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 | 323.1 | ||
Root | \(-0.217724 + 1.71831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.323 |
Dual form | 363.3.h.m.245.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
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 | 0.256624 | + | 0.966511i | \(0.417390\pi\) |
−0.998508 | + | 0.0546047i | \(0.982610\pi\) | |||||||
\(3\) | −2.10059 | + | 2.14185i | −0.700195 | + | 0.713951i | ||||
\(4\) | −0.733075 | − | 2.25617i | −0.183269 | − | 0.564043i | ||||
\(5\) | 0.465695 | + | 0.640974i | 0.0931389 | + | 0.128195i | 0.853043 | − | 0.521840i | \(-0.174754\pi\) |
−0.759904 | + | 0.650035i | \(0.774754\pi\) | |||||||
\(6\) | −1.25738 | − | 7.46790i | −0.209563 | − | 1.24465i | ||||
\(7\) | 2.08418 | + | 6.41446i | 0.297741 | + | 0.916351i | 0.982287 | + | 0.187382i | \(0.0600003\pi\) |
−0.684546 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(8\) | −3.90781 | − | 1.26972i | −0.488476 | − | 0.158715i | ||||
\(9\) | −0.175073 | − | 8.99830i | −0.0194526 | − | 0.999811i | ||||
\(10\) | −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 | 0.251976 | − | 0.967733i | \(-0.418920\pi\) |
−0.842504 | + | 0.538690i | \(0.818920\pi\) | |||||||
\(14\) | −16.1923 | − | 5.26119i | −1.15659 | − | 0.375799i | ||||
\(15\) | −2.35110 | − | 0.348971i | −0.156740 | − | 0.0232647i | ||||
\(16\) | 16.0682 | − | 11.6742i | 1.00426 | − | 0.729640i | ||||
\(17\) | −17.2206 | − | 23.7021i | −1.01297 | − | 1.39424i | −0.917014 | − | 0.398855i | \(-0.869408\pi\) |
−0.0959609 | − | 0.995385i | \(-0.530592\pi\) | |||||||
\(18\) | 18.6364 | + | 12.9939i | 1.03535 | + | 0.721881i | ||||
\(19\) | −8.10666 | + | 24.9497i | −0.426666 | + | 1.31314i | 0.474724 | + | 0.880135i | \(0.342548\pi\) |
−0.901390 | + | 0.433008i | \(0.857452\pi\) | |||||||
\(20\) | 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 | \(-0.198995\pi\) | |||||||
\(24\) | 10.9282 | − | 5.70279i | 0.455344 | − | 0.237616i | ||||
\(25\) | 7.53145 | − | 23.1794i | 0.301258 | − | 0.927177i | ||||
\(26\) | 22.7814 | − | 7.40212i | 0.876207 | − | 0.284697i | ||||
\(27\) | 19.6408 | + | 18.5267i | 0.727437 | + | 0.686175i | ||||
\(28\) | 12.9443 | − | 9.40456i | 0.462295 | − | 0.335877i | ||||
\(29\) | −24.6733 | + | 8.01686i | −0.850805 | + | 0.276443i | −0.701783 | − | 0.712391i | \(-0.747612\pi\) |
−0.149022 | + | 0.988834i | \(0.547612\pi\) | |||||||
\(30\) | 4.20117 | − | 4.28371i | 0.140039 | − | 0.142790i | ||||
\(31\) | 2.31493 | + | 1.68189i | 0.0746751 | + | 0.0542546i | 0.624496 | − | 0.781028i | \(-0.285304\pi\) |
−0.549821 | + | 0.835282i | \(0.685304\pi\) | |||||||
\(32\) | 33.7013i | 1.05316i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 73.9565 | 2.17519 | ||||||||
\(35\) | −3.14091 | + | 4.32309i | −0.0897402 | + | 0.123517i | ||||
\(36\) | −20.1734 | + | 6.99142i | −0.560372 | + | 0.194206i | ||||
\(37\) | −0.739796 | − | 2.27686i | −0.0199945 | − | 0.0615367i | 0.940561 | − | 0.339624i | \(-0.110300\pi\) |
−0.960556 | + | 0.278087i | \(0.910300\pi\) | |||||||
\(38\) | −38.9247 | − | 53.5753i | −1.02433 | − | 1.40988i | ||||
\(39\) | 28.0722 | − | 4.72655i | 0.719801 | − | 0.121194i | ||||
\(40\) | −1.00599 | − | 3.09610i | −0.0251496 | − | 0.0774026i | ||||
\(41\) | 16.7533 | + | 5.44348i | 0.408617 | + | 0.132768i | 0.506111 | − | 0.862468i | \(-0.331083\pi\) |
−0.0974939 | + | 0.995236i | \(0.531083\pi\) | |||||||
\(42\) | 45.2819 | − | 23.6299i | 1.07814 | − | 0.562616i | ||||
\(43\) | 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 | \(-0.253774\pi\) |
0.144712 | + | 0.989474i | \(0.453774\pi\) | |||||||
\(48\) | −8.74816 | + | 58.9385i | −0.182253 | + | 1.22789i | ||||
\(49\) | 2.84036 | − | 2.06364i | 0.0579665 | − | 0.0421151i | ||||
\(50\) | 36.1628 | + | 49.7739i | 0.723256 | + | 0.995477i | ||||
\(51\) | 86.9397 | + | 12.9043i | 1.70470 | + | 0.253026i | ||||
\(52\) | −6.95624 | + | 21.4091i | −0.133774 | + | 0.411714i | ||||
\(53\) | −52.6576 | + | 72.4770i | −0.993541 | + | 1.36749i | −0.0643348 | + | 0.997928i | \(0.520493\pi\) |
−0.929206 | + | 0.369563i | \(0.879507\pi\) | |||||||
\(54\) | −66.9783 | + | 12.6217i | −1.24034 | + | 0.233735i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 27.7128i | − | 0.494872i | ||||||
\(57\) | −36.4099 | − | 69.7723i | −0.638770 | − | 1.22408i | ||||
\(58\) | 20.2373 | − | 62.2839i | 0.348918 | − | 1.07386i | ||||
\(59\) | 14.0362 | − | 4.56063i | 0.237901 | − | 0.0772988i | −0.187640 | − | 0.982238i | \(-0.560084\pi\) |
0.425541 | + | 0.904939i | \(0.360084\pi\) | |||||||
\(60\) | 0.936197 | + | 5.56032i | 0.0156033 | + | 0.0926720i | ||||
\(61\) | 51.3286 | − | 37.2924i | 0.841452 | − | 0.611351i | −0.0813237 | − | 0.996688i | \(-0.525915\pi\) |
0.922776 | + | 0.385337i | \(0.125915\pi\) | |||||||
\(62\) | −6.86963 | + | 2.23208i | −0.110800 | + | 0.0360013i | ||||
\(63\) | 57.3543 | − | 19.8771i | 0.910386 | − | 0.315510i | ||||
\(64\) | −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 | ||||
\(69\) | 57.6598 | + | 56.5489i | 0.835650 | + | 0.819549i | ||||
\(70\) | −4.16837 | − | 12.8289i | −0.0595481 | − | 0.183270i | ||||
\(71\) | −2.67521 | − | 3.68211i | −0.0376790 | − | 0.0518607i | 0.789762 | − | 0.613414i | \(-0.210204\pi\) |
−0.827441 | + | 0.561553i | \(0.810204\pi\) | |||||||
\(72\) | −10.7412 | + | 35.3859i | −0.149183 | + | 0.491471i | ||||
\(73\) | −16.6147 | − | 51.1348i | −0.227599 | − | 0.700477i | −0.998017 | − | 0.0629385i | \(-0.979953\pi\) |
0.770419 | − | 0.637538i | \(-0.220047\pi\) | |||||||
\(74\) | 5.74756 | + | 1.86750i | 0.0776697 | + | 0.0252364i | ||||
\(75\) | 33.8265 | + | 64.8216i | 0.451019 | + | 0.864288i | ||||
\(76\) | 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 | 0.264980 | − | 0.964254i | \(-0.414635\pi\) |
−0.835177 | + | 0.549982i | \(0.814635\pi\) | |||||||
\(80\) | 14.9658 | + | 4.86267i | 0.187072 | + | 0.0607834i | ||||
\(81\) | −80.9387 | + | 3.15072i | −0.999243 | + | 0.0388977i | ||||
\(82\) | −35.9749 | + | 26.1373i | −0.438718 | + | 0.318747i | ||||
\(83\) | −38.4046 | − | 52.8594i | −0.462706 | − | 0.636860i | 0.512361 | − | 0.858770i | \(-0.328771\pi\) |
−0.975067 | + | 0.221910i | \(0.928771\pi\) | |||||||
\(84\) | −7.04736 | + | 47.4798i | −0.0838972 | + | 0.565236i | ||||
\(85\) | 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 | \(0.974698\pi\) | |||||||
\(90\) | 0.350146 | + | 17.9966i | 0.00389051 | + | 0.199962i | ||||
\(91\) | 19.7771 | − | 60.8676i | 0.217331 | − | 0.668875i | ||||
\(92\) | −60.7374 | + | 19.7348i | −0.660189 | + | 0.214508i | ||||
\(93\) | −8.46507 | + | 1.42527i | −0.0910223 | + | 0.0153255i | ||||
\(94\) | −85.1182 | + | 61.8420i | −0.905513 | + | 0.657894i | ||||
\(95\) | −19.7673 | + | 6.42280i | −0.208077 | + | 0.0676084i | ||||
\(96\) | −72.1831 | − | 70.7924i | −0.751908 | − | 0.737421i | ||||
\(97\) | −120.774 | − | 87.7477i | −1.24510 | − | 0.904615i | −0.247169 | − | 0.968972i | \(-0.579500\pi\) |
−0.997927 | + | 0.0643570i | \(0.979500\pi\) | |||||||
\(98\) | 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 | \(-0.768417\pi\) |
0.863262 | + | 0.504755i | \(0.168417\pi\) | |||||||
\(102\) | −155.352 | + | 158.404i | −1.52306 | + | 1.55298i | ||||
\(103\) | −55.7540 | − | 171.593i | −0.541301 | − | 1.66595i | −0.729625 | − | 0.683847i | \(-0.760305\pi\) |
0.188324 | − | 0.982107i | \(-0.439695\pi\) | |||||||
\(104\) | 22.9177 | + | 31.5436i | 0.220363 | + | 0.303303i | ||||
\(105\) | −2.66167 | − | 15.8084i | −0.0253493 | − | 0.150556i | ||||
\(106\) | −69.8832 | − | 215.078i | −0.659275 | − | 2.02904i | ||||
\(107\) | −61.3701 | − | 19.9403i | −0.573552 | − | 0.186358i | 0.00785789 | − | 0.999969i | \(-0.497499\pi\) |
−0.581410 | + | 0.813611i | \(0.697499\pi\) | |||||||
\(108\) | 27.4013 | − | 57.8945i | 0.253716 | − | 0.536060i | ||||
\(109\) | 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 | \(-0.586959\pi\) |
−0.784264 | + | 0.620427i | \(0.786959\pi\) | |||||||
\(114\) | 196.515 | + | 29.1685i | 1.72382 | + | 0.255864i | ||||
\(115\) | 17.2553 | − | 12.5367i | 0.150047 | − | 0.109015i | ||||
\(116\) | 36.1748 | + | 49.7904i | 0.311852 | + | 0.429228i | ||||
\(117\) | −48.8446 | + | 70.0552i | −0.417475 | + | 0.598762i | ||||
\(118\) | −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 | ||||||||
\(123\) | −46.8509 | + | 24.4486i | −0.380902 | + | 0.198769i | ||||
\(124\) | 2.09763 | − | 6.45583i | 0.0169163 | − | 0.0520631i | ||||
\(125\) | 37.2025 | − | 12.0878i | 0.297620 | − | 0.0967026i | ||||
\(126\) | −44.5069 | + | 146.624i | −0.353229 | + | 1.16368i | ||||
\(127\) | −156.017 | + | 113.353i | −1.22848 | + | 0.892544i | −0.996775 | − | 0.0802421i | \(-0.974431\pi\) |
−0.231706 | + | 0.972786i | \(0.574431\pi\) | |||||||
\(128\) | −114.696 | + | 37.2671i | −0.896064 | + | 0.291149i | ||||
\(129\) | −26.2802 | + | 26.7965i | −0.203722 | + | 0.207725i | ||||
\(130\) | 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 | ||||
\(135\) | −2.72853 | + | 21.2170i | −0.0202113 | + | 0.157163i | ||||
\(136\) | 37.1996 | + | 114.489i | 0.273526 | + | 0.841828i | ||||
\(137\) | 114.792 | + | 157.998i | 0.837901 | + | 1.15327i | 0.986401 | + | 0.164359i | \(0.0525556\pi\) |
−0.148500 | + | 0.988912i | \(0.547444\pi\) | |||||||
\(138\) | −201.040 | + | 33.8493i | −1.45681 | + | 0.245285i | ||||
\(139\) | 2.14296 | + | 6.59534i | 0.0154170 | + | 0.0474485i | 0.958469 | − | 0.285197i | \(-0.0920589\pi\) |
−0.943052 | + | 0.332645i | \(0.892059\pi\) | |||||||
\(140\) | 12.0562 | + | 3.91728i | 0.0861154 | + | 0.0279806i | ||||
\(141\) | −110.851 | + | 57.8466i | −0.786180 | + | 0.410260i | ||||
\(142\) | 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 | ||||
\(147\) | −1.54640 | + | 10.4185i | −0.0105197 | + | 0.0708740i | ||||
\(148\) | −4.59466 | + | 3.33822i | −0.0310450 | + | 0.0225555i | ||||
\(149\) | −39.7916 | − | 54.7684i | −0.267058 | − | 0.367573i | 0.654336 | − | 0.756204i | \(-0.272948\pi\) |
−0.921394 | + | 0.388631i | \(0.872948\pi\) | |||||||
\(150\) | −182.571 | − | 27.0988i | −1.21714 | − | 0.180659i | ||||
\(151\) | 8.72469 | − | 26.8518i | 0.0577794 | − | 0.177827i | −0.918001 | − | 0.396577i | \(-0.870198\pi\) |
0.975781 | + | 0.218750i | \(0.0701980\pi\) | |||||||
\(152\) | 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 | ||||||||
\(156\) | −31.2430 | − | 59.8709i | −0.200276 | − | 0.383788i | ||||
\(157\) | −20.9502 | + | 64.4780i | −0.133441 | + | 0.410688i | −0.995344 | − | 0.0963843i | \(-0.969272\pi\) |
0.861904 | + | 0.507072i | \(0.169272\pi\) | |||||||
\(158\) | 133.674 | − | 43.4334i | 0.846039 | − | 0.274895i | ||||
\(159\) | −44.6232 | − | 265.029i | −0.280649 | − | 1.66685i | ||||
\(160\) | −21.6016 | + | 15.6945i | −0.135010 | + | 0.0980906i | ||||
\(161\) | 172.681 | − | 56.1073i | 1.07255 | − | 0.348493i | ||||
\(162\) | 113.660 | − | 169.971i | 0.701604 | − | 1.04920i | ||||
\(163\) | 54.9076 | + | 39.8927i | 0.336856 | + | 0.244740i | 0.743334 | − | 0.668920i | \(-0.233243\pi\) |
−0.406478 | + | 0.913661i | \(0.633243\pi\) | |||||||
\(164\) | − | 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 | \(-0.746150\pi\) |
0.896432 | + | 0.443181i | \(0.146150\pi\) | |||||||
\(168\) | 59.3568 | + | 58.2132i | 0.353314 | + | 0.346507i | ||||
\(169\) | −24.3989 | − | 75.0921i | −0.144372 | − | 0.444332i | ||||
\(170\) | 34.4411 | + | 47.4042i | 0.202595 | + | 0.278848i | ||||
\(171\) | 225.924 | + | 68.5781i | 1.32119 | + | 0.401041i | ||||
\(172\) | −9.17141 | − | 28.2267i | −0.0533222 | − | 0.164109i | ||||
\(173\) | −213.546 | − | 69.3854i | −1.23437 | − | 0.401072i | −0.382075 | − | 0.924131i | \(-0.624791\pi\) |
−0.852296 | + | 0.523060i | \(0.824791\pi\) | |||||||
\(174\) | 90.8928 | + | 174.178i | 0.522372 | + | 1.00102i | ||||
\(175\) | 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 | \(-0.528337\pi\) |
−0.657385 | + | 0.753555i | \(0.728337\pi\) | |||||||
\(180\) | −13.8760 | − | 9.67474i | −0.0770886 | − | 0.0537485i | ||||
\(181\) | −105.869 | + | 76.9184i | −0.584912 | + | 0.424964i | −0.840492 | − | 0.541824i | \(-0.817734\pi\) |
0.255579 | + | 0.966788i | \(0.417734\pi\) | |||||||
\(182\) | 94.9612 | + | 130.703i | 0.521765 | + | 0.718148i | ||||
\(183\) | −27.9453 | + | 188.274i | −0.152706 | + | 1.02882i | ||||
\(184\) | −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 | ||||||
\(189\) | −77.9039 | + | 164.598i | −0.412190 | + | 0.870890i | ||||
\(190\) | 16.2133 | − | 49.8994i | 0.0853332 | − | 0.262629i | ||||
\(191\) | −334.202 | + | 108.589i | −1.74975 | + | 0.568528i | −0.996058 | − | 0.0887021i | \(-0.971728\pi\) |
−0.753690 | + | 0.657230i | \(0.771728\pi\) | |||||||
\(192\) | 16.6488 | − | 2.80318i | 0.0867126 | − | 0.0145999i | ||||
\(193\) | 198.618 | − | 144.304i | 1.02911 | − | 0.747691i | 0.0609786 | − | 0.998139i | \(-0.480578\pi\) |
0.968130 | + | 0.250448i | \(0.0805779\pi\) | |||||||
\(194\) | 358.402 | − | 116.452i | 1.84743 | − | 0.600268i | ||||
\(195\) | 16.1027 | + | 15.7924i | 0.0825779 | + | 0.0809869i | ||||
\(196\) | −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 | ||||
\(201\) | 133.028 | − | 135.641i | 0.661829 | − | 0.674831i | ||||
\(202\) | 15.6087 | + | 48.0387i | 0.0772709 | + | 0.237815i | ||||
\(203\) | −102.848 | − | 141.558i | −0.506638 | − | 0.697328i | ||||
\(204\) | −34.6189 | − | 205.611i | −0.169701 | − | 1.00790i | ||||
\(205\) | 4.31280 | + | 13.2734i | 0.0210380 | + | 0.0647484i | ||||
\(206\) | 433.159 | + | 140.742i | 2.10272 | + | 0.683214i | ||||
\(207\) | −242.239 | + | 4.71306i | −1.17024 | + | 0.0227684i | ||||
\(208\) | −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 | 0.773378 | − | 0.633945i | \(-0.218566\pi\) |
−0.363931 | + | 0.931426i | \(0.618566\pi\) | |||||||
\(212\) | 202.123 | + | 65.6737i | 0.953409 | + | 0.309781i | ||||
\(213\) | 13.5061 | + | 2.00469i | 0.0634087 | + | 0.00941167i | ||||
\(214\) | 131.782 | − | 95.7451i | 0.615803 | − | 0.447407i | ||||
\(215\) | 5.82625 | + | 8.01914i | 0.0270988 | + | 0.0372983i | ||||
\(216\) | −53.2286 | − | 97.3372i | −0.246429 | − | 0.450635i | ||||
\(217\) | −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 | ||||||||
\(222\) | −16.0731 | + | 8.38760i | −0.0724016 | + | 0.0377820i | ||||
\(223\) | 23.7112 | − | 72.9754i | 0.106328 | − | 0.327244i | −0.883712 | − | 0.468031i | \(-0.844963\pi\) |
0.990040 | + | 0.140787i | \(0.0449634\pi\) | |||||||
\(224\) | −216.175 | + | 70.2396i | −0.965068 | + | 0.313570i | ||||
\(225\) | −209.894 | − | 63.7121i | −0.932861 | − | 0.283165i | ||||
\(226\) | 255.768 | − | 185.826i | 1.13172 | − | 0.822241i | ||||
\(227\) | 45.8822 | − | 14.9080i | 0.202124 | − | 0.0656741i | −0.206205 | − | 0.978509i | \(-0.566111\pi\) |
0.408329 | + | 0.912835i | \(0.366111\pi\) | |||||||
\(228\) | −130.727 | + | 133.295i | −0.573365 | + | 0.584629i | ||||
\(229\) | 12.4716 | + | 9.06117i | 0.0544613 | + | 0.0395684i | 0.614683 | − | 0.788774i | \(-0.289284\pi\) |
−0.560222 | + | 0.828343i | \(0.689284\pi\) | |||||||
\(230\) | 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 | \(-0.921220\pi\) |
0.532587 | + | 0.846375i | \(0.321220\pi\) | |||||||
\(234\) | −70.5949 | − | 203.698i | −0.301687 | − | 0.870503i | ||||
\(235\) | 10.2043 | + | 31.4055i | 0.0434225 | + | 0.133641i | ||||
\(236\) | −20.5791 | − | 28.3247i | −0.0871997 | − | 0.120020i | ||||
\(237\) | 164.719 | − | 27.7340i | 0.695019 | − | 0.117021i | ||||
\(238\) | 154.139 | + | 474.391i | 0.647643 | + | 1.99324i | ||||
\(239\) | 281.890 | + | 91.5917i | 1.17946 | + | 0.383229i | 0.832165 | − | 0.554528i | \(-0.187101\pi\) |
0.347292 | + | 0.937757i | \(0.387101\pi\) | |||||||
\(240\) | −41.8520 | + | 21.8400i | −0.174383 | + | 0.0910000i | ||||
\(241\) | 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 | ||||
\(246\) | 19.5861 | − | 131.956i | 0.0796183 | − | 0.536408i | ||||
\(247\) | 201.392 | − | 146.320i | 0.815354 | − | 0.592389i | ||||
\(248\) | −6.91075 | − | 9.51183i | −0.0278659 | − | 0.0383541i | ||||
\(249\) | 193.889 | + | 28.7787i | 0.778672 | + | 0.115577i | ||||
\(250\) | −30.5137 | + | 93.9117i | −0.122055 | + | 0.375647i | ||||
\(251\) | 122.135 | − | 168.104i | 0.486592 | − | 0.669737i | −0.493163 | − | 0.869937i | \(-0.664159\pi\) |
0.979755 | + | 0.200200i | \(0.0641592\pi\) | |||||||
\(252\) | −86.8913 | − | 114.830i | −0.344807 | − | 0.455674i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 486.813i | − | 1.91659i | ||||||
\(255\) | 32.2160 | + | 61.7355i | 0.126337 | + | 0.242100i | ||||
\(256\) | 101.031 | − | 310.941i | 0.394652 | − | 1.21461i | ||||
\(257\) | 189.962 | − | 61.7225i | 0.739153 | − | 0.240165i | 0.0848454 | − | 0.996394i | \(-0.472960\pi\) |
0.654307 | + | 0.756229i | \(0.272960\pi\) | |||||||
\(258\) | −15.7309 | − | 93.4300i | −0.0609725 | − | 0.362132i | ||||
\(259\) | 13.0629 | − | 9.49079i | 0.0504361 | − | 0.0366440i | ||||
\(260\) | −16.9622 | + | 5.51134i | −0.0652391 | + | 0.0211975i | ||||
\(261\) | 76.4577 | + | 220.615i | 0.292941 | + | 0.845267i | ||||
\(262\) | 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 | ||||
\(267\) | −30.2732 | − | 29.6900i | −0.113383 | − | 0.111198i | ||||
\(268\) | 46.4248 | + | 142.881i | 0.173227 | + | 0.533137i | ||||
\(269\) | 29.6108 | + | 40.7558i | 0.110077 | + | 0.151509i | 0.860501 | − | 0.509448i | \(-0.170151\pi\) |
−0.750424 | + | 0.660957i | \(0.770151\pi\) | |||||||
\(270\) | −39.2816 | − | 37.0534i | −0.145487 | − | 0.137235i | ||||
\(271\) | −38.4357 | − | 118.293i | −0.141829 | − | 0.436505i | 0.854761 | − | 0.519022i | \(-0.173704\pi\) |
−0.996590 | + | 0.0825177i | \(0.973704\pi\) | |||||||
\(272\) | −553.408 | − | 179.813i | −2.03459 | − | 0.661077i | ||||
\(273\) | 88.8260 | + | 170.217i | 0.325370 | + | 0.623507i | ||||
\(274\) | −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 | 0.0694432 | − | 0.997586i | \(-0.477878\pi\) |
−0.927301 | + | 0.374315i | \(0.877878\pi\) | |||||||
\(278\) | −16.6489 | − | 5.40955i | −0.0598880 | − | 0.0194588i | ||||
\(279\) | 14.7289 | − | 21.1249i | 0.0527917 | − | 0.0757163i | ||||
\(280\) | 17.7632 | − | 12.9057i | 0.0634399 | − | 0.0460918i | ||||
\(281\) | −154.985 | − | 213.319i | −0.551549 | − | 0.759141i | 0.438673 | − | 0.898647i | \(-0.355449\pi\) |
−0.990221 | + | 0.139505i | \(0.955449\pi\) | |||||||
\(282\) | 46.3417 | − | 312.215i | 0.164332 | − | 1.10715i | ||||
\(283\) | 123.232 | − | 379.270i | 0.435450 | − | 1.34018i | −0.457175 | − | 0.889377i | \(-0.651139\pi\) |
0.892625 | − | 0.450800i | \(-0.148861\pi\) | |||||||
\(284\) | −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 | ||||||||
\(288\) | 303.254 | − | 5.90018i | 1.05296 | − | 0.0204867i | ||||
\(289\) | −175.935 | + | 541.472i | −0.608771 | + | 1.87360i | ||||
\(290\) | 49.3467 | − | 16.0337i | 0.170161 | − | 0.0552887i | ||||
\(291\) | 441.640 | − | 74.3593i | 1.51766 | − | 0.255530i | ||||
\(292\) | −103.189 | + | 74.9713i | −0.353388 | + | 0.256751i | ||||
\(293\) | −331.765 | + | 107.797i | −1.13230 | + | 0.367908i | −0.814451 | − | 0.580232i | \(-0.802962\pi\) |
−0.317853 | + | 0.948140i | \(0.602962\pi\) | |||||||
\(294\) | −18.9825 | − | 18.6167i | −0.0645662 | − | 0.0633222i | ||||
\(295\) | 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 | ||||
\(300\) | 121.452 | − | 123.837i | 0.404838 | − | 0.412792i | ||||
\(301\) | 26.0750 | + | 80.2505i | 0.0866278 | + | 0.266613i | ||||
\(302\) | 41.8923 | + | 57.6597i | 0.138716 | + | 0.190926i | ||||
\(303\) | 9.96680 | + | 59.1955i | 0.0328937 | + | 0.195365i | ||||
\(304\) | 161.010 | + | 495.537i | 0.529637 | + | 1.63005i | ||||
\(305\) | 47.8069 | + | 15.5334i | 0.156744 | + | 0.0509292i | ||||
\(306\) | −12.9478 | − | 665.483i | −0.0423130 | − | 2.17478i | ||||
\(307\) | −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 | \(-0.650380\pi\) |
−0.891548 | + | 0.452925i | \(0.850380\pi\) | |||||||
\(312\) | −115.702 | − | 17.1735i | −0.370841 | − | 0.0550434i | ||||
\(313\) | −428.698 | + | 311.467i | −1.36964 | + | 0.995102i | −0.371876 | + | 0.928283i | \(0.621285\pi\) |
−0.997765 | + | 0.0668198i | \(0.978715\pi\) | |||||||
\(314\) | −100.594 | − | 138.455i | −0.320362 | − | 0.440941i | ||||
\(315\) | 39.4503 | + | 27.5060i | 0.125239 | + | 0.0873205i | ||||
\(316\) | −40.8171 | + | 125.622i | −0.129168 | + | 0.397539i | ||||
\(317\) | 216.556 | − | 298.063i | 0.683140 | − | 0.940262i | −0.316826 | − | 0.948484i | \(-0.602617\pi\) |
0.999966 | + | 0.00822156i | \(0.00261703\pi\) | |||||||
\(318\) | 607.462 | + | 302.111i | 1.91026 | + | 0.950035i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 4.45877i | − | 0.0139337i | ||||||
\(321\) | 171.622 | − | 89.5593i | 0.534649 | − | 0.279001i | ||||
\(322\) | −141.634 | + | 435.904i | −0.439857 | + | 1.35374i | ||||
\(323\) | 730.962 | − | 237.504i | 2.26304 | − | 0.735306i | ||||
\(324\) | 66.4427 | + | 180.302i | 0.205070 | + | 0.556488i | ||||
\(325\) | −187.103 | + | 135.938i | −0.575701 | + | 0.418271i | ||||
\(326\) | −162.940 | + | 52.9425i | −0.499817 | + | 0.162400i | ||||
\(327\) | −231.647 | + | 236.198i | −0.708400 | + | 0.722317i | ||||
\(328\) | −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 | ||||
\(333\) | −20.3583 | + | 7.05552i | −0.0611361 | + | 0.0211878i | ||||
\(334\) | 43.8670 | + | 135.009i | 0.131338 | + | 0.404218i | ||||
\(335\) | −29.4919 | − | 40.5921i | −0.0880354 | − | 0.121170i | ||||
\(336\) | −396.292 | + | 66.7240i | −1.17944 | + | 0.198583i | ||||
\(337\) | −16.4618 | − | 50.6643i | −0.0488482 | − | 0.150339i | 0.923657 | − | 0.383220i | \(-0.125185\pi\) |
−0.972505 | + | 0.232881i | \(0.925185\pi\) | |||||||
\(338\) | 189.558 | + | 61.5911i | 0.560822 | + | 0.182222i | ||||
\(339\) | 333.093 | − | 173.821i | 0.982574 | − | 0.512745i | ||||
\(340\) | −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 | ||||
\(345\) | −9.39448 | + | 63.2929i | −0.0272304 | + | 0.183458i | ||||
\(346\) | 458.554 | − | 333.159i | 1.32530 | − | 0.962888i | ||||
\(347\) | 6.58804 | + | 9.06766i | 0.0189857 | + | 0.0261316i | 0.818404 | − | 0.574643i | \(-0.194859\pi\) |
−0.799419 | + | 0.600774i | \(0.794859\pi\) | |||||||
\(348\) | −182.632 | − | 27.1078i | −0.524805 | − | 0.0778960i | ||||
\(349\) | −66.1346 | + | 203.541i | −0.189498 | + | 0.583213i | −0.999997 | − | 0.00252619i | \(-0.999196\pi\) |
0.810499 | + | 0.585740i | \(0.199196\pi\) | |||||||
\(350\) | −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 | \(-0.271332\pi\) | |||||||
\(354\) | −51.7071 | − | 99.0863i | −0.146065 | − | 0.279905i | ||||
\(355\) | 1.11431 | − | 3.42948i | 0.00313889 | − | 0.00966051i | ||||
\(356\) | 31.8890 | − | 10.3614i | 0.0895760 | − | 0.0291050i | ||||
\(357\) | 98.4240 | + | 584.566i | 0.275698 | + | 1.63744i | ||||
\(358\) | 286.854 | − | 208.411i | 0.801267 | − | 0.582155i | ||||
\(359\) | −166.620 | + | 54.1381i | −0.464122 | + | 0.150802i | −0.531738 | − | 0.846909i | \(-0.678461\pi\) |
0.0676158 | + | 0.997711i | \(0.478461\pi\) | |||||||
\(360\) | −27.6836 | + | 9.59420i | −0.0768988 | + | 0.0266506i | ||||
\(361\) | −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 | ||||
\(366\) | −343.035 | − | 336.426i | −0.937255 | − | 0.919197i | ||||
\(367\) | 42.9643 | + | 132.231i | 0.117069 | + | 0.360301i | 0.992373 | − | 0.123272i | \(-0.0393387\pi\) |
−0.875304 | + | 0.483573i | \(0.839339\pi\) | |||||||
\(368\) | −314.277 | − | 432.565i | −0.854013 | − | 1.17545i | ||||
\(369\) | 46.0490 | − | 151.704i | 0.124794 | − | 0.411122i | ||||
\(370\) | 1.47959 | + | 4.55372i | 0.00399890 | + | 0.0123073i | ||||
\(371\) | −574.649 | − | 186.715i | −1.54892 | − | 0.503275i | ||||
\(372\) | 9.42120 | + | 18.0538i | 0.0253258 | + | 0.0485318i | ||||
\(373\) | 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 | ||||
\(378\) | −220.556 | − | 403.323i | −0.583482 | − | 1.06699i | ||||
\(379\) | −218.753 | + | 158.934i | −0.577186 | + | 0.419350i | −0.837708 | − | 0.546118i | \(-0.816105\pi\) |
0.260523 | + | 0.965468i | \(0.416105\pi\) | |||||||
\(380\) | 28.9819 | + | 39.8902i | 0.0762681 | + | 0.104974i | ||||
\(381\) | 84.9418 | − | 572.274i | 0.222944 | − | 1.50203i | ||||
\(382\) | 274.115 | − | 843.639i | 0.717578 | − | 2.20848i | ||||
\(383\) | −371.364 | + | 511.138i | −0.969618 | + | 1.33456i | −0.0273778 | + | 0.999625i | \(0.508716\pi\) |
−0.942240 | + | 0.334939i | \(0.891284\pi\) | |||||||
\(384\) | 161.109 | − | 323.945i | 0.419554 | − | 0.843607i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 619.738i | 1.60554i | ||||||||
\(387\) | −2.19032 | − | 112.577i | −0.00565973 | − | 0.290896i | ||||
\(388\) | −109.437 | + | 336.814i | −0.282055 | + | 0.868076i | ||||
\(389\) | −437.482 | + | 142.147i | −1.12463 | + | 0.365415i | −0.811534 | − | 0.584305i | \(-0.801367\pi\) |
−0.313098 | + | 0.949721i | \(0.601367\pi\) | |||||||
\(390\) | −56.1445 | + | 9.45311i | −0.143960 | + | 0.0242387i | ||||
\(391\) | −638.073 | + | 463.587i | −1.63190 | + | 1.18564i | ||||
\(392\) | −13.7198 | + | 4.45784i | −0.0349995 | + | 0.0113720i | ||||
\(393\) | 227.245 | + | 222.867i | 0.578232 | + | 0.567092i | ||||
\(394\) | 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 | ||||
\(399\) | 371.667 | − | 378.968i | 0.931496 | − | 0.949795i | ||||
\(400\) | −149.585 | − | 460.376i | −0.373963 | − | 1.15094i | ||||
\(401\) | 105.710 | + | 145.497i | 0.263616 | + | 0.362837i | 0.920222 | − | 0.391398i | \(-0.128008\pi\) |
−0.656605 | + | 0.754234i | \(0.728008\pi\) | |||||||
\(402\) | 79.6282 | + | 472.933i | 0.198080 | + | 1.17645i | ||||
\(403\) | −8.39051 | − | 25.8233i | −0.0208201 | − | 0.0640777i | ||||
\(404\) | −45.1450 | − | 14.6685i | −0.111745 | − | 0.0363082i | ||||
\(405\) | −39.7122 | − | 50.4123i | −0.0980549 | − | 0.124475i | ||||
\(406\) | 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 | 0.445436 | − | 0.895314i | \(-0.353049\pi\) |
−0.713847 | + | 0.700302i | \(0.753049\pi\) | |||||||
\(410\) | −33.5066 | − | 10.8870i | −0.0817234 | − | 0.0265535i | ||||
\(411\) | −579.540 | − | 86.0204i | −1.41007 | − | 0.209295i | ||||
\(412\) | −346.272 | + | 251.582i | −0.840467 | + | 0.610635i | ||||
\(413\) | 58.5079 | + | 80.5292i | 0.141666 | + | 0.194986i | ||||
\(414\) | 349.801 | − | 501.701i | 0.844931 | − | 1.21184i | ||||
\(415\) | 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 | \(-0.0191314\pi\) | |||||||
\(420\) | −33.7152 | + | 17.5939i | −0.0802744 | + | 0.0418903i | ||||
\(421\) | −16.2805 | + | 50.1063i | −0.0386711 | + | 0.119017i | −0.968528 | − | 0.248903i | \(-0.919930\pi\) |
0.929857 | + | 0.367920i | \(0.119930\pi\) | |||||||
\(422\) | −256.375 | + | 83.3014i | −0.607525 | + | 0.197397i | ||||
\(423\) | 108.954 | − | 358.939i | 0.257575 | − | 0.848556i | ||||
\(424\) | 297.802 | − | 216.366i | 0.702363 | − | 0.510296i | ||||
\(425\) | −679.096 | + | 220.652i | −1.59787 | + | 0.519181i | ||||
\(426\) | −24.1339 | + | 24.6080i | −0.0566524 | + | 0.0577653i | ||||
\(427\) | 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 | \(-0.604480\pi\) |
0.999901 | + | 0.0140726i | \(0.00447961\pi\) | |||||||
\(432\) | 531.878 | + | 68.4000i | 1.23120 | + | 0.158333i | ||||
\(433\) | 159.336 | + | 490.386i | 0.367982 | + | 1.13253i | 0.948093 | + | 0.317994i | \(0.103009\pi\) |
−0.580111 | + | 0.814537i | \(0.696991\pi\) | |||||||
\(434\) | −28.6352 | − | 39.4129i | −0.0659796 | − | 0.0908132i | ||||
\(435\) | 60.8072 | − | 10.2382i | 0.139787 | − | 0.0235360i | ||||
\(436\) | −80.8415 | − | 248.804i | −0.185416 | − | 0.570652i | ||||
\(437\) | 671.660 | + | 218.235i | 1.53698 | + | 0.499395i | ||||
\(438\) | −360.979 | + | 188.373i | −0.824152 | + | 0.430075i | ||||
\(439\) | −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 | 0.992029 | + | 0.126011i | \(0.0402173\pi\) |
0.876635 | + | 0.481155i | \(0.159783\pi\) | |||||||
\(444\) | 2.50151 | − | 16.8533i | 0.00563404 | − | 0.0379579i | ||||
\(445\) | −9.05960 | + | 6.58219i | −0.0203587 | + | 0.0147914i | ||||
\(446\) | 113.851 | + | 156.702i | 0.255271 | + | 0.351351i | ||||
\(447\) | 200.892 | + | 29.8180i | 0.449422 | + | 0.0667070i | ||||
\(448\) | 11.7292 | − | 36.0988i | 0.0261813 | − | 0.0805776i | ||||
\(449\) | −338.354 | + | 465.704i | −0.753572 | + | 1.03720i | 0.244150 | + | 0.969737i | \(0.421491\pi\) |
−0.997722 | + | 0.0674648i | \(0.978509\pi\) | |||||||
\(450\) | 441.549 | − | 334.118i | 0.981220 | − | 0.742484i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 297.103i | 0.657308i | ||||||||
\(453\) | 39.1857 | + | 75.0916i | 0.0865027 | + | 0.165765i | ||||
\(454\) | −37.6329 | + | 115.822i | −0.0828918 | + | 0.255115i | ||||
\(455\) | 48.2246 | − | 15.6691i | 0.105988 | − | 0.0344376i | ||||
\(456\) | 53.6914 | + | 318.887i | 0.117744 | + | 0.699314i | ||||
\(457\) | −20.7046 | + | 15.0428i | −0.0453055 | + | 0.0329164i | −0.610208 | − | 0.792242i | \(-0.708914\pi\) |
0.564902 | + | 0.825158i | \(0.308914\pi\) | |||||||
\(458\) | −37.0100 | + | 12.0253i | −0.0808079 | + | 0.0262561i | ||||
\(459\) | 100.896 | − | 784.568i | 0.219818 | − | 1.70930i | ||||
\(460\) | −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 | ||||
\(465\) | −4.85570 | − | 4.76215i | −0.0104424 | − | 0.0102412i | ||||
\(466\) | −135.111 | − | 415.829i | −0.289938 | − | 0.892336i | ||||
\(467\) | −64.8441 | − | 89.2503i | −0.138853 | − | 0.191114i | 0.733928 | − | 0.679228i | \(-0.237685\pi\) |
−0.872780 | + | 0.488114i | \(0.837685\pi\) | |||||||
\(468\) | 193.863 | + | 58.8462i | 0.414238 | + | 0.125740i | ||||
\(469\) | −131.989 | − | 406.220i | −0.281426 | − | 0.866141i | ||||
\(470\) | −79.2782 | − | 25.7591i | −0.168677 | − | 0.0548065i | ||||
\(471\) | −94.0948 | − | 180.314i | −0.199777 | − | 0.382832i | ||||
\(472\) | −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 | ||||
\(477\) | 661.389 | + | 461.140i | 1.38656 | + | 0.966751i | ||||
\(478\) | −605.312 | + | 439.785i | −1.26634 | + | 0.920052i | ||||
\(479\) | 401.770 | + | 552.989i | 0.838769 | + | 1.15447i | 0.986227 | + | 0.165398i | \(0.0528909\pi\) |
−0.147458 | + | 0.989068i | \(0.547109\pi\) | |||||||
\(480\) | 11.7608 | − | 79.2351i | 0.0245016 | − | 0.165073i | ||||
\(481\) | −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 | ||||||
\(486\) | 125.300 | + | 600.480i | 0.257818 | + | 1.23556i | ||||
\(487\) | −40.2033 | + | 123.733i | −0.0825530 | + | 0.254072i | −0.983811 | − | 0.179212i | \(-0.942645\pi\) |
0.901258 | + | 0.433284i | \(0.142645\pi\) | |||||||
\(488\) | −247.933 | + | 80.5584i | −0.508060 | + | 0.165079i | ||||
\(489\) | −200.782 | + | 33.8059i | −0.410598 | + | 0.0691328i | ||||
\(490\) | −5.68071 | + | 4.12728i | −0.0115933 | + | 0.00842302i | ||||
\(491\) | 757.592 | − | 246.157i | 1.54296 | − | 0.501338i | 0.590767 | − | 0.806842i | \(-0.298825\pi\) |
0.952191 | + | 0.305504i | \(0.0988251\pi\) | |||||||
\(492\) | 89.5056 | + | 87.7811i | 0.181922 | + | 0.178417i | ||||
\(493\) | 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 | ||||
\(498\) | −346.460 | + | 353.266i | −0.695702 | + | 0.709370i | ||||
\(499\) | 151.428 | + | 466.048i | 0.303464 | + | 0.933965i | 0.980246 | + | 0.197782i | \(0.0633738\pi\) |
−0.676782 | + | 0.736183i | \(0.736626\pi\) | |||||||
\(500\) | −54.5445 | − | 75.0740i | −0.109089 | − | 0.150148i | ||||
\(501\) | 28.0108 | + | 166.364i | 0.0559099 | + | 0.332063i | ||||
\(502\) | 162.088 | + | 498.855i | 0.322884 | + | 0.993735i | ||||
\(503\) | −269.417 | − | 87.5387i | −0.535619 | − | 0.174033i | 0.0287028 | − | 0.999588i | \(-0.490862\pi\) |
−0.564322 | + | 0.825555i | \(0.690862\pi\) | |||||||
\(504\) | −249.368 | + | 4.85176i | −0.494778 | + | 0.00962652i | ||||
\(505\) | 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 | \(-0.323068\pi\) |
−0.0724082 | + | 0.997375i | \(0.523068\pi\) | |||||||
\(510\) | −173.879 | − | 25.8087i | −0.340940 | − | 0.0506052i | ||||
\(511\) | 293.374 | − | 213.149i | 0.574118 | − | 0.417121i | ||||
\(512\) | 201.563 | + | 277.427i | 0.393677 | + | 0.541851i | ||||
\(513\) | −621.458 | + | 339.842i | −1.21142 | + | 0.662461i | ||||
\(514\) | −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 | ||||||||
\(519\) | 597.186 | − | 311.635i | 1.15065 | − | 0.600452i | ||||
\(520\) | −9.54592 | + | 29.3793i | −0.0183575 | + | 0.0564987i | ||||
\(521\) | 357.858 | − | 116.275i | 0.686867 | − | 0.223177i | 0.0552676 | − | 0.998472i | \(-0.482399\pi\) |
0.631599 | + | 0.775295i | \(0.282399\pi\) | |||||||
\(522\) | −563.992 | − | 171.197i | −1.08044 | − | 0.327963i | ||||
\(523\) | −449.686 | + | 326.716i | −0.859820 | + | 0.624696i | −0.927836 | − | 0.372989i | \(-0.878333\pi\) |
0.0680161 | + | 0.997684i | \(0.478333\pi\) | |||||||
\(524\) | −239.374 | + | 77.7775i | −0.456821 | + | 0.148430i | ||||
\(525\) | −345.295 | + | 352.079i | −0.657705 | + | 0.670626i | ||||
\(526\) | −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 | ||||
\(531\) | −43.4952 | − | 125.503i | −0.0819119 | − | 0.236352i | ||||
\(532\) | 129.706 | + | 399.196i | 0.243809 | + | 0.750368i | ||||
\(533\) | −98.2514 | − | 135.231i | −0.184337 | − | 0.253718i | ||||
\(534\) | 105.552 | − | 17.7719i | 0.197663 | − | 0.0332808i | ||||
\(535\) | −15.7985 | − | 48.6227i | −0.0295299 | − | 0.0908836i | ||||
\(536\) | 247.477 | + | 80.4100i | 0.461710 | + | 0.150019i | ||||
\(537\) | 373.576 | − | 194.947i | 0.695672 | − | 0.363029i | ||||
\(538\) | −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 | −0.995410 | − | 0.0957073i | \(-0.969489\pi\) |
−0.398622 | − | 0.917116i | \(-0.630511\pi\) | |||||||
\(542\) | 298.611 | + | 97.0246i | 0.550943 | + | 0.179012i | ||||
\(543\) | 57.6392 | − | 388.330i | 0.106150 | − | 0.715156i | ||||
\(544\) | 798.790 | − | 580.355i | 1.46836 | − | 1.06683i | ||||
\(545\) | 51.3555 | + | 70.6848i | 0.0942303 | + | 0.129697i | ||||
\(546\) | −479.421 | − | 71.1597i | −0.878060 | − | 0.130329i | ||||
\(547\) | 227.740 | − | 700.913i | 0.416344 | − | 1.28138i | −0.494699 | − | 0.869065i | \(-0.664722\pi\) |
0.911043 | − | 0.412312i | \(-0.135278\pi\) | |||||||
\(548\) | 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 | ||||||
\(552\) | −153.522 | − | 294.194i | −0.278120 | − | 0.532961i | ||||
\(553\) | 116.046 | − | 357.153i | 0.209848 | − | 0.645846i | ||||
\(554\) | 705.166 | − | 229.122i | 1.27286 | − | 0.413578i | ||||
\(555\) | 0.944780 | + | 5.61130i | 0.00170231 | + | 0.0101104i | ||||
\(556\) | 13.3093 | − | 9.66976i | 0.0239376 | − | 0.0173917i | ||||
\(557\) | 604.548 | − | 196.430i | 1.08536 | − | 0.352656i | 0.288911 | − | 0.957356i | \(-0.406707\pi\) |
0.796454 | + | 0.604700i | \(0.206707\pi\) | |||||||
\(558\) | 21.2876 | + | 61.4242i | 0.0381498 | + | 0.110079i | ||||
\(559\) | −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 | −0.151271 | − | 0.988492i | \(-0.548337\pi\) |
0.986857 | − | 0.161593i | \(-0.0516633\pi\) | |||||||
\(564\) | 211.774 | + | 207.694i | 0.375487 | + | 0.368252i | ||||
\(565\) | −30.6624 | − | 94.3691i | −0.0542697 | − | 0.167025i | ||||
\(566\) | 591.709 | + | 814.418i | 1.04542 | + | 1.43890i | ||||
\(567\) | −188.901 | − | 512.611i | −0.333159 | − | 0.904077i | ||||
\(568\) | 5.77895 | + | 17.7858i | 0.0101742 | + | 0.0313130i | ||||
\(569\) | −49.9733 | − | 16.2373i | −0.0878265 | − | 0.0285366i | 0.264774 | − | 0.964310i | \(-0.414703\pi\) |
−0.352601 | + | 0.935774i | \(0.614703\pi\) | |||||||
\(570\) | 72.8198 | + | 139.545i | 0.127754 | + | 0.244815i | ||||
\(571\) | 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 | ||||
\(576\) | −28.9683 | + | 41.5476i | −0.0502922 | + | 0.0721313i | ||||
\(577\) | 71.4329 | − | 51.8990i | 0.123801 | − | 0.0899463i | −0.524162 | − | 0.851619i | \(-0.675621\pi\) |
0.647962 | + | 0.761672i | \(0.275621\pi\) | |||||||
\(578\) | −844.764 | − | 1162.72i | −1.46153 | − | 2.01162i | ||||
\(579\) | −108.135 | + | 728.534i | −0.186762 | + | 1.25826i | ||||
\(580\) | −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 | ||||||||
\(585\) | −67.6502 | + | 1.31622i | −0.115641 | + | 0.00224995i | ||||
\(586\) | 272.116 | − | 837.488i | 0.464362 | − | 1.42916i | ||||
\(587\) | −715.396 | + | 232.446i | −1.21873 | + | 0.395990i | −0.846620 | − | 0.532198i | \(-0.821366\pi\) |
−0.372112 | + | 0.928188i | \(0.621366\pi\) | |||||||
\(588\) | 24.6395 | − | 4.14858i | 0.0419040 | − | 0.00705542i | ||||
\(589\) | −60.7291 | + | 44.1222i | −0.103105 | + | 0.0749104i | ||||
\(590\) | −28.0723 | + | 9.12125i | −0.0475802 | + | 0.0154598i | ||||
\(591\) | 13.1791 | + | 12.9252i | 0.0222997 | + | 0.0218701i | ||||
\(592\) | −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 | ||||
\(597\) | −405.984 | + | 413.960i | −0.680040 | + | 0.693400i | ||||
\(598\) | −199.269 | − | 613.287i | −0.333226 | − | 1.02556i | ||||
\(599\) | 237.419 | + | 326.780i | 0.396360 | + | 0.545542i | 0.959826 | − | 0.280597i | \(-0.0905324\pi\) |
−0.563466 | + | 0.826139i | \(0.690532\pi\) | |||||||
\(600\) | −49.8817 | − | 296.261i | −0.0831362 | − | 0.493768i | ||||
\(601\) | −255.483 | − | 786.296i | −0.425097 | − | 1.30831i | −0.902902 | − | 0.429847i | \(-0.858567\pi\) |
0.477805 | − | 0.878466i | \(-0.341433\pi\) | |||||||
\(602\) | −202.579 | − | 65.8220i | −0.336511 | − | 0.109339i | ||||
\(603\) | 11.0872 | + | 569.851i | 0.0183867 | + | 0.945027i | ||||
\(604\) | −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 | 0.949503 | + | 0.313759i | \(0.101588\pi\) |
0.591815 | + | 0.806074i | \(0.298412\pi\) | |||||||
\(608\) | −840.837 | − | 273.204i | −1.38296 | − | 0.449349i | ||||
\(609\) | 519.236 | + | 77.0694i | 0.852604 | + | 0.126551i | ||||
\(610\) | −102.657 | + | 74.5848i | −0.168290 | + | 0.122270i | ||||
\(611\) | −232.468 | − | 319.964i | −0.380471 | − | 0.523673i | ||||
\(612\) | 513.108 | + | 357.755i | 0.838412 | + | 0.584567i | ||||
\(613\) | −277.574 | + | 854.286i | −0.452813 | + | 1.39362i | 0.420870 | + | 0.907121i | \(0.361725\pi\) |
−0.873683 | + | 0.486495i | \(0.838275\pi\) | |||||||
\(614\) | 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 | \(0.803912\pi\) | |||||||
\(618\) | −1211.34 | + | 632.123i | −1.96009 | + | 1.02285i | ||||
\(619\) | −12.4874 | + | 38.4324i | −0.0201736 | + | 0.0620879i | −0.960637 | − | 0.277808i | \(-0.910392\pi\) |
0.940463 | + | 0.339896i | \(0.110392\pi\) | |||||||
\(620\) | 5.11487 | − | 1.66192i | 0.00824979 | − | 0.00268052i | ||||
\(621\) | 498.749 | − | 528.740i | 0.803139 | − | 0.851434i | ||||
\(622\) | 899.288 | − | 653.371i | 1.44580 | − | 1.05044i | ||||
\(623\) | −90.6628 | + | 29.4581i | −0.145526 | + | 0.0472843i | ||||
\(624\) | 395.892 | − | 403.670i | 0.634442 | − | 0.646906i | ||||
\(625\) | −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 | ||||
\(630\) | −114.709 | + | 39.7542i | −0.182077 | + | 0.0631019i | ||||
\(631\) | −231.300 | − | 711.868i | −0.366561 | − | 1.12816i | −0.948998 | − | 0.315283i | \(-0.897901\pi\) |
0.582437 | − | 0.812876i | \(-0.302099\pi\) | |||||||
\(632\) | 134.474 | + | 185.088i | 0.212776 | + | 0.292861i | ||||
\(633\) | −315.918 | + | 53.1914i | −0.499080 | + | 0.0840306i | ||||
\(634\) | 287.396 | + | 884.513i | 0.453306 | + | 1.39513i | ||||
\(635\) | −145.313 | − | 47.2149i | −0.228839 | − | 0.0743542i | ||||
\(636\) | −565.240 | + | 294.964i | −0.888742 | + | 0.463780i | ||||
\(637\) | −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 | \(-0.430413\pi\) |
−0.398338 | + | 0.917239i | \(0.630413\pi\) | |||||||
\(642\) | −71.7471 | + | 483.378i | −0.111756 | + | 0.752925i | ||||
\(643\) | 509.125 | − | 369.901i | 0.791796 | − | 0.575273i | −0.116700 | − | 0.993167i | \(-0.537232\pi\) |
0.908496 | + | 0.417894i | \(0.137232\pi\) | |||||||
\(644\) | −253.176 | − | 348.467i | −0.393130 | − | 0.541097i | ||||
\(645\) | −29.4144 | − | 4.36593i | −0.0456037 | − | 0.00676889i | ||||
\(646\) | −599.540 | + | 1845.19i | −0.928080 | + | 2.85634i | ||||
\(647\) | 109.228 | − | 150.340i | 0.168822 | − | 0.232364i | −0.716220 | − | 0.697875i | \(-0.754129\pi\) |
0.885042 | + | 0.465510i | \(0.154129\pi\) | |||||||
\(648\) | 320.293 | + | 90.4574i | 0.494280 | + | 0.139595i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 583.808i | − | 0.898166i | ||||||
\(651\) | −26.7851 | − | 51.3283i | −0.0411446 | − | 0.0788454i | ||||
\(652\) | 49.7535 | − | 153.125i | 0.0763090 | − | 0.234855i | ||||
\(653\) | 192.509 | − | 62.5501i | 0.294808 | − | 0.0957888i | −0.157879 | − | 0.987458i | \(-0.550466\pi\) |
0.452687 | + | 0.891670i | \(0.350466\pi\) | |||||||
\(654\) | −138.660 | − | 823.539i | −0.212019 | − | 1.25923i | ||||
\(655\) | 68.0057 | − | 49.4090i | 0.103826 | − | 0.0754337i | ||||
\(656\) | 332.744 | − | 108.115i | 0.507232 | − | 0.164810i | ||||
\(657\) | −457.217 | + | 158.456i | −0.695917 | + | 0.241182i | ||||
\(658\) | −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 | ||||
\(663\) | −595.449 | − | 583.977i | −0.898114 | − | 0.880810i | ||||
\(664\) | 82.9610 | + | 255.328i | 0.124941 | + | 0.384530i | ||||
\(665\) | −82.3976 | − | 113.411i | −0.123906 | − | 0.170542i | ||||
\(666\) | 15.7980 | − | 52.0452i | 0.0237208 | − | 0.0781459i | ||||
\(667\) | 215.818 | + | 664.219i | 0.323565 | + | 0.995831i | ||||
\(668\) | −126.876 | − | 41.2246i | −0.189935 | − | 0.0617135i | ||||
\(669\) | 106.495 | + | 204.077i | 0.159186 | + | 0.305048i | ||||
\(670\) | 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 | 0.420792 | − | 0.907157i | \(-0.361752\pi\) |
−0.732726 | + | 0.680524i | \(0.761752\pi\) | |||||||
\(674\) | 127.894 | + | 41.5552i | 0.189754 | + | 0.0616547i | ||||
\(675\) | 577.362 | − | 315.729i | 0.855351 | − | 0.467747i | ||||
\(676\) | −151.535 | + | 110.096i | −0.224164 | + | 0.162864i | ||||
\(677\) | −68.5153 | − | 94.3032i | −0.101204 | − | 0.139296i | 0.755411 | − | 0.655251i | \(-0.227437\pi\) |
−0.856616 | + | 0.515955i | \(0.827437\pi\) | |||||||
\(678\) | −139.250 | + | 938.162i | −0.205384 | + | 1.38372i | ||||
\(679\) | 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 | \(0.817941\pi\) | |||||||
\(684\) | −10.8954 | − | 559.997i | −0.0159290 | − | 0.818709i | ||||
\(685\) | −47.8145 | + | 147.158i | −0.0698022 | + | 0.214829i | ||||
\(686\) | −850.270 | + | 276.269i | −1.23946 | + | 0.402725i | ||||
\(687\) | −45.6054 | + | 7.67863i | −0.0663834 | + | 0.0111770i | ||||
\(688\) | 201.027 | − | 146.055i | 0.292191 | − | 0.212289i | ||||
\(689\) | 808.491 | − | 262.695i | 1.17343 | − | 0.381270i | ||||
\(690\) | −115.320 | − | 113.098i | −0.167130 | − | 0.163910i | ||||
\(691\) | −314.727 | − | 228.663i | −0.455466 | − | 0.330916i | 0.336284 | − | 0.941761i | \(-0.390830\pi\) |
−0.791750 | + | 0.610845i | \(0.790830\pi\) | |||||||
\(692\) | 532.662i | 0.769743i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.2934 | −0.0407686 | ||||||||
\(695\) | −3.22948 | + | 4.44499i | −0.00464673 | + | 0.00639567i | ||||
\(696\) | −223.918 | + | 228.317i | −0.321721 | + | 0.328042i | ||||
\(697\) | −159.480 | − | 490.828i | −0.228809 | − | 0.704201i | ||||
\(698\) | −317.550 | − | 437.071i | −0.454943 | − | 0.626176i | ||||
\(699\) | −86.2738 | − | 512.403i | −0.123425 | − | 0.733051i | ||||
\(700\) | −120.503 | − | 370.871i | −0.172147 | − | 0.529815i | ||||
\(701\) | 1107.15 | + | 359.734i | 1.57938 | + | 0.513172i | 0.961897 | − | 0.273410i | \(-0.0881517\pi\) |
0.617485 | + | 0.786583i | \(0.288152\pi\) | |||||||
\(702\) | 584.581 | + | 276.681i | 0.832737 | + | 0.394132i | ||||
\(703\) | 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 | ||||
\(708\) | 103.896 | + | 15.4211i | 0.146745 | + | 0.0217812i | ||||
\(709\) | −1075.94 | + | 781.714i | −1.51754 | + | 1.10256i | −0.554853 | + | 0.831948i | \(0.687226\pi\) |
−0.962689 | + | 0.270611i | \(0.912774\pi\) | |||||||
\(710\) | 5.35042 | + | 7.36423i | 0.00753581 | + | 0.0103721i | ||||
\(711\) | −286.605 | + | 411.063i | −0.403102 | + | 0.578147i | ||||
\(712\) | 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 | ||||||||
\(717\) | −788.311 | + | 411.372i | −1.09946 | + | 0.573740i | ||||
\(718\) | 136.663 | − | 420.605i | 0.190338 | − | 0.585800i | ||||
\(719\) | −797.573 | + | 259.147i | −1.10928 | + | 0.360427i | −0.805668 | − | 0.592368i | \(-0.798193\pi\) |
−0.303614 | + | 0.952795i | \(0.598193\pi\) | |||||||
\(720\) | 41.1357 | − | 135.518i | 0.0571329 | − | 0.188219i | ||||
\(721\) | 984.477 | − | 715.264i | 1.36543 | − | 0.992045i | ||||
\(722\) | 785.553 | − | 255.242i | 1.08802 | − | 0.353520i | ||||
\(723\) | −98.0996 | + | 100.027i | −0.135684 | + | 0.138350i | ||||
\(724\) | 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 | ||||
\(729\) | 42.5213 | + | 727.759i | 0.0583282 | + | 0.998297i | ||||
\(730\) | 33.2294 | + | 102.270i | 0.0455197 | + | 0.140095i | ||||
\(731\) | −215.444 | − | 296.534i | −0.294726 | − | 0.405655i | ||||
\(732\) | 445.265 | − | 74.9698i | 0.608286 | − | 0.102418i | ||||
\(733\) | 137.519 | + | 423.241i | 0.187612 | + | 0.577409i | 0.999984 | − | 0.00573049i | \(-0.00182408\pi\) |
−0.812372 | + | 0.583140i | \(0.801824\pi\) | |||||||
\(734\) | −333.795 | − | 108.456i | −0.454761 | − | 0.147761i | ||||
\(735\) | −7.39812 | + | 3.86063i | −0.0100655 | + | 0.00525256i | ||||
\(736\) | 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 | 0.553692 | − | 0.832721i | \(-0.313218\pi\) |
−0.620865 | + | 0.783918i | \(0.713218\pi\) | |||||||
\(740\) | −4.27942 | − | 1.39047i | −0.00578300 | − | 0.00187901i | ||||
\(741\) | −109.646 | + | 738.711i | −0.147970 | + | 0.996911i | ||||
\(742\) | 1233.96 | − | 896.526i | 1.66302 | − | 1.20826i | ||||
\(743\) | 425.116 | + | 585.122i | 0.572161 | + | 0.787512i | 0.992809 | − | 0.119712i | \(-0.0381970\pi\) |
−0.420647 | + | 0.907224i | \(0.638197\pi\) | |||||||
\(744\) | 34.8896 | + | 5.17861i | 0.0468946 | + | 0.00696050i | ||||
\(745\) | 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 | ||||||
\(750\) | −137.048 | − | 262.626i | −0.182731 | − | 0.350167i | ||||
\(751\) | 397.509 | − | 1223.41i | 0.529306 | − | 1.62904i | −0.226333 | − | 0.974050i | \(-0.572674\pi\) |
0.755639 | − | 0.654988i | \(-0.227326\pi\) | |||||||
\(752\) | 787.288 | − | 255.806i | 1.04693 | − | 0.340167i | ||||
\(753\) | 103.500 | + | 614.712i | 0.137450 | + | 0.816350i | ||||
\(754\) | −502.751 | + | 365.270i | −0.666779 | + | 0.484443i | ||||
\(755\) | 21.2744 | − | 6.91246i | 0.0281780 | − | 0.00915557i | ||||
\(756\) | 428.471 | + | 55.1018i | 0.566761 | + | 0.0728860i | ||||
\(757\) | 220.633 | + | 160.299i | 0.291457 | + | 0.211756i | 0.723899 | − | 0.689906i | \(-0.242348\pi\) |
−0.432442 | + | 0.901662i | \(0.642348\pi\) | |||||||
\(758\) | − | 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 | \(-0.901389\pi\) |
0.584251 | + | 0.811573i | \(0.301389\pi\) | |||||||
\(762\) | 1042.68 | + | 1022.59i | 1.36835 | + | 1.34198i | ||||
\(763\) | 229.838 | + | 707.369i | 0.301229 | + | 0.927089i | ||||
\(764\) | 489.990 | + | 674.414i | 0.641349 | + | 0.882741i | ||||
\(765\) | −199.901 | − | 60.6788i | −0.261308 | − | 0.0793188i | ||||
\(766\) | −492.845 | − | 1516.82i | −0.643401 | − | 1.98018i | ||||
\(767\) | −133.191 | − | 43.2764i | −0.173652 | − | 0.0564229i | ||||
\(768\) | 453.766 | + | 869.552i | 0.590841 | + | 1.13223i | ||||
\(769\) | −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 | \(-0.107905\pi\) |
0.567514 | + | 0.823364i | \(0.307905\pi\) | |||||||
\(774\) | 233.157 | + | 162.564i | 0.301237 | + | 0.210032i | ||||
\(775\) | 56.4200 | − | 40.9916i | 0.0728001 | − | 0.0528923i | ||||
\(776\) | 360.548 | + | 496.251i | 0.464623 | + | 0.639499i | ||||
\(777\) | −7.11198 | + | 47.9151i | −0.00915312 | + | 0.0616668i | ||||
\(778\) | 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 | ||||||
\(783\) | −633.130 | − | 299.659i | −0.808595 | − | 0.382706i | ||||
\(784\) | 21.5480 | − | 66.3180i | 0.0274847 | − | 0.0845893i | ||||
\(785\) | −51.0851 | + | 16.5985i | −0.0650765 | + | 0.0211446i | ||||
\(786\) | −792.326 | + | 133.405i | −1.00805 | + | 0.169726i | ||||
\(787\) | −705.687 | + | 512.712i | −0.896680 | + | 0.651476i | −0.937611 | − | 0.347686i | \(-0.886968\pi\) |
0.0409312 | + | 0.999162i | \(0.486968\pi\) | |||||||
\(788\) | −13.8826 | + | 4.51072i | −0.0176175 | + | 0.00572426i | ||||
\(789\) | −213.670 | − | 209.553i | −0.270811 | − | 0.265593i | ||||
\(790\) | 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 | ||||
\(795\) | 149.096 | − | 152.025i | 0.187542 | − | 0.191226i | ||||
\(796\) | −141.683 | − | 436.054i | −0.177993 | − | 0.547807i | ||||
\(797\) | −32.7783 | − | 45.1155i | −0.0411272 | − | 0.0566067i | 0.787958 | − | 0.615729i | \(-0.211138\pi\) |
−0.829085 | + | 0.559122i | \(0.811138\pi\) | |||||||
\(798\) | 222.474 | + | 1321.33i | 0.278789 | + | 1.65580i | ||||
\(799\) | −377.336 | − | 1161.32i | −0.472261 | − | 1.45347i | ||||
\(800\) | 781.175 | + | 253.819i | 0.976469 | + | 0.317274i | ||||
\(801\) | 127.183 | − | 2.47450i | 0.158780 | − | 0.00308927i | ||||
\(802\) | −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 | ||||
\(807\) | −149.493 | − | 22.1890i | −0.185245 | − | 0.0274957i | ||||
\(808\) | −66.5153 | + | 48.3262i | −0.0823210 | + | 0.0598097i | ||||
\(809\) | 778.882 | + | 1072.04i | 0.962771 | + | 1.32514i | 0.945615 | + | 0.325288i | \(0.105461\pi\) |
0.0171558 | + | 0.999853i | \(0.494539\pi\) | |||||||
\(810\) | 161.877 | − | 6.30143i | 0.199849 | − | 0.00777955i | ||||
\(811\) | −317.710 | + | 977.810i | −0.391751 | + | 1.20568i | 0.539713 | + | 0.841849i | \(0.318533\pi\) |
−0.931463 | + | 0.363835i | \(0.881467\pi\) | |||||||
\(812\) | −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 | ||||||||
\(816\) | 1547.61 | − | 807.605i | 1.89659 | − | 0.989712i | ||||
\(817\) | −101.421 | + | 312.143i | −0.124139 | + | 0.382060i | ||||
\(818\) | 325.776 | − | 105.851i | 0.398259 | − | 0.129402i | ||||
\(819\) | −551.167 | − | 167.304i | −0.672976 | − | 0.204278i | ||||
\(820\) | 26.7855 | − | 19.4608i | 0.0326653 | − | 0.0237327i | ||||
\(821\) | −848.423 | + | 275.669i | −1.03340 | + | 0.335773i | −0.776134 | − | 0.630568i | \(-0.782822\pi\) |
−0.257268 | + | 0.966340i | \(0.582822\pi\) | |||||||
\(822\) | 1035.58 | − | 1055.92i | 1.25983 | − | 1.28458i | ||||
\(823\) | 335.986 | + | 244.108i | 0.408245 | + | 0.296608i | 0.772891 | − | 0.634539i | \(-0.218810\pi\) |
−0.364646 | + | 0.931146i | \(0.618810\pi\) | |||||||
\(824\) | 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 | \(-0.890623\pi\) |
0.611359 | + | 0.791353i | \(0.290623\pi\) | |||||||
\(828\) | 188.213 | + | 543.078i | 0.227310 | + | 0.655891i | ||||
\(829\) | −273.849 | − | 842.819i | −0.330336 | − | 1.01667i | −0.968974 | − | 0.247163i | \(-0.920502\pi\) |
0.638638 | − | 0.769507i | \(-0.279498\pi\) | |||||||
\(830\) | 76.8092 | + | 105.719i | 0.0925412 | + | 0.127372i | ||||
\(831\) | 868.938 | − | 146.304i | 1.04565 | − | 0.176058i | ||||
\(832\) | 16.5022 | + | 50.7884i | 0.0198343 | + | 0.0610438i | ||||
\(833\) | −97.8252 | − | 31.7853i | −0.117437 | − | 0.0381576i | ||||
\(834\) | 46.5588 | − | 24.2962i | 0.0558259 | − | 0.0291322i | ||||
\(835\) | 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 | \(-0.431061\pi\) |
−0.400205 | + | 0.916425i | \(0.631061\pi\) | |||||||
\(840\) | −9.67097 | + | 65.1557i | −0.0115131 | + | 0.0775663i | ||||
\(841\) | −135.879 | + | 98.7221i | −0.161569 | + | 0.117387i | ||||
\(842\) | −78.1722 | − | 107.595i | −0.0928410 | − | 0.127785i | ||||
\(843\) | 782.457 | + | 116.139i | 0.928182 | + | 0.137769i | ||||
\(844\) | 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 | ||||||||
\(849\) | 553.481 | + | 1060.63i | 0.651921 | + | 1.24928i | ||||
\(850\) | 557.000 | − | 1714.27i | 0.655294 | − | 2.01679i | ||||
\(851\) | −61.2942 | + | 19.9157i | −0.0720261 | + | 0.0234027i | ||||
\(852\) | −5.37804 | − | 31.9416i | −0.00631225 | − | 0.0374901i | ||||
\(853\) | 365.390 | − | 265.471i | 0.428359 | − | 0.311221i | −0.352634 | − | 0.935762i | \(-0.614714\pi\) |
0.780992 | + | 0.624541i | \(0.214714\pi\) | |||||||
\(854\) | −1027.33 | + | 333.799i | −1.20296 | + | 0.390866i | ||||
\(855\) | 61.2550 | + | 176.748i | 0.0716432 | + | 0.206723i | ||||
\(856\) | 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 | ||||
\(861\) | −254.471 | − | 249.568i | −0.295552 | − | 0.289858i | ||||
\(862\) | 387.541 | + | 1192.73i | 0.449583 | + | 1.38367i | ||||
\(863\) | −672.067 | − | 925.021i | −0.778756 | − | 1.07187i | −0.995418 | − | 0.0956195i | \(-0.969517\pi\) |
0.216662 | − | 0.976247i | \(-0.430483\pi\) | |||||||
\(864\) | −624.374 | + | 661.919i | −0.722655 | + | 0.766110i | ||||
\(865\) | −54.9731 | − | 169.190i | −0.0635528 | − | 0.195595i | ||||
\(866\) | −1237.90 | − | 402.218i | −1.42945 | − | 0.464455i | ||||
\(867\) | −790.187 | − | 1514.23i | −0.911403 | − | 1.74652i | ||||
\(868\) | 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 | ||||
\(873\) | −768.435 | + | 1102.13i | −0.880224 | + | 1.26246i | ||||
\(874\) | −1442.27 | + | 1047.87i | −1.65020 | + | 1.19894i | ||||
\(875\) | 155.074 | + | 213.441i | 0.177227 | + | 0.243932i | ||||
\(876\) | 56.1802 | − | 378.500i | 0.0641326 | − | 0.432077i | ||||
\(877\) | −333.849 | + | 1027.48i | −0.380672 | + | 1.17159i | 0.558900 | + | 0.829235i | \(0.311223\pi\) |
−0.939572 | + | 0.342352i | \(0.888777\pi\) | |||||||
\(878\) | 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 | \(0.882062\pi\) | |||||||
\(882\) | 79.7486 | − | 1.55161i | 0.0904179 | − | 0.00175919i | ||||
\(883\) | −300.425 | + | 924.613i | −0.340232 | + | 1.04713i | 0.623855 | + | 0.781540i | \(0.285566\pi\) |
−0.964087 | + | 0.265586i | \(0.914434\pi\) | |||||||
\(884\) | 627.231 | − | 203.800i | 0.709537 | − | 0.230543i | ||||
\(885\) | −34.5920 | + | 5.82429i | −0.0390870 | + | 0.00658112i | ||||
\(886\) | −1777.60 | + | 1291.50i | −2.00632 | + | 1.45768i | ||||
\(887\) | −500.232 | + | 162.535i | −0.563960 | + | 0.183242i | −0.577102 | − | 0.816672i | \(-0.695817\pi\) |
0.0131425 | + | 0.999914i | \(0.495817\pi\) | |||||||
\(888\) | −21.0691 | − | 20.6632i | −0.0237265 | − | 0.0232693i | ||||
\(889\) | −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 | ||||
\(894\) | −358.972 | + | 366.024i | −0.401535 | + | 0.409423i | ||||
\(895\) | −34.3890 | − | 105.839i | −0.0384235 | − | 0.118255i | ||||
\(896\) | −478.096 | − | 658.043i | −0.533589 | − | 0.734423i | ||||
\(897\) | −127.241 | − | 755.720i | −0.141852 | − | 0.842497i | ||||
\(898\) | −449.037 | − | 1381.99i | −0.500041 | − | 1.53897i | ||||
\(899\) | −70.6005 | − | 22.9395i | −0.0785322 | − | 0.0255167i | ||||
\(900\) | 10.1224 | + | 520.263i | 0.0112471 | + | 0.578070i | ||||
\(901\) | 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 | ||||
\(906\) | −211.497 | − | 31.3922i | −0.233440 | − | 0.0346492i | ||||
\(907\) | 464.947 | − | 337.804i | 0.512621 | − | 0.372441i | −0.301196 | − | 0.953562i | \(-0.597386\pi\) |
0.813817 | + | 0.581121i | \(0.197386\pi\) | |||||||
\(908\) | −67.2701 | − | 92.5894i | −0.0740861 | − | 0.101971i | ||||
\(909\) | −147.724 | − | 102.998i | −0.162513 | − | 0.113309i | ||||
\(910\) | −39.5542 | + | 121.735i | −0.0434661 | + | 0.133775i | ||||
\(911\) | −751.875 | + | 1034.87i | −0.825329 | + | 1.13597i | 0.163445 | + | 0.986552i | \(0.447739\pi\) |
−0.988774 | + | 0.149416i | \(0.952261\pi\) | |||||||
\(912\) | −1399.58 | − | 696.058i | −1.53463 | − | 0.763222i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 64.6037i | − | 0.0706823i | ||||||
\(915\) | −133.693 | + | 69.7661i | −0.146112 | + | 0.0762471i | ||||
\(916\) | 11.3009 | − | 34.7807i | 0.0123373 | − | 0.0379702i | ||||
\(917\) | 680.558 | − | 221.127i | 0.742157 | − | 0.241142i | ||||
\(918\) | 1452.56 | + | 1370.17i | 1.58231 | + | 1.49256i | ||||
\(919\) | 389.889 | − | 283.271i | 0.424253 | − | 0.308238i | −0.355094 | − | 0.934831i | \(-0.615551\pi\) |
0.779347 | + | 0.626593i | \(0.215551\pi\) | |||||||
\(920\) | −83.3488 | + | 27.0817i | −0.0905965 | + | 0.0294366i | ||||
\(921\) | 837.141 | − | 853.587i | 0.908947 | − | 0.926804i | ||||
\(922\) | 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 | ||||
\(927\) | −1534.29 | + | 531.733i | −1.65511 | + | 0.573606i | ||||
\(928\) | −270.178 | − | 831.523i | −0.291140 | − | 0.896037i | ||||
\(929\) | 653.769 | + | 899.836i | 0.703734 | + | 0.968607i | 0.999909 | + | 0.0134736i | \(0.00428891\pi\) |
−0.296175 | + | 0.955134i | \(0.595711\pi\) | |||||||
\(930\) | 16.9301 | − | 2.85055i | 0.0182045 | − | 0.00306510i | ||||
\(931\) | 28.4615 | + | 87.5953i | 0.0305708 | + | 0.0940874i | ||||
\(932\) | 390.781 | + | 126.972i | 0.419293 | + | 0.136236i | ||||
\(933\) | 1171.16 | − | 611.159i | 1.25527 | − | 0.655047i | ||||
\(934\) | 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 | −0.968155 | − | 0.250350i | \(-0.919454\pi\) |
−0.537273 | − | 0.843408i | \(-0.680546\pi\) | |||||||
\(938\) | 1025.44 | + | 333.184i | 1.09322 | + | 0.355207i | ||||
\(939\) | 233.400 | − | 1572.47i | 0.248562 | − | 1.67462i | ||||
\(940\) | 63.3759 | − | 46.0453i | 0.0674211 | − | 0.0489843i | ||||
\(941\) | −491.503 | − | 676.495i | −0.522319 | − | 0.718911i | 0.463616 | − | 0.886036i | \(-0.346552\pi\) |
−0.985936 | + | 0.167125i | \(0.946552\pi\) | |||||||
\(942\) | 507.857 | + | 75.3805i | 0.539127 | + | 0.0800218i | ||||
\(943\) | 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 | \(-0.0192927\pi\) | |||||||
\(948\) | −183.324 | − | 351.305i | −0.193380 | − | 0.370574i | ||||
\(949\) | −157.659 | + | 485.225i | −0.166132 | + | 0.511301i | ||||
\(950\) | −1535.00 | + | 498.753i | −1.61579 | + | 0.525003i | ||||
\(951\) | 183.514 | + | 1089.94i | 0.192969 | + | 1.14610i | ||||
\(952\) | −656.851 | + | 477.230i | −0.689970 | + | 0.501293i | ||||
\(953\) | −311.052 | + | 101.067i | −0.326392 | + | 0.106051i | −0.467630 | − | 0.883924i | \(-0.654892\pi\) |
0.141237 | + | 0.989976i | \(0.454892\pi\) | |||||||
\(954\) | −1923.10 | + | 666.484i | −2.01583 | + | 0.698620i | ||||
\(955\) | −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 | ||||
\(960\) | 9.55003 | + | 9.36603i | 0.00994795 | + | 0.00975628i | ||||
\(961\) | −294.435 | − | 906.178i | −0.306384 | − | 0.942954i | ||||
\(962\) | −33.7072 | − | 46.3939i | −0.0350386 | − | 0.0482265i | ||||
\(963\) | −168.685 | + | 555.717i | −0.175166 | + | 0.577069i | ||||
\(964\) | −34.2354 | − | 105.366i | −0.0355139 | − | 0.109301i | ||||
\(965\) | 184.991 | + | 60.1071i | 0.191700 | + | 0.0622872i | ||||
\(966\) | −636.129 | − | 1219.01i | −0.658519 | − | 1.26192i | ||||
\(967\) | 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 | \(-0.386599\pi\) |
−0.268714 | + | 0.963220i | \(0.586599\pi\) | |||||||
\(972\) | −525.749 | − | 236.429i | −0.540894 | − | 0.243240i | ||||
\(973\) | −37.8392 | + | 27.4918i | −0.0388892 | + | 0.0282547i | ||||
\(974\) | −193.039 | − | 265.696i | −0.198192 | − | 0.272788i | ||||
\(975\) | 101.866 | − | 686.296i | 0.104478 | − | 0.703894i | ||||
\(976\) | 389.398 | − | 1198.44i | 0.398974 | − | 1.22791i | ||||
\(977\) | 11.9651 | − | 16.4685i | 0.0122468 | − | 0.0168562i | −0.802850 | − | 0.596181i | \(-0.796684\pi\) |
0.815096 | + | 0.579325i | \(0.196684\pi\) | |||||||
\(978\) | 228.875 | − | 460.205i | 0.234024 | − | 0.470557i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 6.59879i | − | 0.00673346i | ||||||
\(981\) | −19.3066 | − | 992.307i | −0.0196805 | − | 1.01153i | ||||
\(982\) | −621.383 | + | 1912.42i | −0.632773 | + | 1.94747i | ||||
\(983\) | 758.379 | − | 246.412i | 0.771494 | − | 0.250674i | 0.103290 | − | 0.994651i | \(-0.467063\pi\) |
0.668204 | + | 0.743978i | \(0.267063\pi\) | |||||||
\(984\) | 214.127 | − | 36.0528i | 0.217609 | − | 0.0366390i | ||||
\(985\) | 3.94401 | − | 2.86549i | 0.00400407 | − | 0.00290912i | ||||
\(986\) | −1824.75 | + | 592.899i | −1.85066 | + | 0.601317i | ||||
\(987\) | −602.090 | − | 590.489i | −0.610020 | − | 0.598267i | ||||
\(988\) | −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 | ||||
\(993\) | 242.932 | − | 247.704i | 0.244644 | − | 0.249450i | ||||
\(994\) | 23.9455 | + | 73.6965i | 0.0240900 | + | 0.0741414i | ||||
\(995\) | 90.0056 | + | 123.882i | 0.0904578 | + | 0.124505i | ||||
\(996\) | −77.2057 | − | 458.545i | −0.0775158 | − | 0.460387i | ||||
\(997\) | 547.355 | + | 1684.58i | 0.549002 | + | 1.68965i | 0.711280 | + | 0.702908i | \(0.248116\pi\) |
−0.162279 | + | 0.986745i | \(0.551884\pi\) | |||||||
\(998\) | −1176.46 | − | 382.256i | −1.17882 | − | 0.383022i | ||||
\(999\) | 27.6525 | − | 58.4253i | 0.0276802 | − | 0.0584838i |
(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.323.1 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.m.323.4 | 16 | ||
11.2 | odd | 10 | 363.3.h.l.269.1 | 16 | |||
11.3 | even | 5 | inner | 363.3.h.m.245.4 | 16 | ||
11.4 | even | 5 | inner | 363.3.h.m.251.1 | 16 | ||
11.5 | even | 5 | 33.3.b.b.23.1 | ✓ | 4 | ||
11.6 | odd | 10 | 363.3.b.h.122.4 | 4 | |||
11.7 | odd | 10 | 363.3.h.l.251.4 | 16 | |||
11.8 | odd | 10 | 363.3.h.l.245.1 | 16 | |||
11.9 | even | 5 | inner | 363.3.h.m.269.4 | 16 | ||
11.10 | odd | 2 | 363.3.h.l.323.4 | 16 | |||
33.2 | even | 10 | 363.3.h.l.269.4 | 16 | |||
33.5 | odd | 10 | 33.3.b.b.23.4 | yes | 4 | ||
33.8 | even | 10 | 363.3.h.l.245.4 | 16 | |||
33.14 | odd | 10 | inner | 363.3.h.m.245.1 | 16 | ||
33.17 | even | 10 | 363.3.b.h.122.1 | 4 | |||
33.20 | odd | 10 | inner | 363.3.h.m.269.1 | 16 | ||
33.26 | odd | 10 | inner | 363.3.h.m.251.4 | 16 | ||
33.29 | even | 10 | 363.3.h.l.251.1 | 16 | |||
33.32 | even | 2 | 363.3.h.l.323.1 | 16 | |||
44.27 | odd | 10 | 528.3.i.d.353.4 | 4 | |||
132.71 | 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 | 11.5 | even | 5 | ||
33.3.b.b.23.4 | yes | 4 | 33.5 | odd | 10 | ||
363.3.b.h.122.1 | 4 | 33.17 | even | 10 | |||
363.3.b.h.122.4 | 4 | 11.6 | odd | 10 | |||
363.3.h.l.245.1 | 16 | 11.8 | odd | 10 | |||
363.3.h.l.245.4 | 16 | 33.8 | even | 10 | |||
363.3.h.l.251.1 | 16 | 33.29 | even | 10 | |||
363.3.h.l.251.4 | 16 | 11.7 | odd | 10 | |||
363.3.h.l.269.1 | 16 | 11.2 | odd | 10 | |||
363.3.h.l.269.4 | 16 | 33.2 | even | 10 | |||
363.3.h.l.323.1 | 16 | 33.32 | even | 2 | |||
363.3.h.l.323.4 | 16 | 11.10 | odd | 2 | |||
363.3.h.m.245.1 | 16 | 33.14 | odd | 10 | inner | ||
363.3.h.m.245.4 | 16 | 11.3 | even | 5 | inner | ||
363.3.h.m.251.1 | 16 | 11.4 | even | 5 | inner | ||
363.3.h.m.251.4 | 16 | 33.26 | odd | 10 | inner | ||
363.3.h.m.269.1 | 16 | 33.20 | odd | 10 | inner | ||
363.3.h.m.269.4 | 16 | 11.9 | even | 5 | inner | ||
363.3.h.m.323.1 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.m.323.4 | 16 | 3.2 | odd | 2 | inner | ||
528.3.i.d.353.3 | 4 | 132.71 | even | 10 | |||
528.3.i.d.353.4 | 4 | 44.27 | odd | 10 |