Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(90\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 13.12 | ||
Character | \(\chi\) | \(=\) | 108.13 |
Dual form | 108.6.i.a.25.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 11.6047 | + | 10.4082i | 0.744441 | + | 0.667688i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 50.4250 | + | 42.3116i | 0.902029 | + | 0.756892i | 0.970586 | − | 0.240755i | \(-0.0773950\pi\) |
−0.0685567 | + | 0.997647i | \(0.521839\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 105.429 | + | 38.3730i | 0.813233 | + | 0.295993i | 0.714959 | − | 0.699167i | \(-0.246446\pi\) |
0.0982743 | + | 0.995159i | \(0.468668\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 26.3374 | + | 241.569i | 0.108384 | + | 0.994109i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8754 | − | 13.3211i | 0.0395589 | − | 0.0331939i | −0.622794 | − | 0.782386i | \(-0.714002\pi\) |
0.662353 | + | 0.749192i | \(0.269558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 66.0301 | − | 374.475i | 0.108364 | − | 0.614561i | −0.881460 | − | 0.472259i | \(-0.843439\pi\) |
0.989823 | − | 0.142302i | \(-0.0454503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 144.777 | + | 1015.85i | 0.166139 | + | 1.16574i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 93.8720 | − | 162.591i | 0.0787796 | − | 0.136450i | −0.823944 | − | 0.566671i | \(-0.808231\pi\) |
0.902724 | + | 0.430221i | \(0.141564\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.9773 | + | 41.5299i | 0.0152376 | + | 0.0263923i | 0.873544 | − | 0.486746i | \(-0.161816\pi\) |
−0.858306 | + | 0.513138i | \(0.828483\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 824.075 | + | 1542.64i | 0.407773 | + | 0.763335i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2001.53 | + | 728.498i | −0.788938 | + | 0.287150i | −0.704895 | − | 0.709312i | \(-0.749006\pi\) |
−0.0840437 | + | 0.996462i | \(0.526784\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 209.758 | + | 1189.60i | 0.0671225 | + | 0.380671i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2208.66 | + | 3077.45i | −0.583069 | + | 0.812422i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 192.854 | + | 1093.73i | 0.0425828 | + | 0.241499i | 0.998668 | − | 0.0515884i | \(-0.0164284\pi\) |
−0.956086 | + | 0.293087i | \(0.905317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5304.29 | − | 1930.61i | 0.991342 | − | 0.360819i | 0.205102 | − | 0.978741i | \(-0.434247\pi\) |
0.786240 | + | 0.617922i | \(0.212025\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 322.878 | + | 10.6484i | 0.0516124 | + | 0.00170216i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3692.63 | + | 6395.82i | 0.509525 | + | 0.882524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5133.04 | + | 8890.68i | −0.616411 | + | 1.06765i | 0.373725 | + | 0.927540i | \(0.378080\pi\) |
−0.990135 | + | 0.140115i | \(0.955253\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4663.88 | − | 3658.41i | 0.491005 | − | 0.385151i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −632.010 | + | 3584.31i | −0.0587171 | + | 0.333001i | −0.999989 | − | 0.00464783i | \(-0.998521\pi\) |
0.941272 | + | 0.337649i | \(0.109632\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4373.32 | + | 3669.65i | −0.360695 | + | 0.302659i | −0.805068 | − | 0.593183i | \(-0.797871\pi\) |
0.444373 | + | 0.895842i | \(0.353427\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8893.08 | + | 13295.5i | −0.654668 | + | 0.978751i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10589.0 | + | 3854.10i | 0.699217 | + | 0.254494i | 0.667077 | − | 0.744989i | \(-0.267545\pi\) |
0.0321405 | + | 0.999483i | \(0.489768\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3232.12 | − | 2712.07i | −0.192308 | − | 0.161366i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2781.64 | − | 909.776i | 0.149753 | − | 0.0489789i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 40756.1 | 1.99298 | 0.996490 | − | 0.0837151i | \(-0.0266786\pi\) | ||||
0.996490 | + | 0.0837151i | \(0.0266786\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1364.15 | 0.0608075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −154.004 | + | 731.502i | −0.00627833 | + | 0.0298214i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6950.23 | − | 5831.93i | −0.259938 | − | 0.218113i | 0.503500 | − | 0.863995i | \(-0.332045\pi\) |
−0.763437 | + | 0.645882i | \(0.776490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37315.2 | − | 13581.6i | −1.28399 | − | 0.467334i | −0.392240 | − | 0.919863i | \(-0.628300\pi\) |
−0.891750 | + | 0.452529i | \(0.850522\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6492.99 | + | 26479.0i | −0.206107 | + | 0.840523i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19174.2 | − | 16089.1i | 0.562904 | − | 0.472332i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8375.85 | − | 47501.8i | 0.227951 | − | 1.29278i | −0.629011 | − | 0.777396i | \(-0.716540\pi\) |
0.856962 | − | 0.515379i | \(-0.172349\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −30809.5 | − | 12378.4i | −0.779045 | − | 0.312999i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1152.02 | + | 1995.35i | −0.0271215 | + | 0.0469758i | −0.879268 | − | 0.476328i | \(-0.841967\pi\) |
0.852146 | + | 0.523304i | \(0.175301\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17866.4 | − | 30945.5i | −0.392401 | − | 0.679659i | 0.600364 | − | 0.799727i | \(-0.295022\pi\) |
−0.992766 | + | 0.120068i | \(0.961689\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9947.41 | + | 15988.1i | −0.204201 | + | 0.328204i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2184.90 | − | 795.239i | 0.0419957 | − | 0.0152852i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15966.2 | − | 90549.1i | −0.287829 | − | 1.63236i | −0.695000 | − | 0.719009i | \(-0.744596\pi\) |
0.407171 | − | 0.913352i | \(-0.366515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −57661.7 | + | 12724.6i | −0.976506 | + | 0.215492i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16547.1 | − | 93843.4i | −0.263650 | − | 1.49523i | −0.772853 | − | 0.634585i | \(-0.781171\pi\) |
0.509203 | − | 0.860646i | \(-0.329940\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11613.0 | − | 4226.78i | 0.174340 | − | 0.0634544i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9145.79 | + | 14699.7i | −0.129546 | + | 0.208214i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13047.3 | − | 22598.6i | −0.174600 | − | 0.302417i | 0.765423 | − | 0.643528i | \(-0.222530\pi\) |
−0.940023 | + | 0.341111i | \(0.889197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21331.2 | − | 36946.8i | 0.270030 | − | 0.467706i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 81648.9 | + | 32804.3i | 0.978910 | + | 0.393299i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −548.141 | + | 3108.66i | −0.00623136 | + | 0.0353398i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13856.1 | − | 11626.7i | 0.149524 | − | 0.125466i | −0.564957 | − | 0.825120i | \(-0.691107\pi\) |
0.714481 | + | 0.699655i | \(0.246663\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3636.07 | + | 3484.16i | 0.0372859 | + | 0.0357282i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 172922. | + | 62938.3i | 1.68673 | + | 0.613920i | 0.994208 | − | 0.107476i | \(-0.0342770\pi\) |
0.692523 | + | 0.721396i | \(0.256499\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −70924.5 | − | 59512.7i | −0.658724 | − | 0.552735i | 0.250980 | − | 0.967992i | \(-0.419247\pi\) |
−0.909704 | + | 0.415257i | \(0.863692\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −23717.4 | + | 112655.i | −0.209939 | + | 0.997191i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 606.415 | 0.00512048 | 0.00256024 | − | 0.999997i | \(-0.499185\pi\) | ||||
0.00256024 | + | 0.999997i | \(0.499185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 81329.8 | 0.655667 | 0.327834 | − | 0.944735i | \(-0.393681\pi\) | ||||
0.327834 | + | 0.944735i | \(0.393681\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −152104. | + | 49747.7i | −1.17174 | + | 0.383235i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 167369. | + | 140439.i | 1.23305 | + | 1.03465i | 0.998035 | + | 0.0626552i | \(0.0199568\pi\) |
0.235010 | + | 0.971993i | \(0.424488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −131751. | − | 47953.5i | −0.928987 | − | 0.338124i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 92200.5 | + | 6088.09i | 0.622685 | + | 0.0411165i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16135.9 | − | 13539.7i | 0.104454 | − | 0.0876476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27891.6 | + | 158181.i | −0.173185 | + | 0.982182i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −44640.6 | + | 35016.6i | −0.266052 | + | 0.208695i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 63095.1 | − | 109284.i | 0.361178 | − | 0.625578i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −154548. | − | 267684.i | −0.850262 | − | 1.47270i | −0.880972 | − | 0.473169i | \(-0.843110\pi\) |
0.0307091 | − | 0.999528i | \(-0.490223\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −88945.5 | − | 2933.39i | −0.470598 | − | 0.0155201i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 175212. | − | 63772.1i | 0.892045 | − | 0.324678i | 0.144984 | − | 0.989434i | \(-0.453687\pi\) |
0.747060 | + | 0.664756i | \(0.231465\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 934.275 | + | 5298.53i | 0.00457979 | + | 0.0259733i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −241584. | + | 61728.4i | −1.14086 | + | 0.291508i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 35228.9 | + | 199793.i | 0.160361 | + | 0.909451i | 0.953720 | + | 0.300697i | \(0.0972192\pi\) |
−0.793359 | + | 0.608754i | \(0.791670\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −289065. | + | 105211.i | −1.26899 | + | 0.461875i | −0.886776 | − | 0.462199i | \(-0.847060\pi\) |
−0.382214 | + | 0.924074i | \(0.624838\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 82768.2 | + | 154939.i | 0.350603 | + | 0.656315i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3940.16 | − | 6824.55i | −0.0161129 | − | 0.0279084i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36552.8 | + | 63311.3i | −0.144378 | + | 0.250070i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9279.88 | − | 65113.5i | −0.0354200 | − | 0.248529i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −24420.3 | + | 138494.i | −0.0901124 | + | 0.511053i | 0.906023 | + | 0.423227i | \(0.139103\pi\) |
−0.996136 | + | 0.0878254i | \(0.972008\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −45605.6 | + | 38267.6i | −0.162770 | + | 0.136581i | −0.720535 | − | 0.693419i | \(-0.756104\pi\) |
0.557765 | + | 0.829999i | \(0.311659\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 41749.2 | + | 18394.3i | 0.144185 | + | 0.0635264i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 349156. | + | 127082.i | 1.16732 | + | 0.424870i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 272711. | + | 228831.i | 0.882984 | + | 0.740912i | 0.966791 | − | 0.255570i | \(-0.0822632\pi\) |
−0.0838060 | + | 0.996482i | \(0.526708\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 472962. | + | 424199.i | 1.48366 | + | 1.33069i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −238974. | −0.726585 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 579999. | 1.70985 | 0.854926 | − | 0.518750i | \(-0.173603\pi\) | ||||
0.854926 | + | 0.518750i | \(0.173603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15830.6 | + | 14198.4i | 0.0452676 | + | 0.0406004i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −136225. | − | 114307.i | −0.377978 | − | 0.317161i | 0.433930 | − | 0.900947i | \(-0.357126\pi\) |
−0.811908 | + | 0.583785i | \(0.801571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 213030. | + | 77536.4i | 0.573750 | + | 0.208828i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9400.81 | + | 6885.95i | −0.0245853 | + | 0.0180083i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −273574. | + | 229555.i | −0.694958 | + | 0.583139i | −0.920334 | − | 0.391133i | \(-0.872083\pi\) |
0.225376 | + | 0.974272i | \(0.427639\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23533.8 | + | 133467.i | −0.0580894 | + | 0.329442i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19955.1 | − | 140017.i | −0.0478763 | − | 0.335930i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 133930. | − | 231974.i | 0.312426 | − | 0.541137i | −0.666461 | − | 0.745540i | \(-0.732192\pi\) |
0.978887 | + | 0.204403i | \(0.0655252\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −316166. | − | 547615.i | −0.717329 | − | 1.24245i | −0.962055 | − | 0.272857i | \(-0.912031\pi\) |
0.244726 | − | 0.969592i | \(-0.421302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −291671. | − | 545996.i | −0.643821 | − | 1.20521i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −635012. | + | 231125.i | −1.36412 | + | 0.496499i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −675.629 | − | 3831.68i | −0.00141288 | − | 0.00801282i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −350948. | + | 239700.i | −0.714642 | + | 0.488104i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −31083.5 | − | 176283.i | −0.0616519 | − | 0.349645i | −0.999992 | − | 0.00393252i | \(-0.998748\pi\) |
0.938340 | − | 0.345713i | \(-0.112363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 399489. | − | 145402.i | 0.771990 | − | 0.280981i | 0.0741616 | − | 0.997246i | \(-0.476372\pi\) |
0.697829 | + | 0.716265i | \(0.254150\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 389969. | + | 12861.0i | 0.734419 | + | 0.0242208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −498292. | − | 863067.i | −0.914783 | − | 1.58445i | −0.807219 | − | 0.590253i | \(-0.799028\pi\) |
−0.107564 | − | 0.994198i | \(-0.534305\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −57000.7 | + | 98728.1i | −0.102035 | + | 0.176729i | −0.912523 | − | 0.409026i | \(-0.865869\pi\) |
0.810488 | + | 0.585755i | \(0.199202\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 591609. | − | 464066.i | 1.03287 | − | 0.810194i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21637.3 | + | 122711.i | −0.0368522 | + | 0.208999i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −183527. | + | 153997.i | −0.305011 | + | 0.255934i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −228697. | − | 464320.i | −0.370967 | − | 0.753168i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 933.873 | + | 339.902i | 0.00147884 | + | 0.000538255i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8500.53 | + | 7132.79i | 0.0131444 | + | 0.0110294i | 0.649336 | − | 0.760502i | \(-0.275047\pi\) |
−0.636192 | + | 0.771531i | \(0.719491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −34136.9 | + | 11165.0i | −0.0515555 | + | 0.0168620i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −375793. | −0.554437 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 633310. | 0.912992 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 114754. | − | 545071.i | 0.161681 | − | 0.767968i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −54687.9 | − | 45888.6i | −0.0753201 | − | 0.0632011i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.08720e6 | − | 395708.i | −1.46402 | − | 0.532860i | −0.517551 | − | 0.855652i | \(-0.673156\pi\) |
−0.946470 | + | 0.322792i | \(0.895379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −281844. | + | 82001.7i | −0.371153 | + | 0.107986i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 990520. | − | 831145.i | 1.27585 | − | 1.07056i | 0.282045 | − | 0.959401i | \(-0.408987\pi\) |
0.993802 | − | 0.111162i | \(-0.0354571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −165477. | + | 938466.i | −0.208521 | + | 1.18258i | 0.683282 | + | 0.730154i | \(0.260552\pi\) |
−0.891803 | + | 0.452424i | \(0.850559\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 33632.1 | + | 13512.5i | 0.0414691 | + | 0.0166611i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 51142.1 | − | 88580.8i | 0.0617147 | − | 0.106893i | −0.833517 | − | 0.552493i | \(-0.813676\pi\) |
0.895232 | + | 0.445600i | \(0.147010\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 370879. | + | 642382.i | 0.438090 | + | 0.758793i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 757173. | − | 1.21697e6i | 0.875637 | − | 1.40738i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.45627e6 | + | 530039.i | −1.64910 | + | 0.600224i | −0.988595 | − | 0.150596i | \(-0.951881\pi\) |
−0.660507 | + | 0.750820i | \(0.729659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −71022.4 | − | 402788.i | −0.0787686 | − | 0.446719i | −0.998528 | − | 0.0542364i | \(-0.982728\pi\) |
0.919760 | − | 0.392482i | \(-0.128384\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −801586. | − | 452492.i | −0.870832 | − | 0.491581i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −48227.6 | − | 273513.i | −0.0513311 | − | 0.291113i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17135.1 | − | 6236.68i | 0.0178708 | − | 0.00650446i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 784720. | − | 1.26125e6i | 0.802077 | − | 1.28915i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 86526.5 | + | 149868.i | 0.0866892 | + | 0.150150i | 0.906110 | − | 0.423043i | \(-0.139038\pi\) |
−0.819421 | + | 0.573193i | \(0.805705\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22070.8 | + | 38227.8i | −0.0216779 | + | 0.0375472i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 178758. | + | 71820.1i | 0.172153 | + | 0.0691665i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −248173. | + | 1.40746e6i | −0.234381 | + | 1.32924i | 0.609532 | + | 0.792761i | \(0.291357\pi\) |
−0.843913 | + | 0.536480i | \(0.819754\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −882333. | + | 740365.i | −0.817303 | + | 0.685799i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −259132. | + | 75393.5i | −0.235461 | + | 0.0685067i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 252535. | + | 91915.4i | 0.225130 | + | 0.0819405i | 0.452122 | − | 0.891956i | \(-0.350667\pi\) |
−0.226992 | + | 0.973897i | \(0.572889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.05512e6 | + | 1.72445e6i | 1.79773 | + | 1.50847i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 83801.4 | − | 398048.i | 0.0719405 | − | 0.341710i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.05143e6 | −0.885927 | −0.442963 | − | 0.896540i | \(-0.646073\pi\) | ||||
−0.442963 | + | 0.896540i | \(0.646073\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.24688e6 | 1.85847 | 0.929237 | − | 0.369484i | \(-0.120466\pi\) | ||||
0.929237 | + | 0.369484i | \(0.120466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 632093. | − | 206735.i | 0.513304 | − | 0.167883i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19176.7 | + | 16091.2i | 0.0152912 | + | 0.0128309i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −964358. | − | 350997.i | −0.755159 | − | 0.274856i | −0.0643843 | − | 0.997925i | \(-0.520508\pi\) |
−0.690775 | + | 0.723070i | \(0.742731\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 606075. | + | 1.23050e6i | 0.466139 | + | 0.946395i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 388199. | − | 325738.i | 0.293284 | − | 0.246095i | −0.484258 | − | 0.874925i | \(-0.660911\pi\) |
0.777542 | + | 0.628830i | \(0.216466\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −295011. | + | 1.67309e6i | −0.218964 | + | 1.24181i | 0.654930 | + | 0.755690i | \(0.272698\pi\) |
−0.873894 | + | 0.486117i | \(0.838413\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −38716.6 | + | 30369.8i | −0.0282349 | + | 0.0221478i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −204173. | + | 353638.i | −0.146317 | + | 0.253428i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 692305. | + | 1.19911e6i | 0.487588 | + | 0.844526i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 281809. | + | 9293.94i | 0.195084 | + | 0.00643380i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.83054e6 | + | 666263.i | −1.24569 | + | 0.453395i | −0.878944 | − | 0.476925i | \(-0.841751\pi\) |
−0.366749 | + | 0.930320i | \(0.619529\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −103707. | − | 588150.i | −0.0693828 | − | 0.393489i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5931.45 | + | 78277.7i | 0.00390185 | + | 0.0514929i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 140643. | + | 797627.i | 0.0909789 | + | 0.515967i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −601890. | + | 219070.i | −0.382914 | + | 0.139369i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.35162e6 | + | 2.53019e6i | 0.845764 | + | 1.58324i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.30696e6 | − | 2.26372e6i | −0.804474 | − | 1.39339i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 940971. | − | 1.62981e6i | 0.569810 | − | 0.986941i | −0.426774 | − | 0.904358i | \(-0.640350\pi\) |
0.996584 | − | 0.0825822i | \(-0.0263167\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −203634. | − | 1.42883e6i | −0.121326 | − | 0.851301i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −278916. | + | 1.58181e6i | −0.163521 | + | 0.927371i | 0.787056 | + | 0.616881i | \(0.211604\pi\) |
−0.950577 | + | 0.310490i | \(0.899507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 64593.6 | − | 54200.5i | 0.0372674 | − | 0.0312710i | −0.623964 | − | 0.781453i | \(-0.714479\pi\) |
0.661231 | + | 0.750182i | \(0.270034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.44778e6 | + | 1.06047e6i | −0.822100 | + | 0.602176i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −385099. | − | 140164.i | −0.215240 | − | 0.0783411i | 0.232150 | − | 0.972680i | \(-0.425424\pi\) |
−0.447390 | + | 0.894339i | \(0.647646\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17631.3 | + | 14794.4i | 0.00970081 | + | 0.00813995i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7037.25 | + | 6311.71i | 0.00381189 | + | 0.00341888i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9003.18 | 0.00480164 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 459324. | 0.241219 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 943807. | + | 846500.i | 0.488106 | + | 0.437782i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 968499. | + | 812667.i | 0.493298 | + | 0.413926i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.20156e6 | − | 437333.i | −0.602804 | − | 0.219403i | 0.0225477 | − | 0.999746i | \(-0.492822\pi\) |
−0.625352 | + | 0.780343i | \(0.715044\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.28290e6 | − | 1.00582e6i | −1.12817 | − | 0.497062i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.43223e6 | − | 2.04088e6i | 1.18411 | − | 0.993587i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −171503. | + | 972644.i | −0.0822617 | + | 0.466530i | 0.915652 | + | 0.401971i | \(0.131675\pi\) |
−0.997914 | + | 0.0645581i | \(0.979436\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 480540. | + | 3.37177e6i | 0.227107 | + | 1.59352i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 58490.3 | − | 101308.i | 0.0272394 | − | 0.0471801i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.17952e6 | − | 2.04299e6i | −0.541341 | − | 0.937629i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.02982e6 | − | 1.92778e6i | −0.465815 | − | 0.871987i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22562.9 | + | 8212.24i | −0.0100594 | + | 0.00366132i | −0.347045 | − | 0.937848i | \(-0.612815\pi\) |
0.336986 | + | 0.941510i | \(0.390593\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −226.526 | − | 1284.69i | −9.95530e−5 | − | 0.000564593i | 0.984758 | − | 0.173930i | \(-0.0556468\pi\) |
−0.984857 | + | 0.173366i | \(0.944536\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00659e6 | + | 1.03029e6i | 0.436099 | + | 0.446369i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 580092. | + | 3.28987e6i | 0.247777 | + | 1.40521i | 0.813955 | + | 0.580928i | \(0.197310\pi\) |
−0.566178 | + | 0.824283i | \(0.691579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −142517. | + | 51872.0i | −0.0600200 | + | 0.0218455i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 328176. | + | 10823.1i | 0.136281 | + | 0.00449451i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.03014e6 | − | 1.78425e6i | −0.421850 | − | 0.730666i | 0.574270 | − | 0.818666i | \(-0.305286\pi\) |
−0.996121 | + | 0.0879996i | \(0.971953\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.23690e6 | − | 2.14237e6i | 0.499536 | − | 0.865221i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.97006e6 | + | 1.54534e6i | −0.784717 | + | 0.615542i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 408441. | − | 2.31638e6i | 0.160471 | − | 0.910078i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −613458. | + | 514752.i | −0.237749 | + | 0.199495i | −0.753876 | − | 0.657017i | \(-0.771818\pi\) |
0.516126 | + | 0.856512i | \(0.327374\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −882501. | − | 58272.5i | −0.337403 | − | 0.0222791i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.29687e6 | + | 1.56393e6i | 1.62076 | + | 0.589907i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 357268. | + | 299783.i | 0.132960 | + | 0.111567i | 0.706843 | − | 0.707371i | \(-0.250119\pi\) |
−0.573882 | + | 0.818938i | \(0.694563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.86965e6 | − | 611497.i | 0.686567 | − | 0.224552i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 422309. | 0.153030 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.64393e6 | −1.30308 | −0.651541 | − | 0.758613i | \(-0.725877\pi\) | ||||
−0.651541 | + | 0.758613i | \(0.725877\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 992644. | − | 4.71496e6i | 0.350333 | − | 1.66405i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.96855e6 | + | 2.49091e6i | 1.03406 | + | 0.867683i | 0.991329 | − | 0.131404i | \(-0.0419485\pi\) |
0.0427349 | + | 0.999086i | \(0.486393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 143821. | + | 52346.7i | 0.0494506 | + | 0.0179986i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.00165e6 | − | 959807.i | −0.339970 | − | 0.325766i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −327734. | + | 275001.i | −0.109811 | + | 0.0921427i | −0.696040 | − | 0.718003i | \(-0.745056\pi\) |
0.586229 | + | 0.810146i | \(0.300612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −69440.5 | + | 393817.i | −0.0229705 | + | 0.130272i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.69704e6 | + | 1.08360e6i | 0.880858 | + | 0.353905i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.02618e6 | − | 5.24149e6i | 0.975892 | − | 1.69029i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −698113. | − | 1.20917e6i | −0.222305 | − | 0.385044i | 0.733202 | − | 0.680011i | \(-0.238025\pi\) |
−0.955508 | + | 0.294967i | \(0.904691\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −44306.4 | + | 71212.0i | −0.0139327 | + | 0.0223934i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.70691e6 | + | 621263.i | −0.530089 | + | 0.192937i | −0.593178 | − | 0.805071i | \(-0.702127\pi\) |
0.0630889 | + | 0.998008i | \(0.479905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −372721. | − | 2.11381e6i | −0.114320 | − | 0.648339i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.44599e6 | − | 1.79812e6i | −1.04394 | − | 0.544730i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36944.2 | + | 209521.i | 0.0110550 | + | 0.0626963i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.94043e6 | + | 1.07023e6i | −0.869166 | + | 0.316351i | −0.737829 | − | 0.674987i | \(-0.764149\pi\) |
−0.131337 | + | 0.991338i | \(0.541927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.67067e6 | + | 2.68521e6i | −0.487851 | + | 0.784103i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −508967. | − | 881556.i | −0.146830 | − | 0.254317i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.13627e6 | − | 5.43218e6i | 0.893910 | − | 1.54830i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.44957e6 | − | 1.78771e6i | −1.25308 | − | 0.503452i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 379779. | − | 2.15383e6i | 0.105681 | − | 0.599345i | −0.885266 | − | 0.465086i | \(-0.846023\pi\) |
0.990946 | − | 0.134259i | \(-0.0428654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 689302. | − | 578393.i | 0.189541 | − | 0.159044i | −0.543079 | − | 0.839682i | \(-0.682742\pi\) |
0.732620 | + | 0.680638i | \(0.238297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −652141. | + | 2.65949e6i | −0.177211 | + | 0.722681i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 213108. | + | 77564.9i | 0.0572305 | + | 0.0208302i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.41294e6 | − | 2.86380e6i | −0.905855 | − | 0.760103i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25307.3 | − | 120207.i | 0.00663899 | − | 0.0315345i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.40307e6 | −0.363820 | −0.181910 | − | 0.983315i | \(-0.558228\pi\) | ||||
−0.181910 | + | 0.983315i | \(0.558228\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −516851. | −0.132479 | −0.0662393 | − | 0.997804i | \(-0.521100\pi\) | ||||
−0.0662393 | + | 0.997804i | \(0.521100\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.08314e6 | + | 354258.i | −0.274450 | + | 0.0897628i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −78245.8 | − | 65656.0i | −0.0196001 | − | 0.0164464i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.95225e6 | − | 1.43850e6i | −0.978775 | − | 0.356245i | −0.197411 | − | 0.980321i | \(-0.563253\pi\) |
−0.781364 | + | 0.624076i | \(0.785476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 570026. | − | 852208.i | 0.139572 | − | 0.208665i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 768945. | − | 645221.i | 0.186160 | − | 0.156207i | −0.544945 | − | 0.838472i | \(-0.683449\pi\) |
0.731105 | + | 0.682265i | \(0.239005\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 298272. | − | 1.69158e6i | 0.0714022 | − | 0.404942i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.72487e6 | + | 1.35301e6i | −0.408307 | + | 0.320282i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27453.5 | + | 47550.8i | −0.00642661 | + | 0.0111312i | −0.869221 | − | 0.494424i | \(-0.835379\pi\) |
0.862794 | + | 0.505555i | \(0.168712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37713.4 | + | 65321.5i | 0.00873081 | + | 0.0151222i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −927536. | − | 30589.8i | −0.212366 | − | 0.00700375i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.63890e6 | − | 960482.i | 0.597579 | − | 0.217501i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −373230. | − | 2.11669e6i | −0.0835962 | − | 0.474098i | −0.997651 | − | 0.0685062i | \(-0.978177\pi\) |
0.914055 | − | 0.405591i | \(-0.132934\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 293034. | + | 647995.i | 0.0649212 | + | 0.143562i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −247406. | − | 1.40311e6i | −0.0542198 | − | 0.307496i | 0.945622 | − | 0.325267i | \(-0.105454\pi\) |
−0.999842 | + | 0.0177712i | \(0.994343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.90834e6 | − | 1.05855e6i | 0.630510 | − | 0.229487i | −0.00694314 | − | 0.999976i | \(-0.502210\pi\) |
0.637453 | + | 0.770489i | \(0.279988\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.72914e6 | + | 5.10885e6i | 0.585320 | + | 1.09570i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.84631e6 | + | 3.19790e6i | 0.391753 | + | 0.678536i | 0.992681 | − | 0.120767i | \(-0.0385355\pi\) |
−0.600928 | + | 0.799303i | \(0.705202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.70584e6 | − | 4.68666e6i | 0.568029 | − | 0.983856i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 782991. | + | 5.49395e6i | 0.162631 | + | 1.14112i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20544.7 | + | 116515.i | −0.00422227 | + | 0.0239457i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −44374.3 | + | 37234.5i | −0.00902397 | + | 0.00757201i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.07341e6 | + | 9.84539e6i | 0.216008 | + | 1.98124i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.93158e6 | + | 1.43098e6i | 0.782939 | + | 0.284966i | 0.702398 | − | 0.711785i | \(-0.252113\pi\) |
0.0805413 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.99041e6 | + | 2.50925e6i | 0.589342 | + | 0.494517i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.77322e6 | − | 2.48730e6i | −0.540899 | − | 0.485132i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.19064e6 | 0.229840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.17953e6 | −0.798556 | −0.399278 | − | 0.916830i | \(-0.630739\pi\) | ||||
−0.399278 | + | 0.916830i | \(0.630739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.73071e6 | + | 6.03677e6i | 1.27288 | + | 1.14165i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.58207e6 | + | 3.84481e6i | 0.857745 | + | 0.719733i | 0.961481 | − | 0.274872i | \(-0.0886353\pi\) |
−0.103736 | + | 0.994605i | \(0.533080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 195934. | + | 71314.3i | 0.0363073 | + | 0.0132148i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 35928.3 | + | 329537.i | 0.00659057 | + | 0.0604493i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −198024. | + | 166162.i | −0.0359606 | + | 0.0301745i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −696332. | + | 3.94909e6i | −0.125189 | + | 0.709980i | 0.856007 | + | 0.516964i | \(0.172938\pi\) |
−0.981196 | + | 0.193016i | \(0.938173\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −391122. | − | 2.74435e6i | −0.0696174 | − | 0.488479i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31468.3 | + | 54504.6i | −0.00554565 | + | 0.00960535i | −0.868785 | − | 0.495190i | \(-0.835099\pi\) |
0.863239 | + | 0.504795i | \(0.168432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.05655e6 | + | 1.04902e7i | 1.05681 | + | 1.83045i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.66512e6 | + | 3.11705e6i | 0.287691 | + | 0.538547i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.67397e6 | + | 3.15707e6i | −1.48396 | + | 0.540119i | −0.951853 | − | 0.306555i | \(-0.900824\pi\) |
−0.532111 | + | 0.846674i | \(0.678601\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −696165. | − | 3.94815e6i | −0.117940 | − | 0.668869i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −180764. | − | 17936.6i | −0.0303262 | − | 0.00300917i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.05829e6 | − | 6.00186e6i | −0.175827 | − | 0.997166i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 219446. | − | 79872.0i | 0.0361079 | − | 0.0131422i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.56400e6 | − | 183499.i | −0.906711 | − | 0.0299030i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.62625e6 | + | 4.54879e6i | 0.423878 | + | 0.734179i | 0.996315 | − | 0.0857702i | \(-0.0273351\pi\) |
−0.572437 | + | 0.819949i | \(0.694002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.99299e6 | + | 5.18400e6i | −0.478465 | + | 0.828726i | −0.999695 | − | 0.0246901i | \(-0.992140\pi\) |
0.521230 | + | 0.853416i | \(0.325473\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.66226e6 | + | 1.30390e6i | −0.263208 | + | 0.206464i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 184025. | − | 1.04366e6i | 0.0288637 | − | 0.163694i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.45510e6 | + | 1.22098e6i | −0.226076 | + | 0.189700i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22576e6 | − | 1.83255e6i | 0.188655 | − | 0.282046i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.30050e6 | + | 473344.i | 0.198287 | + | 0.0721704i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30578.5 | + | 25658.4i | 0.00461882 | + | 0.00387565i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.96866e6 | − | 1.29801e6i | 0.593893 | − | 0.194242i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −87439.2 | −0.0129639 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 584809. | 0.0859054 | 0.0429527 | − | 0.999077i | \(-0.486324\pi\) | ||||
0.0429527 | + | 0.999077i | \(0.486324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.03070e6 | − | 9.64562e6i | 0.295560 | − | 1.40388i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.10105e6 | + | 3.44119e6i | 0.591431 | + | 0.496270i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.12856e6 | − | 774732.i | −0.304171 | − | 0.110709i | 0.185426 | − | 0.982658i | \(-0.440634\pi\) |
−0.489596 | + | 0.871949i | \(0.662856\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.29811e6 | − | 9.37189e6i | 0.325417 | − | 1.32708i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40798.4 | + | 34233.9i | −0.00572485 | + | 0.00480372i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.79134e6 | − | 1.01592e7i | 0.249095 | − | 1.41269i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.77472e6 | − | 3.92721e6i | −1.34701 | − | 0.541193i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.87071e6 | + | 1.19004e7i | −0.938348 | + | 1.62527i | −0.169796 | + | 0.985479i | \(0.554311\pi\) |
−0.768552 | + | 0.639787i | \(0.779022\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.08542e6 | + | 1.88001e6i | 0.146916 | + | 0.254466i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32040.6 | − | 51497.5i | 0.00429826 | − | 0.00690843i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.28717e6 | + | 2.28834e6i | −0.835957 | + | 0.304264i | −0.724301 | − | 0.689483i | \(-0.757838\pi\) |
−0.111656 | + | 0.993747i | \(0.535615\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.49737e6 | + | 1.41633e7i | 0.329126 | + | 1.86657i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.56749e6 | − | 871115.i | −0.857911 | − | 0.113794i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −781637. | − | 4.43288e6i | −0.101210 | − | 0.573992i | −0.992667 | − | 0.120885i | \(-0.961427\pi\) |
0.891456 | − | 0.453107i | \(-0.149684\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.78221e6 | + | 648672.i | −0.228754 | + | 0.0832598i | −0.453854 | − | 0.891076i | \(-0.649951\pi\) |
0.225100 | + | 0.974336i | \(0.427729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.47408e6 | − | 2.36924e6i | 0.187558 | − | 0.301455i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.28646e6 | − | 2.22821e6i | −0.162265 | − | 0.281051i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.65512e6 | + | 9.79495e6i | −0.707134 | + | 1.22479i | 0.258781 | + | 0.965936i | \(0.416679\pi\) |
−0.965916 | + | 0.258857i | \(0.916654\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.14933e6 | + | 2.47063e6i | 0.762309 | + | 0.306275i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.85651e6 | − | 1.05288e7i | 0.228169 | − | 1.29401i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 647021. | − | 542915.i | 0.0788401 | − | 0.0661547i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.39161e6 | + | 4.20814e6i | 0.530560 | + | 0.508394i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.04029e7 | − | 3.78633e6i | −1.24611 | − | 0.453548i | −0.367026 | − | 0.930211i | \(-0.619624\pi\) |
−0.879086 | + | 0.476663i | \(0.841846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 207360. | + | 173996.i | 0.0246285 | + | 0.0206657i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.20048e6 | − | 1.52020e7i | 0.376918 | − | 1.79032i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.05137e7 | 1.22777 | 0.613885 | − | 0.789396i | \(-0.289606\pi\) | ||||
0.613885 | + | 0.789396i | \(0.289606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.38654e6 | 0.160561 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.68906e6 | + | 552432.i | −0.193959 | + | 0.0634370i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.84673e6 | + | 3.22779e6i | 0.438051 | + | 0.367569i | 0.834980 | − | 0.550281i | \(-0.185479\pi\) |
−0.396928 | + | 0.917850i | \(0.629924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.01180e7 | + | 3.68265e6i | 1.14264 | + | 0.415886i | 0.842865 | − | 0.538124i | \(-0.180867\pi\) |
0.299773 | + | 0.954011i | \(0.403089\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.16955e7 | + | 772268.i | 1.30987 | + | 0.0864918i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.09934e6 | + | 6.79615e6i | −0.899624 | + | 0.754874i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.16395e6 | + | 6.60111e6i | −0.128222 | + | 0.727186i | 0.851119 | + | 0.524973i | \(0.175924\pi\) |
−0.979342 | + | 0.202213i | \(0.935187\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.52830e6 | + | 1.19882e6i | −0.166981 | + | 0.130982i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.14246e6 | − | 3.71085e6i | 0.232172 | − | 0.402133i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.05972e6 | − | 5.29959e6i | −0.328875 | − | 0.569628i | 0.653414 | − | 0.757001i | \(-0.273336\pi\) |
−0.982289 | + | 0.187373i | \(0.940003\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.73261e6 | − | 123100.i | −0.397947 | − | 0.0131241i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.73684e6 | + | 2.45201e6i | −0.712432 | + | 0.259304i | −0.672709 | − | 0.739907i | \(-0.734870\pi\) |
−0.0397223 | + | 0.999211i | \(0.512647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.72523e6 | − | 9.78426e6i | −0.180976 | − | 1.02636i | −0.931018 | − | 0.364974i | \(-0.881078\pi\) |
0.750042 | − | 0.661390i | \(-0.230033\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.17879e6 | − | 7.76863e6i | 0.226719 | − | 0.808380i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −508387. | − | 2.88321e6i | −0.0524776 | − | 0.297616i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.13527e7 | − | 4.13206e6i | 1.16252 | − | 0.423123i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7299.52 | + | 13664.4i | 0.000741525 | + | 0.00138811i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 963696. | + | 1.66917e6i | 0.0971211 | + | 0.168219i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.84921e6 | + | 3.20292e6i | −0.184890 | + | 0.320238i | −0.943539 | − | 0.331261i | \(-0.892526\pi\) |
0.758650 | + | 0.651499i | \(0.225859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24406.2 | + | 171249.i | 0.00242098 | + | 0.0169871i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.53309e6 | − | 2.00371e7i | 0.347712 | − | 1.97197i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.22902e6 | + | 1.03127e6i | −0.120008 | + | 0.100699i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −512356. | − | 225739.i | −0.0496386 | − | 0.0218703i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.21072e6 | − | 1.53258e6i | −0.404773 | − | 0.147325i | 0.131607 | − | 0.991302i | \(-0.457986\pi\) |
−0.536380 | + | 0.843977i | \(0.680209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.76660e6 | − | 5.67785e6i | −0.645421 | − | 0.541572i | 0.260257 | − | 0.965539i | \(-0.416193\pi\) |
−0.905678 | + | 0.423967i | \(0.860637\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.36096e6 | − | 3.91134e6i | −0.412746 | − | 0.370191i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.74262e6 | −0.914987 | −0.457494 | − | 0.889213i | \(-0.651253\pi\) | ||||
−0.457494 | + | 0.889213i | \(0.651253\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −188026. | −0.0175229 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.34936e6 | + | 6.59163e6i | 0.679668 | + | 0.609594i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.36921e7 | − | 1.14890e7i | −1.25657 | − | 1.05439i | −0.996038 | − | 0.0889232i | \(-0.971657\pi\) |
−0.260532 | − | 0.965465i | \(-0.583898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.15334e7 | + | 4.19781e6i | 1.05040 | + | 0.382313i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.00491e6 | − | 5.13099e6i | 0.633125 | − | 0.463754i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.13956e7 | + | 9.56204e6i | −1.02217 | + | 0.857703i | −0.989899 | − | 0.141776i | \(-0.954719\pi\) |
−0.0322720 | + | 0.999479i | \(0.510274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.40722e6 | − | 1.36520e7i | 0.214295 | − | 1.21533i | −0.667830 | − | 0.744314i | \(-0.732777\pi\) |
0.882125 | − | 0.471015i | \(-0.156112\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −157017. | − | 1.10173e6i | −0.0138727 | − | 0.0973398i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −177079. | + | 306709.i | −0.0155279 | + | 0.0268951i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.18279e6 | − | 2.04864e6i | −0.102942 | − | 0.178300i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.49799e6 | − | 1.59079e7i | −0.734093 | − | 1.37419i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −773318. | + | 281465.i | −0.0663058 | + | 0.0241333i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.04279e6 | + | 1.72565e7i | 0.258961 | + | 1.46864i | 0.785696 | + | 0.618613i | \(0.212305\pi\) |
−0.526735 | + | 0.850030i | \(0.676584\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.12421e6 | − | 1.98190e6i | −0.348402 | − | 0.167426i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 963707. | + | 5.46545e6i | 0.0808115 | + | 0.458305i | 0.998182 | + | 0.0602706i | \(0.0191964\pi\) |
−0.917371 | + | 0.398034i | \(0.869693\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.90699e6 | − | 694086.i | 0.158735 | − | 0.0577749i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.01454e7 | + | 664388.i | 1.66460 | + | 0.0548977i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.72992e6 | + | 2.99631e6i | 0.141898 | + | 0.245774i | 0.928211 | − | 0.372054i | \(-0.121346\pi\) |
−0.786314 | + | 0.617828i | \(0.788013\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.67714e6 | + | 1.15652e7i | −0.543706 | + | 0.941727i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.16881e7 | + | 9.16828e6i | −0.944825 | + | 0.741133i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.69113e6 | − | 1.52621e7i | 0.215967 | − | 1.22481i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.67902e7 | − | 1.40887e7i | 1.33771 | − | 1.12247i | 0.355501 | − | 0.934676i | \(-0.384310\pi\) |
0.982208 | − | 0.187796i | \(-0.0601342\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 249649. | + | 506859.i | 0.0197468 | + | 0.0400917i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.90277e7 | − | 6.92552e6i | −1.49426 | − | 0.543864i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 523448. | + | 439225.i | 0.0408124 | + | 0.0342456i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.51546e6 | − | 495653.i | 0.117314 | − | 0.0383693i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.30263e6 | −0.176982 | −0.0884911 | − | 0.996077i | \(-0.528204\pi\) | ||||
−0.0884911 | + | 0.996077i | \(0.528204\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −492305. | −0.0375704 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.38212e6 | + | 1.13148e7i | −0.180506 | + | 0.857384i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.58158e7 | + | 1.32710e7i | 1.18999 | + | 0.998519i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.75353e7 | + | 6.38232e6i | 1.31008 | + | 0.476829i | 0.900266 | − | 0.435341i | \(-0.143372\pi\) |
0.409812 | + | 0.912170i | \(0.365594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.14533e7 | − | 6.24177e6i | 1.59155 | − | 0.463056i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.21028e6 | + | 7.72834e6i | −0.678498 | + | 0.569328i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 90075.3 | − | 510842.i | 0.00658932 | − | 0.0373699i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.24163e7 | − | 9.00627e6i | −1.62842 | − | 0.654255i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.34649e6 | + | 1.09924e7i | −0.457837 | + | 0.792997i | −0.998846 | − | 0.0480194i | \(-0.984709\pi\) |
0.541009 | + | 0.841017i | \(0.318042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.19382e6 | − | 8.99596e6i | −0.372090 | − | 0.644480i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.36812e6 | − | 5.41345e6i | 0.239630 | − | 0.385149i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.26064e6 | + | 458837.i | −0.0890733 | + | 0.0324200i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.35493e6 | + | 1.90267e7i | 0.235422 | + | 1.33515i | 0.841723 | + | 0.539910i | \(0.181542\pi\) |
−0.606301 | + | 0.795235i | \(0.707347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.59251e6 | − | 1.35941e7i | −0.320060 | − | 0.947397i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 186120. | + | 1.05554e6i | 0.0128825 | + | 0.0730602i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.02668e7 | + | 7.37652e6i | −1.39324 | + | 0.507097i | −0.926164 | − | 0.377121i | \(-0.876914\pi\) |
−0.467074 | + | 0.884218i | \(0.654692\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.28712e6 | − | 3.67599e6i | 0.156160 | − | 0.250990i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −499805. | − | 865687.i | −0.0338947 | − | 0.0587073i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.82686e6 | + | 8.36037e6i | −0.325127 | + | 0.563137i | −0.981538 | − | 0.191266i | \(-0.938741\pi\) |
0.656411 | + | 0.754404i | \(0.272074\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 263761. | + | 105972.i | 0.0176467 | + | 0.00708998i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.02349e6 | − | 1.71470e7i | 0.200926 | − | 1.13951i | −0.702797 | − | 0.711390i | \(-0.748066\pi\) |
0.903723 | − | 0.428117i | \(-0.140823\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.09130e6 | + | 5.95030e6i | −0.468096 | + | 0.392779i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.22338e7 | − | 6.46885e6i | 1.45785 | − | 0.424156i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 63933.7 | + | 23270.0i | 0.00416414 | + | 0.00151562i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.11243e6 | + | 1.77254e6i | 0.136673 | + | 0.114682i | 0.708561 | − | 0.705649i | \(-0.249345\pi\) |
−0.571888 | + | 0.820331i | \(0.693789\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −555752. | + | 2.63976e6i | −0.0357185 | + | 0.169659i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.91882e6 | −0.250200 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.48248e7 | −0.940264 | −0.470132 | − | 0.882596i | \(-0.655794\pi\) | ||||
−0.470132 | + | 0.882596i | \(0.655794\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −654009. | + | 213903.i | −0.0412078 | + | 0.0134776i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.77510e7 | + | 1.48949e7i | 1.11112 | + | 0.932342i | 0.998122 | − | 0.0612528i | \(-0.0195096\pi\) |
0.113000 | + | 0.993595i | \(0.463954\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.57452e6 | + | 3.12087e6i | 0.533210 | + | 0.194073i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.32691e6 | + | 2.69401e6i | 0.0819763 | + | 0.166435i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.64284e6 | + | 2.21761e6i | −0.162212 | + | 0.136112i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.40904e6 | − | 7.99108e6i | 0.0859228 | − | 0.487292i | −0.911231 | − | 0.411896i | \(-0.864867\pi\) |
0.997154 | − | 0.0753963i | \(-0.0240222\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.75292e7 | + | 1.37501e7i | −1.06200 | + | 0.833048i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.32621e6 | − | 7.49321e6i | 0.260411 | − | 0.451044i | −0.705940 | − | 0.708271i | \(-0.749475\pi\) |
0.966351 | + | 0.257227i | \(0.0828087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.40926e6 | + | 5.90501e6i | 0.203894 | + | 0.353156i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.79451e7 | − | 591822.i | −1.06633 | − | 0.0351673i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −164010. | + | 59694.7i | −0.00968336 | + | 0.00352445i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8291.47 | + | 47023.3i | 0.000486412 | + | 0.00275858i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.79185e6 | − | 1.82218e6i | −0.221028 | − | 0.106216i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.06921e6 | + | 2.30776e7i | 0.235687 | + | 1.33665i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.59758e6 | + | 581473.i | −0.0919448 | + | 0.0334652i | −0.387583 | − | 0.921835i | \(-0.626690\pi\) |
0.295638 | + | 0.955300i | \(0.404468\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.97392e6 | + | 3.69510e6i | 0.112885 | + | 0.211316i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.22565e7 | + | 2.12288e7i | 0.696505 | + | 1.20638i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.54991e6 | + | 1.30768e7i | −0.426343 | + | 0.738447i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.90055e6 | + | 4.14020e7i | 0.331112 | + | 2.32329i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.03888e6 | − | 1.72344e7i | 0.169460 | − | 0.961057i | −0.774885 | − | 0.632102i | \(-0.782192\pi\) |
0.944345 | − | 0.328955i | \(-0.106697\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.62066e6 | − | 1.35989e6i | 0.0898098 | − | 0.0753594i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.11547e6 | − | 3.74700e6i | 0.281711 | − | 0.206349i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −695865. | − | 253274.i | −0.0380835 | − | 0.0138612i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.20503e7 | − | 1.01114e7i | −0.655401 | − | 0.549947i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.22015e7 | − | 1.09435e7i | −0.659520 | − | 0.591523i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.00572e7 | 1.61465 | 0.807323 | − | 0.590110i | \(-0.200916\pi\) | ||||
0.807323 | + | 0.590110i | \(0.200916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.59135e7 | 1.38348 | 0.691741 | − | 0.722146i | \(-0.256844\pi\) | ||||
0.691741 | + | 0.722146i | \(0.256844\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.60743e7 | + | 2.33860e7i | 1.38352 | + | 1.24088i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.92464e7 | + | 2.45407e7i | 1.54234 | + | 1.29417i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −257260. | − | 93635.1i | −0.0134840 | − | 0.00490776i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.48699e6 | + | 4.17987e6i | 0.494218 | + | 0.217748i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.33044e7 | − | 1.95548e7i | 1.20665 | − | 1.01250i | 0.207234 | − | 0.978291i | \(-0.433554\pi\) |
0.999415 | − | 0.0342072i | \(-0.0108906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.81266e6 | + | 1.59514e7i | −0.144750 | + | 0.820916i | 0.822818 | + | 0.568305i | \(0.192401\pi\) |
−0.967568 | + | 0.252612i | \(0.918711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 55059.0 | + | 386328.i | 0.00281639 | + | 0.0197616i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.62710e7 | + | 2.81821e7i | −0.827274 | + | 1.43288i | 0.0728953 | + | 0.997340i | \(0.476776\pi\) |
−0.900169 | + | 0.435541i | \(0.856557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.12068e7 | − | 1.94107e7i | −0.566362 | − | 0.980968i | −0.996922 | − | 0.0784058i | \(-0.975017\pi\) |
0.430559 | − | 0.902562i | \(-0.358316\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.53780e6 | − | 1.41105e7i | −0.378654 | − | 0.708825i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −744365. | + | 270927.i | −0.0371683 | + | 0.0135282i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.03266e6 | − | 1.15278e7i | −0.100890 | − | 0.572177i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.77406e6 | + | 2.05878e7i | −0.284884 | + | 1.01577i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.71713e6 | − | 1.54096e7i | −0.133262 | − | 0.755765i | −0.976054 | − | 0.217527i | \(-0.930201\pi\) |
0.842793 | − | 0.538239i | \(-0.180910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.81151e7 | − | 6.59336e6i | 0.883184 | − | 0.321453i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.89528e6 | + | 260383.i | 0.382647 | + | 0.0126196i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.46132e6 | + | 1.29234e7i | 0.359479 | + | 0.622636i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.01048e6 | + | 1.56066e7i | −0.431558 | + | 0.747481i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.08375e7 | + | 1.63452e7i | −0.992146 | + | 0.778252i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.79709e6 | − | 2.15344e7i | 0.179733 | − | 1.01932i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.40573e7 | − | 1.17955e7i | 0.661500 | − | 0.555064i | −0.249036 | − | 0.968494i | \(-0.580114\pi\) |
0.910536 | + | 0.413430i | \(0.135669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −765391. | − | 50539.5i | −0.0358070 | − | 0.00236437i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.62701e7 | − | 9.56155e6i | −1.22183 | − | 0.444709i | −0.351037 | − | 0.936361i | \(-0.614171\pi\) |
−0.870792 | + | 0.491652i | \(0.836393\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.28653e7 | − | 1.91863e7i | −1.05729 | − | 0.887171i | −0.0634481 | − | 0.997985i | \(-0.520210\pi\) |
−0.993841 | + | 0.110814i | \(0.964654\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.05011e6 | + | 1.97878e6i | −0.278135 | + | 0.0909680i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.00275e7 | −0.915378 | −0.457689 | − | 0.889112i | \(-0.651323\pi\) | ||||
−0.457689 | + | 0.889112i | \(0.651323\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.35078e7 | −1.06825 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.44661e6 | + | 2.11209e7i | −0.200900 | + | 0.954257i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.45968e6 | − | 1.22482e6i | −0.0655706 | − | 0.0550203i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.72352e7 | − | 6.27310e6i | −0.769787 | − | 0.280180i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.17357e6 | + | 3.04099e6i | 0.140933 | + | 0.135045i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.08456e7 | − | 9.10055e6i | 0.478888 | − | 0.401835i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.13000e6 | − | 4.04362e7i | 0.313033 | − | 1.77530i | −0.270009 | − | 0.962858i | \(-0.587027\pi\) |
0.583042 | − | 0.812442i | \(-0.301862\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.81775e7 | − | 1.13209e7i | −1.23007 | − | 0.494209i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.79921e7 | − | 3.11632e7i | 0.780984 | − | 1.35270i | −0.150385 | − | 0.988627i | \(-0.548051\pi\) |
0.931369 | − | 0.364076i | \(-0.118615\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.86566e6 | + | 4.96347e6i | 0.123687 | + | 0.214231i | 0.921219 | − | 0.389045i | \(-0.127195\pi\) |
−0.797532 | + | 0.603276i | \(0.793862\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.91812e6 | − | 7.90470e6i | 0.211077 | − | 0.339256i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.87802e7 | + | 1.04751e7i | −1.22824 | + | 0.447044i | −0.872995 | − | 0.487729i | \(-0.837826\pi\) |
−0.355247 | + | 0.934772i | \(0.615603\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.02194e6 | − | 3.41521e7i | −0.255554 | − | 1.44932i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −745900. | + | 970124.i | −0.0314765 | + | 0.0409386i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 93836.4 | + | 532172.i | 0.00393770 | + | 0.0223318i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.65686e7 | − | 6.03049e6i | 0.691400 | − | 0.251649i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.66977e6 | + | 1.07201e7i | −0.276777 | + | 0.444853i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.13452e6 | + | 5.42915e6i | 0.129352 | + | 0.224043i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.82585e6 | − | 6.62657e6i | 0.157006 | − | 0.271942i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.26487e6 | − | 3.72237e6i | −0.378112 | − | 0.151915i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.22781e6 | − | 4.09909e7i | 0.293349 | − | 1.66367i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.18768e7 | + | 9.96584e6i | −0.479383 | + | 0.402250i | −0.850203 | − | 0.526455i | \(-0.823521\pi\) |
0.370820 | + | 0.928705i | \(0.379077\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.06496e7 | + | 4.34300e7i | −0.427488 | + | 1.74333i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.77900e6 | − | 2.10338e6i | −0.230705 | − | 0.0839697i | 0.224081 | − | 0.974571i | \(-0.428062\pi\) |
−0.454786 | + | 0.890601i | \(0.650284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.51279e6 | − | 1.26938e6i | −0.0600622 | − | 0.0503982i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.39447e6 | − | 3.98729e7i | 0.331467 | − | 1.57444i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.09196e7 | 0.821542 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.34851e7 | 1.30786 | 0.653932 | − | 0.756553i | \(-0.273118\pi\) | ||||
0.653932 | + | 0.756553i | \(0.273118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.78831e7 | − | 9.11958e6i | 1.08316 | − | 0.354263i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 671143. | + | 563156.i | 0.0259305 | + | 0.0217583i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.16530e7 | − | 4.24135e6i | −0.447800 | − | 0.162986i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.25084e7 | − | 1.87005e7i | 0.478083 | − | 0.714751i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.36347e7 | + | 1.14409e7i | −0.518330 | + | 0.434930i | −0.864049 | − | 0.503408i | \(-0.832079\pi\) |
0.345719 | + | 0.938338i | \(0.387635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35134.5 | − | 199258.i | 0.00132850 | − | 0.00753427i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.97006e7 | + | 1.54534e7i | −0.740926 | + | 0.581192i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 128056. | − | 221799.i | 0.00479039 | − | 0.00829719i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.50774e7 | − | 2.61148e7i | −0.561018 | − | 0.971712i | −0.997408 | − | 0.0719540i | \(-0.977077\pi\) |
0.436390 | − | 0.899758i | \(-0.356257\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.31372e6 | + | 43325.9i | 0.0486226 | + | 0.00160356i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.97047e6 | + | 2.90101e6i | −0.293434 | + | 0.106801i | −0.484542 | − | 0.874768i | \(-0.661014\pi\) |
0.191109 | + | 0.981569i | \(0.438792\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.34617e6 | − | 7.63453e6i | −0.0492971 | − | 0.279578i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.78386e7 | − | 2.76233e6i | −1.01407 | − | 0.100623i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.85012e6 | − | 1.61638e7i | −0.103273 | − | 0.585692i | −0.991896 | − | 0.127053i | \(-0.959448\pi\) |
0.888623 | − | 0.458639i | \(-0.151663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.27681e7 | + | 4.64720e6i | −0.460214 | + | 0.167504i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.01008e6 | − | 5.63476e6i | −0.107926 | − | 0.202034i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.40183e6 | + | 1.10883e7i | 0.228335 | + | 0.395487i | 0.957315 | − | 0.289048i | \(-0.0933386\pi\) |
−0.728980 | + | 0.684535i | \(0.760005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.89144e6 | − | 1.02043e7i | 0.209032 | − | 0.362054i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 50622.0 | + | 355196.i | 0.00178673 | + | 0.0125368i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.95252e6 | + | 2.24158e7i | −0.138780 | + | 0.787061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.47710e6 | − | 2.07854e6i | 0.0865239 | − | 0.0726021i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15971.4 | + | 146491.i | 0.000554979 | + | 0.00509031i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.62964e7 | + | 9.57112e6i | 0.909031 | + | 0.330860i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.28518e7 | + | 1.07839e7i | 0.441974 | + | 0.370860i | 0.836447 | − | 0.548047i | \(-0.184629\pi\) |
−0.394473 | + | 0.918907i | \(0.629073\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 104479. | + | 93707.2i | 0.00357454 | + | 0.00320600i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.79370e7 | 1.29126 | 0.645632 | − | 0.763648i | \(-0.276594\pi\) | ||||
0.645632 | + | 0.763648i | \(0.276594\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.45131e7 | −1.16870 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.33032e6 | + | 4.78076e6i | 0.179573 | + | 0.161059i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.75585e7 | + | 1.47334e7i | 0.588507 | + | 0.493816i | 0.887728 | − | 0.460368i | \(-0.152282\pi\) |
−0.299221 | + | 0.954184i | \(0.596727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −508168. | − | 184958.i | −0.0169454 | − | 0.00616761i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.14201e6 | + | 1.96467e7i | 0.0710641 | + | 0.651805i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.42875e7 | − | 2.03796e7i | 0.801676 | − | 0.672686i | −0.146929 | − | 0.989147i | \(-0.546939\pi\) |
0.948606 | + | 0.316461i | \(0.102495\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.13914e7 | − | 6.46036e7i | 0.374098 | − | 2.12161i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.78070e6 | + | 1.95111e7i | 0.0908575 | + | 0.637513i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.08000e6 | − | 1.05309e7i | 0.197657 | − | 0.342353i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.41122e7 | + | 2.44430e7i | 0.456467 | + | 0.790624i | 0.998771 | − | 0.0495580i | \(-0.0157813\pi\) |
−0.542304 | + | 0.840182i | \(0.682448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.39188e6 | − | 1.75812e7i | −0.302259 | − | 0.565818i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.05160e6 | + | 2.56657e6i | −0.225803 | + | 0.0821856i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.86069e6 | + | 2.75663e7i | 0.154867 | + | 0.878297i | 0.958907 | + | 0.283721i | \(0.0915689\pi\) |
−0.804039 | + | 0.594576i | \(0.797320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.60235e7 | − | 3.54332e7i | −0.507976 | − | 1.12330i |
(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.i.a.13.12 | ✓ | 90 | |
3.2 | odd | 2 | 324.6.i.a.253.3 | 90 | |||
27.2 | odd | 18 | 324.6.i.a.73.3 | 90 | |||
27.25 | even | 9 | inner | 108.6.i.a.25.12 | yes | 90 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.i.a.13.12 | ✓ | 90 | 1.1 | even | 1 | trivial | |
108.6.i.a.25.12 | yes | 90 | 27.25 | even | 9 | inner | |
324.6.i.a.73.3 | 90 | 27.2 | odd | 18 | |||
324.6.i.a.253.3 | 90 | 3.2 | odd | 2 |