Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 71.12 | ||
Character | \(\chi\) | \(=\) | 108.71 |
Dual form | 108.6.h.a.35.12 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.72594 | + | 5.38713i | −0.305106 | + | 0.952318i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −26.0423 | − | 18.5957i | −0.813820 | − | 0.581116i | ||||
\(5\) | 20.1454 | + | 11.6310i | 0.360372 | + | 0.208061i | 0.669244 | − | 0.743043i | \(-0.266618\pi\) |
−0.308872 | + | 0.951104i | \(0.599951\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −156.832 | + | 90.5473i | −1.20974 | + | 0.698442i | −0.962702 | − | 0.270565i | \(-0.912790\pi\) |
−0.247035 | + | 0.969007i | \(0.579456\pi\) | |||||||
\(8\) | 145.125 | − | 108.198i | 0.801710 | − | 0.597714i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −97.4272 | + | 88.4515i | −0.308092 | + | 0.279708i | ||||
\(11\) | −41.2642 | − | 71.4718i | −0.102823 | − | 0.178095i | 0.810023 | − | 0.586398i | \(-0.199454\pi\) |
−0.912847 | + | 0.408302i | \(0.866121\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −70.1922 | + | 121.577i | −0.115194 | + | 0.199522i | −0.917857 | − | 0.396910i | \(-0.870082\pi\) |
0.802663 | + | 0.596433i | \(0.203416\pi\) | |||||||
\(14\) | −217.106 | − | 1001.16i | −0.296041 | − | 1.36515i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 332.398 | + | 968.549i | 0.324607 | + | 0.945849i | ||||
\(17\) | − | 901.814i | − | 0.756824i | −0.925637 | − | 0.378412i | \(-0.876470\pi\) | ||
0.925637 | − | 0.378412i | \(-0.123530\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2363.52i | − | 1.50202i | −0.660290 | − | 0.751011i | \(-0.729567\pi\) | ||
0.660290 | − | 0.751011i | \(-0.270433\pi\) | |||||||
\(20\) | −308.346 | − | 677.515i | −0.172371 | − | 0.378742i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 456.247 | − | 98.9396i | 0.200976 | − | 0.0435826i | ||||
\(23\) | −160.190 | + | 277.458i | −0.0631417 | + | 0.109365i | −0.895868 | − | 0.444320i | \(-0.853445\pi\) |
0.832726 | + | 0.553685i | \(0.186779\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1291.94 | − | 2237.71i | −0.413421 | − | 0.716067i | ||||
\(26\) | −533.800 | − | 587.968i | −0.154862 | − | 0.170577i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5768.06 | + | 558.359i | 1.39038 | + | 0.134592i | ||||
\(29\) | 7037.98 | − | 4063.38i | 1.55401 | − | 0.897207i | 0.556198 | − | 0.831050i | \(-0.312260\pi\) |
0.997809 | − | 0.0661569i | \(-0.0210738\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1533.72 | + | 885.495i | 0.286644 | + | 0.165494i | 0.636427 | − | 0.771337i | \(-0.280412\pi\) |
−0.349784 | + | 0.936831i | \(0.613745\pi\) | |||||||
\(32\) | −5791.40 | + | 119.010i | −0.999789 | + | 0.0205452i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4858.19 | + | 1556.48i | 0.720737 | + | 0.230912i | ||||
\(35\) | −4212.61 | −0.581274 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13713.9 | 1.64686 | 0.823429 | − | 0.567419i | \(-0.192058\pi\) | ||||
0.823429 | + | 0.567419i | \(0.192058\pi\) | |||||||
\(38\) | 12732.6 | + | 4079.30i | 1.43040 | + | 0.458276i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4182.05 | − | 491.747i | 0.413275 | − | 0.0485950i | ||||
\(41\) | 4374.37 | + | 2525.55i | 0.406402 | + | 0.234637i | 0.689243 | − | 0.724530i | \(-0.257943\pi\) |
−0.282840 | + | 0.959167i | \(0.591277\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17261.6 | + | 9966.01i | −1.42367 | + | 0.821959i | −0.996611 | − | 0.0822625i | \(-0.973785\pi\) |
−0.427064 | + | 0.904221i | \(0.640452\pi\) | |||||||
\(44\) | −254.456 | + | 2628.62i | −0.0198144 | + | 0.204690i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1218.22 | − | 1341.84i | −0.0848851 | − | 0.0934989i | ||||
\(47\) | −6620.98 | − | 11467.9i | −0.437197 | − | 0.757248i | 0.560275 | − | 0.828307i | \(-0.310696\pi\) |
−0.997472 | + | 0.0710587i | \(0.977362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7994.11 | − | 13846.2i | 0.475642 | − | 0.823836i | ||||
\(50\) | 14284.6 | − | 3097.70i | 0.808061 | − | 0.175232i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4088.77 | − | 1860.85i | 0.209693 | − | 0.0954340i | ||||
\(53\) | − | 25022.9i | − | 1.22362i | −0.791003 | − | 0.611812i | \(-0.790441\pi\) | ||
0.791003 | − | 0.611812i | \(-0.209559\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1919.77i | − | 0.0855742i | ||||||
\(56\) | −12963.3 | + | 30109.6i | −0.552389 | + | 1.28302i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9742.80 | + | 44927.6i | 0.380289 | + | 1.75365i | ||||
\(59\) | 20189.4 | − | 34969.0i | 0.755079 | − | 1.30784i | −0.190256 | − | 0.981735i | \(-0.560932\pi\) |
0.945335 | − | 0.326101i | \(-0.105735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8934.10 | − | 15474.3i | −0.307416 | − | 0.532460i | 0.670381 | − | 0.742017i | \(-0.266131\pi\) |
−0.977796 | + | 0.209558i | \(0.932798\pi\) | |||||||
\(62\) | −7417.39 | + | 6734.04i | −0.245060 | + | 0.222483i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9354.49 | − | 31404.4i | 0.285476 | − | 0.958386i | ||||
\(65\) | −2828.10 | + | 1632.81i | −0.0830256 | + | 0.0479348i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −29089.1 | − | 16794.6i | −0.791668 | − | 0.457070i | 0.0488814 | − | 0.998805i | \(-0.484434\pi\) |
−0.840549 | + | 0.541735i | \(0.817768\pi\) | |||||||
\(68\) | −16769.9 | + | 23485.3i | −0.439803 | + | 0.615919i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7270.71 | − | 22693.8i | 0.177350 | − | 0.553558i | ||||
\(71\) | −55855.2 | −1.31498 | −0.657488 | − | 0.753465i | \(-0.728381\pi\) | ||||
−0.657488 | + | 0.753465i | \(0.728381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −69860.7 | −1.53435 | −0.767177 | − | 0.641435i | \(-0.778339\pi\) | ||||
−0.767177 | + | 0.641435i | \(0.778339\pi\) | |||||||
\(74\) | −23669.4 | + | 73878.5i | −0.502467 | + | 1.56833i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −43951.5 | + | 61551.5i | −0.872849 | + | 1.22238i | ||||
\(77\) | 12943.1 | + | 7472.73i | 0.248779 | + | 0.143632i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −33076.3 | + | 19096.6i | −0.596278 | + | 0.344261i | −0.767576 | − | 0.640958i | \(-0.778537\pi\) |
0.171298 | + | 0.985219i | \(0.445204\pi\) | |||||||
\(80\) | −4568.86 | + | 23377.9i | −0.0798148 | + | 0.408396i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −21155.4 | + | 19206.4i | −0.347445 | + | 0.315435i | ||||
\(83\) | 11121.7 | + | 19263.4i | 0.177205 | + | 0.306929i | 0.940922 | − | 0.338623i | \(-0.109961\pi\) |
−0.763717 | + | 0.645551i | \(0.776628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10489.0 | − | 18167.4i | 0.157465 | − | 0.272738i | ||||
\(86\) | −23895.6 | − | 110191.i | −0.348395 | − | 1.60658i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13721.6 | − | 5907.63i | −0.188885 | − | 0.0813218i | ||||
\(89\) | 98921.0i | 1.32377i | 0.749604 | + | 0.661886i | \(0.230244\pi\) | ||||
−0.749604 | + | 0.661886i | \(0.769756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 25422.9i | − | 0.321826i | ||||||
\(92\) | 9331.24 | − | 4246.77i | 0.114940 | − | 0.0523105i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 73206.3 | − | 15875.2i | 0.854533 | − | 0.185310i | ||||
\(95\) | 27490.1 | − | 47614.2i | 0.312512 | − | 0.541287i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −20762.4 | − | 35961.6i | −0.224052 | − | 0.388069i | 0.731983 | − | 0.681323i | \(-0.238595\pi\) |
−0.956035 | + | 0.293254i | \(0.905262\pi\) | |||||||
\(98\) | 60793.9 | + | 66963.0i | 0.639433 | + | 0.704320i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7966.74 | + | 82299.6i | −0.0796674 | + | 0.822996i | ||||
\(101\) | 100768. | − | 58178.3i | 0.982920 | − | 0.567489i | 0.0797694 | − | 0.996813i | \(-0.474582\pi\) |
0.903150 | + | 0.429324i | \(0.141248\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 34298.4 | + | 19802.2i | 0.318552 | + | 0.183916i | 0.650747 | − | 0.759295i | \(-0.274456\pi\) |
−0.332195 | + | 0.943211i | \(0.607789\pi\) | |||||||
\(104\) | 2967.67 | + | 25238.4i | 0.0269049 | + | 0.228812i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 134802. | + | 43188.1i | 1.16528 | + | 0.373335i | ||||
\(107\) | −82118.9 | −0.693400 | −0.346700 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346700 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −48617.2 | −0.391944 | −0.195972 | − | 0.980610i | \(-0.562786\pi\) | ||||
−0.195972 | + | 0.980610i | \(0.562786\pi\) | |||||||
\(110\) | 10342.0 | + | 3313.41i | 0.0814938 | + | 0.0261092i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −139830. | − | 121802.i | −1.05331 | − | 0.917509i | ||||
\(113\) | −14619.7 | − | 8440.70i | −0.107707 | − | 0.0621845i | 0.445179 | − | 0.895442i | \(-0.353140\pi\) |
−0.552886 | + | 0.833257i | \(0.686473\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6454.20 | + | 3726.33i | −0.0455090 | + | 0.0262747i | ||||
\(116\) | −258846. | − | 25056.8i | −1.78606 | − | 0.172894i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 153537. | + | 169117.i | 1.01510 | + | 1.11810i | ||||
\(119\) | 81656.8 | + | 141434.i | 0.528597 | + | 0.915557i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 77120.0 | − | 133576.i | 0.478855 | − | 0.829401i | ||||
\(122\) | 98781.8 | − | 21421.4i | 0.600865 | − | 0.130301i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −23475.2 | − | 51580.9i | −0.137105 | − | 0.301256i | ||||
\(125\) | − | 132800.i | − | 0.760189i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 45880.3i | − | 0.252416i | −0.992004 | − | 0.126208i | \(-0.959719\pi\) | ||
0.992004 | − | 0.126208i | \(-0.0402807\pi\) | |||||||
\(128\) | 153034. | + | 104596.i | 0.825588 | + | 0.564274i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3914.99 | − | 18053.5i | −0.0203176 | − | 0.0936920i | ||||
\(131\) | 11973.3 | − | 20738.4i | 0.0609588 | − | 0.105584i | −0.833935 | − | 0.551862i | \(-0.813918\pi\) |
0.894894 | + | 0.446278i | \(0.147251\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 214011. | + | 370677.i | 1.04907 | + | 1.81705i | ||||
\(134\) | 140681. | − | 127720.i | 0.676819 | − | 0.614465i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −97574.3 | − | 130876.i | −0.452364 | − | 0.606753i | ||||
\(137\) | −179077. | + | 103390.i | −0.815152 | + | 0.470628i | −0.848742 | − | 0.528807i | \(-0.822639\pi\) |
0.0335896 | + | 0.999436i | \(0.489306\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 150292. | + | 86771.1i | 0.659780 | + | 0.380924i | 0.792193 | − | 0.610271i | \(-0.208939\pi\) |
−0.132413 | + | 0.991195i | \(0.542273\pi\) | |||||||
\(140\) | 109706. | + | 78336.5i | 0.473052 | + | 0.337788i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 96402.9 | − | 300899.i | 0.401207 | − | 1.25228i | ||||
\(143\) | 11585.7 | 0.0473787 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 189044. | 0.746695 | ||||||||
\(146\) | 120575. | − | 376348.i | 0.468141 | − | 1.46119i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −357141. | − | 255020.i | −1.34025 | − | 0.957017i | ||||
\(149\) | −195995. | − | 113158.i | −0.723234 | − | 0.417559i | 0.0927081 | − | 0.995693i | \(-0.470448\pi\) |
−0.815942 | + | 0.578134i | \(0.803781\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 48433.2 | − | 27962.9i | 0.172862 | − | 0.0998021i | −0.411072 | − | 0.911603i | \(-0.634846\pi\) |
0.583935 | + | 0.811801i | \(0.301512\pi\) | |||||||
\(152\) | −255728. | − | 343006.i | −0.897779 | − | 1.20418i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −62595.6 | + | 56828.9i | −0.212688 | + | 0.193093i | ||||
\(155\) | 20598.3 | + | 35677.3i | 0.0688656 | + | 0.119279i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −67323.6 | + | 116608.i | −0.217981 | + | 0.377554i | −0.954191 | − | 0.299200i | \(-0.903280\pi\) |
0.736210 | + | 0.676754i | \(0.236614\pi\) | |||||||
\(158\) | −45788.1 | − | 211146.i | −0.145918 | − | 0.672883i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −118054. | − | 64962.0i | −0.364571 | − | 0.200613i | ||||
\(161\) | − | 58019.2i | − | 0.176403i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 93835.4i | − | 0.276629i | −0.990388 | − | 0.138314i | \(-0.955832\pi\) | ||
0.990388 | − | 0.138314i | \(-0.0441685\pi\) | |||||||
\(164\) | −66954.2 | − | 147116.i | −0.194387 | − | 0.427119i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −122970. | + | 26666.6i | −0.346360 | + | 0.0751100i | ||||
\(167\) | 67439.6 | − | 116809.i | 0.187121 | − | 0.324104i | −0.757168 | − | 0.653220i | \(-0.773418\pi\) |
0.944289 | + | 0.329116i | \(0.106751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 175793. | + | 304482.i | 0.473461 | + | 0.820058i | ||||
\(170\) | 79766.8 | + | 87861.3i | 0.211690 | + | 0.233171i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 634857. | + | 61455.3i | 1.63627 | + | 0.158394i | ||||
\(173\) | −179808. | + | 103812.i | −0.456767 | + | 0.263715i | −0.710684 | − | 0.703511i | \(-0.751614\pi\) |
0.253917 | + | 0.967226i | \(0.418281\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 405237. | + | 233964.i | 1.00026 | + | 0.577501i | ||||
\(176\) | 55507.8 | − | 63723.5i | 0.135074 | − | 0.155067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −532900. | − | 170732.i | −1.26065 | − | 0.403891i | ||||
\(179\) | 525249. | 1.22527 | 0.612636 | − | 0.790365i | \(-0.290109\pi\) | ||||
0.612636 | + | 0.790365i | \(0.290109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −825837. | −1.87369 | −0.936846 | − | 0.349743i | \(-0.886269\pi\) | ||||
−0.936846 | + | 0.349743i | \(0.886269\pi\) | |||||||
\(182\) | 136956. | + | 43878.4i | 0.306481 | + | 0.0981910i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6772.70 | + | 57598.3i | 0.0147475 | + | 0.125419i | ||||
\(185\) | 276272. | + | 159506.i | 0.593482 | + | 0.342647i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −64454.3 | + | 37212.7i | −0.134787 | + | 0.0778192i | ||||
\(188\) | −40828.2 | + | 421771.i | −0.0842492 | + | 0.870327i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 209057. | + | 230272.i | 0.420128 | + | 0.462761i | ||||
\(191\) | 187497. | + | 324754.i | 0.371886 | + | 0.644126i | 0.989856 | − | 0.142076i | \(-0.0453778\pi\) |
−0.617970 | + | 0.786202i | \(0.712045\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 238572. | − | 413219.i | 0.461027 | − | 0.798522i | −0.537985 | − | 0.842954i | \(-0.680814\pi\) |
0.999012 | + | 0.0444321i | \(0.0141478\pi\) | |||||||
\(194\) | 229564. | − | 49782.2i | 0.437925 | − | 0.0949664i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −465665. | + | 211930.i | −0.865832 | + | 0.394051i | ||||
\(197\) | 443928.i | 0.814979i | 0.913210 | + | 0.407490i | \(0.133596\pi\) | ||||
−0.913210 | + | 0.407490i | \(0.866404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 601252.i | − | 1.07628i | −0.842857 | − | 0.538138i | \(-0.819128\pi\) | ||
0.842857 | − | 0.538138i | \(-0.180872\pi\) | |||||||
\(200\) | −429608. | − | 184962.i | −0.759447 | − | 0.326970i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 139495. | + | 643261.i | 0.240535 | + | 1.10920i | ||||
\(203\) | −735856. | + | 1.27454e6i | −1.25329 | + | 2.17077i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 58749.1 | + | 101756.i | 0.0976374 | + | 0.169113i | ||||
\(206\) | −165874. | + | 150592.i | −0.272339 | + | 0.247249i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −141085. | − | 27572.9i | −0.226111 | − | 0.0441899i | ||||
\(209\) | −168925. | + | 97529.1i | −0.267503 | + | 0.154443i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 345252. | + | 199331.i | 0.533863 | + | 0.308226i | 0.742588 | − | 0.669748i | \(-0.233598\pi\) |
−0.208725 | + | 0.977974i | \(0.566931\pi\) | |||||||
\(212\) | −465319. | + | 651653.i | −0.711068 | + | 0.995811i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 141732. | − | 442385.i | 0.211560 | − | 0.660337i | ||||
\(215\) | −463657. | −0.684070 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −320716. | −0.462351 | ||||||||
\(218\) | 83910.4 | − | 261907.i | 0.119584 | − | 0.373255i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −35699.5 | + | 49995.2i | −0.0497286 | + | 0.0696420i | ||||
\(221\) | 109639. | + | 63300.4i | 0.151003 | + | 0.0871817i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −290097. | + | 167488.i | −0.390644 | + | 0.225538i | −0.682439 | − | 0.730942i | \(-0.739081\pi\) |
0.291795 | + | 0.956481i | \(0.405747\pi\) | |||||||
\(224\) | 897503. | − | 543060.i | 1.19513 | − | 0.723149i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 70703.9 | − | 64190.1i | 0.0920815 | − | 0.0835982i | ||||
\(227\) | −425099. | − | 736293.i | −0.547552 | − | 0.948388i | −0.998442 | − | 0.0558079i | \(-0.982227\pi\) |
0.450890 | − | 0.892580i | \(-0.351107\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −204162. | + | 353618.i | −0.257268 | + | 0.445601i | −0.965509 | − | 0.260370i | \(-0.916156\pi\) |
0.708241 | + | 0.705971i | \(0.249489\pi\) | |||||||
\(230\) | −8934.66 | − | 41201.0i | −0.0111367 | − | 0.0513557i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 581738. | − | 1.35119e6i | 0.709590 | − | 1.64815i | ||||
\(233\) | 677571.i | 0.817645i | 0.912614 | + | 0.408823i | \(0.134061\pi\) | ||||
−0.912614 | + | 0.408823i | \(0.865939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 308033.i | − | 0.363855i | ||||||
\(236\) | −1.17605e6 | + | 535236.i | −1.37450 | + | 0.625554i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −902856. | + | 195789.i | −1.03318 | + | 0.224051i | ||||
\(239\) | 660239. | − | 1.14357e6i | 0.747664 | − | 1.29499i | −0.201275 | − | 0.979535i | \(-0.564509\pi\) |
0.948940 | − | 0.315458i | \(-0.102158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −418674. | − | 725165.i | −0.464337 | − | 0.804256i | 0.534834 | − | 0.844957i | \(-0.320374\pi\) |
−0.999171 | + | 0.0407014i | \(0.987041\pi\) | |||||||
\(242\) | 586485. | + | 645999.i | 0.643752 | + | 0.709077i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −55092.0 | + | 569122.i | −0.0592399 | + | 0.611971i | ||||
\(245\) | 322089. | − | 185958.i | 0.342816 | − | 0.197925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 287349. | + | 165901.i | 0.299687 | + | 0.173024i | ||||
\(248\) | 318390. | − | 37437.9i | 0.328723 | − | 0.0386529i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 715408. | + | 229204.i | 0.723942 | + | 0.231938i | ||||
\(251\) | 1.41641e6 | 1.41907 | 0.709534 | − | 0.704671i | \(-0.248905\pi\) | ||||
0.709534 | + | 0.704671i | \(0.248905\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26440.5 | 0.0259698 | ||||||||
\(254\) | 247163. | + | 79186.7i | 0.240380 | + | 0.0770137i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −827599. | + | 643888.i | −0.789260 | + | 0.614059i | ||||
\(257\) | −887077. | − | 512154.i | −0.837777 | − | 0.483691i | 0.0187311 | − | 0.999825i | \(-0.494037\pi\) |
−0.856508 | + | 0.516134i | \(0.827371\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.15078e6 | + | 1.24176e6i | −1.99227 | + | 1.15023i | ||||
\(260\) | 104013. | + | 10068.7i | 0.0954236 | + | 0.00923718i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 91055.1 | + | 100295.i | 0.0819504 | + | 0.0902664i | ||||
\(263\) | −841677. | − | 1.45783e6i | −0.750337 | − | 1.29962i | −0.947660 | − | 0.319283i | \(-0.896558\pi\) |
0.197323 | − | 0.980339i | \(-0.436775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 291040. | − | 504097.i | 0.254588 | − | 0.440960i | ||||
\(266\) | −2.36626e6 | + | 513135.i | −2.05049 | + | 0.444660i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 445238. | + | 978302.i | 0.378665 | + | 0.832024i | ||||
\(269\) | − | 2.11837e6i | − | 1.78493i | −0.451117 | − | 0.892465i | \(-0.648974\pi\) | ||
0.451117 | − | 0.892465i | \(-0.351026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 596748.i | − | 0.493592i | −0.969067 | − | 0.246796i | \(-0.920622\pi\) | ||
0.969067 | − | 0.246796i | \(-0.0793778\pi\) | |||||||
\(272\) | 873451. | − | 299761.i | 0.715841 | − | 0.245671i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −247900. | − | 1.14316e6i | −0.199480 | − | 0.919876i | ||||
\(275\) | −106622. | + | 184675.i | −0.0850188 | + | 0.147257i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 532237. | + | 921861.i | 0.416779 | + | 0.721882i | 0.995613 | − | 0.0935631i | \(-0.0298257\pi\) |
−0.578835 | + | 0.815445i | \(0.696492\pi\) | |||||||
\(278\) | −726842. | + | 659880.i | −0.564064 | + | 0.512098i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −611354. | + | 455795.i | −0.466013 | + | 0.347435i | ||||
\(281\) | 890207. | − | 513961.i | 0.672551 | − | 0.388298i | −0.124492 | − | 0.992221i | \(-0.539730\pi\) |
0.797043 | + | 0.603923i | \(0.206397\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −958119. | − | 553170.i | −0.711137 | − | 0.410575i | 0.100345 | − | 0.994953i | \(-0.468005\pi\) |
−0.811482 | + | 0.584377i | \(0.801339\pi\) | |||||||
\(284\) | 1.45460e6 | + | 1.03867e6i | 1.07015 | + | 0.764154i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19996.3 | + | 62413.7i | −0.0144555 | + | 0.0451196i | ||||
\(287\) | −914725. | −0.655520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 606588. | 0.427218 | ||||||||
\(290\) | −326279. | + | 1.01840e6i | −0.227821 | + | 0.711091i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.81933e6 | + | 1.29911e6i | 1.24869 | + | 0.891639i | ||||
\(293\) | 989169. | + | 571097.i | 0.673134 | + | 0.388634i | 0.797263 | − | 0.603632i | \(-0.206280\pi\) |
−0.124129 | + | 0.992266i | \(0.539614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 813446. | − | 469643.i | 0.544219 | − | 0.314205i | ||||
\(296\) | 1.99023e6 | − | 1.48381e6i | 1.32030 | − | 0.984350i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 947869. | − | 860545.i | 0.618312 | − | 0.561349i | ||||
\(299\) | −22488.2 | − | 38950.7i | −0.0145471 | − | 0.0251964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.80479e6 | − | 3.12599e6i | 1.14818 | − | 1.98871i | ||||
\(302\) | 67046.9 | + | 309178.i | 0.0423020 | + | 0.195070i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.28919e6 | − | 785631.i | 1.42069 | − | 0.487567i | ||||
\(305\) | − | 415648.i | − | 0.255845i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.32248e6i | 0.800836i | 0.916333 | + | 0.400418i | \(0.131135\pi\) | ||||
−0.916333 | + | 0.400418i | \(0.868865\pi\) | |||||||
\(308\) | −198108. | − | 435294.i | −0.118994 | − | 0.261460i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −227750. | + | 49388.7i | −0.134603 | + | 0.0291893i | ||||
\(311\) | −139474. | + | 241576.i | −0.0817698 | + | 0.141629i | −0.904010 | − | 0.427511i | \(-0.859391\pi\) |
0.822240 | + | 0.569140i | \(0.192724\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 68921.8 | + | 119376.i | 0.0397645 | + | 0.0688742i | 0.885223 | − | 0.465167i | \(-0.154006\pi\) |
−0.845458 | + | 0.534042i | \(0.820673\pi\) | |||||||
\(314\) | −511985. | − | 563939.i | −0.293044 | − | 0.322781i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.21650e6 | + | 117759.i | 0.685319 | + | 0.0663401i | ||||
\(317\) | 1.13038e6 | − | 652623.i | 0.631793 | − | 0.364766i | −0.149653 | − | 0.988739i | \(-0.547816\pi\) |
0.781446 | + | 0.623973i | \(0.214482\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −580834. | − | 335345.i | −0.319577 | − | 0.184508i | ||||
\(320\) | 553713. | − | 523853.i | 0.302280 | − | 0.285979i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 312557. | + | 100138.i | 0.167992 | + | 0.0538217i | ||||
\(323\) | −2.13146e6 | −1.13677 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 362737. | 0.190495 | ||||||||
\(326\) | 505503. | + | 161954.i | 0.263439 | + | 0.0844012i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 908089. | − | 106778.i | 0.466062 | − | 0.0548020i | ||||
\(329\) | 2.07677e6 | + | 1.19902e6i | 1.05779 | + | 0.610714i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 552755. | − | 319133.i | 0.277308 | − | 0.160104i | −0.354896 | − | 0.934906i | \(-0.615484\pi\) |
0.632204 | + | 0.774802i | \(0.282150\pi\) | |||||||
\(332\) | 68582.0 | − | 708478.i | 0.0341479 | − | 0.352762i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 512867. | + | 564910.i | 0.251558 | + | 0.277085i | ||||
\(335\) | −390674. | − | 676668.i | −0.190197 | − | 0.329430i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −491457. | + | 851229.i | −0.235728 | + | 0.408293i | −0.959484 | − | 0.281763i | \(-0.909081\pi\) |
0.723756 | + | 0.690056i | \(0.242414\pi\) | |||||||
\(338\) | −1.94369e6 | + | 421499.i | −0.925412 | + | 0.200680i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −610993. | + | 278071.i | −0.286641 | + | 0.130454i | ||||
\(341\) | − | 146157.i | − | 0.0680666i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 148276.i | − | 0.0680511i | ||||||
\(344\) | −1.42679e6 | + | 3.31399e6i | −0.650077 | + | 1.50992i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −248912. | − | 1.14783e6i | −0.111778 | − | 0.515449i | ||||
\(347\) | −675607. | + | 1.17018e6i | −0.301211 | + | 0.521712i | −0.976410 | − | 0.215923i | \(-0.930724\pi\) |
0.675200 | + | 0.737635i | \(0.264057\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −376947. | − | 652891.i | −0.165660 | − | 0.286931i | 0.771230 | − | 0.636557i | \(-0.219642\pi\) |
−0.936889 | + | 0.349626i | \(0.886309\pi\) | |||||||
\(350\) | −1.95981e6 | + | 1.77925e6i | −0.855151 | + | 0.776368i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 247483. | + | 409010.i | 0.106461 | + | 0.175945i | ||||
\(353\) | −389941. | + | 225133.i | −0.166557 | + | 0.0961616i | −0.580961 | − | 0.813931i | \(-0.697323\pi\) |
0.414404 | + | 0.910093i | \(0.363990\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.12523e6 | − | 649650.i | −0.473881 | − | 0.273595i | ||||
\(356\) | 1.83951e6 | − | 2.57612e6i | 0.769266 | − | 1.07731i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −906549. | + | 2.82958e6i | −0.373838 | + | 1.16685i | ||||
\(359\) | 3.02244e6 | 1.23772 | 0.618860 | − | 0.785502i | \(-0.287595\pi\) | ||||
0.618860 | + | 0.785502i | \(0.287595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.11015e6 | −1.25607 | ||||||||
\(362\) | 1.42535e6 | − | 4.44889e6i | 0.571675 | − | 1.78435i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −472756. | + | 662068.i | −0.187018 | + | 0.261908i | ||||
\(365\) | −1.40737e6 | − | 812547.i | −0.552939 | − | 0.319239i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.33704e6 | − | 1.34929e6i | 0.905735 | − | 0.522927i | 0.0266788 | − | 0.999644i | \(-0.491507\pi\) |
0.879057 | + | 0.476718i | \(0.158174\pi\) | |||||||
\(368\) | −321978. | − | 62925.8i | −0.123939 | − | 0.0242220i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.33611e6 | + | 1.21301e6i | −0.507384 | + | 0.460640i | ||||
\(371\) | 2.26576e6 | + | 3.92440e6i | 0.854630 | + | 1.48026i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −922996. | + | 1.59868e6i | −0.343501 | + | 0.594961i | −0.985080 | − | 0.172096i | \(-0.944946\pi\) |
0.641579 | + | 0.767057i | \(0.278279\pi\) | |||||||
\(374\) | −89225.1 | − | 411450.i | −0.0329844 | − | 0.152103i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.20167e6 | − | 947899.i | −0.803123 | − | 0.345774i | ||||
\(377\) | 1.14087e6i | 0.413412i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.35806e6i | 0.485649i | 0.970070 | + | 0.242824i | \(0.0780739\pi\) | ||||
−0.970070 | + | 0.242824i | \(0.921926\pi\) | |||||||
\(380\) | −1.60132e6 | + | 728783.i | −0.568879 | + | 0.258904i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.07310e6 | + | 449562.i | −0.726877 | + | 0.157627i | ||||
\(383\) | 1.84507e6 | − | 3.19575e6i | 0.642710 | − | 1.11321i | −0.342115 | − | 0.939658i | \(-0.611143\pi\) |
0.984825 | − | 0.173548i | \(-0.0555233\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 173830. | + | 301082.i | 0.0597686 | + | 0.103522i | ||||
\(386\) | 1.81430e6 | + | 1.99841e6i | 0.619785 | + | 0.682678i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −128031. | + | 1.32261e6i | −0.0431754 | + | 0.446019i | ||||
\(389\) | −2.87005e6 | + | 1.65702e6i | −0.961645 | + | 0.555206i | −0.896679 | − | 0.442681i | \(-0.854027\pi\) |
−0.0649663 | + | 0.997887i | \(0.520694\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 250215. | + | 144462.i | 0.0827698 | + | 0.0477872i | ||||
\(392\) | −337984. | − | 2.87438e6i | −0.111092 | − | 0.944775i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.39149e6 | − | 766193.i | −0.776120 | − | 0.248655i | ||||
\(395\) | −888447. | −0.286509 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −119467. | −0.0380427 | −0.0190214 | − | 0.999819i | \(-0.506055\pi\) | ||||
−0.0190214 | + | 0.999819i | \(0.506055\pi\) | |||||||
\(398\) | 3.23902e6 | + | 1.03773e6i | 1.02496 | + | 0.328379i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.73789e6 | − | 1.99512e6i | 0.543091 | − | 0.623475i | ||||
\(401\) | −4.09522e6 | − | 2.36438e6i | −1.27179 | − | 0.734271i | −0.296469 | − | 0.955043i | \(-0.595809\pi\) |
−0.975325 | + | 0.220772i | \(0.929142\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −215311. | + | 124310.i | −0.0660394 | + | 0.0381279i | ||||
\(404\) | −3.70609e6 | − | 358756.i | −1.12970 | − | 0.109357i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.59606e6 | − | 6.16393e6i | −1.68487 | − | 1.85585i | ||||
\(407\) | −565893. | − | 980156.i | −0.169336 | − | 0.293298i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.11750e6 | + | 5.39967e6i | −0.921507 | + | 1.59610i | −0.124422 | + | 0.992229i | \(0.539708\pi\) |
−0.797085 | + | 0.603867i | \(0.793626\pi\) | |||||||
\(410\) | −649572. | + | 140863.i | −0.190839 | + | 0.0413845i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −524971. | − | 1.15350e6i | −0.152367 | − | 0.334790i | ||||
\(413\) | 7.31236e6i | 2.10952i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 517425.i | 0.147478i | ||||||||
\(416\) | 392042. | − | 712451.i | 0.111071 | − | 0.201847i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −233846. | − | 1.07835e6i | −0.0654621 | − | 0.301870i | ||||
\(419\) | −347632. | + | 602117.i | −0.0967353 | + | 0.167551i | −0.910332 | − | 0.413880i | \(-0.864173\pi\) |
0.813596 | + | 0.581430i | \(0.197507\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −585766. | − | 1.01458e6i | −0.161071 | − | 0.278984i | 0.774182 | − | 0.632963i | \(-0.218162\pi\) |
−0.935253 | + | 0.353979i | \(0.884828\pi\) | |||||||
\(422\) | −1.66971e6 | + | 1.51588e6i | −0.456414 | + | 0.414366i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.70742e6 | − | 3.63145e6i | −0.731377 | − | 0.980991i | ||||
\(425\) | −2.01800e6 | + | 1.16509e6i | −0.541936 | + | 0.312887i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.80231e6 | + | 1.61792e6i | 0.743784 | + | 0.429424i | ||||
\(428\) | 2.13856e6 | + | 1.52706e6i | 0.564303 | + | 0.402946i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 800245. | − | 2.49778e6i | 0.208714 | − | 0.651453i | ||||
\(431\) | −2.98148e6 | −0.773104 | −0.386552 | − | 0.922268i | \(-0.626334\pi\) | ||||
−0.386552 | + | 0.922268i | \(0.626334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.90562e6 | 1.51372 | 0.756861 | − | 0.653576i | \(-0.226732\pi\) | ||||
0.756861 | + | 0.653576i | \(0.226732\pi\) | |||||||
\(434\) | 553538. | − | 1.72774e6i | 0.141066 | − | 0.440305i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.26610e6 | + | 904072.i | 0.318972 | + | 0.227765i | ||||
\(437\) | 655778. | + | 378614.i | 0.164268 | + | 0.0948403i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.85286e6 | − | 1.64710e6i | 0.706512 | − | 0.407905i | −0.103256 | − | 0.994655i | \(-0.532926\pi\) |
0.809768 | + | 0.586750i | \(0.199593\pi\) | |||||||
\(440\) | −207715. | − | 278607.i | −0.0511489 | − | 0.0686056i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −530238. | + | 481389.i | −0.129097 | + | 0.117203i | ||||
\(443\) | 3.05039e6 | + | 5.28344e6i | 0.738493 | + | 1.27911i | 0.953174 | + | 0.302423i | \(0.0977956\pi\) |
−0.214681 | + | 0.976684i | \(0.568871\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.15055e6 | + | 1.99280e6i | −0.275425 | + | 0.477051i | ||||
\(446\) | −401586. | − | 1.85186e6i | −0.0955965 | − | 0.440831i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.37649e6 | + | 5.77225e6i | 0.324026 | + | 1.35878i | ||||
\(449\) | − | 5.38289e6i | − | 1.26008i | −0.776561 | − | 0.630042i | \(-0.783038\pi\) | ||
0.776561 | − | 0.630042i | \(-0.216962\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 416859.i | − | 0.0965046i | ||||||
\(452\) | 223770. | + | 491679.i | 0.0515175 | + | 0.113197i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.70020e6 | − | 1.01926e6i | 1.07023 | − | 0.232085i | ||||
\(455\) | 295692. | − | 512154.i | 0.0669594 | − | 0.115977i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −231952. | − | 401752.i | −0.0519526 | − | 0.0899846i | 0.838880 | − | 0.544317i | \(-0.183211\pi\) |
−0.890832 | + | 0.454332i | \(0.849878\pi\) | |||||||
\(458\) | −1.55262e6 | − | 1.71017e6i | −0.345860 | − | 0.380956i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 237376. | + | 22978.4i | 0.0523048 | + | 0.00506320i | ||||
\(461\) | −3.61068e6 | + | 2.08463e6i | −0.791291 | + | 0.456852i | −0.840417 | − | 0.541940i | \(-0.817690\pi\) |
0.0491256 | + | 0.998793i | \(0.484357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.46488e6 | + | 3.15515e6i | 1.18475 | + | 0.684018i | 0.957110 | − | 0.289726i | \(-0.0935643\pi\) |
0.227644 | + | 0.973744i | \(0.426898\pi\) | |||||||
\(464\) | 6.27499e6 | + | 5.46597e6i | 1.35306 | + | 1.17862i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.65016e6 | − | 1.16945e6i | −0.778658 | − | 0.249469i | ||||
\(467\) | 763795. | 0.162063 | 0.0810316 | − | 0.996712i | \(-0.474179\pi\) | ||||
0.0810316 | + | 0.996712i | \(0.474179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.08282e6 | 1.27695 | ||||||||
\(470\) | 1.65941e6 | + | 531648.i | 0.346506 | + | 0.111014i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −853588. | − | 7.25932e6i | −0.176357 | − | 1.49983i | ||||
\(473\) | 1.42458e6 | + | 822480.i | 0.292774 | + | 0.169033i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.28888e6 | + | 3.05354e6i | −1.07555 | + | 0.620968i | ||||
\(476\) | 503536. | − | 5.20172e6i | 0.101862 | − | 1.05228i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.02101e6 | + | 5.53052e6i | 1.00513 | + | 1.10712i | ||||
\(479\) | 1.97328e6 | + | 3.41782e6i | 0.392962 | + | 0.680629i | 0.992839 | − | 0.119463i | \(-0.0381172\pi\) |
−0.599877 | + | 0.800092i | \(0.704784\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −962608. | + | 1.66729e6i | −0.189709 | + | 0.328585i | ||||
\(482\) | 4.62916e6 | − | 1.00386e6i | 0.907580 | − | 0.196813i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.49232e6 | + | 2.04451e6i | −0.871680 | + | 0.396713i | ||||
\(485\) | − | 965947.i | − | 0.186466i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.97847e6i | − | 0.378012i | −0.981976 | − | 0.189006i | \(-0.939473\pi\) | ||
0.981976 | − | 0.189006i | \(-0.0605266\pi\) | |||||||
\(488\) | −2.97085e6 | − | 1.27906e6i | −0.564717 | − | 0.243131i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 445874. | + | 2.05609e6i | 0.0838923 | + | 0.386858i | ||||
\(491\) | 547411. | − | 948143.i | 0.102473 | − | 0.177488i | −0.810230 | − | 0.586112i | \(-0.800658\pi\) |
0.912703 | + | 0.408624i | \(0.133991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.66441e6 | − | 6.34695e6i | −0.679027 | − | 1.17611i | ||||
\(494\) | −1.38968e6 | + | 1.26165e6i | −0.256210 | + | 0.232606i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −347839. | + | 1.77982e6i | −0.0634855 | + | 0.324842i | ||||
\(497\) | 8.75991e6 | − | 5.05754e6i | 1.59078 | − | 0.918435i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.07104e6 | − | 5.23717e6i | −1.63082 | − | 0.941554i | −0.983841 | − | 0.179045i | \(-0.942699\pi\) |
−0.646978 | − | 0.762508i | \(-0.723968\pi\) | |||||||
\(500\) | −2.46950e6 | + | 3.45840e6i | −0.441758 | + | 0.618657i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.44463e6 | + | 7.63035e6i | −0.432967 | + | 1.35140i | ||||
\(503\) | −639826. | −0.112757 | −0.0563783 | − | 0.998409i | \(-0.517955\pi\) | ||||
−0.0563783 | + | 0.998409i | \(0.517955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.70668e6 | 0.472289 | ||||||||
\(506\) | −45634.8 | + | 142438.i | −0.00792355 | + | 0.0247315i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −853177. | + | 1.19483e6i | −0.146683 | + | 0.205421i | ||||
\(509\) | 2.75241e6 | + | 1.58911e6i | 0.470890 | + | 0.271868i | 0.716612 | − | 0.697472i | \(-0.245692\pi\) |
−0.245722 | + | 0.969340i | \(0.579025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.09564e7 | − | 6.32570e6i | 1.85617 | − | 1.07166i | ||||
\(512\) | −2.04032e6 | − | 5.56969e6i | −0.343971 | − | 0.938980i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.29008e6 | − | 3.89485e6i | 0.716238 | − | 0.650253i | ||||
\(515\) | 460636. | + | 797845.i | 0.0765315 | + | 0.132556i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −546419. | + | 946426.i | −0.0899083 | + | 0.155726i | ||||
\(518\) | −2.97737e6 | − | 1.37297e7i | −0.487537 | − | 2.24821i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −233762. | + | 542955.i | −0.0379111 | + | 0.0880553i | ||||
\(521\) | − | 1.76213e6i | − | 0.284408i | −0.989837 | − | 0.142204i | \(-0.954581\pi\) | ||
0.989837 | − | 0.142204i | \(-0.0454190\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.86393e6i | 1.41701i | 0.705708 | + | 0.708503i | \(0.250629\pi\) | ||||
−0.705708 | + | 0.708503i | \(0.749371\pi\) | |||||||
\(524\) | −697458. | + | 317422.i | −0.110966 | + | 0.0505020i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.30619e6 | − | 2.01810e6i | 1.46659 | − | 0.318037i | ||||
\(527\) | 798552. | − | 1.38313e6i | 0.125250 | − | 0.216939i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.16685e6 | + | 5.48514e6i | 0.492026 | + | 0.852214i | ||||
\(530\) | 2.21331e6 | + | 2.43791e6i | 0.342258 | + | 0.376989i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.31969e6 | − | 1.36330e7i | 0.202160 | − | 2.08839i | ||||
\(533\) | −614094. | + | 354547.i | −0.0936304 | + | 0.0540575i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.65432e6 | − | 955121.i | −0.249882 | − | 0.144269i | ||||
\(536\) | −6.03869e6 | + | 710060.i | −0.907885 | + | 0.106754i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.14119e7 | + | 3.65618e6i | 1.69982 | + | 0.544593i | ||||
\(539\) | −1.31948e6 | −0.195629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.03815e6 | −0.886974 | −0.443487 | − | 0.896281i | \(-0.646259\pi\) | ||||
−0.443487 | + | 0.896281i | \(0.646259\pi\) | |||||||
\(542\) | 3.21476e6 | + | 1.02995e6i | 0.470057 | + | 0.150598i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 107325. | + | 5.22276e6i | 0.0155491 | + | 0.756664i | ||||
\(545\) | −979414. | − | 565465.i | −0.141246 | − | 0.0815482i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 544056. | − | 314111.i | 0.0777455 | − | 0.0448864i | −0.460623 | − | 0.887596i | \(-0.652374\pi\) |
0.538369 | + | 0.842709i | \(0.319041\pi\) | |||||||
\(548\) | 6.58619e6 | + | 637555.i | 0.936878 | + | 0.0906914i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −810842. | − | 893124.i | −0.114296 | − | 0.125894i | ||||
\(551\) | −9.60390e6 | − | 1.66344e7i | −1.34762 | − | 2.33415i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.45829e6 | − | 5.98993e6i | 0.480893 | − | 0.832931i | ||||
\(554\) | −5.88479e6 | + | 1.27615e6i | −0.814623 | + | 0.176655i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.30037e6 | − | 5.05451e6i | −0.315581 | − | 0.693413i | ||||
\(557\) | − | 2.33240e6i | − | 0.318541i | −0.987235 | − | 0.159270i | \(-0.949086\pi\) | ||
0.987235 | − | 0.159270i | \(-0.0509142\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.79815e6i | − | 0.378740i | ||||||
\(560\) | −1.40026e6 | − | 4.08012e6i | −0.188686 | − | 0.549797i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.23233e6 | + | 5.68272e6i | 0.164583 | + | 0.758955i | ||||
\(563\) | −4.06546e6 | + | 7.04158e6i | −0.540553 | + | 0.936266i | 0.458319 | + | 0.888788i | \(0.348452\pi\) |
−0.998872 | + | 0.0474781i | \(0.984882\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −196347. | − | 340083.i | −0.0258763 | − | 0.0448191i | ||||
\(566\) | 4.63366e6 | − | 4.20677e6i | 0.607971 | − | 0.551960i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.10599e6 | + | 6.04341e6i | −1.05423 | + | 0.785980i | ||||
\(569\) | 5.81782e6 | − | 3.35892e6i | 0.753320 | − | 0.434929i | −0.0735725 | − | 0.997290i | \(-0.523440\pi\) |
0.826892 | + | 0.562361i | \(0.190107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.04309e7 | − | 6.02229e6i | −1.33885 | − | 0.772985i | −0.352213 | − | 0.935920i | \(-0.614571\pi\) |
−0.986637 | + | 0.162935i | \(0.947904\pi\) | |||||||
\(572\) | −301718. | − | 215445.i | −0.0385577 | − | 0.0275325i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.57876e6 | − | 4.92774e6i | 0.200003 | − | 0.624264i | ||||
\(575\) | 827826. | 0.104417 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −906368. | −0.113335 | −0.0566676 | − | 0.998393i | \(-0.518048\pi\) | ||||
−0.0566676 | + | 0.998393i | \(0.518048\pi\) | |||||||
\(578\) | −1.04694e6 | + | 3.26777e6i | −0.130347 | + | 0.406847i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.92313e6 | − | 3.51541e6i | −0.607675 | − | 0.433916i | ||||
\(581\) | −3.48849e6 | − | 2.01408e6i | −0.428743 | − | 0.247535i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.78843e6 | + | 1.03255e6i | −0.217922 | + | 0.125817i | ||||
\(584\) | −1.01385e7 | + | 7.55877e6i | −1.23011 | + | 0.917105i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.78382e6 | + | 4.34310e6i | −0.575480 | + | 0.522463i | ||||
\(587\) | 4.78919e6 | + | 8.29511e6i | 0.573676 | + | 0.993636i | 0.996184 | + | 0.0872766i | \(0.0278164\pi\) |
−0.422508 | + | 0.906359i | \(0.638850\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.09289e6 | − | 3.62499e6i | 0.248575 | − | 0.430545i | ||||
\(590\) | 1.12607e6 | + | 5.19271e6i | 0.133179 | + | 0.614136i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.55847e6 | + | 1.32826e7i | 0.534582 | + | 1.55768i | ||||
\(593\) | 6.46951e6i | 0.755501i | 0.925907 | + | 0.377750i | \(0.123302\pi\) | ||||
−0.925907 | + | 0.377750i | \(0.876698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.79899e6i | 0.439922i | ||||||||
\(596\) | 2.99990e6 | + | 6.59154e6i | 0.345932 | + | 0.760101i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 248646. | − | 53920.2i | 0.0284334 | − | 0.00616593i | ||||
\(599\) | 2.38231e6 | − | 4.12628e6i | 0.271288 | − | 0.469885i | −0.697904 | − | 0.716192i | \(-0.745884\pi\) |
0.969192 | + | 0.246306i | \(0.0792169\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.09387e6 | − | 1.22869e7i | −0.801119 | − | 1.38758i | −0.918880 | − | 0.394537i | \(-0.870905\pi\) |
0.117761 | − | 0.993042i | \(-0.462428\pi\) | |||||||
\(602\) | 1.37251e7 | + | 1.51179e7i | 1.54357 | + | 1.70020i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.78130e6 | − | 172433.i | −0.198676 | − | 0.0192322i | ||||
\(605\) | 3.10723e6 | − | 1.79396e6i | 0.345132 | − | 0.199262i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.94805e6 | − | 4.01146e6i | −0.765404 | − | 0.441906i | 0.0658283 | − | 0.997831i | \(-0.479031\pi\) |
−0.831233 | + | 0.555924i | \(0.812364\pi\) | |||||||
\(608\) | 281284. | + | 1.36881e7i | 0.0308593 | + | 1.50170i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.23915e6 | + | 717385.i | 0.243646 | + | 0.0780598i | ||||
\(611\) | 1.85897e6 | 0.201450 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.92638e6 | 0.529513 | 0.264757 | − | 0.964315i | \(-0.414708\pi\) | ||||
0.264757 | + | 0.964315i | \(0.414708\pi\) | |||||||
\(614\) | −7.12437e6 | − | 2.28252e6i | −0.762651 | − | 0.244340i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.68691e6 | − | 315940.i | 0.285299 | − | 0.0335470i | ||||
\(617\) | −1.81236e6 | − | 1.04636e6i | −0.191660 | − | 0.110655i | 0.401100 | − | 0.916034i | \(-0.368628\pi\) |
−0.592759 | + | 0.805380i | \(0.701961\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.46071e6 | + | 4.30745e6i | −0.782625 | + | 0.451849i | −0.837360 | − | 0.546652i | \(-0.815902\pi\) |
0.0547347 | + | 0.998501i | \(0.482569\pi\) | |||||||
\(620\) | 127019. | − | 1.31216e6i | 0.0132706 | − | 0.137090i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.06068e6 | − | 1.16831e6i | −0.109928 | − | 0.121083i | ||||
\(623\) | −8.95702e6 | − | 1.55140e7i | −0.924578 | − | 1.60142i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.49273e6 | + | 4.31754e6i | −0.255256 | + | 0.442116i | ||||
\(626\) | −762049. | + | 165254.i | −0.0777225 | + | 0.0168545i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.92167e6 | − | 1.78480e6i | 0.396800 | − | 0.180589i | ||||
\(629\) | − | 1.23674e7i | − | 1.24638i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.15818e7i | 1.15798i | 0.815334 | + | 0.578991i | \(0.196554\pi\) | ||||
−0.815334 | + | 0.578991i | \(0.803446\pi\) | |||||||
\(632\) | −2.73398e6 | + | 6.35017e6i | −0.272272 | + | 0.632401i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.56480e6 | + | 7.21587e6i | 0.154609 | + | 0.712960i | ||||
\(635\) | 533632. | − | 924277.i | 0.0525179 | − | 0.0909637i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.12225e6 | + | 1.94379e6i | 0.109582 | + | 0.189802i | ||||
\(638\) | 2.80903e6 | − | 2.55024e6i | 0.273215 | − | 0.248044i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.86638e6 | + | 3.88706e6i | 0.180115 | + | 0.375121i | ||||
\(641\) | −1.51197e7 | + | 8.72938e6i | −1.45345 | + | 0.839147i | −0.998675 | − | 0.0514611i | \(-0.983612\pi\) |
−0.454771 | + | 0.890608i | \(0.650279\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.37838e6 | + | 4.83726e6i | 0.799158 | + | 0.461394i | 0.843177 | − | 0.537637i | \(-0.180683\pi\) |
−0.0440186 | + | 0.999031i | \(0.514016\pi\) | |||||||
\(644\) | −1.07891e6 | + | 1.51095e6i | −0.102511 | + | 0.143561i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.67878e6 | − | 1.14824e7i | 0.346834 | − | 1.08256i | ||||
\(647\) | 1.26182e7 | 1.18505 | 0.592525 | − | 0.805552i | \(-0.298131\pi\) | ||||
0.592525 | + | 0.805552i | \(0.298131\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.33239e6 | −0.310559 | ||||||||
\(650\) | −626063. | + | 1.95411e6i | −0.0581212 | + | 0.181412i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.74494e6 | + | 2.44368e6i | −0.160754 | + | 0.225126i | ||||
\(653\) | 1.65281e7 | + | 9.54250e6i | 1.51684 | + | 0.875748i | 0.999804 | + | 0.0197840i | \(0.00629786\pi\) |
0.517036 | + | 0.855964i | \(0.327035\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 482415. | − | 278522.i | 0.0439357 | − | 0.0253663i | ||||
\(656\) | −992083. | + | 5.07628e6i | −0.0900095 | + | 0.460560i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.00437e7 | + | 9.11837e6i | −0.904332 | + | 0.821018i | ||||
\(659\) | −5.33197e6 | − | 9.23524e6i | −0.478271 | − | 0.828390i | 0.521419 | − | 0.853301i | \(-0.325403\pi\) |
−0.999690 | + | 0.0249112i | \(0.992070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.35400e6 | − | 2.34520e6i | 0.120535 | − | 0.208774i | −0.799443 | − | 0.600741i | \(-0.794872\pi\) |
0.919979 | + | 0.391968i | \(0.128206\pi\) | |||||||
\(662\) | 765188. | + | 3.52857e6i | 0.0678615 | + | 0.312934i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.69829e6 | + | 1.59225e6i | 0.325523 | + | 0.140149i | ||||
\(665\) | 9.95660e6i | 0.873086i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.60366e6i | 0.226605i | ||||||||
\(668\) | −3.92842e6 | + | 1.78788e6i | −0.340625 | + | 0.155023i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.31958e6 | − | 936723.i | 0.371753 | − | 0.0806166i | ||||
\(671\) | −737317. | + | 1.27707e6i | −0.0632191 | + | 0.109499i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.61627e6 | − | 4.53151e6i | −0.222661 | − | 0.385660i | 0.732954 | − | 0.680278i | \(-0.238141\pi\) |
−0.955615 | + | 0.294618i | \(0.904808\pi\) | |||||||
\(674\) | −3.73745e6 | − | 4.11671e6i | −0.316903 | − | 0.349061i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.08402e6 | − | 1.11984e7i | 0.0912372 | − | 0.942516i | ||||
\(677\) | 1.63183e6 | − | 942135.i | 0.136837 | − | 0.0790026i | −0.430019 | − | 0.902820i | \(-0.641493\pi\) |
0.566855 | + | 0.823817i | \(0.308160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.51244e6 | + | 3.75996e6i | 0.542087 | + | 0.312974i | ||||
\(680\) | −443464. | − | 3.77143e6i | −0.0367778 | − | 0.312776i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 787366. | + | 252259.i | 0.0648210 | + | 0.0207675i | ||||
\(683\) | −8.13981e6 | −0.667671 | −0.333835 | − | 0.942631i | \(-0.608343\pi\) | ||||
−0.333835 | + | 0.942631i | \(0.608343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.81011e6 | −0.391678 | ||||||||
\(686\) | 798780. | + | 255915.i | 0.0648063 | + | 0.0207628i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.53903e7 | − | 1.34061e7i | −1.23958 | − | 1.07977i | ||||
\(689\) | 3.04220e6 | + | 1.75641e6i | 0.244140 | + | 0.140954i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.22215e7 | + | 7.05606e6i | −0.973706 | + | 0.562169i | −0.900364 | − | 0.435138i | \(-0.856700\pi\) |
−0.0733417 | + | 0.997307i | \(0.523366\pi\) | |||||||
\(692\) | 6.61309e6 | + | 640158.i | 0.524975 | + | 0.0508186i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.13788e6 | − | 5.65925e6i | −0.404935 | − | 0.446026i | ||||
\(695\) | 2.01846e6 | + | 3.49608e6i | 0.158511 | + | 0.274549i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.27757e6 | − | 3.94487e6i | 0.177579 | − | 0.307575i | ||||
\(698\) | 4.16779e6 | − | 903808.i | 0.323793 | − | 0.0702163i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.20256e6 | − | 1.36286e7i | −0.478438 | − | 1.05125i | ||||
\(701\) | 2.52168e6i | 0.193818i | 0.995293 | + | 0.0969090i | \(0.0308956\pi\) | ||||
−0.995293 | + | 0.0969090i | \(0.969104\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.24131e7i | − | 2.47362i | ||||||
\(704\) | −2.63053e6 | + | 627297.i | −0.200038 | + | 0.0477025i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −539802. | − | 2.48923e6i | −0.0407590 | − | 0.187955i | ||||
\(707\) | −1.05358e7 | + | 1.82485e7i | −0.792716 | + | 1.37302i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.59486e6 | + | 1.31547e7i | 0.567419 | + | 0.982799i | 0.996820 | + | 0.0796849i | \(0.0253914\pi\) |
−0.429401 | + | 0.903114i | \(0.641275\pi\) | |||||||
\(710\) | 5.44182e6 | − | 4.94048e6i | 0.405134 | − | 0.367810i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.07030e7 | + | 1.43559e7i | 0.791237 | + | 1.06128i | ||||
\(713\) | −491375. | + | 283695.i | −0.0361984 | + | 0.0208991i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 233399. | + | 134753.i | 0.0170739 | + | 0.00985765i | ||||
\(716\) | −1.36787e7 | − | 9.76739e6i | −0.997152 | − | 0.712026i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.21656e6 | + | 1.62823e7i | −0.377636 | + | 1.17870i | ||||
\(719\) | 4.45507e6 | 0.321390 | 0.160695 | − | 0.987004i | \(-0.448626\pi\) | ||||
0.160695 | + | 0.987004i | \(0.448626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.17213e6 | −0.513819 | ||||||||
\(722\) | 5.36794e6 | − | 1.67548e7i | 0.383234 | − | 1.19618i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.15067e7 | + | 1.53570e7i | 1.52485 | + | 1.08883i | ||||
\(725\) | −1.81853e7 | − | 1.04993e7i | −1.28492 | − | 0.741849i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.03556e7 | − | 5.97878e6i | 0.726670 | − | 0.419543i | −0.0905324 | − | 0.995894i | \(-0.528857\pi\) |
0.817203 | + | 0.576350i | \(0.195524\pi\) | |||||||
\(728\) | −2.75070e6 | − | 3.68949e6i | −0.192360 | − | 0.258011i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.80634e6 | − | 6.17929e6i | 0.472722 | − | 0.429172i | ||||
\(731\) | 8.98749e6 | + | 1.55668e7i | 0.622078 | + | 1.07747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.24966e6 | + | 1.08247e7i | −0.429632 | + | 0.744144i | −0.996840 | − | 0.0794302i | \(-0.974690\pi\) |
0.567209 | + | 0.823574i | \(0.308023\pi\) | |||||||
\(734\) | 3.23521e6 | + | 1.49187e7i | 0.221647 | + | 1.02210i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 894705. | − | 1.62593e6i | 0.0608815 | − | 0.110639i | ||||
\(737\) | 2.77206e6i | 0.187990i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3.34559e6i | − | 0.225352i | −0.993632 | − | 0.112676i | \(-0.964058\pi\) | ||
0.993632 | − | 0.112676i | \(-0.0359422\pi\) | |||||||
\(740\) | −4.22862e6 | − | 9.29137e6i | −0.283870 | − | 0.623735i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.50518e7 | + | 5.43262e6i | −1.67044 | + | 0.362243i | ||||
\(743\) | 1.84277e6 | − | 3.19177e6i | 0.122461 | − | 0.212109i | −0.798276 | − | 0.602291i | \(-0.794255\pi\) |
0.920738 | + | 0.390182i | \(0.127588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.63226e6 | − | 4.55921e6i | −0.173755 | − | 0.300953i | ||||
\(746\) | −7.01923e6 | − | 7.73152e6i | −0.461788 | − | 0.508648i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.37053e6 | + | 229472.i | 0.154914 | + | 0.0149960i | ||||
\(749\) | 1.28789e7 | − | 7.43564e6i | 0.838831 | − | 0.484299i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.11291e7 | + | 6.42540e6i | 0.720048 | + | 0.415720i | 0.814770 | − | 0.579784i | \(-0.196863\pi\) |
−0.0947225 | + | 0.995504i | \(0.530196\pi\) | |||||||
\(752\) | 8.90640e6 | − | 1.02246e7i | 0.574325 | − | 0.659331i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.14601e6 | − | 1.96908e6i | −0.393700 | − | 0.126135i | ||||
\(755\) | 1.30094e6 | 0.0830597 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.81332e6 | 0.178435 | 0.0892175 | − | 0.996012i | \(-0.471563\pi\) | ||||
0.0892175 | + | 0.996012i | \(0.471563\pi\) | |||||||
\(758\) | −7.31606e6 | − | 2.34394e6i | −0.462492 | − | 0.148174i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.16226e6 | − | 9.88437e6i | −0.0729907 | − | 0.620747i | ||||
\(761\) | −2.67932e6 | − | 1.54691e6i | −0.167712 | − | 0.0968283i | 0.413795 | − | 0.910370i | \(-0.364203\pi\) |
−0.581506 | + | 0.813542i | \(0.697536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.62475e6 | − | 4.40215e6i | 0.474149 | − | 0.273750i | ||||
\(764\) | 1.15620e6 | − | 1.19440e7i | 0.0716635 | − | 0.740312i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.40314e7 | + | 1.54553e7i | 0.864032 | + | 0.951711i | ||||
\(767\) | 2.83427e6 | + | 4.90910e6i | 0.173962 | + | 0.301310i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 602040. | − | 1.04276e6i | 0.0367122 | − | 0.0635873i | −0.847086 | − | 0.531457i | \(-0.821645\pi\) |
0.883798 | + | 0.467869i | \(0.154978\pi\) | |||||||
\(770\) | −1.92199e6 | + | 416794.i | −0.116822 | + | 0.0253334i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.38971e7 | + | 6.32473e6i | −0.839227 | + | 0.381943i | ||||
\(773\) | − | 2.76278e7i | − | 1.66302i | −0.555510 | − | 0.831510i | \(-0.687477\pi\) | ||
0.555510 | − | 0.831510i | \(-0.312523\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.57603e6i | − | 0.273675i | ||||||
\(776\) | −6.90410e6 | − | 2.97247e6i | −0.411579 | − | 0.177200i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.97305e6 | − | 1.83212e7i | −0.235329 | − | 1.08519i | ||||
\(779\) | 5.96919e6 | − | 1.03389e7i | 0.352429 | − | 0.610425i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.30482e6 | + | 3.99207e6i | 0.135210 | + | 0.234191i | ||||
\(782\) | −1.21009e6 | + | 1.09861e6i | −0.0707622 | + | 0.0642430i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.60680e7 | + | 3.14024e6i | 0.933621 | + | 0.182462i | ||||
\(785\) | −2.71252e6 | + | 1.56608e6i | −0.157108 | + | 0.0907066i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.86919e6 | + | 3.38858e6i | 0.337786 | + | 0.195021i | 0.659292 | − | 0.751887i | \(-0.270856\pi\) |
−0.321507 | + | 0.946907i | \(0.604189\pi\) | |||||||
\(788\) | 8.25516e6 | − | 1.15609e7i | 0.473598 | − | 0.663247i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.53341e6 | − | 4.78618e6i | 0.0874158 | − | 0.272848i | ||||
\(791\) | 3.05713e6 | 0.173729 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.50842e6 | 0.141650 | ||||||||
\(794\) | 206193. | − | 643584.i | 0.0116071 | − | 0.0362288i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.11807e7 | + | 1.56580e7i | −0.625442 | + | 0.875896i | ||||
\(797\) | 7.51105e6 | + | 4.33650e6i | 0.418846 | + | 0.241821i | 0.694584 | − | 0.719412i | \(-0.255589\pi\) |
−0.275737 | + | 0.961233i | \(0.588922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.03419e7 | + | 5.97089e6i | −0.573103 | + | 0.330881i | ||||
\(800\) | 7.74846e6 | + | 1.28057e7i | 0.428046 | + | 0.707422i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.98053e7 | − | 1.79807e7i | 1.08729 | − | 0.987122i | ||||
\(803\) | 2.88275e6 | + | 4.99307e6i | 0.157768 | + | 0.273262i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 674819. | − | 1.16882e6i | 0.0367026 | − | 0.0635708i | ||||
\(806\) | −298058. | − | 1.37446e6i | −0.0161608 | − | 0.0745236i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.32915e6 | − | 1.93460e7i | 0.448820 | − | 1.04247i | ||||
\(809\) | 2.35011e7i | 1.26246i | 0.775596 | + | 0.631230i | \(0.217450\pi\) | ||||
−0.775596 | + | 0.631230i | \(0.782550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 335741.i | − | 0.0179247i | −0.999960 | − | 0.00896235i | \(-0.997147\pi\) | ||
0.999960 | − | 0.00896235i | \(-0.00285284\pi\) | |||||||
\(812\) | 4.28643e7 | − | 1.95081e7i | 2.28142 | − | 1.03831i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.25692e6 | − | 1.35685e6i | 0.330978 | − | 0.0717744i | ||||
\(815\) | 1.09140e6 | − | 1.89035e6i | 0.0575557 | − | 0.0996894i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.35549e7 | + | 4.07983e7i | 1.23460 | + | 2.13839i | ||||
\(818\) | −2.37081e7 | − | 2.61139e7i | −1.23883 | − | 1.36455i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 362275. | − | 3.74245e6i | 0.0188150 | − | 0.194366i | ||||
\(821\) | −2.09922e7 | + | 1.21198e7i | −1.08692 | + | 0.627536i | −0.932756 | − | 0.360509i | \(-0.882603\pi\) |
−0.154168 | + | 0.988045i | \(0.549270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.59148e6 | + | 2.07354e6i | 0.184831 | + | 0.106712i | 0.589560 | − | 0.807724i | \(-0.299301\pi\) |
−0.404730 | + | 0.914436i | \(0.632634\pi\) | |||||||
\(824\) | 7.12010e6 | − | 837218.i | 0.365315 | − | 0.0429557i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.93926e7 | − | 1.26207e7i | −2.00893 | − | 0.643626i | ||||
\(827\) | 2.18621e6 | 0.111155 | 0.0555773 | − | 0.998454i | \(-0.482300\pi\) | ||||
0.0555773 | + | 0.998454i | \(0.482300\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.24847e6 | 0.467395 | 0.233697 | − | 0.972309i | \(-0.424918\pi\) | ||||
0.233697 | + | 0.972309i | \(0.424918\pi\) | |||||||
\(830\) | −2.78743e6 | − | 893045.i | −0.140446 | − | 0.0449964i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.16142e6 | + | 3.34163e6i | 0.158334 | + | 0.167359i | ||||
\(833\) | −1.24867e7 | − | 7.20920e6i | −0.623499 | − | 0.359977i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.71720e6 | − | 1.56877e6i | 0.134867 | − | 0.0778653i | ||||
\(836\) | 6.21282e6 | + | 601412.i | 0.307449 | + | 0.0297616i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.64369e6 | − | 2.91196e6i | −0.130047 | − | 0.143244i | ||||
\(839\) | 3.55904e6 | + | 6.16444e6i | 0.174553 | + | 0.302335i | 0.940007 | − | 0.341156i | \(-0.110819\pi\) |
−0.765453 | + | 0.643491i | \(0.777485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.27665e7 | − | 3.94328e7i | 1.10996 | − | 1.92251i | ||||
\(842\) | 6.47664e6 | − | 1.40449e6i | 0.314825 | − | 0.0682716i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.28443e6 | − | 1.16112e7i | −0.255353 | − | 0.561077i | ||||
\(845\) | 8.17855e6i | 0.394035i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.79320e7i | 1.33781i | ||||||||
\(848\) | 2.42359e7 | − | 8.31756e6i | 1.15736 | − | 0.397198i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.79355e6 | − | 1.28821e7i | −0.132620 | − | 0.611560i | ||||
\(851\) | −2.19683e6 | + | 3.80502e6i | −0.103986 | + | 0.180108i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.61575e6 | + | 9.72676e6i | 0.264262 | + | 0.457715i | 0.967370 | − | 0.253368i | \(-0.0815383\pi\) |
−0.703108 | + | 0.711083i | \(0.748205\pi\) | |||||||
\(854\) | −1.35525e7 | + | 1.23040e7i | −0.635881 | + | 0.577299i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.19175e7 | + | 8.88508e6i | −0.555905 | + | 0.414455i | ||||
\(857\) | 2.03104e7 | − | 1.17262e7i | 0.944641 | − | 0.545389i | 0.0532292 | − | 0.998582i | \(-0.483049\pi\) |
0.891412 | + | 0.453193i | \(0.149715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.00517e7 | + | 1.73504e7i | 1.38959 | + | 0.802279i | 0.993269 | − | 0.115834i | \(-0.0369540\pi\) |
0.396319 | + | 0.918113i | \(0.370287\pi\) | |||||||
\(860\) | 1.20747e7 | + | 8.62204e6i | 0.556710 | + | 0.397524i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.14585e6 | − | 1.60616e7i | 0.235879 | − | 0.736242i | ||||
\(863\) | −2.83896e7 | −1.29757 | −0.648787 | − | 0.760970i | \(-0.724724\pi\) | ||||
−0.648787 | + | 0.760970i | \(0.724724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.82975e6 | −0.219475 | ||||||||
\(866\) | −1.01928e7 | + | 3.18143e7i | −0.461846 | + | 1.44154i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.35218e6 | + | 5.96396e6i | 0.376271 | + | 0.268680i | ||||
\(869\) | 2.72974e6 | + | 1.57601e6i | 0.122623 | + | 0.0707963i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.08366e6 | − | 2.35770e6i | 0.182391 | − | 0.105304i | ||||
\(872\) | −7.05557e6 | + | 5.26027e6i | −0.314225 | + | 0.234270i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.17147e6 | + | 2.87929e6i | −0.140437 | + | 0.127499i | ||||
\(875\) | 1.20246e7 | + | 2.08273e7i | 0.530948 | + | 0.919629i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.61791e7 | + | 2.80230e7i | −0.710323 | + | 1.23031i | 0.254414 | + | 0.967096i | \(0.418118\pi\) |
−0.964736 | + | 0.263219i | \(0.915216\pi\) | |||||||
\(878\) | 3.94927e6 | + | 1.82115e7i | 0.172894 | + | 0.797279i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.85939e6 | − | 638128.i | 0.0809402 | − | 0.0277780i | ||||
\(881\) | 5.73331e6i | 0.248866i | 0.992228 | + | 0.124433i | \(0.0397112\pi\) | ||||
−0.992228 | + | 0.124433i | \(0.960289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.49947e7i | − | 1.07881i | −0.842046 | − | 0.539406i | \(-0.818649\pi\) | ||
0.842046 | − | 0.539406i | \(-0.181351\pi\) | |||||||
\(884\) | −1.67814e6 | − | 3.68731e6i | −0.0722267 | − | 0.158701i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.37273e7 | + | 7.31395e6i | −1.44344 | + | 0.313017i | ||||
\(887\) | 2.27170e6 | − | 3.93469e6i | 0.0969485 | − | 0.167920i | −0.813472 | − | 0.581605i | \(-0.802425\pi\) |
0.910420 | + | 0.413685i | \(0.135758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.15433e6 | + | 7.19552e6i | 0.176298 | + | 0.305357i | ||||
\(890\) | −8.74971e6 | − | 9.63760e6i | −0.370270 | − | 0.407844i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.06693e7 | + | 1.03281e6i | 0.448978 | + | 0.0434619i | ||||
\(893\) | −2.71046e7 | + | 1.56488e7i | −1.13740 | + | 0.656680i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.05814e7 | + | 6.10915e6i | 0.441554 | + | 0.254931i | ||||
\(896\) | −3.34716e7 | − | 2.54722e6i | −1.39286 | − | 0.105998i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.89983e7 | + | 9.29054e6i | 1.20000 | + | 0.384459i | ||||
\(899\) | 1.43924e7 | 0.593928 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.25660e7 | −0.926068 | ||||||||
\(902\) | 2.24567e6 | + | 719474.i | 0.0919031 | + | 0.0294441i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.03495e6 | + | 356865.i | −0.123518 | + | 0.0145239i | ||||
\(905\) | −1.66368e7 | − | 9.60528e6i | −0.675226 | − | 0.389842i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.72617e7 | + | 1.57395e7i | −1.10036 | + | 0.635292i | −0.936315 | − | 0.351161i | \(-0.885787\pi\) |
−0.164043 | + | 0.986453i | \(0.552454\pi\) | |||||||
\(908\) | −2.62137e6 | + | 2.70797e7i | −0.105515 | + | 1.09001i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.24869e6 | + | 2.47688e6i | 0.0900173 | + | 0.0991519i | ||||
\(911\) | 2.63528e6 | + | 4.56443e6i | 0.105204 | + | 0.182218i | 0.913821 | − | 0.406116i | \(-0.133117\pi\) |
−0.808618 | + | 0.588334i | \(0.799784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 917858. | − | 1.58978e6i | 0.0364417 | − | 0.0631189i | ||||
\(914\) | 2.56463e6 | − | 556153.i | 0.101545 | − | 0.0220206i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.18926e7 | − | 5.41248e6i | 0.468316 | − | 0.213137i | ||||
\(917\) | 4.33661e6i | 0.170305i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.29683e7i | − | 1.28768i | −0.765161 | − | 0.643839i | \(-0.777341\pi\) | ||
0.765161 | − | 0.643839i | \(-0.222659\pi\) | |||||||
\(920\) | −533484. | + | 1.23911e6i | −0.0207803 | + | 0.0482660i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.99832e6 | − | 2.30491e7i | −0.193641 | − | 0.892950i | ||||
\(923\) | 3.92060e6 | − | 6.79068e6i | 0.151478 | − | 0.262367i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.77175e7 | − | 3.06877e7i | −0.680846 | − | 1.17926i | ||||
\(926\) | −2.64293e7 | + | 2.39944e7i | −1.01288 | + | 0.919565i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.02761e7 | + | 2.43702e7i | −1.53525 | + | 0.928945i | ||||
\(929\) | 1.70431e6 | − | 983982.i | 0.0647901 | − | 0.0374066i | −0.467255 | − | 0.884123i | \(-0.654757\pi\) |
0.532045 | + | 0.846716i | \(0.321424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.27259e7 | − | 1.88943e7i | −1.23742 | − | 0.714424i | ||||
\(932\) | 1.25999e7 | − | 1.76455e7i | 0.475147 | − | 0.665416i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.31826e6 | + | 4.11466e6i | −0.0494465 | + | 0.154336i | ||||
\(935\) | −1.73128e6 | −0.0647646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.97561e7 | −1.47929 | −0.739647 | − | 0.672995i | \(-0.765007\pi\) | ||||
−0.739647 | + | 0.672995i | \(0.765007\pi\) | |||||||
\(938\) | −1.04986e7 | + | 3.27689e7i | −0.389604 | + | 1.21606i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.72810e6 | + | 8.02188e6i | −0.211442 | + | 0.296112i | ||||
\(941\) | 1.93060e7 | + | 1.11463e7i | 0.710751 | + | 0.410352i | 0.811339 | − | 0.584576i | \(-0.198739\pi\) |
−0.100588 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.40146e6 | + | 809136.i | −0.0513219 | + | 0.0296307i | ||||
\(944\) | 4.05801e7 | + | 7.93077e6i | 1.48212 | + | 0.289658i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.88954e6 | + | 6.25482e6i | −0.250301 | + | 0.227241i | ||||
\(947\) | −2.17517e7 | − | 3.76751e7i | −0.788168 | − | 1.36515i | −0.927088 | − | 0.374843i | \(-0.877697\pi\) |
0.138921 | − | 0.990304i | \(-0.455637\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.90368e6 | − | 8.49342e6i | 0.176749 | − | 0.306138i | ||||
\(950\) | −7.32149e6 | − | 3.37621e7i | −0.263203 | − | 1.21372i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.71533e7 | + | 1.16905e7i | 0.971023 | + | 0.418061i | ||||
\(953\) | − | 7.60909e6i | − | 0.271394i | −0.990750 | − | 0.135697i | \(-0.956673\pi\) | ||
0.990750 | − | 0.135697i | \(-0.0433274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.72306e6i | 0.309500i | ||||||||
\(956\) | −3.84596e7 | + | 1.75035e7i | −1.36101 | + | 0.619411i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.18180e7 | + | 4.73135e6i | −0.768071 | + | 0.166560i | ||||
\(959\) | 1.87234e7 | − | 3.24299e7i | 0.657413 | − | 1.13867i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.27464e7 | − | 2.20774e7i | −0.445224 | − | 0.771150i | ||||
\(962\) | −7.32048e6 | − | 8.06333e6i | −0.255036 | − | 0.280916i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.58175e6 | + | 2.66705e7i | −0.0894791 | + | 0.924354i | ||||
\(965\) | 9.61226e6 | − | 5.54964e6i | 0.332282 | − | 0.191843i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.31287e7 | + | 7.57986e6i | 0.451498 | + | 0.260672i | 0.708463 | − | 0.705748i | \(-0.249389\pi\) |
−0.256965 | + | 0.966421i | \(0.582722\pi\) | |||||||
\(968\) | −3.26057e6 | − | 2.77294e7i | −0.111842 | − | 0.951156i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.20368e6 | + | 1.66717e6i | 0.177575 | + | 0.0568919i | ||||
\(971\) | −9.85699e6 | −0.335503 | −0.167751 | − | 0.985829i | \(-0.553651\pi\) | ||||
−0.167751 | + | 0.985829i | \(0.553651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.14276e7 | −1.06421 | ||||||||
\(974\) | 1.06582e7 | + | 3.41471e6i | 0.359988 | + | 0.115334i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.20180e7 | − | 1.37967e7i | 0.403837 | − | 0.463609i | ||||
\(977\) | 430133. | + | 248338.i | 0.0144167 | + | 0.00832350i | 0.507191 | − | 0.861834i | \(-0.330684\pi\) |
−0.492774 | + | 0.870157i | \(0.664017\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.07006e6 | − | 4.08190e6i | 0.235758 | − | 0.136115i | ||||
\(980\) | −1.18460e7 | − | 1.14671e6i | −0.394008 | − | 0.0381407i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.16297e6 | + | 4.58541e6i | 0.137760 | + | 0.151740i | ||||
\(983\) | 2.20843e7 | + | 3.82511e7i | 0.728953 | + | 1.26258i | 0.957326 | + | 0.289010i | \(0.0933260\pi\) |
−0.228373 | + | 0.973574i | \(0.573341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.16330e6 | + | 8.94311e6i | −0.169565 | + | 0.293696i | ||||
\(986\) | 4.05164e7 | − | 8.78619e6i | 1.32721 | − | 0.287812i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.39817e6 | − | 9.66390e6i | −0.143344 | − | 0.314963i | ||||
\(989\) | − | 6.38583e6i | − | 0.207600i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.44990e6i | 0.273317i | 0.990618 | + | 0.136659i | \(0.0436364\pi\) | ||||
−0.990618 | + | 0.136659i | \(0.956364\pi\) | |||||||
\(992\) | −8.98777e6 | − | 4.94572e6i | −0.289983 | − | 0.159570i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.21265e7 | + | 5.59198e7i | 0.389287 | + | 1.79514i | ||||
\(995\) | 6.99314e6 | − | 1.21125e7i | 0.223931 | − | 0.387860i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.98031e6 | + | 1.55544e7i | 0.286123 | + | 0.495580i | 0.972881 | − | 0.231306i | \(-0.0742999\pi\) |
−0.686758 | + | 0.726887i | \(0.740967\pi\) | |||||||
\(998\) | 4.38694e7 | − | 3.98278e7i | 1.39423 | − | 1.26579i | ||||
\(999\) | 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 | 108.6.h.a.71.12 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.23.17 | yes | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.71.2 | 56 | ||
9.2 | odd | 6 | inner | 108.6.h.a.35.2 | 56 | ||
9.7 | even | 3 | 36.6.h.a.11.27 | yes | 56 | ||
12.11 | even | 2 | 36.6.h.a.23.27 | yes | 56 | ||
36.7 | odd | 6 | 36.6.h.a.11.17 | ✓ | 56 | ||
36.11 | even | 6 | inner | 108.6.h.a.35.12 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.17 | ✓ | 56 | 36.7 | odd | 6 | ||
36.6.h.a.11.27 | yes | 56 | 9.7 | even | 3 | ||
36.6.h.a.23.17 | yes | 56 | 3.2 | odd | 2 | ||
36.6.h.a.23.27 | yes | 56 | 12.11 | even | 2 | ||
108.6.h.a.35.2 | 56 | 9.2 | odd | 6 | inner | ||
108.6.h.a.35.12 | 56 | 36.11 | even | 6 | inner | ||
108.6.h.a.71.2 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.71.12 | 56 | 1.1 | even | 1 | trivial |