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 | 71.1 | ||
Character | \(\chi\) | \(=\) | 108.71 |
Dual form | 108.6.h.a.35.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65362 | − | 0.191212i | −0.999429 | − | 0.0338019i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 31.9269 | + | 2.16208i | 0.997715 | + | 0.0675651i | ||||
\(5\) | −3.68052 | − | 2.12495i | −0.0658391 | − | 0.0380122i | 0.466719 | − | 0.884406i | \(-0.345436\pi\) |
−0.532558 | + | 0.846393i | \(0.678769\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.9322 | + | 8.04377i | −0.107467 | + | 0.0620461i | −0.552770 | − | 0.833334i | \(-0.686429\pi\) |
0.445303 | + | 0.895380i | \(0.353096\pi\) | |||||||
\(8\) | −180.089 | − | 18.3284i | −0.994861 | − | 0.101251i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 20.4019 | + | 12.7174i | 0.0645166 | + | 0.0402160i | ||||
\(11\) | −43.3121 | − | 75.0187i | −0.107926 | − | 0.186934i | 0.807004 | − | 0.590546i | \(-0.201088\pi\) |
−0.914930 | + | 0.403613i | \(0.867754\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 162.502 | − | 281.462i | 0.266686 | − | 0.461914i | −0.701318 | − | 0.712849i | \(-0.747405\pi\) |
0.968004 | + | 0.250935i | \(0.0807380\pi\) | |||||||
\(14\) | 80.3056 | − | 42.8124i | 0.109503 | − | 0.0583781i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1014.65 | + | 138.057i | 0.990870 | + | 0.134821i | ||||
\(17\) | 1863.80i | 1.56415i | 0.623187 | + | 0.782073i | \(0.285837\pi\) | ||||
−0.623187 | + | 0.782073i | \(0.714163\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 416.071i | − | 0.264413i | −0.991222 | − | 0.132207i | \(-0.957794\pi\) | ||
0.991222 | − | 0.132207i | \(-0.0422063\pi\) | |||||||
\(20\) | −112.913 | − | 75.8006i | −0.0631204 | − | 0.0423738i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 230.526 | + | 432.409i | 0.101546 | + | 0.190475i | ||||
\(23\) | 1293.41 | − | 2240.24i | 0.509818 | − | 0.883030i | −0.490117 | − | 0.871656i | \(-0.663046\pi\) |
0.999935 | − | 0.0113741i | \(-0.00362056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1553.47 | − | 2690.69i | −0.497110 | − | 0.861020i | ||||
\(26\) | −972.544 | + | 1560.21i | −0.282147 | + | 0.452635i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −462.204 | + | 226.690i | −0.111414 | + | 0.0546433i | ||||
\(29\) | −4342.80 | + | 2507.32i | −0.958904 | + | 0.553623i | −0.895835 | − | 0.444386i | \(-0.853422\pi\) |
−0.0630683 | + | 0.998009i | \(0.520089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6396.76 | − | 3693.17i | −1.19552 | − | 0.690232i | −0.235964 | − | 0.971762i | \(-0.575825\pi\) |
−0.959553 | + | 0.281530i | \(0.909158\pi\) | |||||||
\(32\) | −5710.05 | − | 974.537i | −0.985746 | − | 0.168238i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 356.382 | − | 10537.2i | 0.0528711 | − | 1.56325i | ||||
\(35\) | 68.3704 | 0.00943405 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10519.2 | −1.26322 | −0.631609 | − | 0.775287i | \(-0.717605\pi\) | ||||
−0.631609 | + | 0.775287i | \(0.717605\pi\) | |||||||
\(38\) | −79.5579 | + | 2352.31i | −0.00893767 | + | 0.264262i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 623.874 | + | 450.138i | 0.0616520 | + | 0.0444832i | ||||
\(41\) | −13207.4 | − | 7625.29i | −1.22704 | − | 0.708430i | −0.260628 | − | 0.965439i | \(-0.583930\pi\) |
−0.966409 | + | 0.257009i | \(0.917263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6794.45 | − | 3922.78i | 0.560381 | − | 0.323536i | −0.192917 | − | 0.981215i | \(-0.561795\pi\) |
0.753298 | + | 0.657679i | \(0.228462\pi\) | |||||||
\(44\) | −1220.62 | − | 2488.76i | −0.0950495 | − | 0.193799i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7740.79 | + | 12418.2i | −0.539375 | + | 0.865293i | ||||
\(47\) | −14244.6 | − | 24672.4i | −0.940604 | − | 1.62917i | −0.764323 | − | 0.644833i | \(-0.776927\pi\) |
−0.176280 | − | 0.984340i | \(-0.556406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8274.10 | + | 14331.2i | −0.492301 | + | 0.852690i | ||||
\(50\) | 8268.23 | + | 15509.2i | 0.467722 | + | 0.877331i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5796.72 | − | 8634.85i | 0.297286 | − | 0.442840i | ||||
\(53\) | − | 5483.31i | − | 0.268135i | −0.990972 | − | 0.134067i | \(-0.957196\pi\) | ||
0.990972 | − | 0.134067i | \(-0.0428038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 368.144i | 0.0164101i | ||||||||
\(56\) | 2656.47 | − | 1193.24i | 0.113197 | − | 0.0508461i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 25032.0 | − | 13345.0i | 0.977069 | − | 0.520894i | ||||
\(59\) | 1901.12 | − | 3292.83i | 0.0711015 | − | 0.123151i | −0.828283 | − | 0.560310i | \(-0.810682\pi\) |
0.899384 | + | 0.437159i | \(0.144015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16590.1 | + | 28734.9i | 0.570853 | + | 0.988747i | 0.996479 | + | 0.0838475i | \(0.0267209\pi\) |
−0.425625 | + | 0.904900i | \(0.639946\pi\) | |||||||
\(62\) | 35458.7 | + | 22102.9i | 1.17150 | + | 0.730248i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32096.1 | + | 6601.49i | 0.979496 | + | 0.201462i | ||||
\(65\) | −1196.18 | + | 690.617i | −0.0351168 | + | 0.0202747i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −57592.1 | − | 33250.8i | −1.56738 | − | 0.904930i | −0.996473 | − | 0.0839192i | \(-0.973256\pi\) |
−0.570912 | − | 0.821011i | \(-0.693410\pi\) | |||||||
\(68\) | −4029.69 | + | 59505.3i | −0.105682 | + | 1.56057i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −386.540 | − | 13.0733i | −0.00942866 | − | 0.000318889i | ||||
\(71\) | 43573.3 | 1.02583 | 0.512914 | − | 0.858440i | \(-0.328566\pi\) | ||||
0.512914 | + | 0.858440i | \(0.328566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22901.9 | 0.502996 | 0.251498 | − | 0.967858i | \(-0.419077\pi\) | ||||
0.251498 | + | 0.967858i | \(0.419077\pi\) | |||||||
\(74\) | 59471.5 | + | 2011.40i | 1.26250 | + | 0.0426991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 899.581 | − | 13283.8i | 0.0178651 | − | 0.263809i | ||||
\(77\) | 1206.87 | + | 696.785i | 0.0231970 | + | 0.0133928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31941.7 | + | 18441.5i | −0.575824 | + | 0.332452i | −0.759472 | − | 0.650540i | \(-0.774543\pi\) |
0.183648 | + | 0.982992i | \(0.441209\pi\) | |||||||
\(80\) | −3441.08 | − | 2664.20i | −0.0601132 | − | 0.0465417i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 73211.6 | + | 45635.9i | 1.20239 | + | 0.749501i | ||||
\(83\) | −27504.3 | − | 47638.8i | −0.438233 | − | 0.759041i | 0.559321 | − | 0.828951i | \(-0.311062\pi\) |
−0.997553 | + | 0.0699102i | \(0.977729\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3960.48 | − | 6859.75i | 0.0594567 | − | 0.102982i | ||||
\(86\) | −39163.3 | + | 20878.7i | −0.570997 | + | 0.304409i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6425.06 | + | 14303.9i | 0.0884444 | + | 0.196901i | ||||
\(89\) | 40969.8i | 0.548263i | 0.961692 | + | 0.274132i | \(0.0883904\pi\) | ||||
−0.961692 | + | 0.274132i | \(0.911610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5228.51i | 0.0661873i | ||||||||
\(92\) | 46138.0 | − | 68727.5i | 0.568315 | − | 0.846567i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 75816.1 | + | 142212.i | 0.884997 | + | 1.66004i | ||||
\(95\) | −884.130 | + | 1531.36i | −0.0100509 | + | 0.0174087i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 23339.8 | + | 40425.7i | 0.251865 | + | 0.436243i | 0.964039 | − | 0.265760i | \(-0.0856227\pi\) |
−0.712174 | + | 0.702003i | \(0.752289\pi\) | |||||||
\(98\) | 49518.9 | − | 79440.8i | 0.520842 | − | 0.835562i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −43779.9 | − | 89264.0i | −0.437799 | − | 0.892640i | ||||
\(101\) | 65827.1 | − | 38005.3i | 0.642098 | − | 0.370716i | −0.143324 | − | 0.989676i | \(-0.545779\pi\) |
0.785422 | + | 0.618960i | \(0.212446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3270.29 | + | 1888.10i | 0.0303734 | + | 0.0175361i | 0.515110 | − | 0.857124i | \(-0.327751\pi\) |
−0.484736 | + | 0.874660i | \(0.661084\pi\) | |||||||
\(104\) | −34423.6 | + | 47709.8i | −0.312085 | + | 0.432538i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1048.48 | + | 31000.6i | −0.00906346 | + | 0.267981i | ||||
\(107\) | 57656.6 | 0.486844 | 0.243422 | − | 0.969920i | \(-0.421730\pi\) | ||||
0.243422 | + | 0.969920i | \(0.421730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −176304. | −1.42133 | −0.710667 | − | 0.703529i | \(-0.751607\pi\) | ||||
−0.710667 | + | 0.703529i | \(0.751607\pi\) | |||||||
\(110\) | 70.3936 | − | 2081.35i | 0.000554692 | − | 0.0164007i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −15246.8 | + | 6238.18i | −0.114851 | + | 0.0469908i | ||||
\(113\) | −111854. | − | 64579.2i | −0.824057 | − | 0.475769i | 0.0277568 | − | 0.999615i | \(-0.491164\pi\) |
−0.851813 | + | 0.523845i | \(0.824497\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9520.81 | + | 5496.84i | −0.0671319 | + | 0.0387586i | ||||
\(116\) | −144073. | + | 70661.3i | −0.994118 | + | 0.487570i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11377.8 | + | 18252.9i | −0.0752236 | + | 0.120678i | ||||
\(119\) | −14992.0 | − | 25966.9i | −0.0970491 | − | 0.168094i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 76773.6 | − | 132976.i | 0.476704 | − | 0.825675i | ||||
\(122\) | −88299.7 | − | 165629.i | −0.537106 | − | 1.00748i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −196244. | − | 131742.i | −1.14615 | − | 0.769430i | ||||
\(125\) | 26485.1i | 0.151610i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 43254.5i | − | 0.237970i | −0.992896 | − | 0.118985i | \(-0.962036\pi\) | ||
0.992896 | − | 0.118985i | \(-0.0379640\pi\) | |||||||
\(128\) | −180197. | − | 43459.5i | −0.972127 | − | 0.234455i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6894.82 | − | 3675.76i | 0.0357820 | − | 0.0190761i | ||||
\(131\) | −104818. | + | 181550.i | −0.533650 | + | 0.924309i | 0.465577 | + | 0.885007i | \(0.345847\pi\) |
−0.999227 | + | 0.0393020i | \(0.987487\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3346.78 | + | 5796.79i | 0.0164058 | + | 0.0284157i | ||||
\(134\) | 319246. | + | 199000.i | 1.53590 | + | 0.957394i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 34160.5 | − | 335650.i | 0.158372 | − | 1.55611i | ||||
\(137\) | −99563.4 | + | 57483.0i | −0.453209 | + | 0.261660i | −0.709184 | − | 0.705023i | \(-0.750937\pi\) |
0.255976 | + | 0.966683i | \(0.417603\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 186853. | + | 107880.i | 0.820281 | + | 0.473590i | 0.850514 | − | 0.525953i | \(-0.176291\pi\) |
−0.0302321 | + | 0.999543i | \(0.509625\pi\) | |||||||
\(140\) | 2182.85 | + | 147.823i | 0.00941249 | + | 0.000637413i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −246347. | − | 8331.75i | −1.02524 | − | 0.0346749i | ||||
\(143\) | −28153.2 | −0.115130 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21311.7 | 0.0841779 | ||||||||
\(146\) | −129479. | − | 4379.13i | −0.502709 | − | 0.0170022i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −335845. | − | 22743.4i | −1.26033 | − | 0.0853495i | ||||
\(149\) | 192038. | + | 110873.i | 0.708633 | + | 0.409129i | 0.810555 | − | 0.585663i | \(-0.199166\pi\) |
−0.101922 | + | 0.994792i | \(0.532499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 364405. | − | 210389.i | 1.30059 | − | 0.750898i | 0.320088 | − | 0.947388i | \(-0.396288\pi\) |
0.980506 | + | 0.196490i | \(0.0629543\pi\) | |||||||
\(152\) | −7625.92 | + | 74929.8i | −0.0267722 | + | 0.263055i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6689.94 | − | 4170.13i | −0.0227311 | − | 0.0141693i | ||||
\(155\) | 15695.6 | + | 27185.6i | 0.0524745 | + | 0.0908886i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 110672. | − | 191690.i | 0.358335 | − | 0.620654i | −0.629348 | − | 0.777124i | \(-0.716678\pi\) |
0.987683 | + | 0.156470i | \(0.0500113\pi\) | |||||||
\(158\) | 184112. | − | 98153.8i | 0.586733 | − | 0.312798i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18945.1 | + | 15720.4i | 0.0585056 | + | 0.0485471i | ||||
\(161\) | 41615.4i | 0.126529i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 324082.i | 0.955402i | 0.878522 | + | 0.477701i | \(0.158530\pi\) | ||||
−0.878522 | + | 0.477701i | \(0.841470\pi\) | |||||||
\(164\) | −405184. | − | 272007.i | −1.17637 | − | 0.789716i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 146390. | + | 274591.i | 0.412325 | + | 0.773421i | ||||
\(167\) | −125104. | + | 216686.i | −0.347120 | + | 0.601229i | −0.985737 | − | 0.168296i | \(-0.946174\pi\) |
0.638617 | + | 0.769525i | \(0.279507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 132833. | + | 230073.i | 0.357757 | + | 0.619654i | ||||
\(170\) | −23702.7 | + | 38025.2i | −0.0629037 | + | 0.100913i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 225407. | − | 110552.i | 0.580960 | − | 0.284935i | ||||
\(173\) | 267332. | − | 154344.i | 0.679102 | − | 0.392080i | −0.120414 | − | 0.992724i | \(-0.538422\pi\) |
0.799517 | + | 0.600644i | \(0.205089\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 43286.5 | + | 24991.5i | 0.106846 | + | 0.0616875i | ||||
\(176\) | −33589.8 | − | 82097.4i | −0.0817382 | − | 0.199778i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7833.94 | − | 231628.i | 0.0185323 | − | 0.547950i | ||||
\(179\) | 7856.73 | 0.0183278 | 0.00916388 | − | 0.999958i | \(-0.497083\pi\) | ||||
0.00916388 | + | 0.999958i | \(0.497083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −449713. | −1.02033 | −0.510163 | − | 0.860078i | \(-0.670415\pi\) | ||||
−0.510163 | + | 0.860078i | \(0.670415\pi\) | |||||||
\(182\) | 999.756 | − | 29560.0i | 0.00223726 | − | 0.0661495i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −273988. | + | 379737.i | −0.596606 | + | 0.826873i | ||||
\(185\) | 38716.1 | + | 22352.7i | 0.0831691 | + | 0.0480177i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 139820. | − | 80725.1i | 0.292392 | − | 0.168812i | ||||
\(188\) | −401443. | − | 818512.i | −0.828379 | − | 1.68900i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5291.35 | − | 8488.66i | 0.0106337 | − | 0.0170591i | ||||
\(191\) | 255380. | + | 442331.i | 0.506527 | + | 0.877331i | 0.999971 | + | 0.00755354i | \(0.00240439\pi\) |
−0.493444 | + | 0.869777i | \(0.664262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 439991. | − | 762087.i | 0.850257 | − | 1.47269i | −0.0307186 | − | 0.999528i | \(-0.509780\pi\) |
0.880976 | − | 0.473161i | \(-0.156887\pi\) | |||||||
\(194\) | −124225. | − | 233015.i | −0.236975 | − | 0.444507i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −295151. | + | 439660.i | −0.548788 | + | 0.817479i | ||||
\(197\) | − | 162799.i | − | 0.298873i | −0.988771 | − | 0.149437i | \(-0.952254\pi\) | ||
0.988771 | − | 0.149437i | \(-0.0477460\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 786472.i | 1.40783i | 0.710283 | + | 0.703916i | \(0.248567\pi\) | ||||
−0.710283 | + | 0.703916i | \(0.751433\pi\) | |||||||
\(200\) | 230447. | + | 513036.i | 0.407376 | + | 0.906928i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −379429. | + | 202281.i | −0.654262 | + | 0.348800i | ||||
\(203\) | 40336.6 | − | 69865.0i | 0.0687004 | − | 0.118993i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32406.7 | + | 56130.1i | 0.0538580 | + | 0.0932848i | ||||
\(206\) | −18128.0 | − | 11299.9i | −0.0297633 | − | 0.0185527i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 203741. | − | 263151.i | 0.326527 | − | 0.421741i | ||||
\(209\) | −31213.1 | + | 18020.9i | −0.0494278 | + | 0.0285372i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −879851. | − | 507982.i | −1.36051 | − | 0.785493i | −0.370821 | − | 0.928704i | \(-0.620924\pi\) |
−0.989692 | + | 0.143212i | \(0.954257\pi\) | |||||||
\(212\) | 11855.4 | − | 175065.i | 0.0181166 | − | 0.267522i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −325969. | − | 11024.7i | −0.486566 | − | 0.0164562i | ||||
\(215\) | −33342.8 | −0.0491933 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 118828. | 0.171305 | ||||||||
\(218\) | 996757. | + | 33711.5i | 1.42052 | + | 0.0480438i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −795.958 | + | 11753.7i | −0.00110875 | + | 0.0163726i | ||||
\(221\) | 524588. | + | 302871.i | 0.722500 | + | 0.417136i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 201948. | − | 116595.i | 0.271942 | − | 0.157006i | −0.357828 | − | 0.933788i | \(-0.616482\pi\) |
0.629770 | + | 0.776782i | \(0.283149\pi\) | |||||||
\(224\) | 87392.7 | − | 32352.9i | 0.116374 | − | 0.0430817i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 620034. | + | 386494.i | 0.807504 | + | 0.503352i | ||||
\(227\) | 439493. | + | 761224.i | 0.566092 | + | 0.980501i | 0.996947 | + | 0.0780796i | \(0.0248788\pi\) |
−0.430855 | + | 0.902421i | \(0.641788\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −191288. | + | 331320.i | −0.241045 | + | 0.417503i | −0.961012 | − | 0.276506i | \(-0.910824\pi\) |
0.719967 | + | 0.694008i | \(0.244157\pi\) | |||||||
\(230\) | 54878.1 | − | 29256.6i | 0.0684037 | − | 0.0364673i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 828046. | − | 371944.i | 1.01003 | − | 0.453688i | ||||
\(233\) | − | 224357.i | − | 0.270738i | −0.990795 | − | 0.135369i | \(-0.956778\pi\) | ||
0.990795 | − | 0.135369i | \(-0.0432220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 121076.i | 0.143018i | ||||||||
\(236\) | 67816.1 | − | 101019.i | 0.0792598 | − | 0.118066i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 79793.8 | + | 149674.i | 0.0913118 | + | 0.171278i | ||||
\(239\) | 769108. | − | 1.33213e6i | 0.870949 | − | 1.50853i | 0.00993200 | − | 0.999951i | \(-0.496838\pi\) |
0.861017 | − | 0.508577i | \(-0.169828\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 692903. | + | 1.20014e6i | 0.768475 | + | 1.33104i | 0.938390 | + | 0.345579i | \(0.112318\pi\) |
−0.169914 | + | 0.985459i | \(0.554349\pi\) | |||||||
\(242\) | −459476. | + | 737115.i | −0.504341 | + | 0.809090i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 467543. | + | 953285.i | 0.502744 | + | 1.02506i | ||||
\(245\) | 60905.9 | − | 35164.1i | 0.0648253 | − | 0.0374269i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −117108. | − | 67612.4i | −0.122136 | − | 0.0705154i | ||||
\(248\) | 1.08430e6 | + | 782342.i | 1.11949 | + | 0.807732i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5064.28 | − | 149737.i | 0.00512469 | − | 0.151523i | ||||
\(251\) | −1.31402e6 | −1.31649 | −0.658246 | − | 0.752803i | \(-0.728701\pi\) | ||||
−0.658246 | + | 0.752803i | \(0.728701\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −224080. | −0.220091 | ||||||||
\(254\) | −8270.79 | + | 244544.i | −0.00804382 | + | 0.237834i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.01046e6 | + | 280160.i | 0.963646 | + | 0.267181i | ||||
\(257\) | −542479. | − | 313201.i | −0.512331 | − | 0.295794i | 0.221461 | − | 0.975169i | \(-0.428918\pi\) |
−0.733791 | + | 0.679375i | \(0.762251\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 146556. | − | 84614.0i | 0.135754 | − | 0.0783777i | ||||
\(260\) | −39683.6 | + | 19463.0i | −0.0364064 | + | 0.0178557i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 627315. | − | 1.00637e6i | 0.564589 | − | 0.905743i | ||||
\(263\) | −750127. | − | 1.29926e6i | −0.668722 | − | 1.15826i | −0.978262 | − | 0.207374i | \(-0.933508\pi\) |
0.309540 | − | 0.950887i | \(-0.399825\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11651.8 | + | 20181.4i | −0.0101924 | + | 0.0176538i | ||||
\(266\) | −17813.0 | − | 33412.8i | −0.0154359 | − | 0.0289540i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.76684e6 | − | 1.18611e6i | −1.50266 | − | 1.00876i | ||||
\(269\) | − | 264637.i | − | 0.222982i | −0.993765 | − | 0.111491i | \(-0.964437\pi\) | ||
0.993765 | − | 0.111491i | \(-0.0355626\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 650898.i | − | 0.538381i | −0.963087 | − | 0.269190i | \(-0.913244\pi\) | ||
0.963087 | − | 0.269190i | \(-0.0867561\pi\) | |||||||
\(272\) | −257311. | + | 1.89111e6i | −0.210880 | + | 1.54986i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 573886. | − | 305949.i | 0.461795 | − | 0.246191i | ||||
\(275\) | −134568. | + | 233079.i | −0.107303 | + | 0.185853i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 237366. | + | 411129.i | 0.185874 | + | 0.321943i | 0.943871 | − | 0.330315i | \(-0.107155\pi\) |
−0.757997 | + | 0.652258i | \(0.773822\pi\) | |||||||
\(278\) | −1.03577e6 | − | 645639.i | −0.803804 | − | 0.501046i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12312.8 | − | 1253.12i | −0.00938557 | − | 0.000955208i | ||||
\(281\) | −1.41561e6 | + | 817304.i | −1.06949 | + | 0.617473i | −0.928043 | − | 0.372472i | \(-0.878510\pi\) |
−0.141451 | + | 0.989945i | \(0.545177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.06078e6 | − | 612441.i | −0.787333 | − | 0.454567i | 0.0516895 | − | 0.998663i | \(-0.483539\pi\) |
−0.839023 | + | 0.544096i | \(0.816873\pi\) | |||||||
\(284\) | 1.39116e6 | + | 94209.1i | 1.02348 | + | 0.0693102i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 159168. | + | 5383.24i | 0.115064 | + | 0.00389160i | ||||
\(287\) | 245345. | 0.175821 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.05390e6 | −1.44655 | ||||||||
\(290\) | −120488. | − | 4075.06i | −0.0841298 | − | 0.00284537i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 731186. | + | 49515.9i | 0.501847 | + | 0.0339850i | ||||
\(293\) | −963120. | − | 556058.i | −0.655407 | − | 0.378400i | 0.135117 | − | 0.990830i | \(-0.456859\pi\) |
−0.790525 | + | 0.612430i | \(0.790192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13994.2 | + | 8079.55i | −0.00936253 | + | 0.00540546i | ||||
\(296\) | 1.89439e6 | + | 192800.i | 1.25673 | + | 0.127902i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.06451e6 | − | 663555.i | −0.694399 | − | 0.432849i | ||||
\(299\) | −420362. | − | 728088.i | −0.271923 | − | 0.470984i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −63107.9 | + | 109306.i | −0.0401483 | + | 0.0695389i | ||||
\(302\) | −2.10044e6 | + | 1.11978e6i | −1.32523 | + | 0.706506i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 57441.6 | − | 422167.i | 0.0356486 | − | 0.261999i | ||||
\(305\) | − | 141013.i | − | 0.0867977i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.54327e6i | − | 0.934537i | −0.884115 | − | 0.467269i | \(-0.845238\pi\) | ||
0.884115 | − | 0.467269i | \(-0.154762\pi\) | |||||||
\(308\) | 37025.0 | + | 24855.5i | 0.0222391 | + | 0.0149295i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −83538.7 | − | 156698.i | −0.0493723 | − | 0.0926104i | ||||
\(311\) | 1.17389e6 | − | 2.03323e6i | 0.688218 | − | 1.19203i | −0.284196 | − | 0.958766i | \(-0.591727\pi\) |
0.972414 | − | 0.233262i | \(-0.0749399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −705005. | − | 1.22110e6i | −0.406753 | − | 0.704517i | 0.587770 | − | 0.809028i | \(-0.300006\pi\) |
−0.994524 | + | 0.104510i | \(0.966672\pi\) | |||||||
\(314\) | −662351. | + | 1.06258e6i | −0.379109 | + | 0.608187i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.05967e6 | + | 519720.i | −0.596971 | + | 0.292787i | ||||
\(317\) | −1.72360e6 | + | 995122.i | −0.963360 | + | 0.556196i | −0.897206 | − | 0.441613i | \(-0.854406\pi\) |
−0.0661546 | + | 0.997809i | \(0.521073\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 376192. | + | 217194.i | 0.206982 | + | 0.119501i | ||||
\(320\) | −104103. | − | 92499.6i | −0.0568312 | − | 0.0504969i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7957.38 | − | 235278.i | 0.00427691 | − | 0.126457i | ||||
\(323\) | 775473. | 0.413581 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00977e6 | −0.530289 | ||||||||
\(326\) | 61968.5 | − | 1.83224e6i | 0.0322944 | − | 0.954856i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.23875e6 | + | 1.61530e6i | 1.14900 | + | 0.829028i | ||||
\(329\) | 396919. | + | 229161.i | 0.202168 | + | 0.116722i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.45201e6 | + | 1.41567e6i | −1.23013 | + | 0.710218i | −0.967058 | − | 0.254557i | \(-0.918070\pi\) |
−0.263076 | + | 0.964775i | \(0.584737\pi\) | |||||||
\(332\) | −775126. | − | 1.58042e6i | −0.385946 | − | 0.786916i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 748723. | − | 1.20114e6i | 0.367244 | − | 0.589152i | ||||
\(335\) | 141312. | + | 244760.i | 0.0687968 | + | 0.119160i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −360837. | + | 624988.i | −0.173076 | + | 0.299776i | −0.939494 | − | 0.342566i | \(-0.888704\pi\) |
0.766418 | + | 0.642342i | \(0.222037\pi\) | |||||||
\(338\) | −706993. | − | 1.32615e6i | −0.336607 | − | 0.631392i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 141277. | − | 210448.i | 0.0662788 | − | 0.0987295i | ||||
\(341\) | 639836.i | 0.297977i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 536603.i | − | 0.246274i | ||||||
\(344\) | −1.29550e6 | + | 581918.i | −0.590259 | + | 0.265134i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.54090e6 | + | 821486.i | −0.691967 | + | 0.368901i | ||||
\(347\) | −751022. | + | 1.30081e6i | −0.334833 | + | 0.579948i | −0.983453 | − | 0.181165i | \(-0.942013\pi\) |
0.648619 | + | 0.761113i | \(0.275347\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −506792. | − | 877790.i | −0.222724 | − | 0.385769i | 0.732910 | − | 0.680325i | \(-0.238161\pi\) |
−0.955634 | + | 0.294556i | \(0.904828\pi\) | |||||||
\(350\) | −239947. | − | 149569.i | −0.104700 | − | 0.0652638i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 174206. | + | 470570.i | 0.0749387 | + | 0.202427i | ||||
\(353\) | 1.78252e6 | − | 1.02914e6i | 0.761374 | − | 0.439579i | −0.0684149 | − | 0.997657i | \(-0.521794\pi\) |
0.829789 | + | 0.558077i | \(0.188461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −160372. | − | 92591.0i | −0.0675396 | − | 0.0389940i | ||||
\(356\) | −88580.2 | + | 1.30804e6i | −0.0370435 | + | 0.547010i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −44419.0 | − | 1502.30i | −0.0183173 | − | 0.000619513i | ||||
\(359\) | 301586. | 0.123502 | 0.0617512 | − | 0.998092i | \(-0.480331\pi\) | ||||
0.0617512 | + | 0.998092i | \(0.480331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.30298e6 | 0.930086 | ||||||||
\(362\) | 2.54251e6 | + | 85990.7i | 1.01974 | + | 0.0344889i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11304.5 | + | 166930.i | −0.00447196 | + | 0.0660361i | ||||
\(365\) | −84290.9 | − | 48665.4i | −0.0331168 | − | 0.0191200i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.93072e6 | − | 1.11470e6i | 0.748261 | − | 0.432009i | −0.0768040 | − | 0.997046i | \(-0.524472\pi\) |
0.825065 | + | 0.565037i | \(0.191138\pi\) | |||||||
\(368\) | 1.62164e6 | − | 2.09450e6i | 0.624215 | − | 0.806234i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −214612. | − | 133777.i | −0.0814985 | − | 0.0508016i | ||||
\(371\) | 44106.5 | + | 76394.7i | 0.0166367 | + | 0.0288156i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 898552. | − | 1.55634e6i | 0.334404 | − | 0.579204i | −0.648966 | − | 0.760817i | \(-0.724798\pi\) |
0.983370 | + | 0.181613i | \(0.0581318\pi\) | |||||||
\(374\) | −805925. | + | 429654.i | −0.297931 | + | 0.158833i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.11310e6 | + | 4.70432e6i | 0.770814 | + | 1.71604i | ||||
\(377\) | 1.62978e6i | 0.590574i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.14708e6i | 0.767804i | 0.923374 | + | 0.383902i | \(0.125420\pi\) | ||||
−0.923374 | + | 0.383902i | \(0.874580\pi\) | |||||||
\(380\) | −31538.4 | + | 46979.9i | −0.0112042 | + | 0.0166899i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.35924e6 | − | 2.54960e6i | −0.476582 | − | 0.893951i | ||||
\(383\) | −1.30237e6 | + | 2.25578e6i | −0.453669 | + | 0.785777i | −0.998611 | − | 0.0526965i | \(-0.983218\pi\) |
0.544942 | + | 0.838474i | \(0.316552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2961.27 | − | 5129.06i | −0.00101818 | − | 0.00176354i | ||||
\(386\) | −2.63326e6 | + | 4.22442e6i | −0.899551 | + | 1.44311i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 657764. | + | 1.34113e6i | 0.221815 | + | 0.452264i | ||||
\(389\) | 3.00548e6 | − | 1.73521e6i | 1.00702 | − | 0.581405i | 0.0967049 | − | 0.995313i | \(-0.469170\pi\) |
0.910319 | + | 0.413908i | \(0.135836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.17537e6 | + | 2.41065e6i | 1.38119 | + | 0.797429i | ||||
\(392\) | 1.75274e6 | − | 2.42923e6i | 0.576106 | − | 0.798462i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −31129.2 | + | 920406.i | −0.0101025 | + | 0.298703i | ||||
\(395\) | 156749. | 0.0505490 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.78885e6 | 1.84338 | 0.921692 | − | 0.387922i | \(-0.126807\pi\) | ||||
0.921692 | + | 0.387922i | \(0.126807\pi\) | |||||||
\(398\) | 150383. | − | 4.44642e6i | 0.0475874 | − | 1.40703i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.20476e6 | − | 2.94458e6i | −0.376487 | − | 0.920180i | ||||
\(401\) | 2.02846e6 | + | 1.17113e6i | 0.629950 | + | 0.363702i | 0.780733 | − | 0.624865i | \(-0.214846\pi\) |
−0.150782 | + | 0.988567i | \(0.548179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.07897e6 | + | 1.20029e6i | −0.637655 | + | 0.368150i | ||||
\(404\) | 2.18382e6 | − | 1.07107e6i | 0.665678 | − | 0.326485i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −241407. | + | 387278.i | −0.0726833 | + | 0.116602i | ||||
\(407\) | 455608. | + | 789137.i | 0.136334 | + | 0.236138i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.17070e6 | + | 2.02771e6i | −0.346048 | + | 0.599373i | −0.985544 | − | 0.169422i | \(-0.945810\pi\) |
0.639495 | + | 0.768795i | \(0.279143\pi\) | |||||||
\(410\) | −172483. | − | 323535.i | −0.0506741 | − | 0.0950520i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 100328. | + | 67351.9i | 0.0291192 | + | 0.0195482i | ||||
\(413\) | 61168.6i | 0.0176463i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 233781.i | 0.0666328i | ||||||||
\(416\) | −1.20219e6 | + | 1.44880e6i | −0.340596 | + | 0.410463i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 179913. | − | 95915.0i | 0.0503642 | − | 0.0268501i | ||||
\(419\) | −2.33383e6 | + | 4.04232e6i | −0.649434 | + | 1.12485i | 0.333824 | + | 0.942635i | \(0.391661\pi\) |
−0.983258 | + | 0.182217i | \(0.941673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.03900e6 | + | 3.53165e6i | 0.560676 | + | 0.971119i | 0.997438 | + | 0.0715416i | \(0.0227919\pi\) |
−0.436762 | + | 0.899577i | \(0.643875\pi\) | |||||||
\(422\) | 4.87721e6 | + | 3.04018e6i | 1.33318 | + | 0.831032i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −100500. | + | 987484.i | −0.0271489 | + | 0.266757i | ||||
\(425\) | 5.01490e6 | − | 2.89536e6i | 1.34676 | − | 0.777553i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −462274. | − | 266894.i | −0.122696 | − | 0.0708385i | ||||
\(428\) | 1.84080e6 | + | 124658.i | 0.485731 | + | 0.0328937i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 188508. | + | 6375.56i | 0.0491652 | + | 0.00166283i | ||||
\(431\) | 4.54361e6 | 1.17817 | 0.589085 | − | 0.808071i | \(-0.299488\pi\) | ||||
0.589085 | + | 0.808071i | \(0.299488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6726.40 | −0.00172410 | −0.000862051 | − | 1.00000i | \(-0.500274\pi\) | ||||
−0.000862051 | 1.00000i | \(0.500274\pi\) | ||||||||
\(434\) | −671809. | − | 22721.4i | −0.171207 | − | 0.00579043i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.62884e6 | − | 381184.i | −1.41809 | − | 0.0960326i | ||||
\(437\) | −932101. | − | 538148.i | −0.233485 | − | 0.134803i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.27223e6 | − | 2.46657e6i | 1.05802 | − | 0.610847i | 0.133134 | − | 0.991098i | \(-0.457496\pi\) |
0.924883 | + | 0.380251i | \(0.124162\pi\) | |||||||
\(440\) | 6747.49 | − | 66298.7i | 0.00166154 | − | 0.0163258i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.90791e6 | − | 1.81263e6i | −0.707987 | − | 0.441319i | ||||
\(443\) | 2.52747e6 | + | 4.37771e6i | 0.611895 | + | 1.05983i | 0.990921 | + | 0.134448i | \(0.0429260\pi\) |
−0.379025 | + | 0.925386i | \(0.623741\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 87058.8 | − | 150790.i | 0.0208407 | − | 0.0360972i | ||||
\(446\) | −1.16403e6 | + | 620567.i | −0.277094 | + | 0.147724i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −500271. | + | 166201.i | −0.117763 | + | 0.0391235i | ||||
\(449\) | − | 3.95256e6i | − | 0.925257i | −0.886552 | − | 0.462628i | \(-0.846906\pi\) | ||
0.886552 | − | 0.462628i | \(-0.153094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.32107e6i | 0.305833i | ||||||||
\(452\) | −3.43154e6 | − | 2.30365e6i | −0.790028 | − | 0.530360i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.33917e6 | − | 4.38771e6i | −0.532626 | − | 0.999076i | ||||
\(455\) | 11110.3 | − | 19243.6i | 0.00251593 | − | 0.00435772i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.74368e6 | − | 6.48424e6i | −0.838509 | − | 1.45234i | −0.891141 | − | 0.453726i | \(-0.850094\pi\) |
0.0526320 | − | 0.998614i | \(-0.483239\pi\) | |||||||
\(458\) | 1.14482e6 | − | 1.83658e6i | 0.255020 | − | 0.409116i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −315854. | + | 154912.i | −0.0695973 | + | 0.0341343i | ||||
\(461\) | −4.43539e6 | + | 2.56077e6i | −0.972029 | + | 0.561201i | −0.899854 | − | 0.436191i | \(-0.856327\pi\) |
−0.0721745 | + | 0.997392i | \(0.522994\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.47662e6 | + | 2.00723e6i | 0.753711 | + | 0.435155i | 0.827033 | − | 0.562153i | \(-0.190027\pi\) |
−0.0733224 | + | 0.997308i | \(0.523360\pi\) | |||||||
\(464\) | −4.75258e6 | + | 1.94450e6i | −1.02479 | + | 0.419288i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −42899.8 | + | 1.26843e6i | −0.00915146 | + | 0.270583i | ||||
\(467\) | −5.43636e6 | −1.15350 | −0.576748 | − | 0.816922i | \(-0.695679\pi\) | ||||
−0.576748 | + | 0.816922i | \(0.695679\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.06985e6 | 0.224590 | ||||||||
\(470\) | 23151.3 | − | 684521.i | 0.00483427 | − | 0.142936i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −402723. | + | 558159.i | −0.0832054 | + | 0.115319i | ||||
\(473\) | −588564. | − | 339807.i | −0.120960 | − | 0.0698361i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.11952e6 | + | 646353.i | −0.227665 | + | 0.131443i | ||||
\(476\) | −422505. | − | 861455.i | −0.0854701 | − | 0.174267i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.60297e6 | + | 7.38432e6i | −0.921442 | + | 1.47823i | ||||
\(479\) | −4.63944e6 | − | 8.03575e6i | −0.923904 | − | 1.60025i | −0.793315 | − | 0.608812i | \(-0.791646\pi\) |
−0.130589 | − | 0.991437i | \(-0.541687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70939e6 | + | 2.96075e6i | −0.336882 | + | 0.583497i | ||||
\(482\) | −3.68793e6 | − | 6.91765e6i | −0.723045 | − | 1.35625i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.73865e6 | − | 4.07951e6i | 0.531401 | − | 0.791580i | ||||
\(485\) | − | 198384.i | − | 0.0382958i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.35999e6i | 0.450908i | 0.974254 | + | 0.225454i | \(0.0723865\pi\) | ||||
−0.974254 | + | 0.225454i | \(0.927614\pi\) | |||||||
\(488\) | −2.46103e6 | − | 5.47891e6i | −0.467808 | − | 1.04147i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −351063. | + | 187158.i | −0.0660533 | + | 0.0352143i | ||||
\(491\) | −4.26271e6 | + | 7.38323e6i | −0.797961 | + | 1.38211i | 0.122980 | + | 0.992409i | \(0.460755\pi\) |
−0.920942 | + | 0.389701i | \(0.872579\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.67314e6 | − | 8.09412e6i | −0.865947 | − | 1.49986i | ||||
\(494\) | 649156. | + | 404647.i | 0.119683 | + | 0.0746035i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.98061e6 | − | 4.63040e6i | −1.09154 | − | 0.845111i | ||||
\(497\) | −607073. | + | 350494.i | −0.110243 | + | 0.0636486i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 218746. | + | 126293.i | 0.0393268 | + | 0.0227054i | 0.519535 | − | 0.854449i | \(-0.326105\pi\) |
−0.480208 | + | 0.877155i | \(0.659439\pi\) | |||||||
\(500\) | −57263.0 | + | 845587.i | −0.0102435 | + | 0.151263i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.42898e6 | + | 251257.i | 1.31574 | + | 0.0444999i | ||||
\(503\) | 6.25307e6 | 1.10198 | 0.550989 | − | 0.834512i | \(-0.314251\pi\) | ||||
0.550989 | + | 0.834512i | \(0.314251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −323037. | −0.0563669 | ||||||||
\(506\) | 1.26687e6 | + | 42846.9i | 0.219965 | + | 0.00743949i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 93519.8 | − | 1.38098e6i | 0.0160785 | − | 0.237426i | ||||
\(509\) | −431856. | − | 249332.i | −0.0738830 | − | 0.0426564i | 0.462603 | − | 0.886565i | \(-0.346915\pi\) |
−0.536486 | + | 0.843909i | \(0.680249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −319074. | + | 184218.i | −0.0540555 | + | 0.0312090i | ||||
\(512\) | −5.65917e6 | − | 1.77713e6i | −0.954064 | − | 0.299601i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.00708e6 | + | 1.87445e6i | 0.502039 | + | 0.312943i | ||||
\(515\) | −8024.25 | − | 13898.4i | −0.00133317 | − | 0.00230912i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.23393e6 | + | 2.13723e6i | −0.203032 | + | 0.351661i | ||||
\(518\) | −844750. | + | 450352.i | −0.138326 | + | 0.0737442i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 228077. | − | 102448.i | 0.0369891 | − | 0.0166149i | ||||
\(521\) | 9.81352e6i | 1.58391i | 0.610579 | + | 0.791955i | \(0.290937\pi\) | ||||
−0.610579 | + | 0.791955i | \(0.709063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.10853e7i | − | 1.77211i | −0.463576 | − | 0.886057i | \(-0.653434\pi\) | ||
0.463576 | − | 0.886057i | \(-0.346566\pi\) | |||||||
\(524\) | −3.73903e6 | + | 5.56969e6i | −0.594882 | + | 0.886141i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.99250e6 | + | 7.48895e6i | 0.629188 | + | 1.18020i | ||||
\(527\) | 6.88333e6 | − | 1.19223e7i | 1.07962 | − | 1.86996i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −127624. | − | 221050.i | −0.0198286 | − | 0.0343441i | ||||
\(530\) | 69733.5 | − | 111870.i | 0.0107833 | − | 0.0172991i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 94319.1 | + | 192310.i | 0.0144484 | + | 0.0294592i | ||||
\(533\) | −4.29246e6 | + | 2.47825e6i | −0.654467 | + | 0.377857i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −212206. | − | 122517.i | −0.0320534 | − | 0.0185060i | ||||
\(536\) | 9.76227e6 | + | 7.04368e6i | 1.46770 | + | 1.05898i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −50601.9 | + | 1.49616e6i | −0.00753722 | + | 0.222855i | ||||
\(539\) | 1.43347e6 | 0.212529 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.27509e6 | 0.334200 | 0.167100 | − | 0.985940i | \(-0.446560\pi\) | ||||
0.167100 | + | 0.985940i | \(0.446560\pi\) | |||||||
\(542\) | −124460. | + | 3.67993e6i | −0.0181983 | + | 0.538073i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.81634e6 | − | 1.06424e7i | 0.263148 | − | 1.54185i | ||||
\(545\) | 648891. | + | 374637.i | 0.0935794 | + | 0.0540281i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.20659e6 | + | 4.16072e6i | −1.02982 | + | 0.594567i | −0.916933 | − | 0.399041i | \(-0.869343\pi\) |
−0.112887 | + | 0.993608i | \(0.536010\pi\) | |||||||
\(548\) | −3.30303e6 | + | 1.61999e6i | −0.469852 | + | 0.230441i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 805364. | − | 1.29201e6i | 0.113523 | − | 0.182120i | ||||
\(551\) | 1.04322e6 | + | 1.80691e6i | 0.146385 | + | 0.253547i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 296679. | − | 513863.i | 0.0412547 | − | 0.0714553i | ||||
\(554\) | −1.26336e6 | − | 2.36976e6i | −0.174885 | − | 0.328042i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.73239e6 | + | 3.84825e6i | 0.786409 | + | 0.527930i | ||||
\(557\) | 1.46783e6i | 0.200465i | 0.994964 | + | 0.100232i | \(0.0319586\pi\) | ||||
−0.994964 | + | 0.100232i | \(0.968041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.54984e6i | − | 0.345130i | ||||||
\(560\) | 69372.1 | + | 9439.03i | 0.00934791 | + | 0.00127191i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.15962e6 | − | 4.35005e6i | 1.08976 | − | 0.580969i | ||||
\(563\) | 1.07987e6 | − | 1.87039e6i | 0.143582 | − | 0.248691i | −0.785261 | − | 0.619165i | \(-0.787471\pi\) |
0.928843 | + | 0.370474i | \(0.120805\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 274455. | + | 475370.i | 0.0361701 | + | 0.0626485i | ||||
\(566\) | 5.88014e6 | + | 3.66534e6i | 0.771518 | + | 0.480921i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.84707e6 | − | 798630.i | −1.02056 | − | 0.103866i | ||||
\(569\) | −2.42463e6 | + | 1.39986e6i | −0.313954 | + | 0.181261i | −0.648694 | − | 0.761049i | \(-0.724685\pi\) |
0.334741 | + | 0.942310i | \(0.391351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.90022e6 | − | 5.71589e6i | −1.27073 | − | 0.733658i | −0.295607 | − | 0.955310i | \(-0.595522\pi\) |
−0.975126 | + | 0.221651i | \(0.928855\pi\) | |||||||
\(572\) | −898844. | − | 60869.6i | −0.114867 | − | 0.00777876i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.38709e6 | − | 46912.9i | −0.175721 | − | 0.00594309i | ||||
\(575\) | −8.03706e6 | −1.01374 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 669533. | 0.0837206 | 0.0418603 | − | 0.999123i | \(-0.486672\pi\) | ||||
0.0418603 | + | 0.999123i | \(0.486672\pi\) | |||||||
\(578\) | 1.16119e7 | + | 392730.i | 1.44572 | + | 0.0488961i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 680416. | + | 46077.7i | 0.0839855 | + | 0.00568749i | ||||
\(581\) | 766391. | + | 442476.i | 0.0941911 | + | 0.0543813i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −411351. | + | 237494.i | −0.0501235 | + | 0.0289388i | ||||
\(584\) | −4.12438e6 | − | 419756.i | −0.500411 | − | 0.0509289i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.33879e6 | + | 3.32790e6i | 0.642242 | + | 0.400337i | ||||
\(587\) | 197174. | + | 341516.i | 0.0236187 | + | 0.0409087i | 0.877593 | − | 0.479406i | \(-0.159148\pi\) |
−0.853974 | + | 0.520315i | \(0.825815\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.53662e6 | + | 2.66151e6i | −0.182507 | + | 0.316111i | ||||
\(590\) | 80662.8 | − | 43002.9i | 0.00953989 | − | 0.00508590i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.06733e7 | − | 1.45225e6i | −1.25168 | − | 0.170309i | ||||
\(593\) | − | 5.00148e6i | − | 0.584066i | −0.956408 | − | 0.292033i | \(-0.905668\pi\) | ||
0.956408 | − | 0.292033i | \(-0.0943317\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 127429.i | 0.0147562i | ||||||||
\(596\) | 5.89145e6 | + | 3.95504e6i | 0.679371 | + | 0.456073i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.23735e6 | + | 4.19671e6i | 0.255847 | + | 0.479906i | ||||
\(599\) | 5.30363e6 | − | 9.18615e6i | 0.603957 | − | 1.04608i | −0.388259 | − | 0.921550i | \(-0.626923\pi\) |
0.992215 | − | 0.124533i | \(-0.0397434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.48253e6 | + | 6.03191e6i | 0.393286 | + | 0.681191i | 0.992881 | − | 0.119113i | \(-0.0380050\pi\) |
−0.599595 | + | 0.800304i | \(0.704672\pi\) | |||||||
\(602\) | 377689. | − | 605908.i | 0.0424759 | − | 0.0681421i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.20892e7 | − | 5.92919e6i | 1.34836 | − | 0.661307i | ||||
\(605\) | −565134. | + | 326280.i | −0.0627715 | + | 0.0362412i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.36935e7 | + | 7.90597e6i | 1.50850 | + | 0.870930i | 0.999951 | + | 0.00989422i | \(0.00314948\pi\) |
0.508544 | + | 0.861036i | \(0.330184\pi\) | |||||||
\(608\) | −405477. | + | 2.37579e6i | −0.0444843 | + | 0.260645i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26963.3 | + | 797231.i | −0.00293392 | + | 0.0867481i | ||||
\(611\) | −9.25912e6 | −1.00338 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 133521. | 0.0143515 | 0.00717575 | − | 0.999974i | \(-0.497716\pi\) | ||||
0.00717575 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(614\) | −295093. | + | 8.72508e6i | −0.0315891 | + | 0.934003i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −204573. | − | 147603.i | −0.0217218 | − | 0.0156727i | ||||
\(617\) | −1.06772e7 | − | 6.16447e6i | −1.12913 | − | 0.651902i | −0.185413 | − | 0.982661i | \(-0.559362\pi\) |
−0.943715 | + | 0.330758i | \(0.892696\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.56059e6 | + | 4.94246e6i | −0.898001 | + | 0.518461i | −0.876551 | − | 0.481309i | \(-0.840162\pi\) |
−0.0214502 | + | 0.999770i | \(0.506828\pi\) | |||||||
\(620\) | 442334. | + | 901886.i | 0.0462137 | + | 0.0942263i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.02550e6 | + | 1.12707e7i | −0.728117 | + | 1.16808i | ||||
\(623\) | −329552. | − | 570801.i | −0.0340176 | − | 0.0589202i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.79831e6 | + | 8.31092e6i | −0.491347 | + | 0.851038i | ||||
\(626\) | 3.75234e6 | + | 7.03847e6i | 0.382707 | + | 0.717864i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.94786e6 | − | 5.88077e6i | 0.399450 | − | 0.595025i | ||||
\(629\) | − | 1.96057e7i | − | 1.97586i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.28910e7i | − | 1.28888i | −0.764653 | − | 0.644442i | \(-0.777090\pi\) | ||
0.764653 | − | 0.644442i | \(-0.222910\pi\) | |||||||
\(632\) | 6.09035e6 | − | 2.73568e6i | 0.606526 | − | 0.272441i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.93487e6 | − | 5.29647e6i | 0.981610 | − | 0.523315i | ||||
\(635\) | −91913.5 | + | 159199.i | −0.00904576 | + | 0.0156677i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.68911e6 | + | 4.65768e6i | 0.262579 | + | 0.454801i | ||||
\(638\) | −2.08532e6 | − | 1.29987e6i | −0.202824 | − | 0.126429i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 570870. | + | 542863.i | 0.0550918 | + | 0.0523891i | ||||
\(641\) | 7.67906e6 | − | 4.43351e6i | 0.738181 | − | 0.426189i | −0.0832264 | − | 0.996531i | \(-0.526522\pi\) |
0.821408 | + | 0.570342i | \(0.193189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.18917e6 | − | 5.30537e6i | −0.876494 | − | 0.506044i | −0.00699288 | − | 0.999976i | \(-0.502226\pi\) |
−0.869501 | + | 0.493932i | \(0.835559\pi\) | |||||||
\(644\) | −89976.1 | + | 1.32865e6i | −0.00854894 | + | 0.126240i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.38423e6 | − | 148280.i | −0.413345 | − | 0.0139798i | ||||
\(647\) | 2.37142e6 | 0.222714 | 0.111357 | − | 0.993780i | \(-0.464480\pi\) | ||||
0.111357 | + | 0.993780i | \(0.464480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −329365. | −0.0306949 | ||||||||
\(650\) | 5.70884e6 | + | 193080.i | 0.529986 | + | 0.0179248i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −700693. | + | 1.03469e7i | −0.0645519 | + | 0.953219i | ||||
\(653\) | 8.07136e6 | + | 4.66000e6i | 0.740737 | + | 0.427665i | 0.822337 | − | 0.569001i | \(-0.192670\pi\) |
−0.0816004 | + | 0.996665i | \(0.526003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 771568. | − | 445465.i | 0.0702701 | − | 0.0405705i | ||||
\(656\) | −1.23482e7 | − | 9.56039e6i | −1.12032 | − | 0.867393i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.20021e6 | − | 1.37149e6i | −0.198107 | − | 0.123489i | ||||
\(659\) | 971185. | + | 1.68214e6i | 0.0871141 | + | 0.150886i | 0.906290 | − | 0.422656i | \(-0.138902\pi\) |
−0.819176 | + | 0.573542i | \(0.805569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.93142e6 | + | 1.54697e7i | −0.795091 | + | 1.37714i | 0.127690 | + | 0.991814i | \(0.459244\pi\) |
−0.922781 | + | 0.385324i | \(0.874090\pi\) | |||||||
\(662\) | 1.41334e7 | − | 7.53480e6i | 1.25344 | − | 0.668232i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.08007e6 | + | 9.08333e6i | 0.359127 | + | 0.799512i | ||||
\(665\) | − | 28446.9i | − | 0.00249449i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.29719e7i | 1.12899i | ||||||||
\(668\) | −4.46267e6 | + | 6.64763e6i | −0.386949 | + | 0.576402i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −752126. | − | 1.41080e6i | −0.0647297 | − | 0.121417i | ||||
\(671\) | 1.43710e6 | − | 2.48914e6i | 0.123220 | − | 0.213424i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.31863e6 | + | 5.74803e6i | 0.282436 | + | 0.489194i | 0.971984 | − | 0.235046i | \(-0.0755241\pi\) |
−0.689548 | + | 0.724240i | \(0.742191\pi\) | |||||||
\(674\) | 2.15954e6 | − | 3.46445e6i | 0.183110 | − | 0.293754i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.74350e6 | + | 7.63271e6i | 0.315073 | + | 0.642409i | ||||
\(677\) | 2.38918e6 | − | 1.37940e6i | 0.200345 | − | 0.115669i | −0.396472 | − | 0.918047i | \(-0.629765\pi\) |
0.596816 | + | 0.802378i | \(0.296432\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −650351. | − | 375480.i | −0.0541344 | − | 0.0312545i | ||||
\(680\) | −838968. | + | 1.16278e6i | −0.0695782 | + | 0.0964327i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 122344. | − | 3.61739e6i | 0.0100722 | − | 0.297807i | ||||
\(683\) | 462361. | 0.0379253 | 0.0189627 | − | 0.999820i | \(-0.493964\pi\) | ||||
0.0189627 | + | 0.999820i | \(0.493964\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 488594. | 0.0397852 | ||||||||
\(686\) | −102605. | + | 3.03375e6i | −0.00832451 | + | 0.246133i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.43556e6 | − | 3.04223e6i | 0.598884 | − | 0.245031i | ||||
\(689\) | −1.54334e6 | − | 891048.i | −0.123855 | − | 0.0715078i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.14382e6 | − | 2.39243e6i | 0.330146 | − | 0.190610i | −0.325760 | − | 0.945452i | \(-0.605620\pi\) |
0.655906 | + | 0.754843i | \(0.272287\pi\) | |||||||
\(692\) | 8.86877e6 | − | 4.34973e6i | 0.704041 | − | 0.345300i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.49472e6 | − | 7.21067e6i | 0.354245 | − | 0.568299i | ||||
\(695\) | −458477. | − | 794106.i | −0.0360044 | − | 0.0623615i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.42120e7 | − | 2.46160e7i | 1.10809 | − | 1.91926i | ||||
\(698\) | 2.69737e6 | + | 5.05960e6i | 0.209557 | + | 0.393077i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.32797e6 | + | 891490.i | 0.102434 | + | 0.0687656i | ||||
\(701\) | 1.31247e7i | 1.00877i | 0.863478 | + | 0.504387i | \(0.168281\pi\) | ||||
−0.863478 | + | 0.504387i | \(0.831719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.37673e6i | 0.334012i | ||||||||
\(704\) | −894915. | − | 2.69374e6i | −0.0680534 | − | 0.204844i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.02745e7 | + | 5.47752e6i | −0.775797 | + | 0.413592i | ||||
\(707\) | −611412. | + | 1.05900e6i | −0.0460029 | + | 0.0796794i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.98415e6 | − | 6.90074e6i | −0.297659 | − | 0.515561i | 0.677941 | − | 0.735117i | \(-0.262873\pi\) |
−0.975600 | + | 0.219555i | \(0.929539\pi\) | |||||||
\(710\) | 888980. | + | 554140.i | 0.0661830 | + | 0.0412547i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 750912. | − | 7.37822e6i | 0.0555123 | − | 0.545446i | ||||
\(713\) | −1.65472e7 | + | 9.55353e6i | −1.21899 | + | 0.703785i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 103618. | + | 59824.1i | 0.00758004 | + | 0.00437634i | ||||
\(716\) | 250841. | + | 16986.9i | 0.0182859 | + | 0.00123832i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.70505e6 | − | 57667.0i | −0.123432 | − | 0.00417461i | ||||
\(719\) | 5.58804e6 | 0.403123 | 0.201561 | − | 0.979476i | \(-0.435398\pi\) | ||||
0.201561 | + | 0.979476i | \(0.435398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60749.9 | −0.00435219 | ||||||||
\(722\) | −1.30202e7 | − | 440359.i | −0.929554 | − | 0.0314386i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.43579e7 | − | 972317.i | −1.01799 | − | 0.0689385i | ||||
\(725\) | 1.34928e7 | + | 7.79008e6i | 0.953362 | + | 0.550424i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.72597e6 | − | 1.57384e6i | 0.191287 | − | 0.110439i | −0.401298 | − | 0.915948i | \(-0.631441\pi\) |
0.592585 | + | 0.805508i | \(0.298107\pi\) | |||||||
\(728\) | 95830.4 | − | 941598.i | 0.00670154 | − | 0.0658472i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 467244. | + | 291253.i | 0.0324516 | + | 0.0202285i | ||||
\(731\) | 7.31128e6 | + | 1.26635e7i | 0.506057 | + | 0.876517i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.20330e7 | − | 2.08418e7i | 0.827209 | − | 1.43277i | −0.0730095 | − | 0.997331i | \(-0.523260\pi\) |
0.900219 | − | 0.435438i | \(-0.143406\pi\) | |||||||
\(734\) | −1.11287e7 | + | 5.93291e6i | −0.762436 | + | 0.406469i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.56861e6 | + | 1.15314e7i | −0.651110 | + | 0.784674i | ||||
\(737\) | 5.76065e6i | 0.390663i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.89450e6i | − | 0.329683i | −0.986320 | − | 0.164842i | \(-0.947289\pi\) | ||
0.986320 | − | 0.164842i | \(-0.0527113\pi\) | |||||||
\(740\) | 1.18776e6 | + | 797361.i | 0.0797348 | + | 0.0535273i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −234754. | − | 440340.i | −0.0156532 | − | 0.0293615i | ||||
\(743\) | −2.80417e6 | + | 4.85696e6i | −0.186351 | + | 0.322770i | −0.944031 | − | 0.329857i | \(-0.893000\pi\) |
0.757680 | + | 0.652626i | \(0.226333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −471200. | − | 816142.i | −0.0311039 | − | 0.0538735i | ||||
\(746\) | −5.37766e6 | + | 8.62713e6i | −0.353791 | + | 0.567570i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.63855e6 | − | 2.27500e6i | 0.303129 | − | 0.148671i | ||||
\(749\) | −803285. | + | 463777.i | −0.0523197 | + | 0.0302068i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.23051e7 | − | 7.10437e6i | −0.796134 | − | 0.459648i | 0.0459832 | − | 0.998942i | \(-0.485358\pi\) |
−0.842118 | + | 0.539294i | \(0.818691\pi\) | |||||||
\(752\) | −1.10471e7 | − | 2.70005e7i | −0.712368 | − | 1.74111i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 311633. | − | 9.21414e6i | 0.0199625 | − | 0.590237i | ||||
\(755\) | −1.78826e6 | −0.114173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.75241e7 | −1.11147 | −0.555733 | − | 0.831361i | \(-0.687562\pi\) | ||||
−0.555733 | + | 0.831361i | \(0.687562\pi\) | |||||||
\(758\) | 410548. | − | 1.21388e7i | 0.0259532 | − | 0.767365i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 187289. | − | 259576.i | 0.0117619 | − | 0.0163016i | ||||
\(761\) | 9.78403e6 | + | 5.64882e6i | 0.612430 | + | 0.353587i | 0.773916 | − | 0.633288i | \(-0.218295\pi\) |
−0.161486 | + | 0.986875i | \(0.551629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.45631e6 | − | 1.41815e6i | 0.152747 | − | 0.0881883i | ||||
\(764\) | 7.19712e6 | + | 1.46744e7i | 0.446093 | + | 0.909550i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.79446e6 | − | 1.25043e7i | 0.479970 | − | 0.769993i | ||||
\(767\) | −617871. | − | 1.07018e6i | −0.0379236 | − | 0.0656855i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −465579. | + | 806407.i | −0.0283908 | + | 0.0491743i | −0.879872 | − | 0.475211i | \(-0.842372\pi\) |
0.851481 | + | 0.524386i | \(0.175705\pi\) | |||||||
\(770\) | 15761.1 | + | 29564.0i | 0.000957989 | + | 0.00179695i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.56952e7 | − | 2.33797e7i | 0.947817 | − | 1.41188i | ||||
\(773\) | − | 4.59758e6i | − | 0.276745i | −0.990380 | − | 0.138373i | \(-0.955813\pi\) | ||
0.990380 | − | 0.138373i | \(-0.0441872\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.29489e7i | 1.37249i | ||||||||
\(776\) | −3.46231e6 | − | 7.70802e6i | −0.206401 | − | 0.459503i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.73236e7 | + | 9.23556e6i | −1.02610 | + | 0.547034i | ||||
\(779\) | −3.17266e6 | + | 5.49522e6i | −0.187318 | + | 0.324445i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.88725e6 | − | 3.26881e6i | −0.110714 | − | 0.191762i | ||||
\(782\) | −2.31450e7 | − | 1.44273e7i | −1.35344 | − | 0.843660i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.03738e7 | + | 1.33988e7i | −0.602767 | + | 0.778532i | ||||
\(785\) | −814662. | + | 470345.i | −0.0471849 | + | 0.0272422i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.46443e6 | + | 4.30959e6i | 0.429596 | + | 0.248027i | 0.699174 | − | 0.714951i | \(-0.253551\pi\) |
−0.269579 | + | 0.962978i | \(0.586884\pi\) | |||||||
\(788\) | 351986. | − | 5.19768e6i | 0.0201934 | − | 0.298190i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −886201. | − | 29972.4i | −0.0505201 | − | 0.00170865i | ||||
\(791\) | 2.07784e6 | 0.118079 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07837e7 | 0.608954 | ||||||||
\(794\) | −3.27280e7 | − | 1.10690e6i | −1.84233 | − | 0.0623099i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.70042e6 | + | 2.51096e7i | −0.0951203 | + | 1.40461i | ||||
\(797\) | −7.54210e6 | − | 4.35443e6i | −0.420578 | − | 0.242821i | 0.274747 | − | 0.961517i | \(-0.411406\pi\) |
−0.695324 | + | 0.718696i | \(0.744739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.59845e7 | − | 2.65492e7i | 2.54826 | − | 1.47124i | ||||
\(800\) | 6.24822e6 | + | 1.68779e7i | 0.345169 | + | 0.932380i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.12442e7 | − | 7.00902e6i | −0.617297 | − | 0.384788i | ||||
\(803\) | −991930. | − | 1.71807e6i | −0.0542865 | − | 0.0940270i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 88430.7 | − | 153166.i | 0.00480965 | − | 0.00833055i | ||||
\(806\) | 1.19832e7 | − | 6.38849e6i | 0.649735 | − | 0.346386i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.25513e7 | + | 5.63783e6i | −0.676334 | + | 0.303797i | ||||
\(809\) | 1.21590e7i | 0.653169i | 0.945168 | + | 0.326584i | \(0.105898\pi\) | ||||
−0.945168 | + | 0.326584i | \(0.894102\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.14341e7i | 1.14433i | 0.820137 | + | 0.572167i | \(0.193897\pi\) | ||||
−0.820137 | + | 0.572167i | \(0.806103\pi\) | |||||||
\(812\) | 1.43888e6 | − | 2.14336e6i | 0.0765831 | − | 0.114079i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.42494e6 | − | 4.54860e6i | −0.128275 | − | 0.240612i | ||||
\(815\) | 688658. | − | 1.19279e6i | 0.0363170 | − | 0.0629029i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.63215e6 | − | 2.82697e6i | −0.0855473 | − | 0.148172i | ||||
\(818\) | 7.00641e6 | − | 1.12400e7i | 0.366110 | − | 0.587333i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 913287. | + | 1.86212e6i | 0.0474322 | + | 0.0967106i | ||||
\(821\) | 1.88546e7 | − | 1.08857e7i | 0.976248 | − | 0.563637i | 0.0751127 | − | 0.997175i | \(-0.476068\pi\) |
0.901135 | + | 0.433538i | \(0.142735\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.63030e7 | + | 9.41255e6i | 0.839012 | + | 0.484404i | 0.856928 | − | 0.515436i | \(-0.172370\pi\) |
−0.0179161 | + | 0.999839i | \(0.505703\pi\) | |||||||
\(824\) | −554338. | − | 399966.i | −0.0284418 | − | 0.0205213i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11696.2 | − | 345824.i | 0.000596478 | − | 0.0176362i | ||||
\(827\) | −2.05084e7 | −1.04272 | −0.521361 | − | 0.853336i | \(-0.674576\pi\) | ||||
−0.521361 | + | 0.853336i | \(0.674576\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.27151e7 | −1.65334 | −0.826669 | − | 0.562688i | \(-0.809767\pi\) | ||||
−0.826669 | + | 0.562688i | \(0.809767\pi\) | |||||||
\(830\) | 44701.7 | − | 1.32171e6i | 0.00225231 | − | 0.0665947i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.07375e6 | − | 7.96108e6i | 0.354276 | − | 0.398716i | ||||
\(833\) | −2.67104e7 | − | 1.54213e7i | −1.33373 | − | 0.770030i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 920894. | − | 531679.i | 0.0457082 | − | 0.0263896i | ||||
\(836\) | −1.03550e6 | + | 507866.i | −0.0512430 | + | 0.0251324i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.39676e7 | − | 2.24075e7i | 0.687085 | − | 1.10226i | ||||
\(839\) | 1.82802e6 | + | 3.16623e6i | 0.0896555 | + | 0.155288i | 0.907366 | − | 0.420342i | \(-0.138090\pi\) |
−0.817710 | + | 0.575630i | \(0.804757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.31771e6 | − | 4.01440e6i | 0.112998 | − | 0.195718i | ||||
\(842\) | −1.08524e7 | − | 2.03565e7i | −0.527530 | − | 0.989516i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.69926e7 | − | 1.81206e7i | −1.30433 | − | 0.875621i | ||||
\(845\) | − | 1.12905e6i | − | 0.0543966i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.47020e6i | 0.118310i | ||||||||
\(848\) | 757010. | − | 5.56364e6i | 0.0361503 | − | 0.265687i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.89060e7 | + | 1.54103e7i | −1.37227 | + | 0.731585i | ||||
\(851\) | −1.36056e7 | + | 2.35656e7i | −0.644011 | + | 1.11546i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.25006e7 | + | 2.16517e7i | 0.588245 | + | 1.01887i | 0.994462 | + | 0.105094i | \(0.0335144\pi\) |
−0.406217 | + | 0.913777i | \(0.633152\pi\) | |||||||
\(854\) | 2.56249e6 | + | 1.59731e6i | 0.120231 | + | 0.0749453i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.03833e7 | − | 1.05675e6i | −0.484342 | − | 0.0492935i | ||||
\(857\) | 1.66895e7 | − | 9.63570e6i | 0.776233 | − | 0.448158i | −0.0588609 | − | 0.998266i | \(-0.518747\pi\) |
0.835093 | + | 0.550108i | \(0.185414\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.12055e7 | − | 6.46950e6i | −0.518142 | − | 0.299149i | 0.218032 | − | 0.975942i | \(-0.430036\pi\) |
−0.736174 | + | 0.676792i | \(0.763370\pi\) | |||||||
\(860\) | −1.06453e6 | − | 72090.0i | −0.0490809 | − | 0.00332375i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.56878e7 | − | 868794.i | −1.17750 | − | 0.0398243i | ||||
\(863\) | 8.69765e6 | 0.397535 | 0.198767 | − | 0.980047i | \(-0.436306\pi\) | ||||
0.198767 | + | 0.980047i | \(0.436306\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.31189e6 | −0.0596153 | ||||||||
\(866\) | 38028.5 | + | 1286.17i | 0.00172312 | + | 5.82779e-5i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.79381e6 | + | 256916.i | 0.170913 | + | 0.0115742i | ||||
\(869\) | 2.76692e6 | + | 1.59748e6i | 0.124293 | + | 0.0717607i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.87176e7 | + | 1.08066e7i | −0.835999 | + | 0.482664i | ||||
\(872\) | 3.17504e7 | + | 3.23138e6i | 1.41403 | + | 0.143912i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.16684e6 | + | 3.22072e6i | 0.228795 | + | 0.142618i | ||||
\(875\) | −213040. | − | 368996.i | −0.00940679 | − | 0.0162930i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.12877e7 | − | 1.95509e7i | 0.495573 | − | 0.858357i | −0.504414 | − | 0.863462i | \(-0.668292\pi\) |
0.999987 | + | 0.00510463i | \(0.00162486\pi\) | |||||||
\(878\) | −2.46252e7 | + | 1.31282e7i | −1.07806 | + | 0.574735i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −50824.9 | + | 373537.i | −0.00221243 | + | 0.0162603i | ||||
\(881\) | − | 1.89558e7i | − | 0.822816i | −0.911451 | − | 0.411408i | \(-0.865037\pi\) | ||
0.911451 | − | 0.411408i | \(-0.134963\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.38595e7i | − | 1.02981i | −0.857246 | − | 0.514907i | \(-0.827826\pi\) | ||
0.857246 | − | 0.514907i | \(-0.172174\pi\) | |||||||
\(884\) | 1.60936e7 | + | 1.08039e7i | 0.692665 | + | 0.464998i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.34523e7 | − | 2.52332e7i | −0.575721 | − | 1.07991i | ||||
\(887\) | −1.14641e7 | + | 1.98564e7i | −0.489249 | + | 0.847405i | −0.999923 | − | 0.0123696i | \(-0.996063\pi\) |
0.510674 | + | 0.859774i | \(0.329396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 347929. | + | 602631.i | 0.0147651 | + | 0.0255739i | ||||
\(890\) | −521030. | + | 835864.i | −0.0220490 | + | 0.0353721i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.69965e6 | − | 3.28587e6i | 0.281929 | − | 0.138273i | ||||
\(893\) | −1.02655e7 | + | 5.92678e6i | −0.430775 | + | 0.248708i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28916.9 | − | 16695.2i | −0.00120668 | − | 0.000696679i | ||||
\(896\) | 2.86012e6 | − | 843977.i | 0.119019 | − | 0.0351205i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −755778. | + | 2.23463e7i | −0.0312754 | + | 0.924728i | ||||
\(899\) | 3.70398e7 | 1.52851 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.02198e7 | 0.419402 | ||||||||
\(902\) | 252605. | − | 7.46883e6i | 0.0103377 | − | 0.305658i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.89601e7 | + | 1.36801e7i | 0.771649 | + | 0.556761i | ||||
\(905\) | 1.65518e6 | + | 955617.i | 0.0671774 | + | 0.0387849i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.34957e6 | − | 5.39798e6i | 0.377375 | − | 0.217878i | −0.299300 | − | 0.954159i | \(-0.596753\pi\) |
0.676676 | + | 0.736281i | \(0.263420\pi\) | |||||||
\(908\) | 1.23858e7 | + | 2.52537e7i | 0.498551 | + | 1.01651i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −66493.2 | + | 106672.i | −0.00266179 | + | 0.00427018i | ||||
\(911\) | −1.46710e6 | − | 2.54108e6i | −0.0585683 | − | 0.101443i | 0.835255 | − | 0.549863i | \(-0.185320\pi\) |
−0.893823 | + | 0.448420i | \(0.851987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.38253e6 | + | 4.12667e6i | −0.0945937 | + | 0.163841i | ||||
\(914\) | 1.99255e7 | + | 3.73753e7i | 0.788938 | + | 1.47985i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.82357e6 | + | 1.01644e7i | −0.268703 | + | 0.400263i | ||||
\(917\) | − | 3.37252e6i | − | 0.132444i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.10763e7i | 0.823201i | 0.911364 | + | 0.411600i | \(0.135030\pi\) | ||||
−0.911364 | + | 0.411600i | \(0.864970\pi\) | |||||||
\(920\) | 1.81534e6 | − | 815420.i | 0.0707113 | − | 0.0317623i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.55656e7 | − | 1.36295e7i | 0.990443 | − | 0.528024i | ||||
\(923\) | 7.08075e6 | − | 1.22642e7i | 0.273574 | − | 0.473844i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.63412e7 | + | 2.83039e7i | 0.627958 | + | 1.08766i | ||||
\(926\) | −1.92717e7 | − | 1.20129e7i | −0.738571 | − | 0.460383i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.72411e7 | − | 1.00847e7i | 1.03838 | − | 0.384409i | ||||
\(929\) | 1.43110e7 | − | 8.26248e6i | 0.544041 | − | 0.314102i | −0.202674 | − | 0.979246i | \(-0.564963\pi\) |
0.746715 | + | 0.665144i | \(0.231630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.96278e6 | + | 3.44261e6i | 0.225463 | + | 0.130171i | ||||
\(932\) | 485078. | − | 7.16301e6i | 0.0182925 | − | 0.270119i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.07351e7 | + | 1.03950e6i | 1.15284 | + | 0.0389904i | ||||
\(935\) | −686147. | −0.0256678 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.09551e7 | 0.407633 | 0.203816 | − | 0.979009i | \(-0.434665\pi\) | ||||
0.203816 | + | 0.979009i | \(0.434665\pi\) | |||||||
\(938\) | −6.04851e6 | − | 204568.i | −0.224461 | − | 0.00759155i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −261778. | + | 3.86559e6i | −0.00966302 | + | 0.142691i | ||||
\(941\) | 3.02898e7 | + | 1.74878e7i | 1.11512 | + | 0.643815i | 0.940151 | − | 0.340759i | \(-0.110684\pi\) |
0.174970 | + | 0.984574i | \(0.444017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.41650e7 | + | 1.97252e7i | −1.25113 | + | 0.722341i | ||||
\(944\) | 2.38357e6 | − | 3.07861e6i | 0.0870558 | − | 0.112441i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.26254e6 | + | 2.03368e6i | 0.118530 | + | 0.0738849i | ||||
\(947\) | −1.20408e7 | − | 2.08553e7i | −0.436296 | − | 0.755687i | 0.561104 | − | 0.827745i | \(-0.310377\pi\) |
−0.997400 | + | 0.0720580i | \(0.977043\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.72161e6 | − | 6.44601e6i | 0.134142 | − | 0.232341i | ||||
\(950\) | 6.45292e6 | − | 3.44017e6i | 0.231978 | − | 0.123672i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.22396e6 | + | 4.95113e6i | 0.0795307 | + | 0.177057i | ||||
\(953\) | 3.19780e7i | 1.14056i | 0.821450 | + | 0.570281i | \(0.193166\pi\) | ||||
−0.821450 | + | 0.570281i | \(0.806834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.17067e6i | − | 0.0770170i | ||||||
\(956\) | 2.74354e7 | − | 4.08680e7i | 0.970882 | − | 1.44623i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.46931e7 | + | 4.63182e7i | 0.869285 | + | 1.63056i | ||||
\(959\) | 924760. | − | 1.60173e6i | 0.0324700 | − | 0.0562397i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.29644e7 | + | 2.24551e7i | 0.452840 | + | 0.784343i | ||||
\(962\) | 1.02304e7 | − | 1.64121e7i | 0.356413 | − | 0.571777i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.95274e7 | + | 3.98149e7i | 0.676787 | + | 1.37992i | ||||
\(965\) | −3.23879e6 | + | 1.86992e6i | −0.111960 | + | 0.0646404i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.45189e7 | − | 1.41560e7i | −0.843209 | − | 0.486827i | 0.0151446 | − | 0.999885i | \(-0.495179\pi\) |
−0.858354 | + | 0.513058i | \(0.828512\pi\) | |||||||
\(968\) | −1.62633e7 | + | 2.25404e7i | −0.557855 | + | 0.773165i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −37933.4 | + | 1.12159e6i | −0.00129447 | + | 0.0382740i | ||||
\(971\) | 1.79971e7 | 0.612567 | 0.306284 | − | 0.951940i | \(-0.400914\pi\) | ||||
0.306284 | + | 0.951940i | \(0.400914\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.47103e6 | −0.117538 | ||||||||
\(974\) | 451259. | − | 1.33425e7i | 0.0152415 | − | 0.450650i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.28661e7 | + | 3.14463e7i | 0.432337 | + | 1.05668i | ||||
\(977\) | 6.10203e6 | + | 3.52301e6i | 0.204521 | + | 0.118080i | 0.598763 | − | 0.800927i | \(-0.295659\pi\) |
−0.394242 | + | 0.919007i | \(0.628993\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.07350e6 | − | 1.77449e6i | 0.102489 | − | 0.0591720i | ||||
\(980\) | 2.02056e6 | − | 990995.i | 0.0672059 | − | 0.0329614i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.55115e7 | − | 4.09269e7i | 0.844223 | − | 1.35435i | ||||
\(983\) | −1.13029e7 | − | 1.95773e7i | −0.373085 | − | 0.646202i | 0.616954 | − | 0.787000i | \(-0.288367\pi\) |
−0.990038 | + | 0.140798i | \(0.955033\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −345940. | + | 599186.i | −0.0113608 | + | 0.0196776i | ||||
\(986\) | 2.48725e7 | + | 4.66546e7i | 0.814754 | + | 1.52828i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.59271e6 | − | 2.41185e6i | −0.117093 | − | 0.0786064i | ||||
\(989\) | − | 2.02950e7i | − | 0.659778i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.05378e7i | − | 0.987765i | −0.869529 | − | 0.493883i | \(-0.835577\pi\) | ||
0.869529 | − | 0.493883i | \(-0.164423\pi\) | |||||||
\(992\) | 3.29267e7 | + | 2.73221e7i | 1.06235 | + | 0.881525i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.49918e6 | − | 1.86548e6i | 0.112331 | − | 0.0598859i | ||||
\(995\) | 1.67121e6 | − | 2.89463e6i | 0.0535148 | − | 0.0926904i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.05531e7 | − | 1.82786e7i | −0.336236 | − | 0.582377i | 0.647486 | − | 0.762078i | \(-0.275821\pi\) |
−0.983721 | + | 0.179700i | \(0.942487\pi\) | |||||||
\(998\) | −1.21256e6 | − | 755841.i | −0.0385369 | − | 0.0240217i | ||||
\(999\) | 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.71.1 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.23.28 | yes | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.71.10 | 56 | ||
9.2 | odd | 6 | inner | 108.6.h.a.35.10 | 56 | ||
9.7 | even | 3 | 36.6.h.a.11.19 | ✓ | 56 | ||
12.11 | even | 2 | 36.6.h.a.23.19 | yes | 56 | ||
36.7 | odd | 6 | 36.6.h.a.11.28 | yes | 56 | ||
36.11 | even | 6 | inner | 108.6.h.a.35.1 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.19 | ✓ | 56 | 9.7 | even | 3 | ||
36.6.h.a.11.28 | yes | 56 | 36.7 | odd | 6 | ||
36.6.h.a.23.19 | yes | 56 | 12.11 | even | 2 | ||
36.6.h.a.23.28 | yes | 56 | 3.2 | odd | 2 | ||
108.6.h.a.35.1 | 56 | 36.11 | even | 6 | inner | ||
108.6.h.a.35.10 | 56 | 9.2 | odd | 6 | inner | ||
108.6.h.a.71.1 | 56 | 1.1 | even | 1 | trivial | ||
108.6.h.a.71.10 | 56 | 4.3 | odd | 2 | inner |