Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(43,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.w (of order \(8\), degree \(4\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 99.3 | ||
Character | \(\chi\) | \(=\) | 224.99 |
Dual form | 224.3.w.a.43.3 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99185 | + | 0.180328i | −0.995927 | + | 0.0901639i | ||||
\(3\) | 0.825363 | − | 1.99260i | 0.275121 | − | 0.664201i | −0.724566 | − | 0.689205i | \(-0.757960\pi\) |
0.999687 | + | 0.0250040i | \(0.00795985\pi\) | |||||||
\(4\) | 3.93496 | − | 0.718374i | 0.983741 | − | 0.179593i | ||||
\(5\) | 0.360772 | + | 0.870982i | 0.0721545 | + | 0.174196i | 0.955842 | − | 0.293881i | \(-0.0949469\pi\) |
−0.883688 | + | 0.468077i | \(0.844947\pi\) | |||||||
\(6\) | −1.28468 | + | 4.11781i | −0.214114 | + | 0.686302i | ||||
\(7\) | 1.87083 | + | 1.87083i | 0.267261 | + | 0.267261i | ||||
\(8\) | −7.70833 | + | 2.14048i | −0.963541 | + | 0.267560i | ||||
\(9\) | 3.07472 | + | 3.07472i | 0.341635 | + | 0.341635i | ||||
\(10\) | −0.875668 | − | 1.66981i | −0.0875668 | − | 0.166981i | ||||
\(11\) | 5.69947 | + | 13.7597i | 0.518133 | + | 1.25088i | 0.939048 | + | 0.343785i | \(0.111709\pi\) |
−0.420915 | + | 0.907100i | \(0.638291\pi\) | |||||||
\(12\) | 1.81634 | − | 8.43374i | 0.151362 | − | 0.702812i | ||||
\(13\) | 2.01655 | − | 4.86839i | 0.155119 | − | 0.374491i | −0.827146 | − | 0.561987i | \(-0.810037\pi\) |
0.982265 | + | 0.187496i | \(0.0600371\pi\) | |||||||
\(14\) | −4.06378 | − | 3.38905i | −0.290270 | − | 0.242075i | ||||
\(15\) | 2.03329 | 0.135553 | ||||||||
\(16\) | 14.9679 | − | 5.65355i | 0.935492 | − | 0.353347i | ||||
\(17\) | 19.7416i | 1.16127i | 0.814163 | + | 0.580636i | \(0.197196\pi\) | ||||
−0.814163 | + | 0.580636i | \(0.802804\pi\) | |||||||
\(18\) | −6.67884 | − | 5.56993i | −0.371047 | − | 0.309441i | ||||
\(19\) | −23.8235 | − | 9.86802i | −1.25387 | − | 0.519370i | −0.345847 | − | 0.938291i | \(-0.612408\pi\) |
−0.908023 | + | 0.418921i | \(0.862408\pi\) | |||||||
\(20\) | 2.04532 | + | 3.16811i | 0.102266 | + | 0.158406i | ||||
\(21\) | 5.27193 | − | 2.18371i | 0.251044 | − | 0.103986i | ||||
\(22\) | −13.8338 | − | 26.3796i | −0.628808 | − | 1.19907i | ||||
\(23\) | 18.8473 | − | 18.8473i | 0.819447 | − | 0.819447i | −0.166581 | − | 0.986028i | \(-0.553273\pi\) |
0.986028 | + | 0.166581i | \(0.0532728\pi\) | |||||||
\(24\) | −2.09705 | + | 17.1263i | −0.0873770 | + | 0.713597i | ||||
\(25\) | 17.0492 | − | 17.0492i | 0.681969 | − | 0.681969i | ||||
\(26\) | −3.13877 | + | 10.0608i | −0.120722 | + | 0.386952i | ||||
\(27\) | 26.5979 | − | 11.0172i | 0.985107 | − | 0.408045i | ||||
\(28\) | 8.70560 | + | 6.01769i | 0.310914 | + | 0.214917i | ||||
\(29\) | 45.5859 | + | 18.8823i | 1.57193 | + | 0.651114i | 0.987109 | − | 0.160049i | \(-0.0511652\pi\) |
0.584820 | + | 0.811163i | \(0.301165\pi\) | |||||||
\(30\) | −4.05002 | + | 0.366659i | −0.135001 | + | 0.0122220i | ||||
\(31\) | 37.3014i | 1.20327i | 0.798771 | + | 0.601636i | \(0.205484\pi\) | ||||
−0.798771 | + | 0.601636i | \(0.794516\pi\) | |||||||
\(32\) | −28.7943 | + | 13.9602i | −0.899823 | + | 0.436255i | ||||
\(33\) | 32.1218 | 0.973389 | ||||||||
\(34\) | −3.55997 | − | 39.3224i | −0.104705 | − | 1.15654i | ||||
\(35\) | −0.954514 | + | 2.30440i | −0.0272718 | + | 0.0658400i | ||||
\(36\) | 14.3077 | + | 9.89010i | 0.397436 | + | 0.274725i | ||||
\(37\) | 19.3858 | + | 46.8015i | 0.523941 | + | 1.26491i | 0.935437 | + | 0.353494i | \(0.115007\pi\) |
−0.411496 | + | 0.911412i | \(0.634993\pi\) | |||||||
\(38\) | 49.2324 | + | 15.3596i | 1.29559 | + | 0.404200i | ||||
\(39\) | −8.03638 | − | 8.03638i | −0.206061 | − | 0.206061i | ||||
\(40\) | −4.64527 | − | 5.94159i | −0.116132 | − | 0.148540i | ||||
\(41\) | −16.8279 | − | 16.8279i | −0.410437 | − | 0.410437i | 0.471454 | − | 0.881891i | \(-0.343729\pi\) |
−0.881891 | + | 0.471454i | \(0.843729\pi\) | |||||||
\(42\) | −10.1071 | + | 5.30030i | −0.240646 | + | 0.126198i | ||||
\(43\) | −31.7055 | − | 76.5439i | −0.737338 | − | 1.78009i | −0.616403 | − | 0.787431i | \(-0.711411\pi\) |
−0.120935 | − | 0.992660i | \(-0.538589\pi\) | |||||||
\(44\) | 32.3118 | + | 50.0497i | 0.734360 | + | 1.13749i | ||||
\(45\) | −1.56875 | + | 3.78730i | −0.0348611 | + | 0.0841621i | ||||
\(46\) | −34.1423 | + | 40.9397i | −0.742224 | + | 0.889993i | ||||
\(47\) | 83.8956 | 1.78501 | 0.892506 | − | 0.451035i | \(-0.148945\pi\) | ||||
0.892506 | + | 0.451035i | \(0.148945\pi\) | |||||||
\(48\) | 1.08866 | − | 34.4913i | 0.0226804 | − | 0.718568i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −30.8851 | + | 37.0340i | −0.617702 | + | 0.740680i | ||||
\(51\) | 39.3372 | + | 16.2940i | 0.771319 | + | 0.319491i | ||||
\(52\) | 4.43774 | − | 20.6056i | 0.0853411 | − | 0.396261i | ||||
\(53\) | −25.3103 | + | 10.4839i | −0.477553 | + | 0.197809i | −0.608458 | − | 0.793586i | \(-0.708212\pi\) |
0.130905 | + | 0.991395i | \(0.458212\pi\) | |||||||
\(54\) | −50.9924 | + | 26.7410i | −0.944303 | + | 0.495204i | ||||
\(55\) | −9.92827 | + | 9.92827i | −0.180514 | + | 0.180514i | ||||
\(56\) | −18.4254 | − | 10.4165i | −0.329026 | − | 0.186009i | ||||
\(57\) | −39.3261 | + | 39.3261i | −0.689932 | + | 0.689932i | ||||
\(58\) | −94.2055 | − | 29.3904i | −1.62423 | − | 0.506731i | ||||
\(59\) | −37.1064 | + | 15.3700i | −0.628922 | + | 0.260508i | −0.674295 | − | 0.738462i | \(-0.735552\pi\) |
0.0453732 | + | 0.998970i | \(0.485552\pi\) | |||||||
\(60\) | 8.00092 | − | 1.46066i | 0.133349 | − | 0.0243444i | ||||
\(61\) | −47.4525 | − | 19.6555i | −0.777909 | − | 0.322221i | −0.0418379 | − | 0.999124i | \(-0.513321\pi\) |
−0.736071 | + | 0.676904i | \(0.763321\pi\) | |||||||
\(62\) | −6.72648 | − | 74.2989i | −0.108492 | − | 1.19837i | ||||
\(63\) | 11.5045i | 0.182612i | ||||||||
\(64\) | 54.8367 | − | 32.9990i | 0.856823 | − | 0.515610i | ||||
\(65\) | 4.96779 | 0.0764276 | ||||||||
\(66\) | −63.9820 | + | 5.79246i | −0.969424 | + | 0.0877646i | ||||
\(67\) | 31.7213 | − | 76.5820i | 0.473452 | − | 1.14301i | −0.489175 | − | 0.872186i | \(-0.662702\pi\) |
0.962627 | − | 0.270829i | \(-0.0872979\pi\) | |||||||
\(68\) | 14.1819 | + | 77.6826i | 0.208557 | + | 1.14239i | ||||
\(69\) | −21.9993 | − | 53.1110i | −0.318830 | − | 0.769725i | ||||
\(70\) | 1.48570 | − | 4.76216i | 0.0212244 | − | 0.0680308i | ||||
\(71\) | −22.6464 | − | 22.6464i | −0.318963 | − | 0.318963i | 0.529406 | − | 0.848369i | \(-0.322415\pi\) |
−0.848369 | + | 0.529406i | \(0.822415\pi\) | |||||||
\(72\) | −30.2823 | − | 17.1196i | −0.420587 | − | 0.237772i | ||||
\(73\) | 37.4417 | + | 37.4417i | 0.512899 | + | 0.512899i | 0.915414 | − | 0.402514i | \(-0.131864\pi\) |
−0.402514 | + | 0.915414i | \(0.631864\pi\) | |||||||
\(74\) | −47.0533 | − | 89.7260i | −0.635856 | − | 1.21251i | ||||
\(75\) | −19.9005 | − | 48.0441i | −0.265340 | − | 0.640588i | ||||
\(76\) | −100.834 | − | 21.7161i | −1.32676 | − | 0.285739i | ||||
\(77\) | −15.0794 | + | 36.4048i | −0.195836 | + | 0.472790i | ||||
\(78\) | 17.4565 | + | 14.5581i | 0.223801 | + | 0.186642i | ||||
\(79\) | −11.5269 | −0.145910 | −0.0729549 | − | 0.997335i | \(-0.523243\pi\) | ||||
−0.0729549 | + | 0.997335i | \(0.523243\pi\) | |||||||
\(80\) | 10.3241 | + | 10.9971i | 0.129052 | + | 0.137464i | ||||
\(81\) | − | 22.9575i | − | 0.283426i | ||||||
\(82\) | 36.5533 | + | 30.4842i | 0.445772 | + | 0.371759i | ||||
\(83\) | −147.866 | − | 61.2479i | −1.78151 | − | 0.737927i | −0.992308 | − | 0.123796i | \(-0.960493\pi\) |
−0.789204 | − | 0.614131i | \(-0.789507\pi\) | |||||||
\(84\) | 19.1762 | − | 12.3800i | 0.228288 | − | 0.147381i | ||||
\(85\) | −17.1946 | + | 7.12224i | −0.202289 | + | 0.0837910i | ||||
\(86\) | 76.9558 | + | 146.747i | 0.894835 | + | 1.70636i | ||||
\(87\) | 75.2499 | − | 75.2499i | 0.864942 | − | 0.864942i | ||||
\(88\) | −73.3858 | − | 93.8650i | −0.833930 | − | 1.06665i | ||||
\(89\) | −103.987 | + | 103.987i | −1.16839 | + | 1.16839i | −0.185806 | + | 0.982586i | \(0.559490\pi\) |
−0.982586 | + | 0.185806i | \(0.940510\pi\) | |||||||
\(90\) | 2.44176 | − | 7.82663i | 0.0271307 | − | 0.0869625i | ||||
\(91\) | 12.8805 | − | 5.33530i | 0.141544 | − | 0.0586296i | ||||
\(92\) | 60.6239 | − | 87.7027i | 0.658956 | − | 0.953290i | ||||
\(93\) | 74.3269 | + | 30.7872i | 0.799214 | + | 0.331045i | ||||
\(94\) | −167.108 | + | 15.1287i | −1.77774 | + | 0.160944i | ||||
\(95\) | − | 24.3100i | − | 0.255894i | ||||||
\(96\) | 4.05129 | + | 68.8979i | 0.0422009 | + | 0.717687i | ||||
\(97\) | −82.5634 | −0.851169 | −0.425584 | − | 0.904919i | \(-0.639931\pi\) | ||||
−0.425584 | + | 0.904919i | \(0.639931\pi\) | |||||||
\(98\) | −1.26230 | − | 13.9430i | −0.0128806 | − | 0.142275i | ||||
\(99\) | −24.7830 | + | 59.8315i | −0.250334 | + | 0.604359i | ||||
\(100\) | 54.8403 | − | 79.3358i | 0.548403 | − | 0.793358i | ||||
\(101\) | 44.0037 | + | 106.234i | 0.435680 | + | 1.05183i | 0.977425 | + | 0.211282i | \(0.0677639\pi\) |
−0.541745 | + | 0.840543i | \(0.682236\pi\) | |||||||
\(102\) | −81.2923 | − | 25.3617i | −0.796983 | − | 0.248644i | ||||
\(103\) | −11.9420 | − | 11.9420i | −0.115942 | − | 0.115942i | 0.646756 | − | 0.762697i | \(-0.276125\pi\) |
−0.762697 | + | 0.646756i | \(0.776125\pi\) | |||||||
\(104\) | −5.12357 | + | 41.8435i | −0.0492651 | + | 0.402342i | ||||
\(105\) | 3.80394 | + | 3.80394i | 0.0362280 | + | 0.0362280i | ||||
\(106\) | 48.5239 | − | 25.4465i | 0.457772 | − | 0.240061i | ||||
\(107\) | 21.5408 | + | 52.0041i | 0.201316 | + | 0.486020i | 0.992005 | − | 0.126198i | \(-0.0402775\pi\) |
−0.790689 | + | 0.612218i | \(0.790278\pi\) | |||||||
\(108\) | 96.7472 | − | 62.4595i | 0.895808 | − | 0.578329i | ||||
\(109\) | 34.1859 | − | 82.5321i | 0.313632 | − | 0.757175i | −0.685932 | − | 0.727665i | \(-0.740605\pi\) |
0.999564 | − | 0.0295097i | \(-0.00939461\pi\) | |||||||
\(110\) | 17.9853 | − | 21.5660i | 0.163503 | − | 0.196055i | ||||
\(111\) | 109.257 | 0.984299 | ||||||||
\(112\) | 38.5792 | + | 17.4255i | 0.344457 | + | 0.155585i | ||||
\(113\) | 54.0821i | 0.478603i | 0.970945 | + | 0.239301i | \(0.0769184\pi\) | ||||
−0.970945 | + | 0.239301i | \(0.923082\pi\) | |||||||
\(114\) | 71.2403 | − | 85.4235i | 0.624915 | − | 0.749329i | ||||
\(115\) | 23.2152 | + | 9.61605i | 0.201871 | + | 0.0836179i | ||||
\(116\) | 192.944 | + | 41.5535i | 1.66331 | + | 0.358220i | ||||
\(117\) | 21.1692 | − | 8.76859i | 0.180934 | − | 0.0749452i | ||||
\(118\) | 71.1389 | − | 37.3060i | 0.602872 | − | 0.316153i | ||||
\(119\) | −36.9332 | + | 36.9332i | −0.310363 | + | 0.310363i | ||||
\(120\) | −15.6733 | + | 4.35221i | −0.130611 | + | 0.0362685i | ||||
\(121\) | −71.2864 | + | 71.2864i | −0.589144 | + | 0.589144i | ||||
\(122\) | 98.0628 | + | 30.5938i | 0.803794 | + | 0.250769i | ||||
\(123\) | −47.4205 | + | 19.6422i | −0.385533 | + | 0.159693i | ||||
\(124\) | 26.7963 | + | 146.780i | 0.216100 | + | 1.18371i | ||||
\(125\) | 42.7750 | + | 17.7180i | 0.342200 | + | 0.141744i | ||||
\(126\) | −2.07459 | − | 22.9154i | −0.0164650 | − | 0.181868i | ||||
\(127\) | 48.1308i | 0.378983i | 0.981882 | + | 0.189491i | \(0.0606839\pi\) | ||||
−0.981882 | + | 0.189491i | \(0.939316\pi\) | |||||||
\(128\) | −103.276 | + | 75.6178i | −0.806844 | + | 0.590764i | ||||
\(129\) | −178.690 | −1.38520 | ||||||||
\(130\) | −9.89512 | + | 0.895832i | −0.0761163 | + | 0.00689101i | ||||
\(131\) | 59.6654 | − | 144.045i | 0.455461 | − | 1.09958i | −0.514755 | − | 0.857337i | \(-0.672117\pi\) |
0.970216 | − | 0.242242i | \(-0.0778829\pi\) | |||||||
\(132\) | 126.398 | − | 23.0755i | 0.957562 | − | 0.174814i | ||||
\(133\) | −26.1083 | − | 63.0311i | −0.196303 | − | 0.473918i | ||||
\(134\) | −49.3743 | + | 158.260i | −0.368465 | + | 1.18105i | ||||
\(135\) | 19.1916 | + | 19.1916i | 0.142160 | + | 0.142160i | ||||
\(136\) | −42.2565 | − | 152.175i | −0.310710 | − | 1.11893i | ||||
\(137\) | 40.9566 | + | 40.9566i | 0.298953 | + | 0.298953i | 0.840604 | − | 0.541650i | \(-0.182200\pi\) |
−0.541650 | + | 0.840604i | \(0.682200\pi\) | |||||||
\(138\) | 53.3968 | + | 101.822i | 0.386933 | + | 0.737842i | ||||
\(139\) | −22.0683 | − | 53.2776i | −0.158765 | − | 0.383292i | 0.824401 | − | 0.566006i | \(-0.191512\pi\) |
−0.983166 | + | 0.182713i | \(0.941512\pi\) | |||||||
\(140\) | −2.10056 | + | 9.75343i | −0.0150040 | + | 0.0696674i | ||||
\(141\) | 69.2444 | − | 167.171i | 0.491095 | − | 1.18561i | ||||
\(142\) | 49.1921 | + | 41.0245i | 0.346423 | + | 0.288905i | ||||
\(143\) | 78.4810 | 0.548818 | ||||||||
\(144\) | 63.4050 | + | 28.6389i | 0.440313 | + | 0.198881i | ||||
\(145\) | 46.5167i | 0.320805i | ||||||||
\(146\) | −81.3301 | − | 67.8265i | −0.557055 | − | 0.464565i | ||||
\(147\) | 13.9482 | + | 5.77754i | 0.0948859 | + | 0.0393030i | ||||
\(148\) | 109.903 | + | 170.236i | 0.742591 | + | 1.15024i | ||||
\(149\) | −76.6801 | + | 31.7619i | −0.514632 | + | 0.213167i | −0.624857 | − | 0.780739i | \(-0.714843\pi\) |
0.110225 | + | 0.993907i | \(0.464843\pi\) | |||||||
\(150\) | 48.3026 | + | 92.1083i | 0.322018 | + | 0.614055i | ||||
\(151\) | −42.2155 | + | 42.2155i | −0.279573 | + | 0.279573i | −0.832938 | − | 0.553366i | \(-0.813343\pi\) |
0.553366 | + | 0.832938i | \(0.313343\pi\) | |||||||
\(152\) | 204.762 | + | 25.0722i | 1.34712 | + | 0.164949i | ||||
\(153\) | −60.6999 | + | 60.6999i | −0.396732 | + | 0.396732i | ||||
\(154\) | 23.4711 | − | 75.2323i | 0.152410 | − | 0.488522i | ||||
\(155\) | −32.4888 | + | 13.4573i | −0.209605 | + | 0.0868214i | ||||
\(156\) | −37.3960 | − | 25.8497i | −0.239718 | − | 0.165703i | ||||
\(157\) | −11.7705 | − | 4.87549i | −0.0749712 | − | 0.0310541i | 0.344883 | − | 0.938646i | \(-0.387919\pi\) |
−0.419854 | + | 0.907592i | \(0.637919\pi\) | |||||||
\(158\) | 22.9598 | − | 2.07862i | 0.145315 | − | 0.0131558i | ||||
\(159\) | 59.0864i | 0.371613i | ||||||||
\(160\) | −22.5473 | − | 20.0429i | −0.140920 | − | 0.125268i | ||||
\(161\) | 70.5200 | 0.438013 | ||||||||
\(162\) | 4.13987 | + | 45.7279i | 0.0255548 | + | 0.282271i | ||||
\(163\) | 65.3939 | − | 157.875i | 0.401189 | − | 0.968557i | −0.586188 | − | 0.810175i | \(-0.699372\pi\) |
0.987378 | − | 0.158382i | \(-0.0506278\pi\) | |||||||
\(164\) | −78.3060 | − | 54.1285i | −0.477476 | − | 0.330052i | ||||
\(165\) | 11.5887 | + | 27.9775i | 0.0702344 | + | 0.169561i | ||||
\(166\) | 305.571 | + | 95.3326i | 1.84079 | + | 0.574293i | ||||
\(167\) | −113.503 | − | 113.503i | −0.679657 | − | 0.679657i | 0.280265 | − | 0.959923i | \(-0.409578\pi\) |
−0.959923 | + | 0.280265i | \(0.909578\pi\) | |||||||
\(168\) | −35.9636 | + | 28.1172i | −0.214069 | + | 0.167364i | ||||
\(169\) | 99.8663 | + | 99.8663i | 0.590925 | + | 0.590925i | ||||
\(170\) | 32.9648 | − | 17.2871i | 0.193911 | − | 0.101689i | ||||
\(171\) | −42.9092 | − | 103.592i | −0.250931 | − | 0.605801i | ||||
\(172\) | −179.747 | − | 278.421i | −1.04504 | − | 1.61873i | ||||
\(173\) | 110.682 | − | 267.210i | 0.639781 | − | 1.54457i | −0.187189 | − | 0.982324i | \(-0.559938\pi\) |
0.826971 | − | 0.562245i | \(-0.190062\pi\) | |||||||
\(174\) | −136.317 | + | 163.457i | −0.783432 | + | 0.939405i | ||||
\(175\) | 63.7923 | 0.364528 | ||||||||
\(176\) | 163.100 | + | 173.732i | 0.926706 | + | 0.987113i | ||||
\(177\) | 86.6241i | 0.489402i | ||||||||
\(178\) | 188.375 | − | 225.879i | 1.05829 | − | 1.26898i | ||||
\(179\) | −138.016 | − | 57.1680i | −0.771038 | − | 0.319375i | −0.0377454 | − | 0.999287i | \(-0.512018\pi\) |
−0.733293 | + | 0.679913i | \(0.762018\pi\) | |||||||
\(180\) | −3.45228 | + | 16.0298i | −0.0191793 | + | 0.0890545i | ||||
\(181\) | −57.9483 | + | 24.0030i | −0.320156 | + | 0.132613i | −0.536974 | − | 0.843599i | \(-0.680432\pi\) |
0.216817 | + | 0.976212i | \(0.430432\pi\) | |||||||
\(182\) | −24.6941 | + | 12.9498i | −0.135682 | + | 0.0711530i | ||||
\(183\) | −78.3311 | + | 78.3311i | −0.428039 | + | 0.428039i | ||||
\(184\) | −104.939 | + | 185.623i | −0.570320 | + | 1.00882i | ||||
\(185\) | −33.7694 | + | 33.7694i | −0.182537 | + | 0.182537i | ||||
\(186\) | −153.600 | − | 47.9204i | −0.825807 | − | 0.257637i | ||||
\(187\) | −271.640 | + | 112.517i | −1.45262 | + | 0.601694i | ||||
\(188\) | 330.126 | − | 60.2684i | 1.75599 | − | 0.320577i | ||||
\(189\) | 70.3714 | + | 29.1488i | 0.372335 | + | 0.154226i | ||||
\(190\) | 4.38376 | + | 48.4219i | 0.0230724 | + | 0.254852i | ||||
\(191\) | 323.983i | 1.69625i | 0.529799 | + | 0.848123i | \(0.322267\pi\) | ||||
−0.529799 | + | 0.848123i | \(0.677733\pi\) | |||||||
\(192\) | −20.4938 | − | 136.504i | −0.106739 | − | 0.710958i | ||||
\(193\) | 196.427 | 1.01776 | 0.508879 | − | 0.860838i | \(-0.330060\pi\) | ||||
0.508879 | + | 0.860838i | \(0.330060\pi\) | |||||||
\(194\) | 164.454 | − | 14.8885i | 0.847702 | − | 0.0767447i | ||||
\(195\) | 4.10023 | − | 9.89884i | 0.0210268 | − | 0.0507633i | ||||
\(196\) | 5.02862 | + | 27.5447i | 0.0256562 | + | 0.140534i | ||||
\(197\) | −59.0619 | − | 142.588i | −0.299807 | − | 0.723797i | −0.999952 | − | 0.00979705i | \(-0.996881\pi\) |
0.700145 | − | 0.714000i | \(-0.253119\pi\) | |||||||
\(198\) | 38.5749 | − | 123.645i | 0.194823 | − | 0.624468i | ||||
\(199\) | −86.8897 | − | 86.8897i | −0.436632 | − | 0.436632i | 0.454245 | − | 0.890877i | \(-0.349909\pi\) |
−0.890877 | + | 0.454245i | \(0.849909\pi\) | |||||||
\(200\) | −94.9275 | + | 167.914i | −0.474637 | + | 0.839572i | ||||
\(201\) | −126.416 | − | 126.416i | −0.628935 | − | 0.628935i | ||||
\(202\) | −106.806 | − | 203.668i | −0.528742 | − | 1.00826i | ||||
\(203\) | 49.9579 | + | 120.609i | 0.246098 | + | 0.594133i | ||||
\(204\) | 166.496 | + | 35.8575i | 0.816156 | + | 0.175772i | ||||
\(205\) | 8.58577 | − | 20.7279i | 0.0418818 | − | 0.101112i | ||||
\(206\) | 25.9402 | + | 21.6332i | 0.125923 | + | 0.105016i | ||||
\(207\) | 115.900 | 0.559904 | ||||||||
\(208\) | 2.65984 | − | 84.2701i | 0.0127877 | − | 0.405145i | ||||
\(209\) | − | 384.048i | − | 1.83755i | ||||||
\(210\) | −8.26284 | − | 6.89093i | −0.0393469 | − | 0.0328140i | ||||
\(211\) | −188.416 | − | 78.0443i | −0.892965 | − | 0.369878i | −0.111454 | − | 0.993770i | \(-0.535551\pi\) |
−0.781511 | + | 0.623891i | \(0.785551\pi\) | |||||||
\(212\) | −92.0638 | + | 59.4359i | −0.434263 | + | 0.280358i | ||||
\(213\) | −63.8168 | + | 26.4338i | −0.299609 | + | 0.124102i | ||||
\(214\) | −52.2839 | − | 99.7002i | −0.244317 | − | 0.465889i | ||||
\(215\) | 55.2299 | − | 55.2299i | 0.256883 | − | 0.256883i | ||||
\(216\) | −181.443 | + | 141.856i | −0.840015 | + | 0.656743i | ||||
\(217\) | −69.7845 | + | 69.7845i | −0.321588 | + | 0.321588i | ||||
\(218\) | −53.2105 | + | 170.557i | −0.244085 | + | 0.782369i | ||||
\(219\) | 105.509 | − | 43.7034i | 0.481778 | − | 0.199559i | ||||
\(220\) | −31.9352 | + | 46.1996i | −0.145160 | + | 0.209998i | ||||
\(221\) | 96.1099 | + | 39.8100i | 0.434886 | + | 0.180136i | ||||
\(222\) | −217.624 | + | 19.7021i | −0.980290 | + | 0.0887483i | ||||
\(223\) | 53.3854i | 0.239396i | 0.992810 | + | 0.119698i | \(0.0381927\pi\) | ||||
−0.992810 | + | 0.119698i | \(0.961807\pi\) | |||||||
\(224\) | −79.9864 | − | 27.7522i | −0.357082 | − | 0.123894i | ||||
\(225\) | 104.843 | 0.465969 | ||||||||
\(226\) | −9.75252 | − | 107.724i | −0.0431527 | − | 0.476654i | ||||
\(227\) | 18.0211 | − | 43.5068i | 0.0793882 | − | 0.191660i | −0.879202 | − | 0.476449i | \(-0.841924\pi\) |
0.958590 | + | 0.284789i | \(0.0919236\pi\) | |||||||
\(228\) | −126.496 | + | 182.998i | −0.554807 | + | 0.802621i | ||||
\(229\) | −135.242 | − | 326.504i | −0.590578 | − | 1.42578i | −0.882946 | − | 0.469475i | \(-0.844443\pi\) |
0.292368 | − | 0.956306i | \(-0.405557\pi\) | |||||||
\(230\) | −47.9753 | − | 14.9674i | −0.208588 | − | 0.0650758i | ||||
\(231\) | 60.0944 | + | 60.0944i | 0.260149 | + | 0.260149i | ||||
\(232\) | −391.809 | − | 47.9754i | −1.68883 | − | 0.206790i | ||||
\(233\) | −46.1172 | − | 46.1172i | −0.197928 | − | 0.197928i | 0.601183 | − | 0.799111i | \(-0.294696\pi\) |
−0.799111 | + | 0.601183i | \(0.794696\pi\) | |||||||
\(234\) | −40.5848 | + | 21.2831i | −0.173439 | + | 0.0909536i | ||||
\(235\) | 30.2672 | + | 73.0715i | 0.128797 | + | 0.310943i | ||||
\(236\) | −134.971 | + | 87.1365i | −0.571911 | + | 0.369222i | ||||
\(237\) | −9.51386 | + | 22.9685i | −0.0401429 | + | 0.0969134i | ||||
\(238\) | 66.9055 | − | 80.2256i | 0.281115 | − | 0.337083i | ||||
\(239\) | −210.976 | −0.882743 | −0.441371 | − | 0.897325i | \(-0.645508\pi\) | ||||
−0.441371 | + | 0.897325i | \(0.645508\pi\) | |||||||
\(240\) | 30.4340 | − | 11.4953i | 0.126808 | − | 0.0478971i | ||||
\(241\) | 4.45793i | 0.0184976i | 0.999957 | + | 0.00924882i | \(0.00294403\pi\) | ||||
−0.999957 | + | 0.00924882i | \(0.997056\pi\) | |||||||
\(242\) | 129.137 | − | 154.847i | 0.533625 | − | 0.639864i | ||||
\(243\) | 193.636 | + | 80.2066i | 0.796855 | + | 0.330068i | ||||
\(244\) | −200.844 | − | 43.2549i | −0.823130 | − | 0.177274i | ||||
\(245\) | −6.09687 | + | 2.52541i | −0.0248852 | + | 0.0103078i | ||||
\(246\) | 90.9128 | − | 47.6757i | 0.369564 | − | 0.193804i | ||||
\(247\) | −96.0827 | + | 96.0827i | −0.388999 | + | 0.388999i | ||||
\(248\) | −79.8429 | − | 287.532i | −0.321947 | − | 1.15940i | ||||
\(249\) | −244.086 | + | 244.086i | −0.980263 | + | 0.980263i | ||||
\(250\) | −88.3966 | − | 27.5781i | −0.353586 | − | 0.110312i | ||||
\(251\) | −43.0877 | + | 17.8475i | −0.171664 | + | 0.0711056i | −0.466860 | − | 0.884331i | \(-0.654615\pi\) |
0.295196 | + | 0.955437i | \(0.404615\pi\) | |||||||
\(252\) | 8.26456 | + | 45.2699i | 0.0327959 | + | 0.179643i | ||||
\(253\) | 366.753 | + | 151.914i | 1.44962 | + | 0.600451i | ||||
\(254\) | −8.67933 | − | 95.8696i | −0.0341706 | − | 0.377439i | ||||
\(255\) | 40.1405i | 0.157414i | ||||||||
\(256\) | 192.075 | − | 169.243i | 0.750292 | − | 0.661106i | ||||
\(257\) | −390.515 | −1.51951 | −0.759757 | − | 0.650207i | \(-0.774682\pi\) | ||||
−0.759757 | + | 0.650207i | \(0.774682\pi\) | |||||||
\(258\) | 355.925 | − | 32.2228i | 1.37955 | − | 0.124895i | ||||
\(259\) | −51.2901 | + | 123.825i | −0.198031 | + | 0.478089i | ||||
\(260\) | 19.5481 | − | 3.56873i | 0.0751849 | − | 0.0137259i | ||||
\(261\) | 82.1061 | + | 198.222i | 0.314583 | + | 0.759470i | ||||
\(262\) | −92.8694 | + | 297.676i | −0.354463 | + | 1.13617i | ||||
\(263\) | 135.194 | + | 135.194i | 0.514044 | + | 0.514044i | 0.915763 | − | 0.401719i | \(-0.131587\pi\) |
−0.401719 | + | 0.915763i | \(0.631587\pi\) | |||||||
\(264\) | −247.606 | + | 68.7561i | −0.937900 | + | 0.260440i | ||||
\(265\) | −18.2625 | − | 18.2625i | −0.0689152 | − | 0.0689152i | ||||
\(266\) | 63.3703 | + | 120.841i | 0.238234 | + | 0.454288i | ||||
\(267\) | 121.378 | + | 293.032i | 0.454598 | + | 1.09750i | ||||
\(268\) | 69.8077 | − | 324.135i | 0.260476 | − | 1.20946i | ||||
\(269\) | 70.1917 | − | 169.458i | 0.260936 | − | 0.629954i | −0.738061 | − | 0.674734i | \(-0.764259\pi\) |
0.998997 | + | 0.0447794i | \(0.0142585\pi\) | |||||||
\(270\) | −41.6876 | − | 34.7660i | −0.154398 | − | 0.128763i | ||||
\(271\) | 4.76275 | 0.0175747 | 0.00878737 | − | 0.999961i | \(-0.497203\pi\) | ||||
0.00878737 | + | 0.999961i | \(0.497203\pi\) | |||||||
\(272\) | 111.610 | + | 295.490i | 0.410332 | + | 1.08636i | ||||
\(273\) | − | 30.0694i | − | 0.110144i | ||||||
\(274\) | −88.9652 | − | 74.1940i | −0.324691 | − | 0.270781i | ||||
\(275\) | 331.764 | + | 137.421i | 1.20642 | + | 0.499714i | ||||
\(276\) | −124.720 | − | 193.186i | −0.451884 | − | 0.699950i | ||||
\(277\) | 377.813 | − | 156.495i | 1.36395 | − | 0.564965i | 0.423807 | − | 0.905753i | \(-0.360694\pi\) |
0.940140 | + | 0.340787i | \(0.110694\pi\) | |||||||
\(278\) | 53.5643 | + | 102.142i | 0.192677 | + | 0.367416i | ||||
\(279\) | −114.691 | + | 114.691i | −0.411080 | + | 0.411080i | ||||
\(280\) | 2.42519 | − | 19.8062i | 0.00866139 | − | 0.0707364i | ||||
\(281\) | 67.0196 | − | 67.0196i | 0.238504 | − | 0.238504i | −0.577727 | − | 0.816230i | \(-0.696060\pi\) |
0.816230 | + | 0.577727i | \(0.196060\pi\) | |||||||
\(282\) | −107.779 | + | 345.466i | −0.382195 | + | 1.22506i | ||||
\(283\) | −80.8989 | + | 33.5094i | −0.285862 | + | 0.118408i | −0.521007 | − | 0.853552i | \(-0.674443\pi\) |
0.235145 | + | 0.971960i | \(0.424443\pi\) | |||||||
\(284\) | −105.381 | − | 72.8442i | −0.371061 | − | 0.256494i | ||||
\(285\) | −48.4401 | − | 20.0646i | −0.169965 | − | 0.0704019i | ||||
\(286\) | −156.323 | + | 14.1523i | −0.546583 | + | 0.0494836i | ||||
\(287\) | − | 62.9643i | − | 0.219388i | ||||||
\(288\) | −131.458 | − | 45.6109i | −0.456451 | − | 0.158371i | ||||
\(289\) | −100.732 | −0.348554 | ||||||||
\(290\) | −8.38827 | − | 92.6546i | −0.0289251 | − | 0.319498i | ||||
\(291\) | −68.1448 | + | 164.516i | −0.234174 | + | 0.565347i | ||||
\(292\) | 174.229 | + | 120.434i | 0.596674 | + | 0.412447i | ||||
\(293\) | −97.2004 | − | 234.663i | −0.331742 | − | 0.800896i | −0.998454 | − | 0.0555808i | \(-0.982299\pi\) |
0.666712 | − | 0.745315i | \(-0.267701\pi\) | |||||||
\(294\) | −28.8247 | − | 8.99277i | −0.0980431 | − | 0.0305877i | ||||
\(295\) | −26.7739 | − | 26.7739i | −0.0907591 | − | 0.0907591i | ||||
\(296\) | −249.610 | − | 319.267i | −0.843277 | − | 1.07860i | ||||
\(297\) | 303.188 | + | 303.188i | 1.02083 | + | 1.02083i | ||||
\(298\) | 147.008 | − | 77.0927i | 0.493316 | − | 0.258700i | ||||
\(299\) | −53.7493 | − | 129.762i | −0.179764 | − | 0.433988i | ||||
\(300\) | −112.822 | − | 174.756i | −0.376072 | − | 0.582520i | ||||
\(301\) | 83.8849 | − | 202.516i | 0.278688 | − | 0.672811i | ||||
\(302\) | 76.4745 | − | 91.6997i | 0.253227 | − | 0.303642i | ||||
\(303\) | 248.002 | 0.818488 | ||||||||
\(304\) | −412.377 | − | 13.0160i | −1.35650 | − | 0.0428157i | ||||
\(305\) | − | 48.4214i | − | 0.158759i | ||||||
\(306\) | 109.959 | − | 131.851i | 0.359345 | − | 0.430887i | ||||
\(307\) | 33.4486 | + | 13.8549i | 0.108953 | + | 0.0451298i | 0.436494 | − | 0.899707i | \(-0.356220\pi\) |
−0.327541 | + | 0.944837i | \(0.606220\pi\) | |||||||
\(308\) | −33.1845 | + | 154.084i | −0.107742 | + | 0.500274i | ||||
\(309\) | −33.6521 | + | 13.9392i | −0.108907 | + | 0.0451106i | ||||
\(310\) | 62.2863 | − | 32.6637i | 0.200924 | − | 0.105367i | ||||
\(311\) | 331.934 | − | 331.934i | 1.06731 | − | 1.06731i | 0.0697470 | − | 0.997565i | \(-0.477781\pi\) |
0.997565 | − | 0.0697470i | \(-0.0222192\pi\) | |||||||
\(312\) | 79.1487 | + | 44.7454i | 0.253682 | + | 0.143415i | ||||
\(313\) | 261.126 | − | 261.126i | 0.834269 | − | 0.834269i | −0.153829 | − | 0.988098i | \(-0.549160\pi\) |
0.988098 | + | 0.153829i | \(0.0491604\pi\) | |||||||
\(314\) | 24.3243 | + | 7.58872i | 0.0774658 | + | 0.0241679i | ||||
\(315\) | −10.0202 | + | 4.15052i | −0.0318103 | + | 0.0131763i | ||||
\(316\) | −45.3578 | + | 8.28060i | −0.143537 | + | 0.0262044i | ||||
\(317\) | −89.3605 | − | 37.0143i | −0.281894 | − | 0.116764i | 0.237257 | − | 0.971447i | \(-0.423752\pi\) |
−0.519151 | + | 0.854683i | \(0.673752\pi\) | |||||||
\(318\) | −10.6549 | − | 117.691i | −0.0335061 | − | 0.370099i | ||||
\(319\) | 734.870i | 2.30367i | ||||||||
\(320\) | 48.5251 | + | 35.8566i | 0.151641 | + | 0.112052i | ||||
\(321\) | 121.403 | 0.378201 | ||||||||
\(322\) | −140.466 | + | 12.7167i | −0.436229 | + | 0.0394929i | ||||
\(323\) | 194.811 | − | 470.315i | 0.603130 | − | 1.45608i | ||||
\(324\) | −16.4920 | − | 90.3369i | −0.0509014 | − | 0.278817i | ||||
\(325\) | −48.6216 | − | 117.383i | −0.149605 | − | 0.361178i | ||||
\(326\) | −101.786 | + | 326.256i | −0.312226 | + | 1.00078i | ||||
\(327\) | −136.238 | − | 136.238i | −0.416630 | − | 0.416630i | ||||
\(328\) | 165.735 | + | 93.6954i | 0.505290 | + | 0.285657i | ||||
\(329\) | 156.954 | + | 156.954i | 0.477065 | + | 0.477065i | ||||
\(330\) | −28.1281 | − | 53.6374i | −0.0852366 | − | 0.162538i | ||||
\(331\) | 33.3563 | + | 80.5292i | 0.100774 | + | 0.243291i | 0.966223 | − | 0.257706i | \(-0.0829668\pi\) |
−0.865449 | + | 0.500997i | \(0.832967\pi\) | |||||||
\(332\) | −625.844 | − | 134.786i | −1.88507 | − | 0.405981i | ||||
\(333\) | −84.2955 | + | 203.507i | −0.253140 | + | 0.611133i | ||||
\(334\) | 246.549 | + | 205.613i | 0.738170 | + | 0.615608i | ||||
\(335\) | 78.1457 | 0.233271 | ||||||||
\(336\) | 66.5640 | − | 62.4906i | 0.198107 | − | 0.185984i | ||||
\(337\) | − | 601.688i | − | 1.78542i | −0.450627 | − | 0.892712i | \(-0.648800\pi\) | ||
0.450627 | − | 0.892712i | \(-0.351200\pi\) | |||||||
\(338\) | −216.928 | − | 180.910i | −0.641798 | − | 0.535238i | ||||
\(339\) | 107.764 | + | 44.6374i | 0.317889 | + | 0.131674i | ||||
\(340\) | −62.5437 | + | 40.3779i | −0.183952 | + | 0.118759i | ||||
\(341\) | −513.257 | + | 212.598i | −1.50515 | + | 0.623455i | ||||
\(342\) | 104.149 | + | 198.602i | 0.304530 | + | 0.580708i | ||||
\(343\) | −13.0958 | + | 13.0958i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 408.237 | + | 522.161i | 1.18674 | + | 1.51791i | ||||
\(345\) | 38.3220 | − | 38.3220i | 0.111078 | − | 0.111078i | ||||
\(346\) | −172.277 | + | 552.203i | −0.497911 | + | 1.59596i | ||||
\(347\) | −510.732 | + | 211.552i | −1.47185 | + | 0.609661i | −0.967280 | − | 0.253710i | \(-0.918349\pi\) |
−0.504570 | + | 0.863371i | \(0.668349\pi\) | |||||||
\(348\) | 242.048 | − | 350.163i | 0.695541 | − | 1.00622i | ||||
\(349\) | 396.990 | + | 164.439i | 1.13751 | + | 0.471171i | 0.870326 | − | 0.492475i | \(-0.163908\pi\) |
0.267181 | + | 0.963646i | \(0.413908\pi\) | |||||||
\(350\) | −127.065 | + | 11.5035i | −0.363043 | + | 0.0328672i | ||||
\(351\) | − | 151.706i | − | 0.432210i | ||||||
\(352\) | −356.201 | − | 316.637i | −1.01193 | − | 0.899536i | ||||
\(353\) | −163.628 | −0.463535 | −0.231767 | − | 0.972771i | \(-0.574451\pi\) | ||||
−0.231767 | + | 0.972771i | \(0.574451\pi\) | |||||||
\(354\) | −15.6207 | − | 172.543i | −0.0441264 | − | 0.487408i | ||||
\(355\) | 11.5544 | − | 27.8948i | 0.0325476 | − | 0.0785769i | ||||
\(356\) | −334.483 | + | 483.886i | −0.939560 | + | 1.35923i | ||||
\(357\) | 43.1099 | + | 104.077i | 0.120756 | + | 0.291531i | ||||
\(358\) | 285.216 | + | 88.9823i | 0.796694 | + | 0.248554i | ||||
\(359\) | −229.746 | − | 229.746i | −0.639961 | − | 0.639961i | 0.310585 | − | 0.950546i | \(-0.399475\pi\) |
−0.950546 | + | 0.310585i | \(0.899475\pi\) | |||||||
\(360\) | 3.98581 | − | 32.5516i | 0.0110717 | − | 0.0904211i | ||||
\(361\) | 214.916 | + | 214.916i | 0.595336 | + | 0.595336i | ||||
\(362\) | 111.096 | − | 58.2601i | 0.306896 | − | 0.160940i | ||||
\(363\) | 83.2084 | + | 200.883i | 0.229224 | + | 0.553396i | ||||
\(364\) | 46.8517 | − | 30.2472i | 0.128714 | − | 0.0830968i | ||||
\(365\) | −19.1031 | + | 46.1189i | −0.0523372 | + | 0.126353i | ||||
\(366\) | 141.899 | − | 170.149i | 0.387702 | − | 0.464889i | ||||
\(367\) | 604.291 | 1.64657 | 0.823285 | − | 0.567628i | \(-0.192139\pi\) | ||||
0.823285 | + | 0.567628i | \(0.192139\pi\) | |||||||
\(368\) | 175.550 | − | 388.658i | 0.477037 | − | 1.05613i | ||||
\(369\) | − | 103.482i | − | 0.280440i | ||||||
\(370\) | 61.1741 | − | 73.3533i | 0.165336 | − | 0.198252i | ||||
\(371\) | −66.9647 | − | 27.7377i | −0.180498 | − | 0.0747647i | ||||
\(372\) | 314.590 | + | 67.7521i | 0.845673 | + | 0.182129i | ||||
\(373\) | 66.6128 | − | 27.5919i | 0.178587 | − | 0.0739730i | −0.291599 | − | 0.956541i | \(-0.594187\pi\) |
0.470185 | + | 0.882568i | \(0.344187\pi\) | |||||||
\(374\) | 520.776 | − | 273.101i | 1.39245 | − | 0.730217i | ||||
\(375\) | 70.6098 | − | 70.6098i | 0.188293 | − | 0.188293i | ||||
\(376\) | −646.695 | + | 179.577i | −1.71993 | + | 0.477598i | ||||
\(377\) | 183.853 | − | 183.853i | 0.487673 | − | 0.487673i | ||||
\(378\) | −145.426 | − | 45.3702i | −0.384724 | − | 0.120027i | ||||
\(379\) | −241.151 | + | 99.8880i | −0.636283 | + | 0.263557i | −0.677420 | − | 0.735597i | \(-0.736902\pi\) |
0.0411373 | + | 0.999154i | \(0.486902\pi\) | |||||||
\(380\) | −17.4636 | − | 95.6588i | −0.0459569 | − | 0.251734i | ||||
\(381\) | 95.9057 | + | 39.7254i | 0.251721 | + | 0.104266i | ||||
\(382\) | −58.4232 | − | 645.327i | −0.152940 | − | 1.68934i | ||||
\(383\) | − | 621.449i | − | 1.62258i | −0.584643 | − | 0.811291i | \(-0.698765\pi\) | ||
0.584643 | − | 0.811291i | \(-0.301235\pi\) | |||||||
\(384\) | 65.4361 | + | 268.200i | 0.170407 | + | 0.698439i | ||||
\(385\) | −37.1482 | −0.0964888 | ||||||||
\(386\) | −391.255 | + | 35.4213i | −1.01361 | + | 0.0917651i | ||||
\(387\) | 137.865 | − | 332.836i | 0.356241 | − | 0.860042i | ||||
\(388\) | −324.884 | + | 59.3113i | −0.837329 | + | 0.152864i | ||||
\(389\) | −26.5507 | − | 64.0991i | −0.0682538 | − | 0.164779i | 0.886072 | − | 0.463548i | \(-0.153424\pi\) |
−0.954325 | + | 0.298769i | \(0.903424\pi\) | |||||||
\(390\) | −6.38203 | + | 20.4564i | −0.0163642 | + | 0.0524524i | ||||
\(391\) | 372.076 | + | 372.076i | 0.951601 | + | 0.951601i | ||||
\(392\) | −14.9834 | − | 53.9583i | −0.0382228 | − | 0.137649i | ||||
\(393\) | −237.779 | − | 237.779i | −0.605035 | − | 0.605035i | ||||
\(394\) | 143.355 | + | 273.364i | 0.363846 | + | 0.693818i | ||||
\(395\) | −4.15858 | − | 10.0397i | −0.0105280 | − | 0.0254169i | ||||
\(396\) | −54.5389 | + | 253.238i | −0.137725 | + | 0.639491i | ||||
\(397\) | −98.1441 | + | 236.941i | −0.247214 | + | 0.596828i | −0.997965 | − | 0.0637568i | \(-0.979692\pi\) |
0.750751 | + | 0.660585i | \(0.229692\pi\) | |||||||
\(398\) | 188.740 | + | 157.403i | 0.474222 | + | 0.395485i | ||||
\(399\) | −147.145 | −0.368784 | ||||||||
\(400\) | 158.802 | − | 351.579i | 0.397005 | − | 0.878948i | ||||
\(401\) | − | 25.0122i | − | 0.0623745i | −0.999514 | − | 0.0311873i | \(-0.990071\pi\) | ||
0.999514 | − | 0.0311873i | \(-0.00992883\pi\) | |||||||
\(402\) | 274.598 | + | 229.006i | 0.683081 | + | 0.569666i | ||||
\(403\) | 181.598 | + | 75.2202i | 0.450615 | + | 0.186651i | ||||
\(404\) | 249.469 | + | 386.417i | 0.617497 | + | 0.956478i | ||||
\(405\) | 19.9955 | − | 8.28243i | 0.0493717 | − | 0.0204504i | ||||
\(406\) | −121.258 | − | 231.227i | −0.298665 | − | 0.569524i | ||||
\(407\) | −533.488 | + | 533.488i | −1.31078 | + | 1.31078i | ||||
\(408\) | −338.101 | − | 41.3991i | −0.828680 | − | 0.101468i | ||||
\(409\) | −410.030 | + | 410.030i | −1.00252 | + | 1.00252i | −0.00252225 | + | 0.999997i | \(0.500803\pi\) |
−0.999997 | + | 0.00252225i | \(0.999197\pi\) | |||||||
\(410\) | −13.3638 | + | 42.8351i | −0.0325946 | + | 0.104476i | ||||
\(411\) | 115.414 | − | 47.8062i | 0.280814 | − | 0.116317i | ||||
\(412\) | −55.5701 | − | 38.4125i | −0.134879 | − | 0.0932342i | ||||
\(413\) | −98.1743 | − | 40.6651i | −0.237710 | − | 0.0984627i | ||||
\(414\) | −230.856 | + | 20.9000i | −0.557623 | + | 0.0504831i | ||||
\(415\) | − | 150.885i | − | 0.363578i | ||||||
\(416\) | 9.89823 | + | 168.333i | 0.0237938 | + | 0.404648i | ||||
\(417\) | −124.376 | −0.298263 | ||||||||
\(418\) | 69.2545 | + | 764.967i | 0.165681 | + | 1.83006i | ||||
\(419\) | −39.3223 | + | 94.9324i | −0.0938479 | + | 0.226569i | −0.963832 | − | 0.266511i | \(-0.914129\pi\) |
0.869984 | + | 0.493080i | \(0.164129\pi\) | |||||||
\(420\) | 17.7010 | + | 12.2357i | 0.0421452 | + | 0.0291326i | ||||
\(421\) | −150.378 | − | 363.044i | −0.357192 | − | 0.862338i | −0.995693 | − | 0.0927168i | \(-0.970445\pi\) |
0.638500 | − | 0.769622i | \(-0.279555\pi\) | |||||||
\(422\) | 389.370 | + | 121.476i | 0.922678 | + | 0.287859i | ||||
\(423\) | 257.955 | + | 257.955i | 0.609823 | + | 0.609823i | ||||
\(424\) | 172.660 | − | 134.989i | 0.407216 | − | 0.318371i | ||||
\(425\) | 336.579 | + | 336.579i | 0.791951 | + | 0.791951i | ||||
\(426\) | 122.347 | − | 64.1602i | 0.287200 | − | 0.150611i | ||||
\(427\) | −52.0035 | − | 125.547i | −0.121788 | − | 0.294022i | ||||
\(428\) | 122.121 | + | 189.160i | 0.285329 | + | 0.441962i | ||||
\(429\) | 64.7753 | − | 156.381i | 0.150991 | − | 0.364526i | ||||
\(430\) | −100.050 | + | 119.969i | −0.232675 | + | 0.278998i | ||||
\(431\) | 344.315 | 0.798876 | 0.399438 | − | 0.916760i | \(-0.369205\pi\) | ||||
0.399438 | + | 0.916760i | \(0.369205\pi\) | |||||||
\(432\) | 335.828 | − | 315.277i | 0.777379 | − | 0.729807i | ||||
\(433\) | − | 836.447i | − | 1.93175i | −0.259011 | − | 0.965874i | \(-0.583397\pi\) | ||
0.259011 | − | 0.965874i | \(-0.416603\pi\) | |||||||
\(434\) | 126.416 | − | 151.585i | 0.291282 | − | 0.349273i | ||||
\(435\) | 92.6894 | + | 38.3932i | 0.213079 | + | 0.0882603i | ||||
\(436\) | 75.2314 | − | 349.319i | 0.172549 | − | 0.801190i | ||||
\(437\) | −634.994 | + | 263.023i | −1.45307 | + | 0.601883i | ||||
\(438\) | −202.278 | + | 106.077i | −0.461823 | + | 0.242185i | ||||
\(439\) | −269.081 | + | 269.081i | −0.612942 | + | 0.612942i | −0.943711 | − | 0.330770i | \(-0.892692\pi\) |
0.330770 | + | 0.943711i | \(0.392692\pi\) | |||||||
\(440\) | 55.2791 | − | 97.7816i | 0.125634 | − | 0.222231i | ||||
\(441\) | −21.5230 | + | 21.5230i | −0.0488050 | + | 0.0488050i | ||||
\(442\) | −198.616 | − | 61.9645i | −0.449357 | − | 0.140191i | ||||
\(443\) | −0.0904257 | + | 0.0374556i | −0.000204121 | + | 8.45498e-5i | −0.382785 | − | 0.923837i | \(-0.625035\pi\) |
0.382581 | + | 0.923922i | \(0.375035\pi\) | |||||||
\(444\) | 429.923 | − | 78.4875i | 0.968296 | − | 0.176774i | ||||
\(445\) | −128.086 | − | 53.0551i | −0.287834 | − | 0.119225i | ||||
\(446\) | −9.62688 | − | 106.336i | −0.0215849 | − | 0.238421i | ||||
\(447\) | 179.008i | 0.400466i | ||||||||
\(448\) | 164.326 | + | 40.8545i | 0.366798 | + | 0.0911931i | ||||
\(449\) | 336.165 | 0.748698 | 0.374349 | − | 0.927288i | \(-0.377866\pi\) | ||||
0.374349 | + | 0.927288i | \(0.377866\pi\) | |||||||
\(450\) | −208.832 | + | 18.9061i | −0.464071 | + | 0.0420136i | ||||
\(451\) | 135.638 | − | 327.458i | 0.300748 | − | 0.726071i | ||||
\(452\) | 38.8512 | + | 212.811i | 0.0859539 | + | 0.470821i | ||||
\(453\) | 49.2756 | + | 118.962i | 0.108776 | + | 0.262609i | ||||
\(454\) | −28.0499 | + | 89.9090i | −0.0617840 | + | 0.198037i | ||||
\(455\) | 9.29389 | + | 9.29389i | 0.0204261 | + | 0.0204261i | ||||
\(456\) | 218.962 | − | 387.315i | 0.480180 | − | 0.849376i | ||||
\(457\) | 423.550 | + | 423.550i | 0.926805 | + | 0.926805i | 0.997498 | − | 0.0706935i | \(-0.0225212\pi\) |
−0.0706935 | + | 0.997498i | \(0.522521\pi\) | |||||||
\(458\) | 328.261 | + | 625.960i | 0.716726 | + | 1.36672i | ||||
\(459\) | 217.498 | + | 525.086i | 0.473851 | + | 1.14398i | ||||
\(460\) | 98.2589 | + | 21.1616i | 0.213606 | + | 0.0460035i | ||||
\(461\) | −129.970 | + | 313.776i | −0.281931 | + | 0.680641i | −0.999881 | − | 0.0154537i | \(-0.995081\pi\) |
0.717950 | + | 0.696095i | \(0.245081\pi\) | |||||||
\(462\) | −130.536 | − | 108.863i | −0.282546 | − | 0.235633i | ||||
\(463\) | −15.0541 | −0.0325143 | −0.0162572 | − | 0.999868i | \(-0.505175\pi\) | ||||
−0.0162572 | + | 0.999868i | \(0.505175\pi\) | |||||||
\(464\) | 789.077 | + | 24.9059i | 1.70060 | + | 0.0536765i | ||||
\(465\) | 75.8446i | 0.163107i | ||||||||
\(466\) | 100.175 | + | 83.5424i | 0.214968 | + | 0.179276i | ||||
\(467\) | 128.179 | + | 53.0936i | 0.274474 | + | 0.113691i | 0.515675 | − | 0.856784i | \(-0.327541\pi\) |
−0.241201 | + | 0.970475i | \(0.577541\pi\) | |||||||
\(468\) | 77.0011 | − | 49.7115i | 0.164532 | − | 0.106221i | ||||
\(469\) | 202.617 | − | 83.9267i | 0.432019 | − | 0.178948i | ||||
\(470\) | −73.4647 | − | 140.090i | −0.156308 | − | 0.298063i | ||||
\(471\) | −19.4298 | + | 19.4298i | −0.0412523 | + | 0.0412523i | ||||
\(472\) | 253.129 | − | 197.902i | 0.536291 | − | 0.419284i | ||||
\(473\) | 872.519 | − | 872.519i | 1.84465 | − | 1.84465i | ||||
\(474\) | 14.8084 | − | 47.4655i | 0.0312413 | − | 0.100138i | ||||
\(475\) | −574.414 | + | 237.930i | −1.20929 | + | 0.500906i | ||||
\(476\) | −118.799 | + | 171.863i | −0.249578 | + | 0.361056i | ||||
\(477\) | −110.057 | − | 45.5871i | −0.230727 | − | 0.0955704i | ||||
\(478\) | 420.232 | − | 38.0448i | 0.879147 | − | 0.0795916i | ||||
\(479\) | − | 134.284i | − | 0.280342i | −0.990127 | − | 0.140171i | \(-0.955235\pi\) | ||
0.990127 | − | 0.140171i | \(-0.0447652\pi\) | |||||||
\(480\) | −58.5472 | + | 28.3851i | −0.121973 | + | 0.0591356i | ||||
\(481\) | 266.940 | 0.554970 | ||||||||
\(482\) | −0.803889 | − | 8.87955i | −0.00166782 | − | 0.0184223i | ||||
\(483\) | 58.2047 | − | 140.518i | 0.120507 | − | 0.290929i | ||||
\(484\) | −229.299 | + | 331.720i | −0.473759 | + | 0.685371i | ||||
\(485\) | −29.7866 | − | 71.9112i | −0.0614156 | − | 0.148270i | ||||
\(486\) | −400.158 | − | 124.842i | −0.823370 | − | 0.256876i | ||||
\(487\) | −618.569 | − | 618.569i | −1.27016 | − | 1.27016i | −0.946003 | − | 0.324158i | \(-0.894919\pi\) |
−0.324158 | − | 0.946003i | \(-0.605081\pi\) | |||||||
\(488\) | 407.851 | + | 49.9397i | 0.835761 | + | 0.102336i | ||||
\(489\) | −260.608 | − | 260.608i | −0.532941 | − | 0.532941i | ||||
\(490\) | 11.6887 | − | 6.12968i | 0.0238544 | − | 0.0125095i | ||||
\(491\) | −19.8666 | − | 47.9621i | −0.0404614 | − | 0.0976825i | 0.902357 | − | 0.430990i | \(-0.141835\pi\) |
−0.942818 | + | 0.333307i | \(0.891835\pi\) | |||||||
\(492\) | −172.488 | + | 111.357i | −0.350585 | + | 0.226336i | ||||
\(493\) | −372.768 | + | 899.941i | −0.756121 | + | 1.82544i | ||||
\(494\) | 174.056 | − | 208.709i | 0.352341 | − | 0.422488i | ||||
\(495\) | −61.0532 | −0.123340 | ||||||||
\(496\) | 210.885 | + | 558.323i | 0.425172 | + | 1.12565i | ||||
\(497\) | − | 84.7351i | − | 0.170493i | ||||||
\(498\) | 442.167 | − | 530.198i | 0.887886 | − | 1.06466i | ||||
\(499\) | 328.968 | + | 136.263i | 0.659255 | + | 0.273072i | 0.687125 | − | 0.726539i | \(-0.258872\pi\) |
−0.0278702 | + | 0.999612i | \(0.508872\pi\) | |||||||
\(500\) | 181.046 | + | 38.9912i | 0.362092 | + | 0.0779824i | ||||
\(501\) | −319.847 | + | 132.485i | −0.638417 | + | 0.264441i | ||||
\(502\) | 82.6060 | − | 43.3195i | 0.164554 | − | 0.0862939i | ||||
\(503\) | 474.652 | − | 474.652i | 0.943641 | − | 0.943641i | −0.0548531 | − | 0.998494i | \(-0.517469\pi\) |
0.998494 | + | 0.0548531i | \(0.0174690\pi\) | |||||||
\(504\) | −24.6252 | − | 88.6808i | −0.0488596 | − | 0.175954i | ||||
\(505\) | −76.6528 | + | 76.6528i | −0.151788 | + | 0.151788i | ||||
\(506\) | −757.912 | − | 236.455i | −1.49785 | − | 0.467302i | ||||
\(507\) | 281.420 | − | 116.568i | 0.555069 | − | 0.229917i | ||||
\(508\) | 34.5759 | + | 189.393i | 0.0680628 | + | 0.372821i | ||||
\(509\) | −278.699 | − | 115.441i | −0.547542 | − | 0.226799i | 0.0917249 | − | 0.995784i | \(-0.470762\pi\) |
−0.639267 | + | 0.768985i | \(0.720762\pi\) | |||||||
\(510\) | −7.23844 | − | 79.9539i | −0.0141930 | − | 0.156772i | ||||
\(511\) | 140.094i | 0.274156i | ||||||||
\(512\) | −352.066 | + | 371.744i | −0.687628 | + | 0.726063i | ||||
\(513\) | −742.373 | −1.44712 | ||||||||
\(514\) | 777.849 | − | 70.4208i | 1.51333 | − | 0.137005i | ||||
\(515\) | 6.09291 | − | 14.7096i | 0.0118309 | − | 0.0285623i | ||||
\(516\) | −703.140 | + | 128.366i | −1.36267 | + | 0.248772i | ||||
\(517\) | 478.160 | + | 1154.38i | 0.924875 | + | 2.23285i | ||||
\(518\) | 79.8332 | − | 255.891i | 0.154118 | − | 0.493997i | ||||
\(519\) | −441.091 | − | 441.091i | −0.849887 | − | 0.849887i | ||||
\(520\) | −38.2934 | + | 10.6335i | −0.0736411 | + | 0.0204490i | ||||
\(521\) | −151.306 | − | 151.306i | −0.290415 | − | 0.290415i | 0.546829 | − | 0.837244i | \(-0.315835\pi\) |
−0.837244 | + | 0.546829i | \(0.815835\pi\) | |||||||
\(522\) | −199.288 | − | 380.022i | −0.381778 | − | 0.728012i | ||||
\(523\) | −76.0879 | − | 183.693i | −0.145484 | − | 0.351229i | 0.834293 | − | 0.551321i | \(-0.185876\pi\) |
−0.979777 | + | 0.200092i | \(0.935876\pi\) | |||||||
\(524\) | 131.303 | − | 609.674i | 0.250578 | − | 1.16350i | ||||
\(525\) | 52.6519 | − | 127.113i | 0.100289 | − | 0.242120i | ||||
\(526\) | −293.665 | − | 244.907i | −0.558298 | − | 0.465602i | ||||
\(527\) | −736.391 | −1.39733 | ||||||||
\(528\) | 480.796 | − | 181.602i | 0.910598 | − | 0.343944i | ||||
\(529\) | − | 181.439i | − | 0.342986i | ||||||
\(530\) | 39.6695 | + | 33.0830i | 0.0748481 | + | 0.0624208i | ||||
\(531\) | −161.350 | − | 66.8333i | −0.303860 | − | 0.125863i | ||||
\(532\) | −148.015 | − | 229.270i | −0.278224 | − | 0.430958i | ||||
\(533\) | −115.859 | + | 47.9905i | −0.217372 | + | 0.0900384i | ||||
\(534\) | −294.608 | − | 561.789i | −0.551701 | − | 1.05204i | ||||
\(535\) | −37.5233 | + | 37.5233i | −0.0701370 | + | 0.0701370i | ||||
\(536\) | −80.5961 | + | 658.218i | −0.150366 | + | 1.22802i | ||||
\(537\) | −227.826 | + | 227.826i | −0.424258 | + | 0.424258i | ||||
\(538\) | −109.254 | + | 350.192i | −0.203074 | + | 0.650915i | ||||
\(539\) | −96.3181 | + | 39.8963i | −0.178698 | + | 0.0740191i | ||||
\(540\) | 89.3048 | + | 61.7314i | 0.165379 | + | 0.114317i | ||||
\(541\) | −91.6470 | − | 37.9614i | −0.169403 | − | 0.0701690i | 0.296370 | − | 0.955073i | \(-0.404224\pi\) |
−0.465773 | + | 0.884904i | \(0.654224\pi\) | |||||||
\(542\) | −9.48671 | + | 0.858858i | −0.0175032 | + | 0.00158461i | ||||
\(543\) | 135.279i | 0.249133i | ||||||||
\(544\) | −275.597 | − | 568.447i | −0.506611 | − | 1.04494i | ||||
\(545\) | 84.2173 | 0.154527 | ||||||||
\(546\) | 5.42235 | + | 59.8938i | 0.00993104 | + | 0.109696i | ||||
\(547\) | −195.499 | + | 471.977i | −0.357403 | + | 0.862847i | 0.638261 | + | 0.769820i | \(0.279654\pi\) |
−0.995664 | + | 0.0930265i | \(0.970346\pi\) | |||||||
\(548\) | 190.585 | + | 131.741i | 0.347783 | + | 0.240403i | ||||
\(549\) | −85.4679 | − | 206.338i | −0.155679 | − | 0.375843i | ||||
\(550\) | −685.607 | − | 213.897i | −1.24656 | − | 0.388903i | ||||
\(551\) | −899.686 | − | 899.686i | −1.63282 | − | 1.63282i | ||||
\(552\) | 283.261 | + | 362.308i | 0.513154 | + | 0.656355i | ||||
\(553\) | −21.5648 | − | 21.5648i | −0.0389960 | − | 0.0389960i | ||||
\(554\) | −724.328 | + | 379.846i | −1.30745 | + | 0.685643i | ||||
\(555\) | 39.4170 | + | 95.1610i | 0.0710216 | + | 0.171461i | ||||
\(556\) | −125.111 | − | 193.792i | −0.225020 | − | 0.348547i | ||||
\(557\) | −128.159 | + | 309.403i | −0.230088 | + | 0.555481i | −0.996187 | − | 0.0872413i | \(-0.972195\pi\) |
0.766100 | + | 0.642722i | \(0.222195\pi\) | |||||||
\(558\) | 207.766 | − | 249.130i | 0.372341 | − | 0.446470i | ||||
\(559\) | −436.581 | −0.781004 | ||||||||
\(560\) | −1.25901 | + | 39.8884i | −0.00224823 | + | 0.0712293i | ||||
\(561\) | 634.137i | 1.13037i | ||||||||
\(562\) | −121.408 | + | 145.579i | −0.216028 | + | 0.259037i | ||||
\(563\) | −305.681 | − | 126.617i | −0.542949 | − | 0.224897i | 0.0943148 | − | 0.995542i | \(-0.469934\pi\) |
−0.637264 | + | 0.770645i | \(0.719934\pi\) | |||||||
\(564\) | 152.383 | − | 707.554i | 0.270183 | − | 1.25453i | ||||
\(565\) | −47.1046 | + | 19.5113i | −0.0833709 | + | 0.0345334i | ||||
\(566\) | 155.096 | − | 81.3342i | 0.274022 | − | 0.143700i | ||||
\(567\) | 42.9495 | − | 42.9495i | 0.0757487 | − | 0.0757487i | ||||
\(568\) | 223.040 | + | 126.092i | 0.392676 | + | 0.221993i | ||||
\(569\) | −496.100 | + | 496.100i | −0.871880 | + | 0.871880i | −0.992677 | − | 0.120797i | \(-0.961455\pi\) |
0.120797 | + | 0.992677i | \(0.461455\pi\) | |||||||
\(570\) | 100.104 | + | 31.2305i | 0.175621 | + | 0.0547904i | ||||
\(571\) | −483.761 | + | 200.381i | −0.847218 | + | 0.350929i | −0.763695 | − | 0.645577i | \(-0.776617\pi\) |
−0.0835225 | + | 0.996506i | \(0.526617\pi\) | |||||||
\(572\) | 308.820 | − | 56.3787i | 0.539895 | − | 0.0985641i | ||||
\(573\) | 645.570 | + | 267.404i | 1.12665 | + | 0.466673i | ||||
\(574\) | 11.3542 | + | 125.416i | 0.0197809 | + | 0.218494i | ||||
\(575\) | − | 642.662i | − | 1.11767i | ||||||
\(576\) | 270.070 | + | 67.1446i | 0.468872 | + | 0.116571i | ||||
\(577\) | 760.250 | 1.31759 | 0.658795 | − | 0.752322i | \(-0.271066\pi\) | ||||
0.658795 | + | 0.752322i | \(0.271066\pi\) | |||||||
\(578\) | 200.643 | − | 18.1648i | 0.347134 | − | 0.0314270i | ||||
\(579\) | 162.124 | − | 391.402i | 0.280007 | − | 0.675996i | ||||
\(580\) | 33.4164 | + | 183.042i | 0.0576145 | + | 0.315589i | ||||
\(581\) | −162.047 | − | 391.215i | −0.278910 | − | 0.673348i | ||||
\(582\) | 106.068 | − | 339.980i | 0.182247 | − | 0.584159i | ||||
\(583\) | −288.510 | − | 288.510i | −0.494872 | − | 0.494872i | ||||
\(584\) | −368.756 | − | 208.470i | −0.631431 | − | 0.356968i | ||||
\(585\) | 15.2746 | + | 15.2746i | 0.0261104 | + | 0.0261104i | ||||
\(586\) | 235.925 | + | 449.886i | 0.402603 | + | 0.767723i | ||||
\(587\) | −180.706 | − | 436.264i | −0.307847 | − | 0.743210i | −0.999774 | − | 0.0212420i | \(-0.993238\pi\) |
0.691927 | − | 0.721968i | \(-0.256762\pi\) | |||||||
\(588\) | 59.0362 | + | 12.7144i | 0.100402 | + | 0.0216231i | ||||
\(589\) | 368.091 | − | 888.651i | 0.624942 | − | 1.50874i | ||||
\(590\) | 58.1578 | + | 48.5017i | 0.0985726 | + | 0.0822062i | ||||
\(591\) | −332.869 | −0.563230 | ||||||||
\(592\) | 554.759 | + | 590.921i | 0.937093 | + | 0.998177i | ||||
\(593\) | 534.025i | 0.900547i | 0.892891 | + | 0.450274i | \(0.148674\pi\) | ||||
−0.892891 | + | 0.450274i | \(0.851326\pi\) | |||||||
\(594\) | −658.579 | − | 549.232i | −1.10872 | − | 0.924633i | ||||
\(595\) | −45.4926 | − | 18.8437i | −0.0764582 | − | 0.0316700i | ||||
\(596\) | −278.917 | + | 180.067i | −0.467981 | + | 0.302126i | ||||
\(597\) | −244.852 | + | 101.421i | −0.410138 | + | 0.169885i | ||||
\(598\) | 130.461 | + | 248.775i | 0.218161 | + | 0.416012i | ||||
\(599\) | 373.320 | − | 373.320i | 0.623239 | − | 0.623239i | −0.323119 | − | 0.946358i | \(-0.604731\pi\) |
0.946358 | + | 0.323119i | \(0.104731\pi\) | |||||||
\(600\) | 256.237 | + | 327.743i | 0.427062 | + | 0.546239i | ||||
\(601\) | 68.9545 | − | 68.9545i | 0.114733 | − | 0.114733i | −0.647409 | − | 0.762142i | \(-0.724148\pi\) |
0.762142 | + | 0.647409i | \(0.224148\pi\) | |||||||
\(602\) | −130.567 | + | 418.509i | −0.216889 | + | 0.695198i | ||||
\(603\) | 333.002 | − | 137.934i | 0.552242 | − | 0.228746i | ||||
\(604\) | −135.790 | + | 196.443i | −0.224818 | + | 0.325237i | ||||
\(605\) | −87.8073 | − | 36.3710i | −0.145136 | − | 0.0601173i | ||||
\(606\) | −493.984 | + | 44.7217i | −0.815155 | + | 0.0737981i | ||||
\(607\) | 620.715i | 1.02259i | 0.859404 | + | 0.511297i | \(0.170835\pi\) | ||||
−0.859404 | + | 0.511297i | \(0.829165\pi\) | |||||||
\(608\) | 823.742 | − | 48.4371i | 1.35484 | − | 0.0796663i | ||||
\(609\) | 281.559 | 0.462331 | ||||||||
\(610\) | 8.73173 | + | 96.4483i | 0.0143143 | + | 0.158112i | ||||
\(611\) | 169.180 | − | 408.436i | 0.276890 | − | 0.668472i | ||||
\(612\) | −195.247 | + | 282.457i | −0.319031 | + | 0.461531i | ||||
\(613\) | 189.467 | + | 457.413i | 0.309081 | + | 0.746187i | 0.999735 | + | 0.0230022i | \(0.00732248\pi\) |
−0.690655 | + | 0.723185i | \(0.742678\pi\) | |||||||
\(614\) | −69.1231 | − | 21.5651i | −0.112578 | − | 0.0351224i | ||||
\(615\) | −34.2161 | − | 34.2161i | −0.0556359 | − | 0.0556359i | ||||
\(616\) | 38.3130 | − | 312.898i | 0.0621965 | − | 0.507951i | ||||
\(617\) | −223.382 | − | 223.382i | −0.362046 | − | 0.362046i | 0.502520 | − | 0.864566i | \(-0.332406\pi\) |
−0.864566 | + | 0.502520i | \(0.832406\pi\) | |||||||
\(618\) | 64.5165 | − | 33.8332i | 0.104396 | − | 0.0547463i | ||||
\(619\) | 374.604 | + | 904.373i | 0.605176 | + | 1.46102i | 0.868190 | + | 0.496231i | \(0.165283\pi\) |
−0.263015 | + | 0.964792i | \(0.584717\pi\) | |||||||
\(620\) | −118.175 | + | 76.2932i | −0.190605 | + | 0.123054i | ||||
\(621\) | 293.653 | − | 708.942i | 0.472872 | − | 1.14161i | ||||
\(622\) | −601.307 | + | 721.021i | −0.966731 | + | 1.15920i | ||||
\(623\) | −389.083 | −0.624532 | ||||||||
\(624\) | −165.722 | − | 74.8535i | −0.265579 | − | 0.119957i | ||||
\(625\) | − | 559.132i | − | 0.894612i | ||||||
\(626\) | −473.037 | + | 567.213i | −0.755650 | + | 0.906092i | ||||
\(627\) | −765.255 | − | 316.979i | −1.22050 | − | 0.505549i | ||||
\(628\) | −49.8188 | − | 10.7293i | −0.0793293 | − | 0.0170848i | ||||
\(629\) | −923.938 | + | 382.708i | −1.46890 | + | 0.608438i | ||||
\(630\) | 19.2104 | − | 10.0742i | 0.0304927 | − | 0.0159907i | ||||
\(631\) | 120.246 | − | 120.246i | 0.190564 | − | 0.190564i | −0.605376 | − | 0.795940i | \(-0.706977\pi\) |
0.795940 | + | 0.605376i | \(0.206977\pi\) | |||||||
\(632\) | 88.8529 | − | 24.6730i | 0.140590 | − | 0.0390396i | ||||
\(633\) | −311.023 | + | 311.023i | −0.491347 | + | 0.491347i | ||||
\(634\) | 184.668 | + | 57.6129i | 0.291274 | + | 0.0908721i | ||||
\(635\) | −41.9211 | + | 17.3643i | −0.0660174 | + | 0.0273453i | ||||
\(636\) | 42.4461 | + | 232.503i | 0.0667392 | + | 0.365570i | ||||
\(637\) | 34.0787 | + | 14.1159i | 0.0534988 | + | 0.0221599i | ||||
\(638\) | −132.517 | − | 1463.75i | −0.207708 | − | 2.29428i | ||||
\(639\) | − | 139.263i | − | 0.217938i | ||||||
\(640\) | −103.121 | − | 62.6707i | −0.161126 | − | 0.0979230i | ||||
\(641\) | −278.072 | −0.433810 | −0.216905 | − | 0.976193i | \(-0.569596\pi\) | ||||
−0.216905 | + | 0.976193i | \(0.569596\pi\) | |||||||
\(642\) | −241.816 | + | 21.8923i | −0.376661 | + | 0.0341001i | ||||
\(643\) | −334.195 | + | 806.819i | −0.519744 | + | 1.25477i | 0.418317 | + | 0.908301i | \(0.362620\pi\) |
−0.938061 | + | 0.346471i | \(0.887380\pi\) | |||||||
\(644\) | 277.494 | − | 50.6597i | 0.430891 | − | 0.0786642i | ||||
\(645\) | −64.4665 | − | 155.636i | −0.0999481 | − | 0.241296i | ||||
\(646\) | −303.224 | + | 971.929i | −0.469387 | + | 1.50453i | ||||
\(647\) | 409.640 | + | 409.640i | 0.633137 | + | 0.633137i | 0.948854 | − | 0.315716i | \(-0.102245\pi\) |
−0.315716 | + | 0.948854i | \(0.602245\pi\) | |||||||
\(648\) | 49.1400 | + | 176.964i | 0.0758333 | + | 0.273092i | ||||
\(649\) | −422.973 | − | 422.973i | −0.651731 | − | 0.651731i | ||||
\(650\) | 118.014 | + | 225.042i | 0.181561 | + | 0.346218i | ||||
\(651\) | 81.4553 | + | 196.651i | 0.125123 | + | 0.302075i | ||||
\(652\) | 143.909 | − | 668.209i | 0.220720 | − | 1.02486i | ||||
\(653\) | −457.695 | + | 1104.97i | −0.700911 | + | 1.69215i | 0.0206388 | + | 0.999787i | \(0.493430\pi\) |
−0.721550 | + | 0.692362i | \(0.756570\pi\) | |||||||
\(654\) | 295.934 | + | 246.799i | 0.452498 | + | 0.377368i | ||||
\(655\) | 146.986 | 0.224406 | ||||||||
\(656\) | −347.016 | − | 156.741i | −0.528988 | − | 0.238934i | ||||
\(657\) | 230.245i | 0.350449i | ||||||||
\(658\) | −340.933 | − | 284.327i | −0.518136 | − | 0.432108i | ||||
\(659\) | 820.050 | + | 339.676i | 1.24439 | + | 0.515441i | 0.905083 | − | 0.425236i | \(-0.139809\pi\) |
0.339303 | + | 0.940677i | \(0.389809\pi\) | |||||||
\(660\) | 65.6993 | + | 101.766i | 0.0995444 | + | 0.154190i | ||||
\(661\) | −449.364 | + | 186.133i | −0.679825 | + | 0.281593i | −0.695754 | − | 0.718281i | \(-0.744929\pi\) |
0.0159290 | + | 0.999873i | \(0.494929\pi\) | |||||||
\(662\) | −80.9625 | − | 154.387i | −0.122300 | − | 0.233213i | ||||
\(663\) | 158.651 | − | 158.651i | 0.239293 | − | 0.239293i | ||||
\(664\) | 1270.90 | + | 155.616i | 1.91400 | + | 0.234361i | ||||
\(665\) | 45.4798 | − | 45.4798i | 0.0683906 | − | 0.0683906i | ||||
\(666\) | 131.206 | − | 420.558i | 0.197006 | − | 0.631468i | ||||
\(667\) | 1215.05 | − | 503.291i | 1.82167 | − | 0.754558i | ||||
\(668\) | −528.167 | − | 365.092i | −0.790669 | − | 0.546545i | ||||
\(669\) | 106.376 | + | 44.0624i | 0.159007 | + | 0.0658630i | ||||
\(670\) | −155.655 | + | 14.0918i | −0.232321 | + | 0.0210326i | ||||
\(671\) | − | 764.959i | − | 1.14003i | ||||||
\(672\) | −121.317 | + | 136.475i | −0.180531 | + | 0.203088i | ||||
\(673\) | −460.650 | −0.684473 | −0.342236 | − | 0.939614i | \(-0.611184\pi\) | ||||
−0.342236 | + | 0.939614i | \(0.611184\pi\) | |||||||
\(674\) | 108.501 | + | 1198.47i | 0.160981 | + | 1.77815i | ||||
\(675\) | 265.638 | − | 641.308i | 0.393538 | − | 0.950086i | ||||
\(676\) | 464.712 | + | 321.229i | 0.687443 | + | 0.475191i | ||||
\(677\) | 20.9880 | + | 50.6694i | 0.0310014 | + | 0.0748441i | 0.938622 | − | 0.344947i | \(-0.112103\pi\) |
−0.907621 | + | 0.419791i | \(0.862103\pi\) | |||||||
\(678\) | −222.700 | − | 69.4783i | −0.328466 | − | 0.102475i | ||||
\(679\) | −154.462 | − | 154.462i | −0.227484 | − | 0.227484i | ||||
\(680\) | 117.297 | − | 91.7052i | 0.172495 | − | 0.134861i | ||||
\(681\) | −71.8179 | − | 71.8179i | −0.105459 | − | 0.105459i | ||||
\(682\) | 983.996 | − | 516.019i | 1.44281 | − | 0.756626i | ||||
\(683\) | −29.0552 | − | 70.1454i | −0.0425405 | − | 0.102702i | 0.901181 | − | 0.433443i | \(-0.142701\pi\) |
−0.943722 | + | 0.330741i | \(0.892701\pi\) | |||||||
\(684\) | −243.264 | − | 376.806i | −0.355649 | − | 0.550885i | ||||
\(685\) | −20.8965 | + | 50.4485i | −0.0305058 | + | 0.0736474i | ||||
\(686\) | 23.7234 | − | 28.4465i | 0.0345822 | − | 0.0414671i | ||||
\(687\) | −762.217 | −1.10949 | ||||||||
\(688\) | −907.309 | − | 966.451i | −1.31876 | − | 1.40473i | ||||
\(689\) | 144.362i | 0.209523i | ||||||||
\(690\) | −69.4212 | + | 83.2423i | −0.100610 | + | 0.120641i | ||||
\(691\) | 822.850 | + | 340.836i | 1.19081 | + | 0.493250i | 0.888019 | − | 0.459807i | \(-0.152081\pi\) |
0.302792 | + | 0.953057i | \(0.402081\pi\) | |||||||
\(692\) | 243.573 | − | 1130.97i | 0.351985 | − | 1.63436i | ||||
\(693\) | −158.299 | + | 65.5697i | −0.228426 | + | 0.0946172i | ||||
\(694\) | 979.155 | − | 513.480i | 1.41089 | − | 0.739885i | ||||
\(695\) | 38.4422 | − | 38.4422i | 0.0553125 | − | 0.0553125i | ||||
\(696\) | −418.980 | + | 741.122i | −0.601983 | + | 1.06483i | ||||
\(697\) | 332.211 | − | 332.211i | 0.476629 | − | 0.476629i | ||||
\(698\) | −820.399 | − | 255.949i | −1.17536 | − | 0.366690i | ||||
\(699\) | −129.957 | + | 53.8298i | −0.185918 | + | 0.0770097i | ||||
\(700\) | 251.020 | − | 45.8267i | 0.358601 | − | 0.0654668i | ||||
\(701\) | −305.289 | − | 126.455i | −0.435505 | − | 0.180392i | 0.154150 | − | 0.988048i | \(-0.450736\pi\) |
−0.589655 | + | 0.807655i | \(0.700736\pi\) | |||||||
\(702\) | 27.3567 | + | 302.175i | 0.0389697 | + | 0.430449i | ||||
\(703\) | − | 1306.28i | − | 1.85815i | ||||||
\(704\) | 766.598 | + | 566.461i | 1.08892 | + | 0.804633i | ||||
\(705\) | 170.584 | 0.241963 | ||||||||
\(706\) | 325.923 | − | 29.5067i | 0.461647 | − | 0.0417941i | ||||
\(707\) | −116.423 | + | 281.070i | −0.164672 | + | 0.397553i | ||||
\(708\) | 62.2285 | + | 340.863i | 0.0878933 | + | 0.481445i | ||||
\(709\) | −81.1217 | − | 195.845i | −0.114417 | − | 0.276227i | 0.856289 | − | 0.516497i | \(-0.172764\pi\) |
−0.970706 | + | 0.240270i | \(0.922764\pi\) | |||||||
\(710\) | −17.9845 | + | 57.6459i | −0.0253302 | + | 0.0811915i | ||||
\(711\) | −35.4419 | − | 35.4419i | −0.0498479 | − | 0.0498479i | ||||
\(712\) | 578.984 | − | 1024.15i | 0.813179 | − | 1.43841i | ||||
\(713\) | 703.030 | + | 703.030i | 0.986016 | + | 0.986016i | ||||
\(714\) | −104.637 | − | 199.531i | −0.146550 | − | 0.279456i | ||||
\(715\) | 28.3138 | + | 68.3555i | 0.0395997 | + | 0.0956021i | ||||
\(716\) | −584.155 | − | 125.807i | −0.815860 | − | 0.175708i | ||||
\(717\) | −174.131 | + | 420.391i | −0.242861 | + | 0.586319i | ||||
\(718\) | 499.050 | + | 416.191i | 0.695055 | + | 0.579653i | ||||
\(719\) | 1240.79 | 1.72571 | 0.862855 | − | 0.505451i | \(-0.168674\pi\) | ||||
0.862855 | + | 0.505451i | \(0.168674\pi\) | |||||||
\(720\) | −2.06919 | + | 65.5568i | −0.00287387 | + | 0.0910511i | ||||
\(721\) | − | 44.6828i | − | 0.0619734i | ||||||
\(722\) | −466.838 | − | 389.327i | −0.646589 | − | 0.539234i | ||||
\(723\) | 8.88289 | + | 3.67941i | 0.0122862 | + | 0.00508909i | ||||
\(724\) | −210.781 | + | 136.079i | −0.291135 | + | 0.187955i | ||||
\(725\) | 1099.13 | − | 455.276i | 1.51605 | − | 0.627967i | ||||
\(726\) | −201.964 | − | 385.124i | −0.278187 | − | 0.530474i | ||||
\(727\) | −814.186 | + | 814.186i | −1.11993 | + | 1.11993i | −0.128174 | + | 0.991752i | \(0.540912\pi\) |
−0.991752 | + | 0.128174i | \(0.959088\pi\) | |||||||
\(728\) | −87.8674 | + | 68.6967i | −0.120697 | + | 0.0943637i | ||||
\(729\) | 465.740 | − | 465.740i | 0.638876 | − | 0.638876i | ||||
\(730\) | 29.7340 | − | 95.3070i | 0.0407315 | − | 0.130557i | ||||
\(731\) | 1511.10 | − | 625.919i | 2.06717 | − | 0.856250i | ||||
\(732\) | −251.959 | + | 364.501i | −0.344206 | + | 0.497952i | ||||
\(733\) | 302.729 | + | 125.394i | 0.413000 | + | 0.171070i | 0.579502 | − | 0.814971i | \(-0.303247\pi\) |
−0.166502 | + | 0.986041i | \(0.553247\pi\) | |||||||
\(734\) | −1203.66 | + | 108.971i | −1.63986 | + | 0.148461i | ||||
\(735\) | 14.2330i | 0.0193647i | ||||||||
\(736\) | −279.584 | + | 805.806i | −0.379869 | + | 1.09484i | ||||
\(737\) | 1234.54 | 1.67509 | ||||||||
\(738\) | 18.6607 | + | 206.121i | 0.0252855 | + | 0.279297i | ||||
\(739\) | 212.589 | − | 513.236i | 0.287671 | − | 0.694500i | −0.712301 | − | 0.701874i | \(-0.752347\pi\) |
0.999973 | + | 0.00737358i | \(0.00234710\pi\) | |||||||
\(740\) | −108.622 | + | 157.140i | −0.146787 | + | 0.212352i | ||||
\(741\) | 112.152 | + | 270.758i | 0.151352 | + | 0.365395i | ||||
\(742\) | 138.386 | + | 43.1738i | 0.186504 | + | 0.0581858i | ||||
\(743\) | 308.665 | + | 308.665i | 0.415431 | + | 0.415431i | 0.883625 | − | 0.468195i | \(-0.155095\pi\) |
−0.468195 | + | 0.883625i | \(0.655095\pi\) | |||||||
\(744\) | −638.836 | − | 78.2228i | −0.858650 | − | 0.105138i | ||||
\(745\) | −55.3282 | − | 55.3282i | −0.0742660 | − | 0.0742660i | ||||
\(746\) | −127.707 | + | 66.9712i | −0.171190 | + | 0.0897738i | ||||
\(747\) | −266.325 | − | 642.964i | −0.356526 | − | 0.860729i | ||||
\(748\) | −988.063 | + | 637.888i | −1.32094 | + | 0.852792i | ||||
\(749\) | −56.9916 | + | 137.590i | −0.0760903 | + | 0.183698i | ||||
\(750\) | −127.912 | + | 153.377i | −0.170549 | + | 0.204503i | ||||
\(751\) | −616.146 | −0.820434 | −0.410217 | − | 0.911988i | \(-0.634547\pi\) | ||||
−0.410217 | + | 0.911988i | \(0.634547\pi\) | |||||||
\(752\) | 1255.74 | − | 474.308i | 1.66987 | − | 0.630728i | ||||
\(753\) | 100.587i | 0.133582i | ||||||||
\(754\) | −333.054 | + | 399.362i | −0.441716 | + | 0.529658i | ||||
\(755\) | −51.9991 | − | 21.5387i | −0.0688730 | − | 0.0285281i | ||||
\(756\) | 297.849 | + | 64.1464i | 0.393980 | + | 0.0848498i | ||||
\(757\) | −164.876 | + | 68.2937i | −0.217801 | + | 0.0902163i | −0.488916 | − | 0.872331i | \(-0.662608\pi\) |
0.271115 | + | 0.962547i | \(0.412608\pi\) | |||||||
\(758\) | 462.325 | − | 242.449i | 0.609928 | − | 0.319853i | ||||
\(759\) | 605.409 | − | 605.409i | 0.797640 | − | 0.797640i | ||||
\(760\) | 52.0350 | + | 187.389i | 0.0684670 | + | 0.246565i | ||||
\(761\) | 178.882 | − | 178.882i | 0.235062 | − | 0.235062i | −0.579740 | − | 0.814802i | \(-0.696846\pi\) |
0.814802 | + | 0.579740i | \(0.196846\pi\) | |||||||
\(762\) | −198.194 | − | 61.8328i | −0.260097 | − | 0.0811454i | ||||
\(763\) | 218.359 | − | 90.4474i | 0.286185 | − | 0.118542i | ||||
\(764\) | 232.741 | + | 1274.86i | 0.304635 | + | 1.66867i | ||||
\(765\) | −74.7674 | − | 30.9697i | −0.0977351 | − | 0.0404832i | ||||
\(766\) | 112.065 | + | 1237.84i | 0.146298 | + | 1.61597i | ||||
\(767\) | 211.643i | 0.275936i | ||||||||
\(768\) | −178.703 | − | 522.416i | −0.232686 | − | 0.680229i | ||||
\(769\) | 615.128 | 0.799906 | 0.399953 | − | 0.916536i | \(-0.369026\pi\) | ||||
0.399953 | + | 0.916536i | \(0.369026\pi\) | |||||||
\(770\) | 73.9937 | − | 6.69885i | 0.0960957 | − | 0.00869981i | ||||
\(771\) | −322.317 | + | 778.142i | −0.418051 | + | 1.00926i | ||||
\(772\) | 772.935 | − | 141.108i | 1.00121 | − | 0.182783i | ||||
\(773\) | 354.467 | + | 855.758i | 0.458560 | + | 1.10706i | 0.968981 | + | 0.247136i | \(0.0794896\pi\) |
−0.510421 | + | 0.859925i | \(0.670510\pi\) | |||||||
\(774\) | −214.588 | + | 687.822i | −0.277245 | + | 0.888659i | ||||
\(775\) | 635.960 | + | 635.960i | 0.820593 | + | 0.820593i | ||||
\(776\) | 636.426 | − | 176.725i | 0.820136 | − | 0.227739i | ||||
\(777\) | 204.402 | + | 204.402i | 0.263065 | + | 0.263065i | ||||
\(778\) | 64.4440 | + | 122.888i | 0.0828329 | + | 0.157954i | ||||
\(779\) | 234.842 | + | 566.959i | 0.301466 | + | 0.727803i | ||||
\(780\) | 9.02321 | − | 41.8971i | 0.0115682 | − | 0.0537142i | ||||
\(781\) | 182.536 | − | 440.681i | 0.233721 | − | 0.564252i | ||||
\(782\) | −808.216 | − | 674.025i | −1.03352 | − | 0.861925i | ||||
\(783\) | 1420.52 | 1.81420 | ||||||||
\(784\) | 39.5748 | + | 104.775i | 0.0504781 | + | 0.133642i | ||||
\(785\) | − | 12.0108i | − | 0.0153004i | ||||||
\(786\) | 516.499 | + | 430.743i | 0.657123 | + | 0.548019i | ||||
\(787\) | −441.647 | − | 182.936i | −0.561178 | − | 0.232448i | 0.0840185 | − | 0.996464i | \(-0.473225\pi\) |
−0.645197 | + | 0.764017i | \(0.723225\pi\) | |||||||
\(788\) | −334.838 | − | 518.650i | −0.424921 | − | 0.658186i | ||||
\(789\) | 380.971 | − | 157.803i | 0.482853 | − | 0.200004i | ||||
\(790\) | 10.0937 | + | 19.2477i | 0.0127769 | + | 0.0243642i | ||||
\(791\) | −101.178 | + | 101.178i | −0.127912 | + | 0.127912i | ||||
\(792\) | 62.9676 | − | 514.249i | 0.0795046 | − | 0.649304i | ||||
\(793\) | −191.381 | + | 191.381i | −0.241338 | + | 0.241338i | ||||
\(794\) | 152.762 | − | 489.650i | 0.192395 | − | 0.616687i | ||||
\(795\) | −51.4632 | + | 21.3167i | −0.0647335 | + | 0.0268135i | ||||
\(796\) | −404.327 | − | 279.489i | −0.507949 | − | 0.351116i | ||||
\(797\) | −614.208 | − | 254.413i | −0.770650 | − | 0.319214i | −0.0375142 | − | 0.999296i | \(-0.511944\pi\) |
−0.733136 | + | 0.680082i | \(0.761944\pi\) | |||||||
\(798\) | 293.091 | − | 26.5343i | 0.367282 | − | 0.0332510i | ||||
\(799\) | 1656.24i | 2.07289i | ||||||||
\(800\) | −252.911 | + | 728.931i | −0.316139 | + | 0.911164i | ||||
\(801\) | −639.461 | −0.798328 | ||||||||
\(802\) | 4.51040 | + | 49.8206i | 0.00562394 | + | 0.0621205i | ||||
\(803\) | −301.790 | + | 728.585i | −0.375828 | + | 0.907329i | ||||
\(804\) | −588.256 | − | 406.628i | −0.731662 | − | 0.505757i | ||||
\(805\) | 25.4417 | + | 61.4217i | 0.0316046 | + | 0.0763002i | ||||
\(806\) | −375.280 | − | 117.081i | −0.465608 | − | 0.145261i | ||||
\(807\) | −279.728 | − | 279.728i | −0.346627 | − | 0.346627i | ||||
\(808\) | −566.587 | − | 724.700i | −0.701222 | − | 0.896906i | ||||
\(809\) | −610.914 | − | 610.914i | −0.755147 | − | 0.755147i | 0.220288 | − | 0.975435i | \(-0.429300\pi\) |
−0.975435 | + | 0.220288i | \(0.929300\pi\) | |||||||
\(810\) | −38.3347 | + | 20.1031i | −0.0473267 | + | 0.0248187i | ||||
\(811\) | −210.821 | − | 508.968i | −0.259952 | − | 0.627580i | 0.738983 | − | 0.673725i | \(-0.235307\pi\) |
−0.998935 | + | 0.0461444i | \(0.985307\pi\) | |||||||
\(812\) | 283.225 | + | 438.704i | 0.348799 | + | 0.540276i | ||||
\(813\) | 3.93100 | − | 9.49028i | 0.00483518 | − | 0.0116732i | ||||
\(814\) | 966.427 | − | 1158.83i | 1.18726 | − | 1.42363i | ||||
\(815\) | 161.098 | 0.197667 | ||||||||
\(816\) | 680.914 | + | 21.4919i | 0.834454 | + | 0.0263381i | ||||
\(817\) | 2136.42i | 2.61495i | ||||||||
\(818\) | 742.781 | − | 890.660i | 0.908045 | − | 1.08883i | ||||
\(819\) | 56.0085 | + | 23.1995i | 0.0683865 | + | 0.0283266i | ||||
\(820\) | 18.8943 | − | 87.7312i | 0.0230419 | − | 0.106989i | ||||
\(821\) | 926.220 | − | 383.653i | 1.12816 | − | 0.467299i | 0.261005 | − | 0.965337i | \(-0.415946\pi\) |
0.867155 | + | 0.498038i | \(0.165946\pi\) | |||||||
\(822\) | −221.268 | + | 116.035i | −0.269182 | + | 0.141162i | ||||
\(823\) | 242.079 | − | 242.079i | 0.294142 | − | 0.294142i | −0.544572 | − | 0.838714i | \(-0.683308\pi\) |
0.838714 | + | 0.544572i | \(0.183308\pi\) | |||||||
\(824\) | 117.614 | + | 66.4912i | 0.142736 | + | 0.0806932i | ||||
\(825\) | 547.652 | − | 547.652i | 0.663821 | − | 0.663821i | ||||
\(826\) | 202.882 | + | 63.2954i | 0.245620 | + | 0.0766288i | ||||
\(827\) | 242.507 | − | 100.450i | 0.293237 | − | 0.121463i | −0.231215 | − | 0.972903i | \(-0.574270\pi\) |
0.524452 | + | 0.851440i | \(0.324270\pi\) | |||||||
\(828\) | 456.062 | − | 83.2595i | 0.550800 | − | 0.100555i | ||||
\(829\) | −94.1207 | − | 38.9861i | −0.113535 | − | 0.0470279i | 0.325193 | − | 0.945648i | \(-0.394571\pi\) |
−0.438728 | + | 0.898620i | \(0.644571\pi\) | |||||||
\(830\) | 27.2087 | + | 300.540i | 0.0327816 | + | 0.362097i | ||||
\(831\) | − | 881.998i | − | 1.06137i | ||||||
\(832\) | −50.0710 | − | 333.511i | −0.0601815 | − | 0.400854i | ||||
\(833\) | −138.191 | −0.165896 | ||||||||
\(834\) | 247.738 | − | 22.4284i | 0.297048 | − | 0.0268925i | ||||
\(835\) | 57.9102 | − | 139.808i | 0.0693535 | − | 0.167434i | ||||
\(836\) | −275.890 | − | 1511.21i | −0.330012 | − | 1.80767i | ||||
\(837\) | 410.957 | + | 992.138i | 0.490988 | + | 1.18535i | ||||
\(838\) | 61.2053 | − | 196.182i | 0.0730373 | − | 0.234108i | ||||
\(839\) | 428.770 | + | 428.770i | 0.511049 | + | 0.511049i | 0.914848 | − | 0.403799i | \(-0.132310\pi\) |
−0.403799 | + | 0.914848i | \(0.632310\pi\) | |||||||
\(840\) | −37.4642 | − | 21.1798i | −0.0446003 | − | 0.0252140i | ||||
\(841\) | 1126.86 | + | 1126.86i | 1.33990 | + | 1.33990i | ||||
\(842\) | 364.998 | + | 696.014i | 0.433489 | + | 0.826620i | ||||
\(843\) | −78.2279 | − | 188.859i | −0.0927971 | − | 0.224032i | ||||
\(844\) | −797.474 | − | 171.749i | −0.944874 | − | 0.203494i | ||||
\(845\) | −50.9527 | + | 123.011i | −0.0602991 | + | 0.145575i | ||||
\(846\) | −560.326 | − | 467.293i | −0.662323 | − | 0.552355i | ||||
\(847\) | −266.729 | −0.314911 | ||||||||
\(848\) | −319.570 | + | 300.014i | −0.376852 | + | 0.353790i | ||||
\(849\) | 188.857i | 0.222446i | ||||||||
\(850\) | −731.112 | − | 609.722i | −0.860131 | − | 0.717320i | ||||
\(851\) | 1247.45 | + | 516.711i | 1.46586 | + | 0.607181i | ||||
\(852\) | −232.127 | + | 149.860i | −0.272450 | + | 0.175892i | ||||
\(853\) | 371.009 | − | 153.677i | 0.434946 | − | 0.180161i | −0.154457 | − | 0.987999i | \(-0.549363\pi\) |
0.589403 | + | 0.807839i | \(0.299363\pi\) | |||||||
\(854\) | 126.223 | + | 240.694i | 0.147802 | + | 0.281844i | ||||
\(855\) | 74.7462 | − | 74.7462i | 0.0874225 | − | 0.0874225i | ||||
\(856\) | −277.357 | − | 354.757i | −0.324016 | − | 0.414436i | ||||
\(857\) | −1060.01 | + | 1060.01i | −1.23688 | + | 1.23688i | −0.275614 | + | 0.961268i | \(0.588881\pi\) |
−0.961268 | + | 0.275614i | \(0.911119\pi\) | |||||||
\(858\) | −100.823 | + | 323.170i | −0.117509 | + | 0.376655i | ||||
\(859\) | −274.108 | + | 113.539i | −0.319101 | + | 0.132176i | −0.536484 | − | 0.843910i | \(-0.680248\pi\) |
0.217383 | + | 0.976086i | \(0.430248\pi\) | |||||||
\(860\) | 177.652 | − | 257.003i | 0.206572 | − | 0.298841i | ||||
\(861\) | −125.463 | − | 51.9685i | −0.145718 | − | 0.0603583i | ||||
\(862\) | −685.826 | + | 62.0897i | −0.795622 | + | 0.0720298i | ||||
\(863\) | − | 130.540i | − | 0.151262i | −0.997136 | − | 0.0756312i | \(-0.975903\pi\) | ||
0.997136 | − | 0.0756312i | \(-0.0240972\pi\) | |||||||
\(864\) | −612.066 | + | 688.544i | −0.708410 | + | 0.796926i | ||||
\(865\) | 272.666 | 0.315221 | ||||||||
\(866\) | 150.835 | + | 1666.08i | 0.174174 | + | 1.92388i | ||||
\(867\) | −83.1405 | + | 200.719i | −0.0958945 | + | 0.231510i | ||||
\(868\) | −224.468 | + | 324.731i | −0.258604 | + | 0.374114i | ||||
\(869\) | −65.6970 | − | 158.607i | −0.0756007 | − | 0.182516i | ||||
\(870\) | −191.547 | − | 59.7592i | −0.220169 | − | 0.0686887i | ||||
\(871\) | −308.863 | − | 308.863i | −0.354607 | − | 0.354607i | ||||
\(872\) | −86.8581 | + | 709.359i | −0.0996079 | + | 0.813485i | ||||
\(873\) | −253.859 | − | 253.859i | −0.290789 | − | 0.290789i | ||||
\(874\) | 1217.38 | − | 638.410i | 1.39289 | − | 0.730447i | ||||
\(875\) | 46.8774 | + | 113.172i | 0.0535741 | + | 0.129339i | ||||
\(876\) | 383.780 | − | 247.766i | 0.438105 | − | 0.282838i | ||||
\(877\) | 206.520 | − | 498.583i | 0.235485 | − | 0.568510i | −0.761321 | − | 0.648375i | \(-0.775449\pi\) |
0.996806 | + | 0.0798650i | \(0.0254489\pi\) | |||||||
\(878\) | 487.448 | − | 584.494i | 0.555180 | − | 0.665710i | ||||
\(879\) | −547.815 | −0.623225 | ||||||||
\(880\) | −92.4751 | + | 204.735i | −0.105085 | + | 0.232653i | ||||
\(881\) | − | 755.009i | − | 0.856991i | −0.903544 | − | 0.428495i | \(-0.859044\pi\) | ||
0.903544 | − | 0.428495i | \(-0.140956\pi\) | |||||||
\(882\) | 38.9895 | − | 46.7519i | 0.0442058 | − | 0.0530067i | ||||
\(883\) | 961.253 | + | 398.164i | 1.08862 | + | 0.450922i | 0.853526 | − | 0.521050i | \(-0.174460\pi\) |
0.235096 | + | 0.971972i | \(0.424460\pi\) | |||||||
\(884\) | 406.787 | + | 87.6082i | 0.460167 | + | 0.0991043i | ||||
\(885\) | −75.4480 | + | 31.2516i | −0.0852520 | + | 0.0353125i | ||||
\(886\) | 0.173361 | − | 0.0909123i | 0.000195667 | − | 0.000102610i | ||||
\(887\) | −723.981 | + | 723.981i | −0.816214 | + | 0.816214i | −0.985557 | − | 0.169344i | \(-0.945835\pi\) |
0.169344 | + | 0.985557i | \(0.445835\pi\) | |||||||
\(888\) | −842.191 | + | 233.863i | −0.948413 | + | 0.263359i | ||||
\(889\) | −90.0445 | + | 90.0445i | −0.101287 | + | 0.101287i | ||||
\(890\) | 264.697 | + | 82.5805i | 0.297412 | + | 0.0927870i | ||||
\(891\) | 315.889 | − | 130.845i | 0.354533 | − | 0.146852i | ||||
\(892\) | 38.3507 | + | 210.070i | 0.0429940 | + | 0.235504i | ||||
\(893\) | −1998.69 | − | 827.884i | −2.23817 | − | 0.927081i | ||||
\(894\) | −32.2802 | − | 356.558i | −0.0361076 | − | 0.398835i | ||||
\(895\) | − | 140.834i | − | 0.157356i | ||||||
\(896\) | −334.680 | − | 51.7437i | −0.373527 | − | 0.0577497i | ||||
\(897\) | −302.928 | −0.337712 | ||||||||
\(898\) | −669.592 | + | 60.6200i | −0.745648 | + | 0.0675055i | ||||
\(899\) | −704.337 | + | 1700.42i | −0.783467 | + | 1.89146i | ||||
\(900\) | 412.553 | − | 75.3165i | 0.458393 | − | 0.0836850i | ||||
\(901\) | −206.969 | − | 499.667i | −0.229710 | − | 0.554569i | ||||
\(902\) | −211.120 | + | 676.708i | −0.234058 | + | 0.750230i | ||||
\(903\) | −334.299 | − | 334.299i | −0.370209 | − | 0.370209i | ||||
\(904\) | −115.762 | − | 416.883i | −0.128055 | − | 0.461154i | ||||
\(905\) | −41.8123 | − | 41.8123i | −0.0462015 | − | 0.0462015i | ||||
\(906\) | −119.602 | − | 228.069i | −0.132011 | − | 0.251732i | ||||
\(907\) | −89.4720 | − | 216.005i | −0.0986461 | − | 0.238153i | 0.866851 | − | 0.498568i | \(-0.166141\pi\) |
−0.965497 | + | 0.260415i | \(0.916141\pi\) | |||||||
\(908\) | 39.6583 | − | 184.144i | 0.0436765 | − | 0.202801i | ||||
\(909\) | −191.342 | + | 461.939i | −0.210497 | + | 0.508184i | ||||
\(910\) | −20.1880 | − | 16.8361i | −0.0221846 | − | 0.0185012i | ||||
\(911\) | −203.292 | −0.223152 | −0.111576 | − | 0.993756i | \(-0.535590\pi\) | ||||
−0.111576 | + | 0.993756i | \(0.535590\pi\) | |||||||
\(912\) | −366.296 | + | 810.961i | −0.401641 | + | 0.889211i | ||||
\(913\) | − | 2383.67i | − | 2.61081i | ||||||
\(914\) | −920.027 | − | 767.271i | −1.00659 | − | 0.839465i | ||||
\(915\) | −96.4846 | − | 39.9652i | −0.105448 | − | 0.0436779i | ||||
\(916\) | −766.725 | − | 1187.63i | −0.837036 | − | 1.29654i | ||||
\(917\) | 381.107 | − | 157.860i | 0.415602 | − | 0.172148i | ||||
\(918\) | −527.911 | − | 1006.67i | −0.575066 | − | 1.09659i | ||||
\(919\) | 492.142 | − | 492.142i | 0.535519 | − | 0.535519i | −0.386690 | − | 0.922210i | \(-0.626382\pi\) |
0.922210 | + | 0.386690i | \(0.126382\pi\) | |||||||
\(920\) | −199.533 | − | 24.4320i | −0.216884 | − | 0.0265566i | ||||
\(921\) | 55.2145 | − | 55.2145i | 0.0599505 | − | 0.0599505i | ||||
\(922\) | 202.299 | − | 648.432i | 0.219413 | − | 0.703289i | ||||
\(923\) | −155.919 | + | 64.5838i | −0.168926 | + | 0.0699716i | ||||
\(924\) | 279.640 | + | 193.299i | 0.302640 | + | 0.209198i | ||||
\(925\) | 1128.44 | + | 467.416i | 1.21994 | + | 0.505315i | ||||
\(926\) | 29.9857 | − | 2.71468i | 0.0323819 | − | 0.00293162i | ||||
\(927\) | − | 73.4365i | − | 0.0792195i | ||||||
\(928\) | −1576.22 | + | 92.6837i | −1.69851 | + | 0.0998747i | ||||
\(929\) | 905.540 | 0.974747 | 0.487373 | − | 0.873194i | \(-0.337955\pi\) | ||||
0.487373 | + | 0.873194i | \(0.337955\pi\) | |||||||
\(930\) | −13.6769 | − | 151.071i | −0.0147063 | − | 0.162442i | ||||
\(931\) | 69.0762 | − | 166.765i | 0.0741957 | − | 0.179124i | ||||
\(932\) | −214.599 | − | 148.340i | −0.230256 | − | 0.159163i | ||||
\(933\) | −387.447 | − | 935.379i | −0.415270 | − | 1.00255i | ||||
\(934\) | −264.889 | − | 82.6403i | −0.283607 | − | 0.0884800i | ||||
\(935\) | −196.000 | − | 196.000i | −0.209626 | − | 0.209626i | ||||
\(936\) | −144.410 | + | 112.903i | −0.154285 | + | 0.120623i | ||||
\(937\) | −1264.02 | − | 1264.02i | −1.34901 | − | 1.34901i | −0.886744 | − | 0.462262i | \(-0.847038\pi\) |
−0.462262 | − | 0.886744i | \(-0.652962\pi\) | |||||||
\(938\) | −388.449 | + | 203.707i | −0.414125 | + | 0.217172i | ||||
\(939\) | −304.797 | − | 735.845i | −0.324597 | − | 0.783647i | ||||
\(940\) | 171.593 | + | 265.791i | 0.182546 | + | 0.282756i | ||||
\(941\) | −6.43069 | + | 15.5250i | −0.00683389 | + | 0.0164985i | −0.927260 | − | 0.374419i | \(-0.877842\pi\) |
0.920426 | + | 0.390917i | \(0.127842\pi\) | |||||||
\(942\) | 35.1977 | − | 42.2051i | 0.0373648 | − | 0.0448038i | ||||
\(943\) | −634.321 | −0.672663 | ||||||||
\(944\) | −468.509 | + | 439.839i | −0.496302 | + | 0.465931i | ||||
\(945\) | 71.8083i | 0.0759876i | ||||||||
\(946\) | −1580.59 | + | 1895.27i | −1.67082 | + | 2.00346i | ||||
\(947\) | −1063.74 | − | 440.616i | −1.12327 | − | 0.465275i | −0.257784 | − | 0.966202i | \(-0.582992\pi\) |
−0.865489 | + | 0.500927i | \(0.832992\pi\) | |||||||
\(948\) | −20.9367 | + | 97.2146i | −0.0220852 | + | 0.102547i | ||||
\(949\) | 257.784 | − | 106.777i | 0.271637 | − | 0.112516i | ||||
\(950\) | 1101.24 | − | 577.505i | 1.15920 | − | 0.607900i | ||||
\(951\) | −147.510 | + | 147.510i | −0.155110 | + | 0.155110i | ||||
\(952\) | 205.639 | − | 363.748i | 0.216007 | − | 0.382088i | ||||
\(953\) | 31.8270 | − | 31.8270i | 0.0333967 | − | 0.0333967i | −0.690211 | − | 0.723608i | \(-0.742482\pi\) |
0.723608 | + | 0.690211i | \(0.242482\pi\) | |||||||
\(954\) | 227.438 | + | 70.9564i | 0.238405 | + | 0.0743778i | ||||
\(955\) | −282.183 | + | 116.884i | −0.295480 | + | 0.122392i | ||||
\(956\) | −830.181 | + | 151.559i | −0.868390 | + | 0.158535i | ||||
\(957\) | 1464.30 | + | 606.534i | 1.53010 | + | 0.633787i | ||||
\(958\) | 24.2151 | + | 267.474i | 0.0252767 | + | 0.279200i | ||||
\(959\) | 153.246i | 0.159797i | ||||||||
\(960\) | 111.499 | − | 67.0966i | 0.116145 | − | 0.0698923i | ||||
\(961\) | −430.395 | −0.447861 | ||||||||
\(962\) | −531.706 | + | 48.1368i | −0.552709 | + | 0.0500383i | ||||
\(963\) | −93.6660 | + | 226.130i | −0.0972648 | + | 0.234818i | ||||
\(964\) | 3.20246 | + | 17.5418i | 0.00332205 | + | 0.0181969i | ||||
\(965\) | 70.8656 | + | 171.085i | 0.0734358 | + | 0.177290i | ||||
\(966\) | −90.5958 | + | 290.388i | −0.0937844 | + | 0.300609i | ||||
\(967\) | 427.458 | + | 427.458i | 0.442046 | + | 0.442046i | 0.892699 | − | 0.450653i | \(-0.148809\pi\) |
−0.450653 | + | 0.892699i | \(0.648809\pi\) | |||||||
\(968\) | 396.912 | − | 702.086i | 0.410033 | − | 0.725296i | ||||
\(969\) | −776.362 | − | 776.362i | −0.801199 | − | 0.801199i | ||||
\(970\) | 72.2981 | + | 137.865i | 0.0745341 | + | 0.142129i | ||||
\(971\) | 487.038 | + | 1175.81i | 0.501584 | + | 1.21093i | 0.948621 | + | 0.316415i | \(0.102479\pi\) |
−0.447037 | + | 0.894515i | \(0.647521\pi\) | |||||||
\(972\) | 819.568 | + | 176.507i | 0.843177 | + | 0.181592i | ||||
\(973\) | 58.3873 | − | 140.959i | 0.0600075 | − | 0.144871i | ||||
\(974\) | 1343.64 | + | 1120.55i | 1.37951 | + | 1.15047i | ||||
\(975\) | −274.028 | −0.281054 | ||||||||
\(976\) | −821.386 | − | 25.9257i | −0.841584 | − | 0.0265632i | ||||
\(977\) | − | 1111.86i | − | 1.13803i | −0.822327 | − | 0.569015i | \(-0.807325\pi\) | ||
0.822327 | − | 0.569015i | \(-0.192675\pi\) | |||||||
\(978\) | 566.088 | + | 472.098i | 0.578822 | + | 0.482718i | ||||
\(979\) | −2023.50 | − | 838.162i | −2.06691 | − | 0.856141i | ||||
\(980\) | −22.1768 | + | 14.3172i | −0.0226294 | + | 0.0146094i | ||||
\(981\) | 358.875 | − | 148.651i | 0.365825 | − | 0.151530i | ||||
\(982\) | 48.2202 | + | 91.9510i | 0.0491041 | + | 0.0936365i | ||||
\(983\) | −162.181 | + | 162.181i | −0.164986 | + | 0.164986i | −0.784771 | − | 0.619786i | \(-0.787220\pi\) |
0.619786 | + | 0.784771i | \(0.287220\pi\) | |||||||
\(984\) | 323.489 | − | 252.911i | 0.328749 | − | 0.257024i | ||||
\(985\) | 102.884 | − | 102.884i | 0.104450 | − | 0.104450i | ||||
\(986\) | 580.214 | − | 1859.77i | 0.588453 | − | 1.88618i | ||||
\(987\) | 442.292 | − | 183.203i | 0.448118 | − | 0.185616i | ||||
\(988\) | −309.059 | + | 447.105i | −0.312812 | + | 0.452536i | ||||
\(989\) | −2040.21 | − | 845.081i | −2.06290 | − | 0.854481i | ||||
\(990\) | 121.609 | − | 11.0096i | 0.122837 | − | 0.0111208i | ||||
\(991\) | 856.333i | 0.864110i | 0.901847 | + | 0.432055i | \(0.142211\pi\) | ||||
−0.901847 | + | 0.432055i | \(0.857789\pi\) | |||||||
\(992\) | −520.734 | − | 1074.07i | −0.524933 | − | 1.08273i | ||||
\(993\) | 187.994 | 0.189319 | ||||||||
\(994\) | 15.2801 | + | 168.780i | 0.0153723 | + | 0.169799i | ||||
\(995\) | 44.3319 | − | 107.027i | 0.0445547 | − | 0.107565i | ||||
\(996\) | −785.123 | + | 1135.81i | −0.788276 | + | 1.14037i | ||||
\(997\) | −660.978 | − | 1595.74i | −0.662967 | − | 1.60054i | −0.793131 | − | 0.609051i | \(-0.791551\pi\) |
0.130165 | − | 0.991492i | \(-0.458449\pi\) | |||||||
\(998\) | −679.828 | − | 212.094i | −0.681191 | − | 0.212519i | ||||
\(999\) | 1031.24 | + | 1031.24i | 1.03228 | + | 1.03228i |
(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 | 224.3.w.a.99.3 | yes | 192 | |
32.11 | odd | 8 | inner | 224.3.w.a.43.3 | ✓ | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.w.a.43.3 | ✓ | 192 | 32.11 | odd | 8 | inner | |
224.3.w.a.99.3 | yes | 192 | 1.1 | even | 1 | trivial |