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 | 269.1 | ||
Root | \(1.56693 - 0.738055i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.269 |
Dual form | 363.3.h.l.251.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.40079 | + | 0.780063i | −1.20039 | + | 0.390032i | −0.839906 | − | 0.542732i | \(-0.817390\pi\) |
−0.360488 | + | 0.932764i | \(0.617390\pi\) | |||||||
\(3\) | 1.38791 | + | 2.65965i | 0.462636 | + | 0.886549i | ||||
\(4\) | 1.91922 | − | 1.39439i | 0.479804 | − | 0.348598i | ||||
\(5\) | −0.753510 | − | 0.244830i | −0.150702 | − | 0.0489660i | 0.232695 | − | 0.972550i | \(-0.425246\pi\) |
−0.383397 | + | 0.923584i | \(0.625246\pi\) | |||||||
\(6\) | −5.40676 | − | 5.30259i | −0.901127 | − | 0.883765i | ||||
\(7\) | 5.45647 | − | 3.96435i | 0.779495 | − | 0.566336i | −0.125332 | − | 0.992115i | \(-0.540000\pi\) |
0.904827 | + | 0.425778i | \(0.140000\pi\) | |||||||
\(8\) | 2.41516 | − | 3.32418i | 0.301895 | − | 0.415522i | ||||
\(9\) | −5.14743 | + | 7.38268i | −0.571937 | + | 0.820298i | ||||
\(10\) | 2.00000 | 0.200000 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.37228 | + | 3.16915i | 0.531023 | + | 0.264096i | ||||
\(13\) | −2.93230 | − | 9.02469i | −0.225562 | − | 0.694207i | −0.998234 | − | 0.0594024i | \(-0.981080\pi\) |
0.772673 | − | 0.634805i | \(-0.218920\pi\) | |||||||
\(14\) | −10.0074 | + | 13.7740i | −0.714812 | + | 0.983854i | ||||
\(15\) | −0.394640 | − | 2.34387i | −0.0263093 | − | 0.156258i | ||||
\(16\) | −6.13751 | + | 18.8893i | −0.383595 | + | 1.18058i | ||||
\(17\) | −27.8635 | − | 9.05339i | −1.63903 | − | 0.532552i | −0.662707 | − | 0.748879i | \(-0.730592\pi\) |
−0.976321 | + | 0.216327i | \(0.930592\pi\) | |||||||
\(18\) | 6.59893 | − | 21.7396i | 0.366607 | − | 1.20775i | ||||
\(19\) | −21.2235 | − | 15.4198i | −1.11703 | − | 0.811567i | −0.133271 | − | 0.991080i | \(-0.542548\pi\) |
−0.983756 | + | 0.179513i | \(0.942548\pi\) | |||||||
\(20\) | −1.78754 | + | 0.580806i | −0.0893769 | + | 0.0290403i | ||||
\(21\) | 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 | \(-0.198995\pi\) | |||||||
\(24\) | 12.1932 | + | 1.80981i | 0.508048 | + | 0.0754088i | ||||
\(25\) | −19.7176 | − | 14.3257i | −0.788704 | − | 0.573027i | ||||
\(26\) | 14.0797 | + | 19.3790i | 0.541526 | + | 0.745346i | ||||
\(27\) | −26.7795 | − | 3.44386i | −0.991832 | − | 0.127551i | ||||
\(28\) | 4.94427 | − | 15.2169i | 0.176581 | − | 0.543461i | ||||
\(29\) | 15.2490 | + | 20.9884i | 0.525826 | + | 0.723738i | 0.986487 | − | 0.163838i | \(-0.0523875\pi\) |
−0.460661 | + | 0.887576i | \(0.652388\pi\) | |||||||
\(30\) | 2.77581 | + | 5.31929i | 0.0925271 | + | 0.177310i | ||||
\(31\) | −0.884223 | − | 2.72136i | −0.0285233 | − | 0.0877858i | 0.935781 | − | 0.352581i | \(-0.114696\pi\) |
−0.964305 | + | 0.264795i | \(0.914696\pi\) | |||||||
\(32\) | − | 33.7013i | − | 1.05316i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 73.9565 | 2.17519 | ||||||||
\(35\) | −5.08209 | + | 1.65127i | −0.145203 | + | 0.0471792i | ||||
\(36\) | 0.415322 | + | 21.3465i | 0.0115367 | + | 0.592958i | ||||
\(37\) | 1.93681 | − | 1.40718i | 0.0523463 | − | 0.0380318i | −0.561304 | − | 0.827609i | \(-0.689700\pi\) |
0.613651 | + | 0.789578i | \(0.289700\pi\) | |||||||
\(38\) | 62.9815 | + | 20.4639i | 1.65741 | + | 0.538525i | ||||
\(39\) | 19.9327 | − | 20.3243i | 0.511096 | − | 0.521136i | ||||
\(40\) | −2.63370 | + | 1.91350i | −0.0658426 | + | 0.0478375i | ||||
\(41\) | −10.3541 | + | 14.2512i | −0.252539 | + | 0.347590i | −0.916399 | − | 0.400267i | \(-0.868917\pi\) |
0.663859 | + | 0.747857i | \(0.268917\pi\) | |||||||
\(42\) | −50.5232 | − | 7.49908i | −1.20293 | − | 0.178550i | ||||
\(43\) | −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 | ||||
\(46\) | 20.9997 | + | 64.6305i | 0.456516 | + | 1.40501i | ||||
\(47\) | 24.4983 | − | 33.7190i | 0.521241 | − | 0.717426i | −0.464523 | − | 0.885561i | \(-0.653774\pi\) |
0.985764 | + | 0.168135i | \(0.0537743\pi\) | |||||||
\(48\) | −58.7572 | + | 9.89301i | −1.22411 | + | 0.206104i | ||||
\(49\) | −1.08492 | + | 3.33904i | −0.0221412 | + | 0.0681437i | ||||
\(50\) | 58.5127 | + | 19.0119i | 1.17025 | + | 0.380238i | ||||
\(51\) | −14.5931 | − | 86.6722i | −0.286139 | − | 1.69946i | ||||
\(52\) | −18.2117 | − | 13.2316i | −0.350225 | − | 0.254453i | ||||
\(53\) | 85.2019 | − | 27.6838i | 1.60758 | − | 0.522335i | 0.638616 | − | 0.769526i | \(-0.279507\pi\) |
0.968967 | + | 0.247191i | \(0.0795075\pi\) | |||||||
\(54\) | 66.9783 | − | 12.6217i | 1.24034 | − | 0.233735i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 27.7128i | − | 0.494872i | ||||||
\(57\) | 11.5549 | − | 77.8482i | 0.202717 | − | 1.36576i | ||||
\(58\) | −52.9818 | − | 38.4935i | −0.913480 | − | 0.663682i | ||||
\(59\) | 8.67483 | + | 11.9399i | 0.147031 | + | 0.202371i | 0.876180 | − | 0.481984i | \(-0.160084\pi\) |
−0.729149 | + | 0.684355i | \(0.760084\pi\) | |||||||
\(60\) | −4.02567 | − | 3.94811i | −0.0670945 | − | 0.0658018i | ||||
\(61\) | 19.6058 | − | 60.3404i | 0.321406 | − | 0.989186i | −0.651631 | − | 0.758536i | \(-0.725915\pi\) |
0.973037 | − | 0.230650i | \(-0.0740853\pi\) | |||||||
\(62\) | 4.24567 | + | 5.84366i | 0.0684785 | + | 0.0942525i | ||||
\(63\) | 1.18079 | + | 60.6896i | 0.0187427 | + | 0.963327i | ||||
\(64\) | 1.73906 | + | 5.35228i | 0.0271728 | + | 0.0836294i | ||||
\(65\) | 7.51811i | 0.115663i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63.3288 | −0.945206 | −0.472603 | − | 0.881276i | \(-0.656685\pi\) | ||||
−0.472603 | + | 0.881276i | \(0.656685\pi\) | |||||||
\(68\) | −66.1000 | + | 21.4772i | −0.972059 | + | 0.315841i | ||||
\(69\) | 71.5991 | − | 37.3632i | 1.03767 | − | 0.541495i | ||||
\(70\) | 10.9129 | − | 7.92871i | 0.155899 | − | 0.113267i | ||||
\(71\) | 4.32858 | + | 1.40644i | 0.0609660 | + | 0.0198090i | 0.339341 | − | 0.940663i | \(-0.389796\pi\) |
−0.278375 | + | 0.960472i | \(0.589796\pi\) | |||||||
\(72\) | 12.1095 | + | 34.9413i | 0.168188 | + | 0.485296i | ||||
\(73\) | −43.4979 | + | 31.6030i | −0.595861 | + | 0.432918i | −0.844407 | − | 0.535702i | \(-0.820047\pi\) |
0.248546 | + | 0.968620i | \(0.420047\pi\) | |||||||
\(74\) | −3.55219 | + | 4.88917i | −0.0480025 | + | 0.0660698i | ||||
\(75\) | 10.7350 | − | 72.3245i | 0.143134 | − | 0.964327i | ||||
\(76\) | −62.2337 | −0.818864 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.0000 | + | 64.3432i | −0.410256 | + | 0.824912i | ||||
\(79\) | −17.2059 | − | 52.9542i | −0.217796 | − | 0.670306i | −0.998943 | − | 0.0459597i | \(-0.985365\pi\) |
0.781148 | − | 0.624346i | \(-0.214635\pi\) | |||||||
\(80\) | 9.24935 | − | 12.7306i | 0.115617 | − | 0.159133i | ||||
\(81\) | −28.0079 | − | 76.0037i | −0.345777 | − | 0.938317i | ||||
\(82\) | 13.7412 | − | 42.2910i | 0.167575 | − | 0.515744i | ||||
\(83\) | −62.1400 | − | 20.1905i | −0.748674 | − | 0.243259i | −0.0902636 | − | 0.995918i | \(-0.528771\pi\) |
−0.658411 | + | 0.752659i | \(0.728771\pi\) | |||||||
\(84\) | 47.3338 | − | 7.96963i | 0.563497 | − | 0.0948766i | ||||
\(85\) | 18.7789 | + | 13.6436i | 0.220928 | + | 0.160513i | ||||
\(86\) | 30.0360 | − | 9.75927i | 0.349255 | − | 0.113480i | ||||
\(87\) | −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 | \(0.974698\pi\) | |||||||
\(90\) | −10.2949 | + | 14.7654i | −0.114387 | + | 0.164060i | ||||
\(91\) | −51.7771 | − | 37.6183i | −0.568979 | − | 0.413387i | ||||
\(92\) | −37.5378 | − | 51.6663i | −0.408019 | − | 0.561590i | ||||
\(93\) | 6.01063 | − | 6.12871i | 0.0646305 | − | 0.0659001i | ||||
\(94\) | −32.5123 | + | 100.062i | −0.345875 | + | 1.06449i | ||||
\(95\) | 12.2169 | + | 16.8151i | 0.128599 | + | 0.177001i | ||||
\(96\) | 89.6334 | − | 46.7742i | 0.933681 | − | 0.487231i | ||||
\(97\) | 46.1317 | + | 141.979i | 0.475584 | + | 1.46370i | 0.845168 | + | 0.534501i | \(0.179500\pi\) |
−0.369584 | + | 0.929198i | \(0.620500\pi\) | |||||||
\(98\) | − | 8.86263i | − | 0.0904350i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −57.8179 | −0.578179 | ||||||||
\(101\) | 19.0302 | − | 6.18329i | 0.188418 | − | 0.0612207i | −0.213288 | − | 0.976989i | \(-0.568417\pi\) |
0.401706 | + | 0.915769i | \(0.368417\pi\) | |||||||
\(102\) | 102.645 | + | 196.698i | 1.00632 | + | 1.92841i | ||||
\(103\) | 145.966 | − | 106.050i | 1.41715 | − | 1.02962i | 0.424911 | − | 0.905235i | \(-0.360305\pi\) |
0.992234 | − | 0.124381i | \(-0.0396946\pi\) | |||||||
\(104\) | −37.0817 | − | 12.0486i | −0.356555 | − | 0.115852i | ||||
\(105\) | −11.4453 | − | 11.2248i | −0.109003 | − | 0.106902i | ||||
\(106\) | −182.957 | + | 132.926i | −1.72600 | + | 1.25402i | ||||
\(107\) | 37.9288 | − | 52.2045i | 0.354475 | − | 0.487893i | −0.594124 | − | 0.804373i | \(-0.702501\pi\) |
0.948599 | + | 0.316481i | \(0.102501\pi\) | |||||||
\(108\) | −56.1977 | + | 30.7316i | −0.520349 | + | 0.284551i | ||||
\(109\) | −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 | ||||
\(112\) | 41.3948 | + | 127.400i | 0.369597 | + | 1.13750i | ||||
\(113\) | −73.6139 | + | 101.321i | −0.651450 | + | 0.896645i | −0.999161 | − | 0.0409573i | \(-0.986959\pi\) |
0.347710 | + | 0.937602i | \(0.386959\pi\) | |||||||
\(114\) | 32.9857 | + | 195.911i | 0.289348 | + | 1.71851i | ||||
\(115\) | −6.59096 | + | 20.2849i | −0.0573127 | + | 0.176390i | ||||
\(116\) | 58.5321 | + | 19.0182i | 0.504587 | + | 0.163950i | ||||
\(117\) | 81.7202 | + | 24.8057i | 0.698464 | + | 0.212015i | ||||
\(118\) | −30.1403 | − | 21.8982i | −0.255426 | − | 0.185578i | ||||
\(119\) | −187.927 | + | 61.0612i | −1.57922 | + | 0.513119i | ||||
\(120\) | −8.74456 | − | 4.34896i | −0.0728714 | − | 0.0362414i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 160.158i | 1.31277i | ||||||||
\(123\) | −52.2737 | − | 7.75891i | −0.424989 | − | 0.0630806i | ||||
\(124\) | −5.49166 | − | 3.98992i | −0.0442876 | − | 0.0321768i | ||||
\(125\) | 22.9924 | + | 31.6463i | 0.183939 | + | 0.253171i | ||||
\(126\) | −50.1765 | − | 144.782i | −0.398227 | − | 1.14906i | ||||
\(127\) | −59.5932 | + | 183.409i | −0.469238 | + | 1.44417i | 0.384335 | + | 0.923194i | \(0.374431\pi\) |
−0.853573 | + | 0.520973i | \(0.825569\pi\) | |||||||
\(128\) | 70.8862 | + | 97.5664i | 0.553798 | + | 0.762238i | ||||
\(129\) | −17.3639 | − | 33.2745i | −0.134604 | − | 0.257942i | ||||
\(130\) | −5.86460 | − | 18.0494i | −0.0451123 | − | 0.138841i | ||||
\(131\) | 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 | ||||||||
\(134\) | 152.039 | − | 49.4005i | 1.13462 | − | 0.368660i | ||||
\(135\) | 19.3354 | + | 9.15141i | 0.143225 | + | 0.0677882i | ||||
\(136\) | −97.3898 | + | 70.7578i | −0.716101 | + | 0.520278i | ||||
\(137\) | −185.738 | − | 60.3500i | −1.35575 | − | 0.440511i | −0.461129 | − | 0.887333i | \(-0.652556\pi\) |
−0.894623 | + | 0.446822i | \(0.852556\pi\) | |||||||
\(138\) | −142.749 | + | 145.553i | −1.03441 | + | 1.05473i | ||||
\(139\) | 5.61033 | − | 4.07614i | 0.0403621 | − | 0.0293248i | −0.567421 | − | 0.823428i | \(-0.692059\pi\) |
0.607783 | + | 0.794103i | \(0.292059\pi\) | |||||||
\(140\) | −7.45111 | + | 10.2556i | −0.0532222 | + | 0.0732541i | ||||
\(141\) | 123.682 | + | 18.3580i | 0.877178 | + | 0.130198i | ||||
\(142\) | −11.4891 | −0.0809093 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −107.861 | − | 142.543i | −0.749038 | − | 0.989880i | ||||
\(145\) | −6.35165 | − | 19.5484i | −0.0438045 | − | 0.134816i | ||||
\(146\) | 79.7768 | − | 109.803i | 0.546416 | − | 0.752077i | ||||
\(147\) | −10.3864 | + | 1.74877i | −0.0706560 | + | 0.0118964i | ||||
\(148\) | 1.75500 | − | 5.40135i | 0.0118581 | − | 0.0364956i | ||||
\(149\) | −64.3841 | − | 20.9197i | −0.432108 | − | 0.140400i | 0.0848835 | − | 0.996391i | \(-0.472948\pi\) |
−0.516992 | + | 0.855990i | \(0.672948\pi\) | |||||||
\(150\) | 30.6452 | + | 182.010i | 0.204301 | + | 1.21340i | ||||
\(151\) | 22.8415 | + | 16.5953i | 0.151268 | + | 0.109903i | 0.660845 | − | 0.750522i | \(-0.270198\pi\) |
−0.509577 | + | 0.860425i | \(0.670198\pi\) | |||||||
\(152\) | −102.516 | + | 33.3095i | −0.674449 | + | 0.219142i | ||||
\(153\) | 210.264 | − | 159.105i | 1.37427 | − | 1.03990i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.26706i | 0.0146262i | ||||||||
\(156\) | 9.91515 | − | 66.8008i | 0.0635586 | − | 0.428210i | ||||
\(157\) | 54.8482 | + | 39.8496i | 0.349352 | + | 0.253819i | 0.748597 | − | 0.663025i | \(-0.230728\pi\) |
−0.399245 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(158\) | 82.6152 | + | 113.710i | 0.522881 | + | 0.719684i | ||||
\(159\) | 191.881 | + | 188.184i | 1.20680 | + | 1.18355i | ||||
\(160\) | −8.25108 | + | 25.3942i | −0.0515693 | + | 0.158714i | ||||
\(161\) | −106.723 | − | 146.891i | −0.662873 | − | 0.912366i | ||||
\(162\) | 126.529 | + | 160.621i | 0.781042 | + | 0.991486i | ||||
\(163\) | −20.9728 | − | 64.5477i | −0.128668 | − | 0.395998i | 0.865884 | − | 0.500245i | \(-0.166757\pi\) |
−0.994551 | + | 0.104247i | \(0.966757\pi\) | |||||||
\(164\) | 41.7888i | 0.254810i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 164.935 | 0.993583 | ||||||||
\(167\) | 53.4828 | − | 17.3776i | 0.320256 | − | 0.104058i | −0.144477 | − | 0.989508i | \(-0.546150\pi\) |
0.464734 | + | 0.885451i | \(0.346150\pi\) | |||||||
\(168\) | 73.7063 | − | 38.4628i | 0.438728 | − | 0.228945i | ||||
\(169\) | 63.8772 | − | 46.4095i | 0.377971 | − | 0.274612i | ||||
\(170\) | −55.7269 | − | 18.1068i | −0.327806 | − | 0.106510i | ||||
\(171\) | 223.086 | − | 77.3141i | 1.30459 | − | 0.452129i | ||||
\(172\) | −24.0111 | + | 17.4451i | −0.139599 | + | 0.101425i | ||||
\(173\) | 131.979 | − | 181.653i | 0.762883 | − | 1.05002i | −0.234085 | − | 0.972216i | \(-0.575209\pi\) |
0.996969 | − | 0.0778030i | \(-0.0247905\pi\) | |||||||
\(174\) | 28.8454 | − | 194.338i | 0.165778 | − | 1.11689i | ||||
\(175\) | −164.380 | −0.939316 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.7160 | + | 39.6434i | −0.111390 | + | 0.223974i | ||||
\(178\) | −11.0255 | − | 33.9330i | −0.0619411 | − | 0.190635i | ||||
\(179\) | −82.5608 | + | 113.635i | −0.461234 | + | 0.634833i | −0.974764 | − | 0.223238i | \(-0.928337\pi\) |
0.513530 | + | 0.858071i | \(0.328337\pi\) | |||||||
\(180\) | 4.91332 | − | 16.1865i | 0.0272962 | − | 0.0899248i | ||||
\(181\) | 40.4384 | − | 124.457i | 0.223417 | − | 0.687605i | −0.775032 | − | 0.631922i | \(-0.782266\pi\) |
0.998448 | − | 0.0556834i | \(-0.0177337\pi\) | |||||||
\(182\) | 153.650 | + | 49.9240i | 0.844233 | + | 0.274308i | ||||
\(183\) | 187.695 | − | 31.6024i | 1.02566 | − | 0.172691i | ||||
\(184\) | −89.4887 | − | 65.0173i | −0.486351 | − | 0.353355i | ||||
\(185\) | −1.80393 | + | 0.586131i | −0.00975095 | + | 0.00316828i | ||||
\(186\) | −9.64947 | + | 19.4024i | −0.0518789 | + | 0.104314i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 98.8744i | − | 0.525928i | ||||||
\(189\) | −159.774 | + | 87.3720i | −0.845365 | + | 0.462286i | ||||
\(190\) | −42.4470 | − | 30.8395i | −0.223405 | − | 0.162313i | ||||
\(191\) | −206.548 | − | 284.289i | −1.08140 | − | 1.48842i | −0.857966 | − | 0.513707i | \(-0.828272\pi\) |
−0.223438 | − | 0.974718i | \(-0.571728\pi\) | |||||||
\(192\) | −11.8215 | + | 12.0537i | −0.0615704 | + | 0.0627799i | ||||
\(193\) | 75.8653 | − | 233.489i | 0.393085 | − | 1.20979i | −0.537359 | − | 0.843354i | \(-0.680578\pi\) |
0.930443 | − | 0.366436i | \(-0.119422\pi\) | |||||||
\(194\) | −221.505 | − | 304.875i | −1.14178 | − | 1.57152i | ||||
\(195\) | −19.9955 | + | 10.4344i | −0.102541 | + | 0.0535099i | ||||
\(196\) | 2.57374 | + | 7.92114i | 0.0131313 | + | 0.0404140i | ||||
\(197\) | 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 | \(0.338599\pi\) | |||||||
\(200\) | −95.2422 | + | 30.9461i | −0.476211 | + | 0.154730i | ||||
\(201\) | −87.8944 | − | 168.432i | −0.437286 | − | 0.837971i | ||||
\(202\) | −40.8642 | + | 29.6895i | −0.202298 | + | 0.146978i | ||||
\(203\) | 166.411 | + | 54.0702i | 0.819758 | + | 0.266356i | ||||
\(204\) | −148.862 | − | 145.994i | −0.729717 | − | 0.715658i | ||||
\(205\) | 11.2910 | − | 8.20343i | 0.0550783 | − | 0.0400167i | ||||
\(206\) | −267.707 | + | 368.467i | −1.29955 | + | 1.78868i | ||||
\(207\) | 198.746 | + | 138.572i | 0.960124 | + | 0.669428i | ||||
\(208\) | 188.467 | 0.906093 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 36.2337 | + | 18.0202i | 0.172541 | + | 0.0858106i | ||||
\(211\) | 32.9993 | + | 101.561i | 0.156395 | + | 0.481334i | 0.998300 | − | 0.0582923i | \(-0.0185655\pi\) |
−0.841905 | + | 0.539626i | \(0.818566\pi\) | |||||||
\(212\) | 124.919 | − | 171.936i | 0.589239 | − | 0.811018i | ||||
\(213\) | 2.26703 | + | 13.4645i | 0.0106433 | + | 0.0632137i | ||||
\(214\) | −50.3362 | + | 154.919i | −0.235216 | + | 0.723920i | ||||
\(215\) | 9.42707 | + | 3.06304i | 0.0438468 | + | 0.0142467i | ||||
\(216\) | −76.1247 | + | 80.7023i | −0.352429 | + | 0.373622i | ||||
\(217\) | −15.6132 | − | 11.3436i | −0.0719501 | − | 0.0522748i | ||||
\(218\) | 264.752 | − | 86.0232i | 1.21446 | − | 0.394602i | ||||
\(219\) | −144.424 | − | 71.8268i | −0.659470 | − | 0.327976i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 278.007i | 1.25795i | ||||||||
\(222\) | −17.9336 | − | 2.66185i | −0.0807818 | − | 0.0119903i | ||||
\(223\) | −62.0766 | − | 45.1013i | −0.278370 | − | 0.202248i | 0.439836 | − | 0.898078i | \(-0.355037\pi\) |
−0.718206 | + | 0.695830i | \(0.755037\pi\) | |||||||
\(224\) | −133.604 | − | 183.890i | −0.596445 | − | 0.820936i | ||||
\(225\) | 207.257 | − | 71.8283i | 0.921141 | − | 0.319237i | ||||
\(226\) | 97.6947 | − | 300.673i | 0.432277 | − | 1.33041i | ||||
\(227\) | −28.3567 | − | 39.0297i | −0.124920 | − | 0.171937i | 0.741977 | − | 0.670426i | \(-0.233889\pi\) |
−0.866896 | + | 0.498489i | \(0.833889\pi\) | |||||||
\(228\) | −86.3746 | − | 165.520i | −0.378836 | − | 0.725963i | ||||
\(229\) | −4.76374 | − | 14.6613i | −0.0208023 | − | 0.0640230i | 0.940116 | − | 0.340853i | \(-0.110716\pi\) |
−0.960919 | + | 0.276830i | \(0.910716\pi\) | |||||||
\(230\) | − | 53.8411i | − | 0.234092i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 106.598 | 0.459474 | ||||||||
\(233\) | −164.728 | + | 53.5233i | −0.706986 | + | 0.229714i | −0.640372 | − | 0.768065i | \(-0.721220\pi\) |
−0.0666145 | + | 0.997779i | \(0.521220\pi\) | |||||||
\(234\) | −215.543 | + | 4.19366i | −0.921124 | + | 0.0179216i | ||||
\(235\) | −26.7152 | + | 19.4097i | −0.113682 | + | 0.0825945i | ||||
\(236\) | 33.2977 | + | 10.8191i | 0.141092 | + | 0.0458436i | ||||
\(237\) | 116.959 | − | 119.257i | 0.493499 | − | 0.503194i | ||||
\(238\) | 403.541 | − | 293.190i | 1.69555 | − | 1.23189i | ||||
\(239\) | −174.218 | + | 239.790i | −0.728945 | + | 1.00331i | 0.270234 | + | 0.962795i | \(0.412899\pi\) |
−0.999179 | + | 0.0405120i | \(0.987101\pi\) | |||||||
\(240\) | 46.6962 | + | 6.93105i | 0.194568 | + | 0.0288794i | ||||
\(241\) | −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 | ||||
\(244\) | −46.5104 | − | 143.144i | −0.190616 | − | 0.586657i | ||||
\(245\) | 1.63500 | − | 2.25038i | 0.00667345 | − | 0.00918522i | ||||
\(246\) | 131.551 | − | 22.1493i | 0.534758 | − | 0.0900378i | ||||
\(247\) | −76.9251 | + | 236.751i | −0.311438 | + | 0.958506i | ||||
\(248\) | −11.1818 | − | 3.63320i | −0.0450880 | − | 0.0146500i | ||||
\(249\) | −32.5449 | − | 193.293i | −0.130702 | − | 0.776276i | ||||
\(250\) | −79.8860 | − | 58.0406i | −0.319544 | − | 0.232162i | ||||
\(251\) | −197.618 | + | 64.2100i | −0.787323 | + | 0.255817i | −0.674964 | − | 0.737851i | \(-0.735841\pi\) |
−0.112359 | + | 0.993668i | \(0.535841\pi\) | |||||||
\(252\) | 86.8913 | + | 114.830i | 0.344807 | + | 0.455674i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 486.813i | − | 1.91659i | ||||||
\(255\) | −10.2239 | + | 68.8812i | −0.0400939 | + | 0.270122i | ||||
\(256\) | −264.502 | − | 192.172i | −1.03321 | − | 0.750673i | ||||
\(257\) | 117.403 | + | 161.592i | 0.456821 | + | 0.628761i | 0.973846 | − | 0.227210i | \(-0.0729604\pi\) |
−0.517024 | + | 0.855971i | \(0.672960\pi\) | |||||||
\(258\) | 67.6433 | + | 66.3400i | 0.262183 | + | 0.257132i | ||||
\(259\) | 4.98960 | − | 15.3564i | 0.0192649 | − | 0.0592912i | ||||
\(260\) | 10.4832 | + | 14.4289i | 0.0403200 | + | 0.0554957i | ||||
\(261\) | −233.444 | + | 4.54193i | −0.894420 | + | 0.0174020i | ||||
\(262\) | −82.7628 | − | 254.718i | −0.315888 | − | 0.972205i | ||||
\(263\) | − | 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 | ||||||||
\(266\) | 424.783 | − | 138.020i | 1.59693 | − | 0.518873i | ||||
\(267\) | −37.5918 | + | 19.6169i | −0.140793 | + | 0.0734714i | ||||
\(268\) | −121.542 | + | 88.3051i | −0.453513 | + | 0.329497i | ||||
\(269\) | −47.9113 | − | 15.5673i | −0.178109 | − | 0.0578711i | 0.218605 | − | 0.975813i | \(-0.429849\pi\) |
−0.396714 | + | 0.917942i | \(0.629849\pi\) | |||||||
\(270\) | −53.5589 | − | 6.88773i | −0.198366 | − | 0.0255101i | ||||
\(271\) | −100.626 | + | 73.1090i | −0.371313 | + | 0.269775i | −0.757755 | − | 0.652539i | \(-0.773704\pi\) |
0.386442 | + | 0.922314i | \(0.373704\pi\) | |||||||
\(272\) | 342.025 | − | 470.757i | 1.25744 | − | 1.73072i | ||||
\(273\) | 28.1895 | − | 189.919i | 0.103258 | − | 0.695675i | ||||
\(274\) | 492.994 | 1.79925 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 85.3151 | − | 171.545i | 0.309113 | − | 0.621540i | ||||
\(277\) | −90.7653 | − | 279.347i | −0.327673 | − | 1.00847i | −0.970220 | − | 0.242227i | \(-0.922122\pi\) |
0.642547 | − | 0.766246i | \(-0.277878\pi\) | |||||||
\(278\) | −10.2896 | + | 14.1624i | −0.0370128 | + | 0.0509438i | ||||
\(279\) | 24.6424 | + | 7.48007i | 0.0883240 | + | 0.0268103i | ||||
\(280\) | −6.78493 | + | 20.8819i | −0.0242319 | + | 0.0745781i | ||||
\(281\) | −250.771 | − | 81.4805i | −0.892424 | − | 0.289966i | −0.173318 | − | 0.984866i | \(-0.555449\pi\) |
−0.719107 | + | 0.694900i | \(0.755449\pi\) | |||||||
\(282\) | −311.255 | + | 52.4063i | −1.10374 | + | 0.185838i | ||||
\(283\) | 322.626 | + | 234.402i | 1.14002 | + | 0.828275i | 0.987122 | − | 0.159967i | \(-0.0511388\pi\) |
0.152900 | + | 0.988242i | \(0.451139\pi\) | |||||||
\(284\) | 10.2686 | − | 3.33648i | 0.0361571 | − | 0.0117482i | ||||
\(285\) | −27.7663 | + | 55.8304i | −0.0974257 | + | 0.195896i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 118.809i | 0.413967i | ||||||||
\(288\) | 248.806 | + | 173.475i | 0.863908 | + | 0.602343i | ||||
\(289\) | 460.603 | + | 334.648i | 1.59378 | + | 1.15795i | ||||
\(290\) | 30.4979 | + | 41.9768i | 0.105165 | + | 0.144748i | ||||
\(291\) | −313.587 | + | 319.747i | −1.07762 | + | 1.09879i | ||||
\(292\) | −39.4148 | + | 121.306i | −0.134982 | + | 0.415432i | ||||
\(293\) | 205.042 | + | 282.216i | 0.699803 | + | 0.963196i | 0.999957 | + | 0.00930526i | \(0.00296200\pi\) |
−0.300154 | + | 0.953891i | \(0.597038\pi\) | |||||||
\(294\) | 23.5715 | − | 12.3005i | 0.0801750 | − | 0.0418385i | ||||
\(295\) | −3.61333 | − | 11.1207i | −0.0122486 | − | 0.0376972i | ||||
\(296\) | − | 9.83686i | − | 0.0332326i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 170.891 | 0.573461 | ||||||||
\(299\) | −242.950 | + | 78.9391i | −0.812540 | + | 0.264010i | ||||
\(300\) | −80.2459 | − | 153.775i | −0.267486 | − | 0.512584i | ||||
\(301\) | −68.2652 | + | 49.5975i | −0.226795 | + | 0.164776i | ||||
\(302\) | −67.7831 | − | 22.0241i | −0.224447 | − | 0.0729274i | ||||
\(303\) | 42.8575 | + | 42.0318i | 0.141444 | + | 0.138719i | ||||
\(304\) | 421.529 | − | 306.258i | 1.38661 | − | 1.00743i | ||||
\(305\) | −29.5463 | + | 40.6670i | −0.0968731 | + | 0.133334i | ||||
\(306\) | −380.686 | + | 545.997i | −1.24407 | + | 1.78430i | ||||
\(307\) | 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 | ||||
\(310\) | −1.76845 | − | 5.44272i | −0.00570467 | − | 0.0175572i | ||||
\(311\) | −258.829 | + | 356.247i | −0.832247 | + | 1.14549i | 0.155254 | + | 0.987875i | \(0.450380\pi\) |
−0.987501 | + | 0.157615i | \(0.949620\pi\) | |||||||
\(312\) | −19.4210 | − | 115.346i | −0.0622468 | − | 0.369700i | ||||
\(313\) | 163.748 | − | 503.964i | 0.523156 | − | 1.61011i | −0.244777 | − | 0.969579i | \(-0.578715\pi\) |
0.767933 | − | 0.640530i | \(-0.221285\pi\) | |||||||
\(314\) | −162.764 | − | 52.8853i | −0.518357 | − | 0.168425i | ||||
\(315\) | 13.9689 | − | 46.0193i | 0.0443457 | − | 0.146093i | ||||
\(316\) | −106.861 | − | 77.6388i | −0.338167 | − | 0.245692i | ||||
\(317\) | −350.394 | + | 113.850i | −1.10534 | + | 0.359148i | −0.804157 | − | 0.594417i | \(-0.797383\pi\) |
−0.301187 | + | 0.953565i | \(0.597383\pi\) | |||||||
\(318\) | −607.462 | − | 302.111i | −1.91026 | − | 0.950035i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 4.45877i | − | 0.0139337i | ||||||
\(321\) | 191.487 | + | 28.4222i | 0.596533 | + | 0.0885425i | ||||
\(322\) | 370.802 | + | 269.404i | 1.15156 | + | 0.836657i | ||||
\(323\) | 451.759 | + | 621.793i | 1.39864 | + | 1.92506i | ||||
\(324\) | −159.732 | − | 106.813i | −0.493001 | − | 0.329671i | ||||
\(325\) | −71.4669 | + | 219.952i | −0.219898 | + | 0.676777i | ||||
\(326\) | 100.703 | + | 138.605i | 0.308904 | + | 0.425170i | ||||
\(327\) | −153.054 | − | 293.298i | −0.468056 | − | 0.896936i | ||||
\(328\) | 22.3668 | + | 68.8378i | 0.0681914 | + | 0.209871i | ||||
\(329\) | − | 281.107i | − | 0.854428i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −115.649 | −0.349394 | −0.174697 | − | 0.984622i | \(-0.555895\pi\) | ||||
−0.174697 | + | 0.984622i | \(0.555895\pi\) | |||||||
\(332\) | −147.413 | + | 47.8975i | −0.444017 | + | 0.144270i | ||||
\(333\) | 0.419130 | + | 21.5422i | 0.00125865 | + | 0.0646913i | ||||
\(334\) | −114.845 | + | 83.4399i | −0.343848 | + | 0.249820i | ||||
\(335\) | 47.7189 | + | 15.5048i | 0.142444 | + | 0.0462830i | ||||
\(336\) | −281.387 | + | 286.915i | −0.837462 | + | 0.853914i | ||||
\(337\) | −43.0977 | + | 31.3123i | −0.127886 | + | 0.0929148i | −0.649890 | − | 0.760029i | \(-0.725185\pi\) |
0.522003 | + | 0.852943i | \(0.325185\pi\) | |||||||
\(338\) | −117.153 | + | 161.248i | −0.346607 | + | 0.477064i | ||||
\(339\) | −371.647 | − | 55.1630i | −1.09630 | − | 0.162723i | ||||
\(340\) | 55.0652 | 0.161957 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −475.272 | + | 359.636i | −1.38968 | + | 1.05157i | ||||
\(343\) | 109.442 | + | 336.829i | 0.319074 | + | 0.982009i | ||||
\(344\) | −30.2157 | + | 41.5884i | −0.0878364 | + | 0.120896i | ||||
\(345\) | −63.0982 | + | 10.6239i | −0.182893 | + | 0.0307939i | ||||
\(346\) | −175.152 | + | 539.063i | −0.506220 | + | 1.55799i | ||||
\(347\) | 10.6597 | + | 3.46354i | 0.0307195 | + | 0.00998137i | 0.324336 | − | 0.945942i | \(-0.394859\pi\) |
−0.293617 | + | 0.955923i | \(0.594859\pi\) | |||||||
\(348\) | 30.6554 | + | 182.070i | 0.0880901 | + | 0.523190i | ||||
\(349\) | −173.143 | − | 125.796i | −0.496111 | − | 0.360446i | 0.311419 | − | 0.950273i | \(-0.399196\pi\) |
−0.807530 | + | 0.589827i | \(0.799196\pi\) | |||||||
\(350\) | 394.642 | − | 128.227i | 1.12755 | − | 0.366363i | ||||
\(351\) | 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 | \(-0.271332\pi\) | |||||||
\(354\) | 16.4095 | − | 110.555i | 0.0463546 | − | 0.312303i | ||||
\(355\) | −2.91729 | − | 2.11954i | −0.00821772 | − | 0.00597052i | ||||
\(356\) | 19.7085 | + | 27.1264i | 0.0553610 | + | 0.0761979i | ||||
\(357\) | −423.226 | − | 415.072i | −1.18551 | − | 1.16267i | ||||
\(358\) | 109.568 | − | 337.217i | 0.306057 | − | 0.941946i | ||||
\(359\) | 102.977 | + | 141.735i | 0.286843 | + | 0.394806i | 0.927986 | − | 0.372616i | \(-0.121539\pi\) |
−0.641142 | + | 0.767422i | \(0.721539\pi\) | |||||||
\(360\) | −0.569939 | − | 29.2934i | −0.00158316 | − | 0.0813705i | ||||
\(361\) | 101.112 | + | 311.192i | 0.280090 | + | 0.862027i | ||||
\(362\) | 330.338i | 0.912537i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −151.826 | −0.417104 | ||||||||
\(365\) | 40.5134 | − | 13.1636i | 0.110996 | − | 0.0360647i | ||||
\(366\) | −425.964 | + | 222.285i | −1.16384 | + | 0.607335i | ||||
\(367\) | −112.482 | + | 81.7230i | −0.306490 | + | 0.222678i | −0.730389 | − | 0.683031i | \(-0.760661\pi\) |
0.423899 | + | 0.905710i | \(0.360661\pi\) | |||||||
\(368\) | 508.510 | + | 165.225i | 1.38182 | + | 0.448981i | ||||
\(369\) | −51.9151 | − | 149.798i | −0.140691 | − | 0.405957i | ||||
\(370\) | 3.87362 | − | 2.81435i | 0.0104693 | − | 0.00760636i | ||||
\(371\) | 355.153 | − | 488.826i | 0.957285 | − | 1.31759i | ||||
\(372\) | 2.98987 | − | 20.1435i | 0.00803729 | − | 0.0541492i | ||||
\(373\) | −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 | ||||
\(376\) | −52.9208 | − | 162.874i | −0.140747 | − | 0.433174i | ||||
\(377\) | 144.699 | − | 199.162i | 0.383818 | − | 0.528280i | ||||
\(378\) | 315.428 | − | 334.395i | 0.834465 | − | 0.884644i | ||||
\(379\) | 83.5564 | − | 257.160i | 0.220465 | − | 0.678522i | −0.778255 | − | 0.627948i | \(-0.783895\pi\) |
0.998720 | − | 0.0505741i | \(-0.0161051\pi\) | |||||||
\(380\) | 46.8937 | + | 15.2367i | 0.123404 | + | 0.0400965i | ||||
\(381\) | −570.513 | + | 96.0579i | −1.49741 | + | 0.252120i | ||||
\(382\) | 717.642 | + | 521.397i | 1.87864 | + | 1.36491i | ||||
\(383\) | 600.879 | − | 195.237i | 1.56887 | − | 0.509758i | 0.609714 | − | 0.792621i | \(-0.291284\pi\) |
0.959160 | + | 0.282863i | \(0.0912843\pi\) | |||||||
\(384\) | −161.109 | + | 323.945i | −0.419554 | + | 0.843607i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 619.738i | 1.60554i | ||||||||
\(387\) | 64.3988 | − | 92.3638i | 0.166405 | − | 0.238666i | ||||
\(388\) | 286.511 | + | 208.162i | 0.738430 | + | 0.536501i | ||||
\(389\) | −270.379 | − | 372.144i | −0.695061 | − | 0.956669i | −0.999991 | − | 0.00429451i | \(-0.998633\pi\) |
0.304930 | − | 0.952375i | \(-0.401367\pi\) | |||||||
\(390\) | 39.8655 | − | 40.6486i | 0.102219 | − | 0.104227i | ||||
\(391\) | −243.722 | + | 750.099i | −0.623330 | + | 1.91841i | ||||
\(392\) | 8.47932 | + | 11.6708i | 0.0216309 | + | 0.0297724i | ||||
\(393\) | −282.182 | + | 147.253i | −0.718020 | + | 0.374691i | ||||
\(394\) | −4.79984 | − | 14.7724i | −0.0121823 | − | 0.0374934i | ||||
\(395\) | 44.1140i | 0.111681i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −561.272 | −1.41378 | −0.706891 | − | 0.707322i | \(-0.749903\pi\) | ||||
−0.706891 | + | 0.707322i | \(0.749903\pi\) | |||||||
\(398\) | −464.004 | + | 150.764i | −1.16584 | + | 0.378804i | ||||
\(399\) | −245.569 | − | 470.584i | −0.615461 | − | 1.17941i | ||||
\(400\) | 391.619 | − | 284.528i | 0.979048 | − | 0.711320i | ||||
\(401\) | −171.043 | − | 55.5751i | −0.426540 | − | 0.138591i | 0.0878772 | − | 0.996131i | \(-0.471992\pi\) |
−0.514417 | + | 0.857540i | \(0.671992\pi\) | |||||||
\(402\) | 342.404 | + | 335.807i | 0.851750 | + | 0.835340i | ||||
\(403\) | −21.9666 | + | 15.9597i | −0.0545078 | + | 0.0396022i | ||||
\(404\) | 27.9012 | − | 38.4027i | 0.0690623 | − | 0.0950561i | ||||
\(405\) | 2.49627 | + | 64.1267i | 0.00616364 | + | 0.158337i | ||||
\(406\) | −441.696 | −1.08792 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −323.359 | − | 160.817i | −0.792546 | − | 0.394159i | ||||
\(409\) | −41.9322 | − | 129.054i | −0.102524 | − | 0.315536i | 0.886618 | − | 0.462503i | \(-0.153049\pi\) |
−0.989141 | + | 0.146968i | \(0.953049\pi\) | |||||||
\(410\) | −20.7082 | + | 28.5024i | −0.0505078 | + | 0.0695181i | ||||
\(411\) | −97.2776 | − | 577.757i | −0.236685 | − | 1.40574i | ||||
\(412\) | 132.264 | − | 407.068i | 0.321030 | − | 0.988028i | ||||
\(413\) | 94.6678 | + | 30.7594i | 0.229220 | + | 0.0744781i | ||||
\(414\) | −585.241 | − | 177.647i | −1.41362 | − | 0.429098i | ||||
\(415\) | 41.8798 | + | 30.4275i | 0.100915 | + | 0.0733192i | ||||
\(416\) | −304.144 | + | 98.8222i | −0.731114 | + | 0.237553i | ||||
\(417\) | 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 | \(-0.0191314\pi\) | |||||||
\(420\) | −37.6177 | − | 5.58353i | −0.0895658 | − | 0.0132941i | ||||
\(421\) | 42.6230 | + | 30.9674i | 0.101242 | + | 0.0735567i | 0.637255 | − | 0.770653i | \(-0.280070\pi\) |
−0.536012 | + | 0.844210i | \(0.680070\pi\) | |||||||
\(422\) | −158.449 | − | 218.086i | −0.375471 | − | 0.516792i | ||||
\(423\) | 122.834 | + | 354.430i | 0.290387 | + | 0.837895i | ||||
\(424\) | 113.750 | − | 350.087i | 0.268279 | − | 0.825677i | ||||
\(425\) | 419.705 | + | 577.674i | 0.987540 | + | 1.35923i | ||||
\(426\) | −15.9458 | − | 30.5570i | −0.0374315 | − | 0.0717301i | ||||
\(427\) | −132.232 | − | 406.969i | −0.309678 | − | 0.953090i | ||||
\(428\) | − | 153.079i | − | 0.357662i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.0217 | −0.0581901 | ||||||||
\(431\) | 472.491 | − | 153.522i | 1.09627 | − | 0.356199i | 0.295603 | − | 0.955311i | \(-0.404480\pi\) |
0.800665 | + | 0.599112i | \(0.204480\pi\) | |||||||
\(432\) | 229.412 | − | 484.709i | 0.531045 | − | 1.12201i | ||||
\(433\) | −417.147 | + | 303.075i | −0.963388 | + | 0.699943i | −0.953935 | − | 0.300013i | \(-0.903009\pi\) |
−0.00945303 | + | 0.999955i | \(0.503009\pi\) | |||||||
\(434\) | 46.3327 | + | 15.0544i | 0.106757 | + | 0.0346875i | ||||
\(435\) | 43.1762 | − | 44.0245i | 0.0992557 | − | 0.101206i | ||||
\(436\) | −211.646 | + | 153.770i | −0.485426 | + | 0.352683i | ||||
\(437\) | −415.108 | + | 571.348i | −0.949905 | + | 1.30743i | ||||
\(438\) | 402.761 | + | 59.7812i | 0.919545 | + | 0.136487i | ||||
\(439\) | 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 | ||||
\(442\) | −216.863 | − | 667.435i | −0.490640 | − | 1.51003i | ||||
\(443\) | 511.620 | − | 704.184i | 1.15490 | − | 1.58958i | 0.426397 | − | 0.904536i | \(-0.359783\pi\) |
0.728501 | − | 0.685045i | \(-0.240217\pi\) | |||||||
\(444\) | 16.8015 | − | 2.82888i | 0.0378411 | − | 0.00637135i | ||||
\(445\) | 3.46046 | − | 10.6502i | 0.00777632 | − | 0.0239330i | ||||
\(446\) | 184.215 | + | 59.8550i | 0.413037 | + | 0.134204i | ||||
\(447\) | −33.7202 | − | 200.273i | −0.0754368 | − | 0.448039i | ||||
\(448\) | 30.7075 | + | 22.3103i | 0.0685434 | + | 0.0497997i | ||||
\(449\) | 547.468 | − | 177.883i | 1.21930 | − | 0.396176i | 0.372476 | − | 0.928042i | \(-0.378509\pi\) |
0.846829 | + | 0.531866i | \(0.178509\pi\) | |||||||
\(450\) | −441.549 | + | 334.118i | −0.981220 | + | 0.742484i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 297.103i | 0.657308i | ||||||||
\(453\) | −12.4358 | + | 83.7832i | −0.0274521 | + | 0.184952i | ||||
\(454\) | 98.5241 | + | 71.5820i | 0.217013 | + | 0.157670i | ||||
\(455\) | 29.8045 | + | 41.0223i | 0.0655043 | + | 0.0901589i | ||||
\(456\) | −230.874 | − | 226.426i | −0.506304 | − | 0.496549i | ||||
\(457\) | −7.90846 | + | 24.3397i | −0.0173052 | + | 0.0532598i | −0.959336 | − | 0.282266i | \(-0.908914\pi\) |
0.942031 | + | 0.335526i | \(0.108914\pi\) | |||||||
\(458\) | 22.8734 | + | 31.4826i | 0.0499420 | + | 0.0687393i | ||||
\(459\) | 714.990 | + | 338.403i | 1.55771 | + | 0.737261i | ||||
\(460\) | 15.6356 | + | 48.1214i | 0.0339904 | + | 0.104612i | ||||
\(461\) | 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 | \(0.569666\pi\) | |||||||
\(464\) | −490.047 | + | 159.226i | −1.05614 | + | 0.343160i | ||||
\(465\) | −6.02956 | + | 3.14646i | −0.0129668 | + | 0.00676658i | ||||
\(466\) | 353.725 | − | 256.996i | 0.759067 | − | 0.551494i | ||||
\(467\) | 104.920 | + | 34.0906i | 0.224668 | + | 0.0729991i | 0.419188 | − | 0.907899i | \(-0.362315\pi\) |
−0.194520 | + | 0.980899i | \(0.562315\pi\) | |||||||
\(468\) | 191.428 | − | 66.3425i | 0.409034 | − | 0.141757i | ||||
\(469\) | −345.551 | + | 251.058i | −0.736783 | + | 0.535304i | ||||
\(470\) | 48.9966 | − | 67.4381i | 0.104248 | − | 0.143485i | ||||
\(471\) | −29.8615 | + | 201.184i | −0.0634002 | + | 0.427143i | ||||
\(472\) | 60.6414 | 0.128477 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −187.766 | + | 377.546i | −0.396131 | + | 0.796511i | ||||
\(475\) | 197.578 | + | 608.082i | 0.415953 | + | 1.28017i | ||||
\(476\) | −275.529 | + | 379.233i | −0.578843 | + | 0.796709i | ||||
\(477\) | −234.190 | + | 771.518i | −0.490965 | + | 1.61744i | ||||
\(478\) | 231.208 | − | 711.587i | 0.483700 | − | 1.48867i | ||||
\(479\) | 650.078 | + | 211.223i | 1.35716 | + | 0.440967i | 0.895093 | − | 0.445880i | \(-0.147109\pi\) |
0.462064 | + | 0.886847i | \(0.347109\pi\) | |||||||
\(480\) | −78.9914 | + | 13.2999i | −0.164565 | + | 0.0277080i | ||||
\(481\) | −18.3786 | − | 13.3529i | −0.0382092 | − | 0.0277606i | ||||
\(482\) | 112.119 | − | 36.4298i | 0.232613 | − | 0.0755805i | ||||
\(483\) | 242.557 | − | 487.715i | 0.502188 | − | 1.00976i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 118.277i | − | 0.243870i | ||||||
\(486\) | −251.584 | + | 559.448i | −0.517662 | + | 1.15113i | ||||
\(487\) | 105.254 | + | 76.4712i | 0.216127 | + | 0.157025i | 0.690581 | − | 0.723255i | \(-0.257355\pi\) |
−0.474455 | + | 0.880280i | \(0.657355\pi\) | |||||||
\(488\) | −153.231 | − | 210.905i | −0.313998 | − | 0.432182i | ||||
\(489\) | 142.566 | − | 145.367i | 0.291546 | − | 0.297273i | ||||
\(490\) | −2.16984 | + | 6.67808i | −0.00442824 | + | 0.0136287i | ||||
\(491\) | −468.218 | − | 644.447i | −0.953601 | − | 1.31252i | −0.949909 | − | 0.312525i | \(-0.898825\pi\) |
−0.00369120 | − | 0.999993i | \(-0.501175\pi\) | |||||||
\(492\) | −111.143 | + | 57.9990i | −0.225901 | + | 0.117884i | ||||
\(493\) | −234.873 | − | 722.865i | −0.476416 | − | 1.46626i | ||||
\(494\) | − | 628.395i | − | 1.27206i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 56.8316 | 0.114580 | ||||||||
\(497\) | 29.1944 | − | 9.48584i | 0.0587413 | − | 0.0190862i | ||||
\(498\) | 228.914 | + | 438.668i | 0.459667 | + | 0.880859i | ||||
\(499\) | −396.445 | + | 288.034i | −0.794478 | + | 0.577222i | −0.909289 | − | 0.416165i | \(-0.863374\pi\) |
0.114811 | + | 0.993387i | \(0.463374\pi\) | |||||||
\(500\) | 88.2548 | + | 28.6757i | 0.176510 | + | 0.0573514i | ||||
\(501\) | 120.447 | + | 118.127i | 0.240414 | + | 0.235782i | ||||
\(502\) | 424.351 | − | 308.309i | 0.845321 | − | 0.614162i | ||||
\(503\) | 166.509 | − | 229.179i | 0.331031 | − | 0.455625i | −0.610764 | − | 0.791813i | \(-0.709138\pi\) |
0.941795 | + | 0.336188i | \(0.109138\pi\) | |||||||
\(504\) | 204.595 | + | 142.650i | 0.405942 | + | 0.283035i | ||||
\(505\) | −15.8533 | −0.0313927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 212.088 | + | 105.479i | 0.418320 | + | 0.208045i | ||||
\(508\) | 141.372 | + | 435.098i | 0.278291 | + | 0.856492i | ||||
\(509\) | 143.214 | − | 197.117i | 0.281363 | − | 0.387263i | −0.644822 | − | 0.764333i | \(-0.723068\pi\) |
0.926185 | + | 0.377070i | \(0.123068\pi\) | |||||||
\(510\) | −29.1862 | − | 173.344i | −0.0572278 | − | 0.339891i | ||||
\(511\) | −112.059 | + | 344.882i | −0.219293 | + | 0.674916i | ||||
\(512\) | 326.136 | + | 105.968i | 0.636983 | + | 0.206968i | ||||
\(513\) | 515.250 | + | 486.024i | 1.00439 | + | 0.947416i | ||||
\(514\) | −407.912 | − | 296.365i | −0.793602 | − | 0.576586i | ||||
\(515\) | −135.951 | + | 44.1732i | −0.263983 | + | 0.0857732i | ||||
\(516\) | −79.7228 | − | 39.6488i | −0.154502 | − | 0.0768388i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 40.7597i | 0.0786867i | ||||||||
\(519\) | 666.308 | + | 98.8991i | 1.28383 | + | 0.190557i | ||||
\(520\) | 24.9915 | + | 18.1574i | 0.0480607 | + | 0.0349181i | ||||
\(521\) | 221.168 | + | 304.412i | 0.424507 | + | 0.584284i | 0.966682 | − | 0.255982i | \(-0.0823988\pi\) |
−0.542174 | + | 0.840266i | \(0.682399\pi\) | |||||||
\(522\) | 556.906 | − | 193.005i | 1.06687 | − | 0.369741i | ||||
\(523\) | −171.765 | + | 528.637i | −0.328422 | + | 1.01078i | 0.641450 | + | 0.767165i | \(0.278333\pi\) |
−0.969872 | + | 0.243614i | \(0.921667\pi\) | |||||||
\(524\) | 147.942 | + | 203.624i | 0.282331 | + | 0.388596i | ||||
\(525\) | −228.145 | − | 437.194i | −0.434561 | − | 0.832750i | ||||
\(526\) | 77.8185 | + | 239.501i | 0.147944 | + | 0.455325i | ||||
\(527\) | 83.8317i | 0.159074i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −195.715 | −0.369971 | ||||||||
\(530\) | 170.404 | − | 55.3675i | 0.321516 | − | 0.104467i | ||||
\(531\) | −132.801 | + | 2.58381i | −0.250097 | + | 0.00486594i | ||||
\(532\) | −339.576 | + | 246.716i | −0.638301 | + | 0.463753i | ||||
\(533\) | 158.974 | + | 51.6538i | 0.298263 | + | 0.0969115i | ||||
\(534\) | 74.9475 | − | 76.4199i | 0.140351 | − | 0.143108i | ||||
\(535\) | −41.3609 | + | 30.0505i | −0.0773102 | + | 0.0561691i | ||||
\(536\) | −152.949 | + | 210.516i | −0.285353 | + | 0.392754i | ||||
\(537\) | −416.816 | − | 61.8674i | −0.776194 | − | 0.115209i | ||||
\(538\) | 127.168 | 0.236373 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 49.8695 | − | 9.39764i | 0.0923509 | − | 0.0174030i | ||||
\(541\) | −288.068 | − | 886.581i | −0.532472 | − | 1.63878i | −0.749048 | − | 0.662516i | \(-0.769489\pi\) |
0.216575 | − | 0.976266i | \(-0.430511\pi\) | |||||||
\(542\) | 184.552 | − | 254.014i | 0.340501 | − | 0.468660i | ||||
\(543\) | 387.135 | − | 65.1823i | 0.712956 | − | 0.120041i | ||||
\(544\) | −305.111 | + | 939.034i | −0.560865 | + | 1.72617i | ||||
\(545\) | 83.0949 | + | 26.9992i | 0.152468 | + | 0.0495398i | ||||
\(546\) | 80.4722 | + | 477.946i | 0.147385 | + | 0.875358i | ||||
\(547\) | 596.232 | + | 433.188i | 1.09000 | + | 0.791934i | 0.979400 | − | 0.201931i | \(-0.0647215\pi\) |
0.110604 | + | 0.993865i | \(0.464722\pi\) | |||||||
\(548\) | −440.623 | + | 143.167i | −0.804056 | + | 0.261254i | ||||
\(549\) | 344.554 | + | 455.341i | 0.627604 | + | 0.829401i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 680.583i | − | 1.23518i | ||||||
\(552\) | 48.7211 | − | 328.246i | 0.0882629 | − | 0.594649i | ||||
\(553\) | −303.812 | − | 220.733i | −0.549389 | − | 0.399155i | ||||
\(554\) | 435.817 | + | 599.850i | 0.786673 | + | 1.08276i | ||||
\(555\) | −4.06258 | − | 3.98431i | −0.00731997 | − | 0.00717893i | ||||
\(556\) | 5.08369 | − | 15.6460i | 0.00914334 | − | 0.0281403i | ||||
\(557\) | −373.631 | − | 514.259i | −0.670792 | − | 0.923266i | 0.328986 | − | 0.944335i | \(-0.393293\pi\) |
−0.999778 | + | 0.0210686i | \(0.993293\pi\) | |||||||
\(558\) | −64.9961 | + | 1.26458i | −0.116480 | + | 0.00226627i | ||||
\(559\) | 36.6857 | + | 112.907i | 0.0656273 | + | 0.201980i | ||||
\(560\) | − | 106.132i | − | 0.189521i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 665.609 | 1.18436 | ||||||||
\(563\) | 761.180 | − | 247.322i | 1.35201 | − | 0.439294i | 0.458640 | − | 0.888622i | \(-0.348337\pi\) |
0.893367 | + | 0.449329i | \(0.148337\pi\) | |||||||
\(564\) | 262.971 | − | 137.228i | 0.466260 | − | 0.243313i | ||||
\(565\) | 80.2752 | − | 58.3233i | 0.142080 | − | 0.103227i | ||||
\(566\) | −957.406 | − | 311.080i | −1.69153 | − | 0.549611i | ||||
\(567\) | −454.130 | − | 303.678i | −0.800934 | − | 0.535587i | ||||
\(568\) | 15.1295 | − | 10.9922i | 0.0266364 | − | 0.0193525i | ||||
\(569\) | 30.8852 | − | 42.5098i | 0.0542798 | − | 0.0747097i | −0.781014 | − | 0.624513i | \(-0.785297\pi\) |
0.835294 | + | 0.549804i | \(0.185297\pi\) | |||||||
\(570\) | 23.1098 | − | 155.696i | 0.0405435 | − | 0.273152i | ||||
\(571\) | −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 | ||||
\(574\) | −92.6782 | − | 285.234i | −0.161460 | − | 0.496924i | ||||
\(575\) | −385.655 | + | 530.808i | −0.670703 | + | 0.923144i | ||||
\(576\) | −48.4659 | − | 14.7115i | −0.0841421 | − | 0.0255409i | ||||
\(577\) | −27.2849 | + | 83.9744i | −0.0472876 | + | 0.145536i | −0.971912 | − | 0.235343i | \(-0.924379\pi\) |
0.924625 | + | 0.380879i | \(0.124379\pi\) | |||||||
\(578\) | −1366.86 | − | 444.119i | −2.36480 | − | 0.768372i | ||||
\(579\) | 726.293 | − | 122.287i | 1.25439 | − | 0.211203i | ||||
\(580\) | −39.4483 | − | 28.6609i | −0.0680143 | − | 0.0494153i | ||||
\(581\) | −419.107 | + | 136.176i | −0.721354 | + | 0.234382i | ||||
\(582\) | 503.432 | − | 1012.26i | 0.865003 | − | 1.73928i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 220.921i | 0.378289i | ||||||||
\(585\) | −55.5038 | − | 38.6989i | −0.0948783 | − | 0.0661520i | ||||
\(586\) | −712.410 | − | 517.596i | −1.21572 | − | 0.883269i | ||||
\(587\) | −442.139 | − | 608.552i | −0.753218 | − | 1.03672i | −0.997748 | − | 0.0670740i | \(-0.978634\pi\) |
0.244530 | − | 0.969642i | \(-0.421366\pi\) | |||||||
\(588\) | −17.4953 | + | 17.8390i | −0.0297540 | + | 0.0303385i | ||||
\(589\) | −23.1964 | + | 71.3913i | −0.0393827 | + | 0.121208i | ||||
\(590\) | 17.3497 | + | 23.8798i | 0.0294062 | + | 0.0404742i | ||||
\(591\) | −16.3652 | + | 8.54000i | −0.0276907 | + | 0.0144501i | ||||
\(592\) | 14.6934 | + | 45.2216i | 0.0248199 | + | 0.0763879i | ||||
\(593\) | 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 | ||||||||
\(596\) | −152.737 | + | 49.6273i | −0.256271 | + | 0.0832673i | ||||
\(597\) | 268.243 | + | 514.034i | 0.449318 | + | 0.861029i | ||||
\(598\) | 521.693 | − | 379.032i | 0.872396 | − | 0.633833i | ||||
\(599\) | −384.153 | − | 124.819i | −0.641323 | − | 0.208379i | −0.0297389 | − | 0.999558i | \(-0.509468\pi\) |
−0.611585 | + | 0.791179i | \(0.709468\pi\) | |||||||
\(600\) | −214.493 | − | 210.360i | −0.357488 | − | 0.350600i | ||||
\(601\) | −668.864 | + | 485.958i | −1.11292 | + | 0.808582i | −0.983121 | − | 0.182959i | \(-0.941433\pi\) |
−0.129797 | + | 0.991541i | \(0.541433\pi\) | |||||||
\(602\) | 125.201 | − | 172.324i | 0.207975 | − | 0.286253i | ||||
\(603\) | 325.980 | − | 467.536i | 0.540598 | − | 0.775350i | ||||
\(604\) | 66.9783 | 0.110891 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −135.679 | − | 67.4778i | −0.223893 | − | 0.111350i | ||||
\(607\) | 357.360 | + | 1099.84i | 0.588731 | + | 1.81193i | 0.583741 | + | 0.811940i | \(0.301588\pi\) |
0.00498960 | + | 0.999988i | \(0.498412\pi\) | |||||||
\(608\) | −519.666 | + | 715.259i | −0.854713 | + | 1.17641i | ||||
\(609\) | 87.1553 | + | 517.638i | 0.143112 | + | 0.849981i | ||||
\(610\) | 39.2116 | − | 120.681i | 0.0642812 | − | 0.197837i | ||||
\(611\) | −376.140 | − | 122.215i | −0.615615 | − | 0.200025i | ||||
\(612\) | 181.686 | − | 598.547i | 0.296872 | − | 0.978019i | ||||
\(613\) | −726.699 | − | 527.978i | −1.18548 | − | 0.861302i | −0.192701 | − | 0.981258i | \(-0.561725\pi\) |
−0.992779 | + | 0.119956i | \(0.961725\pi\) | |||||||
\(614\) | −956.779 | + | 310.876i | −1.55827 | + | 0.506313i | ||||
\(615\) | 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 | \(0.803912\pi\) | |||||||
\(618\) | −1351.55 | − | 200.608i | −2.18697 | − | 0.324608i | ||||
\(619\) | 32.6926 | + | 23.7525i | 0.0528151 | + | 0.0383724i | 0.613880 | − | 0.789400i | \(-0.289608\pi\) |
−0.561064 | + | 0.827772i | \(0.689608\pi\) | |||||||
\(620\) | 3.16116 | + | 4.35097i | 0.00509865 | + | 0.00701769i | ||||
\(621\) | −92.7107 | + | 720.917i | −0.149293 | + | 1.16090i | ||||
\(622\) | 343.497 | − | 1057.18i | 0.552247 | − | 1.69964i | ||||
\(623\) | 56.0327 | + | 77.1224i | 0.0899401 | + | 0.123792i | ||||
\(624\) | 261.575 | + | 501.256i | 0.419191 | + | 0.803296i | ||||
\(625\) | 178.709 | + | 550.010i | 0.285935 | + | 0.880017i | ||||
\(626\) | 1337.64i | 2.13681i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 160.832 | 0.256101 | ||||||||
\(629\) | −66.7060 | + | 21.6741i | −0.106051 | + | 0.0344580i | ||||
\(630\) | 2.36158 | + | 121.379i | 0.00374854 | + | 0.192665i | ||||
\(631\) | 605.551 | − | 439.959i | 0.959669 | − | 0.697240i | 0.00659509 | − | 0.999978i | \(-0.497901\pi\) |
0.953074 | + | 0.302738i | \(0.0979007\pi\) | |||||||
\(632\) | −217.584 | − | 70.6973i | −0.344279 | − | 0.111863i | ||||
\(633\) | −224.318 | + | 228.724i | −0.354372 | + | 0.361334i | ||||
\(634\) | 752.412 | − | 546.659i | 1.18677 | − | 0.862239i | ||||
\(635\) | 89.8082 | − | 123.610i | 0.141430 | − | 0.194662i | ||||
\(636\) | 630.664 | + | 93.6086i | 0.991610 | + | 0.147183i | ||||
\(637\) | 33.3151 | 0.0523000 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32.6644 | + | 24.7170i | −0.0511180 | + | 0.0386807i | ||||
\(640\) | −29.5262 | − | 90.8723i | −0.0461347 | − | 0.141988i | ||||
\(641\) | −71.8878 | + | 98.9450i | −0.112149 | + | 0.154360i | −0.861402 | − | 0.507924i | \(-0.830413\pi\) |
0.749252 | + | 0.662285i | \(0.230413\pi\) | |||||||
\(642\) | −481.891 | + | 81.1365i | −0.750609 | + | 0.126381i | ||||
\(643\) | −194.468 | + | 598.512i | −0.302439 | + | 0.930812i | 0.678181 | + | 0.734894i | \(0.262768\pi\) |
−0.980620 | + | 0.195917i | \(0.937232\pi\) | |||||||
\(644\) | −409.647 | − | 133.102i | −0.636098 | − | 0.206681i | ||||
\(645\) | 4.93729 | + | 29.3239i | 0.00765471 | + | 0.0454634i | ||||
\(646\) | −1569.62 | − | 1140.39i | −2.42975 | − | 1.76531i | ||||
\(647\) | −176.735 | + | 57.4246i | −0.273160 | + | 0.0887552i | −0.442394 | − | 0.896821i | \(-0.645871\pi\) |
0.169234 | + | 0.985576i | \(0.445871\pi\) | |||||||
\(648\) | −320.293 | − | 90.4574i | −0.494280 | − | 0.139595i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 583.808i | − | 0.898166i | ||||||
\(651\) | 8.50041 | − | 57.2694i | 0.0130575 | − | 0.0879714i | ||||
\(652\) | −130.256 | − | 94.6367i | −0.199779 | − | 0.145148i | ||||
\(653\) | 118.977 | + | 163.758i | 0.182201 | + | 0.250778i | 0.890341 | − | 0.455293i | \(-0.150466\pi\) |
−0.708140 | + | 0.706072i | \(0.750466\pi\) | |||||||
\(654\) | 596.242 | + | 584.755i | 0.911686 | + | 0.894120i | ||||
\(655\) | 25.9759 | − | 79.9455i | 0.0396578 | − | 0.122054i | ||||
\(656\) | −205.647 | − | 283.049i | −0.313487 | − | 0.431477i | ||||
\(657\) | −9.41303 | − | 483.805i | −0.0143273 | − | 0.736385i | ||||
\(658\) | 219.281 | + | 674.878i | 0.333254 | + | 1.02565i | ||||
\(659\) | − | 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 | \(0.217758\pi\) | |||||||
\(662\) | 277.650 | − | 90.2139i | 0.419411 | − | 0.136275i | ||||
\(663\) | −739.399 | + | 385.847i | −1.11523 | + | 0.581972i | ||||
\(664\) | −217.195 | + | 157.801i | −0.327100 | + | 0.237652i | ||||
\(665\) | 133.322 | + | 43.3190i | 0.200484 | + | 0.0651413i | ||||
\(666\) | −17.8105 | − | 51.3913i | −0.0267425 | − | 0.0771641i | ||||
\(667\) | 565.019 | − | 410.510i | 0.847105 | − | 0.615458i | ||||
\(668\) | 78.4138 | − | 107.927i | 0.117386 | − | 0.161568i | ||||
\(669\) | 33.7969 | − | 227.698i | 0.0505186 | − | 0.340356i | ||||
\(670\) | −126.658 | −0.189041 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 303.652 | − | 610.560i | 0.451863 | − | 0.908572i | ||||
\(673\) | −80.1865 | − | 246.789i | −0.119148 | − | 0.366700i | 0.873642 | − | 0.486570i | \(-0.161752\pi\) |
−0.992790 | + | 0.119870i | \(0.961752\pi\) | |||||||
\(674\) | 79.0428 | − | 108.793i | 0.117274 | − | 0.161414i | ||||
\(675\) | 478.691 | + | 451.538i | 0.709172 | + | 0.668946i | ||||
\(676\) | 57.8811 | − | 178.140i | 0.0856229 | − | 0.263520i | ||||
\(677\) | −110.860 | − | 36.0206i | −0.163752 | − | 0.0532062i | 0.225994 | − | 0.974129i | \(-0.427437\pi\) |
−0.389746 | + | 0.920923i | \(0.627437\pi\) | |||||||
\(678\) | 935.276 | − | 157.473i | 1.37946 | − | 0.232262i | ||||
\(679\) | 814.570 | + | 591.820i | 1.19966 | + | 0.871605i | ||||
\(680\) | 90.7078 | − | 29.4727i | 0.133394 | − | 0.0433423i | ||||
\(681\) | 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 | \(0.817941\pi\) | |||||||
\(684\) | 320.344 | − | 459.451i | 0.468338 | − | 0.671713i | ||||
\(685\) | 125.180 | + | 90.9485i | 0.182744 | + | 0.132772i | ||||
\(686\) | −525.496 | − | 723.283i | −0.766029 | − | 1.05435i | ||||
\(687\) | 32.3822 | − | 33.0183i | 0.0471356 | − | 0.0480616i | ||||
\(688\) | 76.7856 | − | 236.322i | 0.111607 | − | 0.343491i | ||||
\(689\) | −499.675 | − | 687.744i | −0.725218 | − | 0.998177i | ||||
\(690\) | 143.198 | − | 74.7264i | 0.207534 | − | 0.108299i | ||||
\(691\) | 120.215 | + | 369.984i | 0.173973 | + | 0.535433i | 0.999585 | − | 0.0288049i | \(-0.00917015\pi\) |
−0.825612 | + | 0.564238i | \(0.809170\pi\) | |||||||
\(692\) | − | 532.662i | − | 0.769743i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.2934 | −0.0407686 | ||||||||
\(695\) | −5.22540 | + | 1.69784i | −0.00751857 | + | 0.00244293i | ||||
\(696\) | 147.948 | + | 283.513i | 0.212569 | + | 0.407346i | ||||
\(697\) | 417.523 | − | 303.348i | 0.599029 | − | 0.435220i | ||||
\(698\) | 513.807 | + | 166.946i | 0.736114 | + | 0.239178i | ||||
\(699\) | −370.980 | − | 363.832i | −0.530729 | − | 0.520504i | ||||
\(700\) | −315.481 | + | 229.211i | −0.450688 | + | 0.327444i | ||||
\(701\) | −684.255 | + | 941.796i | −0.976112 | + | 1.34350i | −0.0372140 | + | 0.999307i | \(0.511848\pi\) |
−0.938898 | + | 0.344196i | \(0.888152\pi\) | |||||||
\(702\) | −310.307 | − | 567.448i | −0.442033 | − | 0.808330i | ||||
\(703\) | −62.8043 | −0.0893375 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −88.7011 | − | 44.1140i | −0.125817 | − | 0.0625730i | ||||
\(706\) | 414.625 | + | 1276.09i | 0.587288 | + | 1.80749i | ||||
\(707\) | 79.3250 | − | 109.181i | 0.112199 | − | 0.154429i | ||||
\(708\) | 17.4392 | + | 103.576i | 0.0246317 | + | 0.146294i | ||||
\(709\) | 410.972 | − | 1264.84i | 0.579650 | − | 1.78398i | −0.0401212 | − | 0.999195i | \(-0.512774\pi\) |
0.619771 | − | 0.784783i | \(-0.287226\pi\) | |||||||
\(710\) | 8.65717 | + | 2.81288i | 0.0121932 | + | 0.00396181i | ||||
\(711\) | 479.510 | + | 145.553i | 0.674416 | + | 0.204715i | ||||
\(712\) | 46.9844 | + | 34.1361i | 0.0659893 | + | 0.0479440i | ||||
\(713\) | −73.2604 | + | 23.8038i | −0.102750 | + | 0.0333854i | ||||
\(714\) | 1339.86 | + | 666.356i | 1.87655 | + | 0.933272i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 333.213i | 0.465381i | ||||||||
\(717\) | −879.555 | − | 130.551i | −1.22672 | − | 0.182080i | ||||
\(718\) | −357.788 | − | 259.948i | −0.498312 | − | 0.362045i | ||||
\(719\) | −492.928 | − | 678.457i | −0.685574 | − | 0.943611i | 0.314410 | − | 0.949287i | \(-0.398193\pi\) |
−0.999984 | + | 0.00567596i | \(0.998193\pi\) | |||||||
\(720\) | 46.3759 | + | 133.815i | 0.0644109 | + | 0.185854i | ||||
\(721\) | 376.037 | − | 1157.32i | 0.521549 | − | 1.60516i | ||||
\(722\) | −485.499 | − | 668.231i | −0.672436 | − | 0.925528i | ||||
\(723\) | −64.8167 | − | 124.208i | −0.0896497 | − | 0.171796i | ||||
\(724\) | −95.9313 | − | 295.246i | −0.132502 | − | 0.407798i | ||||
\(725\) | − | 632.292i | − | 0.872127i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 154.628 | 0.212693 | 0.106346 | − | 0.994329i | \(-0.466085\pi\) | ||||
0.106346 | + | 0.994329i | \(0.466085\pi\) | |||||||
\(728\) | −250.100 | + | 81.2623i | −0.343544 | + | 0.111624i | ||||
\(729\) | 705.280 | + | 184.450i | 0.967462 | + | 0.253017i | ||||
\(730\) | −86.9957 | + | 63.2061i | −0.119172 | + | 0.0865837i | ||||
\(731\) | 348.596 | + | 113.266i | 0.476876 | + | 0.154946i | ||||
\(732\) | 316.161 | − | 322.372i | 0.431914 | − | 0.440399i | ||||
\(733\) | 360.030 | − | 261.577i | 0.491173 | − | 0.356858i | −0.314462 | − | 0.949270i | \(-0.601824\pi\) |
0.805635 | + | 0.592412i | \(0.201824\pi\) | |||||||
\(734\) | 206.296 | − | 283.943i | 0.281058 | − | 0.386843i | ||||
\(735\) | 8.25443 | + | 1.22519i | 0.0112305 | + | 0.00166693i | ||||
\(736\) | −907.255 | −1.23268 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 241.489 | + | 319.137i | 0.327221 | + | 0.432434i | ||||
\(739\) | −18.9609 | − | 58.3555i | −0.0256575 | − | 0.0789655i | 0.937408 | − | 0.348233i | \(-0.113218\pi\) |
−0.963065 | + | 0.269268i | \(0.913218\pi\) | |||||||
\(740\) | −2.64483 | + | 3.64029i | −0.00357409 | + | 0.00491931i | ||||
\(741\) | −736.439 | + | 123.995i | −0.993844 | + | 0.167335i | ||||
\(742\) | −471.331 | + | 1450.61i | −0.635218 | + | 1.95500i | ||||
\(743\) | 687.852 | + | 223.497i | 0.925776 | + | 0.300803i | 0.732834 | − | 0.680407i | \(-0.238197\pi\) |
0.192942 | + | 0.981210i | \(0.438197\pi\) | |||||||
\(744\) | −5.85632 | − | 34.7822i | −0.00787140 | − | 0.0467503i | ||||
\(745\) | 43.3923 | + | 31.5263i | 0.0582447 | + | 0.0423172i | ||||
\(746\) | 357.913 | − | 116.293i | 0.479776 | − | 0.155889i | ||||
\(747\) | 468.921 | − | 354.830i | 0.627739 | − | 0.475007i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 435.215i | − | 0.581062i | ||||||
\(750\) | 43.4931 | − | 293.023i | 0.0579907 | − | 0.390698i | ||||
\(751\) | −1040.69 | − | 756.107i | −1.38574 | − | 1.00680i | −0.996317 | − | 0.0857426i | \(-0.972674\pi\) |
−0.389425 | − | 0.921058i | \(-0.627326\pi\) | |||||||
\(752\) | 486.571 | + | 669.708i | 0.647036 | + | 0.890569i | ||||
\(753\) | −445.051 | − | 436.477i | −0.591038 | − | 0.579650i | ||||
\(754\) | −192.034 | + | 591.019i | −0.254687 | + | 0.783845i | ||||
\(755\) | −13.1483 | − | 18.0970i | −0.0174149 | − | 0.0239696i | ||||
\(756\) | −184.810 | + | 390.473i | −0.244458 | + | 0.516499i | ||||
\(757\) | −84.2743 | − | 259.370i | −0.111327 | − | 0.342628i | 0.879837 | − | 0.475276i | \(-0.157652\pi\) |
−0.991163 | + | 0.132648i | \(0.957652\pi\) | |||||||
\(758\) | 682.566i | 0.900483i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 85.4021 | 0.112371 | ||||||||
\(761\) | −453.306 | + | 147.288i | −0.595671 | + | 0.193545i | −0.591309 | − | 0.806445i | \(-0.701389\pi\) |
−0.00436224 | + | 0.999990i | \(0.501389\pi\) | |||||||
\(762\) | 1294.75 | − | 675.651i | 1.69915 | − | 0.886681i | ||||
\(763\) | −601.724 | + | 437.178i | −0.788629 | + | 0.572972i | ||||
\(764\) | −792.821 | − | 257.603i | −1.03772 | − | 0.337177i | ||||
\(765\) | −197.389 | + | 68.4086i | −0.258025 | + | 0.0894230i | ||||
\(766\) | −1290.29 | + | 937.447i | −1.68445 | + | 1.22382i | ||||
\(767\) | 82.3165 | − | 113.299i | 0.107323 | − | 0.147717i | ||||
\(768\) | 144.005 | − | 970.200i | 0.187507 | − | 1.26328i | ||||
\(769\) | 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 | ||||
\(772\) | −179.974 | − | 553.903i | −0.233127 | − | 0.717490i | ||||
\(773\) | 721.676 | − | 993.302i | 0.933604 | − | 1.28500i | −0.0248330 | − | 0.999692i | \(-0.507905\pi\) |
0.958437 | − | 0.285304i | \(-0.0920946\pi\) | |||||||
\(774\) | −82.5584 | + | 271.981i | −0.106665 | + | 0.351397i | ||||
\(775\) | −21.5505 | + | 66.3257i | −0.0278071 | + | 0.0855816i | ||||
\(776\) | 583.378 | + | 189.551i | 0.751776 | + | 0.244267i | ||||
\(777\) | 47.7677 | − | 8.04270i | 0.0614771 | − | 0.0103510i | ||||
\(778\) | 939.418 | + | 682.527i | 1.20748 | + | 0.877284i | ||||
\(779\) | 439.501 | − | 142.802i | 0.564186 | − | 0.183315i | ||||
\(780\) | −23.8260 | + | 47.9075i | −0.0305462 | + | 0.0614199i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 1990.95i | − | 2.54597i | ||||||
\(783\) | −336.078 | − | 614.574i | −0.429218 | − | 0.784896i | ||||
\(784\) | −56.4135 | − | 40.9868i | −0.0719560 | − | 0.0522791i | ||||
\(785\) | −31.5723 | − | 43.4556i | −0.0402195 | − | 0.0553574i | ||||
\(786\) | 562.592 | − | 573.644i | 0.715765 | − | 0.729827i | ||||
\(787\) | −269.548 | + | 829.585i | −0.342501 | + | 1.05411i | 0.620407 | + | 0.784280i | \(0.286968\pi\) |
−0.962908 | + | 0.269830i | \(0.913032\pi\) | |||||||
\(788\) | 8.57990 | + | 11.8092i | 0.0108882 | + | 0.0149863i | ||||
\(789\) | 265.324 | − | 138.457i | 0.336279 | − | 0.175484i | ||||
\(790\) | −34.4117 | − | 105.908i | −0.0435591 | − | 0.134061i | ||||
\(791\) | 844.685i | 1.06787i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −602.043 | −0.759197 | ||||||||
\(794\) | 1347.49 | − | 437.827i | 1.69710 | − | 0.551420i | ||||
\(795\) | −98.5112 | − | 188.777i | −0.123913 | − | 0.237455i | ||||
\(796\) | 370.930 | − | 269.496i | 0.465992 | − | 0.338563i | ||||
\(797\) | 53.0365 | + | 17.2326i | 0.0665451 | + | 0.0216218i | 0.342100 | − | 0.939663i | \(-0.388862\pi\) |
−0.275555 | + | 0.961285i | \(0.588862\pi\) | |||||||
\(798\) | 956.644 | + | 938.212i | 1.19880 | + | 1.17570i | ||||
\(799\) | −987.880 | + | 717.737i | −1.23640 | + | 0.898294i | ||||
\(800\) | −482.793 | + | 664.507i | −0.603491 | + | 0.830634i | ||||
\(801\) | −104.348 | − | 72.7544i | −0.130272 | − | 0.0908295i | ||||
\(802\) | 453.989 | 0.566071 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −403.549 | − | 200.698i | −0.501926 | − | 0.249625i | ||||
\(805\) | 44.4531 | + | 136.813i | 0.0552213 | + | 0.169954i | ||||
\(806\) | 40.2876 | − | 55.4512i | 0.0499847 | − | 0.0687980i | ||||
\(807\) | −25.0929 | − | 149.033i | −0.0310940 | − | 0.184676i | ||||
\(808\) | 25.4066 | − | 78.1935i | 0.0314438 | − | 0.0967741i | ||||
\(809\) | 1260.26 | + | 409.482i | 1.55780 | + | 0.506159i | 0.956218 | − | 0.292655i | \(-0.0945389\pi\) |
0.601578 | + | 0.798814i | \(0.294539\pi\) | |||||||
\(810\) | −56.0159 | − | 152.007i | −0.0691554 | − | 0.187663i | ||||
\(811\) | −831.775 | − | 604.320i | −1.02562 | − | 0.745154i | −0.0581899 | − | 0.998306i | \(-0.518533\pi\) |
−0.967427 | + | 0.253151i | \(0.918533\pi\) | |||||||
\(812\) | 394.774 | − | 128.270i | 0.486174 | − | 0.157968i | ||||
\(813\) | −334.103 | − | 166.161i | −0.410951 | − | 0.204380i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.7721i | 0.0659781i | ||||||||
\(816\) | 1726.74 | + | 256.298i | 2.11611 | + | 0.314091i | ||||
\(817\) | 265.525 | + | 192.915i | 0.324999 | + | 0.236126i | ||||
\(818\) | 201.341 | + | 277.122i | 0.246138 | + | 0.338780i | ||||
\(819\) | 544.242 | − | 188.616i | 0.664521 | − | 0.230301i | ||||
\(820\) | 10.2312 | − | 31.4883i | 0.0124770 | − | 0.0384004i | ||||
\(821\) | 524.354 | + | 721.712i | 0.638678 | + | 0.879064i | 0.998544 | − | 0.0539395i | \(-0.0171778\pi\) |
−0.359867 | + | 0.933004i | \(0.617178\pi\) | |||||||
\(822\) | 684.230 | + | 1311.19i | 0.832397 | + | 1.59512i | ||||
\(823\) | −128.335 | − | 394.975i | −0.155936 | − | 0.479921i | 0.842319 | − | 0.538980i | \(-0.181190\pi\) |
−0.998255 | + | 0.0590586i | \(0.981190\pi\) | |||||||
\(824\) | − | 741.346i | − | 0.899691i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −251.272 | −0.304203 | ||||||||
\(827\) | −441.823 | + | 143.557i | −0.534248 | + | 0.173588i | −0.563701 | − | 0.825979i | \(-0.690623\pi\) |
0.0294539 | + | 0.999566i | \(0.490623\pi\) | |||||||
\(828\) | 574.659 | − | 11.1807i | 0.694032 | − | 0.0135033i | ||||
\(829\) | 716.945 | − | 520.891i | 0.864831 | − | 0.628337i | −0.0643639 | − | 0.997926i | \(-0.520502\pi\) |
0.929195 | + | 0.369590i | \(0.120502\pi\) | |||||||
\(830\) | −124.280 | − | 40.3810i | −0.149735 | − | 0.0486518i | ||||
\(831\) | 616.990 | − | 629.111i | 0.742467 | − | 0.757053i | ||||
\(832\) | 43.2032 | − | 31.3890i | 0.0519270 | − | 0.0377271i | ||||
\(833\) | 60.4593 | − | 83.2150i | 0.0725802 | − | 0.0998980i | ||||
\(834\) | −51.9479 | − | 7.71055i | −0.0622876 | − | 0.00924526i | ||||
\(835\) | −44.5544 | −0.0533585 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.3070 | + | 75.9217i | 0.0170932 | + | 0.0907069i | ||||
\(838\) | 39.2653 | + | 120.846i | 0.0468560 | + | 0.144208i | ||||
\(839\) | −96.0926 | + | 132.260i | −0.114532 | + | 0.157640i | −0.862434 | − | 0.506169i | \(-0.831061\pi\) |
0.747902 | + | 0.663809i | \(0.231061\pi\) | |||||||
\(840\) | −64.9552 | + | 10.9366i | −0.0773277 | + | 0.0130197i | ||||
\(841\) | 51.9013 | − | 159.736i | 0.0617138 | − | 0.189935i | ||||
\(842\) | −126.485 | − | 41.0975i | −0.150220 | − | 0.0488094i | ||||
\(843\) | −131.338 | − | 780.050i | −0.155798 | − | 0.925326i | ||||
\(844\) | 204.949 | + | 148.904i | 0.242831 | + | 0.176427i | ||||
\(845\) | −59.4945 | + | 19.3309i | −0.0704077 | + | 0.0228768i | ||||
\(846\) | −571.375 | − | 755.092i | −0.675384 | − | 0.892544i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1779.31i | 2.09825i | ||||||||
\(849\) | −175.650 | + | 1183.40i | −0.206891 | + | 1.39387i | ||||
\(850\) | −1458.24 | − | 1059.48i | −1.71558 | − | 1.24644i | ||||
\(851\) | −37.8819 | − | 52.1400i | −0.0445146 | − | 0.0612691i | ||||
\(852\) | 23.1257 | + | 22.6802i | 0.0271429 | + | 0.0266199i | ||||
\(853\) | 139.567 | − | 429.542i | 0.163618 | − | 0.503566i | −0.835313 | − | 0.549774i | \(-0.814714\pi\) |
0.998932 | + | 0.0462082i | \(0.0147138\pi\) | |||||||
\(854\) | 634.924 | + | 873.898i | 0.743471 | + | 1.02330i | ||||
\(855\) | −187.026 | + | 3.63882i | −0.218744 | + | 0.00425593i | ||||
\(856\) | −81.9331 | − | 252.164i | −0.0957163 | − | 0.294584i | ||||
\(857\) | − | 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 | \(0.632411\pi\) | |||||||
\(860\) | 22.3637 | − | 7.26639i | 0.0260042 | − | 0.00844929i | ||||
\(861\) | −315.989 | + | 164.895i | −0.367002 | + | 0.191516i | ||||
\(862\) | −1014.59 | + | 737.146i | −1.17702 | + | 0.855158i | ||||
\(863\) | 1087.43 | + | 353.326i | 1.26005 | + | 0.409416i | 0.861514 | − | 0.507734i | \(-0.169517\pi\) |
0.398541 | + | 0.917151i | \(0.369517\pi\) | |||||||
\(864\) | −116.063 | + | 902.502i | −0.134332 | + | 1.04456i | ||||
\(865\) | −143.922 | + | 104.565i | −0.166383 | + | 0.120885i | ||||
\(866\) | 765.064 | − | 1053.02i | 0.883446 | − | 1.21596i | ||||
\(867\) | −250.770 | + | 1689.50i | −0.289239 | + | 1.94868i | ||||
\(868\) | −45.7825 | −0.0527448 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −69.3151 | + | 139.374i | −0.0796726 | + | 0.160200i | ||||
\(871\) | 185.699 | + | 571.523i | 0.213202 | + | 0.656169i | ||||
\(872\) | −266.337 | + | 366.581i | −0.305432 | + | 0.420391i | ||||
\(873\) | −1285.64 | − | 390.250i | −1.47267 | − | 0.447022i | ||||
\(874\) | 550.900 | − | 1695.50i | 0.630320 | − | 1.93993i | ||||
\(875\) | 250.915 | + | 81.5271i | 0.286759 | + | 0.0931738i | ||||
\(876\) | −377.335 | + | 63.5323i | −0.430748 | + | 0.0725255i | ||||
\(877\) | −874.028 | − | 635.019i | −0.996611 | − | 0.724080i | −0.0352523 | − | 0.999378i | \(-0.511223\pi\) |
−0.961359 | + | 0.275298i | \(0.911223\pi\) | |||||||
\(878\) | −60.2808 | + | 19.5864i | −0.0686569 | + | 0.0223080i | ||||
\(879\) | −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 | \(0.882062\pi\) | |||||||
\(882\) | 65.4300 | + | 45.6198i | 0.0741837 | + | 0.0517231i | ||||
\(883\) | 786.522 | + | 571.442i | 0.890739 | + | 0.647160i | 0.936071 | − | 0.351812i | \(-0.114434\pi\) |
−0.0453316 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(884\) | 387.650 | + | 533.555i | 0.438518 | + | 0.603569i | ||||
\(885\) | 24.5621 | − | 25.0446i | 0.0277538 | − | 0.0282990i | ||||
\(886\) | −678.982 | + | 2089.69i | −0.766346 | + | 2.35857i | ||||
\(887\) | 309.160 | + | 425.523i | 0.348546 | + | 0.479733i | 0.946913 | − | 0.321490i | \(-0.104183\pi\) |
−0.598367 | + | 0.801222i | \(0.704183\pi\) | |||||||
\(888\) | 26.1626 | − | 13.6526i | 0.0294623 | − | 0.0153746i | ||||
\(889\) | 401.930 | + | 1237.01i | 0.452115 | + | 1.39147i | ||||
\(890\) | 28.2683i | 0.0317621i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −182.027 | −0.204066 | ||||||||
\(893\) | −1039.88 | + | 337.877i | −1.16448 | + | 0.378362i | ||||
\(894\) | 237.181 | + | 454.510i | 0.265303 | + | 0.508401i | ||||
\(895\) | 90.0317 | − | 65.4118i | 0.100594 | − | 0.0730859i | ||||
\(896\) | 773.576 | + | 251.350i | 0.863366 | + | 0.280525i | ||||
\(897\) | −547.141 | − | 536.600i | −0.609968 | − | 0.598216i | ||||
\(898\) | −1175.59 | + | 854.119i | −1.30912 | + | 0.951135i | ||||
\(899\) | 43.6335 | − | 60.0564i | 0.0485356 | − | 0.0668035i | ||||
\(900\) | 297.614 | − | 426.851i | 0.330682 | − | 0.474279i | ||||
\(901\) | −2624.65 | −2.91304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −226.658 | − | 112.724i | −0.251005 | − | 0.124833i | ||||
\(904\) | 159.019 | + | 489.412i | 0.175907 | + | 0.541385i | ||||
\(905\) | −60.9415 | + | 83.8787i | −0.0673386 | + | 0.0926837i | ||||
\(906\) | −35.5004 | − | 210.846i | −0.0391837 | − | 0.232722i | ||||
\(907\) | −177.594 | + | 546.578i | −0.195804 | + | 0.602622i | 0.804163 | + | 0.594409i | \(0.202614\pi\) |
−0.999966 | + | 0.00821243i | \(0.997386\pi\) | |||||||
\(908\) | −108.845 | − | 35.3660i | −0.119874 | − | 0.0389493i | ||||
\(909\) | −52.3074 | + | 172.322i | −0.0575439 | + | 0.189573i | ||||
\(910\) | −103.554 | − | 75.2365i | −0.113796 | − | 0.0826775i | ||||
\(911\) | 1216.56 | − | 395.284i | 1.33541 | − | 0.433901i | 0.447651 | − | 0.894208i | \(-0.352261\pi\) |
0.887760 | + | 0.460307i | \(0.152261\pi\) | |||||||
\(912\) | 1399.58 | + | 696.058i | 1.53463 | + | 0.763222i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 64.6037i | − | 0.0706823i | ||||||
\(915\) | −149.167 | − | 22.1407i | −0.163024 | − | 0.0241975i | ||||
\(916\) | −29.5862 | − | 21.4956i | −0.0322994 | − | 0.0234669i | ||||
\(917\) | 420.608 | + | 578.918i | 0.458679 | + | 0.631317i | ||||
\(918\) | −1980.52 | − | 254.696i | −2.15742 | − | 0.277447i | ||||
\(919\) | 148.924 | − | 458.342i | 0.162050 | − | 0.498740i | −0.836756 | − | 0.547575i | \(-0.815551\pi\) |
0.998807 | + | 0.0488354i | \(0.0155510\pi\) | |||||||
\(920\) | 51.5124 | + | 70.9007i | 0.0559917 | + | 0.0770660i | ||||
\(921\) | 553.118 | + | 1059.94i | 0.600563 | + | 1.15086i | ||||
\(922\) | −225.723 | − | 694.705i | −0.244819 | − | 0.753476i | ||||
\(923\) | − | 43.1883i | − | 0.0467912i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.3480 | −0.0630789 | ||||||||
\(926\) | 482.682 | − | 156.833i | 0.521255 | − | 0.169366i | ||||
\(927\) | 31.5873 | + | 1623.51i | 0.0340748 | + | 1.75136i | ||||
\(928\) | 707.335 | − | 513.909i | 0.762215 | − | 0.553782i | ||||
\(929\) | −1057.82 | − | 343.707i | −1.13867 | − | 0.369975i | −0.321803 | − | 0.946807i | \(-0.604289\pi\) |
−0.816863 | + | 0.576832i | \(0.804289\pi\) | |||||||
\(930\) | 12.0213 | − | 12.2574i | 0.0129261 | − | 0.0131800i | ||||
\(931\) | 74.5130 | − | 54.1369i | 0.0800355 | − | 0.0581492i | ||||
\(932\) | −241.516 | + | 332.418i | −0.259137 | + | 0.356672i | ||||
\(933\) | −1306.72 | − | 193.955i | −1.40056 | − | 0.207883i | ||||
\(934\) | −278.484 | −0.298162 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 279.826 | − | 211.743i | 0.298959 | − | 0.226221i | ||||
\(937\) | −538.796 | − | 1658.24i | −0.575023 | − | 1.76974i | −0.636102 | − | 0.771605i | \(-0.719454\pi\) |
0.0610795 | − | 0.998133i | \(-0.480546\pi\) | |||||||
\(938\) | 633.755 | − | 872.288i | 0.675645 | − | 0.929945i | ||||
\(939\) | 1567.63 | − | 263.944i | 1.66947 | − | 0.281091i | ||||
\(940\) | −24.2074 | + | 74.5028i | −0.0257526 | + | 0.0792583i | ||||
\(941\) | −795.268 | − | 258.398i | −0.845131 | − | 0.274600i | −0.145726 | − | 0.989325i | \(-0.546552\pi\) |
−0.699405 | + | 0.714725i | \(0.746552\pi\) | |||||||
\(942\) | −85.2454 | − | 506.295i | −0.0904941 | − | 0.537468i | ||||
\(943\) | 383.650 | + | 278.738i | 0.406840 | + | 0.295586i | ||||
\(944\) | −278.778 | + | 90.5805i | −0.295316 | + | 0.0959539i | ||||
\(945\) | 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 | \(-0.0192927\pi\) | |||||||
\(948\) | 58.1791 | − | 391.967i | 0.0613703 | − | 0.413467i | ||||
\(949\) | 412.757 | + | 299.885i | 0.434939 | + | 0.316001i | ||||
\(950\) | −948.684 | − | 1305.75i | −0.998615 | − | 1.37448i | ||||
\(951\) | −789.115 | − | 773.911i | −0.829774 | − | 0.813787i | ||||
\(952\) | −250.895 | + | 772.175i | −0.263545 | + | 0.811108i | ||||
\(953\) | 192.241 | + | 264.597i | 0.201722 | + | 0.277646i | 0.897878 | − | 0.440244i | \(-0.145108\pi\) |
−0.696157 | + | 0.717890i | \(0.745108\pi\) | |||||||
\(954\) | −39.5922 | − | 2034.94i | −0.0415012 | − | 2.13306i | ||||
\(955\) | 86.0335 | + | 264.784i | 0.0900874 | + | 0.277261i | ||||
\(956\) | 703.137i | 0.735499i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1725.47 | −1.80111 | ||||||||
\(959\) | −1252.72 | + | 407.034i | −1.30628 | + | 0.424436i | ||||
\(960\) | 11.8587 | − | 6.18835i | 0.0123529 | − | 0.00644620i | ||||
\(961\) | 770.841 | − | 560.049i | 0.802124 | − | 0.582777i | ||||
\(962\) | 54.5393 | + | 17.7209i | 0.0566937 | + | 0.0184209i | ||||
\(963\) | 190.173 | + | 548.735i | 0.197480 | + | 0.569818i | ||||
\(964\) | −89.6294 | + | 65.1196i | −0.0929766 | + | 0.0675514i | ||||
\(965\) | −114.331 | + | 157.362i | −0.118477 | + | 0.163070i | ||||
\(966\) | −201.879 | + | 1360.11i | −0.208985 | + | 1.40798i | ||||
\(967\) | −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 | ||||
\(970\) | 92.2634 | + | 283.957i | 0.0951169 | + | 0.292740i | ||||
\(971\) | 48.0438 | − | 66.1266i | 0.0494787 | − | 0.0681016i | −0.783561 | − | 0.621315i | \(-0.786599\pi\) |
0.833039 | + | 0.553214i | \(0.186599\pi\) | |||||||
\(972\) | 62.3923 | − | 573.078i | 0.0641896 | − | 0.589586i | ||||
\(973\) | 14.4533 | − | 44.4827i | 0.0148544 | − | 0.0457170i | ||||
\(974\) | −312.344 | − | 101.487i | −0.320682 | − | 0.104196i | ||||
\(975\) | −684.185 | + | 115.197i | −0.701728 | + | 0.118151i | ||||
\(976\) | 1019.46 | + | 740.680i | 1.04453 | + | 0.758893i | ||||
\(977\) | −19.3599 | + | 6.29041i | −0.0198157 | + | 0.00643850i | −0.318908 | − | 0.947786i | \(-0.603316\pi\) |
0.299092 | + | 0.954224i | \(0.403316\pi\) | |||||||
\(978\) | −228.875 | + | 460.205i | −0.234024 | + | 0.470557i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 6.59879i | − | 0.00673346i | ||||||
\(981\) | 567.644 | − | 814.141i | 0.578638 | − | 0.829910i | ||||
\(982\) | 1626.80 | + | 1181.94i | 1.65662 | + | 1.20361i | ||||
\(983\) | 468.704 | + | 645.115i | 0.476810 | + | 0.656272i | 0.977888 | − | 0.209130i | \(-0.0670631\pi\) |
−0.501078 | + | 0.865402i | \(0.667063\pi\) | |||||||
\(984\) | −152.041 | + | 155.028i | −0.154513 | + | 0.157549i | ||||
\(985\) | 1.50648 | − | 4.63646i | 0.00152942 | − | 0.00470706i | ||||
\(986\) | 1127.76 | + | 1552.23i | 1.14377 | + | 1.57427i | ||||
\(987\) | 747.644 | − | 390.150i | 0.757492 | − | 0.395289i | ||||
\(988\) | 182.488 | + | 561.640i | 0.184704 | + | 0.568462i | ||||
\(989\) | 336.799i | 0.340545i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 609.620 | 0.615156 | 0.307578 | − | 0.951523i | \(-0.400481\pi\) | ||||
0.307578 | + | 0.951523i | \(0.400481\pi\) | |||||||
\(992\) | −91.7132 | + | 29.7994i | −0.0924528 | + | 0.0300397i | ||||
\(993\) | −160.511 | − | 307.587i | −0.161642 | − | 0.309755i | ||||
\(994\) | −62.6900 | + | 45.5470i | −0.0630684 | + | 0.0458219i | ||||
\(995\) | −145.632 | − | 47.3187i | −0.146364 | − | 0.0475565i | ||||
\(996\) | −331.987 | − | 325.590i | −0.333320 | − | 0.326898i | ||||
\(997\) | 1432.99 | − | 1041.13i | 1.43730 | − | 1.04426i | 0.448708 | − | 0.893679i | \(-0.351884\pi\) |
0.988597 | − | 0.150585i | \(-0.0481156\pi\) | |||||||
\(998\) | 727.095 | − | 1000.76i | 0.728552 | − | 1.00277i | ||||
\(999\) | −56.7129 | + | 31.0133i | −0.0567697 | + | 0.0310443i |
(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.269.1 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.l.269.4 | 16 | ||
11.2 | odd | 10 | 363.3.h.m.251.1 | 16 | |||
11.3 | even | 5 | 363.3.b.h.122.4 | 4 | |||
11.4 | even | 5 | inner | 363.3.h.l.245.1 | 16 | ||
11.5 | even | 5 | inner | 363.3.h.l.323.4 | 16 | ||
11.6 | odd | 10 | 363.3.h.m.323.1 | 16 | |||
11.7 | odd | 10 | 363.3.h.m.245.4 | 16 | |||
11.8 | odd | 10 | 33.3.b.b.23.1 | ✓ | 4 | ||
11.9 | even | 5 | inner | 363.3.h.l.251.4 | 16 | ||
11.10 | odd | 2 | 363.3.h.m.269.4 | 16 | |||
33.2 | even | 10 | 363.3.h.m.251.4 | 16 | |||
33.5 | odd | 10 | inner | 363.3.h.l.323.1 | 16 | ||
33.8 | even | 10 | 33.3.b.b.23.4 | yes | 4 | ||
33.14 | odd | 10 | 363.3.b.h.122.1 | 4 | |||
33.17 | even | 10 | 363.3.h.m.323.4 | 16 | |||
33.20 | odd | 10 | inner | 363.3.h.l.251.1 | 16 | ||
33.26 | odd | 10 | inner | 363.3.h.l.245.4 | 16 | ||
33.29 | even | 10 | 363.3.h.m.245.1 | 16 | |||
33.32 | even | 2 | 363.3.h.m.269.1 | 16 | |||
44.19 | even | 10 | 528.3.i.d.353.4 | 4 | |||
132.107 | 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 | 11.8 | odd | 10 | ||
33.3.b.b.23.4 | yes | 4 | 33.8 | even | 10 | ||
363.3.b.h.122.1 | 4 | 33.14 | odd | 10 | |||
363.3.b.h.122.4 | 4 | 11.3 | even | 5 | |||
363.3.h.l.245.1 | 16 | 11.4 | even | 5 | inner | ||
363.3.h.l.245.4 | 16 | 33.26 | odd | 10 | inner | ||
363.3.h.l.251.1 | 16 | 33.20 | odd | 10 | inner | ||
363.3.h.l.251.4 | 16 | 11.9 | even | 5 | inner | ||
363.3.h.l.269.1 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.l.269.4 | 16 | 3.2 | odd | 2 | inner | ||
363.3.h.l.323.1 | 16 | 33.5 | odd | 10 | inner | ||
363.3.h.l.323.4 | 16 | 11.5 | even | 5 | inner | ||
363.3.h.m.245.1 | 16 | 33.29 | even | 10 | |||
363.3.h.m.245.4 | 16 | 11.7 | odd | 10 | |||
363.3.h.m.251.1 | 16 | 11.2 | odd | 10 | |||
363.3.h.m.251.4 | 16 | 33.2 | even | 10 | |||
363.3.h.m.269.1 | 16 | 33.32 | even | 2 | |||
363.3.h.m.269.4 | 16 | 11.10 | odd | 2 | |||
363.3.h.m.323.1 | 16 | 11.6 | odd | 10 | |||
363.3.h.m.323.4 | 16 | 33.17 | even | 10 | |||
528.3.i.d.353.3 | 4 | 132.107 | odd | 10 | |||
528.3.i.d.353.4 | 4 | 44.19 | even | 10 |