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 | 71.10 | ||
Character | \(\chi\) | \(=\) | 108.71 |
Dual form | 108.6.h.a.35.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66122 | + | 4.99179i | −0.470441 | + | 0.882431i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −17.8359 | − | 26.5684i | −0.557371 | − | 0.830264i | ||||
\(5\) | −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 | −0.445303 | − | 0.895380i | \(-0.646904\pi\) |
0.552770 | + | 0.833334i | \(0.313571\pi\) | |||||||
\(8\) | 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 | 0.914930 | − | 0.403613i | \(-0.132246\pi\) |
−0.807004 | + | 0.590546i | \(0.798912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 162.502 | − | 281.462i | 0.266686 | − | 0.461914i | −0.701318 | − | 0.712849i | \(-0.747405\pi\) |
0.968004 | + | 0.250935i | \(0.0807380\pi\) | |||||||
\(14\) | 3.07614 | + | 90.9529i | 0.00419455 | + | 0.124021i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −387.764 | + | 947.742i | −0.378676 | + | 0.925529i | ||||
\(17\) | 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 | \(0.0422063\pi\) | ||||
−0.991222 | + | 0.132207i | \(0.957794\pi\) | |||||||
\(20\) | 9.18864 | + | 135.686i | 0.00513660 | + | 0.0758508i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −489.740 | + | 16.5636i | −0.215729 | + | 0.00729623i | ||||
\(23\) | −1293.41 | + | 2240.24i | −0.509818 | + | 0.883030i | 0.490117 | + | 0.871656i | \(0.336954\pi\) |
−0.999935 | + | 0.0113741i | \(0.996379\pi\) | |||||||
\(24\) | 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 | 0.959553 | − | 0.281530i | \(-0.0908418\pi\) |
0.235964 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(32\) | −3699.00 | − | 4457.78i | −0.638571 | − | 0.769563i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9303.69 | − | 4959.98i | −1.38025 | − | 0.735838i | ||||
\(35\) | −68.3704 | −0.00943405 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10519.2 | −1.26322 | −0.631609 | − | 0.775287i | \(-0.717605\pi\) | ||||
−0.631609 | + | 0.775287i | \(0.717605\pi\) | |||||||
\(38\) | −2076.94 | − | 1107.25i | −0.233327 | − | 0.124391i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −701.768 | − | 315.222i | −0.0693496 | − | 0.0311506i | ||||
\(41\) | −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 | −0.753298 | − | 0.657679i | \(-0.771538\pi\) |
0.192917 | + | 0.981215i | \(0.438205\pi\) | |||||||
\(44\) | 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 | \(0.223073\pi\) |
0.176280 | + | 0.984340i | \(0.443594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8274.10 | + | 14331.2i | −0.492301 | + | 0.852690i | ||||
\(50\) | 17565.5 | − | 594.085i | 0.993652 | − | 0.0336065i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10376.4 | + | 702.686i | −0.532153 | + | 0.0360373i | ||||
\(53\) | − | 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 | ||||||
\(56\) | 2361.61 | − | 1703.95i | 0.100633 | − | 0.0726084i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −958.860 | − | 28350.9i | −0.0374270 | − | 1.10661i | ||||
\(59\) | −1901.12 | + | 3292.83i | −0.0711015 | + | 0.123151i | −0.899384 | − | 0.437159i | \(-0.855985\pi\) |
0.828283 | + | 0.560310i | \(0.189318\pi\) | |||||||
\(60\) | 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 | \(0.0267438\pi\) |
0.570912 | + | 0.821011i | \(0.306590\pi\) | |||||||
\(68\) | 49518.3 | − | 33242.5i | 1.29865 | − | 0.871809i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 181.948 | − | 341.290i | 0.00443816 | − | 0.00832490i | ||||
\(71\) | −43573.3 | −1.02583 | −0.512914 | − | 0.858440i | \(-0.671434\pi\) | ||||
−0.512914 | + | 0.858440i | \(0.671434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22901.9 | 0.502996 | 0.251498 | − | 0.967858i | \(-0.419077\pi\) | ||||
0.251498 | + | 0.967858i | \(0.419077\pi\) | |||||||
\(74\) | 27993.8 | − | 52509.6i | 0.594269 | − | 1.11470i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11054.4 | − | 7420.98i | 0.219533 | − | 0.147376i | ||||
\(77\) | 1206.87 | + | 696.785i | 0.0231970 | + | 0.0133928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31941.7 | − | 18441.5i | 0.575824 | − | 0.332452i | −0.183648 | − | 0.982992i | \(-0.558791\pi\) |
0.759472 | + | 0.650540i | \(0.225457\pi\) | |||||||
\(80\) | 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 | 0.997553 | − | 0.0699102i | \(-0.0222713\pi\) |
−0.559321 | + | 0.828951i | \(0.688938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3960.48 | − | 6859.75i | 0.0594567 | − | 0.102982i | ||||
\(86\) | −1500.17 | − | 44355.8i | −0.0218723 | − | 0.646702i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9175.01 | + | 12716.2i | 0.126299 | + | 0.175046i | ||||
\(89\) | 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 | ||||||
\(92\) | 82588.8 | − | 5592.90i | 1.01731 | − | 0.0688918i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −161068. | + | 5447.50i | −1.88013 | + | 0.0635883i | ||||
\(95\) | 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 | 0.484736 | − | 0.874660i | \(-0.338916\pi\) |
−0.515110 | + | 0.857124i | \(0.672249\pi\) | |||||||
\(104\) | 24106.1 | − | 53666.6i | 0.218546 | − | 0.486542i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 27371.5 | + | 14592.3i | 0.236610 | + | 0.126142i | ||||
\(107\) | −57656.6 | −0.486844 | −0.243422 | − | 0.969920i | \(-0.578270\pi\) | ||||
−0.243422 | + | 0.969920i | \(0.578270\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −176304. | −1.42133 | −0.710667 | − | 0.703529i | \(-0.751607\pi\) | ||||
−0.710667 | + | 0.703529i | \(0.751607\pi\) | |||||||
\(110\) | 1837.70 | + | 979.710i | 0.0144808 | + | 0.00771998i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2221.00 | + | 16323.2i | 0.0167303 | + | 0.122959i | ||||
\(113\) | −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 | ||||
\(122\) | −187588. | + | 6344.46i | −1.14105 | + | 0.0385918i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15969.9 | − | 235823.i | −0.0932712 | − | 1.37731i | ||||
\(125\) | 26485.1i | 0.151610i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 43254.5i | 0.237970i | 0.992896 | + | 0.118985i | \(0.0379640\pi\) | ||||
−0.992896 | + | 0.118985i | \(0.962036\pi\) | |||||||
\(128\) | −52461.5 | + | 177785.i | −0.283019 | + | 0.959114i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −264.109 | − | 7808.97i | −0.00137064 | − | 0.0405262i | ||||
\(131\) | 104818. | − | 181550.i | 0.533650 | − | 0.924309i | −0.465577 | − | 0.885007i | \(-0.654153\pi\) |
0.999227 | − | 0.0393020i | \(-0.0125135\pi\) | |||||||
\(132\) | 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 | 0.0302321 | − | 0.999543i | \(-0.490375\pi\) |
−0.850514 | + | 0.525953i | \(0.823709\pi\) | |||||||
\(140\) | 1219.44 | + | 1816.50i | 0.00525826 | + | 0.00783275i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 115958. | − | 217509.i | 0.482592 | − | 0.905223i | ||||
\(143\) | 28153.2 | 0.115130 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21311.7 | 0.0841779 | ||||||||
\(146\) | −60946.9 | + | 114321.i | −0.236630 | + | 0.443860i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 187619. | + | 279479.i | 0.704080 | + | 1.04880i | ||||
\(149\) | 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 | −0.980506 | − | 0.196490i | \(-0.937046\pi\) |
−0.320088 | + | 0.947388i | \(0.603712\pi\) | |||||||
\(152\) | 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 | \(0.0500113\pi\) | |||||||
\(158\) | 7052.50 | + | 208523.i | 0.0224750 | + | 0.664525i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4141.68 | + | 24267.1i | 0.0127902 | + | 0.0749409i | ||||
\(161\) | 41615.4i | 0.126529i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 324082.i | − | 0.955402i | −0.878522 | − | 0.477701i | \(-0.841470\pi\) | ||
0.878522 | − | 0.477701i | \(-0.158530\pi\) | |||||||
\(164\) | 32973.1 | + | 486904.i | 0.0957303 | + | 1.41362i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −310997. | + | 10518.3i | −0.875964 | + | 0.0296262i | ||||
\(167\) | 125104. | − | 216686.i | 0.347120 | − | 0.601229i | −0.638617 | − | 0.769525i | \(-0.720493\pi\) |
0.985737 | + | 0.168296i | \(0.0538263\pi\) | |||||||
\(168\) | 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 | ||||
\(176\) | −87893.3 | + | 11959.1i | −0.213882 | + | 0.0291016i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −204513. | − | 109030.i | −0.483805 | − | 0.257926i | ||||
\(179\) | −7856.73 | −0.0183278 | −0.00916388 | − | 0.999958i | \(-0.502917\pi\) | ||||
−0.00916388 | + | 0.999958i | \(0.502917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −449713. | −1.02033 | −0.510163 | − | 0.860078i | \(-0.670415\pi\) | ||||
−0.510163 | + | 0.860078i | \(0.670415\pi\) | |||||||
\(182\) | 26099.6 | + | 13914.2i | 0.0584058 | + | 0.0311372i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −191868. | + | 427149.i | −0.417790 | + | 0.930112i | ||||
\(185\) | 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 | \(-0.997596\pi\) |
0.493444 | − | 0.869777i | \(-0.335738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 439991. | − | 762087.i | 0.850257 | − | 1.47269i | −0.0307186 | − | 0.999528i | \(-0.509780\pi\) |
0.880976 | − | 0.473161i | \(-0.156887\pi\) | |||||||
\(194\) | −263909. | + | 8925.72i | −0.503442 | + | 0.0170270i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 528332. | − | 35778.6i | 0.982351 | − | 0.0665247i | ||||
\(197\) | − | 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 | \(-0.751433\pi\) | ||
0.710283 | − | 0.703916i | \(-0.248567\pi\) | |||||||
\(200\) | −329079. | − | 456091.i | −0.581735 | − | 0.806262i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14534.2 | + | 429735.i | 0.0250618 | + | 0.741007i | ||||
\(203\) | −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 | 0.989692 | − | 0.143212i | \(-0.0457429\pi\) |
0.370821 | + | 0.928704i | \(0.379076\pi\) | |||||||
\(212\) | −145683. | + | 97799.5i | −0.222623 | + | 0.149450i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 153437. | − | 287810.i | 0.229031 | − | 0.429606i | ||||
\(215\) | 33342.8 | 0.0491933 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 118828. | 0.171305 | ||||||||
\(218\) | 469183. | − | 880072.i | 0.668654 | − | 1.25423i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9781.01 | + | 6566.16i | −0.0136247 | + | 0.00914650i | ||||
\(221\) | 524588. | + | 302871.i | 0.722500 | + | 0.417136i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −201948. | + | 116595.i | −0.271942 | + | 0.157006i | −0.629770 | − | 0.776782i | \(-0.716851\pi\) |
0.357828 | + | 0.933788i | \(0.383518\pi\) | |||||||
\(224\) | −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 | \(-0.975121\pi\) |
0.430855 | − | 0.902421i | \(-0.358212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −191288. | + | 331320.i | −0.241045 | + | 0.417503i | −0.961012 | − | 0.276506i | \(-0.910824\pi\) |
0.719967 | + | 0.694008i | \(0.244157\pi\) | |||||||
\(230\) | 2102.13 | + | 62154.1i | 0.00262023 | + | 0.0774730i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −736136. | + | 531137.i | −0.897921 | + | 0.647868i | ||||
\(233\) | − | 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 | ||||||
\(236\) | 121393. | − | 8220.75i | 0.141878 | − | 0.00960797i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −169518. | + | 5733.30i | −0.193987 | + | 0.00656089i | ||||
\(239\) | −769108. | + | 1.33213e6i | −0.870949 | + | 1.50853i | −0.00993200 | + | 0.999951i | \(0.503162\pi\) |
−0.861017 | + | 0.508577i | \(0.830172\pi\) | |||||||
\(240\) | 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 | ||||
\(248\) | 1.21968e6 | + | 547857.i | 1.25926 | + | 0.565637i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −132208. | − | 70482.6i | −0.133785 | − | 0.0713234i | ||||
\(251\) | 1.31402e6 | 1.31649 | 0.658246 | − | 0.752803i | \(-0.271299\pi\) | ||||
0.658246 | + | 0.752803i | \(0.271299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −224080. | −0.220091 | ||||||||
\(254\) | −215917. | − | 115109.i | −0.209992 | − | 0.111951i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −747854. | − | 735001.i | −0.713209 | − | 0.700952i | ||||
\(257\) | −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 | \(0.0664917\pi\) |
−0.309540 | + | 0.950887i | \(0.600175\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11651.8 | + | 20181.4i | −0.0101924 | + | 0.0176538i | ||||
\(266\) | −37842.9 | + | 1279.89i | −0.0327929 | + | 0.00110910i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −143782. | − | 2.12319e6i | −0.122283 | − | 1.80572i | ||||
\(269\) | − | 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 | \(0.0867561\pi\) | ||||
−0.963087 | + | 0.269190i | \(0.913244\pi\) | |||||||
\(272\) | −1.76640e6 | − | 722715.i | −1.44766 | − | 0.592305i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21982.9 | − | 649974.i | −0.0176892 | − | 0.523022i | ||||
\(275\) | 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 | 0.839023 | − | 0.544096i | \(-0.183127\pi\) |
−0.0516895 | + | 0.998663i | \(0.516461\pi\) | |||||||
\(284\) | 777167. | + | 1.15767e6i | 0.571766 | + | 0.851708i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −74921.7 | + | 140535.i | −0.0541618 | + | 0.101594i | ||||
\(287\) | −245345. | −0.175821 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.05390e6 | −1.44655 | ||||||||
\(290\) | −56715.0 | + | 106383.i | −0.0396007 | + | 0.0742812i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −408475. | − | 608468.i | −0.280355 | − | 0.417619i | ||||
\(293\) | −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 | ||||
\(302\) | −80458.0 | − | 2.37892e6i | −0.0507635 | − | 1.50094i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −394328. | − | 161338.i | −0.244722 | − | 0.100127i | ||||
\(305\) | − | 141013.i | − | 0.0867977i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.54327e6i | 0.934537i | 0.884115 | + | 0.467269i | \(0.154762\pi\) | ||||
−0.884115 | + | 0.467269i | \(0.845238\pi\) | |||||||
\(308\) | −3013.02 | − | 44492.3i | −0.00180978 | − | 0.0267244i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 177474. | − | 6002.38i | 0.104889 | − | 0.00354748i | ||||
\(311\) | −1.17389e6 | + | 2.03323e6i | −0.688218 | + | 1.19203i | 0.284196 | + | 0.958766i | \(0.408273\pi\) |
−0.972414 | + | 0.233262i | \(0.925060\pi\) | |||||||
\(312\) | 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 | ||||
\(320\) | −132158. | − | 43905.7i | −0.0721472 | − | 0.0239688i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −207735. | − | 110748.i | −0.111653 | − | 0.0595244i | ||||
\(323\) | −775473. | −0.413581 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00977e6 | −0.530289 | ||||||||
\(326\) | 1.61775e6 | + | 862453.i | 0.843077 | + | 0.449460i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.51827e6 | − | 1.13116e6i | −1.29246 | − | 0.580550i | ||||
\(329\) | 396919. | + | 229161.i | 0.202168 | + | 0.116722i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.45201e6 | − | 1.41567e6i | 1.23013 | − | 0.710218i | 0.263076 | − | 0.964775i | \(-0.415263\pi\) |
0.967058 | + | 0.254557i | \(0.0819296\pi\) | |||||||
\(332\) | 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 | \(0.222037\pi\) | |||||||
\(338\) | −1.50197e6 | + | 50798.5i | −0.715105 | + | 0.0241857i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −252892. | + | 17125.8i | −0.118642 | + | 0.00803440i | ||||
\(341\) | 639836.i | 0.297977i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 536603.i | 0.246274i | ||||||||
\(344\) | −1.15171e6 | + | 830981.i | −0.524743 | + | 0.378613i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 59024.9 | + | 1.74521e6i | 0.0265061 | + | 0.783712i | ||||
\(347\) | 751022. | − | 1.30081e6i | 0.334833 | − | 0.579948i | −0.648619 | − | 0.761113i | \(-0.724653\pi\) |
0.983453 | + | 0.181165i | \(0.0579866\pi\) | |||||||
\(348\) | 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 | ||||
\(356\) | 1.08850e6 | − | 730732.i | 0.455203 | − | 0.305586i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20908.5 | − | 39219.1i | 0.00862213 | − | 0.0161730i | ||||
\(359\) | −301586. | −0.123502 | −0.0617512 | − | 0.998092i | \(-0.519669\pi\) | ||||
−0.0617512 | + | 0.998092i | \(0.519669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.30298e6 | 0.930086 | ||||||||
\(362\) | 1.19678e6 | − | 2.24487e6i | 0.480003 | − | 0.900368i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −138913. | + | 93255.0i | −0.0549529 | + | 0.0368909i | ||||
\(365\) | −84290.9 | − | 48665.4i | −0.0331168 | − | 0.0191200i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.93072e6 | + | 1.11470e6i | −0.748261 | + | 0.432009i | −0.825065 | − | 0.565037i | \(-0.808862\pi\) |
0.0768040 | + | 0.997046i | \(0.475528\pi\) | |||||||
\(368\) | −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 | \(0.0581318\pi\) | |||||||
\(374\) | −30871.3 | − | 912778.i | −0.0114124 | − | 0.337432i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.01751e6 | + | 4.18215e6i | 1.10073 | + | 1.52556i | ||||
\(377\) | 1.62978e6i | 0.590574i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.14708e6i | − | 0.767804i | −0.923374 | − | 0.383902i | \(-0.874580\pi\) | ||
0.923374 | − | 0.383902i | \(-0.125420\pi\) | |||||||
\(380\) | −56455.0 | + | 3823.13i | −0.0200560 | + | 0.00135819i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.88764e6 | − | 97663.5i | 1.01248 | − | 0.0342431i | ||||
\(383\) | 1.30237e6 | − | 2.25578e6i | 0.453669 | − | 0.785777i | −0.544942 | − | 0.838474i | \(-0.683448\pi\) |
0.998611 | + | 0.0526965i | \(0.0167816\pi\) | |||||||
\(384\) | 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 | ||||
\(392\) | −1.22741e6 | + | 2.73254e6i | −0.403435 | + | 0.898154i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 812660. | + | 433244.i | 0.263735 | + | 0.140602i | ||||
\(395\) | −156749. | −0.0505490 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.78885e6 | 1.84338 | 0.921692 | − | 0.387922i | \(-0.126807\pi\) | ||||
0.921692 | + | 0.387922i | \(0.126807\pi\) | |||||||
\(398\) | 3.92590e6 | + | 2.09297e6i | 1.24231 | + | 0.662302i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.15246e6 | − | 428935.i | 0.985143 | − | 0.134042i | ||||
\(401\) | 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 | \(0.279143\pi\) | |||||||
\(410\) | −366431. | + | 12393.1i | −0.107655 | + | 0.00364101i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8164.48 | + | 120563.i | 0.00236966 | + | 0.0349920i | ||||
\(413\) | 61168.6i | 0.0176463i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 233781.i | − | 0.0666328i | ||||||
\(416\) | −1.85579e6 | + | 316728.i | −0.525770 | + | 0.0897333i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6891.64 | − | 203767.i | −0.00192922 | − | 0.0570417i | ||||
\(419\) | 2.33383e6 | − | 4.04232e6i | 0.649434 | − | 1.12485i | −0.333824 | − | 0.942635i | \(-0.608339\pi\) |
0.983258 | − | 0.182217i | \(-0.0583274\pi\) | |||||||
\(420\) | 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 | ||||
\(428\) | 1.02836e6 | + | 1.53185e6i | 0.271352 | + | 0.404209i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −88732.4 | + | 166440.i | −0.0231426 | + | 0.0434097i | ||||
\(431\) | −4.54361e6 | −1.17817 | −0.589085 | − | 0.808071i | \(-0.700512\pi\) | ||||
−0.589085 | + | 0.808071i | \(0.700512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6726.40 | −0.00172410 | −0.000862051 | − | 1.00000i | \(-0.500274\pi\) | ||||
−0.000862051 | 1.00000i | \(0.500274\pi\) | ||||||||
\(434\) | −316227. | + | 593164.i | −0.0805888 | + | 0.151165i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.14453e6 | + | 4.68413e6i | 0.792210 | + | 1.18008i | ||||
\(437\) | −932101. | − | 538148.i | −0.233485 | − | 0.134803i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.27223e6 | + | 2.46657e6i | −1.05802 | + | 0.610847i | −0.924883 | − | 0.380251i | \(-0.875838\pi\) |
−0.133134 | + | 0.991098i | \(0.542504\pi\) | |||||||
\(440\) | −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 | \(-0.957074\pi\) |
0.379025 | − | 0.925386i | \(-0.376259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 87058.8 | − | 150790.i | 0.0208407 | − | 0.0360972i | ||||
\(446\) | −44588.7 | − | 1.31836e6i | −0.0106142 | − | 0.313833i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 394070. | − | 350147.i | 0.0927637 | − | 0.0824244i | ||||
\(449\) | − | 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 | ||||||
\(452\) | 279251. | + | 4.12362e6i | 0.0642908 | + | 0.949364i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.96945e6 | − | 168073.i | 1.13154 | − | 0.0382700i | ||||
\(455\) | −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 | 0.0733224 | − | 0.997308i | \(-0.476640\pi\) |
−0.827033 | + | 0.562153i | \(0.809973\pi\) | |||||||
\(464\) | −692307. | − | 5.08810e6i | −0.149281 | − | 1.09714i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.11994e6 | + | 597062.i | 0.238908 | + | 0.127366i | ||||
\(467\) | 5.43636e6 | 1.15350 | 0.576748 | − | 0.816922i | \(-0.304321\pi\) | ||||
0.576748 | + | 0.816922i | \(0.304321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.06985e6 | 0.224590 | ||||||||
\(470\) | 604388. | + | 322211.i | 0.126203 | + | 0.0672814i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −282018. | + | 627847.i | −0.0582669 | + | 0.129718i | ||||
\(473\) | −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 | \(0.208354\pi\) |
0.130589 | + | 0.991437i | \(0.458313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70939e6 | + | 2.96075e6i | −0.336882 | + | 0.583497i | ||||
\(482\) | −7.83482e6 | + | 264983.i | −1.53607 | + | 0.0519518i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.90228e6 | + | 331982.i | −0.951229 | + | 0.0644171i | ||||
\(485\) | − | 198384.i | − | 0.0382958i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.35999e6i | − | 0.450908i | −0.974254 | − | 0.225454i | \(-0.927614\pi\) | ||
0.974254 | − | 0.225454i | \(-0.0723865\pi\) | |||||||
\(488\) | 3.51436e6 | + | 4.87077e6i | 0.668031 | + | 0.925866i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13447.6 | + | 397609.i | 0.00253020 | + | 0.0748110i | ||||
\(491\) | 4.26271e6 | − | 7.38323e6i | 0.797961 | − | 1.38211i | −0.122980 | − | 0.992409i | \(-0.539245\pi\) |
0.920942 | − | 0.389701i | \(-0.127421\pi\) | |||||||
\(492\) | 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 | 0.480208 | − | 0.877155i | \(-0.340561\pi\) |
−0.519535 | + | 0.854449i | \(0.673895\pi\) | |||||||
\(500\) | 703668. | − | 472385.i | 0.125876 | − | 0.0845027i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.49689e6 | + | 6.55931e6i | −0.619332 | + | 1.16171i | ||||
\(503\) | −6.25307e6 | −1.10198 | −0.550989 | − | 0.834512i | \(-0.685749\pi\) | ||||
−0.550989 | + | 0.834512i | \(0.685749\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −323037. | −0.0563669 | ||||||||
\(506\) | 596326. | − | 1.11856e6i | 0.103540 | − | 0.194215i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.14920e6 | − | 771481.i | 0.197578 | − | 0.132637i | ||||
\(509\) | −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 | ||||
\(518\) | −32358.5 | − | 956751.i | −0.00529863 | − | 0.156666i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −202762. | + | 146297.i | −0.0328835 | + | 0.0237261i | ||||
\(521\) | 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 | \(0.346566\pi\) | ||||
−0.463576 | + | 0.886057i | \(0.653434\pi\) | |||||||
\(524\) | −6.69301e6 | + | 453250.i | −1.06486 | + | 0.0721123i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.48187e6 | + | 286867.i | −1.33668 | + | 0.0452081i | ||||
\(527\) | −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 | ||||
\(536\) | 1.09811e7 | + | 4.93253e6i | 1.65096 | + | 0.741580i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.32101e6 | + | 704257.i | 0.196766 | + | 0.104900i | ||||
\(539\) | −1.43347e6 | −0.212529 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.27509e6 | 0.334200 | 0.167100 | − | 0.985940i | \(-0.446560\pi\) | ||||
0.167100 | + | 0.985940i | \(0.446560\pi\) | |||||||
\(542\) | −3.24914e6 | − | 1.73218e6i | −0.475084 | − | 0.253276i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.30842e6 | − | 6.89420e6i | 1.20371 | − | 0.998818i | ||||
\(545\) | 648891. | + | 374637.i | 0.0935794 | + | 0.0540281i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.20659e6 | − | 4.16072e6i | 1.02982 | − | 0.594567i | 0.112887 | − | 0.993608i | \(-0.463990\pi\) |
0.916933 | + | 0.399041i | \(0.130657\pi\) | |||||||
\(548\) | 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 | ||||
\(554\) | −2.68395e6 | + | 90774.4i | −0.371535 | + | 0.0125658i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 466489. | + | 6.88852e6i | 0.0639963 | + | 0.945015i | ||||
\(557\) | 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 | ||||||||
\(560\) | 26511.6 | − | 64797.5i | 0.00357245 | − | 0.00873149i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −312557. | − | 9.24146e6i | −0.0417435 | − | 1.23424i | ||||
\(563\) | −1.07987e6 | + | 1.87039e6i | −0.143582 | + | 0.248691i | −0.928843 | − | 0.370474i | \(-0.879195\pi\) |
0.785261 | + | 0.619165i | \(0.212529\pi\) | |||||||
\(564\) | 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 | 0.975126 | − | 0.221651i | \(-0.0711447\pi\) |
0.295607 | + | 0.955310i | \(0.404478\pi\) | |||||||
\(572\) | −502136. | − | 747987.i | −0.0641699 | − | 0.0955881i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 652915. | − | 1.22471e6i | 0.0827136 | − | 0.155150i | ||||
\(575\) | 8.03706e6 | 1.01374 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 669533. | 0.0837206 | 0.0418603 | − | 0.999123i | \(-0.486672\pi\) | ||||
0.0418603 | + | 0.999123i | \(0.486672\pi\) | |||||||
\(578\) | 5.46586e6 | − | 1.02526e7i | 0.680517 | − | 1.27648i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −380112. | − | 566218.i | −0.0469183 | − | 0.0698898i | ||||
\(581\) | 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 | 0.853974 | − | 0.520315i | \(-0.174185\pi\) |
−0.877593 | + | 0.479406i | \(0.840852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.53662e6 | + | 2.66151e6i | −0.182507 | + | 0.316111i | ||||
\(590\) | 3089.82 | + | 91357.5i | 0.000365429 | + | 0.0108047i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.07897e6 | − | 9.96948e6i | 0.478350 | − | 1.16914i | ||||
\(593\) | − | 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 | ||||||
\(596\) | −479434. | − | 7.07967e6i | −0.0552858 | − | 0.816389i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.75313e6 | + | 160757.i | −0.543534 | + | 0.0183830i | ||||
\(599\) | −5.30363e6 | + | 9.18615e6i | −0.603957 | + | 1.04608i | 0.388259 | + | 0.921550i | \(0.373077\pi\) |
−0.992215 | + | 0.124533i | \(0.960257\pi\) | |||||||
\(600\) | 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 | \(-0.996851\pi\) |
−0.508544 | − | 0.861036i | \(-0.669816\pi\) | |||||||
\(608\) | 1.85475e6 | − | 1.53905e6i | 0.203483 | − | 0.168847i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 703904. | + | 375265.i | 0.0765930 | + | 0.0408332i | ||||
\(611\) | 9.25912e6 | 1.00338 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 133521. | 0.0143515 | 0.00717575 | − | 0.999974i | \(-0.497716\pi\) | ||||
0.00717575 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(614\) | −7.70369e6 | − | 4.10698e6i | −0.824665 | − | 0.439645i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 230115. | + | 103363.i | 0.0244339 | + | 0.0109753i | ||||
\(617\) | −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 | 0.0214502 | − | 0.999770i | \(-0.493172\pi\) |
0.876551 | + | 0.481309i | \(0.159838\pi\) | |||||||
\(620\) | −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 | ||||
\(626\) | 7.97166e6 | − | 269611.i | 0.813042 | − | 0.0274981i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.06683e6 | + | 478565.i | −0.715032 | + | 0.0484219i | ||||
\(629\) | − | 1.96057e7i | − | 1.97586i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.28910e7i | 1.28888i | 0.764653 | + | 0.644442i | \(0.222910\pi\) | ||||
−0.764653 | + | 0.644442i | \(0.777090\pi\) | |||||||
\(632\) | 5.41434e6 | − | 3.90656e6i | 0.539204 | − | 0.389047i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −380559. | − | 1.12521e7i | −0.0376010 | − | 1.11176i | ||||
\(635\) | 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 | 0.869501 | − | 0.493932i | \(-0.164441\pi\) |
0.00699288 | + | 0.999976i | \(0.497774\pi\) | |||||||
\(644\) | 1.10566e6 | − | 742247.i | 0.105052 | − | 0.0705235i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.06370e6 | − | 3.87100e6i | 0.194565 | − | 0.364957i | ||||
\(647\) | −2.37142e6 | −0.222714 | −0.111357 | − | 0.993780i | \(-0.535520\pi\) | ||||
−0.111357 | + | 0.993780i | \(0.535520\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −329365. | −0.0306949 | ||||||||
\(650\) | 2.68721e6 | − | 5.04054e6i | 0.249470 | − | 0.467944i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.61036e6 | + | 5.78028e6i | −0.793236 | + | 0.532513i | ||||
\(653\) | 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 | 0.819176 | − | 0.573542i | \(-0.194431\pi\) |
−0.906290 | + | 0.422656i | \(0.861098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.93142e6 | + | 1.54697e7i | −0.795091 | + | 1.37714i | 0.127690 | + | 0.991814i | \(0.459244\pi\) |
−0.922781 | + | 0.385324i | \(0.874090\pi\) | |||||||
\(662\) | 541387. | + | 1.60073e7i | 0.0480134 | + | 1.41962i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.82636e6 | + | 8.07511e6i | 0.512834 | + | 0.710769i | ||||
\(665\) | − | 28446.9i | − | 0.00249449i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.29719e7i | − | 1.12899i | ||||||
\(668\) | −7.98835e6 | + | 540970.i | −0.692653 | + | 0.0469064i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.59785e6 | − | 54041.4i | 0.137515 | − | 0.00465093i | ||||
\(671\) | −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 | ||||
\(680\) | 587511. | − | 1.30796e6i | 0.0487241 | − | 0.108473i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.19392e6 | − | 1.70274e6i | −0.262944 | − | 0.140181i | ||||
\(683\) | −462361. | −0.0379253 | −0.0189627 | − | 0.999820i | \(-0.506036\pi\) | ||||
−0.0189627 | + | 0.999820i | \(0.506036\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 488594. | 0.0397852 | ||||||||
\(686\) | −2.67861e6 | − | 1.42802e6i | −0.217320 | − | 0.115857i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.08314e6 | − | 7.96050e6i | −0.0872392 | − | 0.641164i | ||||
\(689\) | −1.54334e6 | − | 891048.i | −0.123855 | − | 0.0715078i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.14382e6 | + | 2.39243e6i | −0.330146 | + | 0.190610i | −0.655906 | − | 0.754843i | \(-0.727713\pi\) |
0.325760 | + | 0.945452i | \(0.394380\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | 5.73042e6 | − | 193810.i | 0.445193 | − | 0.0150570i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 108067. | + | 1.59580e6i | 0.00833585 | + | 0.123093i | ||||
\(701\) | 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 | ||||||
\(704\) | 1.88539e6 | + | 2.12189e6i | 0.143373 | + | 0.161358i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 393568. | + | 1.16367e7i | 0.0297172 | + | 0.878657i | ||||
\(707\) | 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 | ||||
\(716\) | 140132. | + | 208741.i | 0.0102154 | + | 0.0152169i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 802586. | − | 1.50545e6i | 0.0581006 | − | 0.108982i | ||||
\(719\) | −5.58804e6 | −0.403123 | −0.201561 | − | 0.979476i | \(-0.564602\pi\) | ||||
−0.201561 | + | 0.979476i | \(0.564602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60749.9 | −0.00435219 | ||||||||
\(722\) | −6.12874e6 | + | 1.14960e7i | −0.437550 | + | 0.820737i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.02102e6 | + | 1.19482e7i | 0.568700 | + | 0.847140i | ||||
\(725\) | 1.34928e7 | + | 7.79008e6i | 0.953362 | + | 0.550424i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.72597e6 | + | 1.57384e6i | −0.191287 | + | 0.110439i | −0.592585 | − | 0.805508i | \(-0.701893\pi\) |
0.401298 | + | 0.915948i | \(0.368559\pi\) | |||||||
\(728\) | −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 | \(-0.143406\pi\) | |||||||
\(734\) | −426289. | − | 1.26042e7i | −0.0292054 | − | 0.863524i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.47708e7 | − | 2.52094e6i | 1.00510 | − | 0.171541i | ||||
\(737\) | 5.76065e6i | 0.390663i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.89450e6i | 0.329683i | 0.986320 | + | 0.164842i | \(0.0527113\pi\) | ||||
−0.986320 | + | 0.164842i | \(0.947289\pi\) | |||||||
\(740\) | −96657.0 | − | 1.42731e6i | −0.00648865 | − | 0.0958160i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 498723. | − | 16867.4i | 0.0332544 | − | 0.00112470i | ||||
\(743\) | 2.80417e6 | − | 4.85696e6i | 0.186351 | − | 0.322770i | −0.757680 | − | 0.652626i | \(-0.773667\pi\) |
0.944031 | + | 0.329857i | \(0.107000\pi\) | |||||||
\(744\) | 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 | 0.842118 | − | 0.539294i | \(-0.181309\pi\) |
−0.0459832 | + | 0.998942i | \(0.514642\pi\) | |||||||
\(752\) | −2.89067e7 | + | 3.93315e6i | −1.86403 | + | 0.253627i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.13550e6 | − | 4.33719e6i | −0.521141 | − | 0.277830i | ||||
\(755\) | 1.78826e6 | 0.114173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.75241e7 | −1.11147 | −0.555733 | − | 0.831361i | \(-0.687562\pi\) | ||||
−0.555733 | + | 0.831361i | \(0.687562\pi\) | |||||||
\(758\) | 1.07178e7 | + | 5.71385e6i | 0.677534 | + | 0.361206i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 131155. | − | 291985.i | 0.00823664 | − | 0.0183370i | ||||
\(761\) | 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 | \(0.175705\pi\) | |||||||
\(770\) | 33483.7 | − | 1132.46i | 0.00203520 | − | 6.88329e-5i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.80951e7 | + | 1.90259e6i | −1.69663 | + | 0.114896i | ||||
\(773\) | − | 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 | ||||||
\(776\) | 4.94419e6 | + | 6.85245e6i | 0.294741 | + | 0.408500i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 663589. | + | 1.96205e7i | 0.0393052 | + | 1.16215i | ||||
\(779\) | 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 | 0.269579 | − | 0.962978i | \(-0.413116\pi\) |
−0.699174 | + | 0.714951i | \(0.746449\pi\) | |||||||
\(788\) | −4.32533e6 | + | 2.90367e6i | −0.248144 | + | 0.166583i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 417144. | − | 782459.i | 0.0237803 | − | 0.0446061i | ||||
\(791\) | −2.07784e6 | −0.118079 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07837e7 | 0.608954 | ||||||||
\(794\) | −1.54054e7 | + | 2.88967e7i | −0.867204 | + | 1.62666i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.08953e7 | + | 1.40274e7i | −1.16887 | + | 0.784684i | ||||
\(797\) | −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 | ||||
\(806\) | 459022. | + | 1.35720e7i | 0.0248884 | + | 0.735880i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.11582e7 | − | 8.05085e6i | 0.601263 | − | 0.433824i | ||||
\(809\) | 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 | \(-0.806103\pi\) | ||
0.820137 | − | 0.572167i | \(-0.193897\pi\) | |||||||
\(812\) | 2.57564e6 | − | 174422.i | 0.137087 | − | 0.00928350i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.15167e6 | − | 174236.i | 0.272513 | − | 0.00921672i | ||||
\(815\) | −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 | 0.0179161 | − | 0.999839i | \(-0.494297\pi\) |
−0.856928 | + | 0.515436i | \(0.827630\pi\) | |||||||
\(824\) | −623550. | − | 280088.i | −0.0319929 | − | 0.0143706i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −305341. | − | 162783.i | −0.0155716 | − | 0.00830154i | ||||
\(827\) | 2.05084e7 | 1.04272 | 0.521361 | − | 0.853336i | \(-0.325424\pi\) | ||||
0.521361 | + | 0.853336i | \(0.325424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.27151e7 | −1.65334 | −0.826669 | − | 0.562688i | \(-0.809767\pi\) | ||||
−0.826669 | + | 0.562688i | \(0.809767\pi\) | |||||||
\(830\) | 1.16698e6 | + | 622141.i | 0.0587989 | + | 0.0313468i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.35762e6 | − | 1.01066e7i | 0.168160 | − | 0.506170i | ||||
\(833\) | −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 | 0.817710 | − | 0.575630i | \(-0.195243\pi\) |
−0.907366 | + | 0.420342i | \(0.861910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.31771e6 | − | 4.01440e6i | 0.112998 | − | 0.195718i | ||||
\(842\) | −2.30555e7 | + | 779763.i | −1.12071 | + | 0.0379038i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.19660e6 | − | 3.24366e7i | −0.106144 | − | 1.56740i | ||||
\(845\) | − | 1.12905e6i | − | 0.0543966i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.47020e6i | − | 0.118310i | ||||||
\(848\) | 5.19676e6 | + | 2.12623e6i | 0.248167 | + | 0.101536i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.10726e6 | + | 3.27385e7i | 0.0525655 | + | 1.55422i | ||||
\(851\) | 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 | 0.736174 | − | 0.676792i | \(-0.236630\pi\) |
−0.218032 | + | 0.975942i | \(0.569964\pi\) | |||||||
\(860\) | −594698. | − | 885867.i | −0.0274189 | − | 0.0408434i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.20915e7 | − | 2.26807e7i | 0.554259 | − | 1.03965i | ||||
\(863\) | −8.69765e6 | −0.397535 | −0.198767 | − | 0.980047i | \(-0.563694\pi\) | ||||
−0.198767 | + | 0.980047i | \(0.563694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.31189e6 | −0.0596153 | ||||||||
\(866\) | 17900.4 | − | 33576.8i | 0.000811088 | − | 0.00152140i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.11940e6 | − | 3.15708e6i | −0.0954803 | − | 0.142228i | ||||
\(869\) | 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 | \(0.00162486\pi\) | |||||||
\(878\) | −943278. | − | 2.78901e7i | −0.0412955 | − | 1.22100i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 348905. | + | 142753.i | 0.0151880 | + | 0.00621411i | ||||
\(881\) | − | 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 | \(0.172174\pi\) | ||||
−0.857246 | + | 0.514907i | \(0.827826\pi\) | |||||||
\(884\) | −1.30967e6 | − | 1.93395e7i | −0.0563677 | − | 0.832365i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.85787e7 | − | 966568.i | 1.22309 | − | 0.0413664i | ||||
\(887\) | 1.14641e7 | − | 1.98564e7i | 0.489249 | − | 0.847405i | −0.510674 | − | 0.859774i | \(-0.670604\pi\) |
0.999923 | + | 0.0123696i | \(0.00393747\pi\) | |||||||
\(888\) | 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 | ||||
\(896\) | 699157. | + | 2.89893e6i | 0.0290941 | + | 0.120633i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.97303e7 | + | 1.05186e7i | 0.816476 | + | 0.435279i | ||||
\(899\) | −3.70398e7 | −1.52851 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.02198e7 | 0.419402 | ||||||||
\(902\) | 6.59450e6 | + | 3.51565e6i | 0.269877 | + | 0.143876i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.13274e7 | − | 9.57989e6i | −0.867994 | − | 0.389888i | ||||
\(905\) | 1.65518e6 | + | 955617.i | 0.0671774 | + | 0.0387849i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.34957e6 | + | 5.39798e6i | −0.377375 | + | 0.217878i | −0.676676 | − | 0.736281i | \(-0.736580\pi\) |
0.299300 | + | 0.954159i | \(0.403247\pi\) | |||||||
\(908\) | −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 | 0.893823 | − | 0.448420i | \(-0.148013\pi\) |
−0.835255 | + | 0.549863i | \(0.814680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.38253e6 | + | 4.12667e6i | −0.0945937 | + | 0.163841i | ||||
\(914\) | 4.23307e7 | − | 1.43167e6i | 1.67606 | − | 0.0566864i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.22145e7 | − | 827161.i | 0.480989 | − | 0.0325725i | ||||
\(917\) | − | 3.37252e6i | − | 0.132444i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.10763e7i | − | 0.823201i | −0.911364 | − | 0.411600i | \(-0.864970\pi\) | ||
0.911364 | − | 0.411600i | \(-0.135030\pi\) | |||||||
\(920\) | 1.61384e6 | − | 1.16442e6i | 0.0628626 | − | 0.0453566i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −979302. | − | 2.89553e7i | −0.0379393 | − | 1.12176i | ||||
\(923\) | −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 | ||||
\(932\) | −5.96081e6 | + | 4.00160e6i | −0.224784 | + | 0.150901i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.44673e7 | + | 2.71372e7i | −0.542652 | + | 1.01788i | ||||
\(935\) | 686147. | 0.0256678 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.09551e7 | 0.407633 | 0.203816 | − | 0.979009i | \(-0.434665\pi\) | ||||
0.203816 | + | 0.979009i | \(0.434665\pi\) | |||||||
\(938\) | −2.84709e6 | + | 5.34045e6i | −0.105656 | + | 0.198185i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.21681e6 | + | 2.15950e6i | −0.118743 | + | 0.0797139i | ||||
\(941\) | 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 | 0.997400 | − | 0.0720580i | \(-0.0229567\pi\) |
−0.561104 | + | 0.827745i | \(0.689623\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.72161e6 | − | 6.44601e6i | 0.134142 | − | 0.232341i | ||||
\(950\) | 247181. | + | 7.30848e6i | 0.00888601 | + | 0.262735i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.17582e6 | + | 4.40157e6i | 0.113570 | + | 0.157404i | ||||
\(953\) | 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 | ||||||||
\(956\) | 4.91104e7 | − | 3.32575e6i | 1.73792 | − | 0.117692i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.24593e7 | + | 1.77424e6i | −1.84675 | + | 0.0624594i | ||||
\(959\) | −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 | 0.858354 | − | 0.513058i | \(-0.171488\pi\) |
−0.0151446 | + | 0.999885i | \(0.504821\pi\) | |||||||
\(968\) | 1.13889e7 | − | 2.53546e7i | 0.390653 | − | 0.869699i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 990289. | + | 527942.i | 0.0337935 | + | 0.0180159i | ||||
\(971\) | −1.79971e7 | −0.612567 | −0.306284 | − | 0.951940i | \(-0.599086\pi\) | ||||
−0.306284 | + | 0.951940i | \(0.599086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.47103e6 | −0.117538 | ||||||||
\(974\) | 1.17806e7 | + | 6.28044e6i | 0.397895 | + | 0.212125i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.36663e7 | + | 4.58077e6i | −1.13128 | + | 0.153927i | ||||
\(977\) | 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 | 0.990038 | − | 0.140798i | \(-0.0449667\pi\) |
−0.616954 | + | 0.787000i | \(0.711633\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −345940. | + | 599186.i | −0.0113608 | + | 0.0196776i | ||||
\(986\) | 5.28403e7 | − | 1.78712e6i | 1.73091 | − | 0.0585413i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −292367. | − | 4.31730e6i | −0.00952876 | − | 0.140708i | ||||
\(989\) | − | 2.02950e7i | − | 0.659778i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.05378e7i | 0.987765i | 0.869529 | + | 0.493883i | \(0.164423\pi\) | ||||
−0.869529 | + | 0.493883i | \(0.835577\pi\) | |||||||
\(992\) | −7.19826e6 | − | 4.21764e7i | −0.232246 | − | 1.36079i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −134037. | − | 3.96312e6i | −0.00430289 | − | 0.127225i | ||||
\(995\) | −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.71.10 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.23.19 | yes | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.71.1 | 56 | ||
9.2 | odd | 6 | inner | 108.6.h.a.35.1 | 56 | ||
9.7 | even | 3 | 36.6.h.a.11.28 | yes | 56 | ||
12.11 | even | 2 | 36.6.h.a.23.28 | yes | 56 | ||
36.7 | odd | 6 | 36.6.h.a.11.19 | ✓ | 56 | ||
36.11 | even | 6 | inner | 108.6.h.a.35.10 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.19 | ✓ | 56 | 36.7 | odd | 6 | ||
36.6.h.a.11.28 | yes | 56 | 9.7 | even | 3 | ||
36.6.h.a.23.19 | yes | 56 | 3.2 | odd | 2 | ||
36.6.h.a.23.28 | yes | 56 | 12.11 | even | 2 | ||
108.6.h.a.35.1 | 56 | 9.2 | odd | 6 | inner | ||
108.6.h.a.35.10 | 56 | 36.11 | even | 6 | inner | ||
108.6.h.a.71.1 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.71.10 | 56 | 1.1 | even | 1 | trivial |