Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), degree \(4\), 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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.343361479062744140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 245.4 | ||
Root | \(-1.70149 + 0.323920i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.245 |
Dual form | 363.3.h.m.323.4 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48377 | + | 2.04223i | 0.741884 | + | 1.02112i | 0.998508 | + | 0.0546047i | \(0.0173899\pi\) |
−0.256624 | + | 0.966511i | \(0.582610\pi\) | |||||||
\(3\) | 0.440460 | − | 2.96749i | 0.146820 | − | 0.989163i | ||||
\(4\) | −0.733075 | + | 2.25617i | −0.183269 | + | 0.564043i | ||||
\(5\) | −0.465695 | + | 0.640974i | −0.0931389 | + | 0.128195i | −0.853043 | − | 0.521840i | \(-0.825246\pi\) |
0.759904 | + | 0.650035i | \(0.225246\pi\) | |||||||
\(6\) | 6.71384 | − | 3.50355i | 1.11897 | − | 0.583924i | ||||
\(7\) | 2.08418 | − | 6.41446i | 0.297741 | − | 0.916351i | −0.684546 | − | 0.728969i | \(-0.740000\pi\) |
0.982287 | − | 0.187382i | \(-0.0600003\pi\) | |||||||
\(8\) | 3.90781 | − | 1.26972i | 0.488476 | − | 0.158715i | ||||
\(9\) | −8.61199 | − | 2.61412i | −0.956888 | − | 0.290458i | ||||
\(10\) | −2.00000 | −0.200000 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.37228 | + | 3.16915i | 0.531023 | + | 0.264096i | ||||
\(13\) | −7.67686 | + | 5.57757i | −0.590528 | + | 0.429044i | −0.842504 | − | 0.538690i | \(-0.818920\pi\) |
0.251976 | + | 0.967733i | \(0.418920\pi\) | |||||||
\(14\) | 16.1923 | − | 5.26119i | 1.15659 | − | 0.375799i | ||||
\(15\) | 1.69696 | + | 1.66427i | 0.113131 | + | 0.110951i | ||||
\(16\) | 16.0682 | + | 11.6742i | 1.00426 | + | 0.729640i | ||||
\(17\) | 17.2206 | − | 23.7021i | 1.01297 | − | 1.39424i | 0.0959609 | − | 0.995385i | \(-0.469408\pi\) |
0.917014 | − | 0.398855i | \(-0.130592\pi\) | |||||||
\(18\) | −7.43955 | − | 21.4664i | −0.413309 | − | 1.19258i | ||||
\(19\) | −8.10666 | − | 24.9497i | −0.426666 | − | 1.31314i | −0.901390 | − | 0.433008i | \(-0.857452\pi\) |
0.474724 | − | 0.880135i | \(-0.342548\pi\) | |||||||
\(20\) | −1.10476 | − | 1.52057i | −0.0552379 | − | 0.0760285i | ||||
\(21\) | −18.1168 | − | 9.01011i | −0.862707 | − | 0.429053i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 26.9205i | − | 1.17046i | −0.810868 | − | 0.585229i | \(-0.801005\pi\) | ||
0.810868 | − | 0.585229i | \(-0.198995\pi\) | |||||||
\(24\) | −2.04666 | − | 12.1556i | −0.0852774 | − | 0.506485i | ||||
\(25\) | 7.53145 | + | 23.1794i | 0.301258 | + | 0.927177i | ||||
\(26\) | −22.7814 | − | 7.40212i | −0.876207 | − | 0.284697i | ||||
\(27\) | −11.5506 | + | 24.4046i | −0.427801 | + | 0.903873i | ||||
\(28\) | 12.9443 | + | 9.40456i | 0.462295 | + | 0.335877i | ||||
\(29\) | 24.6733 | + | 8.01686i | 0.850805 | + | 0.276443i | 0.701783 | − | 0.712391i | \(-0.252388\pi\) |
0.149022 | + | 0.988834i | \(0.452388\pi\) | |||||||
\(30\) | −0.880920 | + | 5.93498i | −0.0293640 | + | 0.197833i | ||||
\(31\) | 2.31493 | − | 1.68189i | 0.0746751 | − | 0.0542546i | −0.549821 | − | 0.835282i | \(-0.685304\pi\) |
0.624496 | + | 0.781028i | \(0.285304\pi\) | |||||||
\(32\) | 33.7013i | 1.05316i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 73.9565 | 2.17519 | ||||||||
\(35\) | 3.14091 | + | 4.32309i | 0.0897402 | + | 0.123517i | ||||
\(36\) | 12.2112 | − | 17.5138i | 0.339199 | − | 0.486494i | ||||
\(37\) | −0.739796 | + | 2.27686i | −0.0199945 | + | 0.0615367i | −0.960556 | − | 0.278087i | \(-0.910300\pi\) |
0.940561 | + | 0.339624i | \(0.110300\pi\) | |||||||
\(38\) | 38.9247 | − | 53.5753i | 1.02433 | − | 1.40988i | ||||
\(39\) | 13.1700 | + | 25.2377i | 0.337693 | + | 0.647121i | ||||
\(40\) | −1.00599 | + | 3.09610i | −0.0251496 | + | 0.0774026i | ||||
\(41\) | −16.7533 | + | 5.44348i | −0.408617 | + | 0.132768i | −0.506111 | − | 0.862468i | \(-0.668917\pi\) |
0.0974939 | + | 0.995236i | \(0.468917\pi\) | |||||||
\(42\) | −8.48047 | − | 50.3677i | −0.201916 | − | 1.19923i | ||||
\(43\) | 12.5109 | 0.290951 | 0.145475 | − | 0.989362i | \(-0.453529\pi\) | ||||
0.145475 | + | 0.989362i | \(0.453529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.68614 | − | 4.30268i | 0.126359 | − | 0.0956150i | ||||
\(46\) | 54.9780 | − | 39.9438i | 1.19517 | − | 0.868344i | ||||
\(47\) | −39.6391 | + | 12.8795i | −0.843385 | + | 0.274032i | −0.698673 | − | 0.715441i | \(-0.746226\pi\) |
−0.144712 | + | 0.989474i | \(0.546226\pi\) | |||||||
\(48\) | 41.7206 | − | 42.5402i | 0.869179 | − | 0.886255i | ||||
\(49\) | 2.84036 | + | 2.06364i | 0.0579665 | + | 0.0421151i | ||||
\(50\) | −36.1628 | + | 49.7739i | −0.723256 | + | 0.995477i | ||||
\(51\) | −62.7507 | − | 61.5417i | −1.23041 | − | 1.20670i | ||||
\(52\) | −6.95624 | − | 21.4091i | −0.133774 | − | 0.411714i | ||||
\(53\) | 52.6576 | + | 72.4770i | 0.993541 | + | 1.36749i | 0.929206 | + | 0.369563i | \(0.120493\pi\) |
0.0643348 | + | 0.997928i | \(0.479507\pi\) | |||||||
\(54\) | −66.9783 | + | 12.6217i | −1.24034 | + | 0.233735i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 27.7128i | − | 0.494872i | ||||||
\(57\) | −77.6087 | + | 13.0671i | −1.36156 | + | 0.229247i | ||||
\(58\) | 20.2373 | + | 62.2839i | 0.348918 | + | 1.07386i | ||||
\(59\) | −14.0362 | − | 4.56063i | −0.237901 | − | 0.0772988i | 0.187640 | − | 0.982238i | \(-0.439916\pi\) |
−0.425541 | + | 0.904939i | \(0.639916\pi\) | |||||||
\(60\) | −4.99888 | + | 2.60861i | −0.0833146 | + | 0.0434768i | ||||
\(61\) | 51.3286 | + | 37.2924i | 0.841452 | + | 0.611351i | 0.922776 | − | 0.385337i | \(-0.125915\pi\) |
−0.0813237 | + | 0.996688i | \(0.525915\pi\) | |||||||
\(62\) | 6.86963 | + | 2.23208i | 0.110800 | + | 0.0360013i | ||||
\(63\) | −34.7172 | + | 49.7930i | −0.551066 | + | 0.790364i | ||||
\(64\) | −4.55292 | + | 3.30789i | −0.0711394 | + | 0.0516858i | ||||
\(65\) | − | 7.51811i | − | 0.115663i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63.3288 | −0.945206 | −0.472603 | − | 0.881276i | \(-0.656685\pi\) | ||||
−0.472603 | + | 0.881276i | \(0.656685\pi\) | |||||||
\(68\) | 40.8520 | + | 56.2280i | 0.600765 | + | 0.826883i | ||||
\(69\) | −79.8864 | − | 11.8574i | −1.15777 | − | 0.171847i | ||||
\(70\) | −4.16837 | + | 12.8289i | −0.0595481 | + | 0.183270i | ||||
\(71\) | 2.67521 | − | 3.68211i | 0.0376790 | − | 0.0518607i | −0.789762 | − | 0.613414i | \(-0.789796\pi\) |
0.827441 | + | 0.561553i | \(0.189796\pi\) | |||||||
\(72\) | −36.9732 | + | 0.719359i | −0.513517 | + | 0.00999110i | ||||
\(73\) | −16.6147 | + | 51.1348i | −0.227599 | + | 0.700477i | 0.770419 | + | 0.637538i | \(0.220047\pi\) |
−0.998017 | + | 0.0629385i | \(0.979953\pi\) | |||||||
\(74\) | −5.74756 | + | 1.86750i | −0.0776697 | + | 0.0252364i | ||||
\(75\) | 72.1020 | − | 12.1399i | 0.961360 | − | 0.161865i | ||||
\(76\) | 62.2337 | 0.818864 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.0000 | + | 64.3432i | −0.410256 | + | 0.824912i | ||||
\(79\) | −45.0455 | + | 32.7275i | −0.570196 | + | 0.414272i | −0.835177 | − | 0.549982i | \(-0.814635\pi\) |
0.264980 | + | 0.964254i | \(0.414635\pi\) | |||||||
\(80\) | −14.9658 | + | 4.86267i | −0.187072 | + | 0.0607834i | ||||
\(81\) | 67.3327 | + | 45.0256i | 0.831268 | + | 0.555871i | ||||
\(82\) | −35.9749 | − | 26.1373i | −0.438718 | − | 0.318747i | ||||
\(83\) | 38.4046 | − | 52.8594i | 0.462706 | − | 0.636860i | −0.512361 | − | 0.858770i | \(-0.671229\pi\) |
0.975067 | + | 0.221910i | \(0.0712290\pi\) | |||||||
\(84\) | 33.6094 | − | 34.2697i | 0.400112 | − | 0.407972i | ||||
\(85\) | 7.17288 | + | 22.0759i | 0.0843869 | + | 0.259716i | ||||
\(86\) | 18.5632 | + | 25.5501i | 0.215852 | + | 0.297094i | ||||
\(87\) | 34.6576 | − | 69.6868i | 0.398363 | − | 0.800998i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.1341i | 0.158810i | 0.996842 | + | 0.0794052i | \(0.0253021\pi\) | ||||
−0.996842 | + | 0.0794052i | \(0.974698\pi\) | |||||||
\(90\) | 17.2240 | + | 5.22824i | 0.191378 | + | 0.0580916i | ||||
\(91\) | 19.7771 | + | 60.8676i | 0.217331 | + | 0.668875i | ||||
\(92\) | 60.7374 | + | 19.7348i | 0.660189 | + | 0.214508i | ||||
\(93\) | −3.97137 | − | 7.61033i | −0.0427029 | − | 0.0818315i | ||||
\(94\) | −85.1182 | − | 61.8420i | −0.905513 | − | 0.657894i | ||||
\(95\) | 19.7673 | + | 6.42280i | 0.208077 | + | 0.0676084i | ||||
\(96\) | 100.008 | + | 14.8441i | 1.04175 | + | 0.154626i | ||||
\(97\) | −120.774 | + | 87.7477i | −1.24510 | + | 0.904615i | −0.997927 | − | 0.0643570i | \(-0.979500\pi\) |
−0.247169 | + | 0.968972i | \(0.579500\pi\) | |||||||
\(98\) | 8.86263i | 0.0904350i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −57.8179 | −0.578179 | ||||||||
\(101\) | −11.7613 | − | 16.1881i | −0.116449 | − | 0.160278i | 0.746814 | − | 0.665033i | \(-0.231583\pi\) |
−0.863262 | + | 0.504755i | \(0.831583\pi\) | |||||||
\(102\) | 32.5749 | − | 219.465i | 0.319362 | − | 2.15162i | ||||
\(103\) | −55.7540 | + | 171.593i | −0.541301 | + | 1.66595i | 0.188324 | + | 0.982107i | \(0.439695\pi\) |
−0.729625 | + | 0.683847i | \(0.760305\pi\) | |||||||
\(104\) | −22.9177 | + | 31.5436i | −0.220363 | + | 0.303303i | ||||
\(105\) | 14.2122 | − | 7.41646i | 0.135354 | − | 0.0706329i | ||||
\(106\) | −69.8832 | + | 215.078i | −0.659275 | + | 2.02904i | ||||
\(107\) | 61.3701 | − | 19.9403i | 0.573552 | − | 0.186358i | −0.00785789 | − | 0.999969i | \(-0.502501\pi\) |
0.581410 | + | 0.813611i | \(0.302501\pi\) | |||||||
\(108\) | −46.5935 | − | 43.9506i | −0.431421 | − | 0.406950i | ||||
\(109\) | 110.277 | 1.01172 | 0.505859 | − | 0.862616i | \(-0.331176\pi\) | ||||
0.505859 | + | 0.862616i | \(0.331176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.43070 | + | 3.19820i | 0.0579343 | + | 0.0288126i | ||||
\(112\) | 108.373 | − | 78.7377i | 0.967617 | − | 0.703015i | ||||
\(113\) | 119.110 | − | 38.7011i | 1.05407 | − | 0.342488i | 0.269805 | − | 0.962915i | \(-0.413041\pi\) |
0.784264 | + | 0.620427i | \(0.213041\pi\) | |||||||
\(114\) | −141.839 | − | 139.106i | −1.24420 | − | 1.22023i | ||||
\(115\) | 17.2553 | + | 12.5367i | 0.150047 | + | 0.109015i | ||||
\(116\) | −36.1748 | + | 49.7904i | −0.311852 | + | 0.429228i | ||||
\(117\) | 80.6935 | − | 27.9657i | 0.689688 | − | 0.239023i | ||||
\(118\) | −11.5126 | − | 35.4320i | −0.0975641 | − | 0.300271i | ||||
\(119\) | −116.145 | − | 159.860i | −0.976010 | − | 1.34336i | ||||
\(120\) | 8.74456 | + | 4.34896i | 0.0728714 | + | 0.0362414i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 160.158i | 1.31277i | ||||||||
\(123\) | 8.77430 | + | 52.1129i | 0.0713358 | + | 0.423682i | ||||
\(124\) | 2.09763 | + | 6.45583i | 0.0169163 | + | 0.0520631i | ||||
\(125\) | −37.2025 | − | 12.0878i | −0.297620 | − | 0.0967026i | ||||
\(126\) | −153.201 | + | 2.98071i | −1.21588 | + | 0.0236565i | ||||
\(127\) | −156.017 | − | 113.353i | −1.22848 | − | 0.892544i | −0.231706 | − | 0.972786i | \(-0.574431\pi\) |
−0.996775 | + | 0.0802421i | \(0.974431\pi\) | |||||||
\(128\) | 114.696 | + | 37.2671i | 0.896064 | + | 0.291149i | ||||
\(129\) | 5.51054 | − | 37.1259i | 0.0427174 | − | 0.287798i | ||||
\(130\) | 15.3537 | − | 11.1551i | 0.118106 | − | 0.0858087i | ||||
\(131\) | − | 106.098i | − | 0.809905i | −0.914338 | − | 0.404952i | \(-0.867288\pi\) | ||
0.914338 | − | 0.404952i | \(-0.132712\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −176.935 | −1.33034 | ||||||||
\(134\) | −93.9653 | − | 129.332i | −0.701233 | − | 0.965165i | ||||
\(135\) | −10.2636 | − | 18.7687i | −0.0760269 | − | 0.139028i | ||||
\(136\) | 37.1996 | − | 114.489i | 0.273526 | − | 0.841828i | ||||
\(137\) | −114.792 | + | 157.998i | −0.837901 | + | 1.15327i | 0.148500 | + | 0.988912i | \(0.452556\pi\) |
−0.986401 | + | 0.164359i | \(0.947444\pi\) | |||||||
\(138\) | −94.3173 | − | 180.740i | −0.683459 | − | 1.30971i | ||||
\(139\) | 2.14296 | − | 6.59534i | 0.0154170 | − | 0.0474485i | −0.943052 | − | 0.332645i | \(-0.892059\pi\) |
0.958469 | + | 0.285197i | \(0.0920589\pi\) | |||||||
\(140\) | −12.0562 | + | 3.91728i | −0.0861154 | + | 0.0279806i | ||||
\(141\) | 20.7604 | + | 123.302i | 0.147237 | + | 0.874479i | ||||
\(142\) | 11.4891 | 0.0809093 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −107.861 | − | 142.543i | −0.749038 | − | 0.989880i | ||||
\(145\) | −16.6288 | + | 12.0816i | −0.114682 | + | 0.0833211i | ||||
\(146\) | −129.082 | + | 41.9411i | −0.884120 | + | 0.287268i | ||||
\(147\) | 7.37490 | − | 7.51978i | 0.0501694 | − | 0.0511550i | ||||
\(148\) | −4.59466 | − | 3.33822i | −0.0310450 | − | 0.0225555i | ||||
\(149\) | 39.7916 | − | 54.7684i | 0.267058 | − | 0.367573i | −0.654336 | − | 0.756204i | \(-0.727052\pi\) |
0.921394 | + | 0.388631i | \(0.127052\pi\) | |||||||
\(150\) | 131.775 | + | 129.236i | 0.878501 | + | 0.861575i | ||||
\(151\) | 8.72469 | + | 26.8518i | 0.0577794 | + | 0.177827i | 0.975781 | − | 0.218750i | \(-0.0701980\pi\) |
−0.918001 | + | 0.396577i | \(0.870198\pi\) | |||||||
\(152\) | −63.3585 | − | 87.2055i | −0.416832 | − | 0.573720i | ||||
\(153\) | −210.264 | + | 159.105i | −1.37427 | + | 1.03990i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.26706i | 0.0146262i | ||||||||
\(156\) | −66.5953 | + | 11.2127i | −0.426893 | + | 0.0718764i | ||||
\(157\) | −20.9502 | − | 64.4780i | −0.133441 | − | 0.410688i | 0.861904 | − | 0.507072i | \(-0.169272\pi\) |
−0.995344 | + | 0.0963843i | \(0.969272\pi\) | |||||||
\(158\) | −133.674 | − | 43.4334i | −0.846039 | − | 0.274895i | ||||
\(159\) | 238.268 | − | 124.338i | 1.49854 | − | 0.781999i | ||||
\(160\) | −21.6016 | − | 15.6945i | −0.135010 | − | 0.0980906i | ||||
\(161\) | −172.681 | − | 56.1073i | −1.07255 | − | 0.348493i | ||||
\(162\) | 7.95348 | + | 204.317i | 0.0490955 | + | 1.26121i | ||||
\(163\) | 54.9076 | − | 39.8927i | 0.336856 | − | 0.244740i | −0.406478 | − | 0.913661i | \(-0.633243\pi\) |
0.743334 | + | 0.668920i | \(0.233243\pi\) | |||||||
\(164\) | − | 41.7888i | − | 0.254810i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 164.935 | 0.993583 | ||||||||
\(167\) | −33.0542 | − | 45.4952i | −0.197929 | − | 0.272426i | 0.698503 | − | 0.715607i | \(-0.253850\pi\) |
−0.896432 | + | 0.443181i | \(0.853850\pi\) | |||||||
\(168\) | −82.2375 | − | 12.2064i | −0.489509 | − | 0.0726571i | ||||
\(169\) | −24.3989 | + | 75.0921i | −0.144372 | + | 0.444332i | ||||
\(170\) | −34.4411 | + | 47.4042i | −0.202595 | + | 0.278848i | ||||
\(171\) | 4.59281 | + | 236.059i | 0.0268585 | + | 1.38046i | ||||
\(172\) | −9.17141 | + | 28.2267i | −0.0533222 | + | 0.164109i | ||||
\(173\) | 213.546 | − | 69.3854i | 1.23437 | − | 0.401072i | 0.382075 | − | 0.924131i | \(-0.375209\pi\) |
0.852296 | + | 0.523060i | \(0.175209\pi\) | |||||||
\(174\) | 193.740 | − | 32.6203i | 1.11345 | − | 0.187473i | ||||
\(175\) | 164.380 | 0.939316 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.7160 | + | 39.6434i | −0.111390 | + | 0.223974i | ||||
\(178\) | −28.8652 | + | 20.9718i | −0.162164 | + | 0.117819i | ||||
\(179\) | 133.586 | − | 43.4048i | 0.746292 | − | 0.242485i | 0.0889068 | − | 0.996040i | \(-0.471663\pi\) |
0.657385 | + | 0.753555i | \(0.271663\pi\) | |||||||
\(180\) | 5.53921 | + | 15.9831i | 0.0307734 | + | 0.0887950i | ||||
\(181\) | −105.869 | − | 76.9184i | −0.584912 | − | 0.424964i | 0.255579 | − | 0.966788i | \(-0.417734\pi\) |
−0.840492 | + | 0.541824i | \(0.817734\pi\) | |||||||
\(182\) | −94.9612 | + | 130.703i | −0.521765 | + | 0.718148i | ||||
\(183\) | 133.273 | − | 135.891i | 0.728268 | − | 0.742575i | ||||
\(184\) | −34.1816 | − | 105.200i | −0.185770 | − | 0.571740i | ||||
\(185\) | −1.11489 | − | 1.53451i | −0.00602642 | − | 0.00829465i | ||||
\(186\) | 9.64947 | − | 19.4024i | 0.0518789 | − | 0.104314i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 98.8744i | − | 0.525928i | ||||||
\(189\) | 132.469 | + | 124.955i | 0.700892 | + | 0.661136i | ||||
\(190\) | 16.2133 | + | 49.8994i | 0.0853332 | + | 0.262629i | ||||
\(191\) | 334.202 | + | 108.589i | 1.74975 | + | 0.568528i | 0.996058 | − | 0.0887021i | \(-0.0282719\pi\) |
0.753690 | + | 0.657230i | \(0.228272\pi\) | |||||||
\(192\) | 7.81075 | + | 14.9677i | 0.0406810 | + | 0.0779570i | ||||
\(193\) | 198.618 | + | 144.304i | 1.02911 | + | 0.747691i | 0.968130 | − | 0.250448i | \(-0.0805779\pi\) |
0.0609786 | + | 0.998139i | \(0.480578\pi\) | |||||||
\(194\) | −358.402 | − | 116.452i | −1.84743 | − | 0.600268i | ||||
\(195\) | −22.3099 | − | 3.31143i | −0.114410 | − | 0.0169817i | ||||
\(196\) | −6.73813 | + | 4.89554i | −0.0343782 | + | 0.0249772i | ||||
\(197\) | − | 6.15315i | − | 0.0312343i | −0.999878 | − | 0.0156171i | \(-0.995029\pi\) | ||
0.999878 | − | 0.0156171i | \(-0.00497129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 193.272 | 0.971214 | 0.485607 | − | 0.874177i | \(-0.338599\pi\) | ||||
0.485607 | + | 0.874177i | \(0.338599\pi\) | |||||||
\(200\) | 58.8629 | + | 81.0178i | 0.294315 | + | 0.405089i | ||||
\(201\) | −27.8938 | + | 187.928i | −0.138775 | + | 0.934963i | ||||
\(202\) | 15.6087 | − | 48.0387i | 0.0772709 | − | 0.237815i | ||||
\(203\) | 102.848 | − | 141.558i | 0.506638 | − | 0.697328i | ||||
\(204\) | 184.850 | − | 96.4618i | 0.906126 | − | 0.472852i | ||||
\(205\) | 4.31280 | − | 13.2734i | 0.0210380 | − | 0.0647484i | ||||
\(206\) | −433.159 | + | 140.742i | −2.10272 | + | 0.683214i | ||||
\(207\) | −70.3735 | + | 231.839i | −0.339969 | + | 1.12000i | ||||
\(208\) | −188.467 | −0.906093 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 36.2337 | + | 18.0202i | 0.172541 | + | 0.0858106i | ||||
\(211\) | 86.3934 | − | 62.7684i | 0.409447 | − | 0.297481i | −0.363931 | − | 0.931426i | \(-0.618566\pi\) |
0.773378 | + | 0.633945i | \(0.218566\pi\) | |||||||
\(212\) | −202.123 | + | 65.6737i | −0.953409 | + | 0.309781i | ||||
\(213\) | −9.74831 | − | 9.56049i | −0.0457667 | − | 0.0448849i | ||||
\(214\) | 131.782 | + | 95.7451i | 0.615803 | + | 0.447407i | ||||
\(215\) | −5.82625 | + | 8.01914i | −0.0270988 | + | 0.0372983i | ||||
\(216\) | −14.1505 | + | 110.034i | −0.0655117 | + | 0.509419i | ||||
\(217\) | −5.96370 | − | 18.3544i | −0.0274825 | − | 0.0845824i | ||||
\(218\) | 163.626 | + | 225.212i | 0.750577 | + | 1.03308i | ||||
\(219\) | 144.424 | + | 71.8268i | 0.659470 | + | 0.327976i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 278.007i | 1.25795i | ||||||||
\(222\) | 3.01020 | + | 17.8784i | 0.0135595 | + | 0.0805333i | ||||
\(223\) | 23.7112 | + | 72.9754i | 0.106328 | + | 0.327244i | 0.990040 | − | 0.140787i | \(-0.0449634\pi\) |
−0.883712 | + | 0.468031i | \(0.844963\pi\) | |||||||
\(224\) | 216.175 | + | 70.2396i | 0.965068 | + | 0.313570i | ||||
\(225\) | −4.26693 | − | 219.309i | −0.0189641 | − | 0.974707i | ||||
\(226\) | 255.768 | + | 185.826i | 1.13172 | + | 0.822241i | ||||
\(227\) | −45.8822 | − | 14.9080i | −0.202124 | − | 0.0656741i | 0.206205 | − | 0.978509i | \(-0.433889\pi\) |
−0.408329 | + | 0.912835i | \(0.633889\pi\) | |||||||
\(228\) | 27.4115 | − | 184.678i | 0.120226 | − | 0.809990i | ||||
\(229\) | 12.4716 | − | 9.06117i | 0.0544613 | − | 0.0395684i | −0.560222 | − | 0.828343i | \(-0.689284\pi\) |
0.614683 | + | 0.788774i | \(0.289284\pi\) | |||||||
\(230\) | 53.8411i | 0.234092i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 106.598 | 0.459474 | ||||||||
\(233\) | 101.807 | + | 140.126i | 0.436942 | + | 0.601399i | 0.969529 | − | 0.244976i | \(-0.0787802\pi\) |
−0.532587 | + | 0.846375i | \(0.678780\pi\) | |||||||
\(234\) | 176.843 | + | 123.300i | 0.755739 | + | 0.526924i | ||||
\(235\) | 10.2043 | − | 31.4055i | 0.0434225 | − | 0.133641i | ||||
\(236\) | 20.5791 | − | 28.3247i | 0.0871997 | − | 0.120020i | ||||
\(237\) | 77.2777 | + | 148.087i | 0.326066 | + | 0.624841i | ||||
\(238\) | 154.139 | − | 474.391i | 0.647643 | − | 1.99324i | ||||
\(239\) | −281.890 | + | 91.5917i | −1.17946 | + | 0.383229i | −0.832165 | − | 0.554528i | \(-0.812899\pi\) |
−0.347292 | + | 0.937757i | \(0.612899\pi\) | |||||||
\(240\) | 7.83810 | + | 46.5526i | 0.0326588 | + | 0.193969i | ||||
\(241\) | 46.7011 | 0.193780 | 0.0968902 | − | 0.995295i | \(-0.469110\pi\) | ||||
0.0968902 | + | 0.995295i | \(0.469110\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 163.270 | − | 179.977i | 0.671894 | − | 0.740647i | ||||
\(244\) | −121.766 | + | 88.4681i | −0.499040 | + | 0.362574i | ||||
\(245\) | −2.64548 | + | 0.859568i | −0.0107979 | + | 0.00350844i | ||||
\(246\) | −93.4076 | + | 95.2426i | −0.379706 | + | 0.387165i | ||||
\(247\) | 201.392 | + | 146.320i | 0.815354 | + | 0.592389i | ||||
\(248\) | 6.91075 | − | 9.51183i | 0.0278659 | − | 0.0383541i | ||||
\(249\) | −139.944 | − | 137.248i | −0.562024 | − | 0.551196i | ||||
\(250\) | −30.5137 | − | 93.9117i | −0.122055 | − | 0.375647i | ||||
\(251\) | −122.135 | − | 168.104i | −0.486592 | − | 0.669737i | 0.493163 | − | 0.869937i | \(-0.335841\pi\) |
−0.979755 | + | 0.200200i | \(0.935841\pi\) | |||||||
\(252\) | −86.8913 | − | 114.830i | −0.344807 | − | 0.455674i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 486.813i | − | 1.91659i | ||||||
\(255\) | 68.6693 | − | 11.5619i | 0.269291 | − | 0.0453408i | ||||
\(256\) | 101.031 | + | 310.941i | 0.394652 | + | 1.21461i | ||||
\(257\) | −189.962 | − | 61.7225i | −0.739153 | − | 0.240165i | −0.0848454 | − | 0.996394i | \(-0.527040\pi\) |
−0.654307 | + | 0.756229i | \(0.727040\pi\) | |||||||
\(258\) | 83.9961 | − | 43.8324i | 0.325566 | − | 0.169893i | ||||
\(259\) | 13.0629 | + | 9.49079i | 0.0504361 | + | 0.0366440i | ||||
\(260\) | 16.9622 | + | 5.51134i | 0.0652391 | + | 0.0211975i | ||||
\(261\) | −191.530 | − | 133.540i | −0.733830 | − | 0.511648i | ||||
\(262\) | 216.676 | − | 157.424i | 0.827007 | − | 0.600856i | ||||
\(263\) | 99.7592i | 0.379313i | 0.981851 | + | 0.189656i | \(0.0607374\pi\) | ||||
−0.981851 | + | 0.189656i | \(0.939263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −70.9783 | −0.267842 | ||||||||
\(266\) | −262.530 | − | 361.342i | −0.986956 | − | 1.35843i | ||||
\(267\) | 41.9429 | + | 6.22552i | 0.157089 | + | 0.0233166i | ||||
\(268\) | 46.4248 | − | 142.881i | 0.173227 | − | 0.533137i | ||||
\(269\) | −29.6108 | + | 40.7558i | −0.110077 | + | 0.151509i | −0.860501 | − | 0.509448i | \(-0.829849\pi\) |
0.750424 | + | 0.660957i | \(0.229849\pi\) | |||||||
\(270\) | 23.1012 | − | 48.8091i | 0.0855601 | − | 0.180775i | ||||
\(271\) | −38.4357 | + | 118.293i | −0.141829 | + | 0.436505i | −0.996590 | − | 0.0825177i | \(-0.973704\pi\) |
0.854761 | + | 0.519022i | \(0.173704\pi\) | |||||||
\(272\) | 553.408 | − | 179.813i | 2.03459 | − | 0.661077i | ||||
\(273\) | 189.335 | − | 31.8785i | 0.693535 | − | 0.116771i | ||||
\(274\) | −492.994 | −1.79925 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 85.3151 | − | 171.545i | 0.309113 | − | 0.621540i | ||||
\(277\) | −237.627 | + | 172.646i | −0.857858 | + | 0.623271i | −0.927301 | − | 0.374315i | \(-0.877878\pi\) |
0.0694432 | + | 0.997586i | \(0.477878\pi\) | |||||||
\(278\) | 16.6489 | − | 5.40955i | 0.0598880 | − | 0.0194588i | ||||
\(279\) | −24.3328 | + | 8.43294i | −0.0872143 | + | 0.0302256i | ||||
\(280\) | 17.7632 | + | 12.9057i | 0.0634399 | + | 0.0460918i | ||||
\(281\) | 154.985 | − | 213.319i | 0.551549 | − | 0.759141i | −0.438673 | − | 0.898647i | \(-0.644551\pi\) |
0.990221 | + | 0.139505i | \(0.0445513\pi\) | |||||||
\(282\) | −221.007 | + | 225.349i | −0.783712 | + | 0.799108i | ||||
\(283\) | 123.232 | + | 379.270i | 0.435450 | + | 1.34018i | 0.892625 | + | 0.450800i | \(0.148861\pi\) |
−0.457175 | + | 0.889377i | \(0.651139\pi\) | |||||||
\(284\) | 6.34636 | + | 8.73501i | 0.0223463 | + | 0.0307571i | ||||
\(285\) | 27.7663 | − | 55.8304i | 0.0974257 | − | 0.195896i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 118.809i | 0.413967i | ||||||||
\(288\) | 88.0992 | − | 290.235i | 0.305900 | − | 1.00776i | ||||
\(289\) | −175.935 | − | 541.472i | −0.608771 | − | 1.87360i | ||||
\(290\) | −49.3467 | − | 16.0337i | −0.170161 | − | 0.0552887i | ||||
\(291\) | 207.194 | + | 397.046i | 0.712007 | + | 1.36442i | ||||
\(292\) | −103.189 | − | 74.9713i | −0.353388 | − | 0.256751i | ||||
\(293\) | 331.765 | + | 107.797i | 1.13230 | + | 0.367908i | 0.814451 | − | 0.580232i | \(-0.197038\pi\) |
0.317853 | + | 0.948140i | \(0.397038\pi\) | |||||||
\(294\) | 26.2998 | + | 3.90364i | 0.0894550 | + | 0.0132777i | ||||
\(295\) | 9.45981 | − | 6.87295i | 0.0320671 | − | 0.0232981i | ||||
\(296\) | 9.83686i | 0.0332326i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 170.891 | 0.573461 | ||||||||
\(299\) | 150.151 | + | 206.665i | 0.502177 | + | 0.691188i | ||||
\(300\) | −25.4665 | + | 171.574i | −0.0848883 | + | 0.571913i | ||||
\(301\) | 26.0750 | − | 80.2505i | 0.0866278 | − | 0.266613i | ||||
\(302\) | −41.8923 | + | 57.6597i | −0.138716 | + | 0.190926i | ||||
\(303\) | −53.2183 | + | 27.7714i | −0.175638 | + | 0.0916548i | ||||
\(304\) | 161.010 | − | 495.537i | 0.529637 | − | 1.63005i | ||||
\(305\) | −47.8069 | + | 15.5334i | −0.156744 | + | 0.0509292i | ||||
\(306\) | −636.913 | − | 193.331i | −2.08141 | − | 0.631802i | ||||
\(307\) | −398.527 | −1.29813 | −0.649067 | − | 0.760731i | \(-0.724840\pi\) | ||||
−0.649067 | + | 0.760731i | \(0.724840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 484.644 | + | 241.030i | 1.56843 | + | 0.780031i | ||||
\(310\) | −4.62985 | + | 3.36379i | −0.0149350 | + | 0.0108509i | ||||
\(311\) | 418.794 | − | 136.074i | 1.34660 | − | 0.437538i | 0.455055 | − | 0.890463i | \(-0.349620\pi\) |
0.891548 | + | 0.452925i | \(0.149620\pi\) | |||||||
\(312\) | 83.5108 | + | 81.9018i | 0.267663 | + | 0.262506i | ||||
\(313\) | −428.698 | − | 311.467i | −1.36964 | − | 0.995102i | −0.997765 | − | 0.0668198i | \(-0.978715\pi\) |
−0.371876 | − | 0.928283i | \(-0.621285\pi\) | |||||||
\(314\) | 100.594 | − | 138.455i | 0.320362 | − | 0.440941i | ||||
\(315\) | −15.7484 | − | 45.4411i | −0.0499948 | − | 0.144257i | ||||
\(316\) | −40.8171 | − | 125.622i | −0.129168 | − | 0.397539i | ||||
\(317\) | −216.556 | − | 298.063i | −0.683140 | − | 0.940262i | 0.316826 | − | 0.948484i | \(-0.397383\pi\) |
−0.999966 | + | 0.00822156i | \(0.997383\pi\) | |||||||
\(318\) | 607.462 | + | 302.111i | 1.91026 | + | 0.950035i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 4.45877i | − | 0.0139337i | ||||||
\(321\) | −32.1417 | − | 190.898i | −0.100130 | − | 0.594698i | ||||
\(322\) | −141.634 | − | 435.904i | −0.439857 | − | 1.35374i | ||||
\(323\) | −730.962 | − | 237.504i | −2.26304 | − | 0.735306i | ||||
\(324\) | −150.946 | + | 118.907i | −0.465881 | + | 0.366997i | ||||
\(325\) | −187.103 | − | 135.938i | −0.575701 | − | 0.418271i | ||||
\(326\) | 162.940 | + | 52.9425i | 0.499817 | + | 0.162400i | ||||
\(327\) | 48.5727 | − | 327.246i | 0.148540 | − | 1.00075i | ||||
\(328\) | −58.5570 | + | 42.5441i | −0.178527 | + | 0.129708i | ||||
\(329\) | 281.107i | 0.854428i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −115.649 | −0.349394 | −0.174697 | − | 0.984622i | \(-0.555895\pi\) | ||||
−0.174697 | + | 0.984622i | \(0.555895\pi\) | |||||||
\(332\) | 91.1065 | + | 125.397i | 0.274417 | + | 0.377703i | ||||
\(333\) | 12.3231 | − | 17.6744i | 0.0370063 | − | 0.0530762i | ||||
\(334\) | 43.8670 | − | 135.009i | 0.131338 | − | 0.404218i | ||||
\(335\) | 29.4919 | − | 40.5921i | 0.0880354 | − | 0.121170i | ||||
\(336\) | −185.919 | − | 356.277i | −0.553331 | − | 1.06035i | ||||
\(337\) | −16.4618 | + | 50.6643i | −0.0488482 | + | 0.150339i | −0.972505 | − | 0.232881i | \(-0.925185\pi\) |
0.923657 | + | 0.383220i | \(0.125185\pi\) | |||||||
\(338\) | −189.558 | + | 61.5911i | −0.560822 | + | 0.182222i | ||||
\(339\) | −62.3820 | − | 370.503i | −0.184018 | − | 1.09293i | ||||
\(340\) | −55.0652 | −0.161957 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −475.272 | + | 359.636i | −1.38968 | + | 1.05157i | ||||
\(343\) | 286.524 | − | 208.172i | 0.835346 | − | 0.606915i | ||||
\(344\) | 48.8901 | − | 15.8854i | 0.142122 | − | 0.0461784i | ||||
\(345\) | 44.8030 | − | 45.6831i | 0.129864 | − | 0.132415i | ||||
\(346\) | 458.554 | + | 333.159i | 1.32530 | + | 0.962888i | ||||
\(347\) | −6.58804 | + | 9.06766i | −0.0189857 | + | 0.0261316i | −0.818404 | − | 0.574643i | \(-0.805141\pi\) |
0.799419 | + | 0.600774i | \(0.205141\pi\) | |||||||
\(348\) | 131.819 | + | 129.279i | 0.378790 | + | 0.371492i | ||||
\(349\) | −66.1346 | − | 203.541i | −0.189498 | − | 0.583213i | 0.810499 | − | 0.585740i | \(-0.199196\pi\) |
−0.999997 | + | 0.00252619i | \(0.999196\pi\) | |||||||
\(350\) | 243.902 | + | 335.703i | 0.696864 | + | 0.959151i | ||||
\(351\) | −47.4456 | − | 251.775i | −0.135173 | − | 0.717308i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 531.528i | − | 1.50574i | −0.658167 | − | 0.752872i | \(-0.728668\pi\) | ||
0.658167 | − | 0.752872i | \(-0.271332\pi\) | |||||||
\(354\) | −110.215 | + | 18.5570i | −0.311342 | + | 0.0524209i | ||||
\(355\) | 1.11431 | + | 3.42948i | 0.00313889 | + | 0.00966051i | ||||
\(356\) | −31.8890 | − | 10.3614i | −0.0895760 | − | 0.0291050i | ||||
\(357\) | −525.541 | + | 274.248i | −1.47210 | + | 0.768201i | ||||
\(358\) | 286.854 | + | 208.411i | 0.801267 | + | 0.582155i | ||||
\(359\) | 166.620 | + | 54.1381i | 0.464122 | + | 0.150802i | 0.531738 | − | 0.846909i | \(-0.321539\pi\) |
−0.0676158 | + | 0.997711i | \(0.521539\pi\) | |||||||
\(360\) | 16.7571 | − | 24.0339i | 0.0465476 | − | 0.0667607i | ||||
\(361\) | −264.716 | + | 192.327i | −0.733284 | + | 0.532762i | ||||
\(362\) | − | 330.338i | − | 0.912537i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −151.826 | −0.417104 | ||||||||
\(365\) | −25.0387 | − | 34.4628i | −0.0685991 | − | 0.0944186i | ||||
\(366\) | 475.268 | + | 70.5433i | 1.29855 | + | 0.192741i | ||||
\(367\) | 42.9643 | − | 132.231i | 0.117069 | − | 0.360301i | −0.875304 | − | 0.483573i | \(-0.839339\pi\) |
0.992373 | + | 0.123272i | \(0.0393387\pi\) | |||||||
\(368\) | 314.277 | − | 432.565i | 0.854013 | − | 1.17545i | ||||
\(369\) | 158.509 | − | 3.08399i | 0.429564 | − | 0.00835770i | ||||
\(370\) | 1.47959 | − | 4.55372i | 0.00399890 | − | 0.0123073i | ||||
\(371\) | 574.649 | − | 186.715i | 1.54892 | − | 0.503275i | ||||
\(372\) | 20.0815 | − | 3.38115i | 0.0539826 | − | 0.00908911i | ||||
\(373\) | 149.081 | 0.399682 | 0.199841 | − | 0.979828i | \(-0.435957\pi\) | ||||
0.199841 | + | 0.979828i | \(0.435957\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −52.2567 | + | 105.074i | −0.139351 | + | 0.280197i | ||||
\(376\) | −138.549 | + | 100.661i | −0.368480 | + | 0.267717i | ||||
\(377\) | −234.128 | + | 76.0730i | −0.621030 | + | 0.201785i | ||||
\(378\) | −58.6337 | + | 455.935i | −0.155116 | + | 1.20618i | ||||
\(379\) | −218.753 | − | 158.934i | −0.577186 | − | 0.419350i | 0.260523 | − | 0.965468i | \(-0.416105\pi\) |
−0.837708 | + | 0.546118i | \(0.816105\pi\) | |||||||
\(380\) | −28.9819 | + | 39.8902i | −0.0762681 | + | 0.104974i | ||||
\(381\) | −405.093 | + | 413.052i | −1.06324 | + | 1.08413i | ||||
\(382\) | 274.115 | + | 843.639i | 0.717578 | + | 2.20848i | ||||
\(383\) | 371.364 | + | 511.138i | 0.969618 | + | 1.33456i | 0.942240 | + | 0.334939i | \(0.108716\pi\) |
0.0273778 | + | 0.999625i | \(0.491284\pi\) | |||||||
\(384\) | 161.109 | − | 323.945i | 0.419554 | − | 0.843607i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 619.738i | 1.60554i | ||||||||
\(387\) | −107.744 | − | 32.7050i | −0.278407 | − | 0.0845089i | ||||
\(388\) | −109.437 | − | 336.814i | −0.282055 | − | 0.868076i | ||||
\(389\) | 437.482 | + | 142.147i | 1.12463 | + | 0.365415i | 0.811534 | − | 0.584305i | \(-0.198633\pi\) |
0.313098 | + | 0.949721i | \(0.398633\pi\) | |||||||
\(390\) | −26.3400 | − | 50.4754i | −0.0675386 | − | 0.129424i | ||||
\(391\) | −638.073 | − | 463.587i | −1.63190 | − | 1.18564i | ||||
\(392\) | 13.7198 | + | 4.45784i | 0.0349995 | + | 0.0113720i | ||||
\(393\) | −314.843 | − | 46.7317i | −0.801128 | − | 0.118910i | ||||
\(394\) | 12.5662 | − | 9.12985i | 0.0318938 | − | 0.0231722i | ||||
\(395\) | − | 44.1140i | − | 0.111681i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −561.272 | −1.41378 | −0.706891 | − | 0.707322i | \(-0.749903\pi\) | ||||
−0.706891 | + | 0.707322i | \(0.749903\pi\) | |||||||
\(398\) | 286.770 | + | 394.706i | 0.720529 | + | 0.991722i | ||||
\(399\) | −77.9327 | + | 525.052i | −0.195320 | + | 1.31592i | ||||
\(400\) | −149.585 | + | 460.376i | −0.373963 | + | 1.15094i | ||||
\(401\) | −105.710 | + | 145.497i | −0.263616 | + | 0.362837i | −0.920222 | − | 0.391398i | \(-0.871992\pi\) |
0.656605 | + | 0.754234i | \(0.271992\pi\) | |||||||
\(402\) | −425.180 | + | 221.875i | −1.05766 | + | 0.551929i | ||||
\(403\) | −8.39051 | + | 25.8233i | −0.0208201 | + | 0.0640777i | ||||
\(404\) | 45.1450 | − | 14.6685i | 0.111745 | − | 0.0363082i | ||||
\(405\) | −60.2167 | + | 22.1903i | −0.148683 | + | 0.0547909i | ||||
\(406\) | 441.696 | 1.08792 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −323.359 | − | 160.817i | −0.792546 | − | 0.394159i | ||||
\(409\) | −109.780 | + | 79.7598i | −0.268411 | + | 0.195012i | −0.713847 | − | 0.700302i | \(-0.753049\pi\) |
0.445436 | + | 0.895314i | \(0.353049\pi\) | |||||||
\(410\) | 33.5066 | − | 10.8870i | 0.0817234 | − | 0.0265535i | ||||
\(411\) | 418.297 | + | 410.237i | 1.01775 | + | 0.998144i | ||||
\(412\) | −346.272 | − | 251.582i | −0.840467 | − | 0.610635i | ||||
\(413\) | −58.5079 | + | 80.5292i | −0.141666 | + | 0.194986i | ||||
\(414\) | −577.888 | + | 200.277i | −1.39586 | + | 0.483760i | ||||
\(415\) | 15.9967 | + | 49.2327i | 0.0385462 | + | 0.118633i | ||||
\(416\) | −187.971 | − | 258.720i | −0.451853 | − | 0.621923i | ||||
\(417\) | −18.6277 | − | 9.26419i | −0.0446708 | − | 0.0222163i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 50.3361i | − | 0.120134i | −0.998194 | − | 0.0600669i | \(-0.980869\pi\) | ||
0.998194 | − | 0.0600669i | \(-0.0191314\pi\) | |||||||
\(420\) | 6.31424 | + | 37.5019i | 0.0150339 | + | 0.0892903i | ||||
\(421\) | −16.2805 | − | 50.1063i | −0.0386711 | − | 0.119017i | 0.929857 | − | 0.367920i | \(-0.119930\pi\) |
−0.968528 | + | 0.248903i | \(0.919930\pi\) | |||||||
\(422\) | 256.375 | + | 83.3014i | 0.607525 | + | 0.197397i | ||||
\(423\) | 375.040 | − | 7.29687i | 0.886620 | − | 0.0172503i | ||||
\(424\) | 297.802 | + | 216.366i | 0.702363 | + | 0.510296i | ||||
\(425\) | 679.096 | + | 220.652i | 1.59787 | + | 0.519181i | ||||
\(426\) | 5.06050 | − | 34.0939i | 0.0118791 | − | 0.0800325i | ||||
\(427\) | 346.189 | − | 251.521i | 0.810747 | − | 0.589042i | ||||
\(428\) | 153.079i | 0.357662i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.0217 | −0.0581901 | ||||||||
\(431\) | −292.016 | − | 401.925i | −0.677531 | − | 0.932541i | 0.322370 | − | 0.946614i | \(-0.395520\pi\) |
−0.999901 | + | 0.0140726i | \(0.995520\pi\) | |||||||
\(432\) | −470.503 | + | 257.293i | −1.08913 | + | 0.595586i | ||||
\(433\) | 159.336 | − | 490.386i | 0.367982 | − | 1.13253i | −0.580111 | − | 0.814537i | \(-0.696991\pi\) |
0.948093 | − | 0.317994i | \(-0.103009\pi\) | |||||||
\(434\) | 28.6352 | − | 39.4129i | 0.0659796 | − | 0.0908132i | ||||
\(435\) | 28.5276 | + | 54.6673i | 0.0655806 | + | 0.125672i | ||||
\(436\) | −80.8415 | + | 248.804i | −0.185416 | + | 0.570652i | ||||
\(437\) | −671.660 | + | 218.235i | −1.53698 | + | 0.499395i | ||||
\(438\) | 67.6046 | + | 401.521i | 0.154348 | + | 0.916716i | ||||
\(439\) | −25.1087 | −0.0571953 | −0.0285977 | − | 0.999591i | \(-0.509104\pi\) | ||||
−0.0285977 | + | 0.999591i | \(0.509104\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.0665 | − | 25.1971i | −0.0432347 | − | 0.0571363i | ||||
\(442\) | −567.754 | + | 412.497i | −1.28451 | + | 0.933252i | ||||
\(443\) | −827.818 | + | 268.974i | −1.86866 | + | 0.607166i | −0.876635 | + | 0.481155i | \(0.840217\pi\) |
−0.992029 | + | 0.126011i | \(0.959783\pi\) | |||||||
\(444\) | −11.9299 | + | 12.1643i | −0.0268691 | + | 0.0273970i | ||||
\(445\) | −9.05960 | − | 6.58219i | −0.0203587 | − | 0.0147914i | ||||
\(446\) | −113.851 | + | 156.702i | −0.255271 | + | 0.351351i | ||||
\(447\) | −144.998 | − | 142.204i | −0.324380 | − | 0.318131i | ||||
\(448\) | 11.7292 | + | 36.0988i | 0.0261813 | + | 0.0805776i | ||||
\(449\) | 338.354 | + | 465.704i | 0.753572 | + | 1.03720i | 0.997722 | + | 0.0674648i | \(0.0214910\pi\) |
−0.244150 | + | 0.969737i | \(0.578509\pi\) | |||||||
\(450\) | 441.549 | − | 334.118i | 0.981220 | − | 0.742484i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 297.103i | 0.657308i | ||||||||
\(453\) | 83.5254 | − | 14.0633i | 0.184383 | − | 0.0310447i | ||||
\(454\) | −37.6329 | − | 115.822i | −0.0828918 | − | 0.255115i | ||||
\(455\) | −48.2246 | − | 15.6691i | −0.105988 | − | 0.0344376i | ||||
\(456\) | −286.688 | + | 149.605i | −0.628702 | + | 0.328081i | ||||
\(457\) | −20.7046 | − | 15.0428i | −0.0453055 | − | 0.0329164i | 0.564902 | − | 0.825158i | \(-0.308914\pi\) |
−0.610208 | + | 0.792242i | \(0.708914\pi\) | |||||||
\(458\) | 37.0100 | + | 12.0253i | 0.0808079 | + | 0.0262561i | ||||
\(459\) | 379.531 | + | 694.034i | 0.826865 | + | 1.51206i | ||||
\(460\) | −40.9345 | + | 29.7407i | −0.0889881 | + | 0.0646537i | ||||
\(461\) | − | 289.365i | − | 0.627691i | −0.949474 | − | 0.313845i | \(-0.898383\pi\) | ||
0.949474 | − | 0.313845i | \(-0.101617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −201.052 | −0.434237 | −0.217118 | − | 0.976145i | \(-0.569666\pi\) | ||||
−0.217118 | + | 0.976145i | \(0.569666\pi\) | |||||||
\(464\) | 302.866 | + | 416.859i | 0.652728 | + | 0.898403i | ||||
\(465\) | 6.72746 | + | 0.998548i | 0.0144677 | + | 0.00214741i | ||||
\(466\) | −135.111 | + | 415.829i | −0.289938 | + | 0.892336i | ||||
\(467\) | 64.8441 | − | 89.2503i | 0.138853 | − | 0.191114i | −0.733928 | − | 0.679228i | \(-0.762315\pi\) |
0.872780 | + | 0.488114i | \(0.162315\pi\) | |||||||
\(468\) | 3.94105 | + | 202.560i | 0.00842104 | + | 0.432820i | ||||
\(469\) | −131.989 | + | 406.220i | −0.281426 | + | 0.866141i | ||||
\(470\) | 79.2782 | − | 25.7591i | 0.168677 | − | 0.0548065i | ||||
\(471\) | −200.565 | + | 33.7694i | −0.425829 | + | 0.0716973i | ||||
\(472\) | −60.6414 | −0.128477 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −187.766 | + | 377.546i | −0.396131 | + | 0.796511i | ||||
\(475\) | 517.265 | − | 375.815i | 1.08898 | − | 0.791190i | ||||
\(476\) | 445.816 | − | 144.854i | 0.936587 | − | 0.304316i | ||||
\(477\) | −264.023 | − | 761.825i | −0.553508 | − | 1.59712i | ||||
\(478\) | −605.312 | − | 439.785i | −1.26634 | − | 0.920052i | ||||
\(479\) | −401.770 | + | 552.989i | −0.838769 | + | 1.15447i | 0.147458 | + | 0.989068i | \(0.452891\pi\) |
−0.986227 | + | 0.165398i | \(0.947109\pi\) | |||||||
\(480\) | −56.0879 | + | 57.1898i | −0.116850 | + | 0.119145i | ||||
\(481\) | −7.02002 | − | 21.6054i | −0.0145946 | − | 0.0449177i | ||||
\(482\) | 69.2936 | + | 95.3744i | 0.143763 | + | 0.197872i | ||||
\(483\) | −242.557 | + | 487.715i | −0.502188 | + | 1.00976i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 118.277i | − | 0.243870i | ||||||
\(486\) | 609.811 | + | 66.3915i | 1.25475 | + | 0.136608i | ||||
\(487\) | −40.2033 | − | 123.733i | −0.0825530 | − | 0.254072i | 0.901258 | − | 0.433284i | \(-0.142645\pi\) |
−0.983811 | + | 0.179212i | \(0.942645\pi\) | |||||||
\(488\) | 247.933 | + | 80.5584i | 0.508060 | + | 0.165079i | ||||
\(489\) | −94.1965 | − | 180.509i | −0.192631 | − | 0.369139i | ||||
\(490\) | −5.68071 | − | 4.12728i | −0.0115933 | − | 0.00842302i | ||||
\(491\) | −757.592 | − | 246.157i | −1.54296 | − | 0.501338i | −0.590767 | − | 0.806842i | \(-0.701175\pi\) |
−0.952191 | + | 0.305504i | \(0.901175\pi\) | |||||||
\(492\) | −124.008 | − | 18.4063i | −0.252049 | − | 0.0374112i | ||||
\(493\) | 614.905 | − | 446.755i | 1.24727 | − | 0.906196i | ||||
\(494\) | 628.395i | 1.27206i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 56.8316 | 0.114580 | ||||||||
\(497\) | −18.0431 | − | 24.8342i | −0.0363041 | − | 0.0499683i | ||||
\(498\) | 72.6472 | − | 489.442i | 0.145878 | − | 0.982816i | ||||
\(499\) | 151.428 | − | 466.048i | 0.303464 | − | 0.933965i | −0.676782 | − | 0.736183i | \(-0.736626\pi\) |
0.980246 | − | 0.197782i | \(-0.0633738\pi\) | |||||||
\(500\) | 54.5445 | − | 75.0740i | 0.109089 | − | 0.150148i | ||||
\(501\) | −149.566 | + | 78.0491i | −0.298534 | + | 0.155787i | ||||
\(502\) | 162.088 | − | 498.855i | 0.322884 | − | 0.993735i | ||||
\(503\) | 269.417 | − | 87.5387i | 0.535619 | − | 0.174033i | −0.0287028 | − | 0.999588i | \(-0.509138\pi\) |
0.564322 | + | 0.825555i | \(0.309138\pi\) | |||||||
\(504\) | −72.4447 | + | 238.662i | −0.143739 | + | 0.473537i | ||||
\(505\) | 15.8533 | 0.0313927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 212.088 | + | 105.479i | 0.418320 | + | 0.208045i | ||||
\(508\) | 370.116 | − | 268.905i | 0.728576 | − | 0.529341i | ||||
\(509\) | −231.725 | + | 75.2919i | −0.455255 | + | 0.147921i | −0.527663 | − | 0.849454i | \(-0.676932\pi\) |
0.0724082 | + | 0.997375i | \(0.476932\pi\) | |||||||
\(510\) | 125.501 | + | 123.083i | 0.246081 | + | 0.241340i | ||||
\(511\) | 293.374 | + | 213.149i | 0.574118 | + | 0.417121i | ||||
\(512\) | −201.563 | + | 277.427i | −0.393677 | + | 0.541851i | ||||
\(513\) | 702.524 | + | 90.3453i | 1.36944 | + | 0.176112i | ||||
\(514\) | −155.808 | − | 479.529i | −0.303129 | − | 0.932935i | ||||
\(515\) | −84.0224 | − | 115.647i | −0.163150 | − | 0.224557i | ||||
\(516\) | 79.7228 | + | 39.6488i | 0.154502 | + | 0.0768388i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 40.7597i | 0.0786867i | ||||||||
\(519\) | −111.842 | − | 664.258i | −0.215495 | − | 1.27988i | ||||
\(520\) | −9.54592 | − | 29.3793i | −0.0183575 | − | 0.0564987i | ||||
\(521\) | −357.858 | − | 116.275i | −0.686867 | − | 0.223177i | −0.0552676 | − | 0.998472i | \(-0.517601\pi\) |
−0.631599 | + | 0.775295i | \(0.717601\pi\) | |||||||
\(522\) | −11.4654 | − | 589.291i | −0.0219643 | − | 1.12891i | ||||
\(523\) | −449.686 | − | 326.716i | −0.859820 | − | 0.624696i | 0.0680161 | − | 0.997684i | \(-0.478333\pi\) |
−0.927836 | + | 0.372989i | \(0.878333\pi\) | |||||||
\(524\) | 239.374 | + | 77.7775i | 0.456821 | + | 0.148430i | ||||
\(525\) | 72.4030 | − | 487.797i | 0.137911 | − | 0.929137i | ||||
\(526\) | −203.732 | + | 148.020i | −0.387322 | + | 0.281406i | ||||
\(527\) | − | 83.8317i | − | 0.159074i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −195.715 | −0.369971 | ||||||||
\(530\) | −105.315 | − | 144.954i | −0.198708 | − | 0.273498i | ||||
\(531\) | 108.957 | + | 75.9683i | 0.205193 | + | 0.143067i | ||||
\(532\) | 129.706 | − | 399.196i | 0.243809 | − | 0.750368i | ||||
\(533\) | 98.2514 | − | 135.231i | 0.184337 | − | 0.253718i | ||||
\(534\) | 49.5196 | + | 94.8943i | 0.0927333 | + | 0.177705i | ||||
\(535\) | −15.7985 | + | 48.6227i | −0.0295299 | + | 0.0908836i | ||||
\(536\) | −247.477 | + | 80.4100i | −0.461710 | + | 0.150019i | ||||
\(537\) | −69.9638 | − | 415.534i | −0.130286 | − | 0.773806i | ||||
\(538\) | −127.168 | −0.236373 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 49.8695 | − | 9.39764i | 0.0923509 | − | 0.0174030i | ||||
\(541\) | −754.171 | + | 547.937i | −1.39403 | + | 1.01282i | −0.398622 | + | 0.917116i | \(0.630511\pi\) |
−0.995410 | + | 0.0957073i | \(0.969489\pi\) | |||||||
\(542\) | −298.611 | + | 97.0246i | −0.550943 | + | 0.179012i | ||||
\(543\) | −274.886 | + | 280.286i | −0.506235 | + | 0.516180i | ||||
\(544\) | 798.790 | + | 580.355i | 1.46836 | + | 1.06683i | ||||
\(545\) | −51.3555 | + | 70.6848i | −0.0942303 | + | 0.129697i | ||||
\(546\) | 346.033 | + | 339.366i | 0.633760 | + | 0.621549i | ||||
\(547\) | 227.740 | + | 700.913i | 0.416344 | + | 1.28138i | 0.911043 | + | 0.412312i | \(0.135278\pi\) |
−0.494699 | + | 0.869065i | \(0.664722\pi\) | |||||||
\(548\) | −272.320 | − | 374.816i | −0.496934 | − | 0.683971i | ||||
\(549\) | −344.554 | − | 455.341i | −0.627604 | − | 0.829401i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 680.583i | − | 1.23518i | ||||||
\(552\) | −327.236 | + | 55.0971i | −0.592819 | + | 0.0998136i | ||||
\(553\) | 116.046 | + | 357.153i | 0.209848 | + | 0.645846i | ||||
\(554\) | −705.166 | − | 229.122i | −1.27286 | − | 0.413578i | ||||
\(555\) | −5.04471 | + | 2.63253i | −0.00908956 | + | 0.00474329i | ||||
\(556\) | 13.3093 | + | 9.66976i | 0.0239376 | + | 0.0173917i | ||||
\(557\) | −604.548 | − | 196.430i | −1.08536 | − | 0.352656i | −0.288911 | − | 0.957356i | \(-0.593293\pi\) |
−0.796454 | + | 0.604700i | \(0.793293\pi\) | |||||||
\(558\) | −53.3263 | − | 37.1807i | −0.0955668 | − | 0.0666321i | ||||
\(559\) | −96.0443 | + | 69.7803i | −0.171814 | + | 0.124831i | ||||
\(560\) | 106.132i | 0.189521i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 665.609 | 1.18436 | ||||||||
\(563\) | −470.435 | − | 647.498i | −0.835586 | − | 1.15009i | −0.986857 | − | 0.161593i | \(-0.948337\pi\) |
0.151271 | − | 0.988492i | \(-0.451663\pi\) | |||||||
\(564\) | −293.409 | − | 43.5502i | −0.520228 | − | 0.0772167i | ||||
\(565\) | −30.6624 | + | 94.3691i | −0.0542697 | + | 0.167025i | ||||
\(566\) | −591.709 | + | 814.418i | −1.04542 | + | 1.43890i | ||||
\(567\) | 429.149 | − | 338.061i | 0.756876 | − | 0.596228i | ||||
\(568\) | 5.77895 | − | 17.7858i | 0.0101742 | − | 0.0313130i | ||||
\(569\) | 49.9733 | − | 16.2373i | 0.0878265 | − | 0.0285366i | −0.264774 | − | 0.964310i | \(-0.585297\pi\) |
0.352601 | + | 0.935774i | \(0.385297\pi\) | |||||||
\(570\) | 155.217 | − | 26.1341i | 0.272311 | − | 0.0458493i | ||||
\(571\) | 10.1143 | 0.0177133 | 0.00885666 | − | 0.999961i | \(-0.497181\pi\) | ||||
0.00885666 | + | 0.999961i | \(0.497181\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 469.439 | − | 943.912i | 0.819265 | − | 1.64732i | ||||
\(574\) | −242.635 | + | 176.284i | −0.422709 | + | 0.307116i | ||||
\(575\) | 624.002 | − | 202.751i | 1.08522 | − | 0.352610i | ||||
\(576\) | 47.8569 | − | 16.5856i | 0.0830849 | − | 0.0287945i | ||||
\(577\) | 71.4329 | + | 51.8990i | 0.123801 | + | 0.0899463i | 0.647962 | − | 0.761672i | \(-0.275621\pi\) |
−0.524162 | + | 0.851619i | \(0.675621\pi\) | |||||||
\(578\) | 844.764 | − | 1162.72i | 1.46153 | − | 2.01162i | ||||
\(579\) | 515.705 | − | 525.836i | 0.890682 | − | 0.908180i | ||||
\(580\) | −15.0679 | − | 46.3742i | −0.0259791 | − | 0.0799556i | ||||
\(581\) | −259.022 | − | 356.514i | −0.445822 | − | 0.613621i | ||||
\(582\) | −503.432 | + | 1012.26i | −0.865003 | + | 1.73928i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 220.921i | 0.378289i | ||||||||
\(585\) | −19.6533 | + | 64.7459i | −0.0335953 | + | 0.110677i | ||||
\(586\) | 272.116 | + | 837.488i | 0.464362 | + | 1.42916i | ||||
\(587\) | 715.396 | + | 232.446i | 1.21873 | + | 0.395990i | 0.846620 | − | 0.532198i | \(-0.178634\pi\) |
0.372112 | + | 0.928188i | \(0.378634\pi\) | |||||||
\(588\) | 11.5596 | + | 22.1516i | 0.0196591 | + | 0.0376728i | ||||
\(589\) | −60.7291 | − | 44.1222i | −0.103105 | − | 0.0749104i | ||||
\(590\) | 28.0723 | + | 9.12125i | 0.0475802 | + | 0.0154598i | ||||
\(591\) | −18.2594 | − | 2.71022i | −0.0308958 | − | 0.00458582i | ||||
\(592\) | −38.4678 | + | 27.9485i | −0.0649794 | + | 0.0472103i | ||||
\(593\) | − | 656.836i | − | 1.10765i | −0.832633 | − | 0.553825i | \(-0.813168\pi\) | ||
0.832633 | − | 0.553825i | \(-0.186832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 156.554 | 0.263117 | ||||||||
\(596\) | 94.3968 | + | 129.926i | 0.158384 | + | 0.217997i | ||||
\(597\) | 85.1285 | − | 573.532i | 0.142594 | − | 0.960689i | ||||
\(598\) | −199.269 | + | 613.287i | −0.333226 | + | 1.02556i | ||||
\(599\) | −237.419 | + | 326.780i | −0.396360 | + | 0.545542i | −0.959826 | − | 0.280597i | \(-0.909468\pi\) |
0.563466 | + | 0.826139i | \(0.309468\pi\) | |||||||
\(600\) | 266.346 | − | 138.990i | 0.443911 | − | 0.231650i | ||||
\(601\) | −255.483 | + | 786.296i | −0.425097 | + | 1.30831i | 0.477805 | + | 0.878466i | \(0.341433\pi\) |
−0.902902 | + | 0.429847i | \(0.858567\pi\) | |||||||
\(602\) | 202.579 | − | 65.8220i | 0.336511 | − | 0.109339i | ||||
\(603\) | 545.387 | + | 165.549i | 0.904456 | + | 0.274543i | ||||
\(604\) | −66.9783 | −0.110891 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −135.679 | − | 67.4778i | −0.223893 | − | 0.111350i | ||||
\(607\) | 935.580 | − | 679.738i | 1.54132 | − | 1.11983i | 0.591815 | − | 0.806074i | \(-0.298412\pi\) |
0.949503 | − | 0.313759i | \(-0.101588\pi\) | |||||||
\(608\) | 840.837 | − | 273.204i | 1.38296 | − | 0.449349i | ||||
\(609\) | −374.770 | − | 367.550i | −0.615387 | − | 0.603530i | ||||
\(610\) | −102.657 | − | 74.5848i | −0.168290 | − | 0.122270i | ||||
\(611\) | 232.468 | − | 319.964i | 0.380471 | − | 0.523673i | ||||
\(612\) | −204.830 | − | 591.027i | −0.334690 | − | 0.965731i | ||||
\(613\) | −277.574 | − | 854.286i | −0.452813 | − | 1.39362i | −0.873683 | − | 0.486495i | \(-0.838275\pi\) |
0.420870 | − | 0.907121i | \(-0.361725\pi\) | |||||||
\(614\) | −591.322 | − | 813.885i | −0.963065 | − | 1.32555i | ||||
\(615\) | −37.4891 | − | 18.6446i | −0.0609579 | − | 0.0303164i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 713.002i | 1.15560i | 0.816180 | + | 0.577798i | \(0.196088\pi\) | ||||
−0.816180 | + | 0.577798i | \(0.803912\pi\) | |||||||
\(618\) | 226.861 | + | 1347.39i | 0.367089 | + | 2.18024i | ||||
\(619\) | −12.4874 | − | 38.4324i | −0.0201736 | − | 0.0620879i | 0.940463 | − | 0.339896i | \(-0.110392\pi\) |
−0.960637 | + | 0.277808i | \(0.910392\pi\) | |||||||
\(620\) | −5.11487 | − | 1.66192i | −0.00824979 | − | 0.00268052i | ||||
\(621\) | 656.984 | + | 310.949i | 1.05795 | + | 0.500723i | ||||
\(622\) | 899.288 | + | 653.371i | 1.44580 | + | 1.05044i | ||||
\(623\) | 90.6628 | + | 29.4581i | 0.145526 | + | 0.0472843i | ||||
\(624\) | −83.0124 | + | 559.275i | −0.133033 | + | 0.896274i | ||||
\(625\) | −467.867 | + | 339.925i | −0.748587 | + | 0.543880i | ||||
\(626\) | − | 1337.64i | − | 2.13681i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 160.832 | 0.256101 | ||||||||
\(629\) | 41.2266 | + | 56.7435i | 0.0655431 | + | 0.0902123i | ||||
\(630\) | 69.4343 | − | 99.5859i | 0.110213 | − | 0.158073i | ||||
\(631\) | −231.300 | + | 711.868i | −0.366561 | + | 1.12816i | 0.582437 | + | 0.812876i | \(0.302099\pi\) |
−0.948998 | + | 0.315283i | \(0.897901\pi\) | |||||||
\(632\) | −134.474 | + | 185.088i | −0.212776 | + | 0.292861i | ||||
\(633\) | −148.212 | − | 284.018i | −0.234142 | − | 0.448686i | ||||
\(634\) | 287.396 | − | 884.513i | 0.453306 | − | 1.39513i | ||||
\(635\) | 145.313 | − | 47.2149i | 0.228839 | − | 0.0743542i | ||||
\(636\) | 105.859 | + | 628.724i | 0.166445 | + | 0.988560i | ||||
\(637\) | −33.3151 | −0.0523000 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32.6644 | + | 24.7170i | −0.0511180 | + | 0.0386807i | ||||
\(640\) | −77.3006 | + | 56.1622i | −0.120782 | + | 0.0877534i | ||||
\(641\) | 116.317 | − | 37.7936i | 0.181462 | − | 0.0589604i | −0.216877 | − | 0.976199i | \(-0.569587\pi\) |
0.398338 | + | 0.917239i | \(0.369587\pi\) | |||||||
\(642\) | 342.167 | − | 348.889i | 0.532971 | − | 0.543441i | ||||
\(643\) | 509.125 | + | 369.901i | 0.791796 | + | 0.575273i | 0.908496 | − | 0.417894i | \(-0.137232\pi\) |
−0.116700 | + | 0.993167i | \(0.537232\pi\) | |||||||
\(644\) | 253.176 | − | 348.467i | 0.393130 | − | 0.541097i | ||||
\(645\) | 21.2305 | + | 20.8214i | 0.0329155 | + | 0.0322813i | ||||
\(646\) | −599.540 | − | 1845.19i | −0.928080 | − | 2.85634i | ||||
\(647\) | −109.228 | − | 150.340i | −0.168822 | − | 0.232364i | 0.716220 | − | 0.697875i | \(-0.245871\pi\) |
−0.885042 | + | 0.465510i | \(0.845871\pi\) | |||||||
\(648\) | 320.293 | + | 90.4574i | 0.494280 | + | 0.139595i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 583.808i | − | 0.898166i | ||||||
\(651\) | −57.0932 | + | 9.61284i | −0.0877008 | + | 0.0147663i | ||||
\(652\) | 49.7535 | + | 153.125i | 0.0763090 | + | 0.234855i | ||||
\(653\) | −192.509 | − | 62.5501i | −0.294808 | − | 0.0957888i | 0.157879 | − | 0.987458i | \(-0.449534\pi\) |
−0.452687 | + | 0.891670i | \(0.649534\pi\) | |||||||
\(654\) | 740.384 | − | 386.361i | 1.13209 | − | 0.590766i | ||||
\(655\) | 68.0057 | + | 49.4090i | 0.103826 | + | 0.0754337i | ||||
\(656\) | −332.744 | − | 108.115i | −0.507232 | − | 0.164810i | ||||
\(657\) | 276.758 | − | 396.940i | 0.421245 | − | 0.604170i | ||||
\(658\) | −574.085 | + | 417.097i | −0.872470 | + | 0.633887i | ||||
\(659\) | 1094.02i | 1.66012i | 0.557674 | + | 0.830060i | \(0.311694\pi\) | ||||
−0.557674 | + | 0.830060i | \(0.688306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1024.53 | 1.54997 | 0.774985 | − | 0.631980i | \(-0.217758\pi\) | ||||
0.774985 | + | 0.631980i | \(0.217758\pi\) | |||||||
\(662\) | −171.597 | − | 236.183i | −0.259210 | − | 0.356772i | ||||
\(663\) | 824.982 | + | 122.451i | 1.24432 | + | 0.184692i | ||||
\(664\) | 82.9610 | − | 255.328i | 0.124941 | − | 0.384530i | ||||
\(665\) | 82.3976 | − | 113.411i | 0.123906 | − | 0.170542i | ||||
\(666\) | 54.3798 | − | 1.05803i | 0.0816513 | − | 0.00158863i | ||||
\(667\) | 215.818 | − | 664.219i | 0.323565 | − | 0.995831i | ||||
\(668\) | 126.876 | − | 41.2246i | 0.189935 | − | 0.0617135i | ||||
\(669\) | 226.998 | − | 38.2198i | 0.339309 | − | 0.0571298i | ||||
\(670\) | 126.658 | 0.189041 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 303.652 | − | 610.560i | 0.451863 | − | 0.908572i | ||||
\(673\) | −209.931 | + | 152.524i | −0.311933 | + | 0.226633i | −0.732726 | − | 0.680524i | \(-0.761752\pi\) |
0.420792 | + | 0.907157i | \(0.361752\pi\) | |||||||
\(674\) | −127.894 | + | 41.5552i | −0.189754 | + | 0.0616547i | ||||
\(675\) | −652.677 | − | 83.9348i | −0.966928 | − | 0.124348i | ||||
\(676\) | −151.535 | − | 110.096i | −0.224164 | − | 0.162864i | ||||
\(677\) | 68.5153 | − | 94.3032i | 0.101204 | − | 0.139296i | −0.755411 | − | 0.655251i | \(-0.772563\pi\) |
0.856616 | + | 0.515955i | \(0.172563\pi\) | |||||||
\(678\) | 664.093 | − | 677.140i | 0.979489 | − | 0.998731i | ||||
\(679\) | 311.138 | + | 957.585i | 0.458230 | + | 1.41029i | ||||
\(680\) | 56.0605 | + | 77.1606i | 0.0824419 | + | 0.113472i | ||||
\(681\) | −64.4486 | + | 129.588i | −0.0946382 | + | 0.190291i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 739.385i | 1.08255i | 0.840844 | + | 0.541277i | \(0.182059\pi\) | ||||
−0.840844 | + | 0.541277i | \(0.817941\pi\) | |||||||
\(684\) | −535.956 | − | 162.686i | −0.783561 | − | 0.237846i | ||||
\(685\) | −47.8145 | − | 147.158i | −0.0698022 | − | 0.214829i | ||||
\(686\) | 850.270 | + | 276.269i | 1.23946 | + | 0.402725i | ||||
\(687\) | −21.3957 | − | 41.0005i | −0.0311436 | − | 0.0596805i | ||||
\(688\) | 201.027 | + | 146.055i | 0.292191 | + | 0.212289i | ||||
\(689\) | −808.491 | − | 262.695i | −1.17343 | − | 0.381270i | ||||
\(690\) | 159.773 | + | 23.7148i | 0.231555 | + | 0.0343693i | ||||
\(691\) | −314.727 | + | 228.663i | −0.455466 | + | 0.330916i | −0.791750 | − | 0.610845i | \(-0.790830\pi\) |
0.336284 | + | 0.941761i | \(0.390830\pi\) | |||||||
\(692\) | 532.662i | 0.769743i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.2934 | −0.0407686 | ||||||||
\(695\) | 3.22948 | + | 4.44499i | 0.00464673 | + | 0.00639567i | ||||
\(696\) | 46.9521 | − | 316.328i | 0.0674599 | − | 0.454494i | ||||
\(697\) | −159.480 | + | 490.828i | −0.228809 | + | 0.704201i | ||||
\(698\) | 317.550 | − | 437.071i | 0.454943 | − | 0.626176i | ||||
\(699\) | 460.664 | − | 240.393i | 0.659033 | − | 0.343909i | ||||
\(700\) | −120.503 | + | 370.871i | −0.172147 | + | 0.529815i | ||||
\(701\) | −1107.15 | + | 359.734i | −1.57938 | + | 0.513172i | −0.961897 | − | 0.273410i | \(-0.911848\pi\) |
−0.617485 | + | 0.786583i | \(0.711848\pi\) | |||||||
\(702\) | 443.785 | − | 470.471i | 0.632172 | − | 0.670186i | ||||
\(703\) | 62.8043 | 0.0893375 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −88.7011 | − | 44.1140i | −0.125817 | − | 0.0625730i | ||||
\(706\) | 1085.50 | − | 788.664i | 1.53754 | − | 1.11709i | ||||
\(707\) | −128.350 | + | 41.7036i | −0.181542 | + | 0.0589867i | ||||
\(708\) | −74.9891 | − | 73.5443i | −0.105917 | − | 0.103876i | ||||
\(709\) | −1075.94 | − | 781.714i | −1.51754 | − | 1.10256i | −0.962689 | − | 0.270611i | \(-0.912774\pi\) |
−0.554853 | − | 0.831948i | \(-0.687226\pi\) | |||||||
\(710\) | −5.35042 | + | 7.36423i | −0.00753581 | + | 0.0103721i | ||||
\(711\) | 473.485 | − | 164.094i | 0.665942 | − | 0.230794i | ||||
\(712\) | 17.9464 | + | 55.2335i | 0.0252057 | + | 0.0775751i | ||||
\(713\) | −45.2774 | − | 62.3190i | −0.0635027 | − | 0.0874040i | ||||
\(714\) | −1339.86 | − | 666.356i | −1.87655 | − | 0.933272i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 333.213i | 0.465381i | ||||||||
\(717\) | 147.636 | + | 876.849i | 0.205908 | + | 1.22294i | ||||
\(718\) | 136.663 | + | 420.605i | 0.190338 | + | 0.585800i | ||||
\(719\) | 797.573 | + | 259.147i | 1.10928 | + | 0.360427i | 0.805668 | − | 0.592368i | \(-0.201807\pi\) |
0.303614 | + | 0.952795i | \(0.401807\pi\) | |||||||
\(720\) | 141.597 | − | 2.75494i | 0.196662 | − | 0.00382630i | ||||
\(721\) | 984.477 | + | 715.264i | 1.36543 | + | 0.992045i | ||||
\(722\) | −785.553 | − | 255.242i | −1.08802 | − | 0.353520i | ||||
\(723\) | 20.5700 | − | 138.585i | 0.0284508 | − | 0.191680i | ||||
\(724\) | 251.151 | − | 182.472i | 0.346894 | − | 0.252033i | ||||
\(725\) | 632.292i | 0.872127i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 154.628 | 0.212693 | 0.106346 | − | 0.994329i | \(-0.466085\pi\) | ||||
0.106346 | + | 0.994329i | \(0.466085\pi\) | |||||||
\(728\) | 154.570 | + | 212.747i | 0.212322 | + | 0.292236i | ||||
\(729\) | −462.166 | − | 563.776i | −0.633973 | − | 0.773355i | ||||
\(730\) | 33.2294 | − | 102.270i | 0.0455197 | − | 0.140095i | ||||
\(731\) | 215.444 | − | 296.534i | 0.294726 | − | 0.405655i | ||||
\(732\) | 208.895 | + | 400.306i | 0.285376 | + | 0.546866i | ||||
\(733\) | 137.519 | − | 423.241i | 0.187612 | − | 0.577409i | −0.812372 | − | 0.583140i | \(-0.801824\pi\) |
0.999984 | + | 0.00573049i | \(0.00182408\pi\) | |||||||
\(734\) | 333.795 | − | 108.456i | 0.454761 | − | 0.147761i | ||||
\(735\) | 1.38553 | + | 8.22903i | 0.00188508 | + | 0.0111960i | ||||
\(736\) | 907.255 | 1.23268 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 241.489 | + | 319.137i | 0.327221 | + | 0.432434i | ||||
\(739\) | −49.6402 | + | 36.0657i | −0.0671721 | + | 0.0488034i | −0.620865 | − | 0.783918i | \(-0.713218\pi\) |
0.553692 | + | 0.832721i | \(0.313218\pi\) | |||||||
\(740\) | 4.27942 | − | 1.39047i | 0.00578300 | − | 0.00187901i | ||||
\(741\) | 522.909 | − | 533.182i | 0.705680 | − | 0.719544i | ||||
\(742\) | 1233.96 | + | 896.526i | 1.66302 | + | 1.20826i | ||||
\(743\) | −425.116 | + | 585.122i | −0.572161 | + | 0.787512i | −0.992809 | − | 0.119712i | \(-0.961803\pi\) |
0.420647 | + | 0.907224i | \(0.361803\pi\) | |||||||
\(744\) | −25.1823 | − | 24.6972i | −0.0338472 | − | 0.0331951i | ||||
\(745\) | 16.5744 | + | 51.0107i | 0.0222475 | + | 0.0684707i | ||||
\(746\) | 221.202 | + | 304.459i | 0.296518 | + | 0.408122i | ||||
\(747\) | −468.921 | + | 354.830i | −0.627739 | + | 0.475007i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 435.215i | − | 0.581062i | ||||||
\(750\) | −292.122 | + | 49.1849i | −0.389496 | + | 0.0655798i | ||||
\(751\) | 397.509 | + | 1223.41i | 0.529306 | + | 1.62904i | 0.755639 | + | 0.654988i | \(0.227326\pi\) |
−0.226333 | + | 0.974050i | \(0.572674\pi\) | |||||||
\(752\) | −787.288 | − | 255.806i | −1.04693 | − | 0.340167i | ||||
\(753\) | −552.642 | + | 288.390i | −0.733921 | + | 0.382989i | ||||
\(754\) | −502.751 | − | 365.270i | −0.666779 | − | 0.484443i | ||||
\(755\) | −21.2744 | − | 6.91246i | −0.0281780 | − | 0.00915557i | ||||
\(756\) | −379.029 | + | 207.271i | −0.501361 | + | 0.274168i | ||||
\(757\) | 220.633 | − | 160.299i | 0.291457 | − | 0.211756i | −0.432442 | − | 0.901662i | \(-0.642348\pi\) |
0.723899 | + | 0.689906i | \(0.242348\pi\) | |||||||
\(758\) | − | 682.566i | − | 0.900483i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 85.4021 | 0.112371 | ||||||||
\(761\) | 280.158 | + | 385.605i | 0.368145 | + | 0.506708i | 0.952395 | − | 0.304865i | \(-0.0986115\pi\) |
−0.584251 | + | 0.811573i | \(0.698611\pi\) | |||||||
\(762\) | −1444.61 | − | 214.422i | −1.89582 | − | 0.281393i | ||||
\(763\) | 229.838 | − | 707.369i | 0.301229 | − | 0.927089i | ||||
\(764\) | −489.990 | + | 674.414i | −0.641349 | + | 0.882741i | ||||
\(765\) | −4.06378 | − | 208.868i | −0.00531214 | − | 0.273030i | ||||
\(766\) | −492.845 | + | 1516.82i | −0.643401 | + | 1.98018i | ||||
\(767\) | 133.191 | − | 43.2764i | 0.173652 | − | 0.0564229i | ||||
\(768\) | 967.215 | − | 162.851i | 1.25939 | − | 0.212045i | ||||
\(769\) | −22.4401 | −0.0291808 | −0.0145904 | − | 0.999894i | \(-0.504644\pi\) | ||||
−0.0145904 | + | 0.999894i | \(0.504644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −266.832 | + | 536.525i | −0.346085 | + | 0.695881i | ||||
\(772\) | −471.178 | + | 342.331i | −0.610334 | + | 0.443433i | ||||
\(773\) | −1167.70 | + | 379.407i | −1.51060 | + | 0.490825i | −0.943089 | − | 0.332539i | \(-0.892095\pi\) |
−0.567514 | + | 0.823364i | \(0.692095\pi\) | |||||||
\(774\) | −93.0753 | − | 268.564i | −0.120252 | − | 0.346982i | ||||
\(775\) | 56.4200 | + | 40.9916i | 0.0728001 | + | 0.0528923i | ||||
\(776\) | −360.548 | + | 496.251i | −0.464623 | + | 0.639499i | ||||
\(777\) | 33.9175 | − | 34.5838i | 0.0436519 | − | 0.0445095i | ||||
\(778\) | 358.826 | + | 1104.35i | 0.461216 | + | 1.41948i | ||||
\(779\) | 271.626 | + | 373.862i | 0.348686 | + | 0.479925i | ||||
\(780\) | 23.8260 | − | 47.9075i | 0.0305462 | − | 0.0614199i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 1990.95i | − | 2.54597i | ||||||
\(783\) | −480.640 | + | 509.543i | −0.613845 | + | 0.650757i | ||||
\(784\) | 21.5480 | + | 66.3180i | 0.0274847 | + | 0.0845893i | ||||
\(785\) | 51.0851 | + | 16.5985i | 0.0650765 | + | 0.0211446i | ||||
\(786\) | −371.718 | − | 712.322i | −0.472923 | − | 0.906262i | ||||
\(787\) | −705.687 | − | 512.712i | −0.896680 | − | 0.651476i | 0.0409312 | − | 0.999162i | \(-0.486968\pi\) |
−0.937611 | + | 0.347686i | \(0.886968\pi\) | |||||||
\(788\) | 13.8826 | + | 4.51072i | 0.0176175 | + | 0.00572426i | ||||
\(789\) | 296.034 | + | 43.9400i | 0.375202 | + | 0.0556907i | ||||
\(790\) | 90.0910 | − | 65.4550i | 0.114039 | − | 0.0828544i | ||||
\(791\) | − | 844.685i | − | 1.06787i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −602.043 | −0.759197 | ||||||||
\(794\) | −832.797 | − | 1146.25i | −1.04886 | − | 1.44364i | ||||
\(795\) | −31.2631 | + | 210.627i | −0.0393247 | + | 0.264940i | ||||
\(796\) | −141.683 | + | 436.054i | −0.177993 | + | 0.547807i | ||||
\(797\) | 32.7783 | − | 45.1155i | 0.0411272 | − | 0.0566067i | −0.787958 | − | 0.615729i | \(-0.788862\pi\) |
0.829085 | + | 0.559122i | \(0.188862\pi\) | |||||||
\(798\) | −1187.91 | + | 619.899i | −1.48861 | + | 0.776816i | ||||
\(799\) | −377.336 | + | 1161.32i | −0.472261 | + | 1.45347i | ||||
\(800\) | −781.175 | + | 253.819i | −0.976469 | + | 0.317274i | ||||
\(801\) | 36.9483 | − | 121.723i | 0.0461278 | − | 0.151964i | ||||
\(802\) | −453.989 | −0.566071 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −403.549 | − | 200.698i | −0.501926 | − | 0.249625i | ||||
\(805\) | 116.380 | − | 84.5549i | 0.144571 | − | 0.105037i | ||||
\(806\) | −65.1868 | + | 21.1805i | −0.0808769 | + | 0.0262785i | ||||
\(807\) | 107.900 | + | 105.821i | 0.133705 | + | 0.131129i | ||||
\(808\) | −66.5153 | − | 48.3262i | −0.0823210 | − | 0.0598097i | ||||
\(809\) | −778.882 | + | 1072.04i | −0.962771 | + | 1.32514i | −0.0171558 | + | 0.999853i | \(0.505461\pi\) |
−0.945615 | + | 0.325288i | \(0.894539\pi\) | |||||||
\(810\) | −134.665 | − | 90.0512i | −0.166254 | − | 0.111174i | ||||
\(811\) | −317.710 | − | 977.810i | −0.391751 | − | 1.20568i | −0.931463 | − | 0.363835i | \(-0.881467\pi\) |
0.539713 | − | 0.841849i | \(-0.318533\pi\) | |||||||
\(812\) | 243.983 | + | 335.814i | 0.300472 | + | 0.413565i | ||||
\(813\) | 334.103 | + | 166.161i | 0.410951 | + | 0.204380i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.7721i | 0.0659781i | ||||||||
\(816\) | −289.839 | − | 1721.43i | −0.355195 | − | 2.10960i | ||||
\(817\) | −101.421 | − | 312.143i | −0.124139 | − | 0.382060i | ||||
\(818\) | −325.776 | − | 105.851i | −0.398259 | − | 0.129402i | ||||
\(819\) | −11.2047 | − | 575.891i | −0.0136809 | − | 0.703164i | ||||
\(820\) | 26.7855 | + | 19.4608i | 0.0326653 | + | 0.0237327i | ||||
\(821\) | 848.423 | + | 275.669i | 1.03340 | + | 0.335773i | 0.776134 | − | 0.630568i | \(-0.217178\pi\) |
0.257268 | + | 0.966340i | \(0.417178\pi\) | |||||||
\(822\) | −217.144 | + | 1462.96i | −0.264166 | + | 1.77975i | ||||
\(823\) | 335.986 | − | 244.108i | 0.408245 | − | 0.296608i | −0.364646 | − | 0.931146i | \(-0.618810\pi\) |
0.772891 | + | 0.634539i | \(0.218810\pi\) | |||||||
\(824\) | 741.346i | 0.899691i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −251.272 | −0.304203 | ||||||||
\(827\) | 273.061 | + | 375.837i | 0.330183 | + | 0.454458i | 0.941542 | − | 0.336895i | \(-0.109377\pi\) |
−0.611359 | + | 0.791353i | \(0.709377\pi\) | |||||||
\(828\) | −471.481 | − | 328.731i | −0.569421 | − | 0.397018i | ||||
\(829\) | −273.849 | + | 842.819i | −0.330336 | + | 1.01667i | 0.638638 | + | 0.769507i | \(0.279498\pi\) |
−0.968974 | + | 0.247163i | \(0.920502\pi\) | |||||||
\(830\) | −76.8092 | + | 105.719i | −0.0925412 | + | 0.127372i | ||||
\(831\) | 407.660 | + | 781.199i | 0.490565 | + | 0.940070i | ||||
\(832\) | 16.5022 | − | 50.7884i | 0.0198343 | − | 0.0610438i | ||||
\(833\) | 97.8252 | − | 31.7853i | 0.117437 | − | 0.0381576i | ||||
\(834\) | −8.71960 | − | 51.7880i | −0.0104552 | − | 0.0620960i | ||||
\(835\) | 44.5544 | 0.0533585 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.3070 | + | 75.9217i | 0.0170932 | + | 0.0907069i | ||||
\(838\) | 102.798 | − | 74.6871i | 0.122671 | − | 0.0891254i | ||||
\(839\) | 155.481 | − | 50.5188i | 0.185317 | − | 0.0602132i | −0.214888 | − | 0.976639i | \(-0.568939\pi\) |
0.400205 | + | 0.916425i | \(0.368939\pi\) | |||||||
\(840\) | 46.1215 | − | 47.0276i | 0.0549066 | − | 0.0559852i | ||||
\(841\) | −135.879 | − | 98.7221i | −0.161569 | − | 0.117387i | ||||
\(842\) | 78.1722 | − | 107.595i | 0.0928410 | − | 0.127785i | ||||
\(843\) | −564.756 | − | 553.875i | −0.669936 | − | 0.657029i | ||||
\(844\) | 78.2837 | + | 240.932i | 0.0927532 | + | 0.285465i | ||||
\(845\) | −36.7696 | − | 50.6090i | −0.0435143 | − | 0.0598924i | ||||
\(846\) | 571.375 | + | 755.092i | 0.675384 | + | 0.892544i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1779.31i | 2.09825i | ||||||||
\(849\) | 1179.76 | − | 198.637i | 1.38959 | − | 0.233966i | ||||
\(850\) | 557.000 | + | 1714.27i | 0.655294 | + | 2.01679i | ||||
\(851\) | 61.2942 | + | 19.9157i | 0.0720261 | + | 0.0234027i | ||||
\(852\) | 28.7164 | − | 14.9853i | 0.0337047 | − | 0.0175884i | ||||
\(853\) | 365.390 | + | 265.471i | 0.428359 | + | 0.311221i | 0.780992 | − | 0.624541i | \(-0.214714\pi\) |
−0.352634 | + | 0.935762i | \(0.614714\pi\) | |||||||
\(854\) | 1027.33 | + | 333.799i | 1.20296 | + | 0.390866i | ||||
\(855\) | −153.446 | − | 106.987i | −0.179469 | − | 0.125131i | ||||
\(856\) | 214.504 | − | 155.846i | 0.250588 | − | 0.182063i | ||||
\(857\) | 233.720i | 0.272719i | 0.990659 | + | 0.136360i | \(0.0435402\pi\) | ||||
−0.990659 | + | 0.136360i | \(0.956460\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −694.225 | −0.808178 | −0.404089 | − | 0.914720i | \(-0.632411\pi\) | ||||
−0.404089 | + | 0.914720i | \(0.632411\pi\) | |||||||
\(860\) | −13.8215 | − | 19.0237i | −0.0160715 | − | 0.0221205i | ||||
\(861\) | 352.563 | + | 52.3305i | 0.409481 | + | 0.0607787i | ||||
\(862\) | 387.541 | − | 1192.73i | 0.449583 | − | 1.38367i | ||||
\(863\) | 672.067 | − | 925.021i | 0.778756 | − | 1.07187i | −0.216662 | − | 0.976247i | \(-0.569517\pi\) |
0.995418 | − | 0.0956195i | \(-0.0304832\pi\) | |||||||
\(864\) | −822.465 | − | 389.270i | −0.951927 | − | 0.450544i | ||||
\(865\) | −54.9731 | + | 169.190i | −0.0635528 | + | 0.195595i | ||||
\(866\) | 1237.90 | − | 402.218i | 1.42945 | − | 0.464455i | ||||
\(867\) | −1684.30 | + | 283.588i | −1.94268 | + | 0.327091i | ||||
\(868\) | 45.7825 | 0.0527448 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −69.3151 | + | 139.374i | −0.0796726 | + | 0.160200i | ||||
\(871\) | 486.166 | − | 353.221i | 0.558170 | − | 0.405535i | ||||
\(872\) | 430.942 | − | 140.022i | 0.494200 | − | 0.160575i | ||||
\(873\) | 1269.49 | − | 439.963i | 1.45417 | − | 0.503967i | ||||
\(874\) | −1442.27 | − | 1047.87i | −1.65020 | − | 1.19894i | ||||
\(875\) | −155.074 | + | 213.441i | −0.177227 | + | 0.243932i | ||||
\(876\) | −267.927 | + | 273.191i | −0.305853 | + | 0.311862i | ||||
\(877\) | −333.849 | − | 1027.48i | −0.380672 | − | 1.17159i | −0.939572 | − | 0.342352i | \(-0.888777\pi\) |
0.558900 | − | 0.829235i | \(-0.311223\pi\) | |||||||
\(878\) | −37.2556 | − | 51.2779i | −0.0424323 | − | 0.0584031i | ||||
\(879\) | 466.016 | − | 937.030i | 0.530166 | − | 1.06602i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 638.008i | 0.724186i | 0.932142 | + | 0.362093i | \(0.117938\pi\) | ||||
−0.932142 | + | 0.362093i | \(0.882062\pi\) | |||||||
\(882\) | 23.1680 | − | 76.3249i | 0.0262676 | − | 0.0865362i | ||||
\(883\) | −300.425 | − | 924.613i | −0.340232 | − | 1.04713i | −0.964087 | − | 0.265586i | \(-0.914434\pi\) |
0.623855 | − | 0.781540i | \(-0.285566\pi\) | |||||||
\(884\) | −627.231 | − | 203.800i | −0.709537 | − | 0.230543i | ||||
\(885\) | −16.2287 | − | 31.0991i | −0.0183376 | − | 0.0351403i | ||||
\(886\) | −1777.60 | − | 1291.50i | −2.00632 | − | 1.45768i | ||||
\(887\) | 500.232 | + | 162.535i | 0.563960 | + | 0.183242i | 0.577102 | − | 0.816672i | \(-0.304183\pi\) |
−0.0131425 | + | 0.999914i | \(0.504183\pi\) | |||||||
\(888\) | 29.1908 | + | 4.33275i | 0.0328725 | + | 0.00487922i | ||||
\(889\) | −1052.27 | + | 764.517i | −1.18365 | + | 0.859974i | ||||
\(890\) | − | 28.2683i | − | 0.0317621i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −182.027 | −0.204066 | ||||||||
\(893\) | 642.681 | + | 884.575i | 0.719688 | + | 0.990565i | ||||
\(894\) | 75.2708 | − | 507.118i | 0.0841955 | − | 0.567246i | ||||
\(895\) | −34.3890 | + | 105.839i | −0.0384235 | + | 0.118255i | ||||
\(896\) | 478.096 | − | 658.043i | 0.533589 | − | 0.734423i | ||||
\(897\) | 679.412 | − | 354.544i | 0.757427 | − | 0.395255i | ||||
\(898\) | −449.037 | + | 1381.99i | −0.500041 | + | 1.53897i | ||||
\(899\) | 70.6005 | − | 22.9395i | 0.0785322 | − | 0.0255167i | ||||
\(900\) | 497.927 | + | 151.143i | 0.553252 | + | 0.167937i | ||||
\(901\) | 2624.65 | 2.91304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −226.658 | − | 112.724i | −0.251005 | − | 0.124833i | ||||
\(904\) | 416.318 | − | 302.473i | 0.460529 | − | 0.334594i | ||||
\(905\) | 98.6053 | − | 32.0388i | 0.108956 | − | 0.0354020i | ||||
\(906\) | 152.653 | + | 149.712i | 0.168491 | + | 0.165245i | ||||
\(907\) | 464.947 | + | 337.804i | 0.512621 | + | 0.372441i | 0.813817 | − | 0.581121i | \(-0.197386\pi\) |
−0.301196 | + | 0.953562i | \(0.597386\pi\) | |||||||
\(908\) | 67.2701 | − | 92.5894i | 0.0740861 | − | 0.101971i | ||||
\(909\) | 58.9708 | + | 170.157i | 0.0648743 | + | 0.187191i | ||||
\(910\) | −39.5542 | − | 121.735i | −0.0434661 | − | 0.133775i | ||||
\(911\) | 751.875 | + | 1034.87i | 0.825329 | + | 1.13597i | 0.988774 | + | 0.149416i | \(0.0477394\pi\) |
−0.163445 | + | 0.986552i | \(0.552261\pi\) | |||||||
\(912\) | −1399.58 | − | 696.058i | −1.53463 | − | 0.763222i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 64.6037i | − | 0.0706823i | ||||||
\(915\) | 25.0382 | + | 148.708i | 0.0273641 | + | 0.162523i | ||||
\(916\) | 11.3009 | + | 34.7807i | 0.0123373 | + | 0.0379702i | ||||
\(917\) | −680.558 | − | 221.127i | −0.742157 | − | 0.241142i | ||||
\(918\) | −854.243 | + | 1804.88i | −0.930548 | + | 1.96610i | ||||
\(919\) | 389.889 | + | 283.271i | 0.424253 | + | 0.308238i | 0.779347 | − | 0.626593i | \(-0.215551\pi\) |
−0.355094 | + | 0.934831i | \(0.615551\pi\) | |||||||
\(920\) | 83.3488 | + | 27.0817i | 0.0905965 | + | 0.0294366i | ||||
\(921\) | −175.535 | + | 1182.62i | −0.190592 | + | 1.28407i | ||||
\(922\) | 590.952 | − | 429.351i | 0.640945 | − | 0.465674i | ||||
\(923\) | 43.1883i | 0.0467912i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.3480 | −0.0630789 | ||||||||
\(926\) | −298.314 | − | 410.594i | −0.322153 | − | 0.443406i | ||||
\(927\) | 928.719 | − | 1332.01i | 1.00185 | − | 1.43691i | ||||
\(928\) | −270.178 | + | 831.523i | −0.291140 | + | 0.896037i | ||||
\(929\) | −653.769 | + | 899.836i | −0.703734 | + | 0.968607i | 0.296175 | + | 0.955134i | \(0.404289\pi\) |
−0.999909 | + | 0.0134736i | \(0.995711\pi\) | |||||||
\(930\) | 7.94273 | + | 15.2207i | 0.00854057 | + | 0.0163663i | ||||
\(931\) | 28.4615 | − | 87.5953i | 0.0305708 | − | 0.0940874i | ||||
\(932\) | −390.781 | + | 126.972i | −0.419293 | + | 0.136236i | ||||
\(933\) | −219.337 | − | 1302.70i | −0.235088 | − | 1.39625i | ||||
\(934\) | 278.484 | 0.298162 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 279.826 | − | 211.743i | 0.298959 | − | 0.226221i | ||||
\(937\) | −1410.59 | + | 1024.85i | −1.50543 | + | 1.09376i | −0.537273 | + | 0.843408i | \(0.680546\pi\) |
−0.968155 | + | 0.250350i | \(0.919454\pi\) | |||||||
\(938\) | −1025.44 | + | 333.184i | −1.09322 | + | 0.355207i | ||||
\(939\) | −1113.10 | + | 1134.97i | −1.18541 | + | 1.20870i | ||||
\(940\) | 63.3759 | + | 46.0453i | 0.0674211 | + | 0.0489843i | ||||
\(941\) | 491.503 | − | 676.495i | 0.522319 | − | 0.718911i | −0.463616 | − | 0.886036i | \(-0.653448\pi\) |
0.985936 | + | 0.167125i | \(0.0534484\pi\) | |||||||
\(942\) | −366.558 | − | 359.495i | −0.389127 | − | 0.381630i | ||||
\(943\) | 146.541 | + | 451.008i | 0.155399 | + | 0.478269i | ||||
\(944\) | −172.294 | − | 237.143i | −0.182515 | − | 0.251211i | ||||
\(945\) | −141.783 | + | 26.7181i | −0.150034 | + | 0.0282732i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 114.725i | − | 0.121145i | −0.998164 | − | 0.0605726i | \(-0.980707\pi\) | ||
0.998164 | − | 0.0605726i | \(-0.0192927\pi\) | |||||||
\(948\) | −390.761 | + | 65.7928i | −0.412195 | + | 0.0694017i | ||||
\(949\) | −157.659 | − | 485.225i | −0.166132 | − | 0.511301i | ||||
\(950\) | 1535.00 | + | 498.753i | 1.61579 | + | 0.525003i | ||||
\(951\) | −979.883 | + | 511.341i | −1.03037 | + | 0.537688i | ||||
\(952\) | −656.851 | − | 477.230i | −0.689970 | − | 0.501293i | ||||
\(953\) | 311.052 | + | 101.067i | 0.326392 | + | 0.106051i | 0.467630 | − | 0.883924i | \(-0.345108\pi\) |
−0.141237 | + | 0.989976i | \(0.545108\pi\) | |||||||
\(954\) | 1164.07 | − | 1669.57i | 1.22020 | − | 1.75007i | ||||
\(955\) | −225.239 | + | 163.645i | −0.235852 | + | 0.171356i | ||||
\(956\) | − | 703.137i | − | 0.735499i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1725.47 | −1.80111 | ||||||||
\(959\) | 774.225 | + | 1065.63i | 0.807325 | + | 1.11119i | ||||
\(960\) | −13.2313 | − | 1.96391i | −0.0137827 | − | 0.00204574i | ||||
\(961\) | −294.435 | + | 906.178i | −0.306384 | + | 0.942954i | ||||
\(962\) | 33.7072 | − | 46.3939i | 0.0350386 | − | 0.0482265i | ||||
\(963\) | −580.645 | + | 11.2972i | −0.602954 | + | 0.0117312i | ||||
\(964\) | −34.2354 | + | 105.366i | −0.0355139 | + | 0.109301i | ||||
\(965\) | −184.991 | + | 60.1071i | −0.191700 | + | 0.0622872i | ||||
\(966\) | −1355.93 | + | 228.299i | −1.40365 | + | 0.236334i | ||||
\(967\) | 168.674 | 0.174430 | 0.0872150 | − | 0.996190i | \(-0.472203\pi\) | ||||
0.0872150 | + | 0.996190i | \(0.472203\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1026.75 | + | 2064.51i | −1.05960 | + | 2.13056i | ||||
\(970\) | 241.549 | − | 175.495i | 0.249019 | − | 0.180923i | ||||
\(971\) | −77.7365 | + | 25.2581i | −0.0800582 | + | 0.0260125i | −0.348772 | − | 0.937208i | \(-0.613401\pi\) |
0.268714 | + | 0.963220i | \(0.413401\pi\) | |||||||
\(972\) | 286.370 | + | 500.303i | 0.294620 | + | 0.514715i | ||||
\(973\) | −37.8392 | − | 27.4918i | −0.0388892 | − | 0.0282547i | ||||
\(974\) | 193.039 | − | 265.696i | 0.198192 | − | 0.272788i | ||||
\(975\) | −485.806 | + | 495.350i | −0.498263 | + | 0.508051i | ||||
\(976\) | 389.398 | + | 1198.44i | 0.398974 | + | 1.22791i | ||||
\(977\) | −11.9651 | − | 16.4685i | −0.0122468 | − | 0.0168562i | 0.802850 | − | 0.596181i | \(-0.203316\pi\) |
−0.815096 | + | 0.579325i | \(0.803316\pi\) | |||||||
\(978\) | 228.875 | − | 460.205i | 0.234024 | − | 0.470557i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 6.59879i | − | 0.00673346i | ||||||
\(981\) | −949.706 | − | 288.278i | −0.968100 | − | 0.293861i | ||||
\(982\) | −621.383 | − | 1912.42i | −0.632773 | − | 1.94747i | ||||
\(983\) | −758.379 | − | 246.412i | −0.771494 | − | 0.250674i | −0.103290 | − | 0.994651i | \(-0.532937\pi\) |
−0.668204 | + | 0.743978i | \(0.732937\pi\) | |||||||
\(984\) | 100.457 | + | 192.506i | 0.102091 | + | 0.195636i | ||||
\(985\) | 3.94401 | + | 2.86549i | 0.00400407 | + | 0.00290912i | ||||
\(986\) | 1824.75 | + | 592.899i | 1.85066 | + | 0.601317i | ||||
\(987\) | 834.182 | + | 123.816i | 0.845169 | + | 0.125447i | ||||
\(988\) | −477.760 | + | 347.113i | −0.483562 | + | 0.351329i | ||||
\(989\) | − | 336.799i | − | 0.340545i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 609.620 | 0.615156 | 0.307578 | − | 0.951523i | \(-0.400481\pi\) | ||||
0.307578 | + | 0.951523i | \(0.400481\pi\) | |||||||
\(992\) | 56.6819 | + | 78.0159i | 0.0571390 | + | 0.0786451i | ||||
\(993\) | −50.9390 | + | 343.189i | −0.0512981 | + | 0.345608i | ||||
\(994\) | 23.9455 | − | 73.6965i | 0.0240900 | − | 0.0741414i | ||||
\(995\) | −90.0056 | + | 123.882i | −0.0904578 | + | 0.124505i | ||||
\(996\) | 412.244 | − | 215.125i | 0.413900 | − | 0.215989i | ||||
\(997\) | 547.355 | − | 1684.58i | 0.549002 | − | 1.68965i | −0.162279 | − | 0.986745i | \(-0.551884\pi\) |
0.711280 | − | 0.702908i | \(-0.248116\pi\) | |||||||
\(998\) | 1176.46 | − | 382.256i | 1.17882 | − | 0.383022i | ||||
\(999\) | −47.0207 | − | 44.3535i | −0.0470677 | − | 0.0443979i |
(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 | 363.3.h.m.245.4 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.m.245.1 | 16 | ||
11.2 | odd | 10 | 363.3.b.h.122.4 | 4 | |||
11.3 | even | 5 | inner | 363.3.h.m.269.4 | 16 | ||
11.4 | even | 5 | inner | 363.3.h.m.323.1 | 16 | ||
11.5 | even | 5 | inner | 363.3.h.m.251.1 | 16 | ||
11.6 | odd | 10 | 363.3.h.l.251.4 | 16 | |||
11.7 | odd | 10 | 363.3.h.l.323.4 | 16 | |||
11.8 | odd | 10 | 363.3.h.l.269.1 | 16 | |||
11.9 | even | 5 | 33.3.b.b.23.1 | ✓ | 4 | ||
11.10 | odd | 2 | 363.3.h.l.245.1 | 16 | |||
33.2 | even | 10 | 363.3.b.h.122.1 | 4 | |||
33.5 | odd | 10 | inner | 363.3.h.m.251.4 | 16 | ||
33.8 | even | 10 | 363.3.h.l.269.4 | 16 | |||
33.14 | odd | 10 | inner | 363.3.h.m.269.1 | 16 | ||
33.17 | even | 10 | 363.3.h.l.251.1 | 16 | |||
33.20 | odd | 10 | 33.3.b.b.23.4 | yes | 4 | ||
33.26 | odd | 10 | inner | 363.3.h.m.323.4 | 16 | ||
33.29 | even | 10 | 363.3.h.l.323.1 | 16 | |||
33.32 | even | 2 | 363.3.h.l.245.4 | 16 | |||
44.31 | odd | 10 | 528.3.i.d.353.4 | 4 | |||
132.119 | even | 10 | 528.3.i.d.353.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.b.b.23.1 | ✓ | 4 | 11.9 | even | 5 | ||
33.3.b.b.23.4 | yes | 4 | 33.20 | odd | 10 | ||
363.3.b.h.122.1 | 4 | 33.2 | even | 10 | |||
363.3.b.h.122.4 | 4 | 11.2 | odd | 10 | |||
363.3.h.l.245.1 | 16 | 11.10 | odd | 2 | |||
363.3.h.l.245.4 | 16 | 33.32 | even | 2 | |||
363.3.h.l.251.1 | 16 | 33.17 | even | 10 | |||
363.3.h.l.251.4 | 16 | 11.6 | odd | 10 | |||
363.3.h.l.269.1 | 16 | 11.8 | odd | 10 | |||
363.3.h.l.269.4 | 16 | 33.8 | even | 10 | |||
363.3.h.l.323.1 | 16 | 33.29 | even | 10 | |||
363.3.h.l.323.4 | 16 | 11.7 | odd | 10 | |||
363.3.h.m.245.1 | 16 | 3.2 | odd | 2 | inner | ||
363.3.h.m.245.4 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.m.251.1 | 16 | 11.5 | even | 5 | inner | ||
363.3.h.m.251.4 | 16 | 33.5 | odd | 10 | inner | ||
363.3.h.m.269.1 | 16 | 33.14 | odd | 10 | inner | ||
363.3.h.m.269.4 | 16 | 11.3 | even | 5 | inner | ||
363.3.h.m.323.1 | 16 | 11.4 | even | 5 | inner | ||
363.3.h.m.323.4 | 16 | 33.26 | odd | 10 | inner | ||
528.3.i.d.353.3 | 4 | 132.119 | even | 10 | |||
528.3.i.d.353.4 | 4 | 44.31 | odd | 10 |