.46576i | −0.821752 | − | 0.569845i | ||||
\(93\) | 3.94928 | + | 2.22195i | 0.409521 | + | 0.230405i | ||||
\(94\) | 2.43294 | − | 6.56836i | 0.250939 | − | 0.677475i | ||||
\(95\) | 20.3545i | 2.08833i | ||||||||
\(96\) | 6.42636 | − | 7.39607i | 0.655888 | − | 0.754859i | ||||
\(97\) | − | 17.5303i | − | 1.77993i | −0.456025 | − | 0.889967i | \(-0.650727\pi\) | ||
0.456025 | − | 0.889967i | \(-0.349273\pi\) | |||||||
\(98\) | −9.17365 | − | 3.39795i | −0.926679 | − | 0.343245i | ||||
\(99\) | −6.44756 | + | 3.91618i | −0.648004 | + | 0.393591i | ||||
\(100\) | −16.2732 | − | 13.9723i | −1.62732 | − | 1.39723i | ||||
\(101\) | 11.8142 | 1.17556 | 0.587780 | − | 0.809021i | \(-0.300002\pi\) | ||||
0.587780 | + | 0.809021i | \(0.300002\pi\) | |||||||
\(102\) | −4.97579 | − | 5.86472i | −0.492677 | − | 0.580693i | ||||
\(103\) | − | 1.23502i | − | 0.121690i | −0.998147 | − | 0.0608449i | \(-0.980621\pi\) | ||
0.998147 | − | 0.0608449i | \(-0.0193795\pi\) | |||||||
\(104\) | −11.3324 | + | 6.28828i | −1.11123 | + | 0.616617i | ||||
\(105\) | −1.71992 | − | 0.967664i | −0.167847 | − | 0.0944343i | ||||
\(106\) | −0.496443 | + | 1.34028i | −0.0482188 | + | 0.130179i | ||||
\(107\) | − | 17.1374i | − | 1.65674i | −0.560184 | − | 0.828368i | \(-0.689269\pi\) | ||
0.560184 | − | 0.828368i | \(-0.310731\pi\) | |||||||
\(108\) | −6.50317 | + | 8.10610i | −0.625768 | + | 0.780009i | ||||
\(109\) | −11.6350 | −1.11443 | −0.557217 | − | 0.830367i | \(-0.688131\pi\) | ||||
−0.557217 | + | 0.830367i | \(0.688131\pi\) | |||||||
\(110\) | 13.2235 | + | 4.89803i | 1.26081 | + | 0.467009i | ||||
\(111\) | −4.86370 | − | 2.73641i | −0.461642 | − | 0.259729i | ||||
\(112\) | −1.13609 | + | 0.173862i | −0.107350 | + | 0.0164285i | ||||
\(113\) | 14.8510 | 1.39706 | 0.698532 | − | 0.715579i | \(-0.253837\pi\) | ||||
0.698532 | + | 0.715579i | \(0.253837\pi\) | |||||||
\(114\) | −8.13435 | − | 9.58755i | −0.761851 | − | 0.897956i | ||||
\(115\) | −1.95821 | − | 18.9163i | −0.182604 | − | 1.76395i | ||||
\(116\) | −7.41479 | − | 6.36638i | −0.688446 | − | 0.591104i | ||||
\(117\) | 11.7489 | − | 7.13616i | 1.08619 | − | 0.659738i | ||||
\(118\) | −9.39695 | − | 3.48066i | −0.865059 | − | 0.320421i | ||||
\(119\) | 0.902182i | 0.0827029i | ||||||||
\(120\) | 19.4260 | + | 0.114391i | 1.77335 | + | 0.0104425i | ||||
\(121\) | 4.67694 | 0.425177 | ||||||||
\(122\) | −9.47362 | − | 3.50906i | −0.857701 | − | 0.317695i | ||||
\(123\) | 4.53393 | − | 8.05859i | 0.408810 | − | 0.726619i | ||||
\(124\) | 3.96990 | + | 3.40858i | 0.356507 | + | 0.306099i | ||||
\(125\) | − | 22.6992i | − | 2.03027i | ||||||
\(126\) | 1.19684 | − | 0.231542i | 0.106623 | − | 0.0206274i | ||||
\(127\) | 15.8942 | 1.41039 | 0.705193 | − | 0.709016i | \(-0.250861\pi\) | ||||
0.705193 | + | 0.709016i | \(0.250861\pi\) | |||||||
\(128\) | 8.94848 | − | 6.92276i | 0.790942 | − | 0.611892i | ||||
\(129\) | −14.2765 | − | 8.03223i | −1.25697 | − | 0.707199i | ||||
\(130\) | −24.0962 | − | 8.92531i | −2.11338 | − | 0.782802i | ||||
\(131\) | −3.61861 | −0.316160 | −0.158080 | − | 0.987426i | \(-0.550530\pi\) | ||||
−0.158080 | + | 0.987426i | \(0.550530\pi\) | |||||||
\(132\) | −8.18606 | + | 2.97744i | −0.712505 | + | 0.259153i | ||||
\(133\) | 1.47487i | 0.127888i | ||||||||
\(134\) | 5.48002 | + | 2.02982i | 0.473402 | + | 0.175350i | ||||
\(135\) | −20.5933 | + | 0.687125i | −1.77239 | + | 0.0591383i | ||||
\(136\) | −4.30904 | − | 7.76552i | −0.369497 | − | 0.665888i | ||||
\(137\) | −9.81893 | −0.838888 | −0.419444 | − | 0.907781i | \(-0.637775\pi\) | ||||
−0.419444 | + | 0.907781i | \(0.637775\pi\) | |||||||
\(138\) | 8.48194 | + | 8.12752i | 0.722031 | + | 0.691861i | ||||
\(139\) | 4.01764i | 0.340772i | 0.985377 | + | 0.170386i | \(0.0545014\pi\) | ||||
−0.985377 | + | 0.170386i | \(0.945499\pi\) | |||||||
\(140\) | −1.72890 | − | 1.48445i | −0.146119 | − | 0.125459i | ||||
\(141\) | −4.20648 | + | 7.47659i | −0.354250 | + | 0.629643i | ||||
\(142\) | −3.86724 | + | 10.4406i | −0.324532 | + | 0.876158i | ||||
\(143\) | 11.5220 | 0.963521 | ||||||||
\(144\) | −9.19592 | + | 7.70941i | −0.766327 | + | 0.642451i | ||||
\(145\) | − | 19.3767i | − | 1.60915i | ||||||
\(146\) | −12.4030 | − | 4.59411i | −1.02648 | − | 0.380211i | ||||
\(147\) | 10.4421 | + | 5.87495i | 0.861252 | + | 0.484558i | ||||
\(148\) | −4.88909 | − | 4.19780i | −0.401880 | − | 0.345057i | ||||
\(149\) | − | 20.8517i | − | 1.70824i | −0.520079 | − | 0.854118i | \(-0.674097\pi\) | ||
0.520079 | − | 0.854118i | \(-0.325903\pi\) | |||||||
\(150\) | 16.9949 | + | 20.0310i | 1.38762 | + | 1.63552i | ||||
\(151\) | −4.47289 | −0.363999 | −0.181999 | − | 0.983299i | \(-0.558257\pi\) | ||||
−0.181999 | + | 0.983299i | \(0.558257\pi\) | |||||||
\(152\) | −7.04435 | − | 12.6950i | −0.571372 | − | 1.02970i | ||||
\(153\) | 4.89005 | + | 8.05093i | 0.395337 | + | 0.650879i | ||||
\(154\) | 0.958165 | + | 0.354907i | 0.0772111 | + | 0.0285993i | ||||
\(155\) | 10.3743i | 0.833287i | ||||||||
\(156\) | 14.9168 | − | 5.42558i | 1.19430 | − | 0.434394i | ||||
\(157\) | 13.7855 | 1.10020 | 0.550101 | − | 0.835098i | \(-0.314589\pi\) | ||||
0.550101 | + | 0.835098i | \(0.314589\pi\) | |||||||
\(158\) | 6.87431 | − | 18.5590i | 0.546891 | − | 1.47647i | ||||
\(159\) | 0.858334 | − | 1.52560i | 0.0680703 | − | 0.120988i | ||||
\(160\) | 21.9716 | + | 4.51971i | 1.73701 | + | 0.357315i | ||||
\(161\) | −0.141890 | − | 1.37066i | −0.0111825 | − | 0.108023i | ||||
\(162\) | 9.42543 | − | 8.55343i | 0.740532 | − | 0.672021i | ||||
\(163\) | 15.5113i | 1.21494i | 0.794343 | + | 0.607470i | \(0.207815\pi\) | ||||
−0.794343 | + | 0.607470i | \(0.792185\pi\) | |||||||
\(164\) | 6.95528 | − | 8.10066i | 0.543116 | − | 0.632555i | ||||
\(165\) | −15.0520 | − | 8.46853i | −1.17179 | − | 0.659274i | ||||
\(166\) | 3.19920 | − | 8.63707i | 0.248306 | − | 0.670366i | ||||
\(167\) | − | 4.71846i | − | 0.365125i | −0.983194 | − | 0.182563i | \(-0.941561\pi\) | ||
0.983194 | − | 0.182563i | \(-0.0584392\pi\) | |||||||
\(168\) | 1.40760 | + | 0.00828872i | 0.108598 | + | 0.000639489i | ||||
\(169\) | −7.99576 | −0.615059 | ||||||||
\(170\) | 6.11606 | − | 16.5119i | 0.469081 | − | 1.26640i | ||||
\(171\) | 7.99417 | + | 13.1615i | 0.611330 | + | 1.00649i | ||||
\(172\) | −14.3510 | − | 12.3219i | −1.09425 | − | 0.939533i | ||||
\(173\) | 4.84055 | 0.368020 | 0.184010 | − | 0.982924i | \(-0.441092\pi\) | ||||
0.184010 | + | 0.982924i | \(0.441092\pi\) | |||||||
\(174\) | 7.74359 | + | 9.12698i | 0.587040 | + | 0.691914i | ||||
\(175\) | − | 3.08141i | − | 0.232933i | ||||||
\(176\) | −9.94252 | + | 1.52156i | −0.749446 | + | 0.114692i | ||||
\(177\) | 10.6963 | + | 6.01795i | 0.803983 | + | 0.452337i | ||||
\(178\) | −6.47697 | − | 2.39909i | −0.485469 | − | 0.179819i | ||||
\(179\) | −7.69481 | −0.575137 | −0.287568 | − | 0.957760i | \(-0.592847\pi\) | ||||
−0.287568 | + | 0.957760i | \(0.592847\pi\) | |||||||
\(180\) | −23.4745 | − | 3.87590i | −1.74969 | − | 0.288892i | ||||
\(181\) | 9.72050 | 0.722519 | 0.361260 | − | 0.932465i | \(-0.382347\pi\) | ||||
0.361260 | + | 0.932465i | \(0.382347\pi\) | |||||||
\(182\) | −1.74599 | − | 0.646722i | −0.129422 | − | 0.0479382i | ||||
\(183\) | 10.7836 | + | 6.06705i | 0.797144 | + | 0.448489i | ||||
\(184\) | 7.76791 | + | 11.1202i | 0.572658 | + | 0.819794i | ||||
\(185\) | − | 12.7764i | − | 0.939341i | ||||||
\(186\) | −4.14594 | − | 4.88661i | −0.303995 | − | 0.358303i | ||||
\(187\) | 7.89546i | 0.577374i | ||||||||
\(188\) | −6.45296 | + | 7.51562i | −0.470630 | + | 0.548133i | ||||
\(189\) | −1.49218 | + | 0.0497886i | −0.108540 | + | 0.00362159i | ||||
\(190\) | 9.99844 | − | 26.9934i | 0.725363 | − | 1.95831i | ||||
\(191\) | −22.9872 | −1.66330 | −0.831649 | − | 0.555301i | \(-0.812603\pi\) | ||||
−0.831649 | + | 0.555301i | \(0.812603\pi\) | |||||||
\(192\) | −12.1555 | + | 6.65167i | −0.877245 | + | 0.480043i | ||||
\(193\) | −3.01341 | −0.216910 | −0.108455 | − | 0.994101i | \(-0.534590\pi\) | ||||
−0.108455 | + | 0.994101i | \(0.534590\pi\) | |||||||
\(194\) | −8.61116 | + | 23.2481i | −0.618245 | + | 1.66911i | ||||
\(195\) | 27.4281 | + | 15.4316i | 1.96416 | + | 1.10508i | ||||
\(196\) | 10.4966 | + | 9.01248i | 0.749759 | + | 0.643748i | ||||
\(197\) | −24.2018 | −1.72431 | −0.862154 | − | 0.506647i | \(-0.830885\pi\) | ||||
−0.862154 | + | 0.506647i | \(0.830885\pi\) | |||||||
\(198\) | 10.4742 | − | 2.02635i | 0.744369 | − | 0.144006i | ||||
\(199\) | 11.8884i | 0.842748i | 0.906887 | + | 0.421374i | \(0.138452\pi\) | ||||
−0.906887 | + | 0.421374i | \(0.861548\pi\) | |||||||
\(200\) | 14.7176 | + | 26.5232i | 1.04069 | + | 1.87548i | ||||
\(201\) | −6.23776 | − | 3.50949i | −0.439978 | − | 0.247540i | ||||
\(202\) | −15.6676 | − | 5.80333i | −1.10237 | − | 0.408321i | ||||
\(203\) | − | 1.40402i | − | 0.0985430i | ||||||
\(204\) | 3.71787 | + | 10.2218i | 0.260303 | + | 0.715666i | ||||
\(205\) | 21.1691 | 1.47851 | ||||||||
\(206\) | −0.606658 | + | 1.63783i | −0.0422679 | + | 0.114113i | ||||
\(207\) | −8.69551 | − | 11.4625i | −0.604380 | − | 0.796696i | ||||
\(208\) | 18.1175 | − | 2.77263i | 1.25622 | − | 0.192247i | ||||
\(209\) | 12.9074i | 0.892822i | ||||||||
\(210\) | 1.80557 | + | 2.12813i | 0.124596 | + | 0.146855i | ||||
\(211\) | 12.3839i | 0.852545i | 0.904595 | + | 0.426273i | \(0.140174\pi\) | ||||
−0.904595 | + | 0.426273i | \(0.859826\pi\) | |||||||
\(212\) | 1.31673 | − | 1.53356i | 0.0904333 | − | 0.105326i | ||||
\(213\) | 6.68634 | − | 11.8843i | 0.458141 | − | 0.814298i | ||||
\(214\) | −8.41816 | + | 22.7270i | −0.575454 | + | 1.55359i | ||||
\(215\) | − | 37.5028i | − | 2.55767i | ||||||
\(216\) | 12.6061 | − | 7.55555i | 0.857736 | − | 0.514090i | ||||
\(217\) | 0.751717i | 0.0510299i | ||||||||
\(218\) | 15.4300 | + | 5.71531i | 1.04505 | + | 0.387089i | ||||
\(219\) | 14.1180 | + | 7.94307i | 0.954006 | + | 0.536743i | ||||
\(220\) | −15.1305 | − | 12.9912i | −1.02010 | − | 0.875864i | ||||
\(221\) | − | 14.3873i | − | 0.967796i | ||||||
\(222\) | 5.10589 | + | 6.01805i | 0.342685 | + | 0.403905i | ||||
\(223\) | −4.45336 | −0.298219 | −0.149110 | − | 0.988821i | \(-0.547641\pi\) | ||||
−0.149110 | + | 0.988821i | \(0.547641\pi\) | |||||||
\(224\) | 1.59204 | + | 0.327495i | 0.106373 | + | 0.0218817i | ||||
\(225\) | −16.7020 | − | 27.4980i | −1.11347 | − | 1.83320i | ||||
\(226\) | −19.6948 | − | 7.29503i | −1.31008 | − | 0.485258i | ||||
\(227\) | − | 15.4831i | − | 1.02765i | −0.857894 | − | 0.513826i | \(-0.828228\pi\) | ||
0.857894 | − | 0.513826i | \(-0.171772\pi\) | |||||||
\(228\) | 6.07792 | + | 16.7104i | 0.402520 | + | 1.10667i | ||||
\(229\) | 25.4154 | 1.67950 | 0.839749 | − | 0.542975i | \(-0.182702\pi\) | ||||
0.839749 | + | 0.542975i | \(0.182702\pi\) | |||||||
\(230\) | −6.69505 | + | 26.0479i | −0.441458 | + | 1.71755i | ||||
\(231\) | −1.09065 | − | 0.613624i | −0.0717597 | − | 0.0403735i | ||||
\(232\) | 6.70595 | + | 12.0851i | 0.440267 | + | 0.793427i | ||||
\(233\) | 23.8892i | 1.56503i | 0.622631 | + | 0.782515i | \(0.286064\pi\) | ||||
−0.622631 | + | 0.782515i | \(0.713936\pi\) | |||||||
\(234\) | −19.0864 | + | 3.69247i | −1.24771 | + | 0.241384i | ||||
\(235\) | −19.6402 | −1.28119 | ||||||||
\(236\) | 10.7521 | + | 9.23185i | 0.699904 | + | 0.600942i | ||||
\(237\) | −11.8855 | + | 21.1252i | −0.772043 | + | 1.37223i | ||||
\(238\) | 0.443165 | − | 1.19644i | 0.0287261 | − | 0.0775537i | ||||
\(239\) | − | 0.432286i | − | 0.0279623i | −0.999902 | − | 0.0139811i | \(-0.995550\pi\) | ||
0.999902 | − | 0.0139811i | \(-0.00445048\pi\) | |||||||
\(240\) | −25.7059 | − | 9.69406i | −1.65931 | − | 0.625749i | ||||
\(241\) | 12.5532i | 0.808620i | 0.914622 | + | 0.404310i | \(0.132488\pi\) | ||||
−0.914622 | + | 0.404310i | \(0.867512\pi\) | |||||||
\(242\) | −6.20239 | − | 2.29739i | −0.398705 | − | 0.147682i | ||||
\(243\) | −13.0461 | + | 8.53227i | −0.836907 | + | 0.547345i | ||||
\(244\) | 10.8399 | + | 9.30717i | 0.693951 | + | 0.595830i | ||||
\(245\) | 27.4304i | 1.75246i | ||||||||
\(246\) | −9.97123 | + | 8.45987i | −0.635742 | + | 0.539382i | ||||
\(247\) | − | 23.5202i | − | 1.49655i | ||||||
\(248\) | −3.59038 | − | 6.47040i | −0.227990 | − | 0.410871i | ||||
\(249\) | −5.53131 | + | 9.83134i | −0.350533 | + | 0.623036i | ||||
\(250\) | −11.1502 | + | 30.1028i | −0.705199 | + | 1.90387i | ||||
\(251\) | 4.72082i | 0.297975i | 0.988839 | + | 0.148988i | \(0.0476015\pi\) | ||||
−0.988839 | + | 0.148988i | \(0.952399\pi\) | |||||||
\(252\) | −1.70095 | − | 0.280845i | −0.107150 | − | 0.0176916i | ||||
\(253\) | −1.24176 | − | 11.9953i | −0.0780686 | − | 0.754141i | ||||
\(254\) | −21.0783 | − | 7.80749i | −1.32257 | − | 0.489885i | ||||
\(255\) | −10.5745 | + | 18.7950i | −0.662199 | + | 1.17699i | ||||
\(256\) | −15.2677 | + | 4.78508i | −0.954232 | + | 0.299067i | ||||
\(257\) | − | 9.92306i | − | 0.618984i | −0.950902 | − | 0.309492i | \(-0.899841\pi\) | ||
0.950902 | − | 0.309492i | \(-0.100159\pi\) | |||||||
\(258\) | 14.9874 | + | 17.6649i | 0.933073 | + | 1.09977i | ||||
\(259\) | − | 0.925770i | − | 0.0575245i | ||||||
\(260\) | 27.5712 | + | 23.6728i | 1.70990 | + | 1.46813i | ||||
\(261\) | −7.61015 | − | 12.5293i | −0.471056 | − | 0.775543i | ||||
\(262\) | 4.79887 | + | 1.77752i | 0.296475 | + | 0.109815i | ||||
\(263\) | 20.0077 | 1.23372 | 0.616862 | − | 0.787071i | \(-0.288404\pi\) | ||||
0.616862 | + | 0.787071i | \(0.288404\pi\) | |||||||
\(264\) | 12.3186 | + | 0.0725389i | 0.758158 | + | 0.00446446i | ||||
\(265\) | 4.00759 | 0.246184 | ||||||||
\(266\) | 0.724480 | − | 1.95592i | 0.0444207 | − | 0.119925i | ||||
\(267\) | 7.37256 | + | 4.14795i | 0.451193 | + | 0.253850i | ||||
\(268\) | −6.27033 | − | 5.38374i | −0.383021 | − | 0.328864i | ||||
\(269\) | 17.1022 | 1.04274 | 0.521370 | − | 0.853331i | \(-0.325421\pi\) | ||||
0.521370 | + | 0.853331i | \(0.325421\pi\) | |||||||
\(270\) | 27.6476 | + | 9.20451i | 1.68258 | + | 0.560168i | ||||
\(271\) | 9.11469 | 0.553678 | 0.276839 | − | 0.960916i | \(-0.410713\pi\) | ||||
0.276839 | + | 0.960916i | \(0.410713\pi\) | |||||||
\(272\) | 1.89994 | + | 12.4150i | 0.115201 | + | 0.752771i | ||||
\(273\) | 1.98742 | + | 1.11816i | 0.120284 | + | 0.0676742i | ||||
\(274\) | 13.0215 | + | 4.82321i | 0.786658 | + | 0.291381i | ||||
\(275\) | − | 26.9670i | − | 1.62617i | ||||||
\(276\) | −7.25607 | − | 14.9449i | −0.436764 | − | 0.899576i | ||||
\(277\) | − | 19.2487i | − | 1.15654i | −0.815844 | − | 0.578272i | \(-0.803727\pi\) | ||
0.815844 | − | 0.578272i | \(-0.196273\pi\) | |||||||
\(278\) | 1.97353 | − | 5.32804i | 0.118364 | − | 0.319555i | ||||
\(279\) | 4.07449 | + | 6.70821i | 0.243933 | + | 0.401610i | ||||
\(280\) | 1.56362 | + | 2.81788i | 0.0934443 | + | 0.168400i | ||||
\(281\) | −12.8707 | −0.767799 | −0.383900 | − | 0.923375i | \(-0.625419\pi\) | ||||
−0.383900 | + | 0.923375i | \(0.625419\pi\) | |||||||
\(282\) | 9.25110 | − | 7.84889i | 0.550895 | − | 0.467395i | ||||
\(283\) | −15.6946 | −0.932947 | −0.466473 | − | 0.884535i | \(-0.654476\pi\) | ||||
−0.466473 | + | 0.884535i | \(0.654476\pi\) | |||||||
\(284\) | 10.2572 | − | 11.9463i | 0.608652 | − | 0.708884i | ||||
\(285\) | −17.2870 | + | 30.7259i | −1.02399 | + | 1.82004i | ||||
\(286\) | −15.2801 | − | 5.65980i | −0.903531 | − | 0.334671i | ||||
\(287\) | 1.53390 | 0.0905430 | ||||||||
\(288\) | 15.9823 | − | 5.70676i | 0.941764 | − | 0.336274i | ||||
\(289\) | −7.14110 | −0.420065 | ||||||||
\(290\) | −9.51813 | + | 25.6967i | −0.558924 | + | 1.50896i | ||||
\(291\) | 14.8884 | − | 26.4626i | 0.872774 | − | 1.55127i | ||||
\(292\) | 14.1917 | + | 12.1851i | 0.830506 | + | 0.713078i | ||||
\(293\) | − | 10.5441i | − | 0.615991i | −0.951388 | − | 0.307995i | \(-0.900342\pi\) | ||
0.951388 | − | 0.307995i | \(-0.0996581\pi\) | |||||||
\(294\) | −10.9621 | − | 12.9205i | −0.639322 | − | 0.753537i | ||||
\(295\) | 28.0980i | 1.63593i | ||||||||
\(296\) | 4.42170 | + | 7.96856i | 0.257006 | + | 0.463163i | ||||
\(297\) | −13.0588 | + | 0.435726i | −0.757749 | + | 0.0252834i | ||||
\(298\) | −10.2427 | + | 27.6527i | −0.593342 | + | 1.60188i | ||||
\(299\) | 2.26276 | + | 21.8582i | 0.130859 | + | 1.26409i | ||||
\(300\) | −12.6984 | − | 34.9125i | −0.733144 | − | 2.01567i | ||||
\(301\) | − | 2.71742i | − | 0.156630i | ||||||
\(302\) | 5.93178 | + | 2.19715i | 0.341336 | + | 0.126432i | ||||
\(303\) | 17.8340 | + | 10.0338i | 1.02454 | + | 0.576425i | ||||
\(304\) | 3.10599 | + | 20.2959i | 0.178141 | + | 1.16405i | ||||
\(305\) | 28.3273i | 1.62202i | ||||||||
\(306\) | −2.53026 | − | 13.0789i | −0.144645 | − | 0.747672i | ||||
\(307\) | − | 17.4478i | − | 0.995800i | −0.867234 | − | 0.497900i | \(-0.834105\pi\) | ||
0.867234 | − | 0.497900i | \(-0.165895\pi\) | |||||||
\(308\) | −1.09635 | − | 0.941330i | −0.0624701 | − | 0.0536373i | ||||
\(309\) | 1.04889 | − | 1.86430i | 0.0596694 | − | 0.106056i | ||||
\(310\) | 5.09603 | − | 13.7581i | 0.289435 | − | 0.781406i | ||||
\(311\) | 22.5668i | 1.27964i | 0.768523 | + | 0.639822i | \(0.220992\pi\) | ||||
−0.768523 | + | 0.639822i | \(0.779008\pi\) | |||||||
\(312\) | −22.4473 | − | 0.132182i | −1.27083 | − | 0.00748335i | ||||
\(313\) | 20.9556i | 1.18448i | 0.805762 | + | 0.592239i | \(0.201756\pi\) | ||||
−0.805762 | + | 0.592239i | \(0.798244\pi\) | |||||||
\(314\) | −18.2818 | − | 6.77164i | −1.03170 | − | 0.382146i | ||||
\(315\) | −1.77445 | − | 2.92145i | −0.0999791 | − | 0.164605i | ||||
\(316\) | −18.2329 | + | 21.2355i | −1.02568 | + | 1.19459i | ||||
\(317\) | 18.7546 | 1.05336 | 0.526681 | − | 0.850063i | \(-0.323436\pi\) | ||||
0.526681 | + | 0.850063i | \(0.323436\pi\) | |||||||
\(318\) | −1.88769 | + | 1.60157i | −0.105856 | + | 0.0898115i | ||||
\(319\) | − | 12.2873i | − | 0.687959i | ||||||
\(320\) | −26.9177 | − | 16.7866i | −1.50475 | − | 0.938402i | ||||
\(321\) | 14.5547 | − | 25.8695i | 0.812366 | − | 1.44390i | ||||
\(322\) | −0.485118 | + | 1.88741i | −0.0270346 | + | 0.105181i | ||||
\(323\) | 16.1172 | 0.896784 | ||||||||
\(324\) | −16.7012 | + | 6.71333i | −0.927846 | + | 0.372963i | ||||
\(325\) | 49.1400i | 2.72580i | ||||||||
\(326\) | 7.61939 | − | 20.5705i | 0.421999 | − | 1.13930i | ||||
\(327\) | −17.5635 | − | 9.88158i | −0.971264 | − | 0.546453i | ||||
\(328\) | −13.2030 | + | 7.32625i | −0.729014 | + | 0.404525i | ||||
\(329\) | −1.42312 | −0.0784589 | ||||||||
\(330\) | 15.8015 | + | 18.6244i | 0.869842 | + | 1.02524i | ||||
\(331\) | − | 20.0902i | − | 1.10426i | −0.833759 | − | 0.552129i | \(-0.813815\pi\) | ||
0.833759 | − | 0.552129i | \(-0.186185\pi\) | |||||||
\(332\) | −8.48532 | + | 9.88266i | −0.465692 | + | 0.542382i | ||||
\(333\) | −5.01790 | − | 8.26143i | −0.274979 | − | 0.452724i | ||||
\(334\) | −2.31778 | + | 6.25744i | −0.126823 | + | 0.342392i | ||||
\(335\) | − | 16.3859i | − | 0.895260i | ||||||
\(336\) | −1.86263 | − | 0.702425i | −0.101615 | − | 0.0383204i | ||||
\(337\) | − | 9.95962i | − | 0.542535i | −0.962504 | − | 0.271267i | \(-0.912557\pi\) | ||
0.962504 | − | 0.271267i | \(-0.0874428\pi\) | |||||||
\(338\) | 10.6037 | + | 3.92764i | 0.576764 | + | 0.213635i | ||||
\(339\) | 22.4181 | + | 12.6129i | 1.21758 | + | 0.685037i | ||||
\(340\) | −16.2218 | + | 18.8932i | −0.879750 | + | 1.02463i | ||||
\(341\) | 6.57867i | 0.356255i | ||||||||
\(342\) | −4.13643 | − | 21.3812i | −0.223672 | − | 1.15616i | ||||
\(343\) | 3.99889i | 0.215920i | ||||||||
\(344\) | 12.9791 | + | 23.3902i | 0.699785 | + | 1.26112i | ||||
\(345\) | 13.1095 | − | 30.2179i | 0.705792 | − | 1.62687i | ||||
\(346\) | −6.41936 | − | 2.37775i | −0.345107 | − | 0.127829i | ||||
\(347\) | 23.9726 | 1.28691 | 0.643457 | − | 0.765482i | \(-0.277500\pi\) | ||||
0.643457 | + | 0.765482i | \(0.277500\pi\) | |||||||
\(348\) | −5.78594 | − | 15.9076i | −0.310159 | − | 0.852738i | ||||
\(349\) | − | 31.4645i | − | 1.68425i | −0.539279 | − | 0.842127i | \(-0.681303\pi\) | ||
0.539279 | − | 0.842127i | \(-0.318697\pi\) | |||||||
\(350\) | −1.51364 | + | 4.08645i | −0.0809072 | + | 0.218430i | ||||
\(351\) | 23.7961 | − | 0.793991i | 1.27014 | − | 0.0423801i | ||||
\(352\) | 13.9328 | + | 2.86608i | 0.742622 | + | 0.152763i | ||||
\(353\) | − | 8.75860i | − | 0.466173i | −0.972456 | − | 0.233087i | \(-0.925117\pi\) | ||
0.972456 | − | 0.233087i | \(-0.0748826\pi\) | |||||||
\(354\) | −11.2289 | − | 13.2350i | −0.596810 | − | 0.703430i | ||||
\(355\) | 31.2188 | 1.65692 | ||||||||
\(356\) | 7.41104 | + | 6.36317i | 0.392784 | + | 0.337247i | ||||
\(357\) | −0.766219 | + | 1.36188i | −0.0405526 | + | 0.0720781i | ||||
\(358\) | 10.2046 | + | 3.77981i | 0.539328 | + | 0.199769i | ||||
\(359\) | 13.0559 | 0.689066 | 0.344533 | − | 0.938774i | \(-0.388037\pi\) | ||||
0.344533 | + | 0.938774i | \(0.388037\pi\) | |||||||
\(360\) | 29.2271 | + | 16.6711i | 1.54040 | + | 0.878645i | ||||
\(361\) | 7.34811 | 0.386743 | ||||||||
\(362\) | −12.8910 | − | 4.77486i | −0.677534 | − | 0.250961i | ||||
\(363\) | 7.06001 | + | 3.97211i | 0.370555 | + | 0.208481i | ||||
\(364\) | 1.99779 | + | 1.71532i | 0.104713 | + | 0.0899070i | ||||
\(365\) | 37.0865i | 1.94120i | ||||||||
\(366\) | −11.3205 | − | 13.3429i | −0.591734 | − | 0.697447i | ||||
\(367\) | − | 9.05269i | − | 0.472547i | −0.971687 | − | 0.236273i | \(-0.924074\pi\) | ||
0.971687 | − | 0.236273i | \(-0.0759261\pi\) | |||||||
\(368\) | −4.83909 | − | 18.5630i | −0.252255 | − | 0.967661i | ||||
\(369\) | 13.6883 | − | 8.31409i | 0.712582 | − | 0.432814i | ||||
\(370\) | −6.27597 | + | 16.9436i | −0.326272 | + | 0.880857i | ||||
\(371\) | 0.290387 | 0.0150761 | ||||||||
\(372\) | 3.09781 | + | 8.51698i | 0.160614 | + | 0.441585i | ||||
\(373\) | −24.9274 | −1.29069 | −0.645345 | − | 0.763891i | \(-0.723286\pi\) | ||||
−0.645345 | + | 0.763891i | \(0.723286\pi\) | |||||||
\(374\) | 3.87837 | − | 10.4707i | 0.200546 | − | 0.541426i | ||||
\(375\) | 19.2783 | − | 34.2652i | 0.995526 | − | 1.76945i | ||||
\(376\) | 12.2495 | − | 6.79714i | 0.631718 | − | 0.350536i | ||||
\(377\) | 22.3903i | 1.15316i | ||||||||
\(378\) | 2.00333 | + | 0.666952i | 0.103040 | + | 0.0343043i | ||||
\(379\) | −15.4021 | −0.791152 | −0.395576 | − | 0.918433i | \(-0.629455\pi\) | ||||
−0.395576 | + | 0.918433i | \(0.629455\pi\) | |||||||
\(380\) | −26.5191 | + | 30.8862i | −1.36040 | + | 1.58443i | ||||
\(381\) | 23.9929 | + | 13.4989i | 1.22919 | + | 0.691569i | ||||
\(382\) | 30.4848 | + | 11.2917i | 1.55974 | + | 0.577733i | ||||
\(383\) | 6.19991 | 0.316801 | 0.158400 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158400 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(384\) | 19.3875 | − | 2.85025i | 0.989365 | − | 0.145451i | ||||
\(385\) | − | 2.86503i | − | 0.146015i | ||||||
\(386\) | 3.99627 | + | 1.48023i | 0.203405 | + | 0.0753419i | ||||
\(387\) | −14.7291 | − | 24.2499i | −0.748723 | − | 1.23269i | ||||
\(388\) | 22.8396 | − | 26.6008i | 1.15950 | − | 1.35045i | ||||
\(389\) | 17.0295i | 0.863428i | 0.902010 | + | 0.431714i | \(0.142091\pi\) | ||||
−0.902010 | + | 0.431714i | \(0.857909\pi\) | |||||||
\(390\) | −28.7938 | − | 33.9379i | −1.45803 | − | 1.71851i | ||||
\(391\) | −14.9783 | + | 1.55056i | −0.757487 | + | 0.0784149i | ||||
\(392\) | −9.49318 | − | 17.1081i | −0.479478 | − | 0.864090i | ||||
\(393\) | −5.46243 | − | 3.07327i | −0.275543 | − | 0.155026i | ||||
\(394\) | 32.0955 | + | 11.8883i | 1.61695 | + | 0.598924i | ||||
\(395\) | −55.4936 | −2.79219 | ||||||||
\(396\) | −14.8859 | − | 2.45782i | −0.748043 | − | 0.123510i | ||||
\(397\) | − | 0.151454i | − | 0.00760127i | −0.999993 | − | 0.00380063i | \(-0.998790\pi\) | ||
0.999993 | − | 0.00380063i | \(-0.00120978\pi\) | |||||||
\(398\) | 5.83977 | − | 15.7660i | 0.292721 | − | 0.790277i | ||||
\(399\) | −1.25260 | + | 2.22637i | −0.0627086 | + | 0.111458i | ||||
\(400\) | −6.48927 | − | 42.4036i | −0.324463 | − | 2.12018i | ||||
\(401\) | −19.3398 | −0.965786 | −0.482893 | − | 0.875679i | \(-0.660414\pi\) | ||||
−0.482893 | + | 0.875679i | \(0.660414\pi\) | |||||||
\(402\) | 6.54837 | + | 7.71824i | 0.326603 | + | 0.384951i | ||||
\(403\) | − | 11.9878i | − | 0.597156i | ||||||
\(404\) | 17.9271 | + | 15.3923i | 0.891906 | + | 0.765796i | ||||
\(405\) | −31.6699 | − | 16.4526i | −1.57369 | − | 0.817534i | ||||
\(406\) | −0.689677 | + | 1.86196i | −0.0342281 | + | 0.0924076i | ||||
\(407\) | − | 8.10190i | − | 0.401596i | ||||||
\(408\) | 0.0905778 | − | 15.3820i | 0.00448427 | − | 0.761522i | ||||
\(409\) | −11.7458 | −0.580792 | −0.290396 | − | 0.956907i | \(-0.593787\pi\) | ||||
−0.290396 | + | 0.956907i | \(0.593787\pi\) | |||||||
\(410\) | −28.0736 | − | 10.3986i | −1.38646 | − | 0.513549i | ||||
\(411\) | −14.8220 | − | 8.33917i | −0.731117 | − | 0.411341i | ||||
\(412\) | 1.60906 | − | 1.87403i | 0.0792725 | − | 0.0923269i | ||||
\(413\) | 2.03596i | 0.100183i | ||||||||
\(414\) | 5.90113 | + | 19.4725i | 0.290025 | + | 0.957019i | ||||
\(415\) | −25.8259 | −1.26774 | ||||||||
\(416\) | −25.3887 | − | 5.22265i | −1.24479 | − | 0.256061i | ||||
\(417\) | −3.41216 | + | 6.06477i | −0.167094 | + | 0.296993i | ||||
\(418\) | 6.34030 | − | 17.1173i | 0.310114 | − | 0.837234i | ||||
\(419\) | 5.42795i | 0.265173i | 0.991171 | + | 0.132586i | \(0.0423282\pi\) | ||||
−0.991171 | + | 0.132586i | \(0.957672\pi\) | |||||||
\(420\) | −1.34911 | − | 3.70917i | −0.0658296 | − | 0.180989i | ||||
\(421\) | 16.8191 | 0.819713 | 0.409857 | − | 0.912150i | \(-0.365579\pi\) | ||||
0.409857 | + | 0.912150i | \(0.365579\pi\) | |||||||
\(422\) | 6.08318 | − | 16.4231i | 0.296125 | − | 0.799465i | ||||
\(423\) | −12.6997 | + | 7.71364i | −0.617479 | + | 0.375050i | ||||
\(424\) | −2.49951 | + | 1.38696i | −0.121387 | + | 0.0673567i | ||||
\(425\) | −33.6732 | −1.63339 | ||||||||
\(426\) | −14.7049 | + | 12.4761i | −0.712456 | + | 0.604467i | ||||
\(427\) | 2.05257i | 0.0993310i | ||||||||
\(428\) | 22.3277 | − | 26.0046i | 1.07925 | − | 1.25698i | ||||
\(429\) | 17.3929 | + | 9.78561i | 0.839738 | + | 0.472454i | ||||
\(430\) | −18.4219 | + | 49.7348i | −0.888385 | + | 2.39843i | ||||
\(431\) | −11.0468 | −0.532106 | −0.266053 | − | 0.963958i | \(-0.585720\pi\) | ||||
−0.266053 | + | 0.963958i | \(0.585720\pi\) | |||||||
\(432\) | −20.4291 | + | 3.82758i | −0.982897 | + | 0.184155i | ||||
\(433\) | 7.75165i | 0.372520i | 0.982500 | + | 0.186260i | \(0.0596367\pi\) | ||||
−0.982500 | + | 0.186260i | \(0.940363\pi\) | |||||||
\(434\) | 0.369255 | − | 0.996899i | 0.0177248 | − | 0.0478527i | ||||
\(435\) | 16.4565 | − | 29.2498i | 0.789031 | − | 1.40242i | ||||
\(436\) | −17.6552 | − | 15.1589i | −0.845530 | − | 0.725978i | ||||
\(437\) | −24.4863 | + | 2.53482i | −1.17134 | + | 0.121257i | ||||
\(438\) | −14.8210 | − | 17.4688i | −0.708175 | − | 0.834690i | ||||
\(439\) | −26.0172 | −1.24173 | −0.620866 | − | 0.783917i | \(-0.713219\pi\) | ||||
−0.620866 | + | 0.783917i | \(0.713219\pi\) | |||||||
\(440\) | 13.6841 | + | 24.6607i | 0.652363 | + | 1.17565i | ||||
\(441\) | 10.7732 | + | 17.7369i | 0.513009 | + | 0.844614i | ||||
\(442\) | −7.06727 | + | 19.0799i | −0.336156 | + | 0.907540i | ||||
\(443\) | −20.7333 | −0.985068 | −0.492534 | − | 0.870293i | \(-0.663929\pi\) | ||||
−0.492534 | + | 0.870293i | \(0.663929\pi\) | |||||||
\(444\) | −3.81508 | − | 10.4890i | −0.181056 | − | 0.497786i | ||||
\(445\) | 19.3669i | 0.918080i | ||||||||
\(446\) | 5.90588 | + | 2.18756i | 0.279652 | + | 0.103584i | ||||
\(447\) | 17.7092 | − | 31.4764i | 0.837618 | − | 1.48878i | ||||
\(448\) | −1.95044 | − | 1.21635i | −0.0921496 | − | 0.0574670i | ||||
\(449\) | − | 22.8916i | − | 1.08032i | −0.841561 | − | 0.540162i | \(-0.818363\pi\) | ||
0.841561 | − | 0.540162i | \(-0.181637\pi\) | |||||||
\(450\) | 8.64212 | + | 44.6712i | 0.407393 | + | 2.10582i | ||||
\(451\) | 13.4239 | 0.632108 | ||||||||
\(452\) | 22.5351 | + | 19.3488i | 1.05996 | + | 0.910091i | ||||
\(453\) | −6.75199 | − | 3.79881i | −0.317236 | − | 0.178483i | ||||
\(454\) | −7.60556 | + | 20.5332i | −0.356946 | + | 0.963669i | ||||
\(455\) | 5.22073i | 0.244752i | ||||||||
\(456\) | 0.148075 | − | 25.1462i | 0.00693426 | − | 1.17758i | ||||
\(457\) | − | 15.4708i | − | 0.723693i | −0.932238 | − | 0.361846i | \(-0.882146\pi\) | ||
0.932238 | − | 0.361846i | \(-0.117854\pi\) | |||||||
\(458\) | −33.7050 | − | 12.4844i | −1.57493 | − | 0.583359i | ||||
\(459\) | 0.544082 | + | 16.3063i | 0.0253956 | + | 0.761111i | ||||
\(460\) | 21.6739 | − | 31.2551i | 1.01055 | − | 1.45728i | ||||
\(461\) | −26.0194 | −1.21185 | −0.605923 | − | 0.795523i | \(-0.707196\pi\) | ||||
−0.605923 | + | 0.795523i | \(0.707196\pi\) | |||||||
\(462\) | 1.14496 | + | 1.34951i | 0.0532685 | + | 0.0627849i | ||||
\(463\) | −4.90636 | −0.228018 | −0.114009 | − | 0.993480i | \(-0.536369\pi\) | ||||
−0.114009 | + | 0.993480i | \(0.536369\pi\) | |||||||
\(464\) | −2.95679 | − | 19.3209i | −0.137265 | − | 0.896950i | ||||
\(465\) | −8.81088 | + | 15.6604i | −0.408595 | + | 0.726235i | ||||
\(466\) | 11.7347 | − | 31.6809i | 0.543600 | − | 1.46759i | ||||
\(467\) | − | 42.0348i | − | 1.94514i | −0.232615 | − | 0.972569i | \(-0.574728\pi\) | ||
0.232615 | − | 0.972569i | \(-0.425272\pi\) | |||||||
\(468\) | 27.1254 | + | 4.47870i | 1.25387 | + | 0.207028i | ||||
\(469\) | − | 1.18731i | − | 0.0548250i | ||||||
\(470\) | 26.0461 | + | 9.64757i | 1.20142 | + | 0.445009i | ||||
\(471\) | 20.8097 | + | 11.7080i | 0.958860 | + | 0.539474i | ||||
\(472\) | −9.72425 | − | 17.5245i | −0.447595 | − | 0.806632i | ||||
\(473\) | − | 23.7816i | − | 1.09348i | ||||||
\(474\) | 26.1391 | − | 22.1771i | 1.20061 | − | 1.01863i | ||||
\(475\) | −55.0484 | −2.52579 | ||||||||
\(476\) | −1.17542 | + | 1.36898i | −0.0538752 | + | 0.0627473i | ||||
\(477\) | 2.59137 | − | 1.57397i | 0.118651 | − | 0.0720671i | ||||
\(478\) | −0.212346 | + | 0.573282i | −0.00971246 | + | 0.0262213i | ||||
\(479\) | 10.7256 | 0.490067 | 0.245033 | − | 0.969515i | \(-0.421201\pi\) | ||||
0.245033 | + | 0.969515i | \(0.421201\pi\) | |||||||
\(480\) | 29.3283 | + | 25.4830i | 1.33865 | + | 1.16314i | ||||
\(481\) | 14.7635i | 0.673157i | ||||||||
\(482\) | 6.16630 | − | 16.6475i | 0.280867 | − | 0.758274i | ||||
\(483\) | 0.949905 | − | 2.18956i | 0.0432222 | − | 0.0996286i | ||||
\(484\) | 7.09687 | + | 6.09341i | 0.322585 | + | 0.276973i | ||||
\(485\) | 69.5145 | 3.15649 | ||||||||
\(486\) | 21.4924 | − | 4.90674i | 0.974916 | − | 0.222574i | ||||
\(487\) | 23.2899 | 1.05537 | 0.527684 | − | 0.849441i | \(-0.323061\pi\) | ||||
0.527684 | + | 0.849441i | \(0.323061\pi\) | |||||||
\(488\) | −9.80359 | − | 17.6675i | −0.443788 | − | 0.799771i | ||||
\(489\) | −13.1737 | + | 23.4149i | −0.595734 | + | 1.05886i | ||||
\(490\) | 13.4742 | − | 36.3771i | 0.608703 | − | 1.64335i | ||||
\(491\) | 11.6656 | 0.526462 | 0.263231 | − | 0.964733i | \(-0.415212\pi\) | ||||
0.263231 | + | 0.964733i | \(0.415212\pi\) | |||||||
\(492\) | 17.3791 | − | 6.32115i | 0.783510 | − | 0.284979i | ||||
\(493\) | −15.3429 | −0.691011 | ||||||||
\(494\) | −11.5535 | + | 31.1916i | −0.519815 | + | 1.40338i | ||||
\(495\) | −15.5292 | − | 25.5671i | −0.697984 | − | 1.14916i | ||||
\(496\) | 1.58307 | + | 10.3445i | 0.0710820 | + | 0.464480i | ||||
\(497\) | 2.26209 | 0.101469 | ||||||||
\(498\) | 12.1647 | − | 10.3209i | 0.545114 | − | 0.462490i | ||||
\(499\) | − | 6.95526i | − | 0.311360i | −0.987808 | − | 0.155680i | \(-0.950243\pi\) | ||
0.987808 | − | 0.155680i | \(-0.0497569\pi\) | |||||||
\(500\) | 29.5739 | − | 34.4440i | 1.32258 | − | 1.54038i | ||||
\(501\) | 4.00736 | − | 7.12268i | 0.179036 | − | 0.318218i | ||||
\(502\) | 2.31894 | − | 6.26057i | 0.103499 | − | 0.279423i | ||||
\(503\) | 8.12303 | 0.362188 | 0.181094 | − | 0.983466i | \(-0.442036\pi\) | ||||
0.181094 | + | 0.983466i | \(0.442036\pi\) | |||||||
\(504\) | 2.11778 | + | 1.20798i | 0.0943332 | + | 0.0538075i | ||||
\(505\) | 46.8480i | 2.08471i | ||||||||
\(506\) | −4.24552 | + | 16.5178i | −0.188737 | + | 0.734304i | ||||
\(507\) | −12.0699 | − | 6.79076i | −0.536042 | − | 0.301588i | ||||
\(508\) | 24.1182 | + | 20.7080i | 1.07007 | + | 0.918769i | ||||
\(509\) | −19.3253 | −0.856577 | −0.428289 | − | 0.903642i | \(-0.640883\pi\) | ||||
−0.428289 | + | 0.903642i | \(0.640883\pi\) | |||||||
\(510\) | 23.2559 | − | 19.7310i | 1.02979 | − | 0.873701i | ||||
\(511\) | 2.68726i | 0.118877i | ||||||||
\(512\) | 22.5980 | + | 1.15394i | 0.998699 | + | 0.0509974i | ||||
\(513\) | 0.889456 | + | 26.6572i | 0.0392704 | + | 1.17695i | ||||
\(514\) | −4.87436 | + | 13.1596i | −0.214999 | + | 0.580445i | ||||
\(515\) | 4.89732 | 0.215802 | ||||||||
\(516\) | −11.1984 | − | 30.7885i | −0.492984 | − | 1.35539i | ||||
\(517\) | −12.4544 | −0.547745 | ||||||||
\(518\) | −0.454752 | + | 1.22772i | −0.0199807 | + | 0.0539430i | ||||
\(519\) | 7.30699 | + | 4.11106i | 0.320741 | + | 0.180455i | ||||
\(520\) | −24.9355 | − | 44.9374i | −1.09349 | − | 1.97064i | ||||
\(521\) | 38.7398 | 1.69722 | 0.848611 | − | 0.529018i | \(-0.177440\pi\) | ||||
0.848611 | + | 0.529018i | \(0.177440\pi\) | |||||||
\(522\) | 3.93772 | + | 20.3541i | 0.172349 | + | 0.890874i | ||||
\(523\) | −39.4005 | −1.72286 | −0.861431 | − | 0.507874i | \(-0.830432\pi\) | ||||
−0.861431 | + | 0.507874i | \(0.830432\pi\) | |||||||
\(524\) | −5.49094 | − | 4.71456i | −0.239873 | − | 0.205956i | ||||
\(525\) | 2.61703 | − | 4.65150i | 0.114216 | − | 0.203008i | ||||
\(526\) | −26.5334 | − | 9.82806i | −1.15691 | − | 0.428524i | ||||
\(527\) | 8.21465 | 0.357836 | ||||||||
\(528\) | −16.3008 | − | 6.14729i | −0.709403 | − | 0.267526i | ||||
\(529\) | 22.5123 | − | 4.71143i | 0.978795 | − | 0.204845i | ||||
\(530\) | −5.31472 | − | 1.96859i | −0.230857 | − | 0.0855101i | ||||
\(531\) | 11.0354 | + | 18.1686i | 0.478896 | + | 0.788451i | ||||
\(532\) | −1.92156 | + | 2.23799i | −0.0833100 | + | 0.0970294i | ||||
\(533\) | −24.4614 | −1.05954 | ||||||||
\(534\) | −7.73968 | − | 9.12237i | −0.334929 | − | 0.394764i | ||||
\(535\) | 67.9566 | 2.93802 | ||||||||
\(536\) | 5.67090 | + | 10.2198i | 0.244945 | + | 0.441428i | ||||
\(537\) | −11.6156 | − | 6.53516i | −0.501249 | − | 0.282013i | ||||
\(538\) | −22.6803 | − | 8.40086i | −0.977817 | − | 0.362187i | ||||
\(539\) | 17.3944i | 0.749229i | ||||||||
\(540\) | −32.1438 | − | 25.7876i | −1.38325 | − | 1.10972i | ||||
\(541\) | − | 20.8230i | − | 0.895252i | −0.894221 | − | 0.447626i | \(-0.852270\pi\) | ||
0.894221 | − | 0.447626i | \(-0.147730\pi\) | |||||||
\(542\) | −12.0876 | − | 4.47728i | −0.519206 | − | 0.192315i | ||||
\(543\) | 14.6734 | + | 8.25558i | 0.629698 | + | 0.354281i | ||||
\(544\) | 3.57881 | − | 17.3976i | 0.153440 | − | 0.745916i | ||||
\(545\) | − | 46.1375i | − | 1.97631i | ||||||
\(546\) | −2.08638 | − | 2.45911i | −0.0892889 | − | 0.105240i | ||||
\(547\) | 19.9002i | 0.850870i | 0.904989 | + | 0.425435i | \(0.139879\pi\) | ||||
−0.904989 | + | 0.425435i | \(0.860121\pi\) | |||||||
\(548\) | −14.8994 | − | 12.7927i | −0.636471 | − | 0.546478i | ||||
\(549\) | 11.1255 | + | 18.3169i | 0.474823 | + | 0.781745i | ||||
\(550\) | −13.2466 | + | 35.7627i | −0.564838 | + | 1.52493i | ||||
\(551\) | −25.0824 | −1.06855 | ||||||||
\(552\) | 2.28158 | + | 23.3836i | 0.0971107 | + | 0.995274i | ||||
\(553\) | −4.02103 | −0.170991 | ||||||||
\(554\) | −9.45527 | + | 25.5269i | −0.401716 | + | 1.08454i | ||||
\(555\) | 10.8510 | − | 19.2865i | 0.460597 | − | 0.818665i | ||||
\(556\) | −5.23443 | + | 6.09643i | −0.221989 | + | 0.258546i | ||||
\(557\) | 4.24687i | 0.179946i | 0.995944 | + | 0.0899728i | \(0.0286780\pi\) | ||||
−0.995944 | + | 0.0899728i | \(0.971322\pi\) | |||||||
\(558\) | −2.10827 | − | 10.8976i | −0.0892500 | − | 0.461334i | ||||
\(559\) | 43.3355i | 1.83289i | ||||||||
\(560\) | −0.689432 | − | 4.50504i | −0.0291338 | − | 0.190373i | ||||
\(561\) | −6.70558 | + | 11.9185i | −0.283110 | + | 0.503199i | ||||
\(562\) | 17.0686 | + | 6.32227i | 0.719995 | + | 0.266689i | ||||
\(563\) | 3.87933i | 0.163494i | 0.996653 | + | 0.0817471i | \(0.0260500\pi\) | ||||
−0.996653 | + | 0.0817471i | \(0.973950\pi\) | |||||||
\(564\) | −16.1240 | + | 5.86463i | −0.678941 | + | 0.246945i | ||||
\(565\) | 58.8900i | 2.47752i | ||||||||
\(566\) | 20.8136 | + | 7.70942i | 0.874860 | + | 0.324051i | ||||
\(567\) | −2.29478 | − | 1.19214i | −0.0963716 | − | 0.0500652i | ||||
\(568\) | −19.4709 | + | 10.8043i | −0.816982 | + | 0.453338i | ||||
\(569\) | −25.5810 | −1.07241 | −0.536205 | − | 0.844088i | \(-0.680143\pi\) | ||||
−0.536205 | + | 0.844088i | \(0.680143\pi\) | |||||||
\(570\) | 38.0184 | − | 32.2559i | 1.59241 | − | 1.35105i | ||||
\(571\) | 16.6589 | 0.697155 | 0.348577 | − | 0.937280i | \(-0.386665\pi\) | ||||
0.348577 | + | 0.937280i | \(0.386665\pi\) | |||||||
\(572\) | 17.4837 | + | 15.0116i | 0.731031 | + | 0.627668i | ||||
\(573\) | −34.7001 | − | 19.5230i | −1.44962 | − | 0.815583i | ||||
\(574\) | −2.03419 | − | 0.753473i | −0.0849057 | − | 0.0314493i | ||||
\(575\) | 51.1586 | − | 5.29594i | 2.13346 | − | 0.220856i | ||||
\(576\) | −23.9983 | − | 0.282641i | −0.999931 | − | 0.0117767i | ||||
\(577\) | −17.2222 | −0.716971 | −0.358485 | − | 0.933535i | \(-0.616707\pi\) | ||||
−0.358485 | + | 0.933535i | \(0.616707\pi\) | |||||||
\(578\) | 9.47026 | + | 3.50782i | 0.393911 | + | 0.145906i | ||||
\(579\) | −4.54885 | − | 2.55927i | −0.189044 | − | 0.106360i | ||||
\(580\) | 25.2452 | − | 29.4025i | 1.04825 | − | 1.22087i | ||||
\(581\) | −1.87133 | −0.0776357 | ||||||||
\(582\) | −32.7433 | + | 27.7803i | −1.35725 | + | 1.15153i | ||||
\(583\) | 2.54133 | 0.105251 | ||||||||
\(584\) | −12.8350 | − | 23.1306i | −0.531116 | − | 0.957150i | ||||
\(585\) | 28.2977 | + | 46.5890i | 1.16996 | + | 1.92622i | ||||
\(586\) | −5.17940 | + | 13.9831i | −0.213959 | + | 0.577638i | ||||
\(587\) | 8.24485 | 0.340301 | 0.170151 | − | 0.985418i | \(-0.445575\pi\) | ||||
0.170151 | + | 0.985418i | \(0.445575\pi\) | |||||||
\(588\) | 8.19079 | + | 22.5194i | 0.337782 | + | 0.928684i | ||||
\(589\) | 13.4292 | 0.553340 | ||||||||
\(590\) | 13.8022 | − | 37.2626i | 0.568227 | − | 1.53408i | ||||
\(591\) | −36.5335 | − | 20.5545i | −1.50279 | − | 0.845498i | ||||
\(592\) | −1.94962 | − | 12.7396i | −0.0801288 | − | 0.523595i | ||||
\(593\) | 24.8805i | 1.02172i | 0.859664 | + | 0.510859i | \(0.170673\pi\) | ||||
−0.859664 | + | 0.510859i | \(0.829327\pi\) | |||||||
\(594\) | 17.5322 | + | 5.83685i | 0.719353 | + | 0.239489i | ||||
\(595\) | −3.57750 | −0.146663 | ||||||||
\(596\) | 27.1669 | − | 31.6407i | 1.11280 | − | 1.29605i | ||||
\(597\) | −10.0968 | + | 17.9460i | −0.413234 | + | 0.734481i | ||||
\(598\) | 7.73631 | − | 30.0991i | 0.316361 | − | 1.23084i | ||||
\(599\) | 36.4718i | 1.49020i | 0.666955 | + | 0.745098i | \(0.267597\pi\) | ||||
−0.666955 | + | 0.745098i | \(0.732403\pi\) | |||||||
\(600\) | −0.309369 | + | 52.5373i | −0.0126300 | + | 2.14483i | ||||
\(601\) | −29.5759 | −1.20642 | −0.603212 | − | 0.797581i | \(-0.706113\pi\) | ||||
−0.603212 | + | 0.797581i | \(0.706113\pi\) | |||||||
\(602\) | −1.33484 | + | 3.60375i | −0.0544040 | + | 0.146878i | ||||
\(603\) | −6.43553 | − | 10.5954i | −0.262075 | − | 0.431478i | ||||
\(604\) | −6.78724 | − | 5.82756i | −0.276169 | − | 0.237120i | ||||
\(605\) | 18.5459i | 0.753998i | ||||||||
\(606\) | −18.7220 | − | 22.0667i | −0.760531 | − | 0.896400i | ||||
\(607\) | −6.98238 | −0.283406 | −0.141703 | − | 0.989909i | \(-0.545258\pi\) | ||||
−0.141703 | + | 0.989909i | \(0.545258\pi\) | |||||||
\(608\) | 5.85059 | − | 28.4413i | 0.237273 | − | 1.15345i | ||||
\(609\) | 1.19243 | − | 2.11942i | 0.0483197 | − | 0.0858833i | ||||
\(610\) | 13.9148 | − | 37.5666i | 0.563393 | − | 1.52103i | ||||
\(611\) | 22.6948 | 0.918133 | ||||||||
\(612\) | −3.06903 | + | 18.5877i | −0.124058 | + | 0.751362i | ||||
\(613\) | 34.1148 | 1.37788 | 0.688942 | − | 0.724817i | \(-0.258076\pi\) | ||||
0.688942 | + | 0.724817i | \(0.258076\pi\) | |||||||
\(614\) | −8.57064 | + | 23.1387i | −0.345883 | + | 0.933800i | ||||
\(615\) | 31.9555 | + | 17.9788i | 1.28857 | + | 0.724975i | ||||
\(616\) | 0.991538 | + | 1.78690i | 0.0399502 | + | 0.0719962i | ||||
\(617\) | −39.6240 | −1.59520 | −0.797602 | − | 0.603184i | \(-0.793898\pi\) | ||||
−0.797602 | + | 0.603184i | \(0.793898\pi\) | |||||||
\(618\) | −2.30678 | + | 1.95713i | −0.0927921 | + | 0.0787274i | ||||
\(619\) | −14.2721 | −0.573645 | −0.286822 | − | 0.957984i | \(-0.592599\pi\) | ||||
−0.286822 | + | 0.957984i | \(0.592599\pi\) | |||||||
\(620\) | −13.5163 | + | 15.7422i | −0.542829 | + | 0.632221i | ||||
\(621\) | −3.39117 | − | 24.6881i | −0.136083 | − | 0.990697i | ||||
\(622\) | 11.0851 | − | 29.9272i | 0.444473 | − | 1.19997i | ||||
\(623\) | 1.40331i | 0.0562226i | ||||||||
\(624\) | 29.7038 | + | 11.2017i | 1.18910 | + | 0.448429i | ||||
\(625\) | 36.3894 | 1.45558 | ||||||||
\(626\) | 10.2937 | − | 27.7905i | 0.411418 | − | 1.11073i | ||||
\(627\) | −10.9622 | + | 19.4842i | −0.437787 | + | 0.778122i | ||||
\(628\) | 20.9183 | + | 17.9606i | 0.834732 | + | 0.716706i | ||||
\(629\) | −10.1167 | −0.403378 | ||||||||
\(630\) | 0.918156 | + | 4.74595i | 0.0365802 | + | 0.189083i | ||||
\(631\) | 1.61081i | 0.0641255i | 0.999486 | + | 0.0320627i | \(0.0102076\pi\) | ||||
−0.999486 | + | 0.0320627i | \(0.989792\pi\) | |||||||
\(632\) | 34.6110 | − | 19.2054i | 1.37675 | − | 0.763950i | ||||
\(633\) | −10.5176 | + | 18.6940i | −0.418038 | + | 0.743020i | ||||
\(634\) | −24.8716 | − | 9.21254i | −0.987779 | − | 0.365877i | ||||
\(635\) | 63.0268i | 2.50114i | ||||||||
\(636\) | 3.29010 | − | 1.19668i | 0.130461 | − | 0.0474514i | ||||
\(637\) | − | 31.6965i | − | 1.25586i | ||||||
\(638\) | −6.03573 | + | 16.2950i | −0.238957 | + | 0.645125i | ||||
\(639\) | 20.1865 | − | 12.2611i | 0.798567 | − | 0.485041i | ||||
\(640\) | 27.4515 | + | 35.4842i | 1.08511 | + | 1.40264i | ||||
\(641\) | 0.197384 | 0.00779619 | 0.00389810 | − | 0.999992i | \(-0.498759\pi\) | ||||
0.00389810 | + | 0.999992i | \(0.498759\pi\) | |||||||
\(642\) | −32.0094 | + | 27.1577i | −1.26331 | + | 1.07183i | ||||
\(643\) | −38.0575 | −1.50084 | −0.750421 | − | 0.660961i | \(-0.770149\pi\) | ||||
−0.750421 | + | 0.660961i | \(0.770149\pi\) | |||||||
\(644\) | 1.57047 | − | 2.26472i | 0.0618853 | − | 0.0892425i | ||||
\(645\) | 31.8509 | − | 56.6118i | 1.25413 | − | 2.22909i | ||||
\(646\) | −21.3740 | − | 7.91700i | −0.840949 | − | 0.311490i | ||||
\(647\) | 41.6702i | 1.63822i | 0.573634 | + | 0.819112i | \(0.305533\pi\) | ||||
−0.573634 | + | 0.819112i | \(0.694467\pi\) | |||||||
\(648\) | 25.4462 | − | 0.699071i | 0.999623 | − | 0.0274621i | ||||
\(649\) | 17.8178i | 0.699409i | ||||||||
\(650\) | 24.1383 | − | 65.1677i | 0.946783 | − | 2.55609i | ||||
\(651\) | −0.638430 | + | 1.13474i | −0.0250220 | + | 0.0444741i | ||||
\(652\) | −20.2091 | + | 23.5371i | −0.791449 | + | 0.921784i | ||||
\(653\) | −35.8779 | −1.40401 | −0.702005 | − | 0.712172i | \(-0.747711\pi\) | ||||
−0.702005 | + | 0.712172i | \(0.747711\pi\) | |||||||
\(654\) | 18.4381 | + | 21.7320i | 0.720986 | + | 0.849790i | ||||
\(655\) | − | 14.3492i | − | 0.560670i | ||||||
\(656\) | 21.1081 | − | 3.23029i | 0.824133 | − | 0.126122i | ||||
\(657\) | 14.5656 | + | 23.9807i | 0.568258 | + | 0.935576i | ||||
\(658\) | 1.88728 | + | 0.699056i | 0.0735739 | + | 0.0272520i | ||||
\(659\) | 24.0238i | 0.935836i | 0.883772 | + | 0.467918i | \(0.154996\pi\) | ||||
−0.883772 | + | 0.467918i | \(0.845004\pi\) | |||||||
\(660\) | −11.8067 | − | 32.4609i | −0.459576 | − | 1.26354i | ||||
\(661\) | −1.96209 | −0.0763164 | −0.0381582 | − | 0.999272i | \(-0.512149\pi\) | ||||
−0.0381582 | + | 0.999272i | \(0.512149\pi\) | |||||||
\(662\) | −9.86862 | + | 26.6429i | −0.383555 | + | 1.03551i | ||||
\(663\) | 12.2191 | − | 21.7182i | 0.474550 | − | 0.843464i | ||||
\(664\) | 16.1074 | − | 8.93790i | 0.625089 | − | 0.346858i | ||||
\(665\) | −5.84845 | −0.226793 | ||||||||
\(666\) | 2.59641 | + | 13.4209i | 0.100609 | + | 0.520048i | ||||
\(667\) | 23.3101 | − | 2.41306i | 0.902569 | − | 0.0934339i | ||||
\(668\) | 6.14750 | − | 7.15986i | 0.237854 | − | 0.277023i | ||||
\(669\) | −6.72251 | − | 3.78222i | −0.259907 | − | 0.146229i | ||||
\(670\) | −8.04903 | + | 21.7304i | −0.310961 | + | 0.839520i | ||||
\(671\) | 17.9632i | 0.693460i | ||||||||
\(672\) | 2.12511 | + | 1.84648i | 0.0819778 | + | 0.0712296i | ||||
\(673\) | −21.9447 | −0.845907 | −0.422953 | − | 0.906151i | \(-0.639007\pi\) | ||||
−0.422953 | + | 0.906151i | \(0.639007\pi\) | |||||||
\(674\) | −4.89232 | + | 13.2081i | −0.188445 | + | 0.508756i | ||||
\(675\) | −1.85832 | − | 55.6942i | −0.0715266 | − | 2.14367i | ||||
\(676\) | −12.1329 | − | 10.4174i | −0.466650 | − | 0.400668i | ||||
\(677\) | − | 16.4455i | − | 0.632052i | −0.948750 | − | 0.316026i | \(-0.897651\pi\) | ||
0.948750 | − | 0.316026i | \(-0.102349\pi\) | |||||||
\(678\) | −23.5344 | − | 27.7388i | −0.903833 | − | 1.06530i | ||||
\(679\) | 5.03697 | 0.193301 | ||||||||
\(680\) | 30.7933 | − | 17.0870i | 1.18087 | − | 0.655257i | ||||
\(681\) | 13.1498 | − | 23.3724i | 0.503900 | − | 0.895631i | ||||
\(682\) | 3.23154 | − | 8.72439i | 0.123742 | − | 0.334074i | ||||
\(683\) | 49.6858 | 1.90118 | 0.950588 | − | 0.310457i | \(-0.100482\pi\) | ||||
0.950588 | + | 0.310457i | \(0.100482\pi\) | |||||||
\(684\) | −5.01720 | + | 30.3868i | −0.191837 | + | 1.16187i | ||||
\(685\) | − | 38.9359i | − | 1.48766i | ||||||
\(686\) | 1.96431 | − | 5.30318i | 0.0749979 | − | 0.202476i | ||||
\(687\) | 38.3655 | + | 21.5852i | 1.46373 | + | 0.823526i | ||||
\(688\) | −5.72273 | − | 37.3948i | −0.218177 | − | 1.42566i | ||||
\(689\) | −4.63088 | −0.176422 | ||||||||
\(690\) | −32.2288 | + | 33.6342i | −1.22693 | + | 1.28043i | ||||
\(691\) | 4.13168i | 0.157177i | 0.996907 | + | 0.0785883i | \(0.0250412\pi\) | ||||
−0.996907 | + | 0.0785883i | \(0.974959\pi\) | |||||||
\(692\) | 7.34513 | + | 6.30658i | 0.279220 | + | 0.239740i | ||||
\(693\) | −1.12523 | − | 1.85257i | −0.0427440 | − | 0.0703734i | ||||
\(694\) | −31.7915 | − | 11.7757i | −1.20679 | − | 0.446999i | ||||
\(695\) | −15.9315 | −0.604316 | ||||||||
\(696\) | −0.140962 | + | 23.9382i | −0.00534315 | + | 0.907377i | ||||
\(697\) | − | 16.7622i | − | 0.634912i | ||||||
\(698\) | −15.4558 | + | 41.7270i | −0.585012 | + | 1.57939i | ||||
\(699\) | −20.2889 | + | 36.0615i | −0.767398 | + | 1.36397i | ||||
\(700\) | 4.01465 | − | 4.67578i | 0.151740 | − | 0.176728i | ||||
\(701\) | − | 14.0993i | − | 0.532522i | −0.963901 | − | 0.266261i | \(-0.914212\pi\) | ||
0.963901 | − | 0.266261i | \(-0.0857882\pi\) | |||||||
\(702\) | −31.9475 | − | 10.6361i | −1.20578 | − | 0.401432i | ||||
\(703\) | −16.5386 | −0.623764 | ||||||||
\(704\) | −17.0693 | − | 10.6449i | −0.643324 | − | 0.401195i | ||||
\(705\) | −29.6476 | − | 16.6803i | −1.11659 | − | 0.628218i | ||||
\(706\) | −4.30236 | + | 11.6153i | −0.161921 | + | 0.437149i | ||||
\(707\) | 3.39457i | 0.127666i | ||||||||
\(708\) | 8.39016 | + | 23.0675i | 0.315321 | + | 0.866931i | ||||
\(709\) | −7.17494 | −0.269461 | −0.134730 | − | 0.990882i | \(-0.543017\pi\) | ||||
−0.134730 | + | 0.990882i | \(0.543017\pi\) | |||||||
\(710\) | −41.4012 | − | 15.3351i | −1.55376 | − | 0.575517i | ||||
\(711\) | −35.8830 | + | 21.7950i | −1.34572 | + | 0.817375i | ||||
\(712\) | −6.70256 | − | 12.0790i | −0.251189 | − | 0.452680i | ||||
\(713\) | −12.4803 | + | 1.29196i | −0.467390 | + | 0.0483841i | ||||
\(714\) | 1.68510 | − | 1.42969i | 0.0630634 | − | 0.0535048i | ||||
\(715\) | 45.6894i | 1.70869i | ||||||||
\(716\) | −11.6762 | − | 10.0253i | −0.436361 | − | 0.374662i | ||||
\(717\) | 0.367139 | − | 0.652552i | 0.0137110 | − | 0.0243700i | ||||
\(718\) | −17.3143 | − | 6.41327i | −0.646164 | − | 0.239341i | ||||
\(719\) | − | 0.624362i | − | 0.0232848i | −0.999932 | − | 0.0116424i | \(-0.996294\pi\) | ||
0.999932 | − | 0.0116424i | \(-0.00370597\pi\) | |||||||
\(720\) | −30.5708 | − | 36.4654i | −1.13931 | − | 1.35899i | ||||
\(721\) | 0.354856 | 0.0132155 | ||||||||
\(722\) | −9.74479 | − | 3.60950i | −0.362663 | − | 0.134332i | ||||
\(723\) | −10.6613 | + | 18.9494i | −0.396499 | + | 0.704737i | ||||
\(724\) | 14.7500 | + | 12.6645i | 0.548181 | + | 0.470672i | ||||
\(725\) | 52.4039 | 1.94623 | ||||||||
\(726\) | −7.41157 | − | 8.73564i | −0.275069 | − | 0.324210i | ||||
\(727\) | − | 40.0473i | − | 1.48527i | −0.669695 | − | 0.742636i | \(-0.733575\pi\) | ||
0.669695 | − | 0.742636i | \(-0.266425\pi\) | |||||||
\(728\) | −1.80681 | − | 3.25613i | −0.0669647 | − | 0.120680i | ||||
\(729\) | −26.9399 | + | 1.79978i | −0.997776 | + | 0.0666586i | ||||
\(730\) | 18.2174 | − | 49.1827i | 0.674258 | − | 1.82033i | ||||
\(731\) | −29.6956 | −1.09833 | ||||||||
\(732\) | 8.45861 | + | 23.2557i | 0.312639 | + | 0.859557i | ||||
\(733\) | −13.8789 | −0.512627 | −0.256314 | − | 0.966594i | \(-0.582508\pi\) | ||||
−0.256314 | + | 0.966594i | \(0.582508\pi\) | |||||||
\(734\) | −4.44682 | + | 12.0053i | −0.164135 | + | 0.443125i | ||||
\(735\) | −23.2965 | + | 41.4071i | −0.859303 | + | 1.52732i | ||||
\(736\) | −2.70098 | + | 26.9945i | −0.0995594 | + | 0.995032i | ||||
\(737\) | − | 10.3908i | − | 0.382750i | ||||||
\(738\) | −22.2369 | + | 4.30196i | −0.818550 | + | 0.158357i | ||||
\(739\) | 37.4827i | 1.37882i | 0.724369 | + | 0.689412i | \(0.242131\pi\) | ||||
−0.724369 | + | 0.689412i | \(0.757869\pi\) | |||||||
\(740\) | 16.6459 | − | 19.3871i | 0.611916 | − | 0.712685i | ||||
\(741\) | 19.9756 | − | 35.5045i | 0.733821 | − | 1.30429i | ||||
\(742\) | −0.385101 | − | 0.142643i | −0.0141375 | − | 0.00523657i | ||||
\(743\) | −3.58471 | −0.131510 | −0.0657552 | − | 0.997836i | \(-0.520946\pi\) | ||||
−0.0657552 | + | 0.997836i | \(0.520946\pi\) | |||||||
\(744\) | 0.0754714 | − | 12.8166i | 0.00276691 | − | 0.469879i | ||||
\(745\) | 82.6851 | 3.02935 | ||||||||
\(746\) | 33.0577 | + | 12.2447i | 1.21033 | + | 0.448310i | ||||
\(747\) | −16.6994 | + | 10.1430i | −0.611000 | + | 0.371115i | ||||
\(748\) | −10.2867 | + | 11.9807i | −0.376119 | + | 0.438058i | ||||
\(749\) | 4.92408 | 0.179922 | ||||||||
\(750\) | −42.3977 | + | 35.9714i | −1.54815 | + | 1.31349i | ||||
\(751\) | − | 31.3303i | − | 1.14326i | −0.820512 | − | 0.571630i | \(-0.806311\pi\) | ||
0.820512 | − | 0.571630i | \(-0.193689\pi\) | |||||||
\(752\) | −19.5836 | + | 2.99700i | −0.714142 | + | 0.109289i | ||||
\(753\) | −4.00937 | + | 7.12624i | −0.146109 | + | 0.259695i | ||||
\(754\) | 10.9985 | − | 29.6932i | 0.400540 | − | 1.08136i | ||||
\(755\) | − | 17.7368i | − | 0.645507i | ||||||
\(756\) | −2.32912 | − | 1.86855i | −0.0847092 | − | 0.0679585i | ||||
\(757\) | −23.5815 | −0.857085 | −0.428543 | − | 0.903522i | \(-0.640973\pi\) | ||||
−0.428543 | + | 0.903522i | \(0.640973\pi\) | |||||||
\(758\) | 20.4257 | + | 7.56574i | 0.741894 | + | 0.274800i | ||||
\(759\) | 8.31311 | − | 19.1620i | 0.301747 | − | 0.695537i | ||||
\(760\) | 50.3405 | − | 27.9336i | 1.82604 | − | 1.01326i | ||||
\(761\) | − | 33.9195i | − | 1.22958i | −0.788690 | − | 0.614791i | \(-0.789240\pi\) | ||
0.788690 | − | 0.614791i | \(-0.210760\pi\) | |||||||
\(762\) | −25.1876 | − | 29.6874i | −0.912452 | − | 1.07546i | ||||
\(763\) | − | 3.34309i | − | 0.121028i | ||||||
\(764\) | −34.8812 | − | 29.9492i | −1.26196 | − | 1.08352i | ||||
\(765\) | −31.9251 | + | 19.3909i | −1.15425 | + | 0.701081i | ||||
\(766\) | −8.22209 | − | 3.04549i | −0.297076 | − | 0.110038i | ||||
\(767\) | − | 32.4680i | − | 1.17235i | ||||||
\(768\) | −27.1111 | − | 5.74355i | −0.978287 | − | 0.207252i | ||||
\(769\) | − | 33.4521i | − | 1.20631i | −0.797623 | − | 0.603156i | \(-0.793910\pi\) | ||
0.797623 | − | 0.603156i | \(-0.206090\pi\) | |||||||
\(770\) | −1.40735 | + | 3.79950i | −0.0507173 | + | 0.136924i | ||||
\(771\) | 8.42761 | − | 14.9792i | 0.303513 | − | 0.539463i | ||||
\(772\) | −4.57259 | − | 3.92606i | −0.164571 | − | 0.141302i | ||||
\(773\) | − | 8.93447i | − | 0.321350i | −0.987007 | − | 0.160675i | \(-0.948633\pi\) | ||
0.987007 | − | 0.160675i | \(-0.0513672\pi\) | |||||||
\(774\) | 7.62129 | + | 39.3945i | 0.273941 | + | 1.41600i | ||||
\(775\) | −28.0572 | −1.00784 | ||||||||
\(776\) | −43.3557 | + | 24.0578i | −1.55638 | + | 0.863625i | ||||
\(777\) | 0.786252 | − | 1.39748i | 0.0282066 | − | 0.0501344i | ||||
\(778\) | 8.36513 | − | 22.5838i | 0.299905 | − | 0.809670i | ||||
\(779\) | − | 27.4025i | − | 0.981797i | ||||||
\(780\) | 21.5145 | + | 59.1511i | 0.770344 | + | 2.11795i | ||||
\(781\) | 19.7967 | 0.708383 | ||||||||
\(782\) | 20.6254 | + | 5.30130i | 0.737561 | + | 0.189574i | ||||
\(783\) | −0.846728 | − | 25.3767i | −0.0302596 | − | 0.906888i | ||||
\(784\) | 4.18573 | + | 27.3513i | 0.149490 | + | 0.976833i | ||||
\(785\) | 54.6649i | 1.95107i | ||||||||
\(786\) | 5.73443 | + | 6.75889i | 0.204540 | + | 0.241081i | ||||
\(787\) | 53.3309 | 1.90104 | 0.950521 | − | 0.310661i | \(-0.100550\pi\) | ||||
0.950521 | + | 0.310661i | \(0.100550\pi\) | |||||||
\(788\) | −36.7242 | − | 31.5316i | −1.30825 | − | 1.12327i | ||||
\(789\) | 30.2023 | + | 16.9924i | 1.07523 | + | 0.604946i | ||||
\(790\) | 73.5936 | + | 27.2593i | 2.61834 | + | 0.969843i | ||||
\(791\) | 4.26712i | 0.151721i | ||||||||
\(792\) | 18.5338 | + | 10.5716i | 0.658569 | + | 0.375647i | ||||
\(793\) | − | 32.7329i | − | 1.16238i | ||||||
\(794\) | −0.0743966 | + | 0.200853i | −0.00264024 | + | 0.00712800i | ||||
\(795\) | 6.04960 | + | 3.40363i | 0.214557 | + | 0.120714i | ||||
\(796\) | −15.4890 | + | 18.0397i | −0.548992 | + | 0.639399i | ||||
\(797\) | 27.1714i | 0.962460i | 0.876594 | + | 0.481230i | \(0.159810\pi\) | ||||
−0.876594 | + | 0.481230i | \(0.840190\pi\) | |||||||
\(798\) | 2.75478 | − | 2.33724i | 0.0975182 | − | 0.0827372i | ||||
\(799\) | 15.5516i | 0.550175i | ||||||||
\(800\) | −12.2235 | + | 59.4217i | −0.432165 | + | 2.10087i | ||||
\(801\) | 7.60630 | + | 12.5230i | 0.268756 | + | 0.442477i | ||||
\(802\) | 25.6478 | + | 9.50002i | 0.905655 | + | 0.335458i | ||||
\(803\) | 23.5176i | 0.829919i | ||||||||
\(804\) | −4.89289 | − | 13.4523i | −0.172559 | − | 0.474426i | ||||
\(805\) | 5.43519 | − | 0.562651i | 0.191565 | − | 0.0198308i | ||||
\(806\) | −5.88860 | + | 15.8978i | −0.207417 | + | 0.559976i | ||||
\(807\) | 25.8164 | + | 14.5248i | 0.908780 | + | 0.511298i | ||||
\(808\) | −16.2133 | − | 29.2188i | −0.570382 | − | 1.02791i | ||||
\(809\) | − | 16.9102i | − | 0.594532i | −0.954795 | − | 0.297266i | \(-0.903925\pi\) | ||
0.954795 | − | 0.297266i | \(-0.0960747\pi\) | |||||||
\(810\) | 33.9177 | + | 37.3755i | 1.19175 | + | 1.31324i | ||||
\(811\) | 9.29547i | 0.326408i | 0.986592 | + | 0.163204i | \(0.0521829\pi\) | ||||
−0.986592 | + | 0.163204i | \(0.947817\pi\) | |||||||
\(812\) | 1.82925 | − | 2.13048i | 0.0641940 | − | 0.0747654i | ||||
\(813\) | 13.7590 | + | 7.74107i | 0.482548 | + | 0.271491i | ||||
\(814\) | −3.97978 | + | 10.7444i | −0.139491 | + | 0.376592i | ||||
\(815\) | −61.5084 | −2.15454 | ||||||||
\(816\) | −7.67598 | + | 20.3545i | −0.268713 | + | 0.712551i | ||||
\(817\) | −48.5459 | −1.69841 | ||||||||
\(818\) | 15.5768 | + | 5.76971i | 0.544631 | + | 0.201733i | ||||
\(819\) | 2.05043 | + | 3.37581i | 0.0716478 | + | 0.117960i | ||||
\(820\) | 32.1223 | + | 27.5804i | 1.12176 | + | 0.963149i | ||||
\(821\) | −22.0273 | −0.768759 | −0.384380 | − | 0.923175i | \(-0.625585\pi\) | ||||
−0.384380 | + | 0.923175i | \(0.625585\pi\) | |||||||
\(822\) | 15.5601 | + | 18.3399i | 0.542720 | + | 0.639678i | ||||
\(823\) | 35.3900 | 1.23362 | 0.616808 | − | 0.787113i | \(-0.288425\pi\) | ||||
0.616808 | + | 0.787113i | \(0.288425\pi\) | |||||||
\(824\) | −3.05442 | + | 1.69488i | −0.106406 | + | 0.0590439i | ||||
\(825\) | 22.9030 | − | 40.7077i | 0.797379 | − | 1.41726i | ||||
\(826\) | 1.00010 | − | 2.70002i | 0.0347978 | − | 0.0939456i | ||||
\(827\) | − | 6.38502i | − | 0.222029i | −0.993819 | − | 0.111014i | \(-0.964590\pi\) | ||
0.993819 | − | 0.111014i | \(-0.0354100\pi\) | |||||||
\(828\) | 1.73931 | − | 28.7224i | 0.0604452 | − | 0.998172i | ||||
\(829\) | 21.0446i | 0.730908i | 0.930829 | + | 0.365454i | \(0.119086\pi\) | ||||
−0.930829 | + | 0.365454i | \(0.880914\pi\) | |||||||
\(830\) | 34.2493 | + | 12.6861i | 1.18881 | + | 0.440340i | ||||
\(831\) | 16.3479 | − | 29.0566i | 0.567101 | − | 1.00796i | ||||
\(832\) | 31.1042 | + | 19.3974i | 1.07834 | + | 0.672484i | ||||
\(833\) | 21.7200 | 0.752553 | ||||||||
\(834\) | 7.50419 | − | 6.36677i | 0.259849 | − | 0.220463i | ||||
\(835\) | 18.7105 | 0.647504 | ||||||||
\(836\) | −16.8165 | + | 19.5859i | −0.581612 | + | 0.677391i | ||||
\(837\) | 0.453340 | + | 13.5867i | 0.0156697 | + | 0.469626i | ||||
\(838\) | 2.66629 | − | 7.19834i | 0.0921055 | − | 0.248663i | ||||
\(839\) | 9.43913 | 0.325875 | 0.162937 | − | 0.986636i | \(-0.447903\pi\) | ||||
0.162937 | + | 0.986636i | \(0.447903\pi\) | |||||||
\(840\) | −0.0328680 | + | 5.58167i | −0.00113405 | + | 0.192586i | ||||
\(841\) | −5.12253 | −0.176639 | ||||||||
\(842\) | −22.3049 | − | 8.26180i | −0.768677 | − | 0.284721i | ||||
\(843\) | −19.4287 | − | 10.9310i | −0.669161 | − | 0.376483i | ||||
\(844\) | −16.1346 | + | 18.7916i | −0.555375 | + | 0.646833i | ||||
\(845\) | − | 31.7063i | − | 1.09073i | ||||||
\(846\) | 20.6309 | − | 3.99127i | 0.709304 | − | 0.137223i | ||||
\(847\) | 1.34382i | 0.0461743i | ||||||||
\(848\) | 3.99605 | − | 0.611538i | 0.137225 | − | 0.0210003i | ||||
\(849\) | −23.6915 | − | 13.3293i | −0.813092 | − | 0.457462i | ||||
\(850\) | 44.6561 | + | 16.5408i | 1.53169 | + | 0.567344i | ||||
\(851\) | 15.3700 | − | 1.59110i | 0.526875 | − | 0.0545421i | ||||
\(852\) | 25.6295 | − | 9.32202i | 0.878054 | − | 0.319367i | ||||
\(853\) | 1.79992i | 0.0616279i | 0.999525 | + | 0.0308140i | \(0.00980994\pi\) | ||||
−0.999525 | + | 0.0308140i | \(0.990190\pi\) | |||||||
\(854\) | 1.00826 | − | 2.72205i | 0.0345018 | − | 0.0931465i | ||||
\(855\) | −52.1906 | + | 31.7000i | −1.78488 | + | 1.08412i | ||||
\(856\) | −42.3840 | + | 23.5186i | −1.44866 | + | 0.803849i | ||||
\(857\) | − | 53.5766i | − | 1.83014i | −0.403292 | − | 0.915072i | \(-0.632134\pi\) | ||
0.403292 | − | 0.915072i | \(-0.367866\pi\) | |||||||
\(858\) | −18.2590 | − | 21.5210i | −0.623352 | − | 0.734714i | ||||
\(859\) | − | 56.7146i | − | 1.93508i | −0.252723 | − | 0.967539i | \(-0.581326\pi\) | ||
0.252723 | − | 0.967539i | \(-0.418674\pi\) | |||||||
\(860\) | 48.8610 | − | 56.9073i | 1.66615 | − | 1.94052i | ||||
\(861\) | 2.31547 | + | 1.30273i | 0.0789110 | + | 0.0443969i | ||||
\(862\) | 14.6499 | + | 5.42636i | 0.498976 | + | 0.184822i | ||||
\(863\) | − | 53.0626i | − | 1.80627i | −0.429355 | − | 0.903136i | \(-0.641259\pi\) | ||
0.429355 | − | 0.903136i | \(-0.358741\pi\) | |||||||
\(864\) | 28.9725 | + | 4.95911i | 0.985665 | + | 0.168712i | ||||
\(865\) | 19.1947i | 0.652639i | ||||||||
\(866\) | 3.80773 | − | 10.2799i | 0.129392 | − | 0.349327i | ||||
\(867\) | −10.7797 | − | 6.06490i | −0.366099 | − | 0.205975i | ||||
\(868\) | −0.979384 | + | 1.14067i | −0.0332425 | + | 0.0387168i | ||||
\(869\) | −35.1901 | −1.19374 | ||||||||
\(870\) | −36.1920 | + | 30.7063i | −1.22702 | + | 1.04104i | ||||
\(871\) | 18.9344i | 0.641567i | ||||||||
\(872\) | 15.9674 | + | 28.7756i | 0.540724 | + | 0.974465i | ||||
\(873\) | 44.9492 | − | 27.3016i | 1.52130 | − | 0.924020i | ||||
\(874\) | 33.7180 | + | 8.66648i | 1.14053 | + | 0.293148i | ||||
\(875\) | 6.52213 | 0.220488 | ||||||||
\(876\) | 11.0741 | + | 30.4467i | 0.374160 | + | 1.02870i | ||||
\(877\) | 35.9210i | 1.21296i | 0.795097 | + | 0.606482i | \(0.207420\pi\) | ||||
−0.795097 | + | 0.606482i | \(0.792580\pi\) | |||||||
\(878\) | 34.5030 | + | 12.7800i | 1.16442 | + | 0.431305i | ||||
\(879\) | 8.95502 | − | 15.9166i | 0.302045 | − | 0.536855i | ||||
\(880\) | −6.03359 | − | 39.4260i | −0.203392 | − | 1.32905i | ||||
\(881\) | 4.80430 | 0.161861 | 0.0809305 | − | 0.996720i | \(-0.474211\pi\) | ||||
0.0809305 | + | 0.996720i | \(0.474211\pi\) | |||||||
\(882\) | −5.57437 | − | 28.8140i | −0.187699 | − | 0.970217i | ||||
\(883\) | − | 25.0771i | − | 0.843911i | −0.906617 | − | 0.421955i | \(-0.861344\pi\) | ||
0.906617 | − | 0.421955i | \(-0.138656\pi\) | |||||||
\(884\) | 18.7447 | − | 21.8315i | 0.630453 | − | 0.734274i | ||||
\(885\) | −23.8635 | + | 42.4150i | −0.802164 | + | 1.42576i | ||||
\(886\) | 27.4957 | + | 10.1845i | 0.923736 | + | 0.342155i | ||||
\(887\) | 28.7995i | 0.966993i | 0.875346 | + | 0.483496i | \(0.160633\pi\) | ||||
−0.875346 | + | 0.483496i | \(0.839367\pi\) | |||||||
\(888\) | −0.0929460 | + | 15.7842i | −0.00311906 | + | 0.529682i | ||||
\(889\) | 4.56688i | 0.153168i | ||||||||
\(890\) | 9.51333 | − | 25.6837i | 0.318888 | − | 0.860920i | ||||
\(891\) | −20.0828 | − | 10.4330i | −0.672799 | − | 0.349520i | ||||
\(892\) | −6.75760 | − | 5.80212i | −0.226261 | − | 0.194269i | ||||
\(893\) | 25.4235i | 0.850764i | ||||||||
\(894\) | −38.9470 | + | 33.0437i | −1.30258 | + | 1.10515i | ||||
\(895\) | − | 30.5129i | − | 1.01993i | ||||||
\(896\) | 1.98911 | + | 2.57116i | 0.0664516 | + | 0.0858965i | ||||
\(897\) | −15.1484 | + | 34.9175i | −0.505789 | + | 1.16586i | ||||
\(898\) | −11.2447 | + | 30.3581i | −0.375241 | + | 1.01306i | ||||
\(899\) | −12.7841 | −0.426372 | ||||||||
\(900\) | 10.4823 | − | 63.4864i | 0.349410 | − | 2.11621i | ||||
\(901\) | − | 3.17330i | − | 0.105718i | ||||||
\(902\) | −17.8023 | − | 6.59403i | −0.592752 | − | 0.219557i | ||||
\(903\) | 2.30790 | − | 4.10205i | 0.0768020 | − | 0.136508i | ||||
\(904\) | −20.3808 | − | 36.7292i | −0.677856 | − | 1.22160i | ||||
\(905\) | 38.5456i | 1.28130i | ||||||||
\(906\) | 7.08821 | + | 8.35451i | 0.235490 | + | 0.277560i | ||||
\(907\) | −22.7801 | −0.756402 | −0.378201 | − | 0.925723i | \(-0.623457\pi\) | ||||
−0.378201 | + | 0.925723i | \(0.623457\pi\) | |||||||
\(908\) | 20.1724 | − | 23.4944i | 0.669445 | − | 0.779688i | ||||
\(909\) | 18.3994 | + | 30.2926i | 0.610270 | + | 1.00474i | ||||
\(910\) | 2.56450 | − | 6.92354i | 0.0850125 | − | 0.229513i | ||||
\(911\) | −7.35787 | −0.243777 | −0.121889 | − | 0.992544i | \(-0.538895\pi\) | ||||
−0.121889 | + | 0.992544i | \(0.538895\pi\) | |||||||
\(912\) | −12.5486 | + | 33.2753i | −0.415525 | + | 1.10185i | ||||
\(913\) | −16.3769 | −0.541998 | ||||||||
\(914\) | −7.59948 | + | 20.5168i | −0.251369 | + | 0.678635i | ||||
\(915\) | −24.0582 | + | 42.7610i | −0.795340 | + | 1.41364i | ||||
\(916\) | 38.5657 | + | 33.1128i | 1.27425 | + | 1.09408i | ||||
\(917\) | − | 1.03973i | − | 0.0343350i | ||||||
\(918\) | 7.28834 | − | 21.8920i | 0.240551 | − | 0.722544i | ||||
\(919\) | − | 48.0916i | − | 1.58640i | −0.608964 | − | 0.793198i | \(-0.708415\pi\) | ||
0.608964 | − | 0.793198i | \(-0.291585\pi\) | |||||||
\(920\) | −44.0961 | + | 30.8028i | −1.45380 | + | 1.01554i | ||||
\(921\) | 14.8184 | − | 26.3381i | 0.488281 | − | 0.867870i | ||||
\(922\) | 34.5060 | + | 12.7811i | 1.13639 | + | 0.420924i | ||||
\(923\) | −36.0741 | −1.18739 | ||||||||
\(924\) | −0.855507 | − | 2.35209i | −0.0281441 | − | 0.0773782i | ||||
\(925\) | 34.5536 | 1.13611 | ||||||||
\(926\) | 6.50663 | + | 2.41008i | 0.213821 | + | 0.0792001i | ||||
\(927\) | 3.16668 | − | 1.92341i | 0.104007 | − | 0.0631730i | ||||
\(928\) | −5.56953 | + | 27.0751i | −0.182829 | + | 0.888783i | ||||
\(929\) | − | 31.4154i | − | 1.03071i | −0.856978 | − | 0.515353i | \(-0.827661\pi\) | ||
0.856978 | − | 0.515353i | \(-0.172339\pi\) | |||||||
\(930\) | 19.3773 | − | 16.4403i | 0.635407 | − | 0.539097i | ||||
\(931\) | 35.5075 | 1.16371 | ||||||||
\(932\) | −31.1243 | + | 36.2498i | −1.01951 | + | 1.18740i | ||||
\(933\) | −19.1658 | + | 34.0653i | −0.627461 | + | 1.11525i | ||||
\(934\) | −20.6481 | + | 55.7450i | −0.675627 | + | 1.82403i | ||||
\(935\) | −31.3086 | −1.02390 | ||||||||
\(936\) | −33.7727 | − | 19.2639i | −1.10390 | − | 0.629661i | ||||
\(937\) | 25.0673i | 0.818914i | 0.912329 | + | 0.409457i | \(0.134282\pi\) | ||||
−0.912329 | + | 0.409457i | \(0.865718\pi\) | |||||||
\(938\) | −0.583226 | + | 1.57457i | −0.0190430 | + | 0.0514116i | ||||
\(939\) | −17.7974 | + | 31.6331i | −0.580798 | + | 1.03231i | ||||
\(940\) | −29.8024 | − | 25.5885i | −0.972046 | − | 0.834605i | ||||
\(941\) | 12.8371i | 0.418479i | 0.977864 | + | 0.209239i | \(0.0670988\pi\) | ||||
−0.977864 | + | 0.209239i | \(0.932901\pi\) | |||||||
\(942\) | −21.8459 | − | 25.7487i | −0.711778 | − | 0.838938i | ||||
\(943\) | 2.63626 | + | 25.4663i | 0.0858486 | + | 0.829296i | ||||
\(944\) | 4.28762 | + | 28.0171i | 0.139550 | + | 0.911879i | ||||
\(945\) | −0.197431 | − | 5.91706i | −0.00642243 | − | 0.192482i | ||||
\(946\) | −11.6819 | + | 31.5383i | −0.379811 | + | 1.02540i | ||||
\(947\) | −20.8801 | −0.678512 | −0.339256 | − | 0.940694i | \(-0.610175\pi\) | ||||
−0.339256 | + | 0.940694i | \(0.610175\pi\) | |||||||
\(948\) | −45.5584 | + | 16.5706i | −1.47967 | + | 0.538187i | ||||
\(949\) | − | 42.8544i | − | 1.39111i | ||||||
\(950\) | 73.0031 | + | 27.0406i | 2.36853 | + | 0.877313i | ||||
\(951\) | 28.3107 | + | 15.9282i | 0.918038 | + | 0.516507i | ||||
\(952\) | 2.23126 | − | 1.23811i | 0.0723156 | − | 0.0401275i | ||||
\(953\) | −8.76117 | −0.283802 | −0.141901 | − | 0.989881i | \(-0.545322\pi\) | ||||
−0.141901 | + | 0.989881i | \(0.545322\pi\) | |||||||
\(954\) | −4.20974 | + | 0.814420i | −0.136295 | + | 0.0263678i | ||||
\(955\) | − | 91.1534i | − | 2.94965i | ||||||
\(956\) | 0.563210 | − | 0.655958i | 0.0182155 | − | 0.0212152i | ||||
\(957\) | 10.4356 | − | 18.5482i | 0.337334 | − | 0.599577i | ||||
\(958\) | −14.2239 | − | 5.26859i | −0.459554 | − | 0.170220i | ||||
\(959\) | − | 2.82127i | − | 0.0911034i | ||||||
\(960\) | −26.3765 | − | 48.2012i | −0.851297 | − | 1.55569i | ||||
\(961\) | −24.1554 | −0.779206 | ||||||||
\(962\) | 7.25205 | − | 19.5788i | 0.233816 | − | 0.631246i | ||||
\(963\) | 43.9418 | − | 26.6897i | 1.41600 | − | 0.860065i | ||||
\(964\) | −16.3550 | + | 19.0483i | −0.526760 | + | 0.613506i | ||||
\(965\) | − | 11.9493i | − | 0.384663i | ||||||
\(966\) | −2.33528 | + | 2.43711i | −0.0751362 | + | 0.0784127i | ||||
\(967\) | −41.0937 | −1.32148 | −0.660742 | − | 0.750613i | \(-0.729758\pi\) | ||||
−0.660742 | + | 0.750613i | \(0.729758\pi\) | |||||||
\(968\) | −6.41842 | − | 11.5669i | −0.206296 | − | 0.371776i | ||||
\(969\) | 24.3294 | + | 13.6882i | 0.781574 | + | 0.439730i | ||||
\(970\) | −92.1876 | − | 34.1466i | −2.95997 | − | 1.09638i | ||||
\(971\) | 33.2061i | 1.06563i | 0.846231 | + | 0.532817i | \(0.178867\pi\) | ||||
−0.846231 | + | 0.532817i | \(0.821133\pi\) | |||||||
\(972\) | −30.9127 | − | 4.05026i | −0.991525 | − | 0.129912i | ||||
\(973\) | −1.15439 | −0.0370079 | ||||||||
\(974\) | −30.8862 | − | 11.4404i | −0.989659 | − | 0.366573i | ||||
\(975\) | −41.7344 | + | 74.1786i | −1.33657 | + | 2.37562i | ||||
\(976\) | 4.32260 | + | 28.2457i | 0.138363 | + | 0.904122i | ||||
\(977\) | 16.4427 | 0.526049 | 0.263025 | − | 0.964789i | \(-0.415280\pi\) | ||||
0.263025 | + | 0.964789i | \(0.415280\pi\) | |||||||
\(978\) | 28.9722 | − | 24.5808i | 0.926428 | − | 0.786008i | ||||
\(979\) | 12.2811i | 0.392507i | ||||||||
\(980\) | −35.7380 | + | 41.6232i | −1.14161 | + | 1.32961i | ||||
\(981\) | −18.1204 | − | 29.8332i | −0.578538 | − | 0.952501i | ||||
\(982\) | −15.4705 | − | 5.73033i | −0.493684 | − | 0.182862i | ||||
\(983\) | −14.9568 | −0.477049 | −0.238525 | − | 0.971136i | \(-0.576664\pi\) | ||||
−0.238525 | + | 0.971136i | \(0.576664\pi\) | |||||||
\(984\) | −26.1525 | − | 0.154001i | −0.833713 | − | 0.00490937i | ||||
\(985\) | − | 95.9696i | − | 3.05785i | ||||||
\(986\) | 20.3472 | + | 7.53668i | 0.647988 | + | 0.240017i | ||||
\(987\) | −2.14824 | − | 1.20865i | −0.0683793 | − | 0.0384716i | ||||
\(988\) | 30.6436 | − | 35.6899i | 0.974901 | − | 1.13545i | ||||
\(989\) | 45.1156 | − | 4.67036i | 1.43459 | − | 0.148509i | ||||
\(990\) | 8.03526 | + | 41.5343i | 0.255377 | + | 1.32005i | ||||
\(991\) | 0.819062 | 0.0260184 | 0.0130092 | − | 0.999915i | \(-0.495859\pi\) | ||||
0.0130092 | + | 0.999915i | \(0.495859\pi\) | |||||||
\(992\) | 2.98194 | − | 14.4961i | 0.0946768 | − | 0.460250i | ||||
\(993\) | 17.0625 | − | 30.3269i | 0.541463 | − | 0.962395i | ||||
\(994\) | −2.99990 | − | 1.11117i | −0.0951510 | − | 0.0352442i | ||||
\(995\) | −47.1422 | −1.49451 | ||||||||
\(996\) | −21.2022 | + | 7.71169i | −0.671817 | + | 0.244354i | ||||
\(997\) | 44.2375i | 1.40102i | 0.713644 | + | 0.700508i | \(0.247043\pi\) | ||||
−0.713644 | + | 0.700508i | \(0.752957\pi\) | |||||||
\(998\) | −3.41653 | + | 9.22381i | −0.108148 | + | 0.291975i | ||||
\(999\) | −0.558307 | − | 16.7326i | −0.0176641 | − | 0.529396i |
(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 | 552.2.b.c.413.10 | yes | 80 | |
3.2 | odd | 2 | inner | 552.2.b.c.413.71 | yes | 80 | |
4.3 | odd | 2 | 2208.2.b.c.689.14 | 80 | |||
8.3 | odd | 2 | 2208.2.b.c.689.67 | 80 | |||
8.5 | even | 2 | inner | 552.2.b.c.413.69 | yes | 80 | |
12.11 | even | 2 | 2208.2.b.c.689.65 | 80 | |||
23.22 | odd | 2 | inner | 552.2.b.c.413.9 | ✓ | 80 | |
24.5 | odd | 2 | inner | 552.2.b.c.413.12 | yes | 80 | |
24.11 | even | 2 | 2208.2.b.c.689.16 | 80 | |||
69.68 | even | 2 | inner | 552.2.b.c.413.72 | yes | 80 | |
92.91 | even | 2 | 2208.2.b.c.689.13 | 80 | |||
184.45 | odd | 2 | inner | 552.2.b.c.413.70 | yes | 80 | |
184.91 | even | 2 | 2208.2.b.c.689.68 | 80 | |||
276.275 | odd | 2 | 2208.2.b.c.689.66 | 80 | |||
552.275 | odd | 2 | 2208.2.b.c.689.15 | 80 | |||
552.413 | even | 2 | inner | 552.2.b.c.413.11 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.b.c.413.9 | ✓ | 80 | 23.22 | odd | 2 | inner | |
552.2.b.c.413.10 | yes | 80 | 1.1 | even | 1 | trivial | |
552.2.b.c.413.11 | yes | 80 | 552.413 | even | 2 | inner | |
552.2.b.c.413.12 | yes | 80 | 24.5 | odd | 2 | inner | |
552.2.b.c.413.69 | yes | 80 | 8.5 | even | 2 | inner | |
552.2.b.c.413.70 | yes | 80 | 184.45 | odd | 2 | inner | |
552.2.b.c.413.71 | yes | 80 | 3.2 | odd | 2 | inner | |
552.2.b.c.413.72 | yes | 80 | 69.68 | even | 2 | inner | |
2208.2.b.c.689.13 | 80 | 92.91 | even | 2 | |||
2208.2.b.c.689.14 | 80 | 4.3 | odd | 2 | |||
2208.2.b.c.689.15 | 80 | 552.275 | odd | 2 | |||
2208.2.b.c.689.16 | 80 | 24.11 | even | 2 | |||
2208.2.b.c.689.65 | 80 | 12.11 | even | 2 | |||
2208.2.b.c.689.66 | 80 | 276.275 | odd | 2 | |||
2208.2.b.c.689.67 | 80 | 8.3 | odd | 2 | |||
2208.2.b.c.689.68 | 80 | 184.91 | even | 2 |