Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 245.4 | ||
Root | \(2.91048 + 0.945671i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.245 |
Dual form | 363.3.h.n.323.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.79877 | + | 2.47580i | 0.899386 | + | 1.23790i | 0.970663 | + | 0.240443i | \(0.0772926\pi\) |
−0.0712771 | + | 0.997457i | \(0.522707\pi\) | |||||||
\(3\) | −2.81156 | + | 1.04648i | −0.937188 | + | 0.348825i | ||||
\(4\) | −1.65793 | + | 5.10257i | −0.414481 | + | 1.27564i | ||||
\(5\) | 3.90250 | − | 5.37133i | 0.780499 | − | 1.07427i | −0.214727 | − | 0.976674i | \(-0.568886\pi\) |
0.995227 | − | 0.0975910i | \(-0.0311137\pi\) | |||||||
\(6\) | −7.64823 | − | 5.07849i | −1.27470 | − | 0.846415i | ||||
\(7\) | 0.946512 | − | 2.91306i | 0.135216 | − | 0.416152i | −0.860408 | − | 0.509607i | \(-0.829791\pi\) |
0.995624 | + | 0.0934546i | \(0.0297910\pi\) | |||||||
\(8\) | −3.97326 | + | 1.29099i | −0.496658 | + | 0.161374i | ||||
\(9\) | 6.80977 | − | 5.88447i | 0.756642 | − | 0.653830i | ||||
\(10\) | 20.3180 | 2.03180 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.678356 | − | 16.0812i | −0.0565297 | − | 1.34010i | ||||
\(13\) | 13.1422 | − | 9.54837i | 1.01094 | − | 0.734490i | 0.0465330 | − | 0.998917i | \(-0.485183\pi\) |
0.964406 | + | 0.264427i | \(0.0851827\pi\) | |||||||
\(14\) | 8.91472 | − | 2.89657i | 0.636765 | − | 0.206898i | ||||
\(15\) | −5.35115 | + | 19.1857i | −0.356743 | + | 1.27905i | ||||
\(16\) | 7.01879 | + | 5.09945i | 0.438674 | + | 0.318716i | ||||
\(17\) | 0.473548 | − | 0.651783i | 0.0278557 | − | 0.0383401i | −0.794862 | − | 0.606790i | \(-0.792457\pi\) |
0.822718 | + | 0.568450i | \(0.192457\pi\) | |||||||
\(18\) | 26.8180 | + | 6.27481i | 1.48989 | + | 0.348600i | ||||
\(19\) | −6.39720 | − | 19.6886i | −0.336695 | − | 1.03624i | −0.965881 | − | 0.258986i | \(-0.916612\pi\) |
0.629186 | − | 0.777255i | \(-0.283388\pi\) | |||||||
\(20\) | 20.9375 | + | 28.8180i | 1.04688 | + | 1.44090i | ||||
\(21\) | 0.387274 | + | 9.18076i | 0.0184416 | + | 0.437179i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 27.3224i | 1.18793i | 0.804491 | + | 0.593965i | \(0.202438\pi\) | ||||
−0.804491 | + | 0.593965i | \(0.797562\pi\) | |||||||
\(24\) | 9.82009 | − | 7.78763i | 0.409170 | − | 0.324485i | ||||
\(25\) | −5.89623 | − | 18.1467i | −0.235849 | − | 0.725870i | ||||
\(26\) | 47.2797 | + | 15.3621i | 1.81845 | + | 0.590850i | ||||
\(27\) | −12.9882 | + | 23.6708i | −0.481043 | + | 0.876697i | ||||
\(28\) | 13.2949 | + | 9.65928i | 0.474817 | + | 0.344974i | ||||
\(29\) | 3.59755 | + | 1.16891i | 0.124053 | + | 0.0403074i | 0.370386 | − | 0.928878i | \(-0.379226\pi\) |
−0.246332 | + | 0.969185i | \(0.579226\pi\) | |||||||
\(30\) | −57.1254 | + | 21.2623i | −1.90418 | + | 0.708744i | ||||
\(31\) | 16.8114 | − | 12.2142i | 0.542302 | − | 0.394006i | −0.282637 | − | 0.959227i | \(-0.591209\pi\) |
0.824939 | + | 0.565221i | \(0.191209\pi\) | |||||||
\(32\) | 43.2608i | 1.35190i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.46549 | 0.0725143 | ||||||||
\(35\) | −11.9533 | − | 16.4522i | −0.341522 | − | 0.470064i | ||||
\(36\) | 18.7358 | + | 44.5034i | 0.520439 | + | 1.23620i | ||||
\(37\) | 11.9137 | − | 36.6667i | 0.321993 | − | 0.990991i | −0.650787 | − | 0.759260i | \(-0.725561\pi\) |
0.972780 | − | 0.231731i | \(-0.0744390\pi\) | |||||||
\(38\) | 37.2378 | − | 51.2534i | 0.979942 | − | 1.34877i | ||||
\(39\) | −26.9580 | + | 40.5988i | −0.691231 | + | 1.04100i | ||||
\(40\) | −8.57131 | + | 26.3798i | −0.214283 | + | 0.659494i | ||||
\(41\) | −12.7181 | + | 4.13237i | −0.310199 | + | 0.100790i | −0.459979 | − | 0.887930i | \(-0.652143\pi\) |
0.149781 | + | 0.988719i | \(0.452143\pi\) | |||||||
\(42\) | −22.0331 | + | 17.4729i | −0.524598 | + | 0.416022i | ||||
\(43\) | −43.4125 | −1.00959 | −0.504797 | − | 0.863238i | \(-0.668433\pi\) | ||||
−0.504797 | + | 0.863238i | \(0.668433\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.03227 | − | 59.5416i | −0.111828 | − | 1.32315i | ||||
\(46\) | −67.6447 | + | 49.1468i | −1.47054 | + | 1.06841i | ||||
\(47\) | −18.9168 | + | 6.14644i | −0.402485 | + | 0.130775i | −0.503262 | − | 0.864134i | \(-0.667867\pi\) |
0.100777 | + | 0.994909i | \(0.467867\pi\) | |||||||
\(48\) | −25.0702 | − | 6.99243i | −0.522296 | − | 0.145676i | ||||
\(49\) | 32.0518 | + | 23.2870i | 0.654118 | + | 0.475244i | ||||
\(50\) | 34.3217 | − | 47.2397i | 0.686434 | − | 0.944795i | ||||
\(51\) | −0.649334 | + | 2.32808i | −0.0127320 | + | 0.0456487i | ||||
\(52\) | 26.9324 | + | 82.8895i | 0.517931 | + | 1.59403i | ||||
\(53\) | 10.3894 | + | 14.2997i | 0.196026 | + | 0.269806i | 0.895703 | − | 0.444653i | \(-0.146673\pi\) |
−0.699677 | + | 0.714459i | \(0.746673\pi\) | |||||||
\(54\) | −81.9669 | + | 10.4224i | −1.51791 | + | 0.193007i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.7963i | 0.228505i | ||||||||
\(57\) | 38.5898 | + | 48.6611i | 0.677013 | + | 0.853704i | ||||
\(58\) | 3.57717 | + | 11.0094i | 0.0616754 | + | 0.189817i | ||||
\(59\) | 41.3952 | + | 13.4501i | 0.701614 | + | 0.227968i | 0.638034 | − | 0.770009i | \(-0.279748\pi\) |
0.0635803 | + | 0.997977i | \(0.479748\pi\) | |||||||
\(60\) | −89.0245 | − | 59.1131i | −1.48374 | − | 0.985218i | ||||
\(61\) | 8.61986 | + | 6.26270i | 0.141309 | + | 0.102667i | 0.656194 | − | 0.754592i | \(-0.272165\pi\) |
−0.514885 | + | 0.857259i | \(0.672165\pi\) | |||||||
\(62\) | 60.4797 | + | 19.6510i | 0.975479 | + | 0.316952i | ||||
\(63\) | −10.6963 | − | 25.4070i | −0.169783 | − | 0.403286i | ||||
\(64\) | −79.0299 | + | 57.4185i | −1.23484 | + | 0.897165i | ||||
\(65\) | − | 107.854i | − | 1.65929i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 72.2963 | 1.07905 | 0.539525 | − | 0.841970i | \(-0.318604\pi\) | ||||
0.539525 | + | 0.841970i | \(0.318604\pi\) | |||||||
\(68\) | 2.54066 | + | 3.49692i | 0.0373626 | + | 0.0514253i | ||||
\(69\) | −28.5922 | − | 76.8186i | −0.414380 | − | 1.11331i | ||||
\(70\) | 19.2312 | − | 59.1877i | 0.274732 | − | 0.845538i | ||||
\(71\) | 1.51055 | − | 2.07909i | 0.0212753 | − | 0.0292830i | −0.798247 | − | 0.602330i | \(-0.794239\pi\) |
0.819522 | + | 0.573047i | \(0.194239\pi\) | |||||||
\(72\) | −19.4602 | + | 32.1719i | −0.270281 | + | 0.446832i | ||||
\(73\) | 14.0537 | − | 43.2529i | 0.192517 | − | 0.592505i | −0.807480 | − | 0.589895i | \(-0.799169\pi\) |
0.999997 | − | 0.00261035i | \(-0.000830900\pi\) | |||||||
\(74\) | 112.209 | − | 36.4590i | 1.51634 | − | 0.492690i | ||||
\(75\) | 35.5678 | + | 44.8504i | 0.474237 | + | 0.598006i | ||||
\(76\) | 111.068 | 1.46143 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −149.006 | + | 6.28555i | −1.91033 | + | 0.0805840i | ||||
\(79\) | −79.4797 | + | 57.7454i | −1.00607 | + | 0.730954i | −0.963381 | − | 0.268135i | \(-0.913593\pi\) |
−0.0426901 | + | 0.999088i | \(0.513593\pi\) | |||||||
\(80\) | 54.7816 | − | 17.7996i | 0.684770 | − | 0.222495i | ||||
\(81\) | 11.7461 | − | 80.1438i | 0.145013 | − | 0.989430i | ||||
\(82\) | −33.1080 | − | 24.0543i | −0.403756 | − | 0.293346i | ||||
\(83\) | 18.7507 | − | 25.8081i | 0.225912 | − | 0.310941i | −0.680982 | − | 0.732300i | \(-0.738447\pi\) |
0.906894 | + | 0.421359i | \(0.138447\pi\) | |||||||
\(84\) | −47.4876 | − | 13.2449i | −0.565328 | − | 0.157678i | ||||
\(85\) | −1.65292 | − | 5.08716i | −0.0194461 | − | 0.0598489i | ||||
\(86\) | −78.0893 | − | 107.481i | −0.908015 | − | 1.24978i | ||||
\(87\) | −11.3380 | + | 0.478272i | −0.130321 | + | 0.00549738i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.5409i | 0.208325i | 0.994560 | + | 0.104162i | \(0.0332161\pi\) | ||||
−0.994560 | + | 0.104162i | \(0.966784\pi\) | |||||||
\(90\) | 138.361 | − | 119.561i | 1.53735 | − | 1.32845i | ||||
\(91\) | −15.3758 | − | 47.3217i | −0.168964 | − | 0.520019i | ||||
\(92\) | −139.414 | − | 45.2985i | −1.51537 | − | 0.492375i | ||||
\(93\) | −34.4844 | + | 51.9336i | −0.370800 | + | 0.558426i | ||||
\(94\) | −49.2443 | − | 35.7781i | −0.523876 | − | 0.380618i | ||||
\(95\) | −130.719 | − | 42.4731i | −1.37599 | − | 0.447085i | ||||
\(96\) | −45.2714 | − | 121.630i | −0.471577 | − | 1.26698i | ||||
\(97\) | 51.2123 | − | 37.2079i | 0.527962 | − | 0.383587i | −0.291633 | − | 0.956530i | \(-0.594199\pi\) |
0.819595 | + | 0.572943i | \(0.194199\pi\) | |||||||
\(98\) | 121.242i | 1.23716i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 102.371 | 1.02371 | ||||||||
\(101\) | −88.3786 | − | 121.643i | −0.875036 | − | 1.20438i | −0.977771 | − | 0.209675i | \(-0.932759\pi\) |
0.102735 | − | 0.994709i | \(-0.467241\pi\) | |||||||
\(102\) | −6.93187 | + | 2.58007i | −0.0679595 | + | 0.0252948i | ||||
\(103\) | −46.2807 | + | 142.437i | −0.449327 | + | 1.38289i | 0.428341 | + | 0.903617i | \(0.359098\pi\) |
−0.877668 | + | 0.479269i | \(0.840902\pi\) | |||||||
\(104\) | −39.8906 | + | 54.9047i | −0.383563 | + | 0.527929i | ||||
\(105\) | 50.8242 | + | 33.7477i | 0.484040 | + | 0.321407i | ||||
\(106\) | −16.7152 | + | 51.4440i | −0.157690 | + | 0.485320i | ||||
\(107\) | −19.7358 | + | 6.41256i | −0.184447 | + | 0.0599305i | −0.399784 | − | 0.916609i | \(-0.630915\pi\) |
0.215337 | + | 0.976540i | \(0.430915\pi\) | |||||||
\(108\) | −99.2486 | − | 105.517i | −0.918969 | − | 0.977013i | ||||
\(109\) | 105.794 | 0.970583 | 0.485291 | − | 0.874352i | \(-0.338714\pi\) | ||||
0.485291 | + | 0.874352i | \(0.338714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.87462 | + | 115.558i | 0.0439155 | + | 1.04106i | ||||
\(112\) | 21.4984 | − | 15.6195i | 0.191950 | − | 0.139460i | ||||
\(113\) | −126.271 | + | 41.0279i | −1.11744 | + | 0.363078i | −0.808790 | − | 0.588097i | \(-0.799877\pi\) |
−0.308650 | + | 0.951176i | \(0.599877\pi\) | |||||||
\(114\) | −51.0609 | + | 183.071i | −0.447903 | + | 1.60588i | ||||
\(115\) | 146.757 | + | 106.626i | 1.27615 | + | 0.927179i | ||||
\(116\) | −11.9289 | + | 16.4188i | −0.102836 | + | 0.141541i | ||||
\(117\) | 33.3084 | − | 142.357i | 0.284687 | − | 1.21673i | ||||
\(118\) | 41.1608 | + | 126.680i | 0.348820 | + | 1.07356i | ||||
\(119\) | −1.45047 | − | 1.99639i | −0.0121888 | − | 0.0167764i | ||||
\(120\) | −3.50703 | − | 83.1381i | −0.0292253 | − | 0.692817i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 32.6062i | 0.267264i | ||||||||
\(123\) | 31.4334 | − | 24.9277i | 0.255556 | − | 0.202664i | ||||
\(124\) | 34.4517 | + | 106.031i | 0.277836 | + | 0.855092i | ||||
\(125\) | 37.3772 | + | 12.1446i | 0.299018 | + | 0.0971568i | ||||
\(126\) | 43.6625 | − | 72.1833i | 0.346527 | − | 0.572884i | ||||
\(127\) | −118.647 | − | 86.2019i | −0.934226 | − | 0.678755i | 0.0127976 | − | 0.999918i | \(-0.495926\pi\) |
−0.947024 | + | 0.321163i | \(0.895926\pi\) | |||||||
\(128\) | −119.740 | − | 38.9058i | −0.935466 | − | 0.303951i | ||||
\(129\) | 122.057 | − | 45.4302i | 0.946179 | − | 0.352172i | ||||
\(130\) | 267.024 | − | 194.004i | 2.05403 | − | 1.49234i | ||||
\(131\) | − | 149.467i | − | 1.14097i | −0.821309 | − | 0.570484i | \(-0.806756\pi\) | ||
0.821309 | − | 0.570484i | \(-0.193244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −63.4091 | −0.476760 | ||||||||
\(134\) | 130.045 | + | 178.991i | 0.970482 | + | 1.33575i | ||||
\(135\) | 76.4575 | + | 162.139i | 0.566352 | + | 1.20103i | ||||
\(136\) | −1.04008 | + | 3.20105i | −0.00764768 | + | 0.0235371i | ||||
\(137\) | −89.4650 | + | 123.138i | −0.653029 | + | 0.898817i | −0.999226 | − | 0.0393446i | \(-0.987473\pi\) |
0.346197 | + | 0.938162i | \(0.387473\pi\) | |||||||
\(138\) | 138.757 | − | 208.968i | 1.00548 | − | 1.51426i | ||||
\(139\) | −34.5591 | + | 106.362i | −0.248627 | + | 0.765194i | 0.746392 | + | 0.665506i | \(0.231784\pi\) |
−0.995019 | + | 0.0996878i | \(0.968216\pi\) | |||||||
\(140\) | 103.766 | − | 33.7157i | 0.741188 | − | 0.240827i | ||||
\(141\) | 46.7536 | − | 37.0771i | 0.331586 | − | 0.262958i | ||||
\(142\) | 7.86454 | 0.0553841 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 77.8039 | − | 6.57574i | 0.540305 | − | 0.0456649i | ||||
\(145\) | 20.3180 | − | 14.7619i | 0.140124 | − | 0.101806i | ||||
\(146\) | 132.365 | − | 43.0080i | 0.906609 | − | 0.294575i | ||||
\(147\) | −114.485 | − | 31.9314i | −0.778809 | − | 0.217220i | ||||
\(148\) | 167.342 | + | 121.581i | 1.13069 | + | 0.821495i | ||||
\(149\) | −152.645 | + | 210.098i | −1.02446 | + | 1.41005i | −0.115437 | + | 0.993315i | \(0.536827\pi\) |
−0.909026 | + | 0.416739i | \(0.863173\pi\) | |||||||
\(150\) | −47.0623 | + | 168.734i | −0.313749 | + | 1.12490i | ||||
\(151\) | −27.1990 | − | 83.7098i | −0.180126 | − | 0.554370i | 0.819705 | − | 0.572786i | \(-0.194137\pi\) |
−0.999830 | + | 0.0184166i | \(0.994137\pi\) | |||||||
\(152\) | 50.8355 | + | 69.9691i | 0.334444 | + | 0.460323i | ||||
\(153\) | −0.610640 | − | 7.22507i | −0.00399111 | − | 0.0472227i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 137.965i | − | 0.890098i | ||||||
\(156\) | −162.464 | − | 204.865i | −1.04144 | − | 1.31324i | ||||
\(157\) | −2.36562 | − | 7.28062i | −0.0150676 | − | 0.0463734i | 0.943240 | − | 0.332112i | \(-0.107761\pi\) |
−0.958308 | + | 0.285738i | \(0.907761\pi\) | |||||||
\(158\) | −285.932 | − | 92.9048i | −1.80969 | − | 0.588005i | ||||
\(159\) | −44.1747 | − | 29.3324i | −0.277828 | − | 0.184480i | ||||
\(160\) | 232.368 | + | 168.825i | 1.45230 | + | 1.05516i | ||||
\(161\) | 79.5919 | + | 25.8610i | 0.494360 | + | 0.160627i | ||||
\(162\) | 219.548 | − | 115.080i | 1.35524 | − | 0.710368i | ||||
\(163\) | −212.405 | + | 154.321i | −1.30310 | + | 0.946756i | −0.999981 | − | 0.00619729i | \(-0.998027\pi\) |
−0.303117 | + | 0.952953i | \(0.598027\pi\) | |||||||
\(164\) | − | 71.7464i | − | 0.437478i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 97.6240 | 0.588096 | ||||||||
\(167\) | 94.0494 | + | 129.448i | 0.563170 | + | 0.775137i | 0.991725 | − | 0.128379i | \(-0.0409773\pi\) |
−0.428555 | + | 0.903515i | \(0.640977\pi\) | |||||||
\(168\) | −13.3910 | − | 35.9776i | −0.0797085 | − | 0.214153i | ||||
\(169\) | 29.3223 | − | 90.2447i | 0.173505 | − | 0.533992i | ||||
\(170\) | 9.62155 | − | 13.2429i | 0.0565974 | − | 0.0778996i | ||||
\(171\) | −159.420 | − | 96.4306i | −0.932282 | − | 0.563921i | ||||
\(172\) | 71.9747 | − | 221.515i | 0.418458 | − | 1.28788i | ||||
\(173\) | −157.422 | + | 51.1497i | −0.909956 | + | 0.295663i | −0.726340 | − | 0.687335i | \(-0.758780\pi\) |
−0.183616 | + | 0.982998i | \(0.558780\pi\) | |||||||
\(174\) | −21.5785 | − | 27.2102i | −0.124015 | − | 0.156381i | ||||
\(175\) | −58.4435 | −0.333963 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −130.461 | + | 5.50325i | −0.737065 | + | 0.0310918i | ||||
\(178\) | −45.9035 | + | 33.3508i | −0.257885 | + | 0.187364i | ||||
\(179\) | −55.6720 | + | 18.0889i | −0.311017 | + | 0.101056i | −0.460367 | − | 0.887729i | \(-0.652282\pi\) |
0.149350 | + | 0.988784i | \(0.452282\pi\) | |||||||
\(180\) | 312.158 | + | 73.0381i | 1.73421 | + | 0.405767i | ||||
\(181\) | −230.309 | − | 167.330i | −1.27243 | − | 0.924473i | −0.273131 | − | 0.961977i | \(-0.588059\pi\) |
−0.999296 | + | 0.0375044i | \(0.988059\pi\) | |||||||
\(182\) | 89.5015 | − | 123.188i | 0.491767 | − | 0.676859i | ||||
\(183\) | −30.7890 | − | 8.58748i | −0.168246 | − | 0.0469261i | ||||
\(184\) | −35.2730 | − | 108.559i | −0.191701 | − | 0.589995i | ||||
\(185\) | −150.455 | − | 207.084i | −0.813272 | − | 1.11937i | ||||
\(186\) | −190.607 | + | 8.04041i | −1.02477 | + | 0.0432280i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 106.715i | − | 0.567631i | ||||||
\(189\) | 56.6612 | + | 60.2400i | 0.299795 | + | 0.318730i | ||||
\(190\) | −129.979 | − | 400.033i | −0.684097 | − | 2.10544i | ||||
\(191\) | 130.716 | + | 42.4721i | 0.684375 | + | 0.222367i | 0.630510 | − | 0.776181i | \(-0.282846\pi\) |
0.0538652 | + | 0.998548i | \(0.482846\pi\) | |||||||
\(192\) | 162.110 | − | 244.139i | 0.844324 | − | 1.27156i | ||||
\(193\) | 241.163 | + | 175.215i | 1.24955 | + | 0.907852i | 0.998196 | − | 0.0600426i | \(-0.0191237\pi\) |
0.251356 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(194\) | 184.239 | + | 59.8628i | 0.949684 | + | 0.308571i | ||||
\(195\) | 112.866 | + | 303.237i | 0.578801 | + | 1.55506i | ||||
\(196\) | −171.963 | + | 124.938i | −0.877362 | + | 0.637441i | ||||
\(197\) | 58.1375i | 0.295114i | 0.989054 | + | 0.147557i | \(0.0471410\pi\) | ||||
−0.989054 | + | 0.147557i | \(0.952859\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −125.049 | −0.628385 | −0.314193 | − | 0.949359i | \(-0.601734\pi\) | ||||
−0.314193 | + | 0.949359i | \(0.601734\pi\) | |||||||
\(200\) | 46.8546 | + | 64.4898i | 0.234273 | + | 0.322449i | ||||
\(201\) | −203.266 | + | 75.6564i | −1.01127 | + | 0.376400i | ||||
\(202\) | 142.190 | − | 437.615i | 0.703910 | − | 2.16641i | ||||
\(203\) | 6.81024 | − | 9.37349i | 0.0335480 | − | 0.0461748i | ||||
\(204\) | −10.8027 | − | 7.17306i | −0.0529542 | − | 0.0351621i | ||||
\(205\) | −27.4362 | + | 84.4398i | −0.133835 | + | 0.411902i | ||||
\(206\) | −435.894 | + | 141.631i | −2.11599 | + | 0.687527i | ||||
\(207\) | 160.778 | + | 186.059i | 0.776704 | + | 0.898838i | ||||
\(208\) | 140.934 | 0.677566 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 7.86865 | + | 186.535i | 0.0374698 | + | 0.888262i | ||||
\(211\) | −39.1505 | + | 28.4445i | −0.185547 | + | 0.134808i | −0.676681 | − | 0.736276i | \(-0.736583\pi\) |
0.491134 | + | 0.871084i | \(0.336583\pi\) | |||||||
\(212\) | −90.1902 | + | 29.3046i | −0.425425 | + | 0.138229i | ||||
\(213\) | −2.07128 | + | 7.42625i | −0.00972433 | + | 0.0348650i | ||||
\(214\) | −51.3765 | − | 37.3272i | −0.240077 | − | 0.174426i | ||||
\(215\) | −169.417 | + | 233.183i | −0.787987 | + | 1.08457i | ||||
\(216\) | 21.0465 | − | 110.818i | 0.0974376 | − | 0.513046i | ||||
\(217\) | −19.6685 | − | 60.5335i | −0.0906383 | − | 0.278956i | ||||
\(218\) | 190.298 | + | 261.923i | 0.872929 | + | 1.20148i | ||||
\(219\) | 5.75021 | + | 136.315i | 0.0262567 | + | 0.622444i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.0875i | − | 0.0592193i | ||||||
\(222\) | −277.330 | + | 219.931i | −1.24924 | + | 0.990682i | ||||
\(223\) | 65.4240 | + | 201.354i | 0.293381 | + | 0.902934i | 0.983760 | + | 0.179487i | \(0.0574437\pi\) |
−0.690379 | + | 0.723448i | \(0.742556\pi\) | |||||||
\(224\) | 126.021 | + | 40.9469i | 0.562596 | + | 0.182798i | ||||
\(225\) | −146.936 | − | 88.8790i | −0.653049 | − | 0.395018i | ||||
\(226\) | −328.709 | − | 238.821i | −1.45447 | − | 1.05673i | ||||
\(227\) | −115.444 | − | 37.5101i | −0.508565 | − | 0.165243i | 0.0434848 | − | 0.999054i | \(-0.486154\pi\) |
−0.552049 | + | 0.833811i | \(0.686154\pi\) | |||||||
\(228\) | −312.276 | + | 116.230i | −1.36963 | + | 0.509783i | ||||
\(229\) | −261.267 | + | 189.822i | −1.14090 | + | 0.828915i | −0.987245 | − | 0.159209i | \(-0.949106\pi\) |
−0.153659 | + | 0.988124i | \(0.549106\pi\) | |||||||
\(230\) | 555.137i | 2.41364i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.8030 | −0.0681166 | ||||||||
\(233\) | −236.530 | − | 325.556i | −1.01515 | − | 1.39724i | −0.915548 | − | 0.402209i | \(-0.868243\pi\) |
−0.0996031 | − | 0.995027i | \(-0.531757\pi\) | |||||||
\(234\) | 412.362 | − | 173.603i | 1.76223 | − | 0.741894i | ||||
\(235\) | −40.8082 | + | 125.595i | −0.173652 | + | 0.534445i | ||||
\(236\) | −137.260 | + | 188.923i | −0.581612 | + | 0.800520i | ||||
\(237\) | 163.033 | − | 245.528i | 0.687903 | − | 1.03598i | ||||
\(238\) | 2.33361 | − | 7.18212i | 0.00980509 | − | 0.0301770i | ||||
\(239\) | 0.305711 | − | 0.0993315i | 0.00127912 | − | 0.000415613i | −0.308377 | − | 0.951264i | \(-0.599786\pi\) |
0.309656 | + | 0.950848i | \(0.399786\pi\) | |||||||
\(240\) | −135.395 | + | 107.372i | −0.564146 | + | 0.447385i | ||||
\(241\) | −290.799 | −1.20664 | −0.603318 | − | 0.797500i | \(-0.706155\pi\) | ||||
−0.603318 | + | 0.797500i | \(0.706155\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 50.8438 | + | 237.621i | 0.209234 | + | 0.977866i | ||||
\(244\) | −46.2469 | + | 33.6004i | −0.189537 | + | 0.137706i | ||||
\(245\) | 250.164 | − | 81.2832i | 1.02108 | − | 0.331768i | ||||
\(246\) | 118.257 | + | 32.9836i | 0.480721 | + | 0.134080i | ||||
\(247\) | −272.067 | − | 197.668i | −1.10149 | − | 0.800276i | ||||
\(248\) | −51.0276 | + | 70.2335i | −0.205756 | + | 0.283199i | ||||
\(249\) | −25.7112 | + | 92.1834i | −0.103258 | + | 0.370214i | ||||
\(250\) | 37.1656 | + | 114.384i | 0.148662 | + | 0.457535i | ||||
\(251\) | 66.1972 | + | 91.1127i | 0.263734 | + | 0.362999i | 0.920262 | − | 0.391303i | \(-0.127976\pi\) |
−0.656528 | + | 0.754302i | \(0.727976\pi\) | |||||||
\(252\) | 147.375 | − | 12.4557i | 0.584821 | − | 0.0494272i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 448.803i | − | 1.76694i | ||||||
\(255\) | 9.97087 | + | 12.5731i | 0.0391015 | + | 0.0493064i | ||||
\(256\) | 1.68535 | + | 5.18697i | 0.00658339 | + | 0.0202616i | ||||
\(257\) | 186.948 | + | 60.7430i | 0.727423 | + | 0.236354i | 0.649238 | − | 0.760585i | \(-0.275088\pi\) |
0.0781844 | + | 0.996939i | \(0.475088\pi\) | |||||||
\(258\) | 332.029 | + | 220.470i | 1.28693 | + | 0.854535i | ||||
\(259\) | −95.5359 | − | 69.4109i | −0.368864 | − | 0.267996i | ||||
\(260\) | 550.330 | + | 178.813i | 2.11665 | + | 0.687743i | ||||
\(261\) | 31.3769 | − | 13.2096i | 0.120218 | − | 0.0506115i | ||||
\(262\) | 370.050 | − | 268.857i | 1.41240 | − | 1.02617i | ||||
\(263\) | − | 378.327i | − | 1.43850i | −0.694749 | − | 0.719252i | \(-0.744485\pi\) | ||
0.694749 | − | 0.719252i | \(-0.255515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 117.353 | 0.442842 | ||||||||
\(266\) | −114.059 | − | 156.988i | −0.428791 | − | 0.590181i | ||||
\(267\) | −19.4026 | − | 52.1289i | −0.0726689 | − | 0.195239i | ||||
\(268\) | −119.862 | + | 368.897i | −0.447246 | + | 1.37648i | ||||
\(269\) | 118.235 | − | 162.737i | 0.439537 | − | 0.604971i | −0.530572 | − | 0.847640i | \(-0.678023\pi\) |
0.970109 | + | 0.242669i | \(0.0780229\pi\) | |||||||
\(270\) | −263.894 | + | 480.944i | −0.977384 | + | 1.78127i | ||||
\(271\) | −24.7877 | + | 76.2886i | −0.0914674 | + | 0.281508i | −0.986317 | − | 0.164860i | \(-0.947283\pi\) |
0.894850 | + | 0.446368i | \(0.147283\pi\) | |||||||
\(272\) | 6.64746 | − | 2.15989i | 0.0244392 | − | 0.00794078i | ||||
\(273\) | 92.7510 | + | 116.958i | 0.339747 | + | 0.428416i | ||||
\(274\) | −465.792 | −1.69997 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 439.376 | − | 18.5343i | 1.59194 | − | 0.0671533i | ||||
\(277\) | 177.106 | − | 128.675i | 0.639371 | − | 0.464530i | −0.220263 | − | 0.975441i | \(-0.570692\pi\) |
0.859634 | + | 0.510910i | \(0.170692\pi\) | |||||||
\(278\) | −325.495 | + | 105.760i | −1.17084 | + | 0.380430i | ||||
\(279\) | 42.6077 | − | 182.102i | 0.152716 | − | 0.652695i | ||||
\(280\) | 68.7331 | + | 49.9375i | 0.245475 | + | 0.178348i | ||||
\(281\) | 291.798 | − | 401.626i | 1.03843 | − | 1.42927i | 0.140001 | − | 0.990151i | \(-0.455289\pi\) |
0.898427 | − | 0.439123i | \(-0.144711\pi\) | |||||||
\(282\) | 175.894 | + | 49.0594i | 0.623739 | + | 0.173969i | ||||
\(283\) | 95.0850 | + | 292.642i | 0.335990 | + | 1.03407i | 0.966233 | + | 0.257672i | \(0.0829553\pi\) |
−0.630243 | + | 0.776398i | \(0.717045\pi\) | |||||||
\(284\) | 8.10433 | + | 11.1547i | 0.0285364 | + | 0.0392770i | ||||
\(285\) | 411.971 | − | 17.3783i | 1.44551 | − | 0.0609764i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40.9601i | 0.142718i | ||||||||
\(288\) | 254.567 | + | 294.596i | 0.883913 | + | 1.02290i | ||||
\(289\) | 89.1053 | + | 274.238i | 0.308323 | + | 0.948921i | ||||
\(290\) | 73.0950 | + | 23.7500i | 0.252052 | + | 0.0818966i | ||||
\(291\) | −105.049 | + | 158.205i | −0.360995 | + | 0.543659i | ||||
\(292\) | 197.401 | + | 143.420i | 0.676030 | + | 0.491165i | ||||
\(293\) | 323.072 | + | 104.972i | 1.10263 | + | 0.358268i | 0.803116 | − | 0.595823i | \(-0.203174\pi\) |
0.299519 | + | 0.954090i | \(0.403174\pi\) | |||||||
\(294\) | −126.877 | − | 340.879i | −0.431553 | − | 1.15945i | ||||
\(295\) | 233.790 | − | 169.858i | 0.792507 | − | 0.575790i | ||||
\(296\) | 161.067i | 0.544145i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −794.734 | −2.66689 | ||||||||
\(299\) | 260.884 | + | 359.077i | 0.872523 | + | 1.20092i | ||||
\(300\) | −287.821 | + | 107.128i | −0.959404 | + | 0.357094i | ||||
\(301\) | −41.0905 | + | 126.463i | −0.136513 | + | 0.420144i | ||||
\(302\) | 158.324 | − | 217.914i | 0.524251 | − | 0.721570i | ||||
\(303\) | 375.778 | + | 249.520i | 1.24019 | + | 0.823499i | ||||
\(304\) | 55.5002 | − | 170.812i | 0.182567 | − | 0.561882i | ||||
\(305\) | 67.2779 | − | 21.8599i | 0.220583 | − | 0.0716719i | ||||
\(306\) | 16.7894 | − | 14.5081i | 0.0548674 | − | 0.0474120i | ||||
\(307\) | 396.129 | 1.29032 | 0.645161 | − | 0.764047i | \(-0.276790\pi\) | ||||
0.645161 | + | 0.764047i | \(0.276790\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.9362 | − | 448.903i | −0.0612821 | − | 1.45276i | ||||
\(310\) | 341.574 | − | 248.168i | 1.10185 | − | 0.800542i | ||||
\(311\) | 82.7760 | − | 26.8955i | 0.266161 | − | 0.0864808i | −0.172896 | − | 0.984940i | \(-0.555313\pi\) |
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(312\) | 54.6984 | − | 196.112i | 0.175315 | − | 0.628565i | ||||
\(313\) | 484.531 | + | 352.033i | 1.54802 | + | 1.12471i | 0.945041 | + | 0.326951i | \(0.106021\pi\) |
0.602982 | + | 0.797755i | \(0.293979\pi\) | |||||||
\(314\) | 13.7701 | − | 18.9530i | 0.0438539 | − | 0.0603598i | ||||
\(315\) | −178.212 | − | 41.6975i | −0.565751 | − | 0.132373i | ||||
\(316\) | −162.878 | − | 501.288i | −0.515438 | − | 1.58635i | ||||
\(317\) | 1.44295 | + | 1.98605i | 0.00455190 | + | 0.00626516i | 0.811287 | − | 0.584648i | \(-0.198767\pi\) |
−0.806735 | + | 0.590913i | \(0.798767\pi\) | |||||||
\(318\) | −6.83917 | − | 162.130i | −0.0215068 | − | 0.509843i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 648.571i | 2.02678i | ||||||||
\(321\) | 48.7780 | − | 38.6824i | 0.151956 | − | 0.120506i | ||||
\(322\) | 79.1412 | + | 243.571i | 0.245780 | + | 0.756433i | ||||
\(323\) | −15.8620 | − | 5.15389i | −0.0491085 | − | 0.0159563i | ||||
\(324\) | 389.465 | + | 192.808i | 1.20205 | + | 0.595085i | ||||
\(325\) | −250.761 | − | 182.189i | −0.771573 | − | 0.560581i | ||||
\(326\) | −764.136 | − | 248.283i | −2.34398 | − | 0.761604i | ||||
\(327\) | −297.445 | + | 110.710i | −0.909618 | + | 0.338564i | ||||
\(328\) | 45.1977 | − | 32.8380i | 0.137798 | − | 0.100116i | ||||
\(329\) | 60.9235i | 0.185178i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 368.074 | 1.11200 | 0.556002 | − | 0.831181i | \(-0.312335\pi\) | ||||
0.556002 | + | 0.831181i | \(0.312335\pi\) | |||||||
\(332\) | 100.601 | + | 138.465i | 0.303014 | + | 0.417063i | ||||
\(333\) | −134.634 | − | 319.798i | −0.404307 | − | 0.960354i | ||||
\(334\) | −151.313 | + | 465.694i | −0.453034 | + | 1.39429i | ||||
\(335\) | 282.136 | − | 388.327i | 0.842197 | − | 1.15919i | ||||
\(336\) | −44.0986 | + | 66.4127i | −0.131246 | + | 0.197657i | ||||
\(337\) | −182.901 | + | 562.911i | −0.542733 | + | 1.67036i | 0.183588 | + | 0.983003i | \(0.441229\pi\) |
−0.726321 | + | 0.687356i | \(0.758771\pi\) | |||||||
\(338\) | 276.172 | − | 89.7336i | 0.817076 | − | 0.265484i | ||||
\(339\) | 312.084 | − | 247.492i | 0.920601 | − | 0.730064i | ||||
\(340\) | 28.6980 | 0.0844059 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −48.0182 | − | 568.149i | −0.140404 | − | 1.66125i | ||||
\(343\) | 219.596 | − | 159.546i | 0.640221 | − | 0.465148i | ||||
\(344\) | 172.489 | − | 56.0452i | 0.501423 | − | 0.162922i | ||||
\(345\) | −524.199 | − | 146.206i | −1.51942 | − | 0.423786i | ||||
\(346\) | −409.803 | − | 297.740i | −1.18440 | − | 0.860519i | ||||
\(347\) | −173.162 | + | 238.337i | −0.499026 | + | 0.686851i | −0.982021 | − | 0.188773i | \(-0.939549\pi\) |
0.482994 | + | 0.875623i | \(0.339549\pi\) | |||||||
\(348\) | 16.3571 | − | 58.6457i | 0.0470031 | − | 0.168522i | ||||
\(349\) | −127.318 | − | 391.843i | −0.364807 | − | 1.12276i | −0.950102 | − | 0.311939i | \(-0.899021\pi\) |
0.585295 | − | 0.810820i | \(-0.300979\pi\) | |||||||
\(350\) | −105.127 | − | 144.694i | −0.300361 | − | 0.413412i | ||||
\(351\) | 55.3248 | + | 435.102i | 0.157620 | + | 1.23961i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 135.577i | − | 0.384070i | −0.981388 | − | 0.192035i | \(-0.938491\pi\) | ||
0.981388 | − | 0.192035i | \(-0.0615086\pi\) | |||||||
\(354\) | −248.294 | − | 313.095i | −0.701395 | − | 0.884449i | ||||
\(355\) | −5.27257 | − | 16.2273i | −0.0148523 | − | 0.0457107i | ||||
\(356\) | −94.6061 | − | 30.7394i | −0.265748 | − | 0.0863466i | ||||
\(357\) | 6.16725 | + | 4.09511i | 0.0172752 | + | 0.0114709i | ||||
\(358\) | −144.926 | − | 105.295i | −0.404821 | − | 0.294120i | ||||
\(359\) | −265.131 | − | 86.1464i | −0.738527 | − | 0.239962i | −0.0844899 | − | 0.996424i | \(-0.526926\pi\) |
−0.654037 | + | 0.756462i | \(0.726926\pi\) | |||||||
\(360\) | 96.8623 | + | 230.078i | 0.269062 | + | 0.639105i | ||||
\(361\) | −54.6603 | + | 39.7131i | −0.151414 | + | 0.110008i | ||||
\(362\) | − | 871.187i | − | 2.40659i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 266.954 | 0.733391 | ||||||||
\(365\) | −177.481 | − | 244.281i | −0.486249 | − | 0.669264i | ||||
\(366\) | −34.1216 | − | 91.6744i | −0.0932285 | − | 0.250476i | ||||
\(367\) | −54.5068 | + | 167.755i | −0.148520 | + | 0.457097i | −0.997447 | − | 0.0714131i | \(-0.977249\pi\) |
0.848927 | + | 0.528510i | \(0.177249\pi\) | |||||||
\(368\) | −139.329 | + | 191.770i | −0.378612 | + | 0.521115i | ||||
\(369\) | −62.2908 | + | 102.980i | −0.168810 | + | 0.279079i | ||||
\(370\) | 242.063 | − | 744.994i | 0.654225 | − | 2.01350i | ||||
\(371\) | 51.4897 | − | 16.7300i | 0.138786 | − | 0.0450944i | ||||
\(372\) | −207.822 | − | 262.061i | −0.558662 | − | 0.704465i | ||||
\(373\) | −163.109 | −0.437289 | −0.218645 | − | 0.975805i | \(-0.570164\pi\) | ||||
−0.218645 | + | 0.975805i | \(0.570164\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −117.797 | + | 4.96908i | −0.314126 | + | 0.0132509i | ||||
\(376\) | 67.2264 | − | 48.8428i | 0.178794 | − | 0.129901i | ||||
\(377\) | 58.4409 | − | 18.9886i | 0.155016 | − | 0.0503676i | ||||
\(378\) | −47.2216 | + | 248.640i | −0.124925 | + | 0.657777i | ||||
\(379\) | −43.0644 | − | 31.2881i | −0.113626 | − | 0.0825545i | 0.529521 | − | 0.848297i | \(-0.322372\pi\) |
−0.643147 | + | 0.765742i | \(0.722372\pi\) | |||||||
\(380\) | 433.444 | − | 596.584i | 1.14064 | − | 1.56996i | ||||
\(381\) | 423.791 | + | 118.201i | 1.11231 | + | 0.310239i | ||||
\(382\) | 129.975 | + | 400.023i | 0.340250 | + | 1.04718i | ||||
\(383\) | −52.7039 | − | 72.5408i | −0.137608 | − | 0.189401i | 0.734651 | − | 0.678445i | \(-0.237346\pi\) |
−0.872259 | + | 0.489044i | \(0.837346\pi\) | |||||||
\(384\) | 377.369 | − | 15.9187i | 0.982733 | − | 0.0414549i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 912.245i | 2.36333i | ||||||||
\(387\) | −295.630 | + | 255.460i | −0.763901 | + | 0.660102i | ||||
\(388\) | 104.950 | + | 323.002i | 0.270489 | + | 0.832480i | ||||
\(389\) | 256.406 | + | 83.3113i | 0.659141 | + | 0.214168i | 0.619440 | − | 0.785044i | \(-0.287360\pi\) |
0.0397008 | + | 0.999212i | \(0.487360\pi\) | |||||||
\(390\) | −547.733 | + | 824.888i | −1.40444 | + | 2.11510i | ||||
\(391\) | 17.8083 | + | 12.9385i | 0.0455454 | + | 0.0330907i | ||||
\(392\) | −157.413 | − | 51.1467i | −0.401565 | − | 0.130476i | ||||
\(393\) | 156.414 | + | 420.236i | 0.397999 | + | 1.06930i | ||||
\(394\) | −143.937 | + | 104.576i | −0.365322 | + | 0.265422i | ||||
\(395\) | 652.262i | 1.65130i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 211.490 | 0.532720 | 0.266360 | − | 0.963874i | \(-0.414179\pi\) | ||||
0.266360 | + | 0.963874i | \(0.414179\pi\) | |||||||
\(398\) | −224.934 | − | 309.595i | −0.565161 | − | 0.777877i | ||||
\(399\) | 178.279 | − | 66.3561i | 0.446814 | − | 0.166306i | ||||
\(400\) | 51.1540 | − | 157.436i | 0.127885 | − | 0.393589i | ||||
\(401\) | −264.385 | + | 363.894i | −0.659314 | + | 0.907468i | −0.999458 | − | 0.0329055i | \(-0.989524\pi\) |
0.340145 | + | 0.940373i | \(0.389524\pi\) | |||||||
\(402\) | −552.939 | − | 367.156i | −1.37547 | − | 0.913324i | ||||
\(403\) | 104.313 | − | 321.042i | 0.258841 | − | 0.796631i | ||||
\(404\) | 767.216 | − | 249.284i | 1.89905 | − | 0.617038i | ||||
\(405\) | −384.639 | − | 375.853i | −0.949727 | − | 0.928032i | ||||
\(406\) | 35.4569 | 0.0873323 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.425560 | − | 10.0884i | −0.00104304 | − | 0.0247264i | ||||
\(409\) | −124.826 | + | 90.6917i | −0.305199 | + | 0.221740i | −0.729834 | − | 0.683625i | \(-0.760403\pi\) |
0.424635 | + | 0.905365i | \(0.360403\pi\) | |||||||
\(410\) | −258.407 | + | 83.9617i | −0.630262 | + | 0.204785i | ||||
\(411\) | 122.675 | − | 439.833i | 0.298480 | − | 1.07015i | ||||
\(412\) | −650.066 | − | 472.301i | −1.57783 | − | 1.14636i | ||||
\(413\) | 78.3621 | − | 107.856i | 0.189739 | − | 0.261153i | ||||
\(414\) | −171.443 | + | 732.732i | −0.414113 | + | 1.76988i | ||||
\(415\) | −65.4493 | − | 201.432i | −0.157709 | − | 0.485379i | ||||
\(416\) | 413.070 | + | 568.542i | 0.992957 | + | 1.36669i | ||||
\(417\) | −14.1402 | − | 335.209i | −0.0339093 | − | 0.803858i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 755.530i | 1.80317i | 0.432599 | + | 0.901587i | \(0.357597\pi\) | ||||
−0.432599 | + | 0.901587i | \(0.642403\pi\) | |||||||
\(420\) | −256.463 | + | 203.383i | −0.610626 | + | 0.484245i | ||||
\(421\) | −135.007 | − | 415.507i | −0.320681 | − | 0.986954i | −0.973353 | − | 0.229313i | \(-0.926352\pi\) |
0.652672 | − | 0.757641i | \(-0.273648\pi\) | |||||||
\(422\) | −140.846 | − | 45.7635i | −0.333758 | − | 0.108444i | ||||
\(423\) | −92.6505 | + | 153.171i | −0.219032 | + | 0.362107i | ||||
\(424\) | −59.7405 | − | 43.4040i | −0.140897 | − | 0.102368i | ||||
\(425\) | −14.6199 | − | 4.75029i | −0.0343997 | − | 0.0111771i | ||||
\(426\) | −22.1117 | + | 8.23006i | −0.0519053 | + | 0.0193194i | ||||
\(427\) | 26.4024 | − | 19.1825i | 0.0618324 | − | 0.0449239i | ||||
\(428\) | − | 111.335i | − | 0.260129i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −882.057 | −2.05129 | ||||||||
\(431\) | 5.72154 | + | 7.87503i | 0.0132750 | + | 0.0182715i | 0.815603 | − | 0.578612i | \(-0.196405\pi\) |
−0.802328 | + | 0.596884i | \(0.796405\pi\) | |||||||
\(432\) | −211.869 | + | 99.9081i | −0.490438 | + | 0.231269i | ||||
\(433\) | −18.3169 | + | 56.3736i | −0.0423023 | + | 0.130193i | −0.969977 | − | 0.243196i | \(-0.921804\pi\) |
0.927675 | + | 0.373389i | \(0.121804\pi\) | |||||||
\(434\) | 114.489 | − | 157.581i | 0.263801 | − | 0.363090i | ||||
\(435\) | −41.6774 | + | 62.7664i | −0.0958101 | + | 0.144290i | ||||
\(436\) | −175.398 | + | 539.819i | −0.402288 | + | 1.23812i | ||||
\(437\) | 537.939 | − | 174.787i | 1.23098 | − | 0.399970i | ||||
\(438\) | −327.145 | + | 259.436i | −0.746907 | + | 0.592320i | ||||
\(439\) | −444.724 | −1.01304 | −0.506519 | − | 0.862229i | \(-0.669068\pi\) | ||||
−0.506519 | + | 0.862229i | \(0.669068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 355.297 | − | 30.0286i | 0.805662 | − | 0.0680920i | ||||
\(442\) | 32.4019 | − | 23.5414i | 0.0733075 | − | 0.0532610i | ||||
\(443\) | 509.149 | − | 165.433i | 1.14932 | − | 0.373437i | 0.328434 | − | 0.944527i | \(-0.393479\pi\) |
0.820888 | + | 0.571090i | \(0.193479\pi\) | |||||||
\(444\) | −597.725 | − | 166.714i | −1.34623 | − | 0.375481i | ||||
\(445\) | 99.5891 | + | 72.3557i | 0.223796 | + | 0.162597i | ||||
\(446\) | −380.830 | + | 524.167i | −0.853878 | + | 1.17526i | ||||
\(447\) | 209.309 | − | 750.443i | 0.468252 | − | 1.67884i | ||||
\(448\) | 92.4612 | + | 284.566i | 0.206387 | + | 0.635193i | ||||
\(449\) | −452.250 | − | 622.469i | −1.00724 | − | 1.38635i | −0.920777 | − | 0.390090i | \(-0.872444\pi\) |
−0.0864624 | − | 0.996255i | \(-0.527556\pi\) | |||||||
\(450\) | −44.2578 | − | 523.657i | −0.0983508 | − | 1.16368i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 712.327i | − | 1.57594i | ||||||
\(453\) | 164.072 | + | 206.892i | 0.362190 | + | 0.456716i | ||||
\(454\) | −114.790 | − | 353.289i | −0.252842 | − | 0.778169i | ||||
\(455\) | −314.184 | − | 102.085i | −0.690515 | − | 0.224362i | ||||
\(456\) | −216.148 | − | 143.524i | −0.474010 | − | 0.314747i | ||||
\(457\) | 137.254 | + | 99.7207i | 0.300337 | + | 0.218207i | 0.727739 | − | 0.685854i | \(-0.240571\pi\) |
−0.427402 | + | 0.904061i | \(0.640571\pi\) | |||||||
\(458\) | −939.919 | − | 305.398i | −2.05223 | − | 0.666809i | ||||
\(459\) | 9.27772 | + | 19.6747i | 0.0202129 | + | 0.0428643i | ||||
\(460\) | −787.377 | + | 572.063i | −1.71169 | + | 1.24362i | ||||
\(461\) | 266.355i | 0.577777i | 0.957363 | + | 0.288888i | \(0.0932857\pi\) | ||||
−0.957363 | + | 0.288888i | \(0.906714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −704.848 | −1.52235 | −0.761175 | − | 0.648547i | \(-0.775377\pi\) | ||||
−0.761175 | + | 0.648547i | \(0.775377\pi\) | |||||||
\(464\) | 19.2896 | + | 26.5499i | 0.0415724 | + | 0.0572195i | ||||
\(465\) | 144.377 | + | 387.898i | 0.310489 | + | 0.834189i | ||||
\(466\) | 380.547 | − | 1171.20i | 0.816624 | − | 2.51331i | ||||
\(467\) | 396.859 | − | 546.230i | 0.849806 | − | 1.16966i | −0.134099 | − | 0.990968i | \(-0.542814\pi\) |
0.983905 | − | 0.178690i | \(-0.0571859\pi\) | |||||||
\(468\) | 671.164 | + | 405.976i | 1.43411 | + | 0.867470i | ||||
\(469\) | 68.4293 | − | 210.604i | 0.145905 | − | 0.449049i | ||||
\(470\) | −384.352 | + | 124.883i | −0.817769 | + | 0.265709i | ||||
\(471\) | 14.2701 | + | 17.9944i | 0.0302974 | + | 0.0382046i | ||||
\(472\) | −181.838 | −0.385250 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 901.138 | − | 38.0129i | 1.90113 | − | 0.0801960i | ||||
\(475\) | −319.564 | + | 232.177i | −0.672766 | + | 0.488793i | ||||
\(476\) | 12.5915 | − | 4.09123i | 0.0264527 | − | 0.00859502i | ||||
\(477\) | 154.896 | + | 36.2421i | 0.324729 | + | 0.0759792i | ||||
\(478\) | 0.795829 | + | 0.578204i | 0.00166491 | + | 0.00120963i | ||||
\(479\) | 411.336 | − | 566.156i | 0.858740 | − | 1.18195i | −0.123128 | − | 0.992391i | \(-0.539293\pi\) |
0.981868 | − | 0.189563i | \(-0.0607073\pi\) | |||||||
\(480\) | −829.988 | − | 231.495i | −1.72914 | − | 0.482281i | ||||
\(481\) | −193.534 | − | 595.638i | −0.402358 | − | 1.23833i | ||||
\(482\) | −523.082 | − | 719.961i | −1.08523 | − | 1.49369i | ||||
\(483\) | −250.841 | + | 10.5813i | −0.519339 | + | 0.0219074i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 420.282i | − | 0.866560i | ||||||
\(486\) | −496.846 | + | 553.306i | −1.02232 | + | 1.13849i | ||||
\(487\) | −201.895 | − | 621.370i | −0.414569 | − | 1.27591i | −0.912636 | − | 0.408774i | \(-0.865956\pi\) |
0.498066 | − | 0.867139i | \(-0.334044\pi\) | |||||||
\(488\) | −42.3341 | − | 13.7552i | −0.0867501 | − | 0.0281868i | ||||
\(489\) | 435.696 | − | 656.161i | 0.890995 | − | 1.34184i | ||||
\(490\) | 651.229 | + | 473.145i | 1.32904 | + | 0.965603i | ||||
\(491\) | 58.8107 | + | 19.1088i | 0.119777 | + | 0.0389180i | 0.368292 | − | 0.929710i | \(-0.379943\pi\) |
−0.248515 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(492\) | 75.0809 | + | 201.719i | 0.152603 | + | 0.409999i | ||||
\(493\) | 2.46549 | − | 1.79128i | 0.00500099 | − | 0.00363343i | ||||
\(494\) | − | 1029.14i | − | 2.08329i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 180.281 | 0.363470 | ||||||||
\(497\) | −4.62677 | − | 6.36821i | −0.00930940 | − | 0.0128133i | ||||
\(498\) | −274.476 | + | 102.161i | −0.551157 | + | 0.205143i | ||||
\(499\) | 101.973 | − | 313.842i | 0.204356 | − | 0.628942i | −0.795384 | − | 0.606106i | \(-0.792731\pi\) |
0.999739 | − | 0.0228356i | \(-0.00726941\pi\) | |||||||
\(500\) | −123.937 | + | 170.585i | −0.247875 | + | 0.341170i | ||||
\(501\) | −399.890 | − | 265.530i | −0.798183 | − | 0.530001i | ||||
\(502\) | −106.503 | + | 327.782i | −0.212157 | + | 0.652952i | ||||
\(503\) | 330.187 | − | 107.284i | 0.656436 | − | 0.213289i | 0.0381861 | − | 0.999271i | \(-0.487842\pi\) |
0.618250 | + | 0.785982i | \(0.287842\pi\) | |||||||
\(504\) | 75.2995 | + | 87.1400i | 0.149404 | + | 0.172897i | ||||
\(505\) | −998.280 | −1.97679 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.9975 | + | 284.414i | 0.0236637 | + | 0.560974i | ||||
\(508\) | 636.559 | − | 462.487i | 1.25307 | − | 0.910407i | ||||
\(509\) | −814.289 | + | 264.578i | −1.59978 | + | 0.519800i | −0.967053 | − | 0.254574i | \(-0.918065\pi\) |
−0.632728 | + | 0.774374i | \(0.718065\pi\) | |||||||
\(510\) | −13.1932 | + | 47.3021i | −0.0258690 | + | 0.0927491i | ||||
\(511\) | −112.696 | − | 81.8787i | −0.220541 | − | 0.160232i | ||||
\(512\) | −305.823 | + | 420.929i | −0.597310 | + | 0.822127i | ||||
\(513\) | 549.132 | + | 104.291i | 1.07043 | + | 0.203297i | ||||
\(514\) | 185.889 | + | 572.108i | 0.361652 | + | 1.11305i | ||||
\(515\) | 584.467 | + | 804.449i | 1.13489 | + | 1.56204i | ||||
\(516\) | 29.4492 | + | 698.125i | 0.0570720 | + | 1.35295i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 361.382i | − | 0.697649i | ||||||
\(519\) | 389.076 | − | 308.549i | 0.749665 | − | 0.594507i | ||||
\(520\) | 139.238 | + | 428.530i | 0.267765 | + | 0.824097i | ||||
\(521\) | −677.779 | − | 220.224i | −1.30092 | − | 0.422695i | −0.425019 | − | 0.905185i | \(-0.639732\pi\) |
−0.875901 | + | 0.482490i | \(0.839732\pi\) | |||||||
\(522\) | 89.1442 | + | 53.9218i | 0.170774 | + | 0.103298i | ||||
\(523\) | 407.684 | + | 296.200i | 0.779510 | + | 0.566347i | 0.904832 | − | 0.425769i | \(-0.139996\pi\) |
−0.125322 | + | 0.992116i | \(0.539996\pi\) | |||||||
\(524\) | 762.665 | + | 247.805i | 1.45547 | + | 0.472910i | ||||
\(525\) | 164.317 | − | 61.1597i | 0.312986 | − | 0.116495i | ||||
\(526\) | 936.660 | − | 680.524i | 1.78072 | − | 1.29377i | ||||
\(527\) | − | 16.7414i | − | 0.0317673i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −217.513 | −0.411179 | ||||||||
\(530\) | 211.091 | + | 290.542i | 0.398286 | + | 0.548193i | ||||
\(531\) | 361.039 | − | 151.997i | 0.679923 | − | 0.286246i | ||||
\(532\) | 105.128 | − | 323.549i | 0.197608 | − | 0.608175i | ||||
\(533\) | −127.687 | + | 175.746i | −0.239563 | + | 0.329730i | ||||
\(534\) | 94.1597 | − | 141.805i | 0.176329 | − | 0.265552i | ||||
\(535\) | −42.5751 | + | 131.033i | −0.0795796 | + | 0.244921i | ||||
\(536\) | −287.252 | + | 93.3339i | −0.535918 | + | 0.174130i | ||||
\(537\) | 137.596 | − | 109.118i | 0.256231 | − | 0.203199i | ||||
\(538\) | 615.583 | 1.14421 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −954.086 | + | 121.315i | −1.76683 | + | 0.224658i | ||||
\(541\) | −474.599 | + | 344.817i | −0.877263 | + | 0.637369i | −0.932526 | − | 0.361103i | \(-0.882400\pi\) |
0.0552628 | + | 0.998472i | \(0.482400\pi\) | |||||||
\(542\) | −233.463 | + | 75.8566i | −0.430743 | + | 0.139957i | ||||
\(543\) | 822.636 | + | 229.444i | 1.51498 | + | 0.422549i | ||||
\(544\) | 28.1966 | + | 20.4861i | 0.0518320 | + | 0.0376582i | ||||
\(545\) | 412.859 | − | 568.251i | 0.757539 | − | 1.04266i | ||||
\(546\) | −122.726 | + | 440.013i | −0.224772 | + | 0.805884i | ||||
\(547\) | −212.865 | − | 655.132i | −0.389151 | − | 1.19768i | −0.933424 | − | 0.358775i | \(-0.883195\pi\) |
0.544273 | − | 0.838908i | \(-0.316805\pi\) | |||||||
\(548\) | −479.994 | − | 660.655i | −0.875901 | − | 1.20557i | ||||
\(549\) | 95.5519 | − | 8.07575i | 0.174047 | − | 0.0147099i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 78.3083i | − | 0.142120i | ||||||
\(552\) | 212.777 | + | 268.308i | 0.385465 | + | 0.486066i | ||||
\(553\) | 92.9875 | + | 286.186i | 0.168151 | + | 0.517515i | ||||
\(554\) | 637.146 | + | 207.021i | 1.15008 | + | 0.373685i | ||||
\(555\) | 639.723 | + | 424.782i | 1.15265 | + | 0.765373i | ||||
\(556\) | −485.423 | − | 352.681i | −0.873063 | − | 0.634317i | ||||
\(557\) | 588.519 | + | 191.222i | 1.05659 | + | 0.343306i | 0.785250 | − | 0.619178i | \(-0.212534\pi\) |
0.271337 | + | 0.962484i | \(0.412534\pi\) | |||||||
\(558\) | 527.489 | − | 222.072i | 0.945321 | − | 0.397978i | ||||
\(559\) | −570.536 | + | 414.519i | −1.02064 | + | 0.741536i | ||||
\(560\) | − | 176.430i | − | 0.315053i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1519.22 | 2.70325 | ||||||||
\(563\) | 334.609 | + | 460.549i | 0.594331 | + | 0.818027i | 0.995175 | − | 0.0981198i | \(-0.0312828\pi\) |
−0.400843 | + | 0.916147i | \(0.631283\pi\) | |||||||
\(564\) | 111.674 | + | 300.035i | 0.198004 | + | 0.531976i | ||||
\(565\) | −272.397 | + | 838.353i | −0.482119 | + | 1.48381i | ||||
\(566\) | −553.485 | + | 761.807i | −0.977889 | + | 1.34595i | ||||
\(567\) | −222.346 | − | 110.074i | −0.392145 | − | 0.194134i | ||||
\(568\) | −3.31772 | + | 10.2109i | −0.00584105 | + | 0.0179769i | ||||
\(569\) | −857.404 | + | 278.588i | −1.50686 | + | 0.489609i | −0.942010 | − | 0.335584i | \(-0.891066\pi\) |
−0.564851 | + | 0.825193i | \(0.691066\pi\) | |||||||
\(570\) | 784.068 | + | 988.698i | 1.37556 | + | 1.73456i | ||||
\(571\) | 804.182 | 1.40837 | 0.704187 | − | 0.710014i | \(-0.251312\pi\) | ||||
0.704187 | + | 0.710014i | \(0.251312\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −411.961 | + | 17.3779i | −0.718955 | + | 0.0303279i | ||||
\(574\) | −101.409 | + | 73.6779i | −0.176671 | + | 0.128359i | ||||
\(575\) | 495.812 | − | 161.099i | 0.862283 | − | 0.280173i | ||||
\(576\) | −200.298 | + | 856.056i | −0.347739 | + | 1.48621i | ||||
\(577\) | 636.777 | + | 462.646i | 1.10360 | + | 0.801812i | 0.981644 | − | 0.190723i | \(-0.0610833\pi\) |
0.121956 | + | 0.992535i | \(0.461083\pi\) | |||||||
\(578\) | −518.678 | + | 713.899i | −0.897366 | + | 1.23512i | ||||
\(579\) | −861.405 | − | 240.258i | −1.48775 | − | 0.414953i | ||||
\(580\) | 41.6379 | + | 128.148i | 0.0717895 | + | 0.220945i | ||||
\(581\) | −57.4330 | − | 79.0497i | −0.0988519 | − | 0.136058i | ||||
\(582\) | −580.643 | + | 24.4934i | −0.997669 | + | 0.0420849i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 189.998i | 0.325340i | ||||||||
\(585\) | −634.661 | − | 734.458i | −1.08489 | − | 1.25548i | ||||
\(586\) | 321.243 | + | 988.683i | 0.548195 | + | 1.68717i | ||||
\(587\) | −173.593 | − | 56.4039i | −0.295730 | − | 0.0960884i | 0.157395 | − | 0.987536i | \(-0.449691\pi\) |
−0.453124 | + | 0.891447i | \(0.649691\pi\) | |||||||
\(588\) | 352.740 | − | 531.227i | 0.599897 | − | 0.903448i | ||||
\(589\) | −348.025 | − | 252.855i | −0.590875 | − | 0.429296i | ||||
\(590\) | 841.069 | + | 273.280i | 1.42554 | + | 0.463186i | ||||
\(591\) | −60.8395 | − | 163.457i | −0.102943 | − | 0.276577i | ||||
\(592\) | 270.600 | − | 196.602i | 0.457094 | − | 0.332098i | ||||
\(593\) | 685.071i | 1.15526i | 0.816297 | + | 0.577632i | \(0.196023\pi\) | ||||
−0.816297 | + | 0.577632i | \(0.803977\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.3837 | −0.0275357 | ||||||||
\(596\) | −818.965 | − | 1127.21i | −1.37410 | − | 1.89129i | ||||
\(597\) | 351.582 | − | 130.860i | 0.588915 | − | 0.219197i | ||||
\(598\) | −419.729 | + | 1291.79i | −0.701889 | + | 2.16019i | ||||
\(599\) | −212.117 | + | 291.955i | −0.354119 | + | 0.487403i | −0.948499 | − | 0.316782i | \(-0.897398\pi\) |
0.594379 | + | 0.804185i | \(0.297398\pi\) | |||||||
\(600\) | −199.222 | − | 132.285i | −0.332036 | − | 0.220475i | ||||
\(601\) | 129.629 | − | 398.956i | 0.215688 | − | 0.663820i | −0.783416 | − | 0.621498i | \(-0.786524\pi\) |
0.999104 | − | 0.0423223i | \(-0.0134756\pi\) | |||||||
\(602\) | −387.010 | + | 125.747i | −0.642874 | + | 0.208883i | ||||
\(603\) | 492.322 | − | 425.425i | 0.816454 | − | 0.705515i | ||||
\(604\) | 472.229 | 0.781836 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 58.1783 | + | 1379.18i | 0.0960039 | + | 2.27588i | ||||
\(607\) | 815.264 | − | 592.324i | 1.34310 | − | 0.975822i | 0.343780 | − | 0.939050i | \(-0.388293\pi\) |
0.999324 | − | 0.0367717i | \(-0.0117074\pi\) | |||||||
\(608\) | 851.743 | − | 276.748i | 1.40089 | − | 0.455178i | ||||
\(609\) | −9.33828 | + | 33.4809i | −0.0153338 | + | 0.0549769i | ||||
\(610\) | 175.138 | + | 127.246i | 0.287112 | + | 0.208599i | ||||
\(611\) | −189.920 | + | 261.402i | −0.310834 | + | 0.427827i | ||||
\(612\) | 37.8788 | + | 8.86279i | 0.0618935 | + | 0.0144817i | ||||
\(613\) | 170.654 | + | 525.219i | 0.278391 | + | 0.856800i | 0.988302 | + | 0.152509i | \(0.0487352\pi\) |
−0.709911 | + | 0.704292i | \(0.751265\pi\) | |||||||
\(614\) | 712.546 | + | 980.735i | 1.16050 | + | 1.59729i | ||||
\(615\) | −11.2258 | − | 266.119i | −0.0182533 | − | 0.432714i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 675.556i | − | 1.09490i | −0.836837 | − | 0.547452i | \(-0.815598\pi\) | ||
0.836837 | − | 0.547452i | \(-0.184402\pi\) | |||||||
\(618\) | 1077.33 | − | 854.357i | 1.74325 | − | 1.38245i | ||||
\(619\) | −83.1625 | − | 255.948i | −0.134350 | − | 0.413486i | 0.861139 | − | 0.508370i | \(-0.169752\pi\) |
−0.995488 | + | 0.0948843i | \(0.969752\pi\) | |||||||
\(620\) | 703.977 | + | 228.736i | 1.13545 | + | 0.368929i | ||||
\(621\) | −646.744 | − | 354.868i | −1.04146 | − | 0.571445i | ||||
\(622\) | 215.483 | + | 156.558i | 0.346436 | + | 0.251700i | ||||
\(623\) | 54.0108 | + | 17.5492i | 0.0866947 | + | 0.0281688i | ||||
\(624\) | −396.244 | + | 147.484i | −0.635007 | + | 0.236352i | ||||
\(625\) | 597.010 | − | 433.754i | 0.955217 | − | 0.694006i | ||||
\(626\) | 1832.83i | 2.92784i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.0719 | 0.0654011 | ||||||||
\(629\) | −18.2570 | − | 25.1286i | −0.0290254 | − | 0.0399501i | ||||
\(630\) | −217.328 | − | 516.220i | −0.344964 | − | 0.819398i | ||||
\(631\) | 28.8464 | − | 88.7801i | 0.0457154 | − | 0.140697i | −0.925593 | − | 0.378519i | \(-0.876433\pi\) |
0.971309 | + | 0.237822i | \(0.0764334\pi\) | |||||||
\(632\) | 241.245 | − | 332.045i | 0.381716 | − | 0.525388i | ||||
\(633\) | 80.3076 | − | 120.944i | 0.126868 | − | 0.191064i | ||||
\(634\) | −2.32153 | + | 7.14492i | −0.00366171 | + | 0.0112696i | ||||
\(635\) | −926.037 | + | 300.888i | −1.45833 | + | 0.473839i | ||||
\(636\) | 222.909 | − | 176.774i | 0.350486 | − | 0.277946i | ||||
\(637\) | 643.584 | 1.01034 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.94785 | − | 23.0469i | −0.00304828 | − | 0.0360672i | ||||
\(640\) | −676.259 | + | 491.331i | −1.05665 | + | 0.767704i | ||||
\(641\) | 14.0474 | − | 4.56426i | 0.0219148 | − | 0.00712054i | −0.298039 | − | 0.954554i | \(-0.596333\pi\) |
0.319954 | + | 0.947433i | \(0.396333\pi\) | |||||||
\(642\) | 183.510 | + | 51.1835i | 0.285842 | + | 0.0797251i | ||||
\(643\) | 352.763 | + | 256.298i | 0.548621 | + | 0.398597i | 0.827277 | − | 0.561794i | \(-0.189889\pi\) |
−0.278656 | + | 0.960391i | \(0.589889\pi\) | |||||||
\(644\) | −263.915 | + | 363.248i | −0.409806 | + | 0.564049i | ||||
\(645\) | 232.307 | − | 832.899i | 0.360166 | − | 1.29132i | ||||
\(646\) | −15.7722 | − | 48.5419i | −0.0244152 | − | 0.0751423i | ||||
\(647\) | 184.783 | + | 254.332i | 0.285600 | + | 0.393095i | 0.927579 | − | 0.373628i | \(-0.121886\pi\) |
−0.641979 | + | 0.766722i | \(0.721886\pi\) | |||||||
\(648\) | 56.7948 | + | 333.596i | 0.0876462 | + | 0.514809i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 948.550i | − | 1.45931i | ||||||
\(651\) | 118.646 | + | 149.611i | 0.182252 | + | 0.229817i | ||||
\(652\) | −435.283 | − | 1339.66i | −0.667612 | − | 2.05470i | ||||
\(653\) | −182.526 | − | 59.3063i | −0.279519 | − | 0.0908213i | 0.165903 | − | 0.986142i | \(-0.446946\pi\) |
−0.445422 | + | 0.895321i | \(0.646946\pi\) | |||||||
\(654\) | −809.133 | − | 537.271i | −1.23721 | − | 0.821516i | ||||
\(655\) | −802.835 | − | 583.294i | −1.22570 | − | 0.890525i | ||||
\(656\) | −110.339 | − | 35.8512i | −0.168199 | − | 0.0546513i | ||||
\(657\) | −158.818 | − | 377.241i | −0.241732 | − | 0.574187i | ||||
\(658\) | −150.834 | + | 109.587i | −0.229231 | + | 0.166546i | ||||
\(659\) | − | 127.678i | − | 0.193745i | −0.995297 | − | 0.0968724i | \(-0.969116\pi\) | ||
0.995297 | − | 0.0968724i | \(-0.0308839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 580.599 | 0.878364 | 0.439182 | − | 0.898398i | \(-0.355268\pi\) | ||||
0.439182 | + | 0.898398i | \(0.355268\pi\) | |||||||
\(662\) | 662.081 | + | 911.276i | 1.00012 | + | 1.37655i | ||||
\(663\) | 13.6957 | + | 36.7962i | 0.0206572 | + | 0.0554996i | ||||
\(664\) | −41.1834 | + | 126.750i | −0.0620232 | + | 0.190888i | ||||
\(665\) | −247.454 | + | 340.591i | −0.372111 | + | 0.512167i | ||||
\(666\) | 549.579 | − | 908.570i | 0.825193 | − | 1.36422i | ||||
\(667\) | −31.9375 | + | 98.2936i | −0.0478823 | + | 0.147367i | ||||
\(668\) | −816.443 | + | 265.279i | −1.22222 | + | 0.397124i | ||||
\(669\) | −394.656 | − | 497.656i | −0.589920 | − | 0.743880i | ||||
\(670\) | 1468.92 | 2.19241 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −397.167 | + | 16.7538i | −0.591023 | + | 0.0249313i | ||||
\(673\) | −442.096 | + | 321.202i | −0.656904 | + | 0.477268i | −0.865616 | − | 0.500709i | \(-0.833073\pi\) |
0.208712 | + | 0.977977i | \(0.433073\pi\) | |||||||
\(674\) | −1722.65 | + | 559.723i | −2.55586 | + | 0.830450i | ||||
\(675\) | 506.129 | + | 96.1240i | 0.749821 | + | 0.142406i | ||||
\(676\) | 411.866 | + | 299.238i | 0.609269 | + | 0.442660i | ||||
\(677\) | −17.1436 | + | 23.5961i | −0.0253229 | + | 0.0348540i | −0.821491 | − | 0.570222i | \(-0.806857\pi\) |
0.796168 | + | 0.605076i | \(0.206857\pi\) | |||||||
\(678\) | 1174.11 | + | 327.475i | 1.73172 | + | 0.483001i | ||||
\(679\) | −59.9160 | − | 184.402i | −0.0882415 | − | 0.271579i | ||||
\(680\) | 13.1350 | + | 18.0787i | 0.0193161 | + | 0.0265863i | ||||
\(681\) | 363.832 | − | 15.3476i | 0.534261 | − | 0.0225369i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 82.4506i | − | 0.120718i | −0.998177 | − | 0.0603592i | \(-0.980775\pi\) | ||
0.998177 | − | 0.0603592i | \(-0.0192246\pi\) | |||||||
\(684\) | 756.351 | − | 653.578i | 1.10578 | − | 0.955524i | ||||
\(685\) | 312.277 | + | 961.091i | 0.455879 | + | 1.40305i | ||||
\(686\) | 790.006 | + | 256.688i | 1.15161 | + | 0.374181i | ||||
\(687\) | 535.925 | − | 807.105i | 0.780094 | − | 1.17483i | ||||
\(688\) | −304.703 | − | 221.380i | −0.442883 | − | 0.321773i | ||||
\(689\) | 273.078 | + | 88.7285i | 0.396340 | + | 0.128779i | ||||
\(690\) | −580.938 | − | 1560.80i | −0.841939 | − | 2.26203i | ||||
\(691\) | −782.898 | + | 568.809i | −1.13299 | + | 0.823168i | −0.986128 | − | 0.165989i | \(-0.946918\pi\) |
−0.146865 | + | 0.989156i | \(0.546918\pi\) | |||||||
\(692\) | − | 888.061i | − | 1.28333i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −901.554 | −1.29907 | ||||||||
\(695\) | 436.438 | + | 600.705i | 0.627968 | + | 0.864324i | ||||
\(696\) | 44.4313 | − | 16.5375i | 0.0638380 | − | 0.0237608i | ||||
\(697\) | −3.32924 | + | 10.2463i | −0.00477652 | + | 0.0147006i | ||||
\(698\) | 741.109 | − | 1020.05i | 1.06176 | − | 1.46139i | ||||
\(699\) | 1005.71 | + | 667.798i | 1.43878 | + | 0.955362i | ||||
\(700\) | 96.8949 | − | 298.212i | 0.138421 | − | 0.426017i | ||||
\(701\) | 298.727 | − | 97.0623i | 0.426144 | − | 0.138463i | −0.0880898 | − | 0.996113i | \(-0.528076\pi\) |
0.514234 | + | 0.857650i | \(0.328076\pi\) | |||||||
\(702\) | −977.709 | + | 919.623i | −1.39275 | + | 1.31000i | ||||
\(703\) | −798.129 | −1.13532 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.6971 | − | 395.822i | −0.0236838 | − | 0.561450i | ||||
\(706\) | 335.660 | − | 243.871i | 0.475439 | − | 0.345427i | ||||
\(707\) | −438.005 | + | 142.316i | −0.619525 | + | 0.201296i | ||||
\(708\) | 188.213 | − | 674.808i | 0.265838 | − | 0.953118i | ||||
\(709\) | −264.833 | − | 192.413i | −0.373531 | − | 0.271386i | 0.385143 | − | 0.922857i | \(-0.374152\pi\) |
−0.758673 | + | 0.651471i | \(0.774152\pi\) | |||||||
\(710\) | 30.6913 | − | 42.2430i | 0.0432272 | − | 0.0594972i | ||||
\(711\) | −201.438 | + | 860.928i | −0.283316 | + | 1.21087i | ||||
\(712\) | −23.9361 | − | 73.6678i | −0.0336181 | − | 0.103466i | ||||
\(713\) | 333.721 | + | 459.327i | 0.468051 | + | 0.644217i | ||||
\(714\) | 0.954820 | + | 22.6351i | 0.00133728 | + | 0.0317018i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 314.061i | − | 0.438632i | ||||||
\(717\) | −0.755577 | + | 0.599196i | −0.00105380 | + | 0.000835699i | ||||
\(718\) | −263.630 | − | 811.369i | −0.367172 | − | 1.13004i | ||||
\(719\) | −1052.06 | − | 341.836i | −1.46323 | − | 0.475433i | −0.534176 | − | 0.845373i | \(-0.679378\pi\) |
−0.929056 | + | 0.369940i | \(0.879378\pi\) | |||||||
\(720\) | 268.309 | − | 443.572i | 0.372652 | − | 0.616072i | ||||
\(721\) | 371.124 | + | 269.637i | 0.514735 | + | 0.373977i | ||||
\(722\) | −196.643 | − | 63.8932i | −0.272359 | − | 0.0884947i | ||||
\(723\) | 817.601 | − | 304.315i | 1.13085 | − | 0.420906i | ||||
\(724\) | 1235.65 | − | 897.750i | 1.70669 | − | 1.23999i | ||||
\(725\) | − | 72.1759i | − | 0.0995530i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 577.040 | 0.793727 | 0.396864 | − | 0.917878i | \(-0.370099\pi\) | ||||
0.396864 | + | 0.917878i | \(0.370099\pi\) | |||||||
\(728\) | 122.184 | + | 168.172i | 0.167835 | + | 0.231005i | ||||
\(729\) | −391.616 | − | 614.881i | −0.537196 | − | 0.843458i | ||||
\(730\) | 285.544 | − | 878.813i | 0.391156 | − | 1.20385i | ||||
\(731\) | −20.5579 | + | 28.2955i | −0.0281230 | + | 0.0387080i | ||||
\(732\) | 94.8642 | − | 142.866i | 0.129596 | − | 0.195172i | ||||
\(733\) | −191.375 | + | 588.991i | −0.261084 | + | 0.803535i | 0.731485 | + | 0.681857i | \(0.238827\pi\) |
−0.992570 | + | 0.121678i | \(0.961173\pi\) | |||||||
\(734\) | −513.372 | + | 166.805i | −0.699417 | + | 0.227254i | ||||
\(735\) | −618.291 | + | 490.323i | −0.841212 | + | 0.667107i | ||||
\(736\) | −1181.99 | −1.60596 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −367.005 | + | 31.0181i | −0.497297 | + | 0.0420299i | ||||
\(739\) | −905.537 | + | 657.911i | −1.22535 | + | 0.890272i | −0.996533 | − | 0.0831961i | \(-0.973487\pi\) |
−0.228821 | + | 0.973468i | \(0.573487\pi\) | |||||||
\(740\) | 1306.10 | − | 424.379i | 1.76501 | − | 0.573485i | ||||
\(741\) | 971.789 | + | 271.045i | 1.31146 | + | 0.365783i | ||||
\(742\) | 134.038 | + | 97.3846i | 0.180645 | + | 0.131246i | ||||
\(743\) | −675.116 | + | 929.218i | −0.908636 | + | 1.25063i | 0.0589948 | + | 0.998258i | \(0.481210\pi\) |
−0.967630 | + | 0.252371i | \(0.918790\pi\) | |||||||
\(744\) | 69.9697 | − | 250.865i | 0.0940453 | − | 0.337184i | ||||
\(745\) | 532.808 | + | 1639.81i | 0.715178 | + | 2.20109i | ||||
\(746\) | −293.396 | − | 403.825i | −0.393292 | − | 0.541320i | ||||
\(747\) | −24.1791 | − | 286.086i | −0.0323682 | − | 0.382979i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 63.5613i | 0.0848616i | ||||||||
\(750\) | −224.193 | − | 282.704i | −0.298924 | − | 0.376939i | ||||
\(751\) | −84.5649 | − | 260.264i | −0.112603 | − | 0.346556i | 0.878837 | − | 0.477123i | \(-0.158320\pi\) |
−0.991440 | + | 0.130567i | \(0.958320\pi\) | |||||||
\(752\) | −164.116 | − | 53.3246i | −0.218240 | − | 0.0709104i | ||||
\(753\) | −281.465 | − | 186.895i | −0.373791 | − | 0.248201i | ||||
\(754\) | 152.134 | + | 110.532i | 0.201769 | + | 0.146594i | ||||
\(755\) | −555.776 | − | 180.583i | −0.736128 | − | 0.239182i | ||||
\(756\) | −401.319 | + | 189.244i | −0.530845 | + | 0.250323i | ||||
\(757\) | 451.436 | − | 327.988i | 0.596349 | − | 0.433273i | −0.248232 | − | 0.968701i | \(-0.579850\pi\) |
0.844581 | + | 0.535428i | \(0.179850\pi\) | |||||||
\(758\) | − | 162.899i | − | 0.214906i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 574.212 | 0.755543 | ||||||||
\(761\) | −247.901 | − | 341.207i | −0.325757 | − | 0.448366i | 0.614457 | − | 0.788950i | \(-0.289375\pi\) |
−0.940214 | + | 0.340584i | \(0.889375\pi\) | |||||||
\(762\) | 469.662 | + | 1261.84i | 0.616354 | + | 1.65596i | ||||
\(763\) | 100.135 | − | 308.183i | 0.131238 | − | 0.403910i | ||||
\(764\) | −433.434 | + | 596.570i | −0.567321 | + | 0.780851i | ||||
\(765\) | −41.1912 | − | 24.9159i | −0.0538447 | − | 0.0325697i | ||||
\(766\) | 84.7939 | − | 260.969i | 0.110697 | − | 0.340690i | ||||
\(767\) | 672.451 | − | 218.493i | 0.876729 | − | 0.284867i | ||||
\(768\) | −10.1665 | − | 12.8198i | −0.0132376 | − | 0.0166925i | ||||
\(769\) | 108.997 | 0.141738 | 0.0708692 | − | 0.997486i | \(-0.477423\pi\) | ||||
0.0708692 | + | 0.997486i | \(0.477423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −589.181 | + | 24.8536i | −0.764178 | + | 0.0322355i | ||||
\(772\) | −1293.88 | + | 940.059i | −1.67601 | + | 1.21769i | ||||
\(773\) | 981.122 | − | 318.786i | 1.26924 | − | 0.412401i | 0.404461 | − | 0.914555i | \(-0.367459\pi\) |
0.864778 | + | 0.502154i | \(0.167459\pi\) | |||||||
\(774\) | −1164.24 | − | 272.405i | −1.50418 | − | 0.351945i | ||||
\(775\) | −320.771 | − | 233.054i | −0.413898 | − | 0.300715i | ||||
\(776\) | −155.445 | + | 213.952i | −0.200316 | + | 0.275711i | ||||
\(777\) | 341.242 | + | 95.1771i | 0.439179 | + | 0.122493i | ||||
\(778\) | 254.954 | + | 784.668i | 0.327704 | + | 1.00857i | ||||
\(779\) | 162.721 | + | 223.966i | 0.208885 | + | 0.287505i | ||||
\(780\) | −1734.41 | + | 73.1631i | −2.22360 | + | 0.0937988i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 67.3630i | 0.0861420i | ||||||||
\(783\) | −74.3946 | + | 69.9748i | −0.0950123 | + | 0.0893676i | ||||
\(784\) | 106.214 | + | 326.893i | 0.135477 | + | 0.416955i | ||||
\(785\) | −48.3384 | − | 15.7061i | −0.0615776 | − | 0.0200078i | ||||
\(786\) | −759.066 | + | 1143.16i | −0.965733 | + | 1.45440i | ||||
\(787\) | 167.812 | + | 121.923i | 0.213230 | + | 0.154921i | 0.689274 | − | 0.724501i | \(-0.257930\pi\) |
−0.476044 | + | 0.879422i | \(0.657930\pi\) | |||||||
\(788\) | −296.651 | − | 96.3877i | −0.376460 | − | 0.122319i | ||||
\(789\) | 395.910 | + | 1063.69i | 0.501787 | + | 1.34815i | ||||
\(790\) | −1614.87 | + | 1173.27i | −2.04414 | + | 1.48515i | ||||
\(791\) | 406.668i | 0.514119i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 173.082 | 0.218263 | ||||||||
\(794\) | 380.422 | + | 523.606i | 0.479121 | + | 0.659453i | ||||
\(795\) | −329.945 | + | 122.807i | −0.415026 | + | 0.154474i | ||||
\(796\) | 207.321 | − | 638.069i | 0.260454 | − | 0.801595i | ||||
\(797\) | −130.723 | + | 179.925i | −0.164019 | + | 0.225753i | −0.883113 | − | 0.469160i | \(-0.844557\pi\) |
0.719094 | + | 0.694912i | \(0.244557\pi\) | |||||||
\(798\) | 484.967 | + | 322.022i | 0.607728 | + | 0.403537i | ||||
\(799\) | −4.95186 | + | 15.2403i | −0.00619757 | + | 0.0190742i | ||||
\(800\) | 785.043 | − | 255.076i | 0.981303 | − | 0.318845i | ||||
\(801\) | 109.103 | + | 126.259i | 0.136209 | + | 0.157627i | ||||
\(802\) | −1376.50 | −1.71633 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −49.0426 | − | 1162.61i | −0.0609983 | − | 1.44603i | ||||
\(805\) | 449.515 | − | 326.592i | 0.558403 | − | 0.405704i | ||||
\(806\) | 982.472 | − | 319.224i | 1.21895 | − | 0.396060i | ||||
\(807\) | −162.126 | + | 581.276i | −0.200899 | + | 0.720293i | ||||
\(808\) | 508.191 | + | 369.223i | 0.628950 | + | 0.456959i | ||||
\(809\) | 442.375 | − | 608.877i | 0.546817 | − | 0.752630i | −0.442759 | − | 0.896641i | \(-0.646000\pi\) |
0.989576 | + | 0.144011i | \(0.0460001\pi\) | |||||||
\(810\) | 238.657 | − | 1628.36i | 0.294638 | − | 2.01033i | ||||
\(811\) | −71.7678 | − | 220.879i | −0.0884930 | − | 0.272354i | 0.897010 | − | 0.442010i | \(-0.145734\pi\) |
−0.985503 | + | 0.169656i | \(0.945734\pi\) | |||||||
\(812\) | 36.5380 | + | 50.2903i | 0.0449976 | + | 0.0619338i | ||||
\(813\) | −10.1421 | − | 240.430i | −0.0124749 | − | 0.295732i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1743.13i | 2.13881i | ||||||||
\(816\) | −16.4295 | + | 13.0291i | −0.0201342 | + | 0.0159670i | ||||
\(817\) | 277.719 | + | 854.730i | 0.339925 | + | 1.04618i | ||||
\(818\) | −449.069 | − | 145.911i | −0.548984 | − | 0.178376i | ||||
\(819\) | −383.169 | − | 231.772i | −0.467849 | − | 0.282994i | ||||
\(820\) | −385.373 | − | 279.990i | −0.469967 | − | 0.341451i | ||||
\(821\) | 461.227 | + | 149.862i | 0.561787 | + | 0.182536i | 0.576125 | − | 0.817361i | \(-0.304564\pi\) |
−0.0143379 | + | 0.999897i | \(0.504564\pi\) | |||||||
\(822\) | 1309.60 | − | 487.440i | 1.59319 | − | 0.592993i | ||||
\(823\) | −126.927 | + | 92.2181i | −0.154225 | + | 0.112051i | −0.662222 | − | 0.749308i | \(-0.730386\pi\) |
0.507997 | + | 0.861359i | \(0.330386\pi\) | |||||||
\(824\) | − | 625.689i | − | 0.759331i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 407.986 | 0.493930 | ||||||||
\(827\) | −92.7092 | − | 127.603i | −0.112103 | − | 0.154297i | 0.749279 | − | 0.662255i | \(-0.230400\pi\) |
−0.861382 | + | 0.507958i | \(0.830400\pi\) | |||||||
\(828\) | −1215.94 | + | 511.907i | −1.46852 | + | 0.618246i | ||||
\(829\) | 403.767 | − | 1242.67i | 0.487053 | − | 1.49900i | −0.341931 | − | 0.939725i | \(-0.611081\pi\) |
0.828985 | − | 0.559271i | \(-0.188919\pi\) | |||||||
\(830\) | 380.977 | − | 524.370i | 0.459009 | − | 0.631771i | ||||
\(831\) | −363.289 | + | 547.114i | −0.437171 | + | 0.658381i | ||||
\(832\) | −490.373 | + | 1509.21i | −0.589390 | + | 1.81396i | ||||
\(833\) | 30.3561 | − | 9.86329i | 0.0364419 | − | 0.0118407i | ||||
\(834\) | 804.474 | − | 637.973i | 0.964597 | − | 0.764955i | ||||
\(835\) | 1062.33 | 1.27226 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 70.7709 | + | 556.579i | 0.0845530 | + | 0.664969i | ||||
\(838\) | −1870.54 | + | 1359.03i | −2.23215 | + | 1.62175i | ||||
\(839\) | −1220.51 | + | 396.569i | −1.45472 | + | 0.472668i | −0.926454 | − | 0.376409i | \(-0.877159\pi\) |
−0.528269 | + | 0.849077i | \(0.677159\pi\) | |||||||
\(840\) | −245.506 | − | 68.4750i | −0.292269 | − | 0.0815178i | ||||
\(841\) | −668.807 | − | 485.917i | −0.795252 | − | 0.577785i | ||||
\(842\) | 785.866 | − | 1081.65i | 0.933333 | − | 1.28462i | ||||
\(843\) | −400.117 | + | 1434.56i | −0.474635 | + | 1.70173i | ||||
\(844\) | −80.2314 | − | 246.927i | −0.0950610 | − | 0.292568i | ||||
\(845\) | −370.304 | − | 509.679i | −0.438229 | − | 0.603170i | ||||
\(846\) | −545.878 | + | 46.1359i | −0.645246 | + | 0.0545342i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 153.347i | 0.180834i | ||||||||
\(849\) | −573.580 | − | 723.276i | −0.675595 | − | 0.851916i | ||||
\(850\) | −14.5371 | − | 44.7405i | −0.0171025 | − | 0.0526359i | ||||
\(851\) | 1001.82 | + | 325.512i | 1.17723 | + | 0.382505i | ||||
\(852\) | −34.4589 | − | 22.8810i | −0.0404447 | − | 0.0268557i | ||||
\(853\) | 401.784 | + | 291.913i | 0.471025 | + | 0.342219i | 0.797840 | − | 0.602869i | \(-0.205976\pi\) |
−0.326816 | + | 0.945088i | \(0.605976\pi\) | |||||||
\(854\) | 94.9839 | + | 30.8621i | 0.111222 | + | 0.0361383i | ||||
\(855\) | −1140.10 | + | 479.978i | −1.33345 | + | 0.561378i | ||||
\(856\) | 70.1371 | − | 50.9576i | 0.0819359 | − | 0.0595299i | ||||
\(857\) | − | 479.970i | − | 0.560059i | −0.959991 | − | 0.280029i | \(-0.909656\pi\) | ||
0.959991 | − | 0.280029i | \(-0.0903442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 658.810 | 0.766950 | 0.383475 | − | 0.923551i | \(-0.374727\pi\) | ||||
0.383475 | + | 0.923551i | \(0.374727\pi\) | |||||||
\(860\) | −908.950 | − | 1251.06i | −1.05692 | − | 1.45472i | ||||
\(861\) | −42.8638 | − | 115.162i | −0.0497837 | − | 0.133754i | ||||
\(862\) | −9.20523 | + | 28.3308i | −0.0106789 | + | 0.0328663i | ||||
\(863\) | −316.707 | + | 435.910i | −0.366984 | + | 0.505110i | −0.952078 | − | 0.305855i | \(-0.901058\pi\) |
0.585094 | + | 0.810965i | \(0.301058\pi\) | |||||||
\(864\) | −1024.02 | − | 561.878i | −1.18521 | − | 0.650322i | ||||
\(865\) | −339.599 | + | 1045.18i | −0.392600 | + | 1.20830i | ||||
\(866\) | −172.518 | + | 56.0544i | −0.199212 | + | 0.0647279i | ||||
\(867\) | −537.509 | − | 677.791i | −0.619964 | − | 0.781766i | ||||
\(868\) | 341.485 | 0.393416 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −230.365 | + | 9.71754i | −0.264787 | + | 0.0111696i | ||||
\(871\) | 950.133 | − | 690.312i | 1.09085 | − | 0.792551i | ||||
\(872\) | −420.345 | + | 136.579i | −0.482048 | + | 0.156627i | ||||
\(873\) | 129.795 | − | 554.735i | 0.148678 | − | 0.635435i | ||||
\(874\) | 1400.37 | + | 1017.43i | 1.60225 | + | 1.16410i | ||||
\(875\) | 70.7560 | − | 97.3872i | 0.0808639 | − | 0.111300i | ||||
\(876\) | −705.091 | − | 196.659i | −0.804898 | − | 0.224497i | ||||
\(877\) | −26.1783 | − | 80.5685i | −0.0298498 | − | 0.0918683i | 0.935022 | − | 0.354591i | \(-0.115380\pi\) |
−0.964872 | + | 0.262722i | \(0.915380\pi\) | |||||||
\(878\) | −799.957 | − | 1101.05i | −0.911113 | − | 1.25404i | ||||
\(879\) | −1018.19 | + | 42.9505i | −1.15835 | + | 0.0488629i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 364.734i | 0.414000i | 0.978341 | + | 0.207000i | \(0.0663701\pi\) | ||||
−0.978341 | + | 0.207000i | \(0.933630\pi\) | |||||||
\(882\) | 713.443 | + | 825.629i | 0.808892 | + | 0.936087i | ||||
\(883\) | 68.8459 | + | 211.886i | 0.0779682 | + | 0.239961i | 0.982442 | − | 0.186567i | \(-0.0597363\pi\) |
−0.904474 | + | 0.426529i | \(0.859736\pi\) | |||||||
\(884\) | 66.7797 | + | 21.6980i | 0.0755427 | + | 0.0245453i | ||||
\(885\) | −479.562 | + | 722.222i | −0.541878 | + | 0.816070i | ||||
\(886\) | 1325.42 | + | 962.975i | 1.49596 | + | 1.08688i | ||||
\(887\) | −1296.73 | − | 421.334i | −1.46193 | − | 0.475010i | −0.533272 | − | 0.845944i | \(-0.679038\pi\) |
−0.928659 | + | 0.370934i | \(0.879038\pi\) | |||||||
\(888\) | −168.553 | − | 452.850i | −0.189812 | − | 0.509966i | ||||
\(889\) | −363.412 | + | 264.034i | −0.408788 | + | 0.297002i | ||||
\(890\) | 376.714i | 0.423274i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1135.89 | −1.27342 | ||||||||
\(893\) | 242.029 | + | 333.124i | 0.271029 | + | 0.373040i | ||||
\(894\) | 2234.44 | − | 831.670i | 2.49938 | − | 0.930280i | ||||
\(895\) | −120.098 | + | 369.625i | −0.134188 | + | 0.412989i | ||||
\(896\) | −226.670 | + | 311.984i | −0.252980 | + | 0.348197i | ||||
\(897\) | −1109.26 | − | 736.557i | −1.23663 | − | 0.821134i | ||||
\(898\) | 727.612 | − | 2239.36i | 0.810259 | − | 2.49372i | ||||
\(899\) | 74.7570 | − | 24.2900i | 0.0831557 | − | 0.0270189i | ||||
\(900\) | 697.120 | − | 602.396i | 0.774578 | − | 0.669329i | ||||
\(901\) | 14.2402 | 0.0158049 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.8126 | − | 398.560i | −0.0186186 | − | 0.441373i | ||||
\(904\) | 448.740 | − | 326.029i | 0.496394 | − | 0.360652i | ||||
\(905\) | −1797.56 | + | 584.064i | −1.98626 | + | 0.645374i | ||||
\(906\) | −217.096 | + | 778.361i | −0.239620 | + | 0.859118i | ||||
\(907\) | −531.719 | − | 386.317i | −0.586239 | − | 0.425928i | 0.254729 | − | 0.967013i | \(-0.418014\pi\) |
−0.840968 | + | 0.541085i | \(0.818014\pi\) | |||||||
\(908\) | 382.796 | − | 526.873i | 0.421581 | − | 0.580257i | ||||
\(909\) | −1317.64 | − | 308.299i | −1.44955 | − | 0.339162i | ||||
\(910\) | −312.405 | − | 961.484i | −0.343302 | − | 1.05658i | ||||
\(911\) | −204.809 | − | 281.895i | −0.224818 | − | 0.309435i | 0.681676 | − | 0.731654i | \(-0.261251\pi\) |
−0.906494 | + | 0.422219i | \(0.861251\pi\) | |||||||
\(912\) | 22.7085 | + | 538.329i | 0.0248996 | + | 0.590273i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 519.188i | 0.568039i | ||||||||
\(915\) | −166.280 | + | 131.865i | −0.181727 | + | 0.144115i | ||||
\(916\) | −535.416 | − | 1647.84i | −0.584516 | − | 1.79895i | ||||
\(917\) | −435.407 | − | 141.472i | −0.474816 | − | 0.154277i | ||||
\(918\) | −32.0221 | + | 58.3601i | −0.0348825 | + | 0.0635731i | ||||
\(919\) | 517.293 | + | 375.836i | 0.562887 | + | 0.408961i | 0.832514 | − | 0.554003i | \(-0.186901\pi\) |
−0.269627 | + | 0.962965i | \(0.586901\pi\) | |||||||
\(920\) | −720.759 | − | 234.189i | −0.783433 | − | 0.254553i | ||||
\(921\) | −1113.74 | + | 414.539i | −1.20927 | + | 0.450097i | ||||
\(922\) | −659.442 | + | 479.112i | −0.715229 | + | 0.519645i | ||||
\(923\) | − | 41.7471i | − | 0.0452298i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −735.627 | −0.795272 | ||||||||
\(926\) | −1267.86 | − | 1745.06i | −1.36918 | − | 1.88452i | ||||
\(927\) | 523.007 | + | 1242.30i | 0.564193 | + | 1.34013i | ||||
\(928\) | −50.5681 | + | 155.633i | −0.0544915 | + | 0.167708i | ||||
\(929\) | 184.827 | − | 254.392i | 0.198952 | − | 0.273834i | −0.697871 | − | 0.716224i | \(-0.745869\pi\) |
0.896823 | + | 0.442389i | \(0.145869\pi\) | |||||||
\(930\) | −700.655 | + | 1055.19i | −0.753392 | + | 1.13461i | ||||
\(931\) | 253.446 | − | 780.025i | 0.272229 | − | 0.837836i | ||||
\(932\) | 2053.32 | − | 667.165i | 2.20313 | − | 0.715842i | ||||
\(933\) | −204.584 | + | 162.242i | −0.219276 | + | 0.173892i | ||||
\(934\) | 2066.22 | 2.21222 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 51.4389 | + | 608.623i | 0.0549561 | + | 0.650238i | ||||
\(937\) | 1229.78 | − | 893.489i | 1.31247 | − | 0.953564i | 0.312474 | − | 0.949926i | \(-0.398842\pi\) |
0.999993 | − | 0.00363731i | \(-0.00115779\pi\) | |||||||
\(938\) | 644.501 | − | 209.411i | 0.687101 | − | 0.223253i | ||||
\(939\) | −1730.68 | − | 482.712i | −1.84311 | − | 0.514070i | ||||
\(940\) | −573.199 | − | 416.453i | −0.609786 | − | 0.443035i | ||||
\(941\) | −659.673 | + | 907.963i | −0.701034 | + | 0.964891i | 0.298909 | + | 0.954282i | \(0.403377\pi\) |
−0.999944 | + | 0.0106096i | \(0.996623\pi\) | |||||||
\(942\) | −18.8818 | + | 67.6976i | −0.0200444 | + | 0.0718658i | ||||
\(943\) | −112.906 | − | 347.490i | −0.119731 | − | 0.368494i | ||||
\(944\) | 221.956 | + | 305.496i | 0.235123 | + | 0.323619i | ||||
\(945\) | 544.689 | − | 69.2591i | 0.576390 | − | 0.0732900i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 865.333i | − | 0.913762i | −0.889528 | − | 0.456881i | \(-0.848967\pi\) | ||
0.889528 | − | 0.456881i | \(-0.151033\pi\) | |||||||
\(948\) | 982.529 | + | 1238.95i | 1.03642 | + | 1.30691i | ||||
\(949\) | −228.298 | − | 702.628i | −0.240567 | − | 0.740388i | ||||
\(950\) | −1149.65 | − | 373.543i | −1.21015 | − | 0.393203i | ||||
\(951\) | −6.13531 | − | 4.07390i | −0.00645143 | − | 0.00428381i | ||||
\(952\) | 8.34041 | + | 6.05966i | 0.00876093 | + | 0.00636519i | ||||
\(953\) | −482.372 | − | 156.732i | −0.506162 | − | 0.164462i | 0.0447943 | − | 0.998996i | \(-0.485737\pi\) |
−0.550956 | + | 0.834534i | \(0.685737\pi\) | |||||||
\(954\) | 188.894 | + | 448.682i | 0.198002 | + | 0.470316i | ||||
\(955\) | 738.249 | − | 536.369i | 0.773035 | − | 0.561643i | ||||
\(956\) | 1.72460i | 0.00180397i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2141.59 | 2.23548 | ||||||||
\(959\) | 274.029 | + | 377.169i | 0.285745 | + | 0.393294i | ||||
\(960\) | −678.714 | − | 1823.50i | −0.706994 | − | 1.89948i | ||||
\(961\) | −163.529 | + | 503.291i | −0.170166 | + | 0.523716i | ||||
\(962\) | 1126.55 | − | 1550.57i | 1.17105 | − | 1.61182i | ||||
\(963\) | −96.6621 | + | 159.803i | −0.100376 | + | 0.165943i | ||||
\(964\) | 482.124 | − | 1483.82i | 0.500128 | − | 1.53924i | ||||
\(965\) | 1882.28 | − | 611.589i | 1.95055 | − | 0.633771i | ||||
\(966\) | −477.402 | − | 601.997i | −0.494205 | − | 0.623185i | ||||
\(967\) | 569.116 | 0.588537 | 0.294269 | − | 0.955723i | \(-0.404924\pi\) | ||||
0.294269 | + | 0.955723i | \(0.404924\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.9906 | − | 2.10876i | 0.0515899 | − | 0.00217623i | ||||
\(970\) | 1040.53 | − | 755.991i | 1.07271 | − | 0.779373i | ||||
\(971\) | 1192.00 | − | 387.303i | 1.22760 | − | 0.398871i | 0.377754 | − | 0.925906i | \(-0.376696\pi\) |
0.849843 | + | 0.527035i | \(0.176696\pi\) | |||||||
\(972\) | −1296.77 | − | 134.525i | −1.33413 | − | 0.138400i | ||||
\(973\) | 277.129 | + | 201.346i | 0.284819 | + | 0.206933i | ||||
\(974\) | 1175.22 | − | 1617.55i | 1.20659 | − | 1.66073i | ||||
\(975\) | 895.687 | + | 249.819i | 0.918654 | + | 0.256225i | ||||
\(976\) | 28.5647 | + | 87.9131i | 0.0292671 | + | 0.0900749i | ||||
\(977\) | 671.043 | + | 923.611i | 0.686840 | + | 0.945354i | 0.999991 | − | 0.00434910i | \(-0.00138437\pi\) |
−0.313150 | + | 0.949704i | \(0.601384\pi\) | |||||||
\(978\) | 2408.24 | − | 101.587i | 2.46241 | − | 0.103873i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1411.24i | 1.44004i | ||||||||
\(981\) | 720.430 | − | 622.539i | 0.734383 | − | 0.634596i | ||||
\(982\) | 58.4777 | + | 179.976i | 0.0595496 | + | 0.183275i | ||||
\(983\) | 632.701 | + | 205.577i | 0.643643 | + | 0.209132i | 0.612609 | − | 0.790386i | \(-0.290120\pi\) |
0.0310339 | + | 0.999518i | \(0.490120\pi\) | |||||||
\(984\) | −92.7118 | + | 139.624i | −0.0942194 | + | 0.141895i | ||||
\(985\) | 312.275 | + | 226.881i | 0.317031 | + | 0.230336i | ||||
\(986\) | 8.86970 | + | 2.88194i | 0.00899564 | + | 0.00292286i | ||||
\(987\) | −63.7550 | − | 171.290i | −0.0645947 | − | 0.173546i | ||||
\(988\) | 1459.68 | − | 1060.52i | 1.47741 | − | 1.07340i | ||||
\(989\) | − | 1186.13i | − | 1.19933i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1471.97 | −1.48534 | −0.742670 | − | 0.669658i | \(-0.766441\pi\) | ||||
−0.742670 | + | 0.669658i | \(0.766441\pi\) | |||||||
\(992\) | 528.395 | + | 727.273i | 0.532656 | + | 0.733139i | ||||
\(993\) | −1034.86 | + | 385.180i | −1.04216 | + | 0.387895i | ||||
\(994\) | 7.44388 | − | 22.9099i | 0.00748881 | − | 0.0230482i | ||||
\(995\) | −488.002 | + | 671.677i | −0.490454 | + | 0.675052i | ||||
\(996\) | −427.745 | − | 284.026i | −0.429463 | − | 0.285167i | ||||
\(997\) | −191.835 | + | 590.409i | −0.192413 | + | 0.592185i | 0.807584 | + | 0.589752i | \(0.200775\pi\) |
−0.999997 | + | 0.00243317i | \(0.999225\pi\) | |||||||
\(998\) | 960.436 | − | 312.065i | 0.962361 | − | 0.312690i | ||||
\(999\) | 713.193 | + | 758.240i | 0.713907 | + | 0.758999i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 363.3.h.n.245.4 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.n.245.1 | 16 | ||
11.2 | odd | 10 | 363.3.b.m.122.7 | 8 | |||
11.3 | even | 5 | 363.3.h.j.269.4 | 16 | |||
11.4 | even | 5 | inner | 363.3.h.n.323.1 | 16 | ||
11.5 | even | 5 | 363.3.h.j.251.1 | 16 | |||
11.6 | odd | 10 | 33.3.h.b.20.4 | yes | 16 | ||
11.7 | odd | 10 | 363.3.h.o.323.4 | 16 | |||
11.8 | odd | 10 | 33.3.h.b.5.1 | ✓ | 16 | ||
11.9 | even | 5 | 363.3.b.l.122.2 | 8 | |||
11.10 | odd | 2 | 363.3.h.o.245.1 | 16 | |||
33.2 | even | 10 | 363.3.b.m.122.2 | 8 | |||
33.5 | odd | 10 | 363.3.h.j.251.4 | 16 | |||
33.8 | even | 10 | 33.3.h.b.5.4 | yes | 16 | ||
33.14 | odd | 10 | 363.3.h.j.269.1 | 16 | |||
33.17 | even | 10 | 33.3.h.b.20.1 | yes | 16 | ||
33.20 | odd | 10 | 363.3.b.l.122.7 | 8 | |||
33.26 | odd | 10 | inner | 363.3.h.n.323.4 | 16 | ||
33.29 | even | 10 | 363.3.h.o.323.1 | 16 | |||
33.32 | even | 2 | 363.3.h.o.245.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.h.b.5.1 | ✓ | 16 | 11.8 | odd | 10 | ||
33.3.h.b.5.4 | yes | 16 | 33.8 | even | 10 | ||
33.3.h.b.20.1 | yes | 16 | 33.17 | even | 10 | ||
33.3.h.b.20.4 | yes | 16 | 11.6 | odd | 10 | ||
363.3.b.l.122.2 | 8 | 11.9 | even | 5 | |||
363.3.b.l.122.7 | 8 | 33.20 | odd | 10 | |||
363.3.b.m.122.2 | 8 | 33.2 | even | 10 | |||
363.3.b.m.122.7 | 8 | 11.2 | odd | 10 | |||
363.3.h.j.251.1 | 16 | 11.5 | even | 5 | |||
363.3.h.j.251.4 | 16 | 33.5 | odd | 10 | |||
363.3.h.j.269.1 | 16 | 33.14 | odd | 10 | |||
363.3.h.j.269.4 | 16 | 11.3 | even | 5 | |||
363.3.h.n.245.1 | 16 | 3.2 | odd | 2 | inner | ||
363.3.h.n.245.4 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.n.323.1 | 16 | 11.4 | even | 5 | inner | ||
363.3.h.n.323.4 | 16 | 33.26 | odd | 10 | inner | ||
363.3.h.o.245.1 | 16 | 11.10 | odd | 2 | |||
363.3.h.o.245.4 | 16 | 33.32 | even | 2 | |||
363.3.h.o.323.1 | 16 | 33.29 | even | 10 | |||
363.3.h.o.323.4 | 16 | 11.7 | odd | 10 |