Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(31,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.o (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: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.41 | ||
Character | \(\chi\) | \(=\) | 980.31 |
Dual form | 980.2.o.g.411.41 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34099 | − | 0.449173i | 0.948220 | − | 0.317614i | ||||
\(3\) | −0.656274 | + | 1.13670i | −0.378900 | + | 0.656274i | −0.990902 | − | 0.134582i | \(-0.957031\pi\) |
0.612002 | + | 0.790856i | \(0.290364\pi\) | |||||||
\(4\) | 1.59649 | − | 1.20467i | 0.798243 | − | 0.602335i | ||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | −0.369479 | + | 1.81908i | −0.150839 | + | 0.742636i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.59976 | − | 2.33255i | 0.565600 | − | 0.824679i | ||||
\(9\) | 0.638609 | + | 1.10610i | 0.212870 | + | 0.368701i | ||||
\(10\) | 0.936741 | − | 1.05949i | 0.296224 | − | 0.335040i | ||||
\(11\) | −0.769955 | − | 0.444533i | −0.232150 | − | 0.134032i | 0.379413 | − | 0.925227i | \(-0.376126\pi\) |
−0.611564 | + | 0.791195i | \(0.709459\pi\) | |||||||
\(12\) | 0.321617 | + | 2.60532i | 0.0928427 | + | 0.752091i | ||||
\(13\) | 6.39664i | 1.77411i | 0.461664 | + | 0.887055i | \(0.347253\pi\) | ||||
−0.461664 | + | 0.887055i | \(0.652747\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.31255i | 0.338898i | ||||||||
\(16\) | 1.09754 | − | 3.84648i | 0.274384 | − | 0.961620i | ||||
\(17\) | 3.36785 | + | 1.94443i | 0.816823 | + | 0.471593i | 0.849320 | − | 0.527879i | \(-0.177013\pi\) |
−0.0324969 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(18\) | 1.35320 | + | 1.19642i | 0.318952 | + | 0.281999i | ||||
\(19\) | −0.471687 | − | 0.816986i | −0.108212 | − | 0.187429i | 0.806834 | − | 0.590779i | \(-0.201179\pi\) |
−0.915046 | + | 0.403349i | \(0.867846\pi\) | |||||||
\(20\) | 0.780262 | − | 1.84152i | 0.174472 | − | 0.411776i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.23217 | − | 0.250270i | −0.262700 | − | 0.0533577i | ||||
\(23\) | 7.61724 | − | 4.39781i | 1.58830 | − | 0.917008i | 0.594717 | − | 0.803935i | \(-0.297264\pi\) |
0.993587 | − | 0.113073i | \(-0.0360693\pi\) | |||||||
\(24\) | 1.60152 | + | 3.34924i | 0.326910 | + | 0.683660i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 2.87320 | + | 8.57781i | 0.563481 | + | 1.68225i | ||||
\(27\) | −5.61405 | −1.08043 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.497418 | −0.0923682 | −0.0461841 | − | 0.998933i | \(-0.514706\pi\) | ||||
−0.0461841 | + | 0.998933i | \(0.514706\pi\) | |||||||
\(30\) | 0.589562 | + | 1.76011i | 0.107639 | + | 0.321350i | ||||
\(31\) | 2.42987 | − | 4.20866i | 0.436418 | − | 0.755897i | −0.560993 | − | 0.827821i | \(-0.689580\pi\) |
0.997410 | + | 0.0719234i | \(0.0229137\pi\) | |||||||
\(32\) | −0.255955 | − | 5.65106i | −0.0452469 | − | 0.998976i | ||||
\(33\) | 1.01060 | − | 0.583472i | 0.175923 | − | 0.101569i | ||||
\(34\) | 5.38962 | + | 1.09470i | 0.924312 | + | 0.187740i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.35202 | + | 0.996565i | 0.392003 | + | 0.166094i | ||||
\(37\) | 1.33043 | + | 2.30437i | 0.218721 | + | 0.378837i | 0.954417 | − | 0.298475i | \(-0.0964780\pi\) |
−0.735696 | + | 0.677312i | \(0.763145\pi\) | |||||||
\(38\) | −0.999494 | − | 0.883697i | −0.162139 | − | 0.143355i | ||||
\(39\) | −7.27106 | − | 4.19795i | −1.16430 | − | 0.672210i | ||||
\(40\) | 0.219160 | − | 2.81992i | 0.0346522 | − | 0.445869i | ||||
\(41\) | − | 0.823314i | − | 0.128580i | −0.997931 | − | 0.0642900i | \(-0.979522\pi\) | ||
0.997931 | − | 0.0642900i | \(-0.0204783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.92015i | 1.51281i | 0.654104 | + | 0.756404i | \(0.273046\pi\) | ||||
−0.654104 | + | 0.756404i | \(0.726954\pi\) | |||||||
\(44\) | −1.76474 | + | 0.217850i | −0.266044 | + | 0.0328421i | ||||
\(45\) | 1.10610 | + | 0.638609i | 0.164888 | + | 0.0951981i | ||||
\(46\) | 8.23923 | − | 9.31887i | 1.21481 | − | 1.37399i | ||||
\(47\) | −3.68744 | − | 6.38683i | −0.537868 | − | 0.931615i | −0.999019 | − | 0.0442929i | \(-0.985897\pi\) |
0.461150 | − | 0.887322i | \(-0.347437\pi\) | |||||||
\(48\) | 3.65201 | + | 3.77192i | 0.527122 | + | 0.544429i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.281497 | − | 1.38591i | 0.0398097 | − | 0.195998i | ||||
\(51\) | −4.42046 | + | 2.55215i | −0.618988 | + | 0.357373i | ||||
\(52\) | 7.70585 | + | 10.2122i | 1.06861 | + | 1.41617i | ||||
\(53\) | 2.35119 | − | 4.07237i | 0.322960 | − | 0.559384i | −0.658137 | − | 0.752898i | \(-0.728655\pi\) |
0.981097 | + | 0.193514i | \(0.0619886\pi\) | |||||||
\(54\) | −7.52837 | + | 2.52168i | −1.02448 | + | 0.343158i | ||||
\(55\) | −0.889067 | −0.119882 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.23822 | 0.164007 | ||||||||
\(58\) | −0.667031 | + | 0.223427i | −0.0875854 | + | 0.0293374i | ||||
\(59\) | 0.942161 | − | 1.63187i | 0.122659 | − | 0.212452i | −0.798156 | − | 0.602450i | \(-0.794191\pi\) |
0.920815 | + | 0.389999i | \(0.127525\pi\) | |||||||
\(60\) | 1.58119 | + | 2.09547i | 0.204131 | + | 0.270523i | ||||
\(61\) | −0.502695 | + | 0.290231i | −0.0643635 | + | 0.0371603i | −0.531836 | − | 0.846847i | \(-0.678498\pi\) |
0.467473 | + | 0.884007i | \(0.345165\pi\) | |||||||
\(62\) | 1.36800 | − | 6.73519i | 0.173737 | − | 0.855369i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.88154 | − | 7.46302i | −0.360192 | − | 0.932878i | ||||
\(65\) | 3.19832 | + | 5.53966i | 0.396703 | + | 0.687110i | ||||
\(66\) | 1.09312 | − | 1.23636i | 0.134554 | − | 0.152186i | ||||
\(67\) | −8.07873 | − | 4.66426i | −0.986975 | − | 0.569830i | −0.0826060 | − | 0.996582i | \(-0.526324\pi\) |
−0.904369 | + | 0.426752i | \(0.859658\pi\) | |||||||
\(68\) | 7.71911 | − | 0.952895i | 0.936080 | − | 0.115555i | ||||
\(69\) | 11.5447i | 1.38982i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3163i | 1.69903i | 0.527563 | + | 0.849516i | \(0.323106\pi\) | ||||
−0.527563 | + | 0.849516i | \(0.676894\pi\) | |||||||
\(72\) | 3.60165 | + | 0.279914i | 0.424459 | + | 0.0329882i | ||||
\(73\) | 7.83276 | + | 4.52225i | 0.916756 | + | 0.529289i | 0.882599 | − | 0.470127i | \(-0.155792\pi\) |
0.0341570 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(74\) | 2.81915 | + | 2.49254i | 0.327720 | + | 0.289752i | ||||
\(75\) | 0.656274 | + | 1.13670i | 0.0757800 | + | 0.131255i | ||||
\(76\) | −1.73724 | − | 0.736079i | −0.199275 | − | 0.0844341i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.6360 | − | 2.36342i | −1.31752 | − | 0.267605i | ||||
\(79\) | −12.8891 | + | 7.44154i | −1.45014 | + | 0.837239i | −0.998489 | − | 0.0549552i | \(-0.982498\pi\) |
−0.451652 | + | 0.892194i | \(0.649165\pi\) | |||||||
\(80\) | −0.972745 | − | 3.87992i | −0.108756 | − | 0.433788i | ||||
\(81\) | 1.76853 | − | 3.06319i | 0.196504 | − | 0.340354i | ||||
\(82\) | −0.369811 | − | 1.10405i | −0.0408388 | − | 0.121922i | ||||
\(83\) | 4.02691 | 0.442011 | 0.221005 | − | 0.975273i | \(-0.429066\pi\) | ||||
0.221005 | + | 0.975273i | \(0.429066\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.88885 | 0.421805 | ||||||||
\(86\) | 4.45587 | + | 13.3028i | 0.480489 | + | 1.43448i | ||||
\(87\) | 0.326443 | − | 0.565415i | 0.0349983 | − | 0.0606189i | ||||
\(88\) | −2.26864 | + | 1.08481i | −0.241837 | + | 0.115641i | ||||
\(89\) | −5.21110 | + | 3.00863i | −0.552375 | + | 0.318914i | −0.750079 | − | 0.661348i | \(-0.769985\pi\) |
0.197704 | + | 0.980262i | \(0.436651\pi\) | |||||||
\(90\) | 1.77011 | + | 0.359533i | 0.186586 | + | 0.0378981i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.86290 | − | 16.1973i | 0.715507 | − | 1.68869i | ||||
\(93\) | 3.18932 | + | 5.52407i | 0.330717 | + | 0.572819i | ||||
\(94\) | −7.81360 | − | 6.90835i | −0.805911 | − | 0.712542i | ||||
\(95\) | −0.816986 | − | 0.471687i | −0.0838210 | − | 0.0483941i | ||||
\(96\) | 6.59154 | + | 3.41770i | 0.672746 | + | 0.348818i | ||||
\(97\) | − | 14.5252i | − | 1.47481i | −0.675451 | − | 0.737404i | \(-0.736051\pi\) | ||
0.675451 | − | 0.737404i | \(-0.263949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.13553i | − | 0.114125i | ||||||
\(100\) | −0.245032 | − | 1.98493i | −0.0245032 | − | 0.198493i | ||||
\(101\) | −12.8372 | − | 7.41157i | −1.27735 | − | 0.737478i | −0.300990 | − | 0.953627i | \(-0.597317\pi\) |
−0.976360 | + | 0.216149i | \(0.930650\pi\) | |||||||
\(102\) | −4.78142 | + | 5.40796i | −0.473431 | + | 0.535467i | ||||
\(103\) | −9.16327 | − | 15.8713i | −0.902884 | − | 1.56384i | −0.823733 | − | 0.566978i | \(-0.808112\pi\) |
−0.0791513 | − | 0.996863i | \(-0.525221\pi\) | |||||||
\(104\) | 14.9205 | + | 10.2331i | 1.46307 | + | 1.00344i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.32371 | − | 6.51709i | 0.128570 | − | 0.632995i | ||||
\(107\) | 7.21079 | − | 4.16315i | 0.697093 | − | 0.402467i | −0.109171 | − | 0.994023i | \(-0.534819\pi\) |
0.806264 | + | 0.591556i | \(0.201486\pi\) | |||||||
\(108\) | −8.96276 | + | 6.76309i | −0.862442 | + | 0.650778i | ||||
\(109\) | −0.497407 | + | 0.861533i | −0.0476429 | + | 0.0825199i | −0.888863 | − | 0.458172i | \(-0.848504\pi\) |
0.841221 | + | 0.540692i | \(0.181838\pi\) | |||||||
\(110\) | −1.19223 | + | 0.399345i | −0.113674 | + | 0.0380761i | ||||
\(111\) | −3.49251 | −0.331494 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.363411 | 0.0341868 | 0.0170934 | − | 0.999854i | \(-0.494559\pi\) | ||||
0.0170934 | + | 0.999854i | \(0.494559\pi\) | |||||||
\(114\) | 1.66044 | − | 0.556177i | 0.155515 | − | 0.0520908i | ||||
\(115\) | 4.39781 | − | 7.61724i | 0.410098 | − | 0.710311i | ||||
\(116\) | −0.794121 | + | 0.599225i | −0.0737323 | + | 0.0556366i | ||||
\(117\) | −7.07534 | + | 4.08495i | −0.654116 | + | 0.377654i | ||||
\(118\) | 0.530432 | − | 2.61151i | 0.0488302 | − | 0.240409i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.06158 | + | 2.09976i | 0.279483 | + | 0.191681i | ||||
\(121\) | −5.10478 | − | 8.84174i | −0.464071 | − | 0.803794i | ||||
\(122\) | −0.543743 | + | 0.614993i | −0.0492282 | + | 0.0556789i | ||||
\(123\) | 0.935861 | + | 0.540319i | 0.0843837 | + | 0.0487190i | ||||
\(124\) | −1.19079 | − | 9.64626i | −0.106936 | − | 0.866260i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.46720i | − | 0.218928i | −0.993991 | − | 0.109464i | \(-0.965087\pi\) | ||
0.993991 | − | 0.109464i | \(-0.0349135\pi\) | |||||||
\(128\) | −7.21630 | − | 8.71350i | −0.637836 | − | 0.770172i | ||||
\(129\) | −11.2762 | − | 6.51034i | −0.992817 | − | 0.573203i | ||||
\(130\) | 6.77717 | + | 5.99200i | 0.594397 | + | 0.525533i | ||||
\(131\) | 0.141458 | + | 0.245013i | 0.0123593 | + | 0.0214069i | 0.872139 | − | 0.489258i | \(-0.162732\pi\) |
−0.859780 | + | 0.510665i | \(0.829399\pi\) | |||||||
\(132\) | 0.910522 | − | 2.14895i | 0.0792508 | − | 0.187042i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.9285 | − | 2.62595i | −1.11685 | − | 0.226848i | ||||
\(135\) | −4.86191 | + | 2.80703i | −0.418447 | + | 0.241590i | ||||
\(136\) | 9.92321 | − | 4.74504i | 0.850908 | − | 0.406884i | ||||
\(137\) | −8.30757 | + | 14.3891i | −0.709764 | + | 1.22935i | 0.255181 | + | 0.966893i | \(0.417865\pi\) |
−0.964945 | + | 0.262454i | \(0.915468\pi\) | |||||||
\(138\) | 5.18557 | + | 15.4813i | 0.441425 | + | 1.31785i | ||||
\(139\) | −18.6029 | −1.57788 | −0.788938 | − | 0.614473i | \(-0.789369\pi\) | ||||
−0.788938 | + | 0.614473i | \(0.789369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.67988 | 0.815193 | ||||||||
\(142\) | 6.43050 | + | 19.1980i | 0.539636 | + | 1.61106i | ||||
\(143\) | 2.84352 | − | 4.92512i | 0.237787 | − | 0.411860i | ||||
\(144\) | 4.95550 | − | 1.24241i | 0.412958 | − | 0.103534i | ||||
\(145\) | −0.430777 | + | 0.248709i | −0.0357741 | + | 0.0206542i | ||||
\(146\) | 12.5349 | + | 2.54600i | 1.03740 | + | 0.210709i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.90003 | + | 2.07617i | 0.402780 | + | 0.170660i | ||||
\(149\) | −7.83270 | − | 13.5666i | −0.641680 | − | 1.11142i | −0.985058 | − | 0.172225i | \(-0.944904\pi\) |
0.343378 | − | 0.939197i | \(-0.388429\pi\) | |||||||
\(150\) | 1.39063 | + | 1.22952i | 0.113544 | + | 0.100390i | ||||
\(151\) | 10.3815 | + | 5.99377i | 0.844836 | + | 0.487766i | 0.858905 | − | 0.512135i | \(-0.171145\pi\) |
−0.0140690 | + | 0.999901i | \(0.504478\pi\) | |||||||
\(152\) | −2.66024 | − | 0.206749i | −0.215774 | − | 0.0167696i | ||||
\(153\) | 4.96691i | 0.401551i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.85974i | − | 0.390344i | ||||||
\(156\) | −16.6653 | + | 2.05727i | −1.33429 | + | 0.164713i | ||||
\(157\) | 9.21060 | + | 5.31774i | 0.735086 | + | 0.424402i | 0.820280 | − | 0.571963i | \(-0.193818\pi\) |
−0.0851942 | + | 0.996364i | \(0.527151\pi\) | |||||||
\(158\) | −13.9416 | + | 15.7685i | −1.10913 | + | 1.25447i | ||||
\(159\) | 3.08605 | + | 5.34519i | 0.244739 | + | 0.423901i | ||||
\(160\) | −3.04719 | − | 4.76598i | −0.240902 | − | 0.376784i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.995674 | − | 4.90207i | 0.0782276 | − | 0.385143i | ||||
\(163\) | −6.79907 | + | 3.92545i | −0.532544 | + | 0.307465i | −0.742052 | − | 0.670342i | \(-0.766147\pi\) |
0.209508 | + | 0.977807i | \(0.432814\pi\) | |||||||
\(164\) | −0.991822 | − | 1.31441i | −0.0774483 | − | 0.102638i | ||||
\(165\) | 0.583472 | − | 1.01060i | 0.0454232 | − | 0.0786753i | ||||
\(166\) | 5.40003 | − | 1.80878i | 0.419124 | − | 0.140389i | ||||
\(167\) | −7.90245 | −0.611510 | −0.305755 | − | 0.952110i | \(-0.598909\pi\) | ||||
−0.305755 | + | 0.952110i | \(0.598909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.9170 | −2.14746 | ||||||||
\(170\) | 5.21490 | − | 1.74677i | 0.399964 | − | 0.133971i | ||||
\(171\) | 0.602447 | − | 1.04347i | 0.0460702 | − | 0.0797960i | ||||
\(172\) | 11.9505 | + | 15.8374i | 0.911218 | + | 1.20759i | ||||
\(173\) | −16.1343 | + | 9.31513i | −1.22667 | + | 0.708216i | −0.966331 | − | 0.257302i | \(-0.917167\pi\) |
−0.260336 | + | 0.965518i | \(0.583833\pi\) | |||||||
\(174\) | 0.183785 | − | 0.904843i | 0.0139327 | − | 0.0685960i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.55494 | + | 2.47372i | −0.192586 | + | 0.186464i | ||||
\(177\) | 1.23663 | + | 2.14191i | 0.0929510 | + | 0.160996i | ||||
\(178\) | −5.63661 | + | 6.37521i | −0.422482 | + | 0.477842i | ||||
\(179\) | −17.7698 | − | 10.2594i | −1.32818 | − | 0.766825i | −0.343162 | − | 0.939276i | \(-0.611498\pi\) |
−0.985018 | + | 0.172451i | \(0.944831\pi\) | |||||||
\(180\) | 2.53519 | − | 0.312959i | 0.188962 | − | 0.0233266i | ||||
\(181\) | − | 13.2693i | − | 0.986296i | −0.869946 | − | 0.493148i | \(-0.835846\pi\) | ||
0.869946 | − | 0.493148i | \(-0.164154\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.761885i | − | 0.0563202i | ||||||
\(184\) | 1.92765 | − | 24.8030i | 0.142108 | − | 1.82850i | ||||
\(185\) | 2.30437 | + | 1.33043i | 0.169421 | + | 0.0978152i | ||||
\(186\) | 6.75810 | + | 5.97514i | 0.495528 | + | 0.438118i | ||||
\(187\) | −1.72873 | − | 2.99424i | −0.126417 | − | 0.218961i | ||||
\(188\) | −13.5810 | − | 5.75434i | −0.990494 | − | 0.419678i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.30744 | − | 0.265557i | −0.0948513 | − | 0.0192655i | ||||
\(191\) | 17.9278 | − | 10.3506i | 1.29721 | − | 0.748945i | 0.317290 | − | 0.948329i | \(-0.397227\pi\) |
0.979922 | + | 0.199383i | \(0.0638939\pi\) | |||||||
\(192\) | 10.3743 | + | 1.62234i | 0.748701 | + | 0.117083i | ||||
\(193\) | 8.79742 | − | 15.2376i | 0.633252 | − | 1.09683i | −0.353630 | − | 0.935385i | \(-0.615053\pi\) |
0.986883 | − | 0.161440i | \(-0.0516138\pi\) | |||||||
\(194\) | −6.52433 | − | 19.4781i | −0.468419 | − | 1.39844i | ||||
\(195\) | −8.39590 | −0.601243 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.8347 | 1.69815 | 0.849075 | − | 0.528272i | \(-0.177160\pi\) | ||||
0.849075 | + | 0.528272i | \(0.177160\pi\) | |||||||
\(198\) | −0.510051 | − | 1.52273i | −0.0362477 | − | 0.108216i | ||||
\(199\) | −9.25434 | + | 16.0290i | −0.656023 | + | 1.13626i | 0.325614 | + | 0.945503i | \(0.394429\pi\) |
−0.981636 | + | 0.190762i | \(0.938904\pi\) | |||||||
\(200\) | −1.22016 | − | 2.55171i | −0.0862786 | − | 0.180433i | ||||
\(201\) | 10.6037 | − | 6.12207i | 0.747929 | − | 0.431817i | ||||
\(202\) | −20.5436 | − | 4.17267i | −1.44544 | − | 0.293588i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.98270 | + | 9.39968i | −0.278845 | + | 0.658109i | ||||
\(205\) | −0.411657 | − | 0.713010i | −0.0287514 | − | 0.0497988i | ||||
\(206\) | −19.4168 | − | 17.1672i | −1.35283 | − | 1.19610i | ||||
\(207\) | 9.72887 | + | 5.61696i | 0.676203 | + | 0.390406i | ||||
\(208\) | 24.6046 | + | 7.02055i | 1.70602 | + | 0.486788i | ||||
\(209\) | 0.838722i | 0.0580156i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.96174i | 0.616952i | 0.951232 | + | 0.308476i | \(0.0998189\pi\) | ||||
−0.951232 | + | 0.308476i | \(0.900181\pi\) | |||||||
\(212\) | −1.15223 | − | 9.33389i | −0.0791357 | − | 0.641055i | ||||
\(213\) | −16.2733 | − | 9.39542i | −1.11503 | − | 0.643763i | ||||
\(214\) | 7.79959 | − | 8.82162i | 0.533169 | − | 0.603034i | ||||
\(215\) | 4.96007 | + | 8.59110i | 0.338274 | + | 0.585908i | ||||
\(216\) | −8.98114 | + | 13.0950i | −0.611089 | + | 0.891004i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.280037 | + | 1.37873i | −0.0189665 | + | 0.0933791i | ||||
\(219\) | −10.2809 | + | 5.93567i | −0.694717 | + | 0.401095i | ||||
\(220\) | −1.41938 | + | 1.07103i | −0.0956948 | + | 0.0722090i | ||||
\(221\) | −12.4378 | + | 21.5429i | −0.836657 | + | 1.44913i | ||||
\(222\) | −4.68341 | + | 1.56874i | −0.314330 | + | 0.105287i | ||||
\(223\) | 16.4225 | 1.09973 | 0.549865 | − | 0.835253i | \(-0.314679\pi\) | ||||
0.549865 | + | 0.835253i | \(0.314679\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.27722 | 0.0851478 | ||||||||
\(226\) | 0.487329 | − | 0.163234i | 0.0324166 | − | 0.0108582i | ||||
\(227\) | −6.35591 | + | 11.0088i | −0.421857 | + | 0.730677i | −0.996121 | − | 0.0879926i | \(-0.971955\pi\) |
0.574264 | + | 0.818670i | \(0.305288\pi\) | |||||||
\(228\) | 1.97681 | − | 1.49165i | 0.130917 | − | 0.0987871i | ||||
\(229\) | 14.9792 | − | 8.64823i | 0.989851 | − | 0.571491i | 0.0846216 | − | 0.996413i | \(-0.473032\pi\) |
0.905230 | + | 0.424922i | \(0.139699\pi\) | |||||||
\(230\) | 2.47595 | − | 12.1900i | 0.163259 | − | 0.803784i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.795749 | + | 1.16025i | −0.0522435 | + | 0.0761742i | ||||
\(233\) | −11.8739 | − | 20.5662i | −0.777885 | − | 1.34734i | −0.933159 | − | 0.359465i | \(-0.882959\pi\) |
0.155274 | − | 0.987872i | \(-0.450374\pi\) | |||||||
\(234\) | −7.65308 | + | 8.65592i | −0.500298 | + | 0.565855i | ||||
\(235\) | −6.38683 | − | 3.68744i | −0.416631 | − | 0.240542i | ||||
\(236\) | −0.461720 | − | 3.74025i | −0.0300554 | − | 0.243470i | ||||
\(237\) | − | 19.5348i | − | 1.26892i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2033i | 0.659997i | 0.943981 | + | 0.329998i | \(0.107048\pi\) | ||||
−0.943981 | + | 0.329998i | \(0.892952\pi\) | |||||||
\(240\) | 5.04869 | + | 1.44057i | 0.325892 | + | 0.0929884i | ||||
\(241\) | −2.01649 | − | 1.16422i | −0.129893 | − | 0.0749939i | 0.433645 | − | 0.901084i | \(-0.357227\pi\) |
−0.563539 | + | 0.826090i | \(0.690560\pi\) | |||||||
\(242\) | −10.8169 | − | 9.56371i | −0.695337 | − | 0.614779i | ||||
\(243\) | −6.09980 | − | 10.5652i | −0.391302 | − | 0.677755i | ||||
\(244\) | −0.452913 | + | 1.06893i | −0.0289948 | + | 0.0684314i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.49767 | + | 0.304197i | 0.0954881 | + | 0.0193949i | ||||
\(247\) | 5.22597 | − | 3.01721i | 0.332520 | − | 0.191981i | ||||
\(248\) | −5.92968 | − | 12.4006i | −0.376535 | − | 0.787441i | ||||
\(249\) | −2.64276 | + | 4.57739i | −0.167478 | + | 0.290080i | ||||
\(250\) | −0.449173 | − | 1.34099i | −0.0284082 | − | 0.0848114i | ||||
\(251\) | 6.54297 | 0.412988 | 0.206494 | − | 0.978448i | \(-0.433795\pi\) | ||||
0.206494 | + | 0.978448i | \(0.433795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.81990 | −0.491633 | ||||||||
\(254\) | −1.10820 | − | 3.30848i | −0.0695346 | − | 0.207592i | ||||
\(255\) | −2.55215 | + | 4.42046i | −0.159822 | + | 0.276820i | ||||
\(256\) | −13.5908 | − | 8.44331i | −0.849427 | − | 0.527707i | ||||
\(257\) | 17.0076 | − | 9.81936i | 1.06091 | − | 0.612515i | 0.135224 | − | 0.990815i | \(-0.456825\pi\) |
0.925683 | + | 0.378300i | \(0.123491\pi\) | |||||||
\(258\) | −18.0455 | − | 3.66528i | −1.12347 | − | 0.228191i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 11.7795 | + | 4.99106i | 0.730536 | + | 0.309532i | ||||
\(261\) | −0.317655 | − | 0.550195i | −0.0196624 | − | 0.0340562i | ||||
\(262\) | 0.299747 | + | 0.265020i | 0.0185184 | + | 0.0163730i | ||||
\(263\) | 9.24916 | + | 5.34000i | 0.570328 | + | 0.329279i | 0.757280 | − | 0.653090i | \(-0.226528\pi\) |
−0.186953 | + | 0.982369i | \(0.559861\pi\) | |||||||
\(264\) | 0.255747 | − | 3.29069i | 0.0157401 | − | 0.202528i | ||||
\(265\) | − | 4.70237i | − | 0.288864i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 7.89794i | − | 0.483346i | ||||||
\(268\) | −18.5165 | + | 2.28579i | −1.13107 | + | 0.139627i | ||||
\(269\) | 5.37695 | + | 3.10438i | 0.327838 | + | 0.189278i | 0.654881 | − | 0.755732i | \(-0.272719\pi\) |
−0.327043 | + | 0.945010i | \(0.606052\pi\) | |||||||
\(270\) | −5.25891 | + | 5.94803i | −0.320047 | + | 0.361985i | ||||
\(271\) | −8.73865 | − | 15.1358i | −0.530835 | − | 0.919433i | −0.999353 | − | 0.0359791i | \(-0.988545\pi\) |
0.468517 | − | 0.883454i | \(-0.344788\pi\) | |||||||
\(272\) | 11.1755 | − | 10.8203i | 0.677616 | − | 0.656075i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.67712 | + | 23.0272i | −0.282555 | + | 1.39112i | ||||
\(275\) | −0.769955 | + | 0.444533i | −0.0464300 | + | 0.0268064i | ||||
\(276\) | 13.9075 | + | 18.4309i | 0.837136 | + | 1.10941i | ||||
\(277\) | −5.49655 | + | 9.52031i | −0.330256 | + | 0.572020i | −0.982562 | − | 0.185936i | \(-0.940468\pi\) |
0.652306 | + | 0.757956i | \(0.273802\pi\) | |||||||
\(278\) | −24.9462 | + | 8.35592i | −1.49617 | + | 0.501155i | ||||
\(279\) | 6.20694 | 0.371600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.5755 | −1.10812 | −0.554060 | − | 0.832477i | \(-0.686922\pi\) | ||||
−0.554060 | + | 0.832477i | \(0.686922\pi\) | |||||||
\(282\) | 12.9806 | − | 4.34795i | 0.772982 | − | 0.258916i | ||||
\(283\) | −3.79275 | + | 6.56924i | −0.225456 | + | 0.390501i | −0.956456 | − | 0.291876i | \(-0.905720\pi\) |
0.731000 | + | 0.682377i | \(0.239054\pi\) | |||||||
\(284\) | 17.2464 | + | 22.8558i | 1.02339 | + | 1.35624i | ||||
\(285\) | 1.07233 | − | 0.619112i | 0.0635195 | − | 0.0366730i | ||||
\(286\) | 1.60089 | − | 7.88176i | 0.0946625 | − | 0.466058i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.08720 | − | 3.89193i | 0.358692 | − | 0.229334i | ||||
\(289\) | −0.938408 | − | 1.62537i | −0.0552004 | − | 0.0956100i | ||||
\(290\) | −0.465952 | + | 0.527009i | −0.0273616 | + | 0.0309470i | ||||
\(291\) | 16.5108 | + | 9.53250i | 0.967879 | + | 0.558805i | ||||
\(292\) | 17.9527 | − | 2.21619i | 1.05060 | − | 0.129693i | ||||
\(293\) | 5.40695i | 0.315878i | 0.987449 | + | 0.157939i | \(0.0504849\pi\) | ||||
−0.987449 | + | 0.157939i | \(0.949515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.88432i | − | 0.109709i | ||||||
\(296\) | 7.50343 | + | 0.583153i | 0.436128 | + | 0.0338951i | ||||
\(297\) | 4.32257 | + | 2.49563i | 0.250821 | + | 0.144811i | ||||
\(298\) | −16.5973 | − | 14.6744i | −0.961457 | − | 0.850067i | ||||
\(299\) | 28.1312 | + | 48.7248i | 1.62687 | + | 2.81783i | ||||
\(300\) | 2.41708 | + | 1.02413i | 0.139550 | + | 0.0591283i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 16.6137 | + | 3.37446i | 0.956012 | + | 0.194178i | ||||
\(303\) | 16.8495 | − | 9.72804i | 0.967976 | − | 0.558861i | ||||
\(304\) | −3.66021 | + | 0.917662i | −0.209928 | + | 0.0526315i | ||||
\(305\) | −0.290231 | + | 0.502695i | −0.0166186 | + | 0.0287842i | ||||
\(306\) | 2.23100 | + | 6.66056i | 0.127538 | + | 0.380759i | ||||
\(307\) | 5.68826 | 0.324646 | 0.162323 | − | 0.986738i | \(-0.448101\pi\) | ||||
0.162323 | + | 0.986738i | \(0.448101\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.0545 | 1.36841 | ||||||||
\(310\) | −2.18287 | − | 6.51684i | −0.123978 | − | 0.370132i | ||||
\(311\) | −0.0626204 | + | 0.108462i | −0.00355087 | + | 0.00615029i | −0.867795 | − | 0.496922i | \(-0.834464\pi\) |
0.864245 | + | 0.503072i | \(0.167797\pi\) | |||||||
\(312\) | −21.4239 | + | 10.2444i | −1.21289 | + | 0.579974i | ||||
\(313\) | 10.0924 | − | 5.82684i | 0.570455 | − | 0.329352i | −0.186876 | − | 0.982384i | \(-0.559836\pi\) |
0.757331 | + | 0.653031i | \(0.226503\pi\) | |||||||
\(314\) | 14.7399 | + | 2.99386i | 0.831819 | + | 0.168953i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.6127 | + | 27.4075i | −0.653266 | + | 1.54179i | ||||
\(317\) | 9.24841 | + | 16.0187i | 0.519442 | + | 0.899701i | 0.999745 | + | 0.0225977i | \(0.00719367\pi\) |
−0.480302 | + | 0.877103i | \(0.659473\pi\) | |||||||
\(318\) | 6.53926 | + | 5.78165i | 0.366703 | + | 0.324219i | ||||
\(319\) | 0.382989 | + | 0.221119i | 0.0214433 | + | 0.0123803i | ||||
\(320\) | −6.22700 | − | 5.02240i | −0.348100 | − | 0.280761i | ||||
\(321\) | 10.9287i | 0.609979i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.66864i | − | 0.204129i | ||||||
\(324\) | −0.866695 | − | 7.02084i | −0.0481497 | − | 0.390047i | ||||
\(325\) | 5.53966 | + | 3.19832i | 0.307285 | + | 0.177411i | ||||
\(326\) | −7.35425 | + | 8.31793i | −0.407314 | + | 0.460688i | ||||
\(327\) | −0.652870 | − | 1.13080i | −0.0361038 | − | 0.0625336i | ||||
\(328\) | −1.92042 | − | 1.31710i | −0.106037 | − | 0.0727249i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.328491 | − | 1.61728i | 0.0180829 | − | 0.0890285i | ||||
\(331\) | −5.99633 | + | 3.46198i | −0.329588 | + | 0.190288i | −0.655658 | − | 0.755058i | \(-0.727609\pi\) |
0.326070 | + | 0.945346i | \(0.394275\pi\) | |||||||
\(332\) | 6.42891 | − | 4.85110i | 0.352832 | − | 0.266239i | ||||
\(333\) | −1.69925 | + | 2.94319i | −0.0931183 | + | 0.161286i | ||||
\(334\) | −10.5971 | + | 3.54957i | −0.579846 | + | 0.194224i | ||||
\(335\) | −9.32852 | −0.509671 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5483 | −0.846970 | −0.423485 | − | 0.905903i | \(-0.639193\pi\) | ||||
−0.423485 | + | 0.905903i | \(0.639193\pi\) | |||||||
\(338\) | −37.4364 | + | 12.5396i | −2.03627 | + | 0.682064i | ||||
\(339\) | −0.238497 | + | 0.413089i | −0.0129534 | + | 0.0224359i | ||||
\(340\) | 6.20850 | − | 4.68479i | 0.336703 | − | 0.254068i | ||||
\(341\) | −3.74178 | + | 2.16032i | −0.202629 | + | 0.116988i | ||||
\(342\) | 0.339174 | − | 1.66988i | 0.0183404 | − | 0.0902967i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 23.1392 | + | 15.8699i | 1.24758 | + | 0.855645i | ||||
\(345\) | 5.77234 | + | 9.99799i | 0.310773 | + | 0.538274i | ||||
\(346\) | −17.4517 | + | 19.7386i | −0.938211 | + | 1.06115i | ||||
\(347\) | 20.2735 | + | 11.7049i | 1.08834 | + | 0.628353i | 0.933134 | − | 0.359529i | \(-0.117063\pi\) |
0.155205 | + | 0.987882i | \(0.450396\pi\) | |||||||
\(348\) | −0.159978 | − | 1.29593i | −0.00857572 | − | 0.0694693i | ||||
\(349\) | 31.1435i | 1.66707i | 0.552465 | + | 0.833536i | \(0.313687\pi\) | ||||
−0.552465 | + | 0.833536i | \(0.686313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 35.9111i | − | 1.91679i | ||||||
\(352\) | −2.31501 | + | 4.46484i | −0.123391 | + | 0.237977i | ||||
\(353\) | 8.85370 | + | 5.11168i | 0.471235 | + | 0.272068i | 0.716756 | − | 0.697324i | \(-0.245626\pi\) |
−0.245522 | + | 0.969391i | \(0.578959\pi\) | |||||||
\(354\) | 2.62040 | + | 2.31681i | 0.139272 | + | 0.123137i | ||||
\(355\) | 7.15815 | + | 12.3983i | 0.379915 | + | 0.658032i | ||||
\(356\) | −4.69504 | + | 11.0809i | −0.248836 | + | 0.587286i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.4374 | − | 5.77600i | −1.50296 | − | 0.305271i | ||||
\(359\) | −9.79157 | + | 5.65316i | −0.516779 | + | 0.298363i | −0.735616 | − | 0.677399i | \(-0.763107\pi\) |
0.218837 | + | 0.975761i | \(0.429774\pi\) | |||||||
\(360\) | 3.25908 | − | 1.55841i | 0.171769 | − | 0.0821357i | ||||
\(361\) | 9.05502 | − | 15.6838i | 0.476580 | − | 0.825461i | ||||
\(362\) | −5.96020 | − | 17.7939i | −0.313261 | − | 0.935225i | ||||
\(363\) | 13.4005 | 0.703346 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.04450 | 0.473411 | ||||||||
\(366\) | −0.342219 | − | 1.02168i | −0.0178881 | − | 0.0534039i | ||||
\(367\) | 11.4577 | − | 19.8454i | 0.598090 | − | 1.03592i | −0.395013 | − | 0.918675i | \(-0.629260\pi\) |
0.993103 | − | 0.117246i | \(-0.0374067\pi\) | |||||||
\(368\) | −8.55590 | − | 34.1263i | −0.446007 | − | 1.77896i | ||||
\(369\) | 0.910669 | − | 0.525775i | 0.0474075 | − | 0.0273708i | ||||
\(370\) | 3.68773 | + | 0.749025i | 0.191716 | + | 0.0389400i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 11.7464 | + | 4.97702i | 0.609022 | + | 0.258046i | ||||
\(373\) | 5.60441 | + | 9.70712i | 0.290185 | + | 0.502616i | 0.973853 | − | 0.227177i | \(-0.0729497\pi\) |
−0.683668 | + | 0.729793i | \(0.739616\pi\) | |||||||
\(374\) | −3.66313 | − | 3.23874i | −0.189416 | − | 0.167471i | ||||
\(375\) | 1.13670 | + | 0.656274i | 0.0586989 | + | 0.0338898i | ||||
\(376\) | −20.7966 | − | 1.61627i | −1.07250 | − | 0.0833530i | ||||
\(377\) | − | 3.18181i | − | 0.163871i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.2647i | − | 1.24639i | −0.782065 | − | 0.623197i | \(-0.785834\pi\) | ||
0.782065 | − | 0.623197i | \(-0.214166\pi\) | |||||||
\(380\) | −1.87253 | + | 0.231157i | −0.0960590 | + | 0.0118581i | ||||
\(381\) | 2.80446 | + | 1.61916i | 0.143677 | + | 0.0829519i | ||||
\(382\) | 19.3917 | − | 21.9327i | 0.992167 | − | 1.12218i | ||||
\(383\) | 4.03102 | + | 6.98193i | 0.205976 | + | 0.356760i | 0.950443 | − | 0.310899i | \(-0.100630\pi\) |
−0.744468 | + | 0.667659i | \(0.767297\pi\) | |||||||
\(384\) | 14.6405 | − | 2.48432i | 0.747120 | − | 0.126777i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.95290 | − | 24.3850i | 0.252096 | − | 1.24116i | ||||
\(387\) | −10.9727 | + | 6.33509i | −0.557774 | + | 0.322031i | ||||
\(388\) | −17.4981 | − | 23.1893i | −0.888330 | − | 1.17726i | ||||
\(389\) | −6.98572 | + | 12.0996i | −0.354190 | + | 0.613475i | −0.986979 | − | 0.160849i | \(-0.948577\pi\) |
0.632789 | + | 0.774324i | \(0.281910\pi\) | |||||||
\(390\) | −11.2588 | + | 3.77122i | −0.570111 | + | 0.190963i | ||||
\(391\) | 34.2049 | 1.72982 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.371342 | −0.0187317 | ||||||||
\(394\) | 31.9620 | − | 10.7059i | 1.61022 | − | 0.539356i | ||||
\(395\) | −7.44154 | + | 12.8891i | −0.374425 | + | 0.648523i | ||||
\(396\) | −1.36794 | − | 1.81286i | −0.0687416 | − | 0.0910997i | ||||
\(397\) | −9.84236 | + | 5.68249i | −0.493974 | + | 0.285196i | −0.726221 | − | 0.687461i | \(-0.758725\pi\) |
0.232248 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(398\) | −5.21014 | + | 25.6514i | −0.261161 | + | 1.28579i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.78238 | − | 2.87374i | −0.139119 | − | 0.143687i | ||||
\(401\) | 1.88851 | + | 3.27099i | 0.0943076 | + | 0.163346i | 0.909319 | − | 0.416099i | \(-0.136603\pi\) |
−0.815012 | + | 0.579444i | \(0.803270\pi\) | |||||||
\(402\) | 11.4696 | − | 12.9725i | 0.572051 | − | 0.647010i | ||||
\(403\) | 26.9213 | + | 15.5430i | 1.34104 | + | 0.774253i | ||||
\(404\) | −29.4229 | + | 3.63215i | −1.46385 | + | 0.180706i | ||||
\(405\) | − | 3.53706i | − | 0.175758i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.36568i | − | 0.117263i | ||||||
\(408\) | −1.11866 | + | 14.3938i | −0.0553818 | + | 0.712597i | ||||
\(409\) | −12.1060 | − | 6.98940i | −0.598603 | − | 0.345603i | 0.169889 | − | 0.985463i | \(-0.445659\pi\) |
−0.768492 | + | 0.639860i | \(0.778992\pi\) | |||||||
\(410\) | −0.872291 | − | 0.771232i | −0.0430794 | − | 0.0380884i | ||||
\(411\) | −10.9041 | − | 18.8864i | −0.537859 | − | 0.931599i | ||||
\(412\) | −33.7487 | − | 14.2995i | −1.66268 | − | 0.704486i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 15.5693 | + | 3.16232i | 0.765188 | + | 0.155420i | ||||
\(415\) | 3.48741 | − | 2.01346i | 0.171190 | − | 0.0988367i | ||||
\(416\) | 36.1478 | − | 1.63725i | 1.77229 | − | 0.0802730i | ||||
\(417\) | 12.2086 | − | 21.1459i | 0.597857 | − | 1.03552i | ||||
\(418\) | 0.376732 | + | 1.12472i | 0.0184266 | + | 0.0550116i | ||||
\(419\) | 6.23483 | 0.304591 | 0.152296 | − | 0.988335i | \(-0.451333\pi\) | ||||
0.152296 | + | 0.988335i | \(0.451333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.67347 | −0.471456 | −0.235728 | − | 0.971819i | \(-0.575747\pi\) | ||||
−0.235728 | + | 0.971819i | \(0.575747\pi\) | |||||||
\(422\) | 4.02538 | + | 12.0176i | 0.195952 | + | 0.585006i | ||||
\(423\) | 4.70966 | − | 8.15737i | 0.228991 | − | 0.396625i | ||||
\(424\) | −5.73767 | − | 11.9991i | −0.278646 | − | 0.582726i | ||||
\(425\) | 3.36785 | − | 1.94443i | 0.163365 | − | 0.0943186i | ||||
\(426\) | −26.0425 | − | 5.28957i | −1.26176 | − | 0.256280i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.49670 | − | 15.3330i | 0.314030 | − | 0.741150i | ||||
\(429\) | 3.73226 | + | 6.46446i | 0.180195 | + | 0.312107i | ||||
\(430\) | 10.5103 | + | 9.29261i | 0.506851 | + | 0.448129i | ||||
\(431\) | −7.34260 | − | 4.23925i | −0.353680 | − | 0.204197i | 0.312625 | − | 0.949877i | \(-0.398792\pi\) |
−0.666305 | + | 0.745679i | \(0.732125\pi\) | |||||||
\(432\) | −6.16163 | + | 21.5943i | −0.296452 | + | 1.03896i | ||||
\(433\) | − | 24.9330i | − | 1.19820i | −0.800674 | − | 0.599101i | \(-0.795525\pi\) | ||
0.800674 | − | 0.599101i | \(-0.204475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.652885i | − | 0.0313035i | ||||||
\(436\) | 0.243761 | + | 1.97464i | 0.0116740 | + | 0.0945680i | ||||
\(437\) | −7.18590 | − | 4.14878i | −0.343748 | − | 0.198463i | ||||
\(438\) | −11.1204 | + | 12.5775i | −0.531352 | + | 0.600978i | ||||
\(439\) | 12.7059 | + | 22.0072i | 0.606418 | + | 1.05035i | 0.991826 | + | 0.127600i | \(0.0407275\pi\) |
−0.385408 | + | 0.922746i | \(0.625939\pi\) | |||||||
\(440\) | −1.42229 | + | 2.07379i | −0.0678052 | + | 0.0988640i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.00242 | + | 34.4755i | −0.333071 | + | 1.63983i | ||||
\(443\) | 20.7750 | − | 11.9944i | 0.987049 | − | 0.569873i | 0.0826584 | − | 0.996578i | \(-0.473659\pi\) |
0.904391 | + | 0.426705i | \(0.140326\pi\) | |||||||
\(444\) | −5.57574 | + | 4.20732i | −0.264613 | + | 0.199671i | ||||
\(445\) | −3.00863 | + | 5.21110i | −0.142623 | + | 0.247030i | ||||
\(446\) | 22.0223 | − | 7.37654i | 1.04279 | − | 0.349289i | ||||
\(447\) | 20.5616 | 0.972530 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.1281 | −0.808326 | −0.404163 | − | 0.914687i | \(-0.632437\pi\) | ||||
−0.404163 | + | 0.914687i | \(0.632437\pi\) | |||||||
\(450\) | 1.71273 | − | 0.573692i | 0.0807389 | − | 0.0270441i | ||||
\(451\) | −0.365990 | + | 0.633914i | −0.0172338 | + | 0.0298498i | ||||
\(452\) | 0.580180 | − | 0.437790i | 0.0272894 | − | 0.0205919i | ||||
\(453\) | −13.6262 | + | 7.86712i | −0.640217 | + | 0.369629i | ||||
\(454\) | −3.57834 | + | 17.6175i | −0.167940 | + | 0.826830i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.98086 | − | 2.88821i | 0.0927623 | − | 0.135253i | ||||
\(457\) | 5.59177 | + | 9.68522i | 0.261572 | + | 0.453056i | 0.966660 | − | 0.256064i | \(-0.0824258\pi\) |
−0.705088 | + | 0.709120i | \(0.749093\pi\) | |||||||
\(458\) | 16.2023 | − | 18.3254i | 0.757084 | − | 0.856290i | ||||
\(459\) | −18.9073 | − | 10.9161i | −0.882516 | − | 0.509521i | ||||
\(460\) | −2.15521 | − | 17.4587i | −0.100487 | − | 0.814018i | ||||
\(461\) | 25.3723i | 1.18170i | 0.806780 | + | 0.590852i | \(0.201208\pi\) | ||||
−0.806780 | + | 0.590852i | \(0.798792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0511973i | 0.00237934i | 0.999999 | + | 0.00118967i | \(0.000378684\pi\) | ||||
−0.999999 | + | 0.00118967i | \(0.999621\pi\) | |||||||
\(464\) | −0.545935 | + | 1.91331i | −0.0253444 | + | 0.0888231i | ||||
\(465\) | 5.52407 | + | 3.18932i | 0.256173 | + | 0.147901i | ||||
\(466\) | −25.1605 | − | 22.2455i | −1.16554 | − | 1.03050i | ||||
\(467\) | 6.64553 | + | 11.5104i | 0.307518 | + | 0.532638i | 0.977819 | − | 0.209452i | \(-0.0671681\pi\) |
−0.670300 | + | 0.742090i | \(0.733835\pi\) | |||||||
\(468\) | −6.37467 | + | 15.0450i | −0.294669 | + | 0.695457i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −10.2209 | − | 2.07601i | −0.471457 | − | 0.0957591i | ||||
\(471\) | −12.0894 | + | 6.97979i | −0.557048 | + | 0.321612i | ||||
\(472\) | −2.29918 | − | 4.80824i | −0.105828 | − | 0.221317i | ||||
\(473\) | 4.40984 | − | 7.63806i | 0.202765 | − | 0.351199i | ||||
\(474\) | −8.77450 | − | 26.1959i | −0.403026 | − | 1.20322i | ||||
\(475\) | −0.943374 | −0.0432850 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00595 | 0.274994 | ||||||||
\(478\) | 4.58305 | + | 13.6825i | 0.209624 | + | 0.625822i | ||||
\(479\) | −4.83560 | + | 8.37550i | −0.220944 | + | 0.382686i | −0.955095 | − | 0.296300i | \(-0.904247\pi\) |
0.734151 | + | 0.678986i | \(0.237580\pi\) | |||||||
\(480\) | 7.41729 | − | 0.335953i | 0.338551 | − | 0.0153341i | ||||
\(481\) | −14.7403 | + | 8.51029i | −0.672098 | + | 0.388036i | ||||
\(482\) | −3.22701 | − | 0.655449i | −0.146986 | − | 0.0298549i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.8011 | − | 7.96614i | −0.854595 | − | 0.362097i | ||||
\(485\) | −7.26259 | − | 12.5792i | −0.329777 | − | 0.571191i | ||||
\(486\) | −12.9253 | − | 11.4279i | −0.586305 | − | 0.518378i | ||||
\(487\) | −5.92989 | − | 3.42363i | −0.268709 | − | 0.155139i | 0.359592 | − | 0.933110i | \(-0.382916\pi\) |
−0.628301 | + | 0.777970i | \(0.716249\pi\) | |||||||
\(488\) | −0.127214 | + | 1.63686i | −0.00575870 | + | 0.0740972i | ||||
\(489\) | − | 10.3047i | − | 0.465993i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 24.0395i | − | 1.08489i | −0.840092 | − | 0.542444i | \(-0.817499\pi\) | ||
0.840092 | − | 0.542444i | \(-0.182501\pi\) | |||||||
\(492\) | 2.14500 | − | 0.264791i | 0.0967039 | − | 0.0119377i | ||||
\(493\) | −1.67523 | − | 0.967193i | −0.0754485 | − | 0.0435602i | ||||
\(494\) | 5.65269 | − | 6.39341i | 0.254327 | − | 0.287653i | ||||
\(495\) | −0.567766 | − | 0.983399i | −0.0255192 | − | 0.0442005i | ||||
\(496\) | −13.5217 | − | 13.9656i | −0.607140 | − | 0.627074i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.48786 | + | 7.32527i | −0.0666725 | + | 0.328253i | ||||
\(499\) | −11.2049 | + | 6.46915i | −0.501600 | + | 0.289599i | −0.729374 | − | 0.684115i | \(-0.760189\pi\) |
0.227774 | + | 0.973714i | \(0.426855\pi\) | |||||||
\(500\) | −1.20467 | − | 1.59649i | −0.0538745 | − | 0.0713970i | ||||
\(501\) | 5.18617 | − | 8.98271i | 0.231701 | − | 0.401318i | ||||
\(502\) | 8.77403 | − | 2.93893i | 0.391604 | − | 0.131171i | ||||
\(503\) | 32.0665 | 1.42978 | 0.714888 | − | 0.699239i | \(-0.246478\pi\) | ||||
0.714888 | + | 0.699239i | \(0.246478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.8231 | −0.659621 | ||||||||
\(506\) | −10.4864 | + | 3.51249i | −0.466176 | + | 0.156149i | ||||
\(507\) | 18.3212 | − | 31.7333i | 0.813674 | − | 1.40933i | ||||
\(508\) | −2.97216 | − | 3.93884i | −0.131868 | − | 0.174758i | ||||
\(509\) | 8.15433 | − | 4.70790i | 0.361434 | − | 0.208674i | −0.308275 | − | 0.951297i | \(-0.599752\pi\) |
0.669710 | + | 0.742623i | \(0.266419\pi\) | |||||||
\(510\) | −1.43685 | + | 7.07414i | −0.0636247 | + | 0.313248i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.0176 | − | 5.21772i | −0.973050 | − | 0.230593i | ||||
\(513\) | 2.64808 | + | 4.58660i | 0.116915 | + | 0.202503i | ||||
\(514\) | 18.3964 | − | 20.8070i | 0.811430 | − | 0.917757i | ||||
\(515\) | −15.8713 | − | 9.16327i | −0.699371 | − | 0.403782i | ||||
\(516\) | −25.8452 | + | 3.19048i | −1.13777 | + | 0.140453i | ||||
\(517\) | 6.55676i | 0.288366i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 24.4531i | − | 1.07337i | ||||||
\(520\) | 18.0380 | + | 1.40189i | 0.791021 | + | 0.0614767i | ||||
\(521\) | 29.5858 | + | 17.0814i | 1.29618 | + | 0.748348i | 0.979742 | − | 0.200266i | \(-0.0641807\pi\) |
0.316435 | + | 0.948614i | \(0.397514\pi\) | |||||||
\(522\) | −0.673105 | − | 0.595122i | −0.0294610 | − | 0.0260478i | ||||
\(523\) | −16.7507 | − | 29.0130i | −0.732456 | − | 1.26865i | −0.955831 | − | 0.293918i | \(-0.905041\pi\) |
0.223375 | − | 0.974733i | \(-0.428293\pi\) | |||||||
\(524\) | 0.520997 | + | 0.220749i | 0.0227598 | + | 0.00964348i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.8016 | + | 3.00639i | 0.645380 | + | 0.131085i | ||||
\(527\) | 16.3669 | − | 9.44941i | 0.712952 | − | 0.411623i | ||||
\(528\) | −1.13514 | − | 4.52764i | −0.0494006 | − | 0.197040i | ||||
\(529\) | 27.1815 | − | 47.0798i | 1.18181 | − | 2.04695i | ||||
\(530\) | −2.11218 | − | 6.30582i | −0.0917473 | − | 0.273907i | ||||
\(531\) | 2.40669 | 0.104441 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.26644 | 0.228115 | ||||||||
\(534\) | −3.54754 | − | 10.5910i | −0.153517 | − | 0.458318i | ||||
\(535\) | 4.16315 | − | 7.21079i | 0.179989 | − | 0.311750i | ||||
\(536\) | −23.8036 | + | 11.3823i | −1.02816 | + | 0.491642i | ||||
\(537\) | 23.3238 | − | 13.4660i | 1.00650 | − | 0.581100i | ||||
\(538\) | 8.60482 | + | 1.74775i | 0.370980 | + | 0.0753509i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.38044 | + | 10.3384i | −0.188504 | + | 0.444893i | ||||
\(541\) | 8.65326 | + | 14.9879i | 0.372033 | + | 0.644380i | 0.989878 | − | 0.141920i | \(-0.0453276\pi\) |
−0.617845 | + | 0.786300i | \(0.711994\pi\) | |||||||
\(542\) | −18.5170 | − | 16.3717i | −0.795373 | − | 0.703225i | ||||
\(543\) | 15.0832 | + | 8.70827i | 0.647280 | + | 0.373707i | ||||
\(544\) | 10.1261 | − | 19.5296i | 0.434151 | − | 0.837324i | ||||
\(545\) | 0.994813i | 0.0426131i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.8897i | − | 0.551122i | −0.961284 | − | 0.275561i | \(-0.911136\pi\) | ||
0.961284 | − | 0.275561i | \(-0.0888636\pi\) | |||||||
\(548\) | 4.07125 | + | 32.9799i | 0.173915 | + | 1.40883i | ||||
\(549\) | −0.642051 | − | 0.370688i | −0.0274021 | − | 0.0158206i | ||||
\(550\) | −0.832826 | + | 0.941956i | −0.0355118 | + | 0.0401651i | ||||
\(551\) | 0.234626 | + | 0.406383i | 0.00999539 | + | 0.0173125i | ||||
\(552\) | 26.9285 | + | 18.4687i | 1.14615 | + | 0.786081i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.09453 | + | 15.2355i | −0.131474 | + | 0.647295i | ||||
\(555\) | −3.02460 | + | 1.74625i | −0.128387 | + | 0.0741244i | ||||
\(556\) | −29.6993 | + | 22.4104i | −1.25953 | + | 0.950411i | ||||
\(557\) | 17.5977 | − | 30.4800i | 0.745636 | − | 1.29148i | −0.204260 | − | 0.978917i | \(-0.565479\pi\) |
0.949897 | − | 0.312564i | \(-0.101188\pi\) | |||||||
\(558\) | 8.32342 | − | 2.78799i | 0.352359 | − | 0.118025i | ||||
\(559\) | −63.4556 | −2.68389 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.53807 | 0.191598 | ||||||||
\(562\) | −24.9094 | + | 8.34360i | −1.05074 | + | 0.351954i | ||||
\(563\) | −2.62715 | + | 4.55035i | −0.110721 | + | 0.191775i | −0.916061 | − | 0.401038i | \(-0.868649\pi\) |
0.805340 | + | 0.592813i | \(0.201983\pi\) | |||||||
\(564\) | 15.4538 | − | 11.6611i | 0.650722 | − | 0.491020i | ||||
\(565\) | 0.314723 | − | 0.181705i | 0.0132405 | − | 0.00764440i | ||||
\(566\) | −2.13530 | + | 10.5129i | −0.0897533 | + | 0.441888i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 33.3934 | + | 22.9026i | 1.40116 | + | 0.960973i | ||||
\(569\) | 7.02532 | + | 12.1682i | 0.294517 | + | 0.510118i | 0.974872 | − | 0.222764i | \(-0.0715080\pi\) |
−0.680356 | + | 0.732882i | \(0.738175\pi\) | |||||||
\(570\) | 1.15990 | − | 1.31188i | 0.0485827 | − | 0.0549488i | ||||
\(571\) | −11.4617 | − | 6.61743i | −0.479659 | − | 0.276931i | 0.240616 | − | 0.970620i | \(-0.422651\pi\) |
−0.720274 | + | 0.693689i | \(0.755984\pi\) | |||||||
\(572\) | −1.39351 | − | 11.2884i | −0.0582655 | − | 0.471992i | ||||
\(573\) | 27.1714i | 1.13510i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.79563i | − | 0.366803i | ||||||
\(576\) | 6.41469 | − | 7.95323i | 0.267279 | − | 0.331385i | ||||
\(577\) | 8.05094 | + | 4.64821i | 0.335165 | + | 0.193508i | 0.658132 | − | 0.752903i | \(-0.271347\pi\) |
−0.322967 | + | 0.946410i | \(0.604680\pi\) | |||||||
\(578\) | −1.98846 | − | 1.75809i | −0.0827092 | − | 0.0731269i | ||||
\(579\) | 11.5470 | + | 20.0001i | 0.479879 | + | 0.831174i | ||||
\(580\) | −0.388117 | + | 0.916005i | −0.0161157 | + | 0.0380350i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 26.4225 | + | 5.36675i | 1.09525 | + | 0.222459i | ||||
\(583\) | −3.62061 | + | 2.09036i | −0.149950 | + | 0.0865739i | ||||
\(584\) | 23.0789 | − | 11.0358i | 0.955011 | − | 0.456663i | ||||
\(585\) | −4.08495 | + | 7.07534i | −0.168892 | + | 0.292529i | ||||
\(586\) | 2.42866 | + | 7.25065i | 0.100327 | + | 0.299522i | ||||
\(587\) | −7.75382 | −0.320034 | −0.160017 | − | 0.987114i | \(-0.551155\pi\) | ||||
−0.160017 | + | 0.987114i | \(0.551155\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.58455 | −0.188903 | ||||||||
\(590\) | −0.846388 | − | 2.52685i | −0.0348452 | − | 0.104029i | ||||
\(591\) | −15.6421 | + | 27.0929i | −0.643429 | + | 1.11445i | ||||
\(592\) | 10.3239 | − | 2.58834i | 0.424311 | − | 0.106380i | ||||
\(593\) | −2.79212 | + | 1.61203i | −0.114659 | + | 0.0661983i | −0.556233 | − | 0.831027i | \(-0.687754\pi\) |
0.441574 | + | 0.897225i | \(0.354420\pi\) | |||||||
\(594\) | 6.91747 | + | 1.40503i | 0.283827 | + | 0.0576490i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.8481 | − | 12.2231i | −1.18167 | − | 0.500679i | ||||
\(597\) | −12.1468 | − | 21.0388i | −0.497134 | − | 0.861061i | ||||
\(598\) | 59.6095 | + | 52.7034i | 2.43761 | + | 2.15520i | ||||
\(599\) | 15.7055 | + | 9.06755i | 0.641707 | + | 0.370490i | 0.785272 | − | 0.619151i | \(-0.212523\pi\) |
−0.143565 | + | 0.989641i | \(0.545856\pi\) | |||||||
\(600\) | 3.70129 | + | 0.287657i | 0.151104 | + | 0.0117436i | ||||
\(601\) | − | 40.6079i | − | 1.65643i | −0.560408 | − | 0.828216i | \(-0.689356\pi\) | ||
0.560408 | − | 0.828216i | \(-0.310644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 11.9145i | − | 0.485198i | ||||||
\(604\) | 23.7945 | − | 2.93734i | 0.968184 | − | 0.119518i | ||||
\(605\) | −8.84174 | − | 5.10478i | −0.359468 | − | 0.207539i | ||||
\(606\) | 18.2253 | − | 20.6135i | 0.740353 | − | 0.837366i | ||||
\(607\) | 9.03433 | + | 15.6479i | 0.366692 | + | 0.635129i | 0.989046 | − | 0.147607i | \(-0.0471570\pi\) |
−0.622354 | + | 0.782736i | \(0.713824\pi\) | |||||||
\(608\) | −4.49611 | + | 2.87464i | −0.182341 | + | 0.116582i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.163399 | + | 0.804471i | −0.00661582 | + | 0.0325721i | ||||
\(611\) | 40.8543 | − | 23.5872i | 1.65279 | − | 0.954237i | ||||
\(612\) | 5.98349 | + | 7.92961i | 0.241868 | + | 0.320535i | ||||
\(613\) | −17.4060 | + | 30.1480i | −0.703020 | + | 1.21767i | 0.264381 | + | 0.964418i | \(0.414832\pi\) |
−0.967401 | + | 0.253248i | \(0.918501\pi\) | |||||||
\(614\) | 7.62787 | − | 2.55501i | 0.307836 | − | 0.103112i | ||||
\(615\) | 1.08064 | 0.0435756 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.5532 | 0.424854 | 0.212427 | − | 0.977177i | \(-0.431863\pi\) | ||||
0.212427 | + | 0.977177i | \(0.431863\pi\) | |||||||
\(618\) | 32.2567 | − | 10.8046i | 1.29756 | − | 0.434626i | ||||
\(619\) | 12.3185 | − | 21.3363i | 0.495123 | − | 0.857579i | −0.504861 | − | 0.863201i | \(-0.668456\pi\) |
0.999984 | + | 0.00562191i | \(0.00178952\pi\) | |||||||
\(620\) | −5.85439 | − | 7.75851i | −0.235118 | − | 0.311589i | ||||
\(621\) | −42.7636 | + | 24.6896i | −1.71604 | + | 0.990758i | ||||
\(622\) | −0.0352549 | + | 0.173573i | −0.00141359 | + | 0.00695964i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −24.1276 | + | 23.3606i | −0.965877 | + | 0.935172i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 10.9165 | − | 12.3469i | 0.436310 | − | 0.493483i | ||||
\(627\) | −0.953376 | − | 0.550432i | −0.0380742 | − | 0.0219821i | ||||
\(628\) | 21.1107 | − | 2.60604i | 0.842409 | − | 0.103992i | ||||
\(629\) | 10.3477i | 0.412590i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.9068i | 0.752668i | 0.926484 | + | 0.376334i | \(0.122815\pi\) | ||||
−0.926484 | + | 0.376334i | \(0.877185\pi\) | |||||||
\(632\) | −3.26177 | + | 41.9692i | −0.129746 | + | 1.66944i | ||||
\(633\) | −10.1868 | − | 5.88136i | −0.404889 | − | 0.233763i | ||||
\(634\) | 19.5972 | + | 17.3267i | 0.778303 | + | 0.688132i | ||||
\(635\) | −1.23360 | − | 2.13665i | −0.0489538 | − | 0.0847905i | ||||
\(636\) | 11.3660 | + | 4.81585i | 0.450692 | + | 0.190961i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.612904 | + | 0.124489i | 0.0242651 | + | 0.00492856i | ||||
\(639\) | −15.8353 | + | 9.14251i | −0.626434 | + | 0.361672i | ||||
\(640\) | −10.6062 | − | 3.93796i | −0.419249 | − | 0.155662i | ||||
\(641\) | 7.64681 | − | 13.2447i | 0.302031 | − | 0.523133i | −0.674565 | − | 0.738216i | \(-0.735669\pi\) |
0.976596 | + | 0.215083i | \(0.0690020\pi\) | |||||||
\(642\) | 4.90887 | + | 14.6552i | 0.193738 | + | 0.578394i | ||||
\(643\) | 13.9558 | 0.550362 | 0.275181 | − | 0.961393i | \(-0.411262\pi\) | ||||
0.275181 | + | 0.961393i | \(0.411262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.0207 | −0.512688 | ||||||||
\(646\) | −1.64786 | − | 4.91960i | −0.0648341 | − | 0.193559i | ||||
\(647\) | −14.1146 | + | 24.4473i | −0.554904 | + | 0.961122i | 0.443007 | + | 0.896518i | \(0.353912\pi\) |
−0.997911 | + | 0.0646035i | \(0.979422\pi\) | |||||||
\(648\) | −4.31580 | − | 9.02555i | −0.169541 | − | 0.354557i | ||||
\(649\) | −1.45084 | + | 0.837644i | −0.0569506 | + | 0.0328804i | ||||
\(650\) | 8.86520 | + | 1.80064i | 0.347722 | + | 0.0706268i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.12576 | + | 14.4576i | −0.239903 | + | 0.566202i | ||||
\(653\) | −12.6553 | − | 21.9196i | −0.495240 | − | 0.857781i | 0.504745 | − | 0.863269i | \(-0.331587\pi\) |
−0.999985 | + | 0.00548743i | \(0.998253\pi\) | |||||||
\(654\) | −1.38342 | − | 1.22314i | −0.0540959 | − | 0.0478286i | ||||
\(655\) | 0.245013 | + | 0.141458i | 0.00957346 | + | 0.00552724i | ||||
\(656\) | −3.16686 | − | 0.903617i | −0.123645 | − | 0.0352803i | ||||
\(657\) | 11.5518i | 0.450678i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.5411i | 1.07285i | 0.843948 | + | 0.536425i | \(0.180226\pi\) | ||||
−0.843948 | + | 0.536425i | \(0.819774\pi\) | |||||||
\(660\) | −0.285939 | − | 2.31630i | −0.0111301 | − | 0.0901620i | ||||
\(661\) | 19.4724 | + | 11.2424i | 0.757390 | + | 0.437279i | 0.828358 | − | 0.560199i | \(-0.189275\pi\) |
−0.0709679 | + | 0.997479i | \(0.522609\pi\) | |||||||
\(662\) | −6.48596 | + | 7.33586i | −0.252084 | + | 0.285116i | ||||
\(663\) | −16.3252 | − | 28.2761i | −0.634019 | − | 1.09815i | ||||
\(664\) | 6.44209 | − | 9.39295i | 0.250002 | − | 0.364517i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.956668 | + | 4.71003i | −0.0370701 | + | 0.182510i | ||||
\(667\) | −3.78895 | + | 2.18755i | −0.146709 | + | 0.0847024i | ||||
\(668\) | −12.6162 | + | 9.51985i | −0.488134 | + | 0.368334i | ||||
\(669\) | −10.7776 | + | 18.6674i | −0.416688 | + | 0.721725i | ||||
\(670\) | −12.5094 | + | 4.19012i | −0.483281 | + | 0.161879i | ||||
\(671\) | 0.516070 | 0.0199227 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.4276 | −0.440501 | −0.220251 | − | 0.975443i | \(-0.570688\pi\) | ||||
−0.220251 | + | 0.975443i | \(0.570688\pi\) | |||||||
\(674\) | −20.8501 | + | 6.98389i | −0.803114 | + | 0.269009i | ||||
\(675\) | −2.80703 | + | 4.86191i | −0.108043 | + | 0.187135i | ||||
\(676\) | −44.5692 | + | 33.6308i | −1.71420 | + | 1.29349i | ||||
\(677\) | −39.9384 | + | 23.0585i | −1.53496 | + | 0.886209i | −0.535836 | + | 0.844322i | \(0.680004\pi\) |
−0.999122 | + | 0.0418868i | \(0.986663\pi\) | |||||||
\(678\) | −0.134273 | + | 0.661073i | −0.00515671 | + | 0.0253884i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.22123 | − | 9.07093i | 0.238573 | − | 0.347854i | ||||
\(681\) | −8.34244 | − | 14.4495i | −0.319683 | − | 0.553707i | ||||
\(682\) | −4.04732 | + | 4.57766i | −0.154980 | + | 0.175288i | ||||
\(683\) | 27.9026 | + | 16.1096i | 1.06766 | + | 0.616416i | 0.927542 | − | 0.373718i | \(-0.121917\pi\) |
0.140122 | + | 0.990134i | \(0.455250\pi\) | |||||||
\(684\) | −0.295238 | − | 2.39163i | −0.0112887 | − | 0.0914464i | ||||
\(685\) | 16.6151i | 0.634832i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.7024i | 0.866152i | ||||||||
\(688\) | 38.1577 | + | 10.8877i | 1.45475 | + | 0.415091i | ||||
\(689\) | 26.0495 | + | 15.0397i | 0.992408 | + | 0.572967i | ||||
\(690\) | 12.2315 | + | 10.8144i | 0.465644 | + | 0.411697i | ||||
\(691\) | 15.5135 | + | 26.8703i | 0.590163 | + | 1.02219i | 0.994210 | + | 0.107454i | \(0.0342699\pi\) |
−0.404047 | + | 0.914738i | \(0.632397\pi\) | |||||||
\(692\) | −14.5365 | + | 34.3080i | −0.552595 | + | 1.30419i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.4440 | + | 6.58980i | 1.23156 | + | 0.250146i | ||||
\(695\) | −16.1106 | + | 9.30144i | −0.611109 | + | 0.352824i | ||||
\(696\) | −0.796627 | − | 1.66597i | −0.0301961 | − | 0.0631485i | ||||
\(697\) | 1.60087 | − | 2.77279i | 0.0606374 | − | 0.105027i | ||||
\(698\) | 13.9888 | + | 41.7630i | 0.529485 | + | 1.58075i | ||||
\(699\) | 31.1701 | 1.17896 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.9213 | 1.20565 | 0.602826 | − | 0.797873i | \(-0.294041\pi\) | ||||
0.602826 | + | 0.797873i | \(0.294041\pi\) | |||||||
\(702\) | −16.1303 | − | 48.1563i | −0.608799 | − | 1.81754i | ||||
\(703\) | 1.25509 | − | 2.17389i | 0.0473368 | − | 0.0819897i | ||||
\(704\) | −1.09891 | + | 7.02713i | −0.0414167 | + | 0.264845i | ||||
\(705\) | 8.38302 | − | 4.83994i | 0.315723 | − | 0.182283i | ||||
\(706\) | 14.1687 | + | 2.87785i | 0.533247 | + | 0.108309i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.55456 | + | 1.92979i | 0.171171 | + | 0.0725261i | ||||
\(709\) | 2.49320 | + | 4.31835i | 0.0936342 | + | 0.162179i | 0.909038 | − | 0.416714i | \(-0.136818\pi\) |
−0.815404 | + | 0.578893i | \(0.803485\pi\) | |||||||
\(710\) | 15.1680 | + | 13.4107i | 0.569243 | + | 0.503293i | ||||
\(711\) | −16.4622 | − | 9.50447i | −0.617381 | − | 0.356445i | ||||
\(712\) | −1.31874 | + | 16.9682i | −0.0494218 | + | 0.635910i | ||||
\(713\) | − | 42.7445i | − | 1.60079i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.68704i | − | 0.212683i | ||||||
\(716\) | −40.7285 | + | 5.02778i | −1.52210 | + | 0.187897i | ||||
\(717\) | −11.5981 | − | 6.69616i | −0.433139 | − | 0.250073i | ||||
\(718\) | −10.5911 | + | 11.9789i | −0.395256 | + | 0.447050i | ||||
\(719\) | 8.64963 | + | 14.9816i | 0.322577 | + | 0.558720i | 0.981019 | − | 0.193912i | \(-0.0621176\pi\) |
−0.658442 | + | 0.752631i | \(0.728784\pi\) | |||||||
\(720\) | 3.67038 | − | 3.55370i | 0.136787 | − | 0.132439i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.09793 | − | 25.0990i | 0.189725 | − | 0.934087i | ||||
\(723\) | 2.64673 | − | 1.52809i | 0.0984331 | − | 0.0568304i | ||||
\(724\) | −15.9851 | − | 21.1842i | −0.594081 | − | 0.787304i | ||||
\(725\) | −0.248709 | + | 0.430777i | −0.00923682 | + | 0.0159986i | ||||
\(726\) | 17.9699 | − | 6.01917i | 0.666927 | − | 0.223392i | ||||
\(727\) | 4.42613 | 0.164156 | 0.0820780 | − | 0.996626i | \(-0.473844\pi\) | ||||
0.0820780 | + | 0.996626i | \(0.473844\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.6237 | 0.986065 | ||||||||
\(730\) | 12.1285 | − | 4.06255i | 0.448897 | − | 0.150362i | ||||
\(731\) | −19.2890 | + | 33.4095i | −0.713430 | + | 1.23570i | ||||
\(732\) | −0.917821 | − | 1.21634i | −0.0339236 | − | 0.0449572i | ||||
\(733\) | 32.3952 | − | 18.7034i | 1.19655 | − | 0.690826i | 0.236762 | − | 0.971568i | \(-0.423914\pi\) |
0.959783 | + | 0.280742i | \(0.0905806\pi\) | |||||||
\(734\) | 6.45065 | − | 31.7589i | 0.238098 | − | 1.17224i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.8020 | − | 41.9198i | −0.987934 | − | 1.54519i | ||||
\(737\) | 4.14684 | + | 7.18254i | 0.152751 | + | 0.264572i | ||||
\(738\) | 0.985030 | − | 1.11411i | 0.0362595 | − | 0.0410108i | ||||
\(739\) | −36.2776 | − | 20.9449i | −1.33449 | − | 0.770469i | −0.348507 | − | 0.937306i | \(-0.613311\pi\) |
−0.985984 | + | 0.166837i | \(0.946645\pi\) | |||||||
\(740\) | 5.28163 | − | 0.651997i | 0.194157 | − | 0.0239679i | ||||
\(741\) | 7.92048i | 0.290966i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.0690i | 1.21318i | 0.795014 | + | 0.606591i | \(0.207464\pi\) | ||||
−0.795014 | + | 0.606591i | \(0.792536\pi\) | |||||||
\(744\) | 17.9873 | + | 1.39794i | 0.659446 | + | 0.0512510i | ||||
\(745\) | −13.5666 | − | 7.83270i | −0.497043 | − | 0.286968i | ||||
\(746\) | 11.8756 | + | 10.4998i | 0.434797 | + | 0.384424i | ||||
\(747\) | 2.57162 | + | 4.45418i | 0.0940907 | + | 0.162970i | ||||
\(748\) | −6.36696 | − | 2.69772i | −0.232799 | − | 0.0986384i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.81908 | + | 0.369479i | 0.0664234 | + | 0.0134915i | ||||
\(751\) | 5.95362 | − | 3.43732i | 0.217251 | − | 0.125430i | −0.387426 | − | 0.921901i | \(-0.626636\pi\) |
0.604677 | + | 0.796471i | \(0.293302\pi\) | |||||||
\(752\) | −28.6139 | + | 7.17387i | −1.04344 | + | 0.261604i | ||||
\(753\) | −4.29398 | + | 7.43739i | −0.156481 | + | 0.271034i | ||||
\(754\) | −1.42918 | − | 4.26676i | −0.0520478 | − | 0.155386i | ||||
\(755\) | 11.9875 | 0.436272 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.4550 | 0.670758 | 0.335379 | − | 0.942083i | \(-0.391136\pi\) | ||||
0.335379 | + | 0.942083i | \(0.391136\pi\) | |||||||
\(758\) | −10.8991 | − | 32.5386i | −0.395871 | − | 1.18186i | ||||
\(759\) | 5.13200 | − | 8.88888i | 0.186280 | − | 0.322646i | ||||
\(760\) | −2.40721 | + | 1.15107i | −0.0873188 | + | 0.0417537i | ||||
\(761\) | 35.2440 | − | 20.3481i | 1.27759 | − | 0.737618i | 0.301187 | − | 0.953565i | \(-0.402617\pi\) |
0.976405 | + | 0.215946i | \(0.0692837\pi\) | |||||||
\(762\) | 4.48803 | + | 0.911577i | 0.162584 | + | 0.0330229i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.1524 | − | 38.1218i | 0.584374 | − | 1.37920i | ||||
\(765\) | 2.48346 | + | 4.30147i | 0.0897895 | + | 0.155520i | ||||
\(766\) | 8.54164 | + | 7.55205i | 0.308622 | + | 0.272866i | ||||
\(767\) | 10.4385 | + | 6.02667i | 0.376912 | + | 0.217610i | ||||
\(768\) | 18.5168 | − | 9.90756i | 0.668168 | − | 0.357508i | ||||
\(769\) | − | 39.5711i | − | 1.42697i | −0.700670 | − | 0.713485i | \(-0.747115\pi\) | ||
0.700670 | − | 0.713485i | \(-0.252885\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.7768i | 0.928327i | ||||||||
\(772\) | −4.31130 | − | 34.9246i | −0.155167 | − | 1.25696i | ||||
\(773\) | −12.9250 | − | 7.46225i | −0.464880 | − | 0.268399i | 0.249214 | − | 0.968448i | \(-0.419828\pi\) |
−0.714094 | + | 0.700050i | \(0.753161\pi\) | |||||||
\(774\) | −11.8687 | + | 13.4239i | −0.426611 | + | 0.482513i | ||||
\(775\) | −2.42987 | − | 4.20866i | −0.0872835 | − | 0.151179i | ||||
\(776\) | −33.8807 | − | 23.2368i | −1.21624 | − | 0.834153i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.93292 | + | 19.3632i | −0.141002 | + | 0.694205i | ||||
\(779\) | −0.672635 | + | 0.388346i | −0.0240997 | + | 0.0139139i | ||||
\(780\) | −13.4039 | + | 10.1143i | −0.479938 | + | 0.362150i | ||||
\(781\) | 6.36407 | − | 11.0229i | 0.227724 | − | 0.394430i | ||||
\(782\) | 45.8683 | − | 15.3639i | 1.64025 | − | 0.549413i | ||||
\(783\) | 2.79253 | 0.0997969 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.6355 | 0.379597 | ||||||||
\(786\) | −0.497964 | + | 0.166797i | −0.0177618 | + | 0.00594945i | ||||
\(787\) | −14.6145 | + | 25.3131i | −0.520952 | + | 0.902315i | 0.478751 | + | 0.877951i | \(0.341090\pi\) |
−0.999703 | + | 0.0243647i | \(0.992244\pi\) | |||||||
\(788\) | 38.0517 | − | 28.7129i | 1.35554 | − | 1.02286i | ||||
\(789\) | −12.1400 | + | 7.00901i | −0.432194 | + | 0.249528i | ||||
\(790\) | −4.18955 | + | 20.6267i | −0.149057 | + | 0.733865i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.64868 | − | 1.81658i | −0.0941167 | − | 0.0645493i | ||||
\(793\) | −1.85651 | − | 3.21556i | −0.0659264 | − | 0.114188i | ||||
\(794\) | −10.6460 | + | 12.0411i | −0.377814 | + | 0.427321i | ||||
\(795\) | 5.34519 | + | 3.08605i | 0.189574 | + | 0.109451i | ||||
\(796\) | 4.53522 | + | 36.7385i | 0.160747 | + | 1.30216i | ||||
\(797\) | 32.2478i | 1.14228i | 0.820854 | + | 0.571138i | \(0.193498\pi\) | ||||
−0.820854 | + | 0.571138i | \(0.806502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 28.6798i | − | 1.01462i | ||||||
\(800\) | −5.02194 | − | 2.60387i | −0.177552 | − | 0.0920606i | ||||
\(801\) | −6.65570 | − | 3.84267i | −0.235168 | − | 0.135774i | ||||
\(802\) | 4.00171 | + | 3.53809i | 0.141305 | + | 0.124934i | ||||
\(803\) | −4.02058 | − | 6.96385i | −0.141883 | − | 0.245749i | ||||
\(804\) | 9.55364 | − | 22.5478i | 0.336931 | − | 0.795199i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43.0826 | + | 8.75063i | 1.51752 | + | 0.308228i | ||||
\(807\) | −7.05750 | + | 4.07465i | −0.248436 | + | 0.143435i | ||||
\(808\) | −37.8243 | + | 18.0867i | −1.33065 | + | 0.636286i | ||||
\(809\) | −9.03143 | + | 15.6429i | −0.317528 | + | 0.549975i | −0.979972 | − | 0.199137i | \(-0.936186\pi\) |
0.662443 | + | 0.749112i | \(0.269519\pi\) | |||||||
\(810\) | −1.58876 | − | 4.74315i | −0.0558232 | − | 0.166657i | ||||
\(811\) | −26.8176 | −0.941692 | −0.470846 | − | 0.882215i | \(-0.656051\pi\) | ||||
−0.470846 | + | 0.882215i | \(0.656051\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.9398 | 0.804534 | ||||||||
\(814\) | −1.06260 | − | 3.17235i | −0.0372442 | − | 0.111191i | ||||
\(815\) | −3.92545 | + | 6.79907i | −0.137502 | + | 0.238161i | ||||
\(816\) | 4.96519 | + | 19.8043i | 0.173816 | + | 0.693289i | ||||
\(817\) | 8.10462 | − | 4.67920i | 0.283545 | − | 0.163705i | ||||
\(818\) | −19.3734 | − | 3.93499i | −0.677375 | − | 0.137584i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.51615 | − | 0.642401i | −0.0529462 | − | 0.0224336i | ||||
\(821\) | −4.09094 | − | 7.08571i | −0.142775 | − | 0.247293i | 0.785766 | − | 0.618524i | \(-0.212269\pi\) |
−0.928540 | + | 0.371231i | \(0.878936\pi\) | |||||||
\(822\) | −23.1055 | − | 20.4286i | −0.805897 | − | 0.712530i | ||||
\(823\) | −29.7686 | − | 17.1869i | −1.03767 | − | 0.599097i | −0.118495 | − | 0.992955i | \(-0.537807\pi\) |
−0.919172 | + | 0.393857i | \(0.871140\pi\) | |||||||
\(824\) | −51.6795 | − | 4.01644i | −1.80034 | − | 0.139919i | ||||
\(825\) | − | 1.16694i | − | 0.0406277i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.6060i | 1.44678i | 0.690439 | + | 0.723391i | \(0.257418\pi\) | ||||
−0.690439 | + | 0.723391i | \(0.742582\pi\) | |||||||
\(828\) | 22.2986 | − | 2.75267i | 0.774930 | − | 0.0956620i | ||||
\(829\) | −2.96337 | − | 1.71090i | −0.102922 | − | 0.0594222i | 0.447655 | − | 0.894206i | \(-0.352259\pi\) |
−0.550578 | + | 0.834784i | \(0.685592\pi\) | |||||||
\(830\) | 3.77217 | − | 4.26647i | 0.130934 | − | 0.148091i | ||||
\(831\) | −7.21449 | − | 12.4959i | −0.250268 | − | 0.433477i | ||||
\(832\) | 47.7383 | − | 18.4322i | 1.65503 | − | 0.639021i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.87337 | − | 33.8401i | 0.238005 | − | 1.17179i | ||||
\(835\) | −6.84372 | + | 3.95122i | −0.236837 | + | 0.136738i | ||||
\(836\) | 1.01038 | + | 1.33901i | 0.0349449 | + | 0.0463106i | ||||
\(837\) | −13.6414 | + | 23.6276i | −0.471517 | + | 0.816691i | ||||
\(838\) | 8.36081 | − | 2.80052i | 0.288820 | − | 0.0967423i | ||||
\(839\) | −42.9230 | −1.48187 | −0.740933 | − | 0.671579i | \(-0.765616\pi\) | ||||
−0.740933 | + | 0.671579i | \(0.765616\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7526 | −0.991468 | ||||||||
\(842\) | −12.9720 | + | 4.34506i | −0.447044 | + | 0.149741i | ||||
\(843\) | 12.1906 | − | 21.1147i | 0.419866 | − | 0.727230i | ||||
\(844\) | 10.7959 | + | 14.3073i | 0.371612 | + | 0.492477i | ||||
\(845\) | −24.1769 | + | 13.9585i | −0.831710 | + | 0.480188i | ||||
\(846\) | 2.65151 | − | 13.0544i | 0.0911609 | − | 0.448818i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −13.0838 | − | 13.5134i | −0.449299 | − | 0.464051i | ||||
\(849\) | −4.97817 | − | 8.62244i | −0.170850 | − | 0.295921i | ||||
\(850\) | 3.64285 | − | 4.12020i | 0.124949 | − | 0.141322i | ||||
\(851\) | 20.2684 | + | 11.7020i | 0.694792 | + | 0.401139i | ||||
\(852\) | −37.2985 | + | 4.60436i | −1.27783 | + | 0.157743i | ||||
\(853\) | − | 31.3541i | − | 1.07355i | −0.843727 | − | 0.536773i | \(-0.819643\pi\) | ||
0.843727 | − | 0.536773i | \(-0.180357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.20489i | − | 0.0412065i | ||||||
\(856\) | 1.82479 | − | 23.4795i | 0.0623700 | − | 0.802514i | ||||
\(857\) | −30.2447 | − | 17.4618i | −1.03314 | − | 0.596484i | −0.115257 | − | 0.993336i | \(-0.536769\pi\) |
−0.917883 | + | 0.396852i | \(0.870103\pi\) | |||||||
\(858\) | 7.90857 | + | 6.99232i | 0.269994 | + | 0.238714i | ||||
\(859\) | −21.1548 | − | 36.6412i | −0.721793 | − | 1.25018i | −0.960281 | − | 0.279036i | \(-0.909985\pi\) |
0.238488 | − | 0.971145i | \(-0.423348\pi\) | |||||||
\(860\) | 18.2681 | + | 7.74032i | 0.622938 | + | 0.263943i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.7505 | − | 2.38667i | −0.400223 | − | 0.0812905i | ||||
\(863\) | 21.0827 | − | 12.1721i | 0.717665 | − | 0.414344i | −0.0962279 | − | 0.995359i | \(-0.530678\pi\) |
0.813893 | + | 0.581015i | \(0.197344\pi\) | |||||||
\(864\) | 1.43695 | + | 31.7254i | 0.0488859 | + | 1.07932i | ||||
\(865\) | −9.31513 | + | 16.1343i | −0.316724 | + | 0.548582i | ||||
\(866\) | −11.1992 | − | 33.4347i | −0.380565 | − | 1.13616i | ||||
\(867\) | 2.46341 | 0.0836618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.2321 | 0.448867 | ||||||||
\(870\) | −0.293259 | − | 0.875510i | −0.00994240 | − | 0.0296826i | ||||
\(871\) | 29.8356 | − | 51.6768i | 1.01094 | − | 1.75100i | ||||
\(872\) | 1.21384 | + | 2.53847i | 0.0411056 | + | 0.0859634i | ||||
\(873\) | 16.0663 | − | 9.27591i | 0.543763 | − | 0.313942i | ||||
\(874\) | −11.4997 | − | 2.33574i | −0.388984 | − | 0.0790077i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.26276 | + | 21.8613i | −0.312960 | + | 0.738624i | ||||
\(877\) | −21.2613 | − | 36.8256i | −0.717942 | − | 1.24351i | −0.961814 | − | 0.273705i | \(-0.911751\pi\) |
0.243871 | − | 0.969808i | \(-0.421583\pi\) | |||||||
\(878\) | 26.9234 | + | 23.8042i | 0.908622 | + | 0.803353i | ||||
\(879\) | −6.14608 | − | 3.54844i | −0.207302 | − | 0.119686i | ||||
\(880\) | −0.975784 | + | 3.41978i | −0.0328937 | + | 0.115281i | ||||
\(881\) | 30.5097i | 1.02790i | 0.857820 | + | 0.513950i | \(0.171818\pi\) | ||||
−0.857820 | + | 0.513950i | \(0.828182\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.7488i | 0.429030i | 0.976721 | + | 0.214515i | \(0.0688170\pi\) | ||||
−0.976721 | + | 0.214515i | \(0.931183\pi\) | |||||||
\(884\) | 6.09533 | + | 49.3764i | 0.205008 | + | 1.66071i | ||||
\(885\) | 2.14191 | + | 1.23663i | 0.0719995 | + | 0.0415689i | ||||
\(886\) | 22.4714 | − | 25.4160i | 0.754941 | − | 0.853866i | ||||
\(887\) | 4.75891 | + | 8.24267i | 0.159788 | + | 0.276762i | 0.934792 | − | 0.355195i | \(-0.115585\pi\) |
−0.775004 | + | 0.631956i | \(0.782252\pi\) | |||||||
\(888\) | −5.58718 | + | 8.14644i | −0.187493 | + | 0.273377i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.69384 | + | 8.33940i | −0.0567777 | + | 0.279537i | ||||
\(891\) | −2.72338 | + | 1.57234i | −0.0912366 | + | 0.0526755i | ||||
\(892\) | 26.2183 | − | 19.7837i | 0.877852 | − | 0.662407i | ||||
\(893\) | −3.47863 | + | 6.02517i | −0.116408 | + | 0.201625i | ||||
\(894\) | 27.5728 | − | 9.23572i | 0.922173 | − | 0.308889i | ||||
\(895\) | −20.5188 | −0.685869 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −73.8472 | −2.46569 | ||||||||
\(898\) | −22.9686 | + | 7.69350i | −0.766471 | + | 0.256735i | ||||
\(899\) | −1.20866 | + | 2.09346i | −0.0403111 | + | 0.0698209i | ||||
\(900\) | 2.03906 | − | 1.53863i | 0.0679687 | − | 0.0512875i | ||||
\(901\) | 15.8369 | − | 9.14342i | 0.527603 | − | 0.304611i | ||||
\(902\) | −0.206051 | + | 1.01446i | −0.00686074 | + | 0.0337779i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.581370 | − | 0.847672i | 0.0193361 | − | 0.0281932i | ||||
\(905\) | −6.63463 | − | 11.4915i | −0.220542 | − | 0.381991i | ||||
\(906\) | −14.7389 | + | 16.6702i | −0.489667 | + | 0.553832i | ||||
\(907\) | 1.34001 | + | 0.773654i | 0.0444942 | + | 0.0256887i | 0.522082 | − | 0.852895i | \(-0.325155\pi\) |
−0.477588 | + | 0.878584i | \(0.658489\pi\) | |||||||
\(908\) | 3.11481 | + | 25.2321i | 0.103368 | + | 0.837357i | ||||
\(909\) | − | 18.9324i | − | 0.627947i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.9439i | 0.660769i | 0.943846 | + | 0.330385i | \(0.107178\pi\) | ||||
−0.943846 | + | 0.330385i | \(0.892822\pi\) | |||||||
\(912\) | 1.35900 | − | 4.76280i | 0.0450009 | − | 0.157712i | ||||
\(913\) | −3.10054 | − | 1.79010i | −0.102613 | − | 0.0592436i | ||||
\(914\) | 11.8488 | + | 10.4761i | 0.391924 | + | 0.346518i | ||||
\(915\) | −0.380943 | − | 0.659812i | −0.0125936 | − | 0.0218127i | ||||
\(916\) | 13.4958 | − | 31.8517i | 0.445913 | − | 1.05241i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −30.2576 | − | 6.14571i | −0.998650 | − | 0.202839i | ||||
\(919\) | −9.06367 | + | 5.23291i | −0.298983 | + | 0.172618i | −0.641986 | − | 0.766716i | \(-0.721889\pi\) |
0.343003 | + | 0.939334i | \(0.388556\pi\) | |||||||
\(920\) | −10.7321 | − | 22.4439i | −0.353827 | − | 0.739952i | ||||
\(921\) | −3.73306 | + | 6.46584i | −0.123008 | + | 0.213057i | ||||
\(922\) | 11.3965 | + | 34.0238i | 0.375325 | + | 1.12052i | ||||
\(923\) | −91.5762 | −3.01427 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.66086 | 0.0874886 | ||||||||
\(926\) | 0.0229965 | + | 0.0686548i | 0.000755710 | + | 0.00225614i | ||||
\(927\) | 11.7035 | − | 20.2710i | 0.384393 | − | 0.665788i | ||||
\(928\) | 0.127317 | + | 2.81094i | 0.00417938 | + | 0.0922736i | ||||
\(929\) | 27.7313 | − | 16.0107i | 0.909836 | − | 0.525294i | 0.0294574 | − | 0.999566i | \(-0.490622\pi\) |
0.880378 | + | 0.474272i | \(0.157289\pi\) | |||||||
\(930\) | 8.84026 | + | 1.79557i | 0.289883 | + | 0.0588791i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −43.7320 | − | 18.5295i | −1.43249 | − | 0.606954i | ||||
\(933\) | −0.0821922 | − | 0.142361i | −0.00269085 | − | 0.00466069i | ||||
\(934\) | 14.0817 | + | 12.4503i | 0.460768 | + | 0.407386i | ||||
\(935\) | −2.99424 | − | 1.72873i | −0.0979221 | − | 0.0565354i | ||||
\(936\) | −1.79051 | + | 23.0385i | −0.0585247 | + | 0.753037i | ||||
\(937\) | 47.3389i | 1.54649i | 0.634106 | + | 0.773247i | \(0.281368\pi\) | ||||
−0.634106 | + | 0.773247i | \(0.718632\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.2960i | 0.499167i | ||||||||
\(940\) | −14.6386 | + | 1.80708i | −0.477460 | + | 0.0589405i | ||||
\(941\) | 4.51106 | + | 2.60446i | 0.147056 | + | 0.0849030i | 0.571723 | − | 0.820447i | \(-0.306275\pi\) |
−0.424667 | + | 0.905350i | \(0.639609\pi\) | |||||||
\(942\) | −13.0765 | + | 14.7900i | −0.426056 | + | 0.481885i | ||||
\(943\) | −3.62078 | − | 6.27138i | −0.117909 | − | 0.204224i | ||||
\(944\) | −5.24290 | − | 5.41504i | −0.170642 | − | 0.176245i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.48271 | − | 12.2233i | 0.0807200 | − | 0.397414i | ||||
\(947\) | −0.543682 | + | 0.313895i | −0.0176673 | + | 0.0102002i | −0.508808 | − | 0.860880i | \(-0.669914\pi\) |
0.491140 | + | 0.871080i | \(0.336580\pi\) | |||||||
\(948\) | −23.5330 | − | 31.1870i | −0.764315 | − | 1.01291i | ||||
\(949\) | −28.9272 | + | 50.1034i | −0.939017 | + | 1.62642i | ||||
\(950\) | −1.26505 | + | 0.423739i | −0.0410437 | + | 0.0137479i | ||||
\(951\) | −24.2780 | −0.787267 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.46691 | −0.144697 | −0.0723487 | − | 0.997379i | \(-0.523049\pi\) | ||||
−0.0723487 | + | 0.997379i | \(0.523049\pi\) | |||||||
\(954\) | 8.05390 | − | 2.69771i | 0.260754 | − | 0.0873417i | ||||
\(955\) | 10.3506 | − | 17.9278i | 0.334939 | − | 0.580131i | ||||
\(956\) | 12.2916 | + | 16.2894i | 0.397539 | + | 0.526838i | ||||
\(957\) | −0.502692 | + | 0.290229i | −0.0162497 | + | 0.00938178i | ||||
\(958\) | −2.72242 | + | 13.4034i | −0.0879572 | + | 0.433046i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.79558 | − | 3.78216i | 0.316151 | − | 0.122069i | ||||
\(961\) | 3.69146 | + | 6.39380i | 0.119079 | + | 0.206252i | ||||
\(962\) | −15.9439 | + | 18.0331i | −0.514051 | + | 0.581411i | ||||
\(963\) | 9.20974 | + | 5.31725i | 0.296780 | + | 0.171346i | ||||
\(964\) | −4.62179 | + | 0.570542i | −0.148858 | + | 0.0183759i | ||||
\(965\) | − | 17.5948i | − | 0.566398i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.90732i | − | 0.0613352i | −0.999530 | − | 0.0306676i | \(-0.990237\pi\) | ||
0.999530 | − | 0.0306676i | \(-0.00976333\pi\) | |||||||
\(968\) | −28.7902 | − | 2.23752i | −0.925351 | − | 0.0719167i | ||||
\(969\) | 4.17015 | + | 2.40764i | 0.133964 | + | 0.0773444i | ||||
\(970\) | −15.3893 | − | 13.6063i | −0.494120 | − | 0.436873i | ||||
\(971\) | −24.4798 | − | 42.4002i | −0.785593 | − | 1.36069i | −0.928644 | − | 0.370971i | \(-0.879025\pi\) |
0.143052 | − | 0.989715i | \(-0.454308\pi\) | |||||||
\(972\) | −22.4658 | − | 9.51888i | −0.720590 | − | 0.305318i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.48971 | − | 1.92748i | −0.304070 | − | 0.0617605i | ||||
\(975\) | −7.27106 | + | 4.19795i | −0.232860 | + | 0.134442i | ||||
\(976\) | 0.564642 | + | 2.25215i | 0.0180738 | + | 0.0720895i | ||||
\(977\) | −3.15593 | + | 5.46623i | −0.100967 | + | 0.174880i | −0.912083 | − | 0.410005i | \(-0.865527\pi\) |
0.811116 | + | 0.584885i | \(0.198860\pi\) | |||||||
\(978\) | −4.62859 | − | 13.8184i | −0.148006 | − | 0.441864i | ||||
\(979\) | 5.34974 | 0.170978 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.27059 | −0.0405669 | ||||||||
\(982\) | −10.7979 | − | 32.2367i | −0.344576 | − | 1.02871i | ||||
\(983\) | −10.7447 | + | 18.6103i | −0.342702 | + | 0.593577i | −0.984933 | − | 0.172934i | \(-0.944675\pi\) |
0.642232 | + | 0.766511i | \(0.278009\pi\) | |||||||
\(984\) | 2.75747 | − | 1.31856i | 0.0879050 | − | 0.0420341i | ||||
\(985\) | 20.6414 | − | 11.9173i | 0.657691 | − | 0.379718i | ||||
\(986\) | −2.68089 | − | 0.544524i | −0.0853771 | − | 0.0173412i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.70844 | − | 11.1125i | 0.149795 | − | 0.353536i | ||||
\(989\) | 43.6270 | + | 75.5641i | 1.38726 | + | 2.40280i | ||||
\(990\) | −1.20308 | − | 1.06370i | −0.0382365 | − | 0.0338066i | ||||
\(991\) | 5.03965 | + | 2.90964i | 0.160090 | + | 0.0924279i | 0.577905 | − | 0.816104i | \(-0.303871\pi\) |
−0.417815 | + | 0.908532i | \(0.637204\pi\) | |||||||
\(992\) | −24.4053 | − | 12.6541i | −0.774870 | − | 0.401769i | ||||
\(993\) | − | 9.08804i | − | 0.288400i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.5087i | 0.586765i | ||||||||
\(996\) | 1.29512 | + | 10.4914i | 0.0410375 | + | 0.332433i | ||||
\(997\) | −21.5362 | − | 12.4339i | −0.682059 | − | 0.393787i | 0.118572 | − | 0.992946i | \(-0.462169\pi\) |
−0.800630 | + | 0.599159i | \(0.795502\pi\) | |||||||
\(998\) | −12.1198 | + | 13.7080i | −0.383647 | + | 0.433918i | ||||
\(999\) | −7.46911 | − | 12.9369i | −0.236312 | − | 0.409305i |
(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 | 980.2.o.g.31.41 | 96 | ||
4.3 | odd | 2 | inner | 980.2.o.g.31.14 | 96 | ||
7.2 | even | 3 | inner | 980.2.o.g.411.13 | 96 | ||
7.3 | odd | 6 | 980.2.g.b.391.19 | yes | 48 | ||
7.4 | even | 3 | 980.2.g.b.391.20 | yes | 48 | ||
7.5 | odd | 6 | inner | 980.2.o.g.411.14 | 96 | ||
7.6 | odd | 2 | inner | 980.2.o.g.31.42 | 96 | ||
28.3 | even | 6 | 980.2.g.b.391.18 | yes | 48 | ||
28.11 | odd | 6 | 980.2.g.b.391.17 | ✓ | 48 | ||
28.19 | even | 6 | inner | 980.2.o.g.411.41 | 96 | ||
28.23 | odd | 6 | inner | 980.2.o.g.411.42 | 96 | ||
28.27 | even | 2 | inner | 980.2.o.g.31.13 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.g.b.391.17 | ✓ | 48 | 28.11 | odd | 6 | ||
980.2.g.b.391.18 | yes | 48 | 28.3 | even | 6 | ||
980.2.g.b.391.19 | yes | 48 | 7.3 | odd | 6 | ||
980.2.g.b.391.20 | yes | 48 | 7.4 | even | 3 | ||
980.2.o.g.31.13 | 96 | 28.27 | even | 2 | inner | ||
980.2.o.g.31.14 | 96 | 4.3 | odd | 2 | inner | ||
980.2.o.g.31.41 | 96 | 1.1 | even | 1 | trivial | ||
980.2.o.g.31.42 | 96 | 7.6 | odd | 2 | inner | ||
980.2.o.g.411.13 | 96 | 7.2 | even | 3 | inner | ||
980.2.o.g.411.14 | 96 | 7.5 | odd | 6 | inner | ||
980.2.o.g.411.41 | 96 | 28.19 | even | 6 | inner | ||
980.2.o.g.411.42 | 96 | 28.23 | odd | 6 | inner |