Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (of order \(4\), degree \(2\), 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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.4 | ||
Root | \(-0.454110 + 0.454110i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.47 |
Dual form | 230.3.f.a.93.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.454110 | + | 0.454110i | −0.151370 | + | 0.151370i | −0.778730 | − | 0.627360i | \(-0.784136\pi\) |
0.627360 | + | 0.778730i | \(0.284136\pi\) | |||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 4.61282 | − | 1.92922i | 0.922564 | − | 0.385844i | ||||
\(6\) | 0.908220 | 0.151370 | ||||||||
\(7\) | −8.21299 | − | 8.21299i | −1.17328 | − | 1.17328i | −0.981422 | − | 0.191863i | \(-0.938547\pi\) |
−0.191863 | − | 0.981422i | \(-0.561453\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 8.58757i | 0.954174i | ||||||||
\(10\) | −6.54204 | − | 2.68360i | −0.654204 | − | 0.268360i | ||||
\(11\) | −1.80844 | −0.164403 | −0.0822017 | − | 0.996616i | \(-0.526195\pi\) | ||||
−0.0822017 | + | 0.996616i | \(0.526195\pi\) | |||||||
\(12\) | −0.908220 | − | 0.908220i | −0.0756850 | − | 0.0756850i | ||||
\(13\) | 12.1431 | − | 12.1431i | 0.934084 | − | 0.934084i | −0.0638744 | − | 0.997958i | \(-0.520346\pi\) |
0.997958 | + | 0.0638744i | \(0.0203457\pi\) | |||||||
\(14\) | 16.4260i | 1.17328i | ||||||||
\(15\) | −1.21865 | + | 2.97081i | −0.0812432 | + | 0.198054i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −13.2264 | − | 13.2264i | −0.778023 | − | 0.778023i | 0.201471 | − | 0.979494i | \(-0.435428\pi\) |
−0.979494 | + | 0.201471i | \(0.935428\pi\) | |||||||
\(18\) | 8.58757 | − | 8.58757i | 0.477087 | − | 0.477087i | ||||
\(19\) | − | 13.8065i | − | 0.726656i | −0.931661 | − | 0.363328i | \(-0.881640\pi\) | ||
0.931661 | − | 0.363328i | \(-0.118360\pi\) | |||||||
\(20\) | 3.85844 | + | 9.22564i | 0.192922 | + | 0.461282i | ||||
\(21\) | 7.45921 | 0.355200 | ||||||||
\(22\) | 1.80844 | + | 1.80844i | 0.0822017 | + | 0.0822017i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | 1.81644i | 0.0756850i | ||||||||
\(25\) | 17.5562 | − | 17.7983i | 0.702248 | − | 0.711932i | ||||
\(26\) | −24.2862 | −0.934084 | ||||||||
\(27\) | −7.98669 | − | 7.98669i | −0.295803 | − | 0.295803i | ||||
\(28\) | 16.4260 | − | 16.4260i | 0.586642 | − | 0.586642i | ||||
\(29\) | − | 47.4104i | − | 1.63484i | −0.576042 | − | 0.817420i | \(-0.695403\pi\) | ||
0.576042 | − | 0.817420i | \(-0.304597\pi\) | |||||||
\(30\) | 4.18945 | − | 1.75216i | 0.139648 | − | 0.0584052i | ||||
\(31\) | −56.5594 | −1.82450 | −0.912248 | − | 0.409637i | \(-0.865655\pi\) | ||||
−0.912248 | + | 0.409637i | \(0.865655\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0.821229 | − | 0.821229i | 0.0248857 | − | 0.0248857i | ||||
\(34\) | 26.4528i | 0.778023i | ||||||||
\(35\) | −53.7297 | − | 22.0404i | −1.53514 | − | 0.629725i | ||||
\(36\) | −17.1751 | −0.477087 | ||||||||
\(37\) | 3.64057 | + | 3.64057i | 0.0983938 | + | 0.0983938i | 0.754590 | − | 0.656196i | \(-0.227836\pi\) |
−0.656196 | + | 0.754590i | \(0.727836\pi\) | |||||||
\(38\) | −13.8065 | + | 13.8065i | −0.363328 | + | 0.363328i | ||||
\(39\) | 11.0286i | 0.282784i | ||||||||
\(40\) | 5.36720 | − | 13.0841i | 0.134180 | − | 0.327102i | ||||
\(41\) | −8.30147 | −0.202475 | −0.101237 | − | 0.994862i | \(-0.532280\pi\) | ||||
−0.101237 | + | 0.994862i | \(0.532280\pi\) | |||||||
\(42\) | −7.45921 | − | 7.45921i | −0.177600 | − | 0.177600i | ||||
\(43\) | 17.7220 | − | 17.7220i | 0.412140 | − | 0.412140i | −0.470343 | − | 0.882484i | \(-0.655870\pi\) |
0.882484 | + | 0.470343i | \(0.155870\pi\) | |||||||
\(44\) | − | 3.61687i | − | 0.0822017i | ||||||
\(45\) | 16.5673 | + | 39.6129i | 0.368163 | + | 0.880287i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 8.93900 | + | 8.93900i | 0.190191 | + | 0.190191i | 0.795779 | − | 0.605587i | \(-0.207062\pi\) |
−0.605587 | + | 0.795779i | \(0.707062\pi\) | |||||||
\(48\) | 1.81644 | − | 1.81644i | 0.0378425 | − | 0.0378425i | ||||
\(49\) | 85.9066i | 1.75320i | ||||||||
\(50\) | −35.3545 | + | 0.242091i | −0.707090 | + | 0.00484182i | ||||
\(51\) | 12.0125 | 0.235539 | ||||||||
\(52\) | 24.2862 | + | 24.2862i | 0.467042 | + | 0.467042i | ||||
\(53\) | 24.9637 | − | 24.9637i | 0.471014 | − | 0.471014i | −0.431229 | − | 0.902243i | \(-0.641920\pi\) |
0.902243 | + | 0.431229i | \(0.141920\pi\) | |||||||
\(54\) | 15.9734i | 0.295803i | ||||||||
\(55\) | −8.34199 | + | 3.48888i | −0.151673 | + | 0.0634341i | ||||
\(56\) | −32.8520 | −0.586642 | ||||||||
\(57\) | 6.26965 | + | 6.26965i | 0.109994 | + | 0.109994i | ||||
\(58\) | −47.4104 | + | 47.4104i | −0.817420 | + | 0.817420i | ||||
\(59\) | 6.35948i | 0.107788i | 0.998547 | + | 0.0538939i | \(0.0171633\pi\) | ||||
−0.998547 | + | 0.0538939i | \(0.982837\pi\) | |||||||
\(60\) | −5.94161 | − | 2.43730i | −0.0990269 | − | 0.0406216i | ||||
\(61\) | 98.9683 | 1.62243 | 0.811215 | − | 0.584748i | \(-0.198806\pi\) | ||||
0.811215 | + | 0.584748i | \(0.198806\pi\) | |||||||
\(62\) | 56.5594 | + | 56.5594i | 0.912248 | + | 0.912248i | ||||
\(63\) | 70.5297 | − | 70.5297i | 1.11952 | − | 1.11952i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 32.5872 | − | 79.4406i | 0.501341 | − | 1.22216i | ||||
\(66\) | −1.64246 | −0.0248857 | ||||||||
\(67\) | −16.0688 | − | 16.0688i | −0.239833 | − | 0.239833i | 0.576948 | − | 0.816781i | \(-0.304244\pi\) |
−0.816781 | + | 0.576948i | \(0.804244\pi\) | |||||||
\(68\) | 26.4528 | − | 26.4528i | 0.389012 | − | 0.389012i | ||||
\(69\) | − | 3.07992i | − | 0.0446366i | ||||||
\(70\) | 31.6894 | + | 75.7701i | 0.452705 | + | 1.08243i | ||||
\(71\) | 110.405 | 1.55500 | 0.777499 | − | 0.628884i | \(-0.216488\pi\) | ||||
0.777499 | + | 0.628884i | \(0.216488\pi\) | |||||||
\(72\) | 17.1751 | + | 17.1751i | 0.238544 | + | 0.238544i | ||||
\(73\) | −72.6670 | + | 72.6670i | −0.995438 | + | 0.995438i | −0.999990 | − | 0.00455142i | \(-0.998551\pi\) |
0.00455142 | + | 0.999990i | \(0.498551\pi\) | |||||||
\(74\) | − | 7.28114i | − | 0.0983938i | ||||||
\(75\) | 0.109936 | + | 16.0548i | 0.00146581 | + | 0.214064i | ||||
\(76\) | 27.6129 | 0.363328 | ||||||||
\(77\) | 14.8527 | + | 14.8527i | 0.192892 | + | 0.192892i | ||||
\(78\) | 11.0286 | − | 11.0286i | 0.141392 | − | 0.141392i | ||||
\(79\) | 81.2609i | 1.02862i | 0.857605 | + | 0.514310i | \(0.171952\pi\) | ||||
−0.857605 | + | 0.514310i | \(0.828048\pi\) | |||||||
\(80\) | −18.4513 | + | 7.71689i | −0.230641 | + | 0.0964611i | ||||
\(81\) | −70.0344 | −0.864623 | ||||||||
\(82\) | 8.30147 | + | 8.30147i | 0.101237 | + | 0.101237i | ||||
\(83\) | 70.5250 | − | 70.5250i | 0.849699 | − | 0.849699i | −0.140396 | − | 0.990095i | \(-0.544838\pi\) |
0.990095 | + | 0.140396i | \(0.0448376\pi\) | |||||||
\(84\) | 14.9184i | 0.177600i | ||||||||
\(85\) | −86.5276 | − | 35.4943i | −1.01797 | − | 0.417580i | ||||
\(86\) | −35.4441 | −0.412140 | ||||||||
\(87\) | 21.5295 | + | 21.5295i | 0.247466 | + | 0.247466i | ||||
\(88\) | −3.61687 | + | 3.61687i | −0.0411008 | + | 0.0411008i | ||||
\(89\) | 131.148i | 1.47358i | 0.676124 | + | 0.736788i | \(0.263658\pi\) | ||||
−0.676124 | + | 0.736788i | \(0.736342\pi\) | |||||||
\(90\) | 23.0456 | − | 56.1802i | 0.256062 | − | 0.624225i | ||||
\(91\) | −199.462 | −2.19189 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 25.6842 | − | 25.6842i | 0.276174 | − | 0.276174i | ||||
\(94\) | − | 17.8780i | − | 0.190191i | ||||||
\(95\) | −26.6357 | − | 63.6867i | −0.280376 | − | 0.670387i | ||||
\(96\) | −3.63288 | −0.0378425 | ||||||||
\(97\) | 79.5123 | + | 79.5123i | 0.819715 | + | 0.819715i | 0.986066 | − | 0.166352i | \(-0.0531987\pi\) |
−0.166352 | + | 0.986066i | \(0.553199\pi\) | |||||||
\(98\) | 85.9066 | − | 85.9066i | 0.876598 | − | 0.876598i | ||||
\(99\) | − | 15.5301i | − | 0.156869i | ||||||
\(100\) | 35.5966 | + | 35.1124i | 0.355966 | + | 0.351124i | ||||
\(101\) | 106.466 | 1.05412 | 0.527060 | − | 0.849828i | \(-0.323294\pi\) | ||||
0.527060 | + | 0.849828i | \(0.323294\pi\) | |||||||
\(102\) | −12.0125 | − | 12.0125i | −0.117769 | − | 0.117769i | ||||
\(103\) | −4.25928 | + | 4.25928i | −0.0413523 | + | 0.0413523i | −0.727481 | − | 0.686128i | \(-0.759309\pi\) |
0.686128 | + | 0.727481i | \(0.259309\pi\) | |||||||
\(104\) | − | 48.5723i | − | 0.467042i | ||||||
\(105\) | 34.4080 | − | 14.3905i | 0.327695 | − | 0.137052i | ||||
\(106\) | −49.9274 | −0.471014 | ||||||||
\(107\) | −22.3097 | − | 22.3097i | −0.208502 | − | 0.208502i | 0.595129 | − | 0.803631i | \(-0.297101\pi\) |
−0.803631 | + | 0.595129i | \(0.797101\pi\) | |||||||
\(108\) | 15.9734 | − | 15.9734i | 0.147902 | − | 0.147902i | ||||
\(109\) | 151.792i | 1.39258i | 0.717759 | + | 0.696292i | \(0.245168\pi\) | ||||
−0.717759 | + | 0.696292i | \(0.754832\pi\) | |||||||
\(110\) | 11.8309 | + | 4.85312i | 0.107553 | + | 0.0441193i | ||||
\(111\) | −3.30644 | −0.0297877 | ||||||||
\(112\) | 32.8520 | + | 32.8520i | 0.293321 | + | 0.293321i | ||||
\(113\) | 35.4658 | − | 35.4658i | 0.313857 | − | 0.313857i | −0.532545 | − | 0.846402i | \(-0.678764\pi\) |
0.846402 | + | 0.532545i | \(0.178764\pi\) | |||||||
\(114\) | − | 12.5393i | − | 0.109994i | ||||||
\(115\) | −9.10052 | + | 22.1851i | −0.0791350 | + | 0.192914i | ||||
\(116\) | 94.8207 | 0.817420 | ||||||||
\(117\) | 104.280 | + | 104.280i | 0.891278 | + | 0.891278i | ||||
\(118\) | 6.35948 | − | 6.35948i | 0.0538939 | − | 0.0538939i | ||||
\(119\) | 217.257i | 1.82569i | ||||||||
\(120\) | 3.50431 | + | 8.37891i | 0.0292026 | + | 0.0698242i | ||||
\(121\) | −117.730 | −0.972972 | ||||||||
\(122\) | −98.9683 | − | 98.9683i | −0.811215 | − | 0.811215i | ||||
\(123\) | 3.76978 | − | 3.76978i | 0.0306486 | − | 0.0306486i | ||||
\(124\) | − | 113.119i | − | 0.912248i | ||||||
\(125\) | 46.6468 | − | 115.970i | 0.373174 | − | 0.927761i | ||||
\(126\) | −141.059 | −1.11952 | ||||||||
\(127\) | −0.468171 | − | 0.468171i | −0.00368639 | − | 0.00368639i | 0.705261 | − | 0.708948i | \(-0.250830\pi\) |
−0.708948 | + | 0.705261i | \(0.750830\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 16.0955i | 0.124771i | ||||||||
\(130\) | −112.028 | + | 46.8534i | −0.861752 | + | 0.360411i | ||||
\(131\) | −57.9083 | −0.442048 | −0.221024 | − | 0.975268i | \(-0.570940\pi\) | ||||
−0.221024 | + | 0.975268i | \(0.570940\pi\) | |||||||
\(132\) | 1.64246 | + | 1.64246i | 0.0124429 | + | 0.0124429i | ||||
\(133\) | −113.392 | + | 113.392i | −0.852575 | + | 0.852575i | ||||
\(134\) | 32.1376i | 0.239833i | ||||||||
\(135\) | −52.2493 | − | 21.4331i | −0.387032 | − | 0.158763i | ||||
\(136\) | −52.9056 | −0.389012 | ||||||||
\(137\) | −90.9859 | − | 90.9859i | −0.664131 | − | 0.664131i | 0.292220 | − | 0.956351i | \(-0.405606\pi\) |
−0.956351 | + | 0.292220i | \(0.905606\pi\) | |||||||
\(138\) | −3.07992 | + | 3.07992i | −0.0223183 | + | 0.0223183i | ||||
\(139\) | 15.9583i | 0.114808i | 0.998351 | + | 0.0574041i | \(0.0182824\pi\) | ||||
−0.998351 | + | 0.0574041i | \(0.981718\pi\) | |||||||
\(140\) | 44.0808 | − | 107.459i | 0.314863 | − | 0.767568i | ||||
\(141\) | −8.11858 | −0.0575785 | ||||||||
\(142\) | −110.405 | − | 110.405i | −0.777499 | − | 0.777499i | ||||
\(143\) | −21.9600 | + | 21.9600i | −0.153566 | + | 0.153566i | ||||
\(144\) | − | 34.3503i | − | 0.238544i | ||||||
\(145\) | −91.4651 | − | 218.695i | −0.630794 | − | 1.50824i | ||||
\(146\) | 145.334 | 0.995438 | ||||||||
\(147\) | −39.0110 | − | 39.0110i | −0.265381 | − | 0.265381i | ||||
\(148\) | −7.28114 | + | 7.28114i | −0.0491969 | + | 0.0491969i | ||||
\(149\) | − | 273.895i | − | 1.83822i | −0.394003 | − | 0.919109i | \(-0.628910\pi\) | ||
0.394003 | − | 0.919109i | \(-0.371090\pi\) | |||||||
\(150\) | 15.9449 | − | 16.1648i | 0.106299 | − | 0.107765i | ||||
\(151\) | −67.1415 | −0.444646 | −0.222323 | − | 0.974973i | \(-0.571364\pi\) | ||||
−0.222323 | + | 0.974973i | \(0.571364\pi\) | |||||||
\(152\) | −27.6129 | − | 27.6129i | −0.181664 | − | 0.181664i | ||||
\(153\) | 113.583 | − | 113.583i | 0.742370 | − | 0.742370i | ||||
\(154\) | − | 29.7054i | − | 0.192892i | ||||||
\(155\) | −260.898 | + | 109.116i | −1.68322 | + | 0.703972i | ||||
\(156\) | −22.0572 | −0.141392 | ||||||||
\(157\) | 20.7386 | + | 20.7386i | 0.132093 | + | 0.132093i | 0.770062 | − | 0.637969i | \(-0.220225\pi\) |
−0.637969 | + | 0.770062i | \(0.720225\pi\) | |||||||
\(158\) | 81.2609 | − | 81.2609i | 0.514310 | − | 0.514310i | ||||
\(159\) | 22.6725i | 0.142595i | ||||||||
\(160\) | 26.1682 | + | 10.7344i | 0.163551 | + | 0.0670900i | ||||
\(161\) | 55.7032 | 0.345983 | ||||||||
\(162\) | 70.0344 | + | 70.0344i | 0.432311 | + | 0.432311i | ||||
\(163\) | −5.13555 | + | 5.13555i | −0.0315064 | + | 0.0315064i | −0.722685 | − | 0.691178i | \(-0.757092\pi\) |
0.691178 | + | 0.722685i | \(0.257092\pi\) | |||||||
\(164\) | − | 16.6029i | − | 0.101237i | ||||||
\(165\) | 2.20385 | − | 5.37252i | 0.0133567 | − | 0.0325607i | ||||
\(166\) | −141.050 | −0.849699 | ||||||||
\(167\) | −4.29668 | − | 4.29668i | −0.0257286 | − | 0.0257286i | 0.694125 | − | 0.719854i | \(-0.255791\pi\) |
−0.719854 | + | 0.694125i | \(0.755791\pi\) | |||||||
\(168\) | 14.9184 | − | 14.9184i | 0.0888001 | − | 0.0888001i | ||||
\(169\) | − | 125.909i | − | 0.745024i | ||||||
\(170\) | 51.0333 | + | 122.022i | 0.300196 | + | 0.717776i | ||||
\(171\) | 118.564 | 0.693357 | ||||||||
\(172\) | 35.4441 | + | 35.4441i | 0.206070 | + | 0.206070i | ||||
\(173\) | −59.7225 | + | 59.7225i | −0.345217 | + | 0.345217i | −0.858324 | − | 0.513107i | \(-0.828494\pi\) |
0.513107 | + | 0.858324i | \(0.328494\pi\) | |||||||
\(174\) | − | 43.0590i | − | 0.247466i | ||||||
\(175\) | −290.366 | + | 1.98829i | −1.65924 | + | 0.0113617i | ||||
\(176\) | 7.23375 | 0.0411008 | ||||||||
\(177\) | −2.88790 | − | 2.88790i | −0.0163158 | − | 0.0163158i | ||||
\(178\) | 131.148 | − | 131.148i | 0.736788 | − | 0.736788i | ||||
\(179\) | − | 186.219i | − | 1.04033i | −0.854065 | − | 0.520166i | \(-0.825870\pi\) | ||
0.854065 | − | 0.520166i | \(-0.174130\pi\) | |||||||
\(180\) | −79.2258 | + | 33.1346i | −0.440143 | + | 0.184081i | ||||
\(181\) | 243.615 | 1.34594 | 0.672970 | − | 0.739670i | \(-0.265018\pi\) | ||||
0.672970 | + | 0.739670i | \(0.265018\pi\) | |||||||
\(182\) | 199.462 | + | 199.462i | 1.09595 | + | 1.09595i | ||||
\(183\) | −44.9425 | + | 44.9425i | −0.245587 | + | 0.245587i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | 23.8168 | + | 9.76983i | 0.128739 | + | 0.0528099i | ||||
\(186\) | −51.3684 | −0.276174 | ||||||||
\(187\) | 23.9191 | + | 23.9191i | 0.127910 | + | 0.127910i | ||||
\(188\) | −17.8780 | + | 17.8780i | −0.0950957 | + | 0.0950957i | ||||
\(189\) | 131.189i | 0.694123i | ||||||||
\(190\) | −37.0510 | + | 90.3225i | −0.195005 | + | 0.475381i | ||||
\(191\) | 325.057 | 1.70187 | 0.850935 | − | 0.525271i | \(-0.176036\pi\) | ||||
0.850935 | + | 0.525271i | \(0.176036\pi\) | |||||||
\(192\) | 3.63288 | + | 3.63288i | 0.0189212 | + | 0.0189212i | ||||
\(193\) | 189.666 | − | 189.666i | 0.982725 | − | 0.982725i | −0.0171285 | − | 0.999853i | \(-0.505452\pi\) |
0.999853 | + | 0.0171285i | \(0.00545243\pi\) | |||||||
\(194\) | − | 159.025i | − | 0.819715i | ||||||
\(195\) | 21.2766 | + | 50.8729i | 0.109111 | + | 0.260887i | ||||
\(196\) | −171.813 | −0.876598 | ||||||||
\(197\) | 29.6698 | + | 29.6698i | 0.150608 | + | 0.150608i | 0.778390 | − | 0.627781i | \(-0.216037\pi\) |
−0.627781 | + | 0.778390i | \(0.716037\pi\) | |||||||
\(198\) | −15.5301 | + | 15.5301i | −0.0784347 | + | 0.0784347i | ||||
\(199\) | − | 71.7477i | − | 0.360541i | −0.983617 | − | 0.180271i | \(-0.942303\pi\) | ||
0.983617 | − | 0.180271i | \(-0.0576974\pi\) | |||||||
\(200\) | −0.484182 | − | 70.7090i | −0.00242091 | − | 0.353545i | ||||
\(201\) | 14.5940 | 0.0726071 | ||||||||
\(202\) | −106.466 | − | 106.466i | −0.527060 | − | 0.527060i | ||||
\(203\) | −389.381 | + | 389.381i | −1.91813 | + | 1.91813i | ||||
\(204\) | 24.0250i | 0.117769i | ||||||||
\(205\) | −38.2932 | + | 16.0154i | −0.186796 | + | 0.0781238i | ||||
\(206\) | 8.51856 | 0.0413523 | ||||||||
\(207\) | −29.1219 | − | 29.1219i | −0.140685 | − | 0.140685i | ||||
\(208\) | −48.5723 | + | 48.5723i | −0.233521 | + | 0.233521i | ||||
\(209\) | 24.9681i | 0.119465i | ||||||||
\(210\) | −48.7984 | − | 20.0175i | −0.232373 | − | 0.0953215i | ||||
\(211\) | 193.990 | 0.919385 | 0.459693 | − | 0.888078i | \(-0.347960\pi\) | ||||
0.459693 | + | 0.888078i | \(0.347960\pi\) | |||||||
\(212\) | 49.9274 | + | 49.9274i | 0.235507 | + | 0.235507i | ||||
\(213\) | −50.1360 | + | 50.1360i | −0.235380 | + | 0.235380i | ||||
\(214\) | 44.6194i | 0.208502i | ||||||||
\(215\) | 47.5588 | − | 115.938i | 0.221204 | − | 0.539248i | ||||
\(216\) | −31.9468 | −0.147902 | ||||||||
\(217\) | 464.522 | + | 464.522i | 2.14065 | + | 2.14065i | ||||
\(218\) | 151.792 | − | 151.792i | 0.696292 | − | 0.696292i | ||||
\(219\) | − | 65.9976i | − | 0.301359i | ||||||
\(220\) | −6.97775 | − | 16.6840i | −0.0317171 | − | 0.0758363i | ||||
\(221\) | −321.219 | −1.45348 | ||||||||
\(222\) | 3.30644 | + | 3.30644i | 0.0148939 | + | 0.0148939i | ||||
\(223\) | −141.481 | + | 141.481i | −0.634445 | + | 0.634445i | −0.949180 | − | 0.314735i | \(-0.898084\pi\) |
0.314735 | + | 0.949180i | \(0.398084\pi\) | |||||||
\(224\) | − | 65.7040i | − | 0.293321i | ||||||
\(225\) | 152.844 | + | 150.765i | 0.679307 | + | 0.670067i | ||||
\(226\) | −70.9316 | −0.313857 | ||||||||
\(227\) | −299.127 | − | 299.127i | −1.31774 | − | 1.31774i | −0.915561 | − | 0.402179i | \(-0.868253\pi\) |
−0.402179 | − | 0.915561i | \(-0.631747\pi\) | |||||||
\(228\) | −12.5393 | + | 12.5393i | −0.0549970 | + | 0.0549970i | ||||
\(229\) | − | 30.5265i | − | 0.133304i | −0.997776 | − | 0.0666518i | \(-0.978768\pi\) | ||
0.997776 | − | 0.0666518i | \(-0.0212317\pi\) | |||||||
\(230\) | 31.2857 | − | 13.0846i | 0.136025 | − | 0.0568896i | ||||
\(231\) | −13.4895 | −0.0583961 | ||||||||
\(232\) | −94.8207 | − | 94.8207i | −0.408710 | − | 0.408710i | ||||
\(233\) | −52.7346 | + | 52.7346i | −0.226329 | + | 0.226329i | −0.811157 | − | 0.584828i | \(-0.801162\pi\) |
0.584828 | + | 0.811157i | \(0.301162\pi\) | |||||||
\(234\) | − | 208.559i | − | 0.891278i | ||||||
\(235\) | 58.4793 | + | 23.9887i | 0.248848 | + | 0.102079i | ||||
\(236\) | −12.7190 | −0.0538939 | ||||||||
\(237\) | −36.9014 | − | 36.9014i | −0.155702 | − | 0.155702i | ||||
\(238\) | 217.257 | − | 217.257i | 0.912843 | − | 0.912843i | ||||
\(239\) | 128.388i | 0.537190i | 0.963253 | + | 0.268595i | \(0.0865593\pi\) | ||||
−0.963253 | + | 0.268595i | \(0.913441\pi\) | |||||||
\(240\) | 4.87459 | − | 11.8832i | 0.0203108 | − | 0.0495134i | ||||
\(241\) | 148.698 | 0.617006 | 0.308503 | − | 0.951223i | \(-0.400172\pi\) | ||||
0.308503 | + | 0.951223i | \(0.400172\pi\) | |||||||
\(242\) | 117.730 | + | 117.730i | 0.486486 | + | 0.486486i | ||||
\(243\) | 103.684 | − | 103.684i | 0.426681 | − | 0.426681i | ||||
\(244\) | 197.937i | 0.811215i | ||||||||
\(245\) | 165.733 | + | 396.271i | 0.676460 | + | 1.61743i | ||||
\(246\) | −7.53956 | −0.0306486 | ||||||||
\(247\) | −167.653 | − | 167.653i | −0.678757 | − | 0.678757i | ||||
\(248\) | −113.119 | + | 113.119i | −0.456124 | + | 0.456124i | ||||
\(249\) | 64.0522i | 0.257238i | ||||||||
\(250\) | −162.617 | + | 69.3234i | −0.650468 | + | 0.277294i | ||||
\(251\) | 410.299 | 1.63466 | 0.817329 | − | 0.576172i | \(-0.195454\pi\) | ||||
0.817329 | + | 0.576172i | \(0.195454\pi\) | |||||||
\(252\) | 141.059 | + | 141.059i | 0.559759 | + | 0.559759i | ||||
\(253\) | 6.13271 | − | 6.13271i | 0.0242400 | − | 0.0242400i | ||||
\(254\) | 0.936342i | 0.00368639i | ||||||||
\(255\) | 55.4114 | − | 23.1747i | 0.217300 | − | 0.0908813i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −222.112 | − | 222.112i | −0.864250 | − | 0.864250i | 0.127578 | − | 0.991829i | \(-0.459280\pi\) |
−0.991829 | + | 0.127578i | \(0.959280\pi\) | |||||||
\(258\) | 16.0955 | − | 16.0955i | 0.0623857 | − | 0.0623857i | ||||
\(259\) | − | 59.8000i | − | 0.230888i | ||||||
\(260\) | 158.881 | + | 65.1743i | 0.611081 | + | 0.250670i | ||||
\(261\) | 407.140 | 1.55992 | ||||||||
\(262\) | 57.9083 | + | 57.9083i | 0.221024 | + | 0.221024i | ||||
\(263\) | 191.483 | − | 191.483i | 0.728071 | − | 0.728071i | −0.242165 | − | 0.970235i | \(-0.577857\pi\) |
0.970235 | + | 0.242165i | \(0.0778574\pi\) | |||||||
\(264\) | − | 3.28492i | − | 0.0124429i | ||||||
\(265\) | 66.9926 | − | 163.314i | 0.252802 | − | 0.616278i | ||||
\(266\) | 226.785 | 0.852575 | ||||||||
\(267\) | −59.5557 | − | 59.5557i | −0.223055 | − | 0.223055i | ||||
\(268\) | 32.1376 | − | 32.1376i | 0.119917 | − | 0.119917i | ||||
\(269\) | 448.520i | 1.66736i | 0.552249 | + | 0.833679i | \(0.313770\pi\) | ||||
−0.552249 | + | 0.833679i | \(0.686230\pi\) | |||||||
\(270\) | 30.8162 | + | 73.6823i | 0.114134 | + | 0.272897i | ||||
\(271\) | −355.709 | −1.31258 | −0.656289 | − | 0.754509i | \(-0.727875\pi\) | ||||
−0.656289 | + | 0.754509i | \(0.727875\pi\) | |||||||
\(272\) | 52.9056 | + | 52.9056i | 0.194506 | + | 0.194506i | ||||
\(273\) | 90.5778 | − | 90.5778i | 0.331787 | − | 0.331787i | ||||
\(274\) | 181.972i | 0.664131i | ||||||||
\(275\) | −31.7493 | + | 32.1871i | −0.115452 | + | 0.117044i | ||||
\(276\) | 6.15985 | 0.0223183 | ||||||||
\(277\) | −74.7381 | − | 74.7381i | −0.269813 | − | 0.269813i | 0.559212 | − | 0.829025i | \(-0.311104\pi\) |
−0.829025 | + | 0.559212i | \(0.811104\pi\) | |||||||
\(278\) | 15.9583 | − | 15.9583i | 0.0574041 | − | 0.0574041i | ||||
\(279\) | − | 485.708i | − | 1.74089i | ||||||
\(280\) | −151.540 | + | 63.3787i | −0.541215 | + | 0.226353i | ||||
\(281\) | −29.5344 | −0.105105 | −0.0525523 | − | 0.998618i | \(-0.516736\pi\) | ||||
−0.0525523 | + | 0.998618i | \(0.516736\pi\) | |||||||
\(282\) | 8.11858 | + | 8.11858i | 0.0287893 | + | 0.0287893i | ||||
\(283\) | −337.330 | + | 337.330i | −1.19198 | + | 1.19198i | −0.215466 | + | 0.976511i | \(0.569127\pi\) |
−0.976511 | + | 0.215466i | \(0.930873\pi\) | |||||||
\(284\) | 220.810i | 0.777499i | ||||||||
\(285\) | 41.0163 | + | 16.8252i | 0.143917 | + | 0.0590359i | ||||
\(286\) | 43.9200 | 0.153566 | ||||||||
\(287\) | 68.1800 | + | 68.1800i | 0.237561 | + | 0.237561i | ||||
\(288\) | −34.3503 | + | 34.3503i | −0.119272 | + | 0.119272i | ||||
\(289\) | 60.8752i | 0.210641i | ||||||||
\(290\) | −127.230 | + | 310.161i | −0.438725 | + | 1.06952i | ||||
\(291\) | −72.2147 | −0.248160 | ||||||||
\(292\) | −145.334 | − | 145.334i | −0.497719 | − | 0.497719i | ||||
\(293\) | −0.725430 | + | 0.725430i | −0.00247587 | + | 0.00247587i | −0.708344 | − | 0.705868i | \(-0.750557\pi\) |
0.705868 | + | 0.708344i | \(0.250557\pi\) | |||||||
\(294\) | 78.0220i | 0.265381i | ||||||||
\(295\) | 12.2688 | + | 29.3351i | 0.0415893 | + | 0.0994412i | ||||
\(296\) | 14.5623 | 0.0491969 | ||||||||
\(297\) | 14.4434 | + | 14.4434i | 0.0486311 | + | 0.0486311i | ||||
\(298\) | −273.895 | + | 273.895i | −0.919109 | + | 0.919109i | ||||
\(299\) | 82.3584i | 0.275446i | ||||||||
\(300\) | −32.1097 | + | 0.219872i | −0.107032 | + | 0.000732907i | ||||
\(301\) | −291.102 | −0.967116 | ||||||||
\(302\) | 67.1415 | + | 67.1415i | 0.222323 | + | 0.222323i | ||||
\(303\) | −48.3473 | + | 48.3473i | −0.159562 | + | 0.159562i | ||||
\(304\) | 55.2259i | 0.181664i | ||||||||
\(305\) | 456.523 | − | 190.932i | 1.49680 | − | 0.626006i | ||||
\(306\) | −227.165 | −0.742370 | ||||||||
\(307\) | 312.017 | + | 312.017i | 1.01634 | + | 1.01634i | 0.999864 | + | 0.0164770i | \(0.00524503\pi\) |
0.0164770 | + | 0.999864i | \(0.494755\pi\) | |||||||
\(308\) | −29.7054 | + | 29.7054i | −0.0964460 | + | 0.0964460i | ||||
\(309\) | − | 3.86836i | − | 0.0125190i | ||||||
\(310\) | 370.014 | + | 151.783i | 1.19359 | + | 0.489622i | ||||
\(311\) | −442.383 | −1.42245 | −0.711227 | − | 0.702962i | \(-0.751860\pi\) | ||||
−0.711227 | + | 0.702962i | \(0.751860\pi\) | |||||||
\(312\) | 22.0572 | + | 22.0572i | 0.0706961 | + | 0.0706961i | ||||
\(313\) | −345.560 | + | 345.560i | −1.10403 | + | 1.10403i | −0.110107 | + | 0.993920i | \(0.535119\pi\) |
−0.993920 | + | 0.110107i | \(0.964881\pi\) | |||||||
\(314\) | − | 41.4772i | − | 0.132093i | ||||||
\(315\) | 189.273 | − | 461.408i | 0.600867 | − | 1.46479i | ||||
\(316\) | −162.522 | −0.514310 | ||||||||
\(317\) | −446.526 | − | 446.526i | −1.40860 | − | 1.40860i | −0.767238 | − | 0.641363i | \(-0.778369\pi\) |
−0.641363 | − | 0.767238i | \(-0.721631\pi\) | |||||||
\(318\) | 22.6725 | − | 22.6725i | 0.0712973 | − | 0.0712973i | ||||
\(319\) | 85.7387i | 0.268773i | ||||||||
\(320\) | −15.4338 | − | 36.9026i | −0.0482305 | − | 0.115320i | ||||
\(321\) | 20.2621 | 0.0631219 | ||||||||
\(322\) | −55.7032 | − | 55.7032i | −0.172991 | − | 0.172991i | ||||
\(323\) | −182.610 | + | 182.610i | −0.565355 | + | 0.565355i | ||||
\(324\) | − | 140.069i | − | 0.432311i | ||||||
\(325\) | −2.93973 | − | 429.313i | −0.00904533 | − | 1.32096i | ||||
\(326\) | 10.2711 | 0.0315064 | ||||||||
\(327\) | −68.9301 | − | 68.9301i | −0.210795 | − | 0.210795i | ||||
\(328\) | −16.6029 | + | 16.6029i | −0.0506187 | + | 0.0506187i | ||||
\(329\) | − | 146.832i | − | 0.446297i | ||||||
\(330\) | −7.57637 | + | 3.16867i | −0.0229587 | + | 0.00960202i | ||||
\(331\) | 541.509 | 1.63598 | 0.817989 | − | 0.575234i | \(-0.195089\pi\) | ||||
0.817989 | + | 0.575234i | \(0.195089\pi\) | |||||||
\(332\) | 141.050 | + | 141.050i | 0.424850 | + | 0.424850i | ||||
\(333\) | −31.2637 | + | 31.2637i | −0.0938848 | + | 0.0938848i | ||||
\(334\) | 8.59336i | 0.0257286i | ||||||||
\(335\) | −105.123 | − | 43.1223i | −0.313800 | − | 0.128723i | ||||
\(336\) | −29.8368 | −0.0888001 | ||||||||
\(337\) | 50.2998 | + | 50.2998i | 0.149258 | + | 0.149258i | 0.777786 | − | 0.628529i | \(-0.216343\pi\) |
−0.628529 | + | 0.777786i | \(0.716343\pi\) | |||||||
\(338\) | −125.909 | + | 125.909i | −0.372512 | + | 0.372512i | ||||
\(339\) | 32.2107i | 0.0950169i | ||||||||
\(340\) | 70.9887 | − | 173.055i | 0.208790 | − | 0.508986i | ||||
\(341\) | 102.284 | 0.299953 | ||||||||
\(342\) | −118.564 | − | 118.564i | −0.346678 | − | 0.346678i | ||||
\(343\) | 303.113 | − | 303.113i | 0.883712 | − | 0.883712i | ||||
\(344\) | − | 70.8881i | − | 0.206070i | ||||||
\(345\) | −5.94185 | − | 14.2071i | −0.0172228 | − | 0.0411801i | ||||
\(346\) | 119.445 | 0.345217 | ||||||||
\(347\) | 286.439 | + | 286.439i | 0.825472 | + | 0.825472i | 0.986887 | − | 0.161414i | \(-0.0516056\pi\) |
−0.161414 | + | 0.986887i | \(0.551606\pi\) | |||||||
\(348\) | −43.0590 | + | 43.0590i | −0.123733 | + | 0.123733i | ||||
\(349\) | 240.906i | 0.690275i | 0.938552 | + | 0.345137i | \(0.112168\pi\) | ||||
−0.938552 | + | 0.345137i | \(0.887832\pi\) | |||||||
\(350\) | 292.355 | + | 288.378i | 0.835299 | + | 0.823937i | ||||
\(351\) | −193.966 | −0.552610 | ||||||||
\(352\) | −7.23375 | − | 7.23375i | −0.0205504 | − | 0.0205504i | ||||
\(353\) | 189.988 | − | 189.988i | 0.538209 | − | 0.538209i | −0.384794 | − | 0.923003i | \(-0.625727\pi\) |
0.923003 | + | 0.384794i | \(0.125727\pi\) | |||||||
\(354\) | 5.77581i | 0.0163158i | ||||||||
\(355\) | 509.278 | − | 212.995i | 1.43459 | − | 0.599987i | ||||
\(356\) | −262.297 | −0.736788 | ||||||||
\(357\) | −98.6584 | − | 98.6584i | −0.276354 | − | 0.276354i | ||||
\(358\) | −186.219 | + | 186.219i | −0.520166 | + | 0.520166i | ||||
\(359\) | − | 467.461i | − | 1.30212i | −0.759026 | − | 0.651060i | \(-0.774324\pi\) | ||
0.759026 | − | 0.651060i | \(-0.225676\pi\) | |||||||
\(360\) | 112.360 | + | 46.0912i | 0.312112 | + | 0.128031i | ||||
\(361\) | 170.382 | 0.471971 | ||||||||
\(362\) | −243.615 | − | 243.615i | −0.672970 | − | 0.672970i | ||||
\(363\) | 53.4622 | − | 53.4622i | 0.147279 | − | 0.147279i | ||||
\(364\) | − | 398.924i | − | 1.09595i | ||||||
\(365\) | −195.009 | + | 475.390i | −0.534271 | + | 1.30244i | ||||
\(366\) | 89.8850 | 0.245587 | ||||||||
\(367\) | 396.041 | + | 396.041i | 1.07913 | + | 1.07913i | 0.996587 | + | 0.0825436i | \(0.0263044\pi\) |
0.0825436 | + | 0.996587i | \(0.473696\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 71.2895i | − | 0.193196i | ||||||
\(370\) | −14.0469 | − | 33.5866i | −0.0379647 | − | 0.0907746i | ||||
\(371\) | −410.054 | −1.10527 | ||||||||
\(372\) | 51.3684 | + | 51.3684i | 0.138087 | + | 0.138087i | ||||
\(373\) | −61.2680 | + | 61.2680i | −0.164257 | + | 0.164257i | −0.784450 | − | 0.620192i | \(-0.787055\pi\) |
0.620192 | + | 0.784450i | \(0.287055\pi\) | |||||||
\(374\) | − | 47.8382i | − | 0.127910i | ||||||
\(375\) | 31.4804 | + | 73.8460i | 0.0839479 | + | 0.196923i | ||||
\(376\) | 35.7560 | 0.0950957 | ||||||||
\(377\) | −575.708 | − | 575.708i | −1.52708 | − | 1.52708i | ||||
\(378\) | 131.189 | − | 131.189i | 0.347062 | − | 0.347062i | ||||
\(379\) | − | 2.27599i | − | 0.00600525i | −0.999995 | − | 0.00300262i | \(-0.999044\pi\) | ||
0.999995 | − | 0.00300262i | \(-0.000955767\pi\) | |||||||
\(380\) | 127.373 | − | 53.2715i | 0.335193 | − | 0.140188i | ||||
\(381\) | 0.425202 | 0.00111602 | ||||||||
\(382\) | −325.057 | − | 325.057i | −0.850935 | − | 0.850935i | ||||
\(383\) | 455.092 | − | 455.092i | 1.18823 | − | 1.18823i | 0.210673 | − | 0.977557i | \(-0.432435\pi\) |
0.977557 | − | 0.210673i | \(-0.0675655\pi\) | |||||||
\(384\) | − | 7.26576i | − | 0.0189212i | ||||||
\(385\) | 97.1669 | + | 39.8586i | 0.252381 | + | 0.103529i | ||||
\(386\) | −379.332 | −0.982725 | ||||||||
\(387\) | 152.189 | + | 152.189i | 0.393254 | + | 0.393254i | ||||
\(388\) | −159.025 | + | 159.025i | −0.409857 | + | 0.409857i | ||||
\(389\) | − | 94.4517i | − | 0.242806i | −0.992603 | − | 0.121403i | \(-0.961261\pi\) | ||
0.992603 | − | 0.121403i | \(-0.0387394\pi\) | |||||||
\(390\) | 29.5963 | − | 72.1495i | 0.0758880 | − | 0.184999i | ||||
\(391\) | 89.7058 | 0.229427 | ||||||||
\(392\) | 171.813 | + | 171.813i | 0.438299 | + | 0.438299i | ||||
\(393\) | 26.2967 | − | 26.2967i | 0.0669128 | − | 0.0669128i | ||||
\(394\) | − | 59.3397i | − | 0.150608i | ||||||
\(395\) | 156.770 | + | 374.842i | 0.396887 | + | 0.948967i | ||||
\(396\) | 31.0602 | 0.0784347 | ||||||||
\(397\) | −166.649 | − | 166.649i | −0.419771 | − | 0.419771i | 0.465354 | − | 0.885125i | \(-0.345927\pi\) |
−0.885125 | + | 0.465354i | \(0.845927\pi\) | |||||||
\(398\) | −71.7477 | + | 71.7477i | −0.180271 | + | 0.180271i | ||||
\(399\) | − | 102.985i | − | 0.258108i | ||||||
\(400\) | −70.2248 | + | 71.1932i | −0.175562 | + | 0.177983i | ||||
\(401\) | −56.3098 | −0.140424 | −0.0702118 | − | 0.997532i | \(-0.522368\pi\) | ||||
−0.0702118 | + | 0.997532i | \(0.522368\pi\) | |||||||
\(402\) | −14.5940 | − | 14.5940i | −0.0363035 | − | 0.0363035i | ||||
\(403\) | −686.806 | + | 686.806i | −1.70423 | + | 1.70423i | ||||
\(404\) | 212.932i | 0.527060i | ||||||||
\(405\) | −323.056 | + | 135.112i | −0.797670 | + | 0.333610i | ||||
\(406\) | 778.762 | 1.91813 | ||||||||
\(407\) | −6.58374 | − | 6.58374i | −0.0161763 | − | 0.0161763i | ||||
\(408\) | 24.0250 | − | 24.0250i | 0.0588847 | − | 0.0588847i | ||||
\(409\) | − | 617.869i | − | 1.51068i | −0.655331 | − | 0.755342i | \(-0.727471\pi\) | ||
0.655331 | − | 0.755342i | \(-0.272529\pi\) | |||||||
\(410\) | 54.3086 | + | 22.2778i | 0.132460 | + | 0.0543361i | ||||
\(411\) | 82.6352 | 0.201059 | ||||||||
\(412\) | −8.51856 | − | 8.51856i | −0.0206761 | − | 0.0206761i | ||||
\(413\) | 52.2304 | − | 52.2304i | 0.126466 | − | 0.126466i | ||||
\(414\) | 58.2437i | 0.140685i | ||||||||
\(415\) | 189.261 | − | 461.378i | 0.456050 | − | 1.11175i | ||||
\(416\) | 97.1447 | 0.233521 | ||||||||
\(417\) | −7.24684 | − | 7.24684i | −0.0173785 | − | 0.0173785i | ||||
\(418\) | 24.9681 | − | 24.9681i | 0.0597324 | − | 0.0597324i | ||||
\(419\) | − | 327.397i | − | 0.781377i | −0.920523 | − | 0.390688i | \(-0.872237\pi\) | ||
0.920523 | − | 0.390688i | \(-0.127763\pi\) | |||||||
\(420\) | 28.7809 | + | 68.8159i | 0.0685260 | + | 0.163847i | ||||
\(421\) | 271.135 | 0.644026 | 0.322013 | − | 0.946735i | \(-0.395641\pi\) | ||||
0.322013 | + | 0.946735i | \(0.395641\pi\) | |||||||
\(422\) | −193.990 | − | 193.990i | −0.459693 | − | 0.459693i | ||||
\(423\) | −76.7642 | + | 76.7642i | −0.181476 | + | 0.181476i | ||||
\(424\) | − | 99.8549i | − | 0.235507i | ||||||
\(425\) | −467.613 | + | 3.20199i | −1.10027 | + | 0.00753410i | ||||
\(426\) | 100.272 | 0.235380 | ||||||||
\(427\) | −812.826 | − | 812.826i | −1.90357 | − | 1.90357i | ||||
\(428\) | 44.6194 | − | 44.6194i | 0.104251 | − | 0.104251i | ||||
\(429\) | − | 19.9445i | − | 0.0464907i | ||||||
\(430\) | −163.497 | + | 68.3795i | −0.380226 | + | 0.159022i | ||||
\(431\) | 148.281 | 0.344039 | 0.172019 | − | 0.985094i | \(-0.444971\pi\) | ||||
0.172019 | + | 0.985094i | \(0.444971\pi\) | |||||||
\(432\) | 31.9468 | + | 31.9468i | 0.0739508 | + | 0.0739508i | ||||
\(433\) | 437.637 | − | 437.637i | 1.01071 | − | 1.01071i | 0.0107659 | − | 0.999942i | \(-0.496573\pi\) |
0.999942 | − | 0.0107659i | \(-0.00342697\pi\) | |||||||
\(434\) | − | 929.044i | − | 2.14065i | ||||||
\(435\) | 140.847 | + | 57.7766i | 0.323786 | + | 0.132820i | ||||
\(436\) | −303.583 | −0.696292 | ||||||||
\(437\) | 46.8200 | + | 46.8200i | 0.107140 | + | 0.107140i | ||||
\(438\) | −65.9976 | + | 65.9976i | −0.150679 | + | 0.150679i | ||||
\(439\) | 387.950i | 0.883712i | 0.897086 | + | 0.441856i | \(0.145680\pi\) | ||||
−0.897086 | + | 0.441856i | \(0.854320\pi\) | |||||||
\(440\) | −9.70624 | + | 23.6617i | −0.0220596 | + | 0.0537767i | ||||
\(441\) | −737.728 | −1.67285 | ||||||||
\(442\) | 321.219 | + | 321.219i | 0.726739 | + | 0.726739i | ||||
\(443\) | 33.5070 | − | 33.5070i | 0.0756366 | − | 0.0756366i | −0.668276 | − | 0.743913i | \(-0.732968\pi\) |
0.743913 | + | 0.668276i | \(0.232968\pi\) | |||||||
\(444\) | − | 6.61288i | − | 0.0148939i | ||||||
\(445\) | 253.014 | + | 604.963i | 0.568571 | + | 1.35947i | ||||
\(446\) | 282.962 | 0.634445 | ||||||||
\(447\) | 124.378 | + | 124.378i | 0.278251 | + | 0.278251i | ||||
\(448\) | −65.7040 | + | 65.7040i | −0.146661 | + | 0.146661i | ||||
\(449\) | 90.3725i | 0.201275i | 0.994923 | + | 0.100638i | \(0.0320883\pi\) | ||||
−0.994923 | + | 0.100638i | \(0.967912\pi\) | |||||||
\(450\) | −2.07897 | − | 303.609i | −0.00461994 | − | 0.674687i | ||||
\(451\) | 15.0127 | 0.0332876 | ||||||||
\(452\) | 70.9316 | + | 70.9316i | 0.156928 | + | 0.156928i | ||||
\(453\) | 30.4896 | − | 30.4896i | 0.0673060 | − | 0.0673060i | ||||
\(454\) | 598.254i | 1.31774i | ||||||||
\(455\) | −920.083 | + | 384.807i | −2.02216 | + | 0.845729i | ||||
\(456\) | 25.0786 | 0.0549970 | ||||||||
\(457\) | −432.641 | − | 432.641i | −0.946698 | − | 0.946698i | 0.0519513 | − | 0.998650i | \(-0.483456\pi\) |
−0.998650 | + | 0.0519513i | \(0.983456\pi\) | |||||||
\(458\) | −30.5265 | + | 30.5265i | −0.0666518 | + | 0.0666518i | ||||
\(459\) | 211.270i | 0.460284i | ||||||||
\(460\) | −44.3703 | − | 18.2010i | −0.0964571 | − | 0.0395675i | ||||
\(461\) | 477.708 | 1.03624 | 0.518121 | − | 0.855307i | \(-0.326632\pi\) | ||||
0.518121 | + | 0.855307i | \(0.326632\pi\) | |||||||
\(462\) | 13.4895 | + | 13.4895i | 0.0291981 | + | 0.0291981i | ||||
\(463\) | −509.566 | + | 509.566i | −1.10058 | + | 1.10058i | −0.106234 | + | 0.994341i | \(0.533879\pi\) |
−0.994341 | + | 0.106234i | \(0.966121\pi\) | |||||||
\(464\) | 189.641i | 0.408710i | ||||||||
\(465\) | 68.9260 | − | 168.027i | 0.148228 | − | 0.361348i | ||||
\(466\) | 105.469 | 0.226329 | ||||||||
\(467\) | 508.548 | + | 508.548i | 1.08897 | + | 1.08897i | 0.995635 | + | 0.0933331i | \(0.0297522\pi\) |
0.0933331 | + | 0.995635i | \(0.470248\pi\) | |||||||
\(468\) | −208.559 | + | 208.559i | −0.445639 | + | 0.445639i | ||||
\(469\) | 263.946i | 0.562785i | ||||||||
\(470\) | −34.4906 | − | 82.4680i | −0.0733843 | − | 0.175464i | ||||
\(471\) | −18.8352 | −0.0399898 | ||||||||
\(472\) | 12.7190 | + | 12.7190i | 0.0269470 | + | 0.0269470i | ||||
\(473\) | −32.0492 | + | 32.0492i | −0.0677573 | + | 0.0677573i | ||||
\(474\) | 73.8028i | 0.155702i | ||||||||
\(475\) | −245.732 | − | 242.389i | −0.517330 | − | 0.510293i | ||||
\(476\) | −434.513 | −0.912843 | ||||||||
\(477\) | 214.378 | + | 214.378i | 0.449429 | + | 0.449429i | ||||
\(478\) | 128.388 | − | 128.388i | 0.268595 | − | 0.268595i | ||||
\(479\) | 213.247i | 0.445192i | 0.974911 | + | 0.222596i | \(0.0714531\pi\) | ||||
−0.974911 | + | 0.222596i | \(0.928547\pi\) | |||||||
\(480\) | −16.7578 | + | 7.00863i | −0.0349121 | + | 0.0146013i | ||||
\(481\) | 88.4155 | 0.183816 | ||||||||
\(482\) | −148.698 | − | 148.698i | −0.308503 | − | 0.308503i | ||||
\(483\) | −25.2954 | + | 25.2954i | −0.0523714 | + | 0.0523714i | ||||
\(484\) | − | 235.459i | − | 0.486486i | ||||||
\(485\) | 520.173 | + | 213.379i | 1.07252 | + | 0.439957i | ||||
\(486\) | −207.367 | −0.426681 | ||||||||
\(487\) | −444.728 | − | 444.728i | −0.913198 | − | 0.913198i | 0.0833241 | − | 0.996523i | \(-0.473446\pi\) |
−0.996523 | + | 0.0833241i | \(0.973446\pi\) | |||||||
\(488\) | 197.937 | − | 197.937i | 0.405608 | − | 0.405608i | ||||
\(489\) | − | 4.66421i | − | 0.00953826i | ||||||
\(490\) | 230.539 | − | 562.004i | 0.470487 | − | 1.14695i | ||||
\(491\) | 488.473 | 0.994854 | 0.497427 | − | 0.867506i | \(-0.334278\pi\) | ||||
0.497427 | + | 0.867506i | \(0.334278\pi\) | |||||||
\(492\) | 7.53956 | + | 7.53956i | 0.0153243 | + | 0.0153243i | ||||
\(493\) | −627.068 | + | 627.068i | −1.27194 | + | 1.27194i | ||||
\(494\) | 335.306i | 0.678757i | ||||||||
\(495\) | −29.9610 | − | 71.6374i | −0.0605272 | − | 0.144722i | ||||
\(496\) | 226.238 | 0.456124 | ||||||||
\(497\) | −906.755 | − | 906.755i | −1.82446 | − | 1.82446i | ||||
\(498\) | 64.0522 | − | 64.0522i | 0.128619 | − | 0.128619i | ||||
\(499\) | − | 727.731i | − | 1.45838i | −0.684312 | − | 0.729189i | \(-0.739897\pi\) | ||
0.684312 | − | 0.729189i | \(-0.260103\pi\) | |||||||
\(500\) | 231.940 | + | 93.2935i | 0.463881 | + | 0.186587i | ||||
\(501\) | 3.90233 | 0.00778909 | ||||||||
\(502\) | −410.299 | − | 410.299i | −0.817329 | − | 0.817329i | ||||
\(503\) | 146.384 | − | 146.384i | 0.291021 | − | 0.291021i | −0.546463 | − | 0.837484i | \(-0.684026\pi\) |
0.837484 | + | 0.546463i | \(0.184026\pi\) | |||||||
\(504\) | − | 282.119i | − | 0.559759i | ||||||
\(505\) | 491.109 | − | 205.397i | 0.972493 | − | 0.406726i | ||||
\(506\) | −12.2654 | −0.0242400 | ||||||||
\(507\) | 57.1766 | + | 57.1766i | 0.112774 | + | 0.112774i | ||||
\(508\) | 0.936342 | − | 0.936342i | 0.00184319 | − | 0.00184319i | ||||
\(509\) | 629.870i | 1.23747i | 0.785601 | + | 0.618733i | \(0.212354\pi\) | ||||
−0.785601 | + | 0.618733i | \(0.787646\pi\) | |||||||
\(510\) | −78.5861 | − | 32.2367i | −0.154090 | − | 0.0632091i | ||||
\(511\) | 1193.63 | 2.33587 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −110.268 | + | 110.268i | −0.214947 | + | 0.214947i | ||||
\(514\) | 444.225i | 0.864250i | ||||||||
\(515\) | −11.4302 | + | 27.8644i | −0.0221946 | + | 0.0541056i | ||||
\(516\) | −32.1910 | −0.0623857 | ||||||||
\(517\) | −16.1656 | − | 16.1656i | −0.0312681 | − | 0.0312681i | ||||
\(518\) | −59.8000 | + | 59.8000i | −0.115444 | + | 0.115444i | ||||
\(519\) | − | 54.2412i | − | 0.104511i | ||||||
\(520\) | −93.7068 | − | 224.055i | −0.180205 | − | 0.430876i | ||||
\(521\) | −299.772 | −0.575379 | −0.287690 | − | 0.957724i | \(-0.592887\pi\) | ||||
−0.287690 | + | 0.957724i | \(0.592887\pi\) | |||||||
\(522\) | −407.140 | − | 407.140i | −0.779961 | − | 0.779961i | ||||
\(523\) | 189.039 | − | 189.039i | 0.361451 | − | 0.361451i | −0.502896 | − | 0.864347i | \(-0.667732\pi\) |
0.864347 | + | 0.502896i | \(0.167732\pi\) | |||||||
\(524\) | − | 115.817i | − | 0.221024i | ||||||
\(525\) | 130.955 | − | 132.761i | 0.249439 | − | 0.252878i | ||||
\(526\) | −382.965 | −0.728071 | ||||||||
\(527\) | 748.077 | + | 748.077i | 1.41950 | + | 1.41950i | ||||
\(528\) | −3.28492 | + | 3.28492i | −0.00622143 | + | 0.00622143i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −230.306 | + | 96.3211i | −0.434540 | + | 0.181738i | ||||
\(531\) | −54.6125 | −0.102848 | ||||||||
\(532\) | −226.785 | − | 226.785i | −0.426287 | − | 0.426287i | ||||
\(533\) | −100.806 | + | 100.806i | −0.189129 | + | 0.189129i | ||||
\(534\) | 119.111i | 0.223055i | ||||||||
\(535\) | −145.951 | − | 59.8703i | −0.272806 | − | 0.111907i | ||||
\(536\) | −64.2753 | −0.119917 | ||||||||
\(537\) | 84.5641 | + | 84.5641i | 0.157475 | + | 0.157475i | ||||
\(538\) | 448.520 | − | 448.520i | 0.833679 | − | 0.833679i | ||||
\(539\) | − | 155.357i | − | 0.288231i | ||||||
\(540\) | 42.8661 | − | 104.499i | 0.0793817 | − | 0.193516i | ||||
\(541\) | −428.185 | −0.791470 | −0.395735 | − | 0.918365i | \(-0.629510\pi\) | ||||
−0.395735 | + | 0.918365i | \(0.629510\pi\) | |||||||
\(542\) | 355.709 | + | 355.709i | 0.656289 | + | 0.656289i | ||||
\(543\) | −110.628 | + | 110.628i | −0.203735 | + | 0.203735i | ||||
\(544\) | − | 105.811i | − | 0.194506i | ||||||
\(545\) | 292.840 | + | 700.187i | 0.537320 | + | 1.28475i | ||||
\(546\) | −181.156 | −0.331787 | ||||||||
\(547\) | 402.240 | + | 402.240i | 0.735356 | + | 0.735356i | 0.971676 | − | 0.236319i | \(-0.0759411\pi\) |
−0.236319 | + | 0.971676i | \(0.575941\pi\) | |||||||
\(548\) | 181.972 | − | 181.972i | 0.332065 | − | 0.332065i | ||||
\(549\) | 849.897i | 1.54808i | ||||||||
\(550\) | 63.9364 | − | 0.437807i | 0.116248 | − | 0.000796012i | ||||
\(551\) | −654.570 | −1.18797 | ||||||||
\(552\) | −6.15985 | − | 6.15985i | −0.0111591 | − | 0.0111591i | ||||
\(553\) | 667.395 | − | 667.395i | 1.20686 | − | 1.20686i | ||||
\(554\) | 149.476i | 0.269813i | ||||||||
\(555\) | −15.2520 | + | 6.37885i | −0.0274811 | + | 0.0114934i | ||||
\(556\) | −31.9167 | −0.0574041 | ||||||||
\(557\) | −133.006 | − | 133.006i | −0.238789 | − | 0.238789i | 0.577560 | − | 0.816349i | \(-0.304005\pi\) |
−0.816349 | + | 0.577560i | \(0.804005\pi\) | |||||||
\(558\) | −485.708 | + | 485.708i | −0.870444 | + | 0.870444i | ||||
\(559\) | − | 430.400i | − | 0.769947i | ||||||
\(560\) | 214.919 | + | 88.1615i | 0.383784 | + | 0.157431i | ||||
\(561\) | −21.7238 | −0.0387234 | ||||||||
\(562\) | 29.5344 | + | 29.5344i | 0.0525523 | + | 0.0525523i | ||||
\(563\) | −490.785 | + | 490.785i | −0.871733 | + | 0.871733i | −0.992661 | − | 0.120929i | \(-0.961413\pi\) |
0.120929 | + | 0.992661i | \(0.461413\pi\) | |||||||
\(564\) | − | 16.2372i | − | 0.0287893i | ||||||
\(565\) | 95.1760 | − | 232.019i | 0.168453 | − | 0.410653i | ||||
\(566\) | 674.659 | 1.19198 | ||||||||
\(567\) | 575.192 | + | 575.192i | 1.01445 | + | 1.01445i | ||||
\(568\) | 220.810 | − | 220.810i | 0.388750 | − | 0.388750i | ||||
\(569\) | − | 258.800i | − | 0.454834i | −0.973798 | − | 0.227417i | \(-0.926972\pi\) | ||
0.973798 | − | 0.227417i | \(-0.0730280\pi\) | |||||||
\(570\) | −24.1911 | − | 57.8416i | −0.0424405 | − | 0.101476i | ||||
\(571\) | −122.892 | −0.215223 | −0.107612 | − | 0.994193i | \(-0.534320\pi\) | ||||
−0.107612 | + | 0.994193i | \(0.534320\pi\) | |||||||
\(572\) | −43.9200 | − | 43.9200i | −0.0767832 | − | 0.0767832i | ||||
\(573\) | −147.612 | + | 147.612i | −0.257612 | + | 0.257612i | ||||
\(574\) | − | 136.360i | − | 0.237561i | ||||||
\(575\) | 0.820971 | + | 119.893i | 0.00142778 | + | 0.208510i | ||||
\(576\) | 68.7005 | 0.119272 | ||||||||
\(577\) | −86.1991 | − | 86.1991i | −0.149392 | − | 0.149392i | 0.628454 | − | 0.777846i | \(-0.283688\pi\) |
−0.777846 | + | 0.628454i | \(0.783688\pi\) | |||||||
\(578\) | 60.8752 | − | 60.8752i | 0.105320 | − | 0.105320i | ||||
\(579\) | 172.258i | 0.297510i | ||||||||
\(580\) | 437.391 | − | 182.930i | 0.754122 | − | 0.315397i | ||||
\(581\) | −1158.44 | −1.99388 | ||||||||
\(582\) | 72.2147 | + | 72.2147i | 0.124080 | + | 0.124080i | ||||
\(583\) | −45.1453 | + | 45.1453i | −0.0774362 | + | 0.0774362i | ||||
\(584\) | 290.668i | 0.497719i | ||||||||
\(585\) | 682.201 | + | 279.844i | 1.16616 | + | 0.478367i | ||||
\(586\) | 1.45086 | 0.00247587 | ||||||||
\(587\) | 41.7886 | + | 41.7886i | 0.0711901 | + | 0.0711901i | 0.741805 | − | 0.670615i | \(-0.233970\pi\) |
−0.670615 | + | 0.741805i | \(0.733970\pi\) | |||||||
\(588\) | 78.0220 | − | 78.0220i | 0.132691 | − | 0.132691i | ||||
\(589\) | 780.885i | 1.32578i | ||||||||
\(590\) | 17.0663 | − | 41.6040i | 0.0289259 | − | 0.0705152i | ||||
\(591\) | −26.9467 | −0.0455952 | ||||||||
\(592\) | −14.5623 | − | 14.5623i | −0.0245985 | − | 0.0245985i | ||||
\(593\) | 0.797812 | − | 0.797812i | 0.00134538 | − | 0.00134538i | −0.706434 | − | 0.707779i | \(-0.749697\pi\) |
0.707779 | + | 0.706434i | \(0.249697\pi\) | |||||||
\(594\) | − | 28.8869i | − | 0.0486311i | ||||||
\(595\) | 419.136 | + | 1002.17i | 0.704431 | + | 1.68431i | ||||
\(596\) | 547.789 | 0.919109 | ||||||||
\(597\) | 32.5814 | + | 32.5814i | 0.0545752 | + | 0.0545752i | ||||
\(598\) | 82.3584 | − | 82.3584i | 0.137723 | − | 0.137723i | ||||
\(599\) | 547.221i | 0.913558i | 0.889580 | + | 0.456779i | \(0.150997\pi\) | ||||
−0.889580 | + | 0.456779i | \(0.849003\pi\) | |||||||
\(600\) | 32.3295 | + | 31.8898i | 0.0538826 | + | 0.0531497i | ||||
\(601\) | −798.410 | −1.32847 | −0.664235 | − | 0.747524i | \(-0.731243\pi\) | ||||
−0.664235 | + | 0.747524i | \(0.731243\pi\) | |||||||
\(602\) | 291.102 | + | 291.102i | 0.483558 | + | 0.483558i | ||||
\(603\) | 137.992 | − | 137.992i | 0.228843 | − | 0.228843i | ||||
\(604\) | − | 134.283i | − | 0.222323i | ||||||
\(605\) | −543.065 | + | 227.126i | −0.897628 | + | 0.375416i | ||||
\(606\) | 96.6947 | 0.159562 | ||||||||
\(607\) | 431.327 | + | 431.327i | 0.710588 | + | 0.710588i | 0.966658 | − | 0.256070i | \(-0.0824279\pi\) |
−0.256070 | + | 0.966658i | \(0.582428\pi\) | |||||||
\(608\) | 55.2259 | − | 55.2259i | 0.0908320 | − | 0.0908320i | ||||
\(609\) | − | 353.644i | − | 0.580696i | ||||||
\(610\) | −647.454 | − | 265.591i | −1.06140 | − | 0.435395i | ||||
\(611\) | 217.094 | 0.355309 | ||||||||
\(612\) | 227.165 | + | 227.165i | 0.371185 | + | 0.371185i | ||||
\(613\) | −538.393 | + | 538.393i | −0.878293 | + | 0.878293i | −0.993358 | − | 0.115065i | \(-0.963292\pi\) |
0.115065 | + | 0.993358i | \(0.463292\pi\) | |||||||
\(614\) | − | 624.034i | − | 1.01634i | ||||||
\(615\) | 10.1166 | − | 24.6621i | 0.0164497 | − | 0.0401009i | ||||
\(616\) | 59.4107 | 0.0964460 | ||||||||
\(617\) | 535.160 | + | 535.160i | 0.867358 | + | 0.867358i | 0.992179 | − | 0.124821i | \(-0.0398358\pi\) |
−0.124821 | + | 0.992179i | \(0.539836\pi\) | |||||||
\(618\) | −3.86836 | + | 3.86836i | −0.00625949 | + | 0.00625949i | ||||
\(619\) | − | 103.368i | − | 0.166991i | −0.996508 | − | 0.0834957i | \(-0.973392\pi\) | ||
0.996508 | − | 0.0834957i | \(-0.0266085\pi\) | |||||||
\(620\) | −218.231 | − | 521.797i | −0.351986 | − | 0.841608i | ||||
\(621\) | 54.1684 | 0.0872276 | ||||||||
\(622\) | 442.383 | + | 442.383i | 0.711227 | + | 0.711227i | ||||
\(623\) | 1077.12 | − | 1077.12i | 1.72892 | − | 1.72892i | ||||
\(624\) | − | 44.1144i | − | 0.0706961i | ||||||
\(625\) | −8.55901 | − | 624.941i | −0.0136944 | − | 0.999906i | ||||
\(626\) | 691.121 | 1.10403 | ||||||||
\(627\) | −11.3383 | − | 11.3383i | −0.0180834 | − | 0.0180834i | ||||
\(628\) | −41.4772 | + | 41.4772i | −0.0660465 | + | 0.0660465i | ||||
\(629\) | − | 96.3033i | − | 0.153105i | ||||||
\(630\) | −650.681 | + | 272.135i | −1.03283 | + | 0.431960i | ||||
\(631\) | 914.802 | 1.44977 | 0.724883 | − | 0.688872i | \(-0.241894\pi\) | ||||
0.724883 | + | 0.688872i | \(0.241894\pi\) | |||||||
\(632\) | 162.522 | + | 162.522i | 0.257155 | + | 0.257155i | ||||
\(633\) | −88.0929 | + | 88.0929i | −0.139167 | + | 0.139167i | ||||
\(634\) | 893.053i | 1.40860i | ||||||||
\(635\) | −3.06279 | − | 1.25638i | −0.00482330 | − | 0.00197856i | ||||
\(636\) | −45.3451 | −0.0712973 | ||||||||
\(637\) | 1043.17 | + | 1043.17i | 1.63763 | + | 1.63763i | ||||
\(638\) | 85.7387 | − | 85.7387i | 0.134387 | − | 0.134387i | ||||
\(639\) | 948.110i | 1.48374i | ||||||||
\(640\) | −21.4688 | + | 52.3363i | −0.0335450 | + | 0.0817755i | ||||
\(641\) | 629.609 | 0.982230 | 0.491115 | − | 0.871095i | \(-0.336590\pi\) | ||||
0.491115 | + | 0.871095i | \(0.336590\pi\) | |||||||
\(642\) | −20.2621 | − | 20.2621i | −0.0315610 | − | 0.0315610i | ||||
\(643\) | 469.588 | − | 469.588i | 0.730307 | − | 0.730307i | −0.240373 | − | 0.970681i | \(-0.577270\pi\) |
0.970681 | + | 0.240373i | \(0.0772698\pi\) | |||||||
\(644\) | 111.406i | 0.172991i | ||||||||
\(645\) | 31.0518 | + | 74.2457i | 0.0481423 | + | 0.115110i | ||||
\(646\) | 365.220 | 0.565355 | ||||||||
\(647\) | −102.877 | − | 102.877i | −0.159007 | − | 0.159007i | 0.623120 | − | 0.782126i | \(-0.285865\pi\) |
−0.782126 | + | 0.623120i | \(0.785865\pi\) | |||||||
\(648\) | −140.069 | + | 140.069i | −0.216156 | + | 0.216156i | ||||
\(649\) | − | 11.5007i | − | 0.0177207i | ||||||
\(650\) | −426.373 | + | 432.253i | −0.655959 | + | 0.665004i | ||||
\(651\) | −421.888 | −0.648062 | ||||||||
\(652\) | −10.2711 | − | 10.2711i | −0.0157532 | − | 0.0157532i | ||||
\(653\) | 108.889 | − | 108.889i | 0.166752 | − | 0.166752i | −0.618798 | − | 0.785550i | \(-0.712380\pi\) |
0.785550 | + | 0.618798i | \(0.212380\pi\) | |||||||
\(654\) | 137.860i | 0.210795i | ||||||||
\(655\) | −267.120 | + | 111.718i | −0.407817 | + | 0.170562i | ||||
\(656\) | 33.2059 | 0.0506187 | ||||||||
\(657\) | −624.033 | − | 624.033i | −0.949822 | − | 0.949822i | ||||
\(658\) | −146.832 | + | 146.832i | −0.223149 | + | 0.223149i | ||||
\(659\) | − | 534.158i | − | 0.810558i | −0.914193 | − | 0.405279i | \(-0.867174\pi\) | ||
0.914193 | − | 0.405279i | \(-0.132826\pi\) | |||||||
\(660\) | 10.7450 | + | 4.40770i | 0.0162804 | + | 0.00667833i | ||||
\(661\) | −596.050 | −0.901740 | −0.450870 | − | 0.892590i | \(-0.648886\pi\) | ||||
−0.450870 | + | 0.892590i | \(0.648886\pi\) | |||||||
\(662\) | −541.509 | − | 541.509i | −0.817989 | − | 0.817989i | ||||
\(663\) | 145.869 | − | 145.869i | 0.220013 | − | 0.220013i | ||||
\(664\) | − | 282.100i | − | 0.424850i | ||||||
\(665\) | −304.300 | + | 741.818i | −0.457594 | + | 1.11552i | ||||
\(666\) | 62.5273 | 0.0938848 | ||||||||
\(667\) | 160.776 | + | 160.776i | 0.241044 | + | 0.241044i | ||||
\(668\) | 8.59336 | − | 8.59336i | 0.0128643 | − | 0.0128643i | ||||
\(669\) | − | 128.496i | − | 0.192072i | ||||||
\(670\) | 62.0006 | + | 148.245i | 0.0925382 | + | 0.221261i | ||||
\(671\) | −178.978 | −0.266733 | ||||||||
\(672\) | 29.8368 | + | 29.8368i | 0.0444000 | + | 0.0444000i | ||||
\(673\) | 159.122 | − | 159.122i | 0.236437 | − | 0.236437i | −0.578936 | − | 0.815373i | \(-0.696532\pi\) |
0.815373 | + | 0.578936i | \(0.196532\pi\) | |||||||
\(674\) | − | 100.600i | − | 0.149258i | ||||||
\(675\) | −282.366 | + | 1.93351i | −0.418319 | + | 0.00286445i | ||||
\(676\) | 251.818 | 0.372512 | ||||||||
\(677\) | −209.613 | − | 209.613i | −0.309621 | − | 0.309621i | 0.535142 | − | 0.844762i | \(-0.320258\pi\) |
−0.844762 | + | 0.535142i | \(0.820258\pi\) | |||||||
\(678\) | 32.2107 | − | 32.2107i | 0.0475085 | − | 0.0475085i | ||||
\(679\) | − | 1306.07i | − | 1.92352i | ||||||
\(680\) | −244.044 | + | 102.067i | −0.358888 | + | 0.150098i | ||||
\(681\) | 271.673 | 0.398933 | ||||||||
\(682\) | −102.284 | − | 102.284i | −0.149977 | − | 0.149977i | ||||
\(683\) | 17.8410 | − | 17.8410i | 0.0261215 | − | 0.0261215i | −0.693925 | − | 0.720047i | \(-0.744120\pi\) |
0.720047 | + | 0.693925i | \(0.244120\pi\) | |||||||
\(684\) | 237.128i | 0.346678i | ||||||||
\(685\) | −595.234 | − | 244.170i | −0.868954 | − | 0.356452i | ||||
\(686\) | −606.227 | −0.883712 | ||||||||
\(687\) | 13.8624 | + | 13.8624i | 0.0201782 | + | 0.0201782i | ||||
\(688\) | −70.8881 | + | 70.8881i | −0.103035 | + | 0.103035i | ||||
\(689\) | − | 606.273i | − | 0.879932i | ||||||
\(690\) | −8.26528 | + | 20.1490i | −0.0119787 | + | 0.0292014i | ||||
\(691\) | 1004.98 | 1.45438 | 0.727190 | − | 0.686436i | \(-0.240826\pi\) | ||||
0.727190 | + | 0.686436i | \(0.240826\pi\) | |||||||
\(692\) | −119.445 | − | 119.445i | −0.172608 | − | 0.172608i | ||||
\(693\) | −127.548 | + | 127.548i | −0.184053 | + | 0.184053i | ||||
\(694\) | − | 572.878i | − | 0.825472i | ||||||
\(695\) | 30.7872 | + | 73.6130i | 0.0442981 | + | 0.105918i | ||||
\(696\) | 86.1181 | 0.123733 | ||||||||
\(697\) | 109.799 | + | 109.799i | 0.157530 | + | 0.157530i | ||||
\(698\) | 240.906 | − | 240.906i | 0.345137 | − | 0.345137i | ||||
\(699\) | − | 47.8946i | − | 0.0685188i | ||||||
\(700\) | −3.97659 | − | 580.733i | −0.00568084 | − | 0.829618i | ||||
\(701\) | −243.834 | −0.347838 | −0.173919 | − | 0.984760i | \(-0.555643\pi\) | ||||
−0.173919 | + | 0.984760i | \(0.555643\pi\) | |||||||
\(702\) | 193.966 | + | 193.966i | 0.276305 | + | 0.276305i | ||||
\(703\) | 50.2634 | − | 50.2634i | 0.0714985 | − | 0.0714985i | ||||
\(704\) | 14.4675i | 0.0205504i | ||||||||
\(705\) | −37.4495 | + | 15.6625i | −0.0531199 | + | 0.0222164i | ||||
\(706\) | −379.976 | −0.538209 | ||||||||
\(707\) | −874.406 | − | 874.406i | −1.23678 | − | 1.23678i | ||||
\(708\) | 5.77581 | − | 5.77581i | 0.00815792 | − | 0.00815792i | ||||
\(709\) | − | 57.7605i | − | 0.0814675i | −0.999170 | − | 0.0407338i | \(-0.987030\pi\) | ||
0.999170 | − | 0.0407338i | \(-0.0129695\pi\) | |||||||
\(710\) | −722.273 | − | 296.282i | −1.01729 | − | 0.417299i | ||||
\(711\) | −697.834 | −0.981482 | ||||||||
\(712\) | 262.297 | + | 262.297i | 0.368394 | + | 0.368394i | ||||
\(713\) | 191.802 | − | 191.802i | 0.269007 | − | 0.269007i | ||||
\(714\) | 197.317i | 0.276354i | ||||||||
\(715\) | −58.9318 | + | 143.663i | −0.0824221 | + | 0.200928i | ||||
\(716\) | 372.439 | 0.520166 | ||||||||
\(717\) | −58.3024 | − | 58.3024i | −0.0813144 | − | 0.0813144i | ||||
\(718\) | −467.461 | + | 467.461i | −0.651060 | + | 0.651060i | ||||
\(719\) | − | 24.2148i | − | 0.0336784i | −0.999858 | − | 0.0168392i | \(-0.994640\pi\) | ||
0.999858 | − | 0.0168392i | \(-0.00536033\pi\) | |||||||
\(720\) | −66.2693 | − | 158.452i | −0.0920407 | − | 0.220072i | ||||
\(721\) | 69.9629 | 0.0970359 | ||||||||
\(722\) | −170.382 | − | 170.382i | −0.235985 | − | 0.235985i | ||||
\(723\) | −67.5255 | + | 67.5255i | −0.0933962 | + | 0.0933962i | ||||
\(724\) | 487.230i | 0.672970i | ||||||||
\(725\) | −843.824 | − | 832.346i | −1.16390 | − | 1.14806i | ||||
\(726\) | −106.924 | −0.147279 | ||||||||
\(727\) | 554.026 | + | 554.026i | 0.762072 | + | 0.762072i | 0.976697 | − | 0.214625i | \(-0.0688529\pi\) |
−0.214625 | + | 0.976697i | \(0.568853\pi\) | |||||||
\(728\) | −398.924 | + | 398.924i | −0.547973 | + | 0.547973i | ||||
\(729\) | − | 536.143i | − | 0.735449i | ||||||
\(730\) | 670.399 | − | 280.381i | 0.918355 | − | 0.384084i | ||||
\(731\) | −468.797 | −0.641310 | ||||||||
\(732\) | −89.8850 | − | 89.8850i | −0.122794 | − | 0.122794i | ||||
\(733\) | 259.853 | − | 259.853i | 0.354507 | − | 0.354507i | −0.507277 | − | 0.861783i | \(-0.669348\pi\) |
0.861783 | + | 0.507277i | \(0.169348\pi\) | |||||||
\(734\) | − | 792.082i | − | 1.07913i | ||||||
\(735\) | −255.212 | − | 104.690i | −0.347227 | − | 0.142435i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | 29.0594 | + | 29.0594i | 0.0394294 | + | 0.0394294i | ||||
\(738\) | −71.2895 | + | 71.2895i | −0.0965982 | + | 0.0965982i | ||||
\(739\) | − | 1082.77i | − | 1.46518i | −0.680668 | − | 0.732592i | \(-0.738310\pi\) | ||
0.680668 | − | 0.732592i | \(-0.261690\pi\) | |||||||
\(740\) | −19.5397 | + | 47.6335i | −0.0264049 | + | 0.0643696i | ||||
\(741\) | 152.266 | 0.205487 | ||||||||
\(742\) | 410.054 | + | 410.054i | 0.552633 | + | 0.552633i | ||||
\(743\) | −477.140 | + | 477.140i | −0.642181 | + | 0.642181i | −0.951091 | − | 0.308910i | \(-0.900036\pi\) |
0.308910 | + | 0.951091i | \(0.400036\pi\) | |||||||
\(744\) | − | 102.737i | − | 0.138087i | ||||||
\(745\) | −528.403 | − | 1263.43i | −0.709266 | − | 1.69587i | ||||
\(746\) | 122.536 | 0.164257 | ||||||||
\(747\) | 605.639 | + | 605.639i | 0.810761 | + | 0.810761i | ||||
\(748\) | −47.8382 | + | 47.8382i | −0.0639548 | + | 0.0639548i | ||||
\(749\) | 366.459i | 0.489265i | ||||||||
\(750\) | 42.3655 | − | 105.326i | 0.0564874 | − | 0.140435i | ||||
\(751\) | 904.489 | 1.20438 | 0.602190 | − | 0.798353i | \(-0.294295\pi\) | ||||
0.602190 | + | 0.798353i | \(0.294295\pi\) | |||||||
\(752\) | −35.7560 | − | 35.7560i | −0.0475479 | − | 0.0475479i | ||||
\(753\) | −186.321 | + | 186.321i | −0.247438 | + | 0.247438i | ||||
\(754\) | 1151.42i | 1.52708i | ||||||||
\(755\) | −309.712 | + | 129.531i | −0.410214 | + | 0.171564i | ||||
\(756\) | −262.379 | −0.347062 | ||||||||
\(757\) | 290.718 | + | 290.718i | 0.384040 | + | 0.384040i | 0.872555 | − | 0.488515i | \(-0.162461\pi\) |
−0.488515 | + | 0.872555i | \(0.662461\pi\) | |||||||
\(758\) | −2.27599 | + | 2.27599i | −0.00300262 | + | 0.00300262i | ||||
\(759\) | 5.56985i | 0.00733840i | ||||||||
\(760\) | −180.645 | − | 74.1020i | −0.237691 | − | 0.0975026i | ||||
\(761\) | −492.010 | −0.646531 | −0.323266 | − | 0.946308i | \(-0.604781\pi\) | ||||
−0.323266 | + | 0.946308i | \(0.604781\pi\) | |||||||
\(762\) | −0.425202 | − | 0.425202i | −0.000558008 | − | 0.000558008i | ||||
\(763\) | 1246.66 | − | 1246.66i | 1.63390 | − | 1.63390i | ||||
\(764\) | 650.114i | 0.850935i | ||||||||
\(765\) | 304.810 | − | 743.062i | 0.398445 | − | 0.971323i | ||||
\(766\) | −910.184 | −1.18823 | ||||||||
\(767\) | 77.2237 | + | 77.2237i | 0.100683 | + | 0.100683i | ||||
\(768\) | −7.26576 | + | 7.26576i | −0.00946062 | + | 0.00946062i | ||||
\(769\) | 1181.65i | 1.53661i | 0.640086 | + | 0.768304i | \(0.278899\pi\) | ||||
−0.640086 | + | 0.768304i | \(0.721101\pi\) | |||||||
\(770\) | −57.3082 | − | 137.026i | −0.0744263 | − | 0.177955i | ||||
\(771\) | 201.727 | 0.261643 | ||||||||
\(772\) | 379.332 | + | 379.332i | 0.491362 | + | 0.491362i | ||||
\(773\) | 60.7545 | − | 60.7545i | 0.0785957 | − | 0.0785957i | −0.666716 | − | 0.745312i | \(-0.732301\pi\) |
0.745312 | + | 0.666716i | \(0.232301\pi\) | |||||||
\(774\) | − | 304.378i | − | 0.393254i | ||||||
\(775\) | −992.969 | + | 1006.66i | −1.28125 | + | 1.29892i | ||||
\(776\) | 318.049 | 0.409857 | ||||||||
\(777\) | 27.1558 | + | 27.1558i | 0.0349495 | + | 0.0349495i | ||||
\(778\) | −94.4517 | + | 94.4517i | −0.121403 | + | 0.121403i | ||||
\(779\) | 114.614i | 0.147130i | ||||||||
\(780\) | −101.746 | + | 42.5532i | −0.130443 | + | 0.0545554i | ||||
\(781\) | −199.660 | −0.255647 | ||||||||
\(782\) | −89.7058 | − | 89.7058i | −0.114713 | − | 0.114713i | ||||
\(783\) | −378.652 | + | 378.652i | −0.483591 | + | 0.483591i | ||||
\(784\) | − | 343.626i | − | 0.438299i | ||||||
\(785\) | 135.673 | + | 55.6541i | 0.172832 | + | 0.0708969i | ||||
\(786\) | −52.5934 | −0.0669128 | ||||||||
\(787\) | −364.615 | − | 364.615i | −0.463297 | − | 0.463297i | 0.436437 | − | 0.899735i | \(-0.356240\pi\) |
−0.899735 | + | 0.436437i | \(0.856240\pi\) | |||||||
\(788\) | −59.3397 | + | 59.3397i | −0.0753042 | + | 0.0753042i | ||||
\(789\) | 173.908i | 0.220416i | ||||||||
\(790\) | 218.072 | − | 531.612i | 0.276040 | − | 0.672927i | ||||
\(791\) | −582.561 | −0.736487 | ||||||||
\(792\) | −31.0602 | − | 31.0602i | −0.0392174 | − | 0.0392174i | ||||
\(793\) | 1201.78 | − | 1201.78i | 1.51549 | − | 1.51549i | ||||
\(794\) | 333.298i | 0.419771i | ||||||||
\(795\) | 43.7404 | + | 104.584i | 0.0550193 | + | 0.131553i | ||||
\(796\) | 143.495 | 0.180271 | ||||||||
\(797\) | 130.697 | + | 130.697i | 0.163986 | + | 0.163986i | 0.784330 | − | 0.620344i | \(-0.213007\pi\) |
−0.620344 | + | 0.784330i | \(0.713007\pi\) | |||||||
\(798\) | −102.985 | + | 102.985i | −0.129054 | + | 0.129054i | ||||
\(799\) | − | 236.461i | − | 0.295947i | ||||||
\(800\) | 141.418 | − | 0.968365i | 0.176773 | − | 0.00121046i | ||||
\(801\) | −1126.24 | −1.40605 | ||||||||
\(802\) | 56.3098 | + | 56.3098i | 0.0702118 | + | 0.0702118i | ||||
\(803\) | 131.414 | − | 131.414i | 0.163653 | − | 0.163653i | ||||
\(804\) | 29.1880i | 0.0363035i | ||||||||
\(805\) | 256.949 | − | 107.464i | 0.319191 | − | 0.133496i | ||||
\(806\) | 1373.61 | 1.70423 | ||||||||
\(807\) | −203.677 | − | 203.677i | −0.252388 | − | 0.252388i | ||||
\(808\) | 212.932 | − | 212.932i | 0.263530 | − | 0.263530i | ||||
\(809\) | 183.753i | 0.227135i | 0.993530 | + | 0.113568i | \(0.0362279\pi\) | ||||
−0.993530 | + | 0.113568i | \(0.963772\pi\) | |||||||
\(810\) | 458.168 | + | 187.944i | 0.565640 | + | 0.232030i | ||||
\(811\) | −1246.28 | −1.53672 | −0.768360 | − | 0.640018i | \(-0.778927\pi\) | ||||
−0.768360 | + | 0.640018i | \(0.778927\pi\) | |||||||
\(812\) | −778.762 | − | 778.762i | −0.959067 | − | 0.959067i | ||||
\(813\) | 161.531 | − | 161.531i | 0.198685 | − | 0.198685i | ||||
\(814\) | 13.1675i | 0.0161763i | ||||||||
\(815\) | −13.7818 | + | 33.5970i | −0.0169101 | + | 0.0412233i | ||||
\(816\) | −48.0499 | −0.0588847 | ||||||||
\(817\) | −244.679 | − | 244.679i | −0.299484 | − | 0.299484i | ||||
\(818\) | −617.869 | + | 617.869i | −0.755342 | + | 0.755342i | ||||
\(819\) | − | 1712.90i | − | 2.09145i | ||||||
\(820\) | −32.0308 | − | 76.5864i | −0.0390619 | − | 0.0933981i | ||||
\(821\) | −50.3398 | −0.0613152 | −0.0306576 | − | 0.999530i | \(-0.509760\pi\) | ||||
−0.0306576 | + | 0.999530i | \(0.509760\pi\) | |||||||
\(822\) | −82.6352 | − | 82.6352i | −0.100529 | − | 0.100529i | ||||
\(823\) | −43.2603 | + | 43.2603i | −0.0525642 | + | 0.0525642i | −0.732900 | − | 0.680336i | \(-0.761834\pi\) |
0.680336 | + | 0.732900i | \(0.261834\pi\) | |||||||
\(824\) | 17.0371i | 0.0206761i | ||||||||
\(825\) | −0.198812 | − | 29.0342i | −0.000240985 | − | 0.0351929i | ||||
\(826\) | −104.461 | −0.126466 | ||||||||
\(827\) | −412.757 | − | 412.757i | −0.499102 | − | 0.499102i | 0.412057 | − | 0.911158i | \(-0.364811\pi\) |
−0.911158 | + | 0.412057i | \(0.864811\pi\) | |||||||
\(828\) | 58.2437 | − | 58.2437i | 0.0703427 | − | 0.0703427i | ||||
\(829\) | − | 375.863i | − | 0.453393i | −0.973965 | − | 0.226697i | \(-0.927207\pi\) | ||
0.973965 | − | 0.226697i | \(-0.0727926\pi\) | |||||||
\(830\) | −650.639 | + | 272.117i | −0.783902 | + | 0.327852i | ||||
\(831\) | 67.8787 | 0.0816831 | ||||||||
\(832\) | −97.1447 | − | 97.1447i | −0.116760 | − | 0.116760i | ||||
\(833\) | 1136.23 | − | 1136.23i | 1.36403 | − | 1.36403i | ||||
\(834\) | 14.4937i | 0.0173785i | ||||||||
\(835\) | −28.1091 | − | 11.5306i | −0.0336636 | − | 0.0138091i | ||||
\(836\) | −49.9362 | −0.0597324 | ||||||||
\(837\) | 451.722 | + | 451.722i | 0.539692 | + | 0.539692i | ||||
\(838\) | −327.397 | + | 327.397i | −0.390688 | + | 0.390688i | ||||
\(839\) | − | 21.1937i | − | 0.0252607i | −0.999920 | − | 0.0126304i | \(-0.995980\pi\) | ||
0.999920 | − | 0.0126304i | \(-0.00402047\pi\) | |||||||
\(840\) | 40.0350 | − | 97.5969i | 0.0476607 | − | 0.116187i | ||||
\(841\) | −1406.74 | −1.67270 | ||||||||
\(842\) | −271.135 | − | 271.135i | −0.322013 | − | 0.322013i | ||||
\(843\) | 13.4119 | − | 13.4119i | 0.0159097 | − | 0.0159097i | ||||
\(844\) | 387.981i | 0.459693i | ||||||||
\(845\) | −242.906 | − | 580.796i | −0.287463 | − | 0.687332i | ||||
\(846\) | 153.528 | 0.181476 | ||||||||
\(847\) | 966.912 | + | 966.912i | 1.14157 | + | 1.14157i | ||||
\(848\) | −99.8549 | + | 99.8549i | −0.117753 | + | 0.117753i | ||||
\(849\) | − | 306.370i | − | 0.360859i | ||||||
\(850\) | 470.815 | + | 464.411i | 0.553900 | + | 0.546366i | ||||
\(851\) | −24.6916 | −0.0290148 | ||||||||
\(852\) | −100.272 | − | 100.272i | −0.117690 | − | 0.117690i | ||||
\(853\) | −53.9548 | + | 53.9548i | −0.0632530 | + | 0.0632530i | −0.738026 | − | 0.674773i | \(-0.764242\pi\) |
0.674773 | + | 0.738026i | \(0.264242\pi\) | |||||||
\(854\) | 1625.65i | 1.90357i | ||||||||
\(855\) | 546.914 | − | 228.736i | 0.639666 | − | 0.267528i | ||||
\(856\) | −89.2389 | −0.104251 | ||||||||
\(857\) | −568.035 | − | 568.035i | −0.662818 | − | 0.662818i | 0.293225 | − | 0.956043i | \(-0.405271\pi\) |
−0.956043 | + | 0.293225i | \(0.905271\pi\) | |||||||
\(858\) | −19.9445 | + | 19.9445i | −0.0232454 | + | 0.0232454i | ||||
\(859\) | − | 1184.25i | − | 1.37864i | −0.724457 | − | 0.689320i | \(-0.757909\pi\) | ||
0.724457 | − | 0.689320i | \(-0.242091\pi\) | |||||||
\(860\) | 231.877 | + | 95.1176i | 0.269624 | + | 0.110602i | ||||
\(861\) | −61.9224 | −0.0719192 | ||||||||
\(862\) | −148.281 | − | 148.281i | −0.172019 | − | 0.172019i | ||||
\(863\) | 781.788 | − | 781.788i | 0.905896 | − | 0.905896i | −0.0900420 | − | 0.995938i | \(-0.528700\pi\) |
0.995938 | + | 0.0900420i | \(0.0287001\pi\) | |||||||
\(864\) | − | 63.8935i | − | 0.0739508i | ||||||
\(865\) | −160.271 | + | 390.707i | −0.185285 | + | 0.451685i | ||||
\(866\) | −875.273 | −1.01071 | ||||||||
\(867\) | −27.6440 | − | 27.6440i | −0.0318847 | − | 0.0318847i | ||||
\(868\) | −929.044 | + | 929.044i | −1.07033 | + | 1.07033i | ||||
\(869\) | − | 146.955i | − | 0.169108i | ||||||
\(870\) | −83.0704 | − | 198.624i | −0.0954833 | − | 0.228303i | ||||
\(871\) | −390.250 | −0.448048 | ||||||||
\(872\) | 303.583 | + | 303.583i | 0.348146 | + | 0.348146i | ||||
\(873\) | −682.818 | + | 682.818i | −0.782151 | + | 0.782151i | ||||
\(874\) | − | 93.6400i | − | 0.107140i | ||||||
\(875\) | −1335.57 | + | 569.353i | −1.52637 | + | 0.650689i | ||||
\(876\) | 131.995 | 0.150679 | ||||||||
\(877\) | −314.824 | − | 314.824i | −0.358978 | − | 0.358978i | 0.504458 | − | 0.863436i | \(-0.331692\pi\) |
−0.863436 | + | 0.504458i | \(0.831692\pi\) | |||||||
\(878\) | 387.950 | − | 387.950i | 0.441856 | − | 0.441856i | ||||
\(879\) | − | 0.658850i | − | 0.000749545i | ||||||
\(880\) | 33.3680 | − | 13.9555i | 0.0379182 | − | 0.0158585i | ||||
\(881\) | −654.884 | −0.743342 | −0.371671 | − | 0.928365i | \(-0.621215\pi\) | ||||
−0.371671 | + | 0.928365i | \(0.621215\pi\) | |||||||
\(882\) | 737.728 | + | 737.728i | 0.836427 | + | 0.836427i | ||||
\(883\) | −899.338 | + | 899.338i | −1.01850 | + | 1.01850i | −0.0186775 | + | 0.999826i | \(0.505946\pi\) |
−0.999826 | + | 0.0186775i | \(0.994054\pi\) | |||||||
\(884\) | − | 642.437i | − | 0.726739i | ||||||
\(885\) | −18.8928 | − | 7.74997i | −0.0213478 | − | 0.00875703i | ||||
\(886\) | −67.0140 | −0.0756366 | ||||||||
\(887\) | −79.8383 | − | 79.8383i | −0.0900094 | − | 0.0900094i | 0.660668 | − | 0.750678i | \(-0.270273\pi\) |
−0.750678 | + | 0.660668i | \(0.770273\pi\) | |||||||
\(888\) | −6.61288 | + | 6.61288i | −0.00744693 | + | 0.00744693i | ||||
\(889\) | 7.69017i | 0.00865036i | ||||||||
\(890\) | 351.949 | − | 857.977i | 0.395449 | − | 0.964019i | ||||
\(891\) | 126.653 | 0.142147 | ||||||||
\(892\) | −282.962 | − | 282.962i | −0.317222 | − | 0.317222i | ||||
\(893\) | 123.416 | − | 123.416i | 0.138204 | − | 0.138204i | ||||
\(894\) | − | 248.756i | − | 0.278251i | ||||||
\(895\) | −359.258 | − | 858.996i | −0.401406 | − | 0.959772i | ||||
\(896\) | 131.408 | 0.146661 | ||||||||
\(897\) | −37.3998 | − | 37.3998i | −0.0416943 | − | 0.0416943i | ||||
\(898\) | 90.3725 | − | 90.3725i | 0.100638 | − | 0.100638i | ||||
\(899\) | 2681.50i | 2.98276i | ||||||||
\(900\) | −301.530 | + | 305.688i | −0.335034 | + | 0.339654i | ||||
\(901\) | −660.360 | −0.732919 | ||||||||
\(902\) | −15.0127 | − | 15.0127i | −0.0166438 | − | 0.0166438i | ||||
\(903\) | 132.192 | − | 132.192i | 0.146392 | − | 0.146392i | ||||
\(904\) | − | 141.863i | − | 0.156928i | ||||||
\(905\) | 1123.75 | − | 469.987i | 1.24172 | − | 0.519323i | ||||
\(906\) | −60.9792 | −0.0673060 | ||||||||
\(907\) | 399.844 | + | 399.844i | 0.440842 | + | 0.440842i | 0.892295 | − | 0.451453i | \(-0.149094\pi\) |
−0.451453 | + | 0.892295i | \(0.649094\pi\) | |||||||
\(908\) | 598.254 | − | 598.254i | 0.658870 | − | 0.658870i | ||||
\(909\) | 914.285i | 1.00581i | ||||||||
\(910\) | 1304.89 | + | 535.276i | 1.43394 | + | 0.588216i | ||||
\(911\) | 375.905 | 0.412629 | 0.206315 | − | 0.978486i | \(-0.433853\pi\) | ||||
0.206315 | + | 0.978486i | \(0.433853\pi\) | |||||||
\(912\) | −25.0786 | − | 25.0786i | −0.0274985 | − | 0.0274985i | ||||
\(913\) | −127.540 | + | 127.540i | −0.139693 | + | 0.139693i | ||||
\(914\) | 865.282i | 0.946698i | ||||||||
\(915\) | −120.608 | + | 294.016i | −0.131812 | + | 0.321328i | ||||
\(916\) | 61.0530 | 0.0666518 | ||||||||
\(917\) | 475.600 | + | 475.600i | 0.518648 | + | 0.518648i | ||||
\(918\) | 211.270 | − | 211.270i | 0.230142 | − | 0.230142i | ||||
\(919\) | 218.112i | 0.237336i | 0.992934 | + | 0.118668i | \(0.0378624\pi\) | ||||
−0.992934 | + | 0.118668i | \(0.962138\pi\) | |||||||
\(920\) | 26.1692 | + | 62.5713i | 0.0284448 | + | 0.0680123i | ||||
\(921\) | −283.380 | −0.307687 | ||||||||
\(922\) | −477.708 | − | 477.708i | −0.518121 | − | 0.518121i | ||||
\(923\) | 1340.66 | − | 1340.66i | 1.45250 | − | 1.45250i | ||||
\(924\) | − | 26.9790i | − | 0.0291981i | ||||||
\(925\) | 128.711 | − | 0.881350i | 0.139147 | − | 0.000952811i | ||||
\(926\) | 1019.13 | 1.10058 | ||||||||
\(927\) | −36.5769 | − | 36.5769i | −0.0394573 | − | 0.0394573i | ||||
\(928\) | 189.641 | − | 189.641i | 0.204355 | − | 0.204355i | ||||
\(929\) | 1273.70i | 1.37104i | 0.728052 | + | 0.685522i | \(0.240426\pi\) | ||||
−0.728052 | + | 0.685522i | \(0.759574\pi\) | |||||||
\(930\) | −236.953 | + | 99.1010i | −0.254788 | + | 0.106560i | ||||
\(931\) | 1186.07 | 1.27397 | ||||||||
\(932\) | −105.469 | − | 105.469i | −0.113164 | − | 0.113164i | ||||
\(933\) | 200.891 | − | 200.891i | 0.215317 | − | 0.215317i | ||||
\(934\) | − | 1017.10i | − | 1.08897i | ||||||
\(935\) | 156.480 | + | 64.1893i | 0.167358 | + | 0.0686516i | ||||
\(936\) | 417.118 | 0.445639 | ||||||||
\(937\) | 636.364 | + | 636.364i | 0.679151 | + | 0.679151i | 0.959808 | − | 0.280657i | \(-0.0905525\pi\) |
−0.280657 | + | 0.959808i | \(0.590552\pi\) | |||||||
\(938\) | 263.946 | − | 263.946i | 0.281393 | − | 0.281393i | ||||
\(939\) | − | 313.845i | − | 0.334233i | ||||||
\(940\) | −47.9774 | + | 116.959i | −0.0510397 | + | 0.124424i | ||||
\(941\) | 1561.91 | 1.65984 | 0.829921 | − | 0.557881i | \(-0.188386\pi\) | ||||
0.829921 | + | 0.557881i | \(0.188386\pi\) | |||||||
\(942\) | 18.8352 | + | 18.8352i | 0.0199949 | + | 0.0199949i | ||||
\(943\) | 28.1517 | − | 28.1517i | 0.0298533 | − | 0.0298533i | ||||
\(944\) | − | 25.4379i | − | 0.0269470i | ||||||
\(945\) | 253.093 | + | 605.152i | 0.267823 | + | 0.640373i | ||||
\(946\) | 64.0984 | 0.0677573 | ||||||||
\(947\) | 689.902 | + | 689.902i | 0.728513 | + | 0.728513i | 0.970324 | − | 0.241810i | \(-0.0777411\pi\) |
−0.241810 | + | 0.970324i | \(0.577741\pi\) | |||||||
\(948\) | 73.8028 | − | 73.8028i | 0.0778510 | − | 0.0778510i | ||||
\(949\) | 1764.80i | 1.85964i | ||||||||
\(950\) | 3.34242 | + | 488.121i | 0.00351834 | + | 0.513811i | ||||
\(951\) | 405.544 | 0.426440 | ||||||||
\(952\) | 434.513 | + | 434.513i | 0.456422 | + | 0.456422i | ||||
\(953\) | 1126.44 | − | 1126.44i | 1.18200 | − | 1.18200i | 0.202771 | − | 0.979226i | \(-0.435005\pi\) |
0.979226 | − | 0.202771i | \(-0.0649946\pi\) | |||||||
\(954\) | − | 428.755i | − | 0.449429i | ||||||
\(955\) | 1499.43 | − | 627.107i | 1.57008 | − | 0.656657i | ||||
\(956\) | −256.777 | −0.268595 | ||||||||
\(957\) | −38.9348 | − | 38.9348i | −0.0406842 | − | 0.0406842i | ||||
\(958\) | 213.247 | − | 213.247i | 0.222596 | − | 0.222596i | ||||
\(959\) | 1494.53i | 1.55843i | ||||||||
\(960\) | 23.7664 | + | 9.74919i | 0.0247567 | + | 0.0101554i | ||||
\(961\) | 2237.97 | 2.32879 | ||||||||
\(962\) | −88.4155 | − | 88.4155i | −0.0919080 | − | 0.0919080i | ||||
\(963\) | 191.586 | − | 191.586i | 0.198947 | − | 0.198947i | ||||
\(964\) | 297.397i | 0.308503i | ||||||||
\(965\) | 508.987 | − | 1240.80i | 0.527448 | − | 1.28581i | ||||
\(966\) | 50.5908 | 0.0523714 | ||||||||
\(967\) | −823.547 | − | 823.547i | −0.851651 | − | 0.851651i | 0.138685 | − | 0.990337i | \(-0.455712\pi\) |
−0.990337 | + | 0.138685i | \(0.955712\pi\) | |||||||
\(968\) | −235.459 | + | 235.459i | −0.243243 | + | 0.243243i | ||||
\(969\) | − | 165.850i | − | 0.171156i | ||||||
\(970\) | −306.794 | − | 733.552i | −0.316282 | − | 0.756239i | ||||
\(971\) | −1767.79 | −1.82059 | −0.910294 | − | 0.413963i | \(-0.864144\pi\) | ||||
−0.910294 | + | 0.413963i | \(0.864144\pi\) | |||||||
\(972\) | 207.367 | + | 207.367i | 0.213341 | + | 0.213341i | ||||
\(973\) | 131.066 | − | 131.066i | 0.134703 | − | 0.134703i | ||||
\(974\) | 889.455i | 0.913198i | ||||||||
\(975\) | 196.290 | + | 193.620i | 0.201323 | + | 0.198585i | ||||
\(976\) | −395.873 | −0.405608 | ||||||||
\(977\) | −355.445 | − | 355.445i | −0.363813 | − | 0.363813i | 0.501402 | − | 0.865215i | \(-0.332818\pi\) |
−0.865215 | + | 0.501402i | \(0.832818\pi\) | |||||||
\(978\) | −4.66421 | + | 4.66421i | −0.00476913 | + | 0.00476913i | ||||
\(979\) | − | 237.173i | − | 0.242261i | ||||||
\(980\) | −792.543 | + | 331.466i | −0.808717 | + | 0.338230i | ||||
\(981\) | −1303.52 | −1.32877 | ||||||||
\(982\) | −488.473 | − | 488.473i | −0.497427 | − | 0.497427i | ||||
\(983\) | −874.521 | + | 874.521i | −0.889644 | + | 0.889644i | −0.994489 | − | 0.104844i | \(-0.966566\pi\) |
0.104844 | + | 0.994489i | \(0.466566\pi\) | |||||||
\(984\) | − | 15.0791i | − | 0.0153243i | ||||||
\(985\) | 194.101 | + | 79.6219i | 0.197057 | + | 0.0808344i | ||||
\(986\) | 1254.14 | 1.27194 | ||||||||
\(987\) | 66.6778 | + | 66.6778i | 0.0675560 | + | 0.0675560i | ||||
\(988\) | 335.306 | − | 335.306i | 0.339379 | − | 0.339379i | ||||
\(989\) | 120.197i | 0.121534i | ||||||||
\(990\) | −41.6765 | + | 101.598i | −0.0420975 | + | 0.102625i | ||||
\(991\) | 1547.23 | 1.56128 | 0.780639 | − | 0.624982i | \(-0.214894\pi\) | ||||
0.780639 | + | 0.624982i | \(0.214894\pi\) | |||||||
\(992\) | −226.238 | − | 226.238i | −0.228062 | − | 0.228062i | ||||
\(993\) | −245.905 | + | 245.905i | −0.247638 | + | 0.247638i | ||||
\(994\) | 1813.51i | 1.82446i | ||||||||
\(995\) | −138.417 | − | 330.959i | −0.139113 | − | 0.332623i | ||||
\(996\) | −128.104 | −0.128619 | ||||||||
\(997\) | 58.7774 | + | 58.7774i | 0.0589543 | + | 0.0589543i | 0.735969 | − | 0.677015i | \(-0.236727\pi\) |
−0.677015 | + | 0.735969i | \(0.736727\pi\) | |||||||
\(998\) | −727.731 | + | 727.731i | −0.729189 | + | 0.729189i | ||||
\(999\) | − | 58.1522i | − | 0.0582104i |
(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 | 230.3.f.a.47.4 | ✓ | 20 | |
5.3 | odd | 4 | inner | 230.3.f.a.93.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.a.47.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
230.3.f.a.93.4 | yes | 20 | 5.3 | odd | 4 | inner |