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 | 323.4 | ||
Root | \(-1.70149 - 0.323920i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.323 |
Dual form | 363.3.h.l.245.4 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
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 | \(-0.582610\pi\) |
0.998508 | − | 0.0546047i | \(-0.0173899\pi\) | |||||||
\(3\) | −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 | \(-0.940000\pi\) |
0.684546 | − | 0.728969i | \(-0.260000\pi\) | |||||||
\(8\) | 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 | 0.842504 | − | 0.538690i | \(-0.181080\pi\) |
−0.251976 | + | 0.967733i | \(0.581080\pi\) | |||||||
\(14\) | −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 | \(0.130592\pi\) |
0.0959609 | + | 0.995385i | \(0.469408\pi\) | |||||||
\(18\) | −18.6364 | − | 12.9939i | −1.03535 | − | 0.721881i | ||||
\(19\) | 8.10666 | − | 24.9497i | 0.426666 | − | 1.31314i | −0.474724 | − | 0.880135i | \(-0.657452\pi\) |
0.901390 | − | 0.433008i | \(-0.142548\pi\) | |||||||
\(20\) | 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 | 0.149022 | − | 0.988834i | \(-0.452388\pi\) |
0.701783 | + | 0.712391i | \(0.252388\pi\) | |||||||
\(30\) | −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 | 0.0974939 | − | 0.995236i | \(-0.468917\pi\) |
−0.506111 | + | 0.862468i | \(0.668917\pi\) | |||||||
\(42\) | 45.2819 | − | 23.6299i | 1.07814 | − | 0.562616i | ||||
\(43\) | −12.5109 | −0.290951 | −0.145475 | − | 0.989362i | \(-0.546471\pi\) | ||||
−0.145475 | + | 0.989362i | \(0.546471\pi\) | |||||||
\(44\) | 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 | −0.922776 | − | 0.385337i | \(-0.874085\pi\) |
0.0813237 | + | 0.996688i | \(0.474085\pi\) | |||||||
\(62\) | 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 | \(0.0200472\pi\) |
−0.770419 | + | 0.637538i | \(0.779953\pi\) | |||||||
\(74\) | −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 | 0.835177 | − | 0.549982i | \(-0.185365\pi\) |
−0.264980 | + | 0.964254i | \(0.585365\pi\) | |||||||
\(80\) | 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 | 0.975067 | − | 0.221910i | \(-0.0712290\pi\) |
−0.512361 | + | 0.858770i | \(0.671229\pi\) | |||||||
\(84\) | 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 | −0.863262 | − | 0.504755i | \(-0.831583\pi\) |
0.746814 | + | 0.665033i | \(0.231583\pi\) | |||||||
\(102\) | −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 | 0.581410 | − | 0.813611i | \(-0.302501\pi\) |
−0.00785789 | + | 0.999969i | \(0.502501\pi\) | |||||||
\(108\) | 27.4013 | − | 57.8945i | 0.253716 | − | 0.536060i | ||||
\(109\) | −110.277 | −1.01172 | −0.505859 | − | 0.862616i | \(-0.668824\pi\) | ||||
−0.505859 | + | 0.862616i | \(0.668824\pi\) | |||||||
\(110\) | 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 | 0.231706 | − | 0.972786i | \(-0.425569\pi\) |
0.996775 | + | 0.0802421i | \(0.0255693\pi\) | |||||||
\(128\) | 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 | \(0.132712\pi\) | ||||
−0.914338 | + | 0.404952i | \(0.867288\pi\) | |||||||
\(132\) | 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 | 0.943052 | − | 0.332645i | \(-0.107941\pi\) |
−0.958469 | + | 0.285197i | \(0.907941\pi\) | |||||||
\(140\) | −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 | 0.921394 | − | 0.388631i | \(-0.127052\pi\) |
−0.654336 | + | 0.756204i | \(0.727052\pi\) | |||||||
\(150\) | 182.571 | + | 27.0988i | 1.21714 | + | 0.180659i | ||||
\(151\) | −8.72469 | + | 26.8518i | −0.0577794 | + | 0.177827i | −0.975781 | − | 0.218750i | \(-0.929802\pi\) |
0.918001 | + | 0.396577i | \(0.129802\pi\) | |||||||
\(152\) | 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 | −0.896432 | − | 0.443181i | \(-0.853850\pi\) |
0.698503 | + | 0.715607i | \(0.253850\pi\) | |||||||
\(168\) | 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 | 0.852296 | − | 0.523060i | \(-0.175209\pi\) |
0.382075 | + | 0.924131i | \(0.375209\pi\) | |||||||
\(174\) | 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 | −0.968130 | − | 0.250448i | \(-0.919422\pi\) |
−0.0609786 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(194\) | −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 | \(0.00497129\pi\) | ||||
−0.999878 | + | 0.0156171i | \(0.995029\pi\) | |||||||
\(198\) | 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 | 0.363931 | − | 0.931426i | \(-0.381434\pi\) |
−0.773378 | + | 0.633945i | \(0.781434\pi\) | |||||||
\(212\) | 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 | −0.408329 | − | 0.912835i | \(-0.633889\pi\) |
0.206205 | + | 0.978509i | \(0.433889\pi\) | |||||||
\(228\) | 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 | −0.532587 | − | 0.846375i | \(-0.678780\pi\) |
0.969529 | + | 0.244976i | \(0.0787802\pi\) | |||||||
\(234\) | −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 | −0.347292 | − | 0.937757i | \(-0.612899\pi\) |
−0.832165 | + | 0.554528i | \(0.812899\pi\) | |||||||
\(240\) | −41.8520 | + | 21.8400i | −0.174383 | + | 0.0910000i | ||||
\(241\) | −46.7011 | −0.193780 | −0.0968902 | − | 0.995295i | \(-0.530890\pi\) | ||||
−0.0968902 | + | 0.995295i | \(0.530890\pi\) | |||||||
\(242\) | 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 | \(-0.939263\pi\) | ||
0.981851 | − | 0.189656i | \(-0.0607374\pi\) | |||||||
\(264\) | 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 | 0.996590 | − | 0.0825177i | \(-0.0262961\pi\) |
−0.854761 | + | 0.519022i | \(0.826296\pi\) | |||||||
\(272\) | 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 | 0.927301 | − | 0.374315i | \(-0.122122\pi\) |
−0.0694432 | + | 0.997586i | \(0.522122\pi\) | |||||||
\(278\) | −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 | 0.990221 | − | 0.139505i | \(-0.0445513\pi\) |
−0.438673 | + | 0.898647i | \(0.644551\pi\) | |||||||
\(282\) | −46.3417 | + | 312.215i | −0.164332 | + | 1.10715i | ||||
\(283\) | −123.232 | + | 379.270i | −0.435450 | + | 1.34018i | 0.457175 | + | 0.889377i | \(0.348861\pi\) |
−0.892625 | + | 0.450800i | \(0.851139\pi\) | |||||||
\(284\) | −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 | 0.317853 | − | 0.948140i | \(-0.397038\pi\) |
0.814451 | + | 0.580232i | \(0.197038\pi\) | |||||||
\(294\) | 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 | \(-0.275160\pi\) | ||||
0.649067 | + | 0.760731i | \(0.275160\pi\) | |||||||
\(308\) | 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 | 0.972505 | − | 0.232881i | \(-0.0748151\pi\) |
−0.923657 | + | 0.383220i | \(0.874815\pi\) | |||||||
\(338\) | −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 | 0.799419 | − | 0.600774i | \(-0.205141\pi\) |
−0.818404 | + | 0.574643i | \(0.805141\pi\) | |||||||
\(348\) | 182.632 | + | 27.1078i | 0.524805 | + | 0.0778960i | ||||
\(349\) | 66.1346 | − | 203.541i | 0.189498 | − | 0.583213i | −0.810499 | − | 0.585740i | \(-0.800804\pi\) |
0.999997 | + | 0.00252619i | \(0.000804112\pi\) | |||||||
\(350\) | −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 | −0.0676158 | − | 0.997711i | \(-0.521539\pi\) |
0.531738 | + | 0.846909i | \(0.321539\pi\) | |||||||
\(360\) | 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 | \(-0.564043\pi\) | ||||
−0.199841 | + | 0.979828i | \(0.564043\pi\) | |||||||
\(374\) | 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 | 0.713847 | − | 0.700302i | \(-0.246951\pi\) |
−0.445436 | + | 0.895314i | \(0.646951\pi\) | |||||||
\(410\) | −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 | −0.999901 | − | 0.0140726i | \(-0.995520\pi\) |
0.322370 | + | 0.946614i | \(0.395520\pi\) | |||||||
\(432\) | 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 | \(-0.490896\pi\) | ||||
0.0285977 | + | 0.999591i | \(0.490896\pi\) | |||||||
\(440\) | 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 | −0.564902 | − | 0.825158i | \(-0.691086\pi\) |
0.610208 | + | 0.792242i | \(0.291086\pi\) | |||||||
\(458\) | 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 | \(0.101617\pi\) | ||||
−0.949474 | + | 0.313845i | \(0.898383\pi\) | |||||||
\(462\) | 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 | \(-0.947109\pi\) |
0.147458 | − | 0.989068i | \(-0.452891\pi\) | |||||||
\(480\) | −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 | −0.952191 | − | 0.305504i | \(-0.901175\pi\) |
−0.590767 | + | 0.806842i | \(0.701175\pi\) | |||||||
\(492\) | −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 | 0.564322 | − | 0.825555i | \(-0.309138\pi\) |
−0.0287028 | + | 0.999588i | \(0.509138\pi\) | |||||||
\(504\) | −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 | −0.0680161 | − | 0.997684i | \(-0.521667\pi\) |
0.927836 | + | 0.372989i | \(0.121667\pi\) | |||||||
\(524\) | 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 | \(0.0305113\pi\) |
0.398622 | + | 0.917116i | \(0.369489\pi\) | |||||||
\(542\) | 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 | \(0.335278\pi\) |
−0.911043 | + | 0.412312i | \(0.864722\pi\) | |||||||
\(548\) | 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 | −0.796454 | − | 0.604700i | \(-0.793293\pi\) |
−0.288911 | + | 0.957356i | \(0.593293\pi\) | |||||||
\(558\) | −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 | \(0.451663\pi\) |
−0.986857 | + | 0.161593i | \(0.948337\pi\) | |||||||
\(564\) | 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 | 0.352601 | − | 0.935774i | \(-0.385297\pi\) |
−0.264774 | + | 0.964310i | \(0.585297\pi\) | |||||||
\(570\) | 72.8198 | + | 139.545i | 0.127754 | + | 0.244815i | ||||
\(571\) | −10.1143 | −0.0177133 | −0.00885666 | − | 0.999961i | \(-0.502819\pi\) | ||||
−0.00885666 | + | 0.999961i | \(0.502819\pi\) | |||||||
\(572\) | 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 | \(0.186832\pi\) | ||||
−0.832633 | + | 0.553825i | \(0.813168\pi\) | |||||||
\(594\) | 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 | \(0.141433\pi\) |
−0.477805 | + | 0.878466i | \(0.658567\pi\) | |||||||
\(602\) | 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 | \(-0.898412\pi\) |
−0.591815 | − | 0.806074i | \(-0.701588\pi\) | |||||||
\(608\) | −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 | \(-0.638275\pi\) |
0.873683 | − | 0.486495i | \(-0.161725\pi\) | |||||||
\(614\) | 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 | \(-0.688306\pi\) | ||
0.557674 | − | 0.830060i | \(-0.311694\pi\) | |||||||
\(660\) | 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 | 0.732726 | − | 0.680524i | \(-0.238248\pi\) |
−0.420792 | + | 0.907157i | \(0.638248\pi\) | |||||||
\(674\) | 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 | 0.856616 | − | 0.515955i | \(-0.172563\pi\) |
−0.755411 | + | 0.655251i | \(0.772563\pi\) | |||||||
\(678\) | 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 | −0.617485 | − | 0.786583i | \(-0.711848\pi\) |
−0.961897 | + | 0.273410i | \(0.911848\pi\) | |||||||
\(702\) | 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 | 0.812372 | − | 0.583140i | \(-0.198176\pi\) |
−0.999984 | + | 0.00573049i | \(0.998176\pi\) | |||||||
\(734\) | 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 | 0.620865 | − | 0.783918i | \(-0.286782\pi\) |
−0.553692 | + | 0.832721i | \(0.686782\pi\) | |||||||
\(740\) | −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 | 0.420647 | − | 0.907224i | \(-0.361803\pi\) |
−0.992809 | + | 0.119712i | \(0.961803\pi\) | |||||||
\(744\) | −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 | −0.584251 | − | 0.811573i | \(-0.698611\pi\) |
0.952395 | + | 0.304865i | \(0.0986115\pi\) | |||||||
\(762\) | 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 | \(-0.495356\pi\) | ||||
0.0145904 | + | 0.999894i | \(0.495356\pi\) | |||||||
\(770\) | 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 | −0.0409312 | − | 0.999162i | \(-0.513032\pi\) |
0.937611 | + | 0.347686i | \(0.113032\pi\) | |||||||
\(788\) | 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 | \(-0.894539\pi\) |
−0.0171558 | − | 0.999853i | \(-0.505461\pi\) | |||||||
\(810\) | −161.877 | + | 6.30143i | −0.199849 | + | 0.00777955i | ||||
\(811\) | 317.710 | − | 977.810i | 0.391751 | − | 1.20568i | −0.539713 | − | 0.841849i | \(-0.681467\pi\) |
0.931463 | − | 0.363835i | \(-0.118533\pi\) | |||||||
\(812\) | −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 | 0.257268 | − | 0.966340i | \(-0.417178\pi\) |
0.776134 | + | 0.630568i | \(0.217178\pi\) | |||||||
\(822\) | −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 | −0.611359 | − | 0.791353i | \(-0.709377\pi\) |
0.941542 | + | 0.336895i | \(0.109377\pi\) | |||||||
\(828\) | 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 | −0.780992 | − | 0.624541i | \(-0.785286\pi\) |
0.352634 | + | 0.935762i | \(0.385286\pi\) | |||||||
\(854\) | 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 | \(-0.956460\pi\) | ||
0.990659 | − | 0.136360i | \(-0.0435402\pi\) | |||||||
\(858\) | 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 | \(-0.688777\pi\) |
0.939572 | − | 0.342352i | \(-0.111223\pi\) | |||||||
\(878\) | 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 | −0.0131425 | − | 0.999914i | \(-0.504183\pi\) |
0.577102 | + | 0.816672i | \(0.304183\pi\) | |||||||
\(888\) | 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 | −0.779347 | − | 0.626593i | \(-0.784449\pi\) |
0.355094 | + | 0.934831i | \(0.384449\pi\) | |||||||
\(920\) | 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 | \(0.0805457\pi\) |
0.537273 | + | 0.843408i | \(0.319454\pi\) | |||||||
\(938\) | 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 | 0.985936 | − | 0.167125i | \(-0.0534484\pi\) |
−0.463616 | + | 0.886036i | \(0.653448\pi\) | |||||||
\(942\) | −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 | −0.141237 | − | 0.989976i | \(-0.545108\pi\) |
0.467630 | + | 0.883924i | \(0.345108\pi\) | |||||||
\(954\) | 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 | \(-0.527797\pi\) | ||||
−0.0872150 | + | 0.996190i | \(0.527797\pi\) | |||||||
\(968\) | 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 | \(-0.751884\pi\) |
0.162279 | − | 0.986745i | \(-0.448116\pi\) | |||||||
\(998\) | 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.l.323.4 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.l.323.1 | 16 | ||
11.2 | odd | 10 | 363.3.h.m.269.4 | 16 | |||
11.3 | even | 5 | inner | 363.3.h.l.245.1 | 16 | ||
11.4 | even | 5 | inner | 363.3.h.l.251.4 | 16 | ||
11.5 | even | 5 | 363.3.b.h.122.4 | 4 | |||
11.6 | odd | 10 | 33.3.b.b.23.1 | ✓ | 4 | ||
11.7 | odd | 10 | 363.3.h.m.251.1 | 16 | |||
11.8 | odd | 10 | 363.3.h.m.245.4 | 16 | |||
11.9 | even | 5 | inner | 363.3.h.l.269.1 | 16 | ||
11.10 | odd | 2 | 363.3.h.m.323.1 | 16 | |||
33.2 | even | 10 | 363.3.h.m.269.1 | 16 | |||
33.5 | odd | 10 | 363.3.b.h.122.1 | 4 | |||
33.8 | even | 10 | 363.3.h.m.245.1 | 16 | |||
33.14 | odd | 10 | inner | 363.3.h.l.245.4 | 16 | ||
33.17 | even | 10 | 33.3.b.b.23.4 | yes | 4 | ||
33.20 | odd | 10 | inner | 363.3.h.l.269.4 | 16 | ||
33.26 | odd | 10 | inner | 363.3.h.l.251.1 | 16 | ||
33.29 | even | 10 | 363.3.h.m.251.4 | 16 | |||
33.32 | even | 2 | 363.3.h.m.323.4 | 16 | |||
44.39 | even | 10 | 528.3.i.d.353.4 | 4 | |||
132.83 | odd | 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 | 11.6 | odd | 10 | ||
33.3.b.b.23.4 | yes | 4 | 33.17 | even | 10 | ||
363.3.b.h.122.1 | 4 | 33.5 | odd | 10 | |||
363.3.b.h.122.4 | 4 | 11.5 | even | 5 | |||
363.3.h.l.245.1 | 16 | 11.3 | even | 5 | inner | ||
363.3.h.l.245.4 | 16 | 33.14 | odd | 10 | inner | ||
363.3.h.l.251.1 | 16 | 33.26 | odd | 10 | inner | ||
363.3.h.l.251.4 | 16 | 11.4 | even | 5 | inner | ||
363.3.h.l.269.1 | 16 | 11.9 | even | 5 | inner | ||
363.3.h.l.269.4 | 16 | 33.20 | odd | 10 | inner | ||
363.3.h.l.323.1 | 16 | 3.2 | odd | 2 | inner | ||
363.3.h.l.323.4 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.m.245.1 | 16 | 33.8 | even | 10 | |||
363.3.h.m.245.4 | 16 | 11.8 | odd | 10 | |||
363.3.h.m.251.1 | 16 | 11.7 | odd | 10 | |||
363.3.h.m.251.4 | 16 | 33.29 | even | 10 | |||
363.3.h.m.269.1 | 16 | 33.2 | even | 10 | |||
363.3.h.m.269.4 | 16 | 11.2 | odd | 10 | |||
363.3.h.m.323.1 | 16 | 11.10 | odd | 2 | |||
363.3.h.m.323.4 | 16 | 33.32 | even | 2 | |||
528.3.i.d.353.3 | 4 | 132.83 | odd | 10 | |||
528.3.i.d.353.4 | 4 | 44.39 | even | 10 |