Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(19,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.p (of order \(6\), degree \(2\), 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: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.10 | ||
Character | \(\chi\) | \(=\) | 216.19 |
Dual form | 216.3.p.b.91.10 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.263796 | − | 1.98253i | 0.131898 | − | 0.991263i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.86082 | − | 1.04596i | −0.965206 | − | 0.261491i | ||||
\(5\) | −4.40783 | + | 2.54486i | −0.881566 | + | 0.508972i | −0.871174 | − | 0.490974i | \(-0.836641\pi\) |
−0.0103914 | + | 0.999946i | \(0.503308\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.9609 | + | 6.32830i | 1.56585 | + | 0.904042i | 0.996645 | + | 0.0818449i | \(0.0260812\pi\) |
0.569202 | + | 0.822198i | \(0.307252\pi\) | |||||||
\(8\) | −3.09212 | + | 7.37826i | −0.386515 | + | 0.922283i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.88249 | + | 9.40996i | 0.388249 | + | 0.940996i | ||||
\(11\) | −4.51244 | + | 7.81578i | −0.410222 | + | 0.710525i | −0.994914 | − | 0.100730i | \(-0.967882\pi\) |
0.584692 | + | 0.811255i | \(0.301215\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.68283 | + | 5.59038i | −0.744833 | + | 0.430029i | −0.823824 | − | 0.566846i | \(-0.808164\pi\) |
0.0789910 | + | 0.996875i | \(0.474830\pi\) | |||||||
\(14\) | 15.4375 | − | 20.0610i | 1.10268 | − | 1.43293i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.8119 | + | 8.07657i | 0.863245 | + | 0.504785i | ||||
\(17\) | 19.2305 | 1.13120 | 0.565602 | − | 0.824678i | \(-0.308644\pi\) | ||||
0.565602 | + | 0.824678i | \(0.308644\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.2413 | 0.749541 | 0.374770 | − | 0.927118i | \(-0.377722\pi\) | ||||
0.374770 | + | 0.927118i | \(0.377722\pi\) | |||||||
\(20\) | 19.6797 | − | 5.21483i | 0.983984 | − | 0.260741i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.3046 | + | 11.0078i | 0.650210 | + | 0.500355i | ||||
\(23\) | 4.28195 | − | 2.47218i | 0.186172 | − | 0.107486i | −0.404017 | − | 0.914751i | \(-0.632386\pi\) |
0.590189 | + | 0.807265i | \(0.299053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.452634 | − | 0.783986i | 0.0181054 | − | 0.0313594i | ||||
\(26\) | 8.52879 | + | 20.6712i | 0.328031 | + | 0.795046i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −35.6990 | − | 35.8972i | −1.27497 | − | 1.28204i | ||||
\(29\) | 7.55576 | + | 4.36232i | 0.260543 | + | 0.150425i | 0.624582 | − | 0.780959i | \(-0.285269\pi\) |
−0.364039 | + | 0.931384i | \(0.618603\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.9931 | + | 19.6259i | −1.09655 | + | 0.633095i | −0.935313 | − | 0.353820i | \(-0.884882\pi\) |
−0.161239 | + | 0.986915i | \(0.551549\pi\) | |||||||
\(32\) | 19.6555 | − | 25.2519i | 0.614236 | − | 0.789123i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.07292 | − | 38.1249i | 0.149203 | − | 1.12132i | ||||
\(35\) | −64.4185 | −1.84053 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.9238i | 0.538482i | 0.963073 | + | 0.269241i | \(0.0867728\pi\) | ||||
−0.963073 | + | 0.269241i | \(0.913227\pi\) | |||||||
\(38\) | 3.75679 | − | 28.2337i | 0.0988629 | − | 0.742992i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.14712 | − | 40.3911i | −0.128678 | − | 1.00978i | ||||
\(41\) | 17.3873 | + | 30.1157i | 0.424081 | + | 0.734529i | 0.996334 | − | 0.0855475i | \(-0.0272639\pi\) |
−0.572253 | + | 0.820077i | \(0.693931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.02841 | + | 5.24536i | −0.0704281 | + | 0.121985i | −0.899089 | − | 0.437766i | \(-0.855770\pi\) |
0.828661 | + | 0.559751i | \(0.189103\pi\) | |||||||
\(44\) | 25.5968 | − | 25.4555i | 0.581745 | − | 0.578534i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.77161 | − | 9.14123i | −0.0819916 | − | 0.198722i | ||||
\(47\) | −52.8256 | − | 30.4989i | −1.12395 | − | 0.648912i | −0.181542 | − | 0.983383i | \(-0.558109\pi\) |
−0.942406 | + | 0.334471i | \(0.891442\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 55.5947 | + | 96.2928i | 1.13459 | + | 1.96516i | ||||
\(50\) | −1.43487 | − | 1.10417i | −0.0286974 | − | 0.0220834i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 43.2310 | − | 11.4556i | 0.831366 | − | 0.220300i | ||||
\(53\) | − | 6.53131i | − | 0.123232i | −0.998100 | − | 0.0616161i | \(-0.980375\pi\) | ||
0.998100 | − | 0.0616161i | \(-0.0196254\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 45.9341i | − | 0.835166i | ||||||
\(56\) | −80.5844 | + | 61.3048i | −1.43901 | + | 1.09473i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.6416 | − | 13.8287i | 0.183476 | − | 0.238426i | ||||
\(59\) | 25.0669 | + | 43.4171i | 0.424862 | + | 0.735882i | 0.996408 | − | 0.0846879i | \(-0.0269893\pi\) |
−0.571546 | + | 0.820570i | \(0.693656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.149359 | − | 0.0862322i | −0.00244850 | − | 0.00141364i | 0.498775 | − | 0.866731i | \(-0.333783\pi\) |
−0.501224 | + | 0.865318i | \(0.667117\pi\) | |||||||
\(62\) | 29.9417 | + | 72.5695i | 0.482931 | + | 1.17048i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −44.8776 | − | 45.6290i | −0.701212 | − | 0.712953i | ||||
\(65\) | 28.4535 | − | 49.2829i | 0.437746 | − | 0.758198i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −40.4370 | − | 70.0389i | −0.603537 | − | 1.04536i | −0.992281 | − | 0.124011i | \(-0.960424\pi\) |
0.388744 | − | 0.921346i | \(-0.372909\pi\) | |||||||
\(68\) | −74.2455 | − | 20.1144i | −1.09185 | − | 0.295800i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −16.9933 | + | 127.711i | −0.242762 | + | 1.82445i | ||||
\(71\) | − | 50.4875i | − | 0.711092i | −0.934659 | − | 0.355546i | \(-0.884295\pi\) | ||
0.934659 | − | 0.355546i | \(-0.115705\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24.0274 | 0.329142 | 0.164571 | − | 0.986365i | \(-0.447376\pi\) | ||||
0.164571 | + | 0.986365i | \(0.447376\pi\) | |||||||
\(74\) | 39.4995 | + | 5.25583i | 0.533778 | + | 0.0710247i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −54.9831 | − | 14.8959i | −0.723461 | − | 0.195998i | ||||
\(77\) | −98.9211 | + | 57.1121i | −1.28469 | + | 0.741716i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.84873 | − | 1.64471i | −0.0360599 | − | 0.0208192i | 0.481862 | − | 0.876247i | \(-0.339961\pi\) |
−0.517922 | + | 0.855428i | \(0.673294\pi\) | |||||||
\(80\) | −81.4343 | − | 0.450718i | −1.01793 | − | 0.00563397i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 64.2919 | − | 26.5264i | 0.784047 | − | 0.323493i | ||||
\(83\) | −18.4770 | + | 32.0032i | −0.222615 | + | 0.385580i | −0.955601 | − | 0.294663i | \(-0.904793\pi\) |
0.732986 | + | 0.680243i | \(0.238126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −84.7646 | + | 48.9389i | −0.997231 | + | 0.575752i | ||||
\(86\) | 9.60018 | + | 7.38761i | 0.111630 | + | 0.0859024i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −43.7139 | − | 57.4613i | −0.496748 | − | 0.652969i | ||||
\(89\) | −13.0096 | −0.146175 | −0.0730876 | − | 0.997326i | \(-0.523285\pi\) | ||||
−0.0730876 | + | 0.997326i | \(0.523285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −141.510 | −1.55506 | ||||||||
\(92\) | −19.1177 | + | 5.06590i | −0.207801 | + | 0.0550642i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −74.4000 | + | 96.6826i | −0.791489 | + | 1.02854i | ||||
\(95\) | −62.7731 | + | 36.2421i | −0.660770 | + | 0.381496i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 44.7519 | − | 77.5126i | 0.461360 | − | 0.799099i | −0.537669 | − | 0.843156i | \(-0.680695\pi\) |
0.999029 | + | 0.0440568i | \(0.0140283\pi\) | |||||||
\(98\) | 205.569 | − | 84.8163i | 2.09764 | − | 0.865472i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.56756 | + | 2.55339i | −0.0256756 | + | 0.0255339i | ||||
\(101\) | 98.5033 | + | 56.8709i | 0.975280 | + | 0.563078i | 0.900842 | − | 0.434147i | \(-0.142950\pi\) |
0.0744384 | + | 0.997226i | \(0.476284\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 169.831 | − | 98.0520i | 1.64885 | − | 0.951961i | 0.671313 | − | 0.741174i | \(-0.265731\pi\) |
0.977532 | − | 0.210787i | \(-0.0676027\pi\) | |||||||
\(104\) | −11.3068 | − | 88.7286i | −0.108720 | − | 0.853160i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.9485 | − | 1.72293i | −0.122156 | − | 0.0162541i | ||||
\(107\) | −31.7982 | −0.297179 | −0.148590 | − | 0.988899i | \(-0.547473\pi\) | ||||
−0.148590 | + | 0.988899i | \(0.547473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 114.940i | − | 1.05449i | −0.849712 | − | 0.527247i | \(-0.823224\pi\) | ||
0.849712 | − | 0.527247i | \(-0.176776\pi\) | |||||||
\(110\) | −91.0657 | − | 12.1172i | −0.827870 | − | 0.110157i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 100.281 | + | 175.933i | 0.895362 | + | 1.57083i | ||||
\(113\) | 16.4795 | + | 28.5433i | 0.145836 | + | 0.252596i | 0.929685 | − | 0.368357i | \(-0.120079\pi\) |
−0.783848 | + | 0.620952i | \(0.786746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.5827 | + | 21.7939i | −0.109415 | + | 0.189512i | ||||
\(116\) | −24.6086 | − | 24.7452i | −0.212143 | − | 0.213321i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 92.6880 | − | 38.2425i | 0.785492 | − | 0.324089i | ||||
\(119\) | 210.784 | + | 121.696i | 1.77129 | + | 1.02266i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.7758 | + | 34.2526i | 0.163436 | + | 0.283079i | ||||
\(122\) | −0.210358 | + | 0.273360i | −0.00172424 | + | 0.00224065i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 151.770 | − | 40.2167i | 1.22395 | − | 0.324328i | ||||
\(125\) | − | 122.635i | − | 0.981084i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 74.7526i | 0.588603i | 0.955713 | + | 0.294302i | \(0.0950870\pi\) | ||||
−0.955713 | + | 0.294302i | \(0.904913\pi\) | |||||||
\(128\) | −102.299 | + | 76.9342i | −0.799212 | + | 0.601049i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −90.1988 | − | 69.4104i | −0.693837 | − | 0.533926i | ||||
\(131\) | −41.0887 | − | 71.1677i | −0.313654 | − | 0.543265i | 0.665497 | − | 0.746401i | \(-0.268220\pi\) |
−0.979150 | + | 0.203136i | \(0.934887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 156.098 | + | 90.1230i | 1.17367 | + | 0.677617i | ||||
\(134\) | −149.521 | + | 61.6914i | −1.11583 | + | 0.460384i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −59.4630 | + | 141.888i | −0.437228 | + | 1.04329i | ||||
\(137\) | 91.7121 | − | 158.850i | 0.669432 | − | 1.15949i | −0.308632 | − | 0.951182i | \(-0.599871\pi\) |
0.978063 | − | 0.208308i | \(-0.0667956\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −103.570 | − | 179.388i | −0.745105 | − | 1.29056i | −0.950146 | − | 0.311807i | \(-0.899066\pi\) |
0.205040 | − | 0.978754i | \(-0.434267\pi\) | |||||||
\(140\) | 248.709 | + | 67.3795i | 1.77649 | + | 0.481282i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −100.093 | − | 13.3184i | −0.704879 | − | 0.0937915i | ||||
\(143\) | − | 100.905i | − | 0.705630i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −44.4060 | −0.306248 | ||||||||
\(146\) | 6.33832 | − | 47.6349i | 0.0434132 | − | 0.326267i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.8396 | − | 76.9224i | 0.140808 | − | 0.519746i | ||||
\(149\) | 195.664 | − | 112.967i | 1.31318 | − | 0.758167i | 0.330561 | − | 0.943785i | \(-0.392762\pi\) |
0.982622 | + | 0.185618i | \(0.0594287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −123.589 | − | 71.3540i | −0.818469 | − | 0.472543i | 0.0314192 | − | 0.999506i | \(-0.489997\pi\) |
−0.849888 | + | 0.526963i | \(0.823331\pi\) | |||||||
\(152\) | −44.0358 | + | 105.076i | −0.289709 | + | 0.691289i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 87.1313 | + | 211.180i | 0.565788 | + | 1.37130i | ||||
\(155\) | 99.8906 | − | 173.016i | 0.644455 | − | 1.11623i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.21204 | − | 4.74122i | 0.0523060 | − | 0.0301989i | −0.473619 | − | 0.880730i | \(-0.657053\pi\) |
0.525925 | + | 0.850531i | \(0.323719\pi\) | |||||||
\(158\) | −4.01217 | + | 5.21381i | −0.0253935 | + | 0.0329988i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −22.3756 | + | 161.327i | −0.139847 | + | 1.00829i | ||||
\(161\) | 62.5789 | 0.388689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 305.669 | 1.87527 | 0.937635 | − | 0.347622i | \(-0.113011\pi\) | ||||
0.937635 | + | 0.347622i | \(0.113011\pi\) | |||||||
\(164\) | −35.6294 | − | 134.458i | −0.217252 | − | 0.819865i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 58.5730 | + | 45.0735i | 0.352849 | + | 0.271527i | ||||
\(167\) | −13.4105 | + | 7.74257i | −0.0803026 | + | 0.0463627i | −0.539614 | − | 0.841913i | \(-0.681430\pi\) |
0.459311 | + | 0.888275i | \(0.348096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.9952 | + | 38.0969i | −0.130149 | + | 0.225425i | ||||
\(170\) | 74.6621 | + | 180.958i | 0.439189 | + | 1.06446i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.1786 | − | 17.0838i | 0.0998757 | − | 0.0993244i | ||||
\(173\) | 79.3643 | + | 45.8210i | 0.458753 | + | 0.264861i | 0.711520 | − | 0.702666i | \(-0.248007\pi\) |
−0.252767 | + | 0.967527i | \(0.581341\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.92259 | − | 5.72881i | 0.0567005 | − | 0.0327361i | ||||
\(176\) | −125.450 | + | 71.5058i | −0.712785 | + | 0.406283i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.43187 | + | 25.7918i | −0.0192802 | + | 0.144898i | ||||
\(179\) | −125.988 | −0.703846 | −0.351923 | − | 0.936029i | \(-0.614472\pi\) | ||||
−0.351923 | + | 0.936029i | \(0.614472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.0017i | 0.127081i | 0.997979 | + | 0.0635405i | \(0.0202392\pi\) | ||||
−0.997979 | + | 0.0635405i | \(0.979761\pi\) | |||||||
\(182\) | −37.3299 | + | 280.548i | −0.205109 | + | 1.54147i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.00012 | + | 39.2376i | 0.0271746 | + | 0.213248i | ||||
\(185\) | −50.7034 | − | 87.8209i | −0.274072 | − | 0.474707i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −86.7764 | + | 150.301i | −0.464045 | + | 0.803749i | ||||
\(188\) | 172.050 | + | 173.004i | 0.915157 | + | 0.920236i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 55.2916 | + | 134.010i | 0.291008 | + | 0.705315i | ||||
\(191\) | 20.4240 | + | 11.7918i | 0.106932 | + | 0.0617371i | 0.552512 | − | 0.833505i | \(-0.313669\pi\) |
−0.445580 | + | 0.895242i | \(0.647003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −31.0142 | − | 53.7183i | −0.160696 | − | 0.278333i | 0.774423 | − | 0.632668i | \(-0.218040\pi\) |
−0.935118 | + | 0.354336i | \(0.884707\pi\) | |||||||
\(194\) | −141.865 | − | 109.169i | −0.731265 | − | 0.562729i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −113.922 | − | 429.920i | −0.581237 | − | 2.19347i | ||||
\(197\) | 385.821i | 1.95848i | 0.202698 | + | 0.979241i | \(0.435029\pi\) | ||||
−0.202698 | + | 0.979241i | \(0.564971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 214.957i | 1.08018i | 0.841606 | + | 0.540092i | \(0.181611\pi\) | ||||
−0.841606 | + | 0.540092i | \(0.818389\pi\) | |||||||
\(200\) | 4.38485 | + | 5.76384i | 0.0219243 | + | 0.0288192i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 138.733 | − | 180.283i | 0.686796 | − | 0.892491i | ||||
\(203\) | 55.2121 | + | 95.6302i | 0.271981 | + | 0.471085i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −153.281 | − | 88.4966i | −0.747710 | − | 0.431691i | ||||
\(206\) | −149.590 | − | 362.560i | −0.726165 | − | 1.76000i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −178.890 | − | 0.990107i | −0.860046 | − | 0.00476013i | ||||
\(209\) | −64.2629 | + | 111.307i | −0.307478 | + | 0.532568i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 50.4896 | + | 87.4505i | 0.239287 | + | 0.414457i | 0.960510 | − | 0.278246i | \(-0.0897530\pi\) |
−0.721223 | + | 0.692703i | \(0.756420\pi\) | |||||||
\(212\) | −6.83151 | + | 25.2162i | −0.0322241 | + | 0.118944i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.38823 | + | 63.0408i | −0.0391973 | + | 0.294583i | ||||
\(215\) | − | 30.8275i | − | 0.143384i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −496.795 | −2.28938 | ||||||||
\(218\) | −227.871 | − | 30.3206i | −1.04528 | − | 0.139085i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −48.0455 | + | 177.344i | −0.218389 | + | 0.806107i | ||||
\(221\) | −186.205 | + | 107.506i | −0.842558 | + | 0.486451i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 66.2290 | + | 38.2373i | 0.296991 | + | 0.171468i | 0.641090 | − | 0.767465i | \(-0.278482\pi\) |
−0.344099 | + | 0.938933i | \(0.611816\pi\) | |||||||
\(224\) | 375.245 | − | 152.399i | 1.67520 | − | 0.680351i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 60.9351 | − | 25.1414i | 0.269624 | − | 0.111245i | ||||
\(227\) | −37.4197 | + | 64.8128i | −0.164844 | + | 0.285519i | −0.936600 | − | 0.350400i | \(-0.886046\pi\) |
0.771756 | + | 0.635919i | \(0.219379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 255.666 | − | 147.609i | 1.11645 | − | 0.644581i | 0.175956 | − | 0.984398i | \(-0.443698\pi\) |
0.940492 | + | 0.339817i | \(0.110365\pi\) | |||||||
\(230\) | 39.8878 | + | 30.6947i | 0.173425 | + | 0.133455i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −55.5497 | + | 42.2596i | −0.239438 | + | 0.182153i | ||||
\(233\) | −354.235 | −1.52032 | −0.760162 | − | 0.649734i | \(-0.774880\pi\) | ||||
−0.760162 | + | 0.649734i | \(0.774880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 310.461 | 1.32111 | ||||||||
\(236\) | −51.3660 | − | 193.845i | −0.217652 | − | 0.821376i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 296.870 | − | 385.782i | 1.24735 | − | 1.62093i | ||||
\(239\) | 107.843 | − | 62.2632i | 0.451226 | − | 0.260516i | −0.257122 | − | 0.966379i | \(-0.582774\pi\) |
0.708348 | + | 0.705863i | \(0.249441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 189.676 | − | 328.528i | 0.787036 | − | 1.36319i | −0.140740 | − | 0.990047i | \(-0.544948\pi\) |
0.927775 | − | 0.373139i | \(-0.121719\pi\) | |||||||
\(242\) | 73.1235 | − | 30.1703i | 0.302163 | − | 0.124671i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.486451 | + | 0.489151i | 0.00199365 | + | 0.00200472i | ||||
\(245\) | −490.104 | − | 282.961i | −2.00042 | − | 1.15494i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −137.896 | + | 79.6142i | −0.558283 | + | 0.322325i | ||||
\(248\) | −39.6945 | − | 311.496i | −0.160059 | − | 1.25603i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −243.128 | − | 32.3507i | −0.972512 | − | 0.129403i | ||||
\(251\) | 385.891 | 1.53741 | 0.768707 | − | 0.639601i | \(-0.220901\pi\) | ||||
0.768707 | + | 0.639601i | \(0.220901\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.6223i | 0.176373i | ||||||||
\(254\) | 148.199 | + | 19.7194i | 0.583461 | + | 0.0776355i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 125.538 | + | 223.106i | 0.490383 | + | 0.871507i | ||||
\(257\) | 228.629 | + | 395.997i | 0.889607 | + | 1.54084i | 0.840341 | + | 0.542058i | \(0.182355\pi\) |
0.0492659 | + | 0.998786i | \(0.484312\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −126.084 | + | 218.384i | −0.486811 | + | 0.843181i | ||||
\(260\) | −161.402 | + | 160.511i | −0.620777 | + | 0.617351i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −151.931 | + | 62.6856i | −0.579889 | + | 0.239258i | ||||
\(263\) | −404.801 | − | 233.712i | −1.53917 | − | 0.888638i | −0.998888 | − | 0.0471517i | \(-0.984986\pi\) |
−0.540278 | − | 0.841486i | \(-0.681681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.6213 | + | 28.7889i | 0.0627218 | + | 0.108637i | ||||
\(266\) | 219.849 | − | 285.694i | 0.826501 | − | 1.07404i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 82.8619 | + | 312.704i | 0.309186 | + | 1.16680i | ||||
\(269\) | − | 463.103i | − | 1.72157i | −0.508966 | − | 0.860787i | \(-0.669972\pi\) | ||
0.508966 | − | 0.860787i | \(-0.330028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 324.633i | − | 1.19791i | −0.800784 | − | 0.598954i | \(-0.795583\pi\) | ||
0.800784 | − | 0.598954i | \(-0.204417\pi\) | |||||||
\(272\) | 265.610 | + | 155.316i | 0.976506 | + | 0.571016i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −290.731 | − | 223.726i | −1.06106 | − | 0.816517i | ||||
\(275\) | 4.08497 | + | 7.07538i | 0.0148544 | + | 0.0257287i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −249.678 | − | 144.151i | −0.901363 | − | 0.520402i | −0.0237212 | − | 0.999719i | \(-0.507551\pi\) |
−0.877642 | + | 0.479316i | \(0.840885\pi\) | |||||||
\(278\) | −382.962 | + | 158.008i | −1.37756 | + | 0.568373i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 199.190 | − | 475.297i | 0.711393 | − | 1.69749i | ||||
\(281\) | −172.969 | + | 299.590i | −0.615546 | + | 1.06616i | 0.374742 | + | 0.927129i | \(0.377731\pi\) |
−0.990288 | + | 0.139028i | \(0.955602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.83064 | − | 13.5631i | −0.0276701 | − | 0.0479260i | 0.851859 | − | 0.523772i | \(-0.175475\pi\) |
−0.879529 | + | 0.475846i | \(0.842142\pi\) | |||||||
\(284\) | −52.8082 | + | 194.923i | −0.185944 | + | 0.686350i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −200.047 | − | 26.6183i | −0.699465 | − | 0.0930711i | ||||
\(287\) | 440.128i | 1.53355i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 80.8112 | 0.279623 | ||||||||
\(290\) | −11.7141 | + | 88.0361i | −0.0403935 | + | 0.303573i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −92.7655 | − | 25.1318i | −0.317690 | − | 0.0860678i | ||||
\(293\) | 91.8784 | − | 53.0460i | 0.313578 | − | 0.181045i | −0.334948 | − | 0.942237i | \(-0.608719\pi\) |
0.648527 | + | 0.761192i | \(0.275386\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −220.981 | − | 127.583i | −0.749087 | − | 0.432486i | ||||
\(296\) | −147.003 | − | 61.6069i | −0.496633 | − | 0.208132i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −172.344 | − | 417.710i | −0.578337 | − | 1.40171i | ||||
\(299\) | −27.6409 | + | 47.8755i | −0.0924445 | + | 0.160119i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −66.3884 | + | 38.3294i | −0.220559 | + | 0.127340i | ||||
\(302\) | −174.064 | + | 226.195i | −0.576369 | + | 0.748991i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 196.699 | + | 115.021i | 0.647037 | + | 0.378357i | ||||
\(305\) | 0.877796 | 0.00287802 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 329.540 | 1.07342 | 0.536710 | − | 0.843767i | \(-0.319667\pi\) | ||||
0.536710 | + | 0.843767i | \(0.319667\pi\) | |||||||
\(308\) | 441.654 | − | 117.032i | 1.43394 | − | 0.379974i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −316.657 | − | 243.677i | −1.02148 | − | 0.786053i | ||||
\(311\) | −342.791 | + | 197.911i | −1.10222 | + | 0.636369i | −0.936804 | − | 0.349855i | \(-0.886231\pi\) |
−0.165419 | + | 0.986223i | \(0.552898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −51.1983 | + | 88.6781i | −0.163573 | + | 0.283317i | −0.936148 | − | 0.351607i | \(-0.885635\pi\) |
0.772575 | + | 0.634924i | \(0.218969\pi\) | |||||||
\(314\) | −7.23330 | − | 17.5313i | −0.0230360 | − | 0.0558322i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.27813 | + | 9.32962i | 0.0293612 | + | 0.0295241i | ||||
\(317\) | 237.016 | + | 136.841i | 0.747685 | + | 0.431676i | 0.824857 | − | 0.565341i | \(-0.191256\pi\) |
−0.0771716 | + | 0.997018i | \(0.524589\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −68.1898 | + | 39.3694i | −0.213761 | + | 0.123415i | ||||
\(320\) | 313.932 | + | 86.9175i | 0.981038 | + | 0.271617i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 16.5080 | − | 124.064i | 0.0512672 | − | 0.385293i | ||||
\(323\) | 273.867 | 0.847884 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1216i | 0.0311434i | ||||||||
\(326\) | 80.6342 | − | 605.997i | 0.247344 | − | 1.85889i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −275.965 | + | 35.1668i | −0.841358 | + | 0.107216i | ||||
\(329\) | −386.012 | − | 668.592i | −1.17329 | − | 2.03219i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −145.019 | + | 251.179i | −0.438122 | + | 0.758850i | −0.997545 | − | 0.0700325i | \(-0.977690\pi\) |
0.559422 | + | 0.828883i | \(0.311023\pi\) | |||||||
\(332\) | 104.811 | − | 104.232i | 0.315695 | − | 0.313953i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.8122 | + | 28.6292i | 0.0353659 | + | 0.0857161i | ||||
\(335\) | 356.479 | + | 205.813i | 1.06412 | + | 0.614367i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 190.788 | + | 330.455i | 0.566137 | + | 0.980578i | 0.996943 | + | 0.0781332i | \(0.0248960\pi\) |
−0.430806 | + | 0.902445i | \(0.641771\pi\) | |||||||
\(338\) | 69.7258 | + | 53.6559i | 0.206289 | + | 0.158745i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 378.450 | − | 100.284i | 1.11309 | − | 0.294952i | ||||
\(341\) | − | 354.244i | − | 1.03884i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 787.105i | 2.29477i | ||||||||
\(344\) | −29.3374 | − | 38.5637i | −0.0852833 | − | 0.112104i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 111.777 | − | 145.254i | 0.323056 | − | 0.419810i | ||||
\(347\) | 71.1923 | + | 123.309i | 0.205165 | + | 0.355356i | 0.950185 | − | 0.311686i | \(-0.100894\pi\) |
−0.745020 | + | 0.667042i | \(0.767560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 533.855 | + | 308.222i | 1.52967 | + | 0.883156i | 0.999375 | + | 0.0353439i | \(0.0112527\pi\) |
0.530296 | + | 0.847812i | \(0.322081\pi\) | |||||||
\(350\) | −8.73998 | − | 21.1830i | −0.0249714 | − | 0.0605230i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 108.669 | + | 267.571i | 0.308719 | + | 0.760145i | ||||
\(353\) | −205.510 | + | 355.953i | −0.582181 | + | 1.00837i | 0.413040 | + | 0.910713i | \(0.364467\pi\) |
−0.995220 | + | 0.0976536i | \(0.968866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 128.484 | + | 222.540i | 0.361926 | + | 0.626874i | ||||
\(356\) | 50.2277 | + | 13.6076i | 0.141089 | + | 0.0382235i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −33.2352 | + | 249.775i | −0.0928358 | + | 0.697697i | ||||
\(359\) | 131.102i | 0.365186i | 0.983189 | + | 0.182593i | \(0.0584491\pi\) | ||||
−0.983189 | + | 0.182593i | \(0.941551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −158.186 | −0.438188 | ||||||||
\(362\) | 45.6014 | + | 6.06774i | 0.125971 | + | 0.0167617i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 546.347 | + | 148.015i | 1.50095 | + | 0.406634i | ||||
\(365\) | −105.909 | + | 61.1463i | −0.290160 | + | 0.167524i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 93.3059 | + | 53.8702i | 0.254239 | + | 0.146785i | 0.621704 | − | 0.783252i | \(-0.286441\pi\) |
−0.367465 | + | 0.930038i | \(0.619774\pi\) | |||||||
\(368\) | 79.1087 | + | 0.437846i | 0.214969 | + | 0.00118980i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −187.483 | + | 77.3541i | −0.506710 | + | 0.209065i | ||||
\(371\) | 41.3320 | − | 71.5892i | 0.111407 | − | 0.192963i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −560.553 | + | 323.636i | −1.50282 | + | 0.867656i | −0.502829 | + | 0.864386i | \(0.667707\pi\) |
−0.999995 | + | 0.00326975i | \(0.998959\pi\) | |||||||
\(374\) | 275.085 | + | 211.685i | 0.735521 | + | 0.566003i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 388.372 | − | 295.455i | 1.03290 | − | 0.785784i | ||||
\(377\) | −97.5482 | −0.258748 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −225.686 | −0.595477 | −0.297739 | − | 0.954647i | \(-0.596232\pi\) | ||||
−0.297739 | + | 0.954647i | \(0.596232\pi\) | |||||||
\(380\) | 280.264 | − | 74.2658i | 0.737536 | − | 0.195436i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.7653 | − | 37.3804i | 0.0753018 | − | 0.0978546i | ||||
\(383\) | 413.047 | − | 238.473i | 1.07845 | − | 0.622644i | 0.147973 | − | 0.988991i | \(-0.452725\pi\) |
0.930478 | + | 0.366348i | \(0.119392\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 290.685 | − | 503.481i | 0.755026 | − | 1.30774i | ||||
\(386\) | −114.679 | + | 47.3159i | −0.297097 | + | 0.122580i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −253.855 | + | 252.454i | −0.654265 | + | 0.650654i | ||||
\(389\) | −10.3892 | − | 5.99823i | −0.0267076 | − | 0.0154196i | 0.486587 | − | 0.873632i | \(-0.338242\pi\) |
−0.513294 | + | 0.858213i | \(0.671575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 82.3439 | − | 47.5413i | 0.210598 | − | 0.121589i | ||||
\(392\) | −882.379 | + | 112.443i | −2.25097 | + | 0.286845i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 764.901 | + | 101.778i | 1.94137 | + | 0.258320i | ||||
\(395\) | 16.7423 | 0.0423855 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.42581i | 0.00862924i | 0.999991 | + | 0.00431462i | \(0.00137339\pi\) | ||||
−0.999991 | + | 0.00431462i | \(0.998627\pi\) | |||||||
\(398\) | 426.157 | + | 56.7047i | 1.07075 | + | 0.142474i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.5837 | − | 7.17261i | 0.0314592 | − | 0.0179315i | ||||
\(401\) | −23.8998 | − | 41.3956i | −0.0596004 | − | 0.103231i | 0.834686 | − | 0.550727i | \(-0.185649\pi\) |
−0.894286 | + | 0.447496i | \(0.852316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 219.433 | − | 380.069i | 0.544499 | − | 0.943100i | ||||
\(404\) | −320.819 | − | 322.600i | −0.794106 | − | 0.798514i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 204.154 | − | 84.2326i | 0.502843 | − | 0.207470i | ||||
\(407\) | −155.720 | − | 89.9052i | −0.382605 | − | 0.220897i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −113.468 | − | 196.532i | −0.277428 | − | 0.480519i | 0.693317 | − | 0.720633i | \(-0.256149\pi\) |
−0.970745 | + | 0.240114i | \(0.922815\pi\) | |||||||
\(410\) | −215.882 | + | 280.538i | −0.526540 | + | 0.684238i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −758.247 | + | 200.924i | −1.84040 | + | 0.487680i | ||||
\(413\) | 634.522i | 1.53637i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 188.086i | − | 0.453219i | ||||||
\(416\) | −49.1532 | + | 354.392i | −0.118157 | + | 0.851904i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 203.716 | + | 156.765i | 0.487359 | + | 0.375036i | ||||
\(419\) | −174.977 | − | 303.068i | −0.417605 | − | 0.723314i | 0.578093 | − | 0.815971i | \(-0.303797\pi\) |
−0.995698 | + | 0.0926575i | \(0.970464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 173.344 | + | 100.080i | 0.411743 | + | 0.237720i | 0.691538 | − | 0.722340i | \(-0.256933\pi\) |
−0.279796 | + | 0.960060i | \(0.590267\pi\) | |||||||
\(422\) | 186.692 | − | 77.0278i | 0.442398 | − | 0.182530i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 48.1897 | + | 20.1956i | 0.113655 | + | 0.0476311i | ||||
\(425\) | 8.70438 | − | 15.0764i | 0.0204809 | − | 0.0354739i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.09141 | − | 1.89037i | −0.00255599 | − | 0.00442710i | ||||
\(428\) | 122.767 | + | 33.2598i | 0.286839 | + | 0.0777098i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −61.1164 | − | 8.13217i | −0.142131 | − | 0.0189120i | ||||
\(431\) | − | 332.817i | − | 0.772198i | −0.922457 | − | 0.386099i | \(-0.873822\pi\) | ||
0.922457 | − | 0.386099i | \(-0.126178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 276.314 | 0.638139 | 0.319069 | − | 0.947731i | \(-0.396630\pi\) | ||||
0.319069 | + | 0.947731i | \(0.396630\pi\) | |||||||
\(434\) | −131.052 | + | 984.910i | −0.301964 | + | 2.26938i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −120.223 | + | 443.762i | −0.275741 | + | 1.01780i | ||||
\(437\) | 60.9804 | − | 35.2071i | 0.139543 | − | 0.0805654i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.6495 | − | 24.0464i | −0.0948736 | − | 0.0547753i | 0.451813 | − | 0.892113i | \(-0.350778\pi\) |
−0.546686 | + | 0.837338i | \(0.684111\pi\) | |||||||
\(440\) | 338.914 | + | 142.034i | 0.770260 | + | 0.322804i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 164.013 | + | 397.517i | 0.371070 | + | 0.899359i | ||||
\(443\) | 190.236 | − | 329.498i | 0.429426 | − | 0.743787i | −0.567397 | − | 0.823445i | \(-0.692049\pi\) |
0.996822 | + | 0.0796575i | \(0.0253827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 57.3440 | − | 33.1076i | 0.128863 | − | 0.0743991i | ||||
\(446\) | 93.2775 | − | 121.214i | 0.209142 | − | 0.271780i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −203.146 | − | 784.135i | −0.453452 | − | 1.75030i | ||||
\(449\) | 638.660 | 1.42240 | 0.711202 | − | 0.702987i | \(-0.248151\pi\) | ||||
0.711202 | + | 0.702987i | \(0.248151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −313.837 | −0.695869 | ||||||||
\(452\) | −33.7691 | − | 127.438i | −0.0747104 | − | 0.281942i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 118.622 | + | 91.2829i | 0.261282 | + | 0.201064i | ||||
\(455\) | 623.754 | − | 360.124i | 1.37089 | − | 0.791482i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −278.126 | + | 481.729i | −0.608591 | + | 1.05411i | 0.382882 | + | 0.923797i | \(0.374932\pi\) |
−0.991473 | + | 0.130313i | \(0.958402\pi\) | |||||||
\(458\) | −225.195 | − | 545.804i | −0.491693 | − | 1.19171i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 71.3754 | − | 70.9814i | 0.155164 | − | 0.154307i | ||||
\(461\) | 181.920 | + | 105.032i | 0.394620 | + | 0.227834i | 0.684160 | − | 0.729332i | \(-0.260169\pi\) |
−0.289540 | + | 0.957166i | \(0.593502\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 156.561 | − | 90.3903i | 0.338144 | − | 0.195227i | −0.321307 | − | 0.946975i | \(-0.604122\pi\) |
0.659451 | + | 0.751748i | \(0.270789\pi\) | |||||||
\(464\) | 69.1270 | + | 121.277i | 0.148981 | + | 0.261372i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −93.4458 | + | 702.281i | −0.200527 | + | 1.50704i | ||||
\(467\) | −10.4709 | −0.0224215 | −0.0112108 | − | 0.999937i | \(-0.503569\pi\) | ||||
−0.0112108 | + | 0.999937i | \(0.503569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1023.59i | − | 2.18249i | ||||||
\(470\) | 81.8984 | − | 615.498i | 0.174252 | − | 1.30957i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −397.852 | + | 50.6990i | −0.842907 | + | 0.107413i | ||||
\(473\) | −27.3310 | − | 47.3388i | −0.0577823 | − | 0.100082i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.44609 | − | 11.1650i | 0.0135707 | − | 0.0235052i | ||||
\(476\) | −686.510 | − | 690.320i | −1.44225 | − | 1.45025i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −94.9900 | − | 230.227i | −0.198724 | − | 0.481645i | ||||
\(479\) | −364.147 | − | 210.240i | −0.760223 | − | 0.438915i | 0.0691526 | − | 0.997606i | \(-0.477970\pi\) |
−0.829376 | + | 0.558691i | \(0.811304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −111.382 | − | 192.919i | −0.231563 | − | 0.401079i | ||||
\(482\) | −601.279 | − | 462.701i | −1.24747 | − | 0.959961i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −40.5237 | − | 152.928i | −0.0837266 | − | 0.315967i | ||||
\(485\) | 455.550i | 0.939278i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 865.055i | − | 1.77629i | −0.459560 | − | 0.888147i | \(-0.651993\pi\) | ||
0.459560 | − | 0.888147i | \(-0.348007\pi\) | |||||||
\(488\) | 1.09808 | − | 0.835367i | 0.00225016 | − | 0.00171182i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −690.266 | + | 896.999i | −1.40871 | + | 1.83061i | ||||
\(491\) | 31.8734 | + | 55.2063i | 0.0649152 | + | 0.112436i | 0.896656 | − | 0.442727i | \(-0.145989\pi\) |
−0.831741 | + | 0.555164i | \(0.812656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 145.301 | + | 83.8895i | 0.294728 | + | 0.170161i | ||||
\(494\) | 121.461 | + | 294.384i | 0.245872 | + | 0.595919i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −628.021 | − | 3.47593i | −1.26617 | − | 0.00700792i | ||||
\(497\) | 319.500 | − | 553.390i | 0.642857 | − | 1.11346i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −363.674 | − | 629.902i | −0.728806 | − | 1.26233i | −0.957388 | − | 0.288805i | \(-0.906742\pi\) |
0.228582 | − | 0.973525i | \(-0.426591\pi\) | |||||||
\(500\) | −128.272 | + | 473.474i | −0.256545 | + | 0.946948i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 101.796 | − | 765.039i | 0.202782 | − | 1.52398i | ||||
\(503\) | 348.449i | 0.692742i | 0.938098 | + | 0.346371i | \(0.112586\pi\) | ||||
−0.938098 | + | 0.346371i | \(0.887414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −578.914 | −1.14636 | ||||||||
\(506\) | 88.4650 | + | 11.7712i | 0.174832 | + | 0.0232632i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 78.1886 | − | 288.607i | 0.153915 | − | 0.568123i | ||||
\(509\) | 706.201 | − | 407.725i | 1.38743 | − | 0.801032i | 0.394403 | − | 0.918938i | \(-0.370952\pi\) |
0.993025 | + | 0.117906i | \(0.0376182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 263.362 | + | 152.052i | 0.515386 | + | 0.297559i | ||||
\(512\) | 475.430 | − | 190.028i | 0.928573 | − | 0.371149i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 845.386 | − | 348.801i | 1.64472 | − | 0.678600i | ||||
\(515\) | −499.057 | + | 864.393i | −0.969043 | + | 1.67843i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 476.745 | − | 275.249i | 0.922136 | − | 0.532396i | ||||
\(518\) | 399.691 | + | 307.574i | 0.771605 | + | 0.593771i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 275.641 | + | 362.326i | 0.530078 | + | 0.696781i | ||||
\(521\) | 335.561 | 0.644072 | 0.322036 | − | 0.946727i | \(-0.395633\pi\) | ||||
0.322036 | + | 0.946727i | \(0.395633\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 215.728 | 0.412481 | 0.206241 | − | 0.978501i | \(-0.433877\pi\) | ||||
0.206241 | + | 0.978501i | \(0.433877\pi\) | |||||||
\(524\) | 84.1973 | + | 317.743i | 0.160682 | + | 0.606380i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −570.125 | + | 740.876i | −1.08389 | + | 1.40851i | ||||
\(527\) | −653.704 | + | 377.416i | −1.24043 | + | 0.716160i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −252.277 | + | 436.956i | −0.476893 | + | 0.826004i | ||||
\(530\) | 61.4593 | − | 25.3577i | 0.115961 | − | 0.0478448i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −508.400 | − | 511.222i | −0.955639 | − | 0.960943i | ||||
\(533\) | −336.717 | − | 194.403i | −0.631739 | − | 0.364734i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 140.161 | − | 80.9220i | 0.261983 | − | 0.151256i | ||||
\(536\) | 641.802 | − | 81.7860i | 1.19739 | − | 0.152586i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −918.115 | − | 122.165i | −1.70653 | − | 0.227072i | ||||
\(539\) | −1003.47 | −1.86173 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 130.450i | 0.241128i | 0.992706 | + | 0.120564i | \(0.0384703\pi\) | ||||
−0.992706 | + | 0.120564i | \(0.961530\pi\) | |||||||
\(542\) | −643.593 | − | 85.6368i | −1.18744 | − | 0.158001i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 377.985 | − | 485.607i | 0.694826 | − | 0.892659i | ||||
\(545\) | 292.506 | + | 506.635i | 0.536708 | + | 0.929605i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 130.466 | − | 225.973i | 0.238511 | − | 0.413114i | −0.721776 | − | 0.692127i | \(-0.756674\pi\) |
0.960287 | + | 0.279013i | \(0.0900072\pi\) | |||||||
\(548\) | −520.236 | + | 517.365i | −0.949336 | + | 0.944096i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.1047 | − | 6.23211i | 0.0274631 | − | 0.0113311i | ||||
\(551\) | 107.604 | + | 62.1250i | 0.195288 | + | 0.112750i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.8165 | − | 36.0552i | −0.0376428 | − | 0.0651993i | ||||
\(554\) | −351.648 | + | 456.966i | −0.634744 | + | 0.824849i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 212.231 | + | 800.915i | 0.381710 | + | 1.44049i | ||||
\(557\) | − | 133.587i | − | 0.239833i | −0.992784 | − | 0.119917i | \(-0.961737\pi\) | ||
0.992784 | − | 0.119917i | \(-0.0382627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 67.7199i | − | 0.121145i | ||||||
\(560\) | −889.744 | − | 520.281i | −1.58883 | − | 0.929073i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 548.317 | + | 421.945i | 0.975654 | + | 0.750792i | ||||
\(563\) | −438.575 | − | 759.634i | −0.778997 | − | 1.34926i | −0.932521 | − | 0.361117i | \(-0.882396\pi\) |
0.153524 | − | 0.988145i | \(-0.450938\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −145.277 | − | 83.8760i | −0.257128 | − | 0.148453i | ||||
\(566\) | −28.9548 | + | 11.9466i | −0.0511569 | + | 0.0211070i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 372.510 | + | 156.114i | 0.655828 | + | 0.274848i | ||||
\(569\) | 346.763 | − | 600.612i | 0.609426 | − | 1.05556i | −0.381909 | − | 0.924200i | \(-0.624733\pi\) |
0.991335 | − | 0.131357i | \(-0.0419335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −159.760 | − | 276.712i | −0.279789 | − | 0.484609i | 0.691543 | − | 0.722335i | \(-0.256931\pi\) |
−0.971332 | + | 0.237726i | \(0.923598\pi\) | |||||||
\(572\) | −105.543 | + | 389.577i | −0.184516 | + | 0.681078i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 872.566 | + | 116.104i | 1.52015 | + | 0.202272i | ||||
\(575\) | − | 4.47598i | − | 0.00778432i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 878.170 | 1.52196 | 0.760979 | − | 0.648776i | \(-0.224719\pi\) | ||||
0.760979 | + | 0.648776i | \(0.224719\pi\) | |||||||
\(578\) | 21.3177 | − | 160.210i | 0.0368818 | − | 0.277180i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 171.444 | + | 46.4471i | 0.295593 | + | 0.0800812i | ||||
\(581\) | −405.051 | + | 233.856i | −0.697162 | + | 0.402507i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 51.0472 | + | 29.4721i | 0.0875596 | + | 0.0505525i | ||||
\(584\) | −74.2956 | + | 177.280i | −0.127218 | + | 0.303562i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −80.9280 | − | 196.145i | −0.138102 | − | 0.334718i | ||||
\(587\) | −277.395 | + | 480.462i | −0.472564 | + | 0.818505i | −0.999507 | − | 0.0313957i | \(-0.990005\pi\) |
0.526943 | + | 0.849901i | \(0.323338\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −484.106 | + | 279.499i | −0.821911 | + | 0.474531i | ||||
\(590\) | −311.231 | + | 404.444i | −0.527510 | + | 0.685499i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −160.916 | + | 275.186i | −0.271818 | + | 0.464842i | ||||
\(593\) | 673.984 | 1.13657 | 0.568283 | − | 0.822833i | \(-0.307608\pi\) | ||||
0.568283 | + | 0.822833i | \(0.307608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1238.80 | −2.08202 | ||||||||
\(596\) | −873.584 | + | 231.487i | −1.46575 | + | 0.388401i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 87.6228 | + | 67.4282i | 0.146526 | + | 0.112756i | ||||
\(599\) | 222.534 | − | 128.480i | 0.371509 | − | 0.214491i | −0.302608 | − | 0.953115i | \(-0.597857\pi\) |
0.674118 | + | 0.738624i | \(0.264524\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 196.757 | − | 340.793i | 0.327383 | − | 0.567044i | −0.654609 | − | 0.755968i | \(-0.727167\pi\) |
0.981992 | + | 0.188924i | \(0.0605000\pi\) | |||||||
\(602\) | 58.4760 | + | 141.728i | 0.0971362 | + | 0.235428i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 402.521 | + | 404.755i | 0.666425 | + | 0.670124i | ||||
\(605\) | −174.336 | − | 100.653i | −0.288159 | − | 0.166369i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −501.576 | + | 289.585i | −0.826319 | + | 0.477076i | −0.852591 | − | 0.522579i | \(-0.824970\pi\) |
0.0262715 | + | 0.999655i | \(0.491637\pi\) | |||||||
\(608\) | 279.920 | − | 359.620i | 0.460395 | − | 0.591480i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.231559 | − | 1.74025i | 0.000379605 | − | 0.00285288i | ||||
\(611\) | 682.001 | 1.11621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 825.194i | 1.34616i | 0.739571 | + | 0.673079i | \(0.235028\pi\) | ||||
−0.739571 | + | 0.673079i | \(0.764972\pi\) | |||||||
\(614\) | 86.9312 | − | 653.321i | 0.141582 | − | 1.06404i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −115.512 | − | 906.464i | −0.187520 | − | 1.47153i | ||||
\(617\) | −146.033 | − | 252.936i | −0.236682 | − | 0.409945i | 0.723078 | − | 0.690766i | \(-0.242727\pi\) |
−0.959760 | + | 0.280821i | \(0.909393\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 230.497 | − | 399.233i | 0.372370 | − | 0.644964i | −0.617559 | − | 0.786524i | \(-0.711878\pi\) |
0.989930 | + | 0.141560i | \(0.0452118\pi\) | |||||||
\(620\) | −566.628 | + | 563.501i | −0.913916 | + | 0.908872i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 301.936 | + | 731.801i | 0.485428 | + | 1.17653i | ||||
\(623\) | −142.597 | − | 82.3285i | −0.228888 | − | 0.132148i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 323.406 | + | 560.156i | 0.517450 | + | 0.896249i | ||||
\(626\) | 162.301 | + | 124.895i | 0.259266 | + | 0.199513i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.6644 | + | 9.71553i | −0.0583828 | + | 0.0154706i | ||||
\(629\) | 383.145i | 0.609133i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 110.500i | − | 0.175119i | −0.996159 | − | 0.0875597i | \(-0.972093\pi\) | ||
0.996159 | − | 0.0875597i | \(-0.0279069\pi\) | |||||||
\(632\) | 20.9438 | − | 15.9330i | 0.0331388 | − | 0.0252105i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 333.816 | − | 433.793i | 0.526523 | − | 0.684216i | ||||
\(635\) | −190.235 | − | 329.497i | −0.299583 | − | 0.518892i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1076.63 | − | 621.591i | −1.69015 | − | 0.975810i | ||||
\(638\) | 60.0627 | + | 145.574i | 0.0941422 | + | 0.228172i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 255.130 | − | 599.450i | 0.398641 | − | 0.936641i | ||||
\(641\) | −134.761 | + | 233.413i | −0.210236 | + | 0.364139i | −0.951788 | − | 0.306756i | \(-0.900756\pi\) |
0.741553 | + | 0.670895i | \(0.234090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 284.721 | + | 493.151i | 0.442800 | + | 0.766953i | 0.997896 | − | 0.0648336i | \(-0.0206517\pi\) |
−0.555096 | + | 0.831787i | \(0.687318\pi\) | |||||||
\(644\) | −241.606 | − | 65.4553i | −0.375165 | − | 0.101639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 72.2448 | − | 542.948i | 0.111834 | − | 0.840476i | ||||
\(647\) | − | 420.048i | − | 0.649223i | −0.945847 | − | 0.324612i | \(-0.894766\pi\) | ||
0.945847 | − | 0.324612i | \(-0.105234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −452.451 | −0.697151 | ||||||||
\(650\) | 20.0663 | + | 2.67004i | 0.0308713 | + | 0.00410775i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1180.13 | − | 319.719i | −1.81002 | − | 0.490366i | ||||
\(653\) | 211.083 | − | 121.869i | 0.323251 | − | 0.186629i | −0.329590 | − | 0.944124i | \(-0.606910\pi\) |
0.652841 | + | 0.757495i | \(0.273577\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 362.224 | + | 209.130i | 0.553013 | + | 0.319282i | ||||
\(656\) | −3.07945 | + | 556.385i | −0.00469428 | + | 0.848149i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1427.33 | + | 588.907i | −2.16919 | + | 0.894995i | ||||
\(659\) | 268.514 | − | 465.080i | 0.407457 | − | 0.705736i | −0.587147 | − | 0.809480i | \(-0.699749\pi\) |
0.994604 | + | 0.103744i | \(0.0330823\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 190.176 | − | 109.798i | 0.287710 | − | 0.166109i | −0.349199 | − | 0.937049i | \(-0.613546\pi\) |
0.636909 | + | 0.770939i | \(0.280213\pi\) | |||||||
\(662\) | 459.715 | + | 353.763i | 0.694433 | + | 0.534385i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −178.995 | − | 235.286i | −0.269570 | − | 0.354347i | ||||
\(665\) | −917.402 | −1.37955 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.1378 | 0.0646744 | ||||||||
\(668\) | 59.8741 | − | 15.8658i | 0.0896319 | − | 0.0237512i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 502.067 | − | 652.436i | 0.749354 | − | 0.973785i | ||||
\(671\) | 1.34794 | − | 0.778236i | 0.00200886 | − | 0.00115981i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 52.2858 | − | 90.5617i | 0.0776907 | − | 0.134564i | −0.824563 | − | 0.565771i | \(-0.808579\pi\) |
0.902253 | + | 0.431207i | \(0.141912\pi\) | |||||||
\(674\) | 705.464 | − | 291.070i | 1.04668 | − | 0.431855i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 124.768 | − | 124.079i | 0.184568 | − | 0.183549i | ||||
\(677\) | 460.805 | + | 266.046i | 0.680657 | + | 0.392977i | 0.800102 | − | 0.599863i | \(-0.204778\pi\) |
−0.119446 | + | 0.992841i | \(0.538112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 981.046 | − | 566.407i | 1.44484 | − | 0.834178i | ||||
\(680\) | −98.9815 | − | 776.741i | −0.145561 | − | 1.14227i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −702.297 | − | 93.4480i | −1.02976 | − | 0.137021i | ||||
\(683\) | −782.844 | −1.14618 | −0.573092 | − | 0.819491i | \(-0.694256\pi\) | ||||
−0.573092 | + | 0.819491i | \(0.694256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 933.579i | 1.36289i | ||||||||
\(686\) | 1560.46 | + | 207.635i | 2.27472 | + | 0.302675i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −84.1927 | + | 47.9893i | −0.122373 | + | 0.0697519i | ||||
\(689\) | 36.5125 | + | 63.2415i | 0.0529935 | + | 0.0917874i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −445.414 | + | 771.480i | −0.644593 | + | 1.11647i | 0.339802 | + | 0.940497i | \(0.389640\pi\) |
−0.984395 | + | 0.175971i | \(0.943693\pi\) | |||||||
\(692\) | −258.484 | − | 259.919i | −0.373532 | − | 0.375605i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 263.243 | − | 108.612i | 0.379312 | − | 0.156502i | ||||
\(695\) | 913.034 | + | 527.141i | 1.31372 | + | 0.758476i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 334.366 | + | 579.139i | 0.479722 | + | 0.830903i | ||||
\(698\) | 751.886 | − | 977.075i | 1.07720 | − | 1.39982i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −44.3015 | + | 11.7392i | −0.0632879 | + | 0.0167704i | ||||
\(701\) | 292.848i | 0.417757i | 0.977942 | + | 0.208878i | \(0.0669813\pi\) | ||||
−0.977942 | + | 0.208878i | \(0.933019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 283.741i | 0.403614i | ||||||||
\(704\) | 559.133 | − | 144.855i | 0.794223 | − | 0.205760i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 651.474 | + | 501.328i | 0.922768 | + | 0.710096i | ||||
\(707\) | 719.792 | + | 1246.72i | 1.01809 | + | 1.76339i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −251.105 | − | 144.976i | −0.354168 | − | 0.204479i | 0.312351 | − | 0.949967i | \(-0.398883\pi\) |
−0.666520 | + | 0.745487i | \(0.732217\pi\) | |||||||
\(710\) | 475.086 | − | 196.017i | 0.669135 | − | 0.276081i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 40.2272 | − | 95.9882i | 0.0564989 | − | 0.134815i | ||||
\(713\) | −97.0379 | + | 168.075i | −0.136098 | + | 0.235729i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 256.789 | + | 444.772i | 0.359146 | + | 0.622059i | ||||
\(716\) | 486.419 | + | 131.779i | 0.679356 | + | 0.184049i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 259.913 | + | 34.5841i | 0.361996 | + | 0.0481673i | ||||
\(719\) | − | 1132.71i | − | 1.57540i | −0.616058 | − | 0.787701i | \(-0.711271\pi\) | ||
0.616058 | − | 0.787701i | \(-0.288729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2482.01 | 3.44245 | ||||||||
\(722\) | −41.7288 | + | 313.608i | −0.0577961 | + | 0.434360i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.0589 | − | 88.8053i | 0.0332305 | − | 0.122659i | ||||
\(725\) | 6.83999 | − | 3.94907i | 0.00943447 | − | 0.00544700i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.5708 | − | 24.5783i | −0.0585569 | − | 0.0338078i | 0.470436 | − | 0.882434i | \(-0.344097\pi\) |
−0.528993 | + | 0.848626i | \(0.677430\pi\) | |||||||
\(728\) | 437.567 | − | 1044.10i | 0.601054 | − | 1.43421i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 93.2860 | + | 226.097i | 0.127789 | + | 0.309722i | ||||
\(731\) | −58.2378 | + | 100.871i | −0.0796686 | + | 0.137990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 827.604 | − | 477.817i | 1.12906 | − | 0.651865i | 0.185364 | − | 0.982670i | \(-0.440653\pi\) |
0.943699 | + | 0.330805i | \(0.107320\pi\) | |||||||
\(734\) | 131.413 | − | 170.771i | 0.179036 | − | 0.232658i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.7366 | − | 156.720i | 0.0295334 | − | 0.212934i | ||||
\(737\) | 729.878 | 0.990337 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −279.034 | −0.377583 | −0.188791 | − | 0.982017i | \(-0.560457\pi\) | ||||
−0.188791 | + | 0.982017i | \(0.560457\pi\) | |||||||
\(740\) | 103.899 | + | 392.095i | 0.140405 | + | 0.529858i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −131.024 | − | 100.827i | −0.176583 | − | 0.135885i | ||||
\(743\) | −19.7539 | + | 11.4049i | −0.0265866 | + | 0.0153498i | −0.513234 | − | 0.858248i | \(-0.671553\pi\) |
0.486648 | + | 0.873598i | \(0.338220\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −574.970 | + | 995.877i | −0.771771 | + | 1.33675i | ||||
\(746\) | 493.745 | + | 1196.69i | 0.661856 | + | 1.60414i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 492.238 | − | 489.521i | 0.658072 | − | 0.654440i | ||||
\(749\) | −348.538 | − | 201.228i | −0.465338 | − | 0.268663i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −983.960 | + | 568.090i | −1.31020 | + | 0.756444i | −0.982129 | − | 0.188209i | \(-0.939732\pi\) |
−0.328071 | + | 0.944653i | \(0.606398\pi\) | |||||||
\(752\) | −483.296 | − | 847.897i | −0.642681 | − | 1.12752i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −25.7328 | + | 193.392i | −0.0341284 | + | 0.256488i | ||||
\(755\) | 726.344 | 0.962046 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1067.71i | 1.41045i | 0.708984 | + | 0.705224i | \(0.249154\pi\) | ||||
−0.708984 | + | 0.705224i | \(0.750846\pi\) | |||||||
\(758\) | −59.5350 | + | 447.428i | −0.0785422 | + | 0.590275i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −73.3015 | − | 575.222i | −0.0964494 | − | 0.756870i | ||||
\(761\) | −291.003 | − | 504.031i | −0.382395 | − | 0.662327i | 0.609009 | − | 0.793163i | \(-0.291567\pi\) |
−0.991404 | + | 0.130836i | \(0.958234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 727.373 | − | 1259.85i | 0.953307 | − | 1.65118i | ||||
\(764\) | −66.5196 | − | 66.8888i | −0.0870675 | − | 0.0875507i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −363.818 | − | 881.784i | −0.474959 | − | 1.15115i | ||||
\(767\) | −485.436 | − | 280.267i | −0.632902 | − | 0.365406i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −517.987 | − | 897.181i | −0.673586 | − | 1.16668i | −0.976880 | − | 0.213788i | \(-0.931420\pi\) |
0.303294 | − | 0.952897i | \(-0.401913\pi\) | |||||||
\(770\) | −921.483 | − | 709.107i | −1.19673 | − | 0.920918i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 63.5532 | + | 239.836i | 0.0823227 | + | 0.310669i | ||||
\(773\) | − | 1067.29i | − | 1.38071i | −0.723471 | − | 0.690355i | \(-0.757454\pi\) | ||
0.723471 | − | 0.690355i | \(-0.242546\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.5335i | 0.0458497i | ||||||||
\(776\) | 433.530 | + | 569.870i | 0.558673 | + | 0.734369i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.6323 | + | 19.0146i | −0.0188076 | + | 0.0244404i | ||||
\(779\) | 247.618 | + | 428.886i | 0.317866 | + | 0.550560i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 394.599 | + | 227.822i | 0.505249 | + | 0.291705i | ||||
\(782\) | −72.5299 | − | 175.790i | −0.0927492 | − | 0.224796i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.84631 | + | 1779.00i | −0.0125591 | + | 2.26914i | ||||
\(785\) | −24.1315 | + | 41.7970i | −0.0307408 | + | 0.0532446i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −549.400 | − | 951.588i | −0.698094 | − | 1.20913i | −0.969127 | − | 0.246564i | \(-0.920699\pi\) |
0.271033 | − | 0.962570i | \(-0.412635\pi\) | |||||||
\(788\) | 403.555 | − | 1489.59i | 0.512126 | − | 1.89034i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.41654 | − | 33.1920i | 0.00559056 | − | 0.0420152i | ||||
\(791\) | 417.148i | 0.527368i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.92828 | 0.00243163 | ||||||||
\(794\) | 6.79176 | + | 0.903714i | 0.00855385 | + | 0.00113818i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 224.837 | − | 829.910i | 0.282459 | − | 1.04260i | ||||
\(797\) | −973.877 | + | 562.268i | −1.22193 | + | 0.705481i | −0.965329 | − | 0.261037i | \(-0.915936\pi\) |
−0.256600 | + | 0.966518i | \(0.582602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1015.86 | − | 586.508i | −1.27142 | − | 0.734052i | ||||
\(800\) | −10.9004 | − | 26.8396i | −0.0136255 | − | 0.0335494i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −88.3725 | + | 36.4619i | −0.110190 | + | 0.0454637i | ||||
\(803\) | −108.422 | + | 187.793i | −0.135021 | + | 0.233864i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −275.837 | + | 159.255i | −0.342655 | + | 0.197832i | ||||
\(806\) | −695.612 | − | 535.293i | −0.863042 | − | 0.664135i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −724.193 | + | 550.932i | −0.896278 | + | 0.681846i | ||||
\(809\) | −1468.01 | −1.81460 | −0.907300 | − | 0.420484i | \(-0.861860\pi\) | ||||
−0.907300 | + | 0.420484i | \(0.861860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −90.2707 | −0.111308 | −0.0556540 | − | 0.998450i | \(-0.517724\pi\) | ||||
−0.0556540 | + | 0.998450i | \(0.517724\pi\) | |||||||
\(812\) | −113.138 | − | 426.961i | −0.139333 | − | 0.525814i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −219.318 | + | 285.003i | −0.269432 | + | 0.350127i | ||||
\(815\) | −1347.34 | + | 777.885i | −1.65317 | + | 0.954460i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.1284 | + | 74.7006i | −0.0527888 | + | 0.0914328i | ||||
\(818\) | −419.562 | + | 173.109i | −0.512913 | + | 0.211624i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 499.225 | + | 501.996i | 0.608811 | + | 0.612190i | ||||
\(821\) | 1001.79 | + | 578.386i | 1.22021 | + | 0.704489i | 0.964963 | − | 0.262386i | \(-0.0845094\pi\) |
0.255248 | + | 0.966875i | \(0.417843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −516.742 | + | 298.341i | −0.627876 | + | 0.362504i | −0.779929 | − | 0.625868i | \(-0.784745\pi\) |
0.152053 | + | 0.988372i | \(0.451412\pi\) | |||||||
\(824\) | 198.315 | + | 1556.25i | 0.240674 | + | 1.88865i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1257.96 | + | 167.384i | 1.52295 | + | 0.202644i | ||||
\(827\) | −601.527 | −0.727360 | −0.363680 | − | 0.931524i | \(-0.618480\pi\) | ||||
−0.363680 | + | 0.931524i | \(0.618480\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 375.459i | − | 0.452906i | −0.974022 | − | 0.226453i | \(-0.927287\pi\) | ||
0.974022 | − | 0.226453i | \(-0.0727130\pi\) | |||||||
\(830\) | −372.885 | − | 49.6163i | −0.449259 | − | 0.0597787i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 689.625 | + | 190.935i | 0.828877 | + | 0.229489i | ||||
\(833\) | 1069.11 | + | 1851.76i | 1.28345 | + | 2.22300i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.4075 | − | 68.2559i | 0.0471947 | − | 0.0817435i | ||||
\(836\) | 364.531 | − | 362.519i | 0.436041 | − | 0.433635i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −646.999 | + | 266.948i | −0.772076 | + | 0.318553i | ||||
\(839\) | −856.558 | − | 494.534i | −1.02093 | − | 0.589433i | −0.106555 | − | 0.994307i | \(-0.533982\pi\) |
−0.914372 | + | 0.404874i | \(0.867315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −382.440 | − | 662.406i | −0.454745 | − | 0.787641i | ||||
\(842\) | 244.139 | − | 317.258i | 0.289951 | − | 0.376791i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −103.461 | − | 390.441i | −0.122584 | − | 0.462608i | ||||
\(845\) | − | 223.899i | − | 0.264969i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 500.587i | 0.591012i | ||||||||
\(848\) | 52.7505 | − | 90.2099i | 0.0622058 | − | 0.106380i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −27.5932 | − | 21.2338i | −0.0324626 | − | 0.0249809i | ||||
\(851\) | 49.2554 | + | 85.3129i | 0.0578795 | + | 0.100250i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 329.989 | + | 190.519i | 0.386857 | + | 0.223352i | 0.680798 | − | 0.732472i | \(-0.261633\pi\) |
−0.293940 | + | 0.955824i | \(0.594967\pi\) | |||||||
\(854\) | −4.03562 | + | 1.66507i | −0.00472555 | + | 0.00194973i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 98.3239 | − | 234.616i | 0.114864 | − | 0.274084i | ||||
\(857\) | 82.2028 | − | 142.379i | 0.0959193 | − | 0.166137i | −0.814073 | − | 0.580763i | \(-0.802754\pi\) |
0.909992 | + | 0.414626i | \(0.136088\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 813.298 | + | 1408.67i | 0.946796 | + | 1.63990i | 0.752114 | + | 0.659033i | \(0.229034\pi\) |
0.194682 | + | 0.980866i | \(0.437632\pi\) | |||||||
\(860\) | −32.2445 | + | 119.020i | −0.0374936 | + | 0.138395i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −659.819 | − | 87.7958i | −0.765451 | − | 0.101851i | ||||
\(863\) | 1256.44i | 1.45590i | 0.685628 | + | 0.727952i | \(0.259527\pi\) | ||||
−0.685628 | + | 0.727952i | \(0.740473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −466.432 | −0.539228 | ||||||||
\(866\) | 72.8905 | − | 547.800i | 0.0841692 | − | 0.632564i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1918.04 | + | 519.630i | 2.20972 | + | 0.598652i | ||||
\(869\) | 25.7094 | − | 14.8434i | 0.0295851 | − | 0.0170810i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 783.089 | + | 452.117i | 0.899069 | + | 0.519077i | ||||
\(872\) | 848.056 | + | 355.408i | 0.972542 | + | 0.407578i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −53.7126 | − | 130.183i | −0.0614560 | − | 0.148951i | ||||
\(875\) | 776.074 | − | 1344.20i | 0.886941 | − | 1.53623i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.97163 | − | 4.02507i | 0.00794940 | − | 0.00458959i | −0.496020 | − | 0.868311i | \(-0.665206\pi\) |
0.503969 | + | 0.863721i | \(0.331872\pi\) | |||||||
\(878\) | −58.6595 | + | 76.2280i | −0.0668104 | + | 0.0868200i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 370.990 | − | 634.439i | 0.421580 | − | 0.720953i | ||||
\(881\) | −842.573 | −0.956382 | −0.478191 | − | 0.878256i | \(-0.658707\pi\) | ||||
−0.478191 | + | 0.878256i | \(0.658707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 621.919 | 0.704325 | 0.352163 | − | 0.935939i | \(-0.385446\pi\) | ||||
0.352163 | + | 0.935939i | \(0.385446\pi\) | |||||||
\(884\) | 831.353 | − | 220.296i | 0.940445 | − | 0.249204i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −603.055 | − | 464.067i | −0.680649 | − | 0.523778i | ||||
\(887\) | −413.440 | + | 238.700i | −0.466110 | + | 0.269109i | −0.714610 | − | 0.699523i | \(-0.753396\pi\) |
0.248500 | + | 0.968632i | \(0.420063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −473.057 | + | 819.358i | −0.532122 | + | 0.921663i | ||||
\(890\) | −50.5096 | − | 122.420i | −0.0567523 | − | 0.137550i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −215.704 | − | 216.901i | −0.241820 | − | 0.243162i | ||||
\(893\) | −752.304 | − | 434.343i | −0.842445 | − | 0.486386i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 555.335 | − | 320.623i | 0.620486 | − | 0.358238i | ||||
\(896\) | −1608.16 | + | 195.891i | −1.79482 | + | 0.218629i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 168.476 | − | 1266.16i | 0.187612 | − | 1.40998i | ||||
\(899\) | −342.459 | −0.380933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 125.600i | − | 0.139401i | ||||||
\(902\) | −82.7888 | + | 622.190i | −0.0917836 | + | 0.689789i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −261.557 | + | 33.3306i | −0.289332 | + | 0.0368702i | ||||
\(905\) | −58.5360 | − | 101.387i | −0.0646807 | − | 0.112030i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −310.221 | + | 537.319i | −0.342030 | + | 0.592414i | −0.984810 | − | 0.173638i | \(-0.944448\pi\) |
0.642779 | + | 0.766051i | \(0.277781\pi\) | |||||||
\(908\) | 212.263 | − | 211.091i | 0.233770 | − | 0.232479i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −549.412 | − | 1331.61i | −0.603750 | − | 1.46330i | ||||
\(911\) | 1065.40 | + | 615.107i | 1.16948 | + | 0.675200i | 0.953558 | − | 0.301210i | \(-0.0973907\pi\) |
0.215923 | + | 0.976410i | \(0.430724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −166.753 | − | 288.825i | −0.182643 | − | 0.316347i | ||||
\(914\) | 881.671 | + | 678.470i | 0.964629 | + | 0.742309i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1141.48 | + | 302.475i | −1.24615 | + | 0.330213i | ||||
\(917\) | − | 1040.09i | − | 1.13423i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 211.088i | − | 0.229693i | −0.993383 | − | 0.114847i | \(-0.963362\pi\) | ||
0.993383 | − | 0.114847i | \(-0.0366377\pi\) | |||||||
\(920\) | −121.894 | − | 160.228i | −0.132494 | − | 0.174161i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 256.218 | − | 332.954i | 0.277893 | − | 0.361122i | ||||
\(923\) | 282.245 | + | 488.862i | 0.305790 | + | 0.529645i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.6200 | + | 9.01822i | 0.0168865 | + | 0.00974942i | ||||
\(926\) | −137.901 | − | 334.230i | −0.148921 | − | 0.360940i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 258.670 | − | 105.054i | 0.278739 | − | 0.113204i | ||||
\(929\) | −524.859 | + | 909.082i | −0.564972 | + | 0.978560i | 0.432081 | + | 0.901835i | \(0.357780\pi\) |
−0.997052 | + | 0.0767247i | \(0.975554\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 791.739 | + | 1371.33i | 0.850418 | + | 1.47297i | ||||
\(932\) | 1367.64 | + | 370.518i | 1.46742 | + | 0.397551i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.76217 | + | 20.7588i | −0.00295735 | + | 0.0222256i | ||||
\(935\) | − | 883.335i | − | 0.944744i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.8972 | −0.0158988 | −0.00794939 | − | 0.999968i | \(-0.502530\pi\) | ||||
−0.00794939 | + | 0.999968i | \(0.502530\pi\) | |||||||
\(938\) | −2029.29 | − | 270.018i | −2.16342 | − | 0.287866i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1198.64 | − | 324.732i | −1.27515 | − | 0.345459i | ||||
\(941\) | −494.297 | + | 285.383i | −0.525289 | + | 0.303276i | −0.739096 | − | 0.673600i | \(-0.764747\pi\) |
0.213807 | + | 0.976876i | \(0.431414\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 148.903 | + | 85.9693i | 0.157904 | + | 0.0911657i | ||||
\(944\) | −4.43956 | + | 802.127i | −0.00470293 | + | 0.849711i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −101.060 | + | 41.6968i | −0.106829 | + | 0.0440769i | ||||
\(947\) | 15.4417 | − | 26.7459i | 0.0163059 | − | 0.0282427i | −0.857757 | − | 0.514055i | \(-0.828143\pi\) |
0.874063 | + | 0.485812i | \(0.161476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −232.653 | + | 134.322i | −0.245156 | + | 0.141541i | ||||
\(950\) | −20.4344 | − | 15.7248i | −0.0215099 | − | 0.0165524i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1549.68 | + | 1178.92i | −1.62781 | + | 1.23836i | ||||
\(953\) | 1048.23 | 1.09993 | 0.549965 | − | 0.835188i | \(-0.314641\pi\) | ||||
0.549965 | + | 0.835188i | \(0.314641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −120.034 | −0.125690 | ||||||||
\(956\) | −481.488 | + | 127.587i | −0.503649 | + | 0.133460i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −512.867 | + | 666.470i | −0.535352 | + | 0.695689i | ||||
\(959\) | 2010.50 | − | 1160.76i | 2.09646 | − | 1.21039i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 289.855 | − | 502.044i | 0.301618 | − | 0.522418i | ||||
\(962\) | −411.849 | + | 169.926i | −0.428118 | + | 0.176639i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1075.93 | + | 1069.99i | −1.11611 | + | 1.10995i | ||||
\(965\) | 273.411 | + | 157.854i | 0.283327 | + | 0.163579i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −833.473 | + | 481.206i | −0.861916 | + | 0.497628i | −0.864654 | − | 0.502369i | \(-0.832462\pi\) |
0.00273711 | + | 0.999996i | \(0.499129\pi\) | |||||||
\(968\) | −313.874 | + | 39.9975i | −0.324250 | + | 0.0413197i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 903.140 | + | 120.172i | 0.931072 | + | 0.123889i | ||||
\(971\) | −848.612 | −0.873957 | −0.436978 | − | 0.899472i | \(-0.643951\pi\) | ||||
−0.436978 | + | 0.899472i | \(0.643951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2621.68i | − | 2.69443i | ||||||
\(974\) | −1714.99 | − | 228.198i | −1.76077 | − | 0.234289i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.36647 | − | 2.39734i | −0.00140007 | − | 0.00245629i | ||||
\(977\) | −559.484 | − | 969.055i | −0.572655 | − | 0.991868i | −0.996292 | − | 0.0860361i | \(-0.972580\pi\) |
0.423637 | − | 0.905832i | \(-0.360753\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.7050 | − | 101.680i | 0.0599642 | − | 0.103861i | ||||
\(980\) | 1596.24 | + | 1605.10i | 1.62881 | + | 1.63785i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 117.856 | − | 48.6266i | 0.120016 | − | 0.0495180i | ||||
\(983\) | 598.966 | + | 345.813i | 0.609324 | + | 0.351793i | 0.772701 | − | 0.634770i | \(-0.218905\pi\) |
−0.163377 | + | 0.986564i | \(0.552239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −981.861 | − | 1700.63i | −0.996813 | − | 1.72653i | ||||
\(986\) | 204.643 | − | 265.933i | 0.207549 | − | 0.269709i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 615.665 | − | 163.142i | 0.623143 | − | 0.165124i | ||||
\(989\) | 29.9472i | 0.0302802i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 361.650i | − | 0.364935i | −0.983212 | − | 0.182467i | \(-0.941592\pi\) | ||
0.983212 | − | 0.182467i | \(-0.0584084\pi\) | |||||||
\(992\) | −172.560 | + | 1244.15i | −0.173952 | + | 1.25418i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1012.83 | − | 779.399i | −1.01894 | − | 0.784104i | ||||
\(995\) | −547.035 | − | 947.492i | −0.549784 | − | 0.952254i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1162.72 | − | 671.298i | −1.16622 | − | 0.673318i | −0.213434 | − | 0.976958i | \(-0.568465\pi\) |
−0.952787 | + | 0.303640i | \(0.901798\pi\) | |||||||
\(998\) | −1344.73 | + | 554.828i | −1.34743 | + | 0.555940i | ||||
\(999\) | 0 | 0 |
(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 | 216.3.p.b.19.10 | 40 | ||
3.2 | odd | 2 | 72.3.p.b.43.11 | yes | 40 | ||
4.3 | odd | 2 | 864.3.t.b.559.6 | 40 | |||
8.3 | odd | 2 | inner | 216.3.p.b.19.16 | 40 | ||
8.5 | even | 2 | 864.3.t.b.559.15 | 40 | |||
9.2 | odd | 6 | 648.3.b.f.163.17 | 20 | |||
9.4 | even | 3 | inner | 216.3.p.b.91.16 | 40 | ||
9.5 | odd | 6 | 72.3.p.b.67.5 | yes | 40 | ||
9.7 | even | 3 | 648.3.b.e.163.4 | 20 | |||
12.11 | even | 2 | 288.3.t.b.79.10 | 40 | |||
24.5 | odd | 2 | 288.3.t.b.79.9 | 40 | |||
24.11 | even | 2 | 72.3.p.b.43.5 | ✓ | 40 | ||
36.7 | odd | 6 | 2592.3.b.f.1135.6 | 20 | |||
36.11 | even | 6 | 2592.3.b.e.1135.15 | 20 | |||
36.23 | even | 6 | 288.3.t.b.175.9 | 40 | |||
36.31 | odd | 6 | 864.3.t.b.847.15 | 40 | |||
72.5 | odd | 6 | 288.3.t.b.175.10 | 40 | |||
72.11 | even | 6 | 648.3.b.f.163.18 | 20 | |||
72.13 | even | 6 | 864.3.t.b.847.6 | 40 | |||
72.29 | odd | 6 | 2592.3.b.e.1135.6 | 20 | |||
72.43 | odd | 6 | 648.3.b.e.163.3 | 20 | |||
72.59 | even | 6 | 72.3.p.b.67.11 | yes | 40 | ||
72.61 | even | 6 | 2592.3.b.f.1135.15 | 20 | |||
72.67 | odd | 6 | inner | 216.3.p.b.91.10 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.p.b.43.5 | ✓ | 40 | 24.11 | even | 2 | ||
72.3.p.b.43.11 | yes | 40 | 3.2 | odd | 2 | ||
72.3.p.b.67.5 | yes | 40 | 9.5 | odd | 6 | ||
72.3.p.b.67.11 | yes | 40 | 72.59 | even | 6 | ||
216.3.p.b.19.10 | 40 | 1.1 | even | 1 | trivial | ||
216.3.p.b.19.16 | 40 | 8.3 | odd | 2 | inner | ||
216.3.p.b.91.10 | 40 | 72.67 | odd | 6 | inner | ||
216.3.p.b.91.16 | 40 | 9.4 | even | 3 | inner | ||
288.3.t.b.79.9 | 40 | 24.5 | odd | 2 | |||
288.3.t.b.79.10 | 40 | 12.11 | even | 2 | |||
288.3.t.b.175.9 | 40 | 36.23 | even | 6 | |||
288.3.t.b.175.10 | 40 | 72.5 | odd | 6 | |||
648.3.b.e.163.3 | 20 | 72.43 | odd | 6 | |||
648.3.b.e.163.4 | 20 | 9.7 | even | 3 | |||
648.3.b.f.163.17 | 20 | 9.2 | odd | 6 | |||
648.3.b.f.163.18 | 20 | 72.11 | even | 6 | |||
864.3.t.b.559.6 | 40 | 4.3 | odd | 2 | |||
864.3.t.b.559.15 | 40 | 8.5 | even | 2 | |||
864.3.t.b.847.6 | 40 | 72.13 | even | 6 | |||
864.3.t.b.847.15 | 40 | 36.31 | odd | 6 | |||
2592.3.b.e.1135.6 | 20 | 72.29 | odd | 6 | |||
2592.3.b.e.1135.15 | 20 | 36.11 | even | 6 | |||
2592.3.b.f.1135.6 | 20 | 36.7 | odd | 6 | |||
2592.3.b.f.1135.15 | 20 | 72.61 | even | 6 |