Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (of order \(2\), degree \(1\), 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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 176.18 | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.6.d.b.176.17 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.56324 | −1.33701 | −0.668503 | − | 0.743710i | \(-0.733064\pi\) | ||||
−0.668503 | + | 0.743710i | \(0.733064\pi\) | |||||||
\(3\) | 11.2364 | − | 10.8048i | 0.720817 | − | 0.693126i | ||||
\(4\) | 25.2027 | 0.787583 | ||||||||
\(5\) | 51.3528i | 0.918627i | 0.888274 | + | 0.459314i | \(0.151905\pi\) | ||||
−0.888274 | + | 0.459314i | \(0.848095\pi\) | |||||||
\(6\) | −84.9838 | + | 81.7190i | −0.963736 | + | 0.926713i | ||||
\(7\) | 90.7178 | 0.699758 | 0.349879 | − | 0.936795i | \(-0.386223\pi\) | ||||
0.349879 | + | 0.936795i | \(0.386223\pi\) | |||||||
\(8\) | 51.4099 | 0.284002 | ||||||||
\(9\) | 9.51431 | − | 242.814i | 0.0391535 | − | 0.999233i | ||||
\(10\) | − | 388.394i | − | 1.22821i | ||||||
\(11\) | −682.512 | −1.70070 | −0.850352 | − | 0.526214i | \(-0.823611\pi\) | ||||
−0.850352 | + | 0.526214i | \(0.823611\pi\) | |||||||
\(12\) | 283.188 | − | 272.309i | 0.567703 | − | 0.545894i | ||||
\(13\) | − | 90.5395i | − | 0.148587i | −0.997236 | − | 0.0742933i | \(-0.976330\pi\) | ||
0.997236 | − | 0.0742933i | \(-0.0236701\pi\) | |||||||
\(14\) | −686.121 | −0.935580 | ||||||||
\(15\) | 554.855 | + | 577.022i | 0.636724 | + | 0.662162i | ||||
\(16\) | −1195.31 | −1.16730 | ||||||||
\(17\) | − | 771.900i | − | 0.647797i | −0.946092 | − | 0.323899i | \(-0.895006\pi\) | ||
0.946092 | − | 0.323899i | \(-0.104994\pi\) | |||||||
\(18\) | −71.9590 | + | 1836.46i | −0.0523485 | + | 1.33598i | ||||
\(19\) | 2480.56 | 1.57640 | 0.788199 | − | 0.615420i | \(-0.211014\pi\) | ||||
0.788199 | + | 0.615420i | \(0.211014\pi\) | |||||||
\(20\) | 1294.23i | 0.723496i | ||||||||
\(21\) | 1019.34 | − | 980.185i | 0.504397 | − | 0.485020i | ||||
\(22\) | 5162.01 | 2.27385 | ||||||||
\(23\) | −440.319 | −0.173559 | −0.0867796 | − | 0.996228i | \(-0.527658\pi\) | ||||
−0.0867796 | + | 0.996228i | \(0.527658\pi\) | |||||||
\(24\) | 577.663 | − | 555.472i | 0.204714 | − | 0.196849i | ||||
\(25\) | 487.887 | 0.156124 | ||||||||
\(26\) | 684.772i | 0.198661i | ||||||||
\(27\) | −2516.64 | − | 2831.16i | −0.664372 | − | 0.747402i | ||||
\(28\) | 2286.33 | 0.551117 | ||||||||
\(29\) | 6844.72i | 1.51133i | 0.654956 | + | 0.755667i | \(0.272687\pi\) | ||||
−0.654956 | + | 0.755667i | \(0.727313\pi\) | |||||||
\(30\) | −4196.50 | − | 4364.16i | −0.851304 | − | 0.885314i | ||||
\(31\) | 1052.51i | 0.196709i | 0.995151 | + | 0.0983544i | \(0.0313579\pi\) | ||||
−0.995151 | + | 0.0983544i | \(0.968642\pi\) | |||||||
\(32\) | 7395.31 | 1.27668 | ||||||||
\(33\) | −7668.99 | + | 7374.38i | −1.22590 | + | 1.17880i | ||||
\(34\) | 5838.07i | 0.866108i | ||||||||
\(35\) | 4658.62i | 0.642816i | ||||||||
\(36\) | 239.786 | − | 6119.55i | 0.0308367 | − | 0.786979i | ||||
\(37\) | − | 10492.0i | − | 1.25995i | −0.776614 | − | 0.629976i | \(-0.783065\pi\) | ||
0.776614 | − | 0.629976i | \(-0.216935\pi\) | |||||||
\(38\) | −18761.1 | −2.10765 | ||||||||
\(39\) | −978.258 | − | 1017.34i | −0.102989 | − | 0.107104i | ||||
\(40\) | 2640.04i | 0.260892i | ||||||||
\(41\) | − | 16643.5i | − | 1.54627i | −0.634242 | − | 0.773134i | \(-0.718688\pi\) | ||
0.634242 | − | 0.773134i | \(-0.281312\pi\) | |||||||
\(42\) | −7709.55 | + | 7413.38i | −0.674381 | + | 0.648474i | ||||
\(43\) | 6372.48i | 0.525578i | 0.964853 | + | 0.262789i | \(0.0846423\pi\) | ||||
−0.964853 | + | 0.262789i | \(0.915358\pi\) | |||||||
\(44\) | −17201.1 | −1.33945 | ||||||||
\(45\) | 12469.2 | + | 488.587i | 0.917923 | + | 0.0359675i | ||||
\(46\) | 3330.24 | 0.232049 | ||||||||
\(47\) | 27748.5 | 1.83229 | 0.916146 | − | 0.400845i | \(-0.131284\pi\) | ||||
0.916146 | + | 0.400845i | \(0.131284\pi\) | |||||||
\(48\) | −13431.0 | + | 12915.0i | −0.841406 | + | 0.809083i | ||||
\(49\) | −8577.27 | −0.510339 | ||||||||
\(50\) | −3690.01 | −0.208738 | ||||||||
\(51\) | −8340.20 | − | 8673.40i | −0.449005 | − | 0.466943i | ||||
\(52\) | − | 2281.84i | − | 0.117024i | ||||||
\(53\) | − | 26135.8i | − | 1.27805i | −0.769187 | − | 0.639023i | \(-0.779339\pi\) | ||
0.769187 | − | 0.639023i | \(-0.220661\pi\) | |||||||
\(54\) | 19033.9 | + | 21412.7i | 0.888269 | + | 0.999281i | ||||
\(55\) | − | 35048.9i | − | 1.56231i | ||||||
\(56\) | 4663.80 | 0.198733 | ||||||||
\(57\) | 27872.6 | − | 26801.9i | 1.13629 | − | 1.09264i | ||||
\(58\) | − | 51768.3i | − | 2.02066i | ||||||
\(59\) | 13187.9 | − | 23259.5i | 0.493225 | − | 0.869902i | ||||
\(60\) | 13983.8 | + | 14542.5i | 0.501473 | + | 0.521508i | ||||
\(61\) | 9403.19i | 0.323557i | 0.986827 | + | 0.161778i | \(0.0517230\pi\) | ||||
−0.986827 | + | 0.161778i | \(0.948277\pi\) | |||||||
\(62\) | − | 7960.42i | − | 0.263001i | ||||||
\(63\) | 863.118 | − | 22027.5i | 0.0273980 | − | 0.699221i | ||||
\(64\) | −17682.6 | −0.539630 | ||||||||
\(65\) | 4649.46 | 0.136496 | ||||||||
\(66\) | 58002.5 | − | 55774.2i | 1.63903 | − | 1.57606i | ||||
\(67\) | − | 73133.4i | − | 1.99035i | −0.0981376 | − | 0.995173i | \(-0.531289\pi\) | ||
0.0981376 | − | 0.995173i | \(-0.468711\pi\) | |||||||
\(68\) | − | 19453.9i | − | 0.510194i | ||||||
\(69\) | −4947.61 | + | 4757.54i | −0.125104 | + | 0.120298i | ||||
\(70\) | − | 35234.3i | − | 0.859449i | ||||||
\(71\) | 43754.6i | 1.03010i | 0.857161 | + | 0.515048i | \(0.172226\pi\) | ||||
−0.857161 | + | 0.515048i | \(0.827774\pi\) | |||||||
\(72\) | 489.130 | − | 12483.0i | 0.0111197 | − | 0.283785i | ||||
\(73\) | − | 37991.9i | − | 0.834419i | −0.908810 | − | 0.417210i | \(-0.863008\pi\) | ||
0.908810 | − | 0.417210i | \(-0.136992\pi\) | |||||||
\(74\) | 79353.6i | 1.68456i | ||||||||
\(75\) | 5482.10 | − | 5271.50i | 0.112537 | − | 0.108213i | ||||
\(76\) | 62516.8 | 1.24155 | ||||||||
\(77\) | −61916.0 | −1.19008 | ||||||||
\(78\) | 7398.80 | + | 7694.39i | 0.137697 | + | 0.143198i | ||||
\(79\) | −18676.1 | −0.336681 | −0.168340 | − | 0.985729i | \(-0.553841\pi\) | ||||
−0.168340 | + | 0.985729i | \(0.553841\pi\) | |||||||
\(80\) | − | 61382.6i | − | 1.07231i | ||||||
\(81\) | −58868.0 | − | 4620.41i | −0.996934 | − | 0.0782470i | ||||
\(82\) | 125879.i | 2.06737i | ||||||||
\(83\) | 108851. | 1.73436 | 0.867179 | − | 0.497996i | \(-0.165931\pi\) | ||||
0.867179 | + | 0.497996i | \(0.165931\pi\) | |||||||
\(84\) | 25690.2 | − | 24703.3i | 0.397255 | − | 0.381994i | ||||
\(85\) | 39639.3 | 0.595084 | ||||||||
\(86\) | − | 48196.6i | − | 0.702700i | ||||||
\(87\) | 73955.5 | + | 76910.1i | 1.04754 | + | 1.08939i | ||||
\(88\) | −35087.9 | −0.483004 | ||||||||
\(89\) | −51749.3 | −0.692516 | −0.346258 | − | 0.938139i | \(-0.612548\pi\) | ||||
−0.346258 | + | 0.938139i | \(0.612548\pi\) | |||||||
\(90\) | −94307.4 | − | 3695.30i | −1.22727 | − | 0.0480887i | ||||
\(91\) | − | 8213.55i | − | 0.103975i | ||||||
\(92\) | −11097.2 | −0.136692 | ||||||||
\(93\) | 11372.2 | + | 11826.5i | 0.136344 | + | 0.141791i | ||||
\(94\) | −209869. | −2.44978 | ||||||||
\(95\) | 127384.i | 1.44812i | ||||||||
\(96\) | 83096.8 | − | 79904.6i | 0.920251 | − | 0.884899i | ||||
\(97\) | − | 90907.7i | − | 0.981005i | −0.871440 | − | 0.490503i | \(-0.836813\pi\) | ||
0.871440 | − | 0.490503i | \(-0.163187\pi\) | |||||||
\(98\) | 64872.0 | 0.682326 | ||||||||
\(99\) | −6493.63 | + | 165723.i | −0.0665886 | + | 1.69940i | ||||
\(100\) | 12296.0 | 0.122960 | ||||||||
\(101\) | −73494.3 | −0.716886 | −0.358443 | − | 0.933552i | \(-0.616692\pi\) | ||||
−0.358443 | + | 0.933552i | \(0.616692\pi\) | |||||||
\(102\) | 63079.0 | + | 65599.0i | 0.600322 | + | 0.624305i | ||||
\(103\) | − | 105537.i | − | 0.980193i | −0.871668 | − | 0.490096i | \(-0.836962\pi\) | ||
0.871668 | − | 0.490096i | \(-0.163038\pi\) | |||||||
\(104\) | − | 4654.63i | − | 0.0421989i | ||||||
\(105\) | 50335.3 | + | 52346.2i | 0.445553 | + | 0.463353i | ||||
\(106\) | 197672.i | 1.70875i | ||||||||
\(107\) | − | 205373.i | − | 1.73414i | −0.498186 | − | 0.867070i | \(-0.666000\pi\) | ||
0.498186 | − | 0.867070i | \(-0.334000\pi\) | |||||||
\(108\) | −63426.0 | − | 71352.7i | −0.523248 | − | 0.588642i | ||||
\(109\) | 15975.9i | 0.128795i | 0.997924 | + | 0.0643976i | \(0.0205126\pi\) | ||||
−0.997924 | + | 0.0643976i | \(0.979487\pi\) | |||||||
\(110\) | 265084.i | 2.08882i | ||||||||
\(111\) | −113364. | − | 117893.i | −0.873305 | − | 0.908195i | ||||
\(112\) | −108436. | −0.816824 | ||||||||
\(113\) | 187107. | 1.37846 | 0.689229 | − | 0.724544i | \(-0.257950\pi\) | ||||
0.689229 | + | 0.724544i | \(0.257950\pi\) | |||||||
\(114\) | −210808. | + | 202709.i | −1.51923 | + | 1.46087i | ||||
\(115\) | − | 22611.6i | − | 0.159436i | ||||||
\(116\) | 172505.i | 1.19030i | ||||||||
\(117\) | −21984.2 | − | 861.421i | −0.148473 | − | 0.00581769i | ||||
\(118\) | −99743.2 | + | 175917.i | −0.659444 | + | 1.16306i | ||||
\(119\) | − | 70025.1i | − | 0.453301i | ||||||
\(120\) | 28525.0 | + | 29664.6i | 0.180831 | + | 0.188056i | ||||
\(121\) | 304772. | 1.89239 | ||||||||
\(122\) | − | 71118.6i | − | 0.432597i | ||||||
\(123\) | −179829. | − | 187013.i | −1.07176 | − | 1.11458i | ||||
\(124\) | 26526.2i | 0.154925i | ||||||||
\(125\) | 185532.i | 1.06205i | ||||||||
\(126\) | −6527.97 | + | 166600.i | −0.0366312 | + | 0.934862i | ||||
\(127\) | −160262. | −0.881703 | −0.440851 | − | 0.897580i | \(-0.645323\pi\) | ||||
−0.440851 | + | 0.897580i | \(0.645323\pi\) | |||||||
\(128\) | −102912. | −0.555190 | ||||||||
\(129\) | 68853.1 | + | 71603.8i | 0.364291 | + | 0.378845i | ||||
\(130\) | −35165.0 | −0.182496 | ||||||||
\(131\) | 16913.4 | 0.0861098 | 0.0430549 | − | 0.999073i | \(-0.486291\pi\) | ||||
0.0430549 | + | 0.999073i | \(0.486291\pi\) | |||||||
\(132\) | −193279. | + | 185854.i | −0.965495 | + | 0.928404i | ||||
\(133\) | 225031. | 1.10310 | ||||||||
\(134\) | 553125.i | 2.66110i | ||||||||
\(135\) | 145388. | − | 129236.i | 0.686584 | − | 0.610310i | ||||
\(136\) | − | 39683.3i | − | 0.183976i | ||||||
\(137\) | − | 125031.i | − | 0.569135i | −0.958656 | − | 0.284568i | \(-0.908150\pi\) | ||
0.958656 | − | 0.284568i | \(-0.0918500\pi\) | |||||||
\(138\) | 37419.9 | − | 35982.4i | 0.167265 | − | 0.160839i | ||||
\(139\) | −85153.3 | −0.373822 | −0.186911 | − | 0.982377i | \(-0.559848\pi\) | ||||
−0.186911 | + | 0.982377i | \(0.559848\pi\) | |||||||
\(140\) | 117410.i | 0.506272i | ||||||||
\(141\) | 311794. | − | 299816.i | 1.32075 | − | 1.27001i | ||||
\(142\) | − | 330927.i | − | 1.37724i | ||||||
\(143\) | 61794.3i | 0.252702i | ||||||||
\(144\) | −11372.6 | + | 290238.i | −0.0457038 | + | 1.16640i | ||||
\(145\) | −351496. | −1.38835 | ||||||||
\(146\) | 287342.i | 1.11562i | ||||||||
\(147\) | −96377.8 | + | 92675.4i | −0.367861 | + | 0.353729i | ||||
\(148\) | − | 264426.i | − | 0.992318i | ||||||
\(149\) | 160185. | 0.591092 | 0.295546 | − | 0.955329i | \(-0.404498\pi\) | ||||
0.295546 | + | 0.955329i | \(0.404498\pi\) | |||||||
\(150\) | −41462.5 | + | 39869.6i | −0.150462 | + | 0.144682i | ||||
\(151\) | 271823.i | 0.970160i | 0.874470 | + | 0.485080i | \(0.161210\pi\) | ||||
−0.874470 | + | 0.485080i | \(0.838790\pi\) | |||||||
\(152\) | 127525. | 0.447701 | ||||||||
\(153\) | −187428. | − | 7344.10i | −0.647300 | − | 0.0253635i | ||||
\(154\) | 468286. | 1.59114 | ||||||||
\(155\) | −54049.6 | −0.180702 | ||||||||
\(156\) | −24654.7 | − | 25639.7i | −0.0811126 | − | 0.0843531i | ||||
\(157\) | 116338.i | 0.376681i | 0.982104 | + | 0.188340i | \(0.0603108\pi\) | ||||
−0.982104 | + | 0.188340i | \(0.939689\pi\) | |||||||
\(158\) | 141252. | 0.450144 | ||||||||
\(159\) | −282391. | − | 293673.i | −0.885847 | − | 0.921237i | ||||
\(160\) | 379770.i | 1.17279i | ||||||||
\(161\) | −39944.8 | −0.121449 | ||||||||
\(162\) | 445233. | + | 34945.3i | 1.33291 | + | 0.104617i | ||||
\(163\) | −157521. | −0.464377 | −0.232188 | − | 0.972671i | \(-0.574589\pi\) | ||||
−0.232188 | + | 0.972671i | \(0.574589\pi\) | |||||||
\(164\) | − | 419461.i | − | 1.21782i | ||||||
\(165\) | −378695. | − | 393825.i | −1.08288 | − | 1.12614i | ||||
\(166\) | −823270. | −2.31885 | ||||||||
\(167\) | 284864.i | 0.790399i | 0.918595 | + | 0.395199i | \(0.129324\pi\) | ||||
−0.918595 | + | 0.395199i | \(0.870676\pi\) | |||||||
\(168\) | 52404.4 | − | 50391.2i | 0.143250 | − | 0.137747i | ||||
\(169\) | 363096. | 0.977922 | ||||||||
\(170\) | −299802. | −0.795631 | ||||||||
\(171\) | 23600.8 | − | 602314.i | 0.0617216 | − | 1.57519i | ||||
\(172\) | 160603.i | 0.413936i | ||||||||
\(173\) | 331355. | 0.841740 | 0.420870 | − | 0.907121i | \(-0.361725\pi\) | ||||
0.420870 | + | 0.907121i | \(0.361725\pi\) | |||||||
\(174\) | −559344. | − | 581690.i | −1.40057 | − | 1.45653i | ||||
\(175\) | 44260.0 | 0.109249 | ||||||||
\(176\) | 815814. | 1.98522 | ||||||||
\(177\) | −103129. | − | 403845.i | −0.247426 | − | 0.968907i | ||||
\(178\) | 391393. | 0.925897 | ||||||||
\(179\) | −284128. | −0.662799 | −0.331399 | − | 0.943491i | \(-0.607521\pi\) | ||||
−0.331399 | + | 0.943491i | \(0.607521\pi\) | |||||||
\(180\) | 314256. | + | 12313.7i | 0.722941 | + | 0.0283274i | ||||
\(181\) | 353188. | 0.801327 | 0.400663 | − | 0.916225i | \(-0.368780\pi\) | ||||
0.400663 | + | 0.916225i | \(0.368780\pi\) | |||||||
\(182\) | 62121.1i | 0.139015i | ||||||||
\(183\) | 101599. | + | 105658.i | 0.224266 | + | 0.233225i | ||||
\(184\) | −22636.7 | −0.0492912 | ||||||||
\(185\) | 538794. | 1.15743 | ||||||||
\(186\) | −86010.4 | − | 89446.6i | −0.182293 | − | 0.189575i | ||||
\(187\) | 526831.i | 1.10171i | ||||||||
\(188\) | 699336. | 1.44308 | ||||||||
\(189\) | −228304. | − | 256836.i | −0.464899 | − | 0.523000i | ||||
\(190\) | − | 963435.i | − | 1.93615i | ||||||
\(191\) | 409474. | 0.812162 | 0.406081 | − | 0.913837i | \(-0.366895\pi\) | ||||
0.406081 | + | 0.913837i | \(0.366895\pi\) | |||||||
\(192\) | −198689. | + | 191056.i | −0.388974 | + | 0.374032i | ||||
\(193\) | −77555.3 | −0.149871 | −0.0749356 | − | 0.997188i | \(-0.523875\pi\) | ||||
−0.0749356 | + | 0.997188i | \(0.523875\pi\) | |||||||
\(194\) | 687557.i | 1.31161i | ||||||||
\(195\) | 52243.3 | − | 50236.3i | 0.0983884 | − | 0.0946087i | ||||
\(196\) | −216170. | −0.401935 | ||||||||
\(197\) | − | 666250.i | − | 1.22313i | −0.791195 | − | 0.611564i | \(-0.790541\pi\) | ||
0.791195 | − | 0.611564i | \(-0.209459\pi\) | |||||||
\(198\) | 49112.9 | − | 1.25341e6i | 0.0890293 | − | 2.27211i | ||||
\(199\) | −151342. | −0.270911 | −0.135456 | − | 0.990783i | \(-0.543250\pi\) | ||||
−0.135456 | + | 0.990783i | \(0.543250\pi\) | |||||||
\(200\) | 25082.2 | 0.0443395 | ||||||||
\(201\) | −790188. | − | 821757.i | −1.37956 | − | 1.43467i | ||||
\(202\) | 555855. | 0.958480 | ||||||||
\(203\) | 620938.i | 1.05757i | ||||||||
\(204\) | −210195. | − | 218593.i | −0.353629 | − | 0.367756i | ||||
\(205\) | 854691. | 1.42044 | ||||||||
\(206\) | 798202.i | 1.31052i | ||||||||
\(207\) | −4189.33 | + | 106915.i | −0.00679545 | + | 0.173426i | ||||
\(208\) | 108223.i | 0.173445i | ||||||||
\(209\) | −1.69301e6 | −2.68099 | ||||||||
\(210\) | −380698. | − | 395907.i | −0.595706 | − | 0.619505i | ||||
\(211\) | − | 252243.i | − | 0.390043i | −0.980799 | − | 0.195021i | \(-0.937522\pi\) | ||
0.980799 | − | 0.195021i | \(-0.0624776\pi\) | |||||||
\(212\) | − | 658693.i | − | 1.00657i | ||||||
\(213\) | 472758. | + | 491645.i | 0.713986 | + | 0.742511i | ||||
\(214\) | 1.55329e6i | 2.31856i | ||||||||
\(215\) | −327245. | −0.482810 | ||||||||
\(216\) | −129380. | − | 145549.i | −0.188683 | − | 0.212264i | ||||
\(217\) | 95481.8i | 0.137648i | ||||||||
\(218\) | − | 120830.i | − | 0.172200i | ||||||
\(219\) | −410494. | − | 426893.i | −0.578357 | − | 0.601463i | ||||
\(220\) | − | 883327.i | − | 1.23045i | ||||||
\(221\) | −69887.5 | −0.0962540 | ||||||||
\(222\) | 857397. | + | 891650.i | 1.16761 | + | 1.21426i | ||||
\(223\) | 278083. | 0.374466 | 0.187233 | − | 0.982315i | \(-0.440048\pi\) | ||||
0.187233 | + | 0.982315i | \(0.440048\pi\) | |||||||
\(224\) | 670887. | 0.893366 | ||||||||
\(225\) | 4641.91 | − | 118466.i | 0.00611280 | − | 0.156004i | ||||
\(226\) | −1.41513e6 | −1.84300 | ||||||||
\(227\) | −1.13709e6 | −1.46463 | −0.732317 | − | 0.680964i | \(-0.761561\pi\) | ||||
−0.732317 | + | 0.680964i | \(0.761561\pi\) | |||||||
\(228\) | 702465. | − | 675479.i | 0.894927 | − | 0.860547i | ||||
\(229\) | 556703.i | 0.701511i | 0.936467 | + | 0.350756i | \(0.114075\pi\) | ||||
−0.936467 | + | 0.350756i | \(0.885925\pi\) | |||||||
\(230\) | 171017.i | 0.213167i | ||||||||
\(231\) | −695715. | + | 668988.i | −0.857830 | + | 0.824875i | ||||
\(232\) | 351886.i | 0.429222i | ||||||||
\(233\) | 1.01799e6 | 1.22844 | 0.614218 | − | 0.789137i | \(-0.289472\pi\) | ||||
0.614218 | + | 0.789137i | \(0.289472\pi\) | |||||||
\(234\) | 166272. | + | 6515.14i | 0.198509 | + | 0.00777828i | ||||
\(235\) | 1.42496e6i | 1.68319i | ||||||||
\(236\) | 332370. | − | 586201.i | 0.388456 | − | 0.685120i | ||||
\(237\) | −209852. | + | 201791.i | −0.242685 | + | 0.233362i | ||||
\(238\) | 529617.i | 0.606066i | ||||||||
\(239\) | 141346.i | 0.160062i | 0.996792 | + | 0.0800311i | \(0.0255020\pi\) | ||||
−0.996792 | + | 0.0800311i | \(0.974498\pi\) | |||||||
\(240\) | −663224. | − | 689721.i | −0.743246 | − | 0.772939i | ||||
\(241\) | 405397. | 0.449612 | 0.224806 | − | 0.974403i | \(-0.427825\pi\) | ||||
0.224806 | + | 0.974403i | \(0.427825\pi\) | |||||||
\(242\) | −2.30506e6 | −2.53014 | ||||||||
\(243\) | −711388. | + | 584137.i | −0.772842 | + | 0.634599i | ||||
\(244\) | 236985.i | 0.254828i | ||||||||
\(245\) | − | 440467.i | − | 0.468812i | ||||||
\(246\) | 1.36009e6 | + | 1.41443e6i | 1.43295 | + | 1.49019i | ||||
\(247\) | − | 224589.i | − | 0.234232i | ||||||
\(248\) | 54109.6i | 0.0558657i | ||||||||
\(249\) | 1.22310e6 | − | 1.17611e6i | 1.25015 | − | 1.20213i | ||||
\(250\) | − | 1.40322e6i | − | 1.41996i | ||||||
\(251\) | − | 1.09091e6i | − | 1.09296i | −0.837471 | − | 0.546482i | \(-0.815967\pi\) | ||
0.837471 | − | 0.546482i | \(-0.184033\pi\) | |||||||
\(252\) | 21752.9 | − | 555153.i | 0.0215782 | − | 0.550695i | ||||
\(253\) | 300523. | 0.295173 | ||||||||
\(254\) | 1.21210e6 | 1.17884 | ||||||||
\(255\) | 445404. | − | 428293.i | 0.428947 | − | 0.412468i | ||||
\(256\) | 1.34419e6 | 1.28192 | ||||||||
\(257\) | − | 4748.15i | − | 0.00448427i | −0.999997 | − | 0.00224213i | \(-0.999286\pi\) | ||
0.999997 | − | 0.00224213i | \(-0.000713694\pi\) | |||||||
\(258\) | −520753. | − | 541557.i | −0.487060 | − | 0.506518i | ||||
\(259\) | − | 951812.i | − | 0.881661i | ||||||
\(260\) | 117179. | 0.107502 | ||||||||
\(261\) | 1.66199e6 | + | 65122.7i | 1.51018 | + | 0.0591741i | ||||
\(262\) | −127920. | −0.115129 | ||||||||
\(263\) | − | 500879.i | − | 0.446522i | −0.974759 | − | 0.223261i | \(-0.928330\pi\) | ||
0.974759 | − | 0.223261i | \(-0.0716703\pi\) | |||||||
\(264\) | −394262. | + | 379116.i | −0.348157 | + | 0.334782i | ||||
\(265\) | 1.34215e6 | 1.17405 | ||||||||
\(266\) | −1.70197e6 | −1.47485 | ||||||||
\(267\) | −581477. | + | 559139.i | −0.499177 | + | 0.480000i | ||||
\(268\) | − | 1.84316e6i | − | 1.56756i | ||||||
\(269\) | −1.84500e6 | −1.55459 | −0.777293 | − | 0.629139i | \(-0.783408\pi\) | ||||
−0.777293 | + | 0.629139i | \(0.783408\pi\) | |||||||
\(270\) | −1.09960e6 | + | 977447.i | −0.917967 | + | 0.815988i | ||||
\(271\) | 417363. | 0.345216 | 0.172608 | − | 0.984991i | \(-0.444781\pi\) | ||||
0.172608 | + | 0.984991i | \(0.444781\pi\) | |||||||
\(272\) | 922661.i | 0.756171i | ||||||||
\(273\) | −88745.4 | − | 92290.9i | −0.0720675 | − | 0.0749467i | ||||
\(274\) | 945638.i | 0.760937i | ||||||||
\(275\) | −332989. | −0.265520 | ||||||||
\(276\) | −124693. | + | 119903.i | −0.0985301 | + | 0.0947449i | ||||
\(277\) | 50456.3 | 0.0395108 | 0.0197554 | − | 0.999805i | \(-0.493711\pi\) | ||||
0.0197554 | + | 0.999805i | \(0.493711\pi\) | |||||||
\(278\) | 644035. | 0.499802 | ||||||||
\(279\) | 255565. | + | 10013.9i | 0.196558 | + | 0.00770184i | ||||
\(280\) | 239499.i | 0.182561i | ||||||||
\(281\) | − | 289552.i | − | 0.218756i | −0.994000 | − | 0.109378i | \(-0.965114\pi\) | ||
0.994000 | − | 0.109378i | \(-0.0348859\pi\) | |||||||
\(282\) | −2.35817e6 | + | 2.26758e6i | −1.76584 | + | 1.69801i | ||||
\(283\) | 1.82269e6i | 1.35284i | 0.736514 | + | 0.676422i | \(0.236470\pi\) | ||||
−0.736514 | + | 0.676422i | \(0.763530\pi\) | |||||||
\(284\) | 1.10273e6i | 0.811287i | ||||||||
\(285\) | 1.37635e6 | + | 1.43134e6i | 1.00373 | + | 1.04383i | ||||
\(286\) | − | 467366.i | − | 0.337864i | ||||||
\(287\) | − | 1.50986e6i | − | 1.08201i | ||||||
\(288\) | 70361.3 | − | 1.79568e6i | 0.0499865 | − | 1.27570i | ||||
\(289\) | 824027. | 0.580359 | ||||||||
\(290\) | 2.65845e6 | 1.85624 | ||||||||
\(291\) | −982236. | − | 1.02148e6i | −0.679960 | − | 0.707125i | ||||
\(292\) | − | 957498.i | − | 0.657175i | ||||||
\(293\) | 2.68342e6i | 1.82608i | 0.407872 | + | 0.913039i | \(0.366271\pi\) | ||||
−0.407872 | + | 0.913039i | \(0.633729\pi\) | |||||||
\(294\) | 728929. | − | 700926.i | 0.491832 | − | 0.472938i | ||||
\(295\) | 1.19444e6 | + | 677235.i | 0.799116 | + | 0.453090i | ||||
\(296\) | − | 539393.i | − | 0.357829i | ||||||
\(297\) | 1.71764e6 | + | 1.93230e6i | 1.12990 | + | 1.27111i | ||||
\(298\) | −1.21151e6 | −0.790293 | ||||||||
\(299\) | 39866.2i | 0.0257886i | ||||||||
\(300\) | 138164. | − | 132856.i | 0.0886320 | − | 0.0852271i | ||||
\(301\) | 578097.i | 0.367777i | ||||||||
\(302\) | − | 2.05586e6i | − | 1.29711i | ||||||
\(303\) | −825813. | + | 794088.i | −0.516743 | + | 0.496892i | ||||
\(304\) | −2.96504e6 | −1.84012 | ||||||||
\(305\) | −482880. | −0.297228 | ||||||||
\(306\) | 1.41756e6 | + | 55545.2i | 0.865444 | + | 0.0339112i | ||||
\(307\) | 509116. | 0.308298 | 0.154149 | − | 0.988048i | \(-0.450736\pi\) | ||||
0.154149 | + | 0.988048i | \(0.450736\pi\) | |||||||
\(308\) | −1.56045e6 | −0.937288 | ||||||||
\(309\) | −1.14030e6 | − | 1.18586e6i | −0.679397 | − | 0.706539i | ||||
\(310\) | 408790. | 0.241600 | ||||||||
\(311\) | − | 1.38212e6i | − | 0.810297i | −0.914251 | − | 0.405148i | \(-0.867220\pi\) | ||
0.914251 | − | 0.405148i | \(-0.132780\pi\) | |||||||
\(312\) | −50292.1 | − | 52301.4i | −0.0292492 | − | 0.0304177i | ||||
\(313\) | − | 1.90212e6i | − | 1.09743i | −0.836009 | − | 0.548716i | \(-0.815117\pi\) | ||
0.836009 | − | 0.548716i | \(-0.184883\pi\) | |||||||
\(314\) | − | 879895.i | − | 0.503624i | ||||||
\(315\) | 1.13118e6 | + | 44323.5i | 0.642324 | + | 0.0251685i | ||||
\(316\) | −470687. | −0.265164 | ||||||||
\(317\) | 3.01161e6i | 1.68326i | 0.540055 | + | 0.841630i | \(0.318403\pi\) | ||||
−0.540055 | + | 0.841630i | \(0.681597\pi\) | |||||||
\(318\) | 2.13579e6 | + | 2.22112e6i | 1.18438 | + | 1.23170i | ||||
\(319\) | − | 4.67160e6i | − | 2.57033i | ||||||
\(320\) | − | 908052.i | − | 0.495719i | ||||||
\(321\) | −2.21901e6 | − | 2.30766e6i | −1.20198 | − | 1.25000i | ||||
\(322\) | 302112. | 0.162378 | ||||||||
\(323\) | − | 1.91475e6i | − | 1.02119i | ||||||
\(324\) | −1.48363e6 | − | 116447.i | −0.785169 | − | 0.0616260i | ||||
\(325\) | − | 44173.0i | − | 0.0231979i | ||||||
\(326\) | 1.19137e6 | 0.620874 | ||||||||
\(327\) | 172616. | + | 179512.i | 0.0892712 | + | 0.0928377i | ||||
\(328\) | − | 855641.i | − | 0.439144i | ||||||
\(329\) | 2.51728e6 | 1.28216 | ||||||||
\(330\) | 2.86417e6 | + | 2.97859e6i | 1.44782 | + | 1.50566i | ||||
\(331\) | −2.25633e6 | −1.13196 | −0.565981 | − | 0.824418i | \(-0.691503\pi\) | ||||
−0.565981 | + | 0.824418i | \(0.691503\pi\) | |||||||
\(332\) | 2.74335e6 | 1.36595 | ||||||||
\(333\) | −2.54760e6 | − | 99824.2i | −1.25899 | − | 0.0493316i | ||||
\(334\) | − | 2.15449e6i | − | 1.05677i | ||||||
\(335\) | 3.75560e6 | 1.82839 | ||||||||
\(336\) | −1.21843e6 | + | 1.17163e6i | −0.588781 | + | 0.566162i | ||||
\(337\) | 893788.i | 0.428706i | 0.976756 | + | 0.214353i | \(0.0687643\pi\) | ||||
−0.976756 | + | 0.214353i | \(0.931236\pi\) | |||||||
\(338\) | −2.74618e6 | −1.30749 | ||||||||
\(339\) | 2.10241e6 | − | 2.02164e6i | 0.993615 | − | 0.955444i | ||||
\(340\) | 999015. | 0.468678 | ||||||||
\(341\) | − | 718354.i | − | 0.334543i | ||||||
\(342\) | −178499. | + | 4.55545e6i | −0.0825221 | + | 2.10604i | ||||
\(343\) | −2.30281e6 | −1.05687 | ||||||||
\(344\) | 327608.i | 0.149265i | ||||||||
\(345\) | −244313. | − | 254074.i | −0.110509 | − | 0.114924i | ||||
\(346\) | −2.50612e6 | −1.12541 | ||||||||
\(347\) | 208504. | 0.0929589 | 0.0464794 | − | 0.998919i | \(-0.485200\pi\) | ||||
0.0464794 | + | 0.998919i | \(0.485200\pi\) | |||||||
\(348\) | 1.86388e6 | + | 1.93834e6i | 0.825029 | + | 0.857989i | ||||
\(349\) | 3.61848e6i | 1.59024i | 0.606454 | + | 0.795119i | \(0.292592\pi\) | ||||
−0.606454 | + | 0.795119i | \(0.707408\pi\) | |||||||
\(350\) | −334750. | −0.146066 | ||||||||
\(351\) | −256332. | + | 227855.i | −0.111054 | + | 0.0987168i | ||||
\(352\) | −5.04739e6 | −2.17125 | ||||||||
\(353\) | −920606. | −0.393221 | −0.196611 | − | 0.980482i | \(-0.562993\pi\) | ||||
−0.196611 | + | 0.980482i | \(0.562993\pi\) | |||||||
\(354\) | 779987. | + | 3.05438e6i | 0.330811 | + | 1.29543i | ||||
\(355\) | −2.24692e6 | −0.946275 | ||||||||
\(356\) | −1.30422e6 | −0.545414 | ||||||||
\(357\) | −756605. | − | 786832.i | −0.314195 | − | 0.326747i | ||||
\(358\) | 2.14893e6 | 0.886166 | ||||||||
\(359\) | 3.37657e6i | 1.38274i | 0.722503 | + | 0.691368i | \(0.242992\pi\) | ||||
−0.722503 | + | 0.691368i | \(0.757008\pi\) | |||||||
\(360\) | 641039. | + | 25118.2i | 0.260692 | + | 0.0102149i | ||||
\(361\) | 3.67709e6 | 1.48503 | ||||||||
\(362\) | −2.67125e6 | −1.07138 | ||||||||
\(363\) | 3.42455e6 | − | 3.29299e6i | 1.36407 | − | 1.31167i | ||||
\(364\) | − | 207003.i | − | 0.0818887i | ||||||
\(365\) | 1.95099e6 | 0.766520 | ||||||||
\(366\) | −768420. | − | 799119.i | −0.299844 | − | 0.311823i | ||||
\(367\) | − | 752319.i | − | 0.291566i | −0.989317 | − | 0.145783i | \(-0.953430\pi\) | ||
0.989317 | − | 0.145783i | \(-0.0465701\pi\) | |||||||
\(368\) | 526318. | 0.202595 | ||||||||
\(369\) | −4.04127e6 | − | 158351.i | −1.54508 | − | 0.0605419i | ||||
\(370\) | −4.07503e6 | −1.54749 | ||||||||
\(371\) | − | 2.37099e6i | − | 0.894323i | ||||||
\(372\) | 286609. | + | 298059.i | 0.107382 | + | 0.111672i | ||||
\(373\) | −3.35113e6 | −1.24715 | −0.623576 | − | 0.781763i | \(-0.714321\pi\) | ||||
−0.623576 | + | 0.781763i | \(0.714321\pi\) | |||||||
\(374\) | − | 3.98456e6i | − | 1.47299i | ||||||
\(375\) | 2.00463e6 | + | 2.08472e6i | 0.736132 | + | 0.765541i | ||||
\(376\) | 1.42655e6 | 0.520375 | ||||||||
\(377\) | 619717. | 0.224564 | ||||||||
\(378\) | 1.72672e6 | + | 1.94252e6i | 0.621573 | + | 0.699254i | ||||
\(379\) | −1.39388e6 | −0.498456 | −0.249228 | − | 0.968445i | \(-0.580177\pi\) | ||||
−0.249228 | + | 0.968445i | \(0.580177\pi\) | |||||||
\(380\) | 3.21041e6i | 1.14052i | ||||||||
\(381\) | −1.80078e6 | + | 1.73160e6i | −0.635546 | + | 0.611131i | ||||
\(382\) | −3.09695e6 | −1.08587 | ||||||||
\(383\) | 5.08435e6i | 1.77108i | 0.464560 | + | 0.885541i | \(0.346212\pi\) | ||||
−0.464560 | + | 0.885541i | \(0.653788\pi\) | |||||||
\(384\) | −1.15636e6 | + | 1.11194e6i | −0.400190 | + | 0.384817i | ||||
\(385\) | − | 3.17956e6i | − | 1.09324i | ||||||
\(386\) | 586569. | 0.200379 | ||||||||
\(387\) | 1.54732e6 | + | 60629.7i | 0.525175 | + | 0.0205782i | ||||
\(388\) | − | 2.29112e6i | − | 0.772623i | ||||||
\(389\) | 133568.i | 0.0447536i | 0.999750 | + | 0.0223768i | \(0.00712335\pi\) | ||||
−0.999750 | + | 0.0223768i | \(0.992877\pi\) | |||||||
\(390\) | −395129. | + | 379949.i | −0.131546 | + | 0.126492i | ||||
\(391\) | 339882.i | 0.112431i | ||||||||
\(392\) | −440957. | −0.144938 | ||||||||
\(393\) | 190046. | − | 182745.i | 0.0620694 | − | 0.0596849i | ||||
\(394\) | 5.03901e6i | 1.63533i | ||||||||
\(395\) | − | 959070.i | − | 0.309284i | ||||||
\(396\) | −163657. | + | 4.17667e6i | −0.0524440 | + | 1.33842i | ||||
\(397\) | 4.15269e6i | 1.32237i | 0.750223 | + | 0.661185i | \(0.229946\pi\) | ||||
−0.750223 | + | 0.661185i | \(0.770054\pi\) | |||||||
\(398\) | 1.14464e6 | 0.362210 | ||||||||
\(399\) | 2.52855e6 | − | 2.43141e6i | 0.795131 | − | 0.764585i | ||||
\(400\) | −583177. | −0.182243 | ||||||||
\(401\) | −2.86291e6 | −0.889092 | −0.444546 | − | 0.895756i | \(-0.646635\pi\) | ||||
−0.444546 | + | 0.895756i | \(0.646635\pi\) | |||||||
\(402\) | 5.97639e6 | + | 6.21515e6i | 1.84448 | + | 1.91817i | ||||
\(403\) | 95294.1 | 0.0292283 | ||||||||
\(404\) | −1.85225e6 | −0.564607 | ||||||||
\(405\) | 237271. | − | 3.02304e6i | 0.0718798 | − | 0.915811i | ||||
\(406\) | − | 4.69631e6i | − | 1.41397i | ||||||
\(407\) | 7.16092e6i | 2.14281i | ||||||||
\(408\) | −428769. | − | 445899.i | −0.127518 | − | 0.132613i | ||||
\(409\) | − | 1.11852e6i | − | 0.330625i | −0.986241 | − | 0.165313i | \(-0.947137\pi\) | ||
0.986241 | − | 0.165313i | \(-0.0528633\pi\) | |||||||
\(410\) | −6.46423e6 | −1.89914 | ||||||||
\(411\) | −1.35093e6 | − | 1.40490e6i | −0.394482 | − | 0.410242i | ||||
\(412\) | − | 2.65981e6i | − | 0.771983i | ||||||
\(413\) | 1.19638e6 | − | 2.11005e6i | 0.345138 | − | 0.608720i | ||||
\(414\) | 31684.9 | − | 808627.i | 0.00908556 | − | 0.231872i | ||||
\(415\) | 5.58983e6i | 1.59323i | ||||||||
\(416\) | − | 669568.i | − | 0.189697i | ||||||
\(417\) | −956818. | + | 920061.i | −0.269457 | + | 0.259105i | ||||
\(418\) | 1.28047e7 | 3.58449 | ||||||||
\(419\) | 2.23799e6 | 0.622764 | 0.311382 | − | 0.950285i | \(-0.399208\pi\) | ||||
0.311382 | + | 0.950285i | \(0.399208\pi\) | |||||||
\(420\) | 1.26858e6 | + | 1.31926e6i | 0.350910 | + | 0.364929i | ||||
\(421\) | 5.55658e6i | 1.52793i | 0.645260 | + | 0.763963i | \(0.276749\pi\) | ||||
−0.645260 | + | 0.763963i | \(0.723251\pi\) | |||||||
\(422\) | 1.90777e6i | 0.521489i | ||||||||
\(423\) | 264008. | − | 6.73771e6i | 0.0717407 | − | 1.83089i | ||||
\(424\) | − | 1.34364e6i | − | 0.362968i | ||||||
\(425\) | − | 376600.i | − | 0.101137i | ||||||
\(426\) | −3.57559e6 | − | 3.71843e6i | −0.954604 | − | 0.992741i | ||||
\(427\) | 853037.i | 0.226411i | ||||||||
\(428\) | − | 5.17595e6i | − | 1.36578i | ||||||
\(429\) | 667673. | + | 694347.i | 0.175154 | + | 0.182152i | ||||
\(430\) | 2.47503e6 | 0.645520 | ||||||||
\(431\) | −4.62303e6 | −1.19876 | −0.599381 | − | 0.800464i | \(-0.704587\pi\) | ||||
−0.599381 | + | 0.800464i | \(0.704587\pi\) | |||||||
\(432\) | 3.00816e6 | + | 3.38411e6i | 0.775518 | + | 0.872440i | ||||
\(433\) | 1.20291e6 | 0.308328 | 0.154164 | − | 0.988045i | \(-0.450732\pi\) | ||||
0.154164 | + | 0.988045i | \(0.450732\pi\) | |||||||
\(434\) | − | 722152.i | − | 0.184037i | ||||||
\(435\) | −3.94955e6 | + | 3.79783e6i | −1.00075 | + | 0.962303i | ||||
\(436\) | 402636.i | 0.101437i | ||||||||
\(437\) | −1.09224e6 | −0.273598 | ||||||||
\(438\) | 3.10466e6 | + | 3.22870e6i | 0.773267 | + | 0.804160i | ||||
\(439\) | 1.81269e6 | 0.448912 | 0.224456 | − | 0.974484i | \(-0.427939\pi\) | ||||
0.224456 | + | 0.974484i | \(0.427939\pi\) | |||||||
\(440\) | − | 1.80186e6i | − | 0.443700i | ||||||
\(441\) | −81606.8 | + | 2.08268e6i | −0.0199816 | + | 0.509948i | ||||
\(442\) | 528576. | 0.128692 | ||||||||
\(443\) | −4.60126e6 | −1.11395 | −0.556977 | − | 0.830528i | \(-0.688039\pi\) | ||||
−0.556977 | + | 0.830528i | \(0.688039\pi\) | |||||||
\(444\) | −2.85706e6 | − | 2.97121e6i | −0.687801 | − | 0.715279i | ||||
\(445\) | − | 2.65747e6i | − | 0.636164i | ||||||
\(446\) | −2.10321e6 | −0.500664 | ||||||||
\(447\) | 1.79990e6 | − | 1.73076e6i | 0.426069 | − | 0.409701i | ||||
\(448\) | −1.60413e6 | −0.377610 | ||||||||
\(449\) | − | 3.94651e6i | − | 0.923840i | −0.886921 | − | 0.461920i | \(-0.847161\pi\) | ||
0.886921 | − | 0.461920i | \(-0.152839\pi\) | |||||||
\(450\) | −35107.9 | + | 895984.i | −0.00817284 | + | 0.208578i | ||||
\(451\) | 1.13594e7i | 2.62975i | ||||||||
\(452\) | 4.71559e6 | 1.08565 | ||||||||
\(453\) | 2.93698e6 | + | 3.05432e6i | 0.672443 | + | 0.699308i | ||||
\(454\) | 8.60007e6 | 1.95822 | ||||||||
\(455\) | 421789. | 0.0955139 | ||||||||
\(456\) | 1.43293e6 | − | 1.37788e6i | 0.322710 | − | 0.310313i | ||||
\(457\) | − | 1.48061e6i | − | 0.331626i | −0.986157 | − | 0.165813i | \(-0.946975\pi\) | ||
0.986157 | − | 0.165813i | \(-0.0530248\pi\) | |||||||
\(458\) | − | 4.21048e6i | − | 0.937924i | ||||||
\(459\) | −2.18537e6 | + | 1.94259e6i | −0.484165 | + | 0.430378i | ||||
\(460\) | − | 569873.i | − | 0.125569i | ||||||
\(461\) | 1.08421e6i | 0.237608i | 0.992918 | + | 0.118804i | \(0.0379060\pi\) | ||||
−0.992918 | + | 0.118804i | \(0.962094\pi\) | |||||||
\(462\) | 5.26186e6 | − | 5.05972e6i | 1.14692 | − | 1.10286i | ||||
\(463\) | − | 5.94024e6i | − | 1.28781i | −0.765106 | − | 0.643904i | \(-0.777313\pi\) | ||
0.765106 | − | 0.643904i | \(-0.222687\pi\) | |||||||
\(464\) | − | 8.18157e6i | − | 1.76417i | ||||||
\(465\) | −607324. | + | 583993.i | −0.130253 | + | 0.125249i | ||||
\(466\) | −7.69928e6 | −1.64242 | ||||||||
\(467\) | −4.27370e6 | −0.906800 | −0.453400 | − | 0.891307i | \(-0.649789\pi\) | ||||
−0.453400 | + | 0.891307i | \(0.649789\pi\) | |||||||
\(468\) | −554061. | − | 21710.1i | −0.116935 | − | 0.00458192i | ||||
\(469\) | − | 6.63450e6i | − | 1.39276i | ||||||
\(470\) | − | 1.07773e7i | − | 2.25044i | ||||||
\(471\) | 1.25701e6 | + | 1.30723e6i | 0.261087 | + | 0.271518i | ||||
\(472\) | 677988. | − | 1.19577e6i | 0.140077 | − | 0.247054i | ||||
\(473\) | − | 4.34929e6i | − | 0.893852i | ||||||
\(474\) | 1.58716e6 | − | 1.52619e6i | 0.324471 | − | 0.312006i | ||||
\(475\) | 1.21023e6 | 0.246113 | ||||||||
\(476\) | − | 1.76482e6i | − | 0.357012i | ||||||
\(477\) | −6.34614e6 | − | 248664.i | −1.27707 | − | 0.0500400i | ||||
\(478\) | − | 1.06903e6i | − | 0.214004i | ||||||
\(479\) | − | 8.56691e6i | − | 1.70602i | −0.521891 | − | 0.853012i | \(-0.674773\pi\) | ||
0.521891 | − | 0.853012i | \(-0.325227\pi\) | |||||||
\(480\) | 4.10333e6 | + | 4.26726e6i | 0.812892 | + | 0.845368i | ||||
\(481\) | −949941. | −0.187212 | ||||||||
\(482\) | −3.06612e6 | −0.601134 | ||||||||
\(483\) | −448836. | + | 431594.i | −0.0875427 | + | 0.0841796i | ||||
\(484\) | 7.68106e6 | 1.49042 | ||||||||
\(485\) | 4.66837e6 | 0.901178 | ||||||||
\(486\) | 5.38040e6 | − | 4.41797e6i | 1.03329 | − | 0.848462i | ||||
\(487\) | 6.39670e6 | 1.22217 | 0.611087 | − | 0.791563i | \(-0.290732\pi\) | ||||
0.611087 | + | 0.791563i | \(0.290732\pi\) | |||||||
\(488\) | 483417.i | 0.0918909i | ||||||||
\(489\) | −1.76998e6 | + | 1.70198e6i | −0.334731 | + | 0.321872i | ||||
\(490\) | 3.33136e6i | 0.626804i | ||||||||
\(491\) | 355606.i | 0.0665681i | 0.999446 | + | 0.0332840i | \(0.0105966\pi\) | ||||
−0.999446 | + | 0.0332840i | \(0.989403\pi\) | |||||||
\(492\) | −4.53217e6 | − | 4.71323e6i | −0.844099 | − | 0.877822i | ||||
\(493\) | 5.28344e6 | 0.979038 | ||||||||
\(494\) | 1.69862e6i | 0.313169i | ||||||||
\(495\) | −8.51036e6 | − | 333466.i | −1.56112 | − | 0.0611701i | ||||
\(496\) | − | 1.25808e6i | − | 0.229617i | ||||||
\(497\) | 3.96932e6i | 0.720818i | ||||||||
\(498\) | −9.25061e6 | + | 8.89523e6i | −1.67146 | + | 1.60725i | ||||
\(499\) | −6.30405e6 | −1.13336 | −0.566681 | − | 0.823937i | \(-0.691773\pi\) | ||||
−0.566681 | + | 0.823937i | \(0.691773\pi\) | |||||||
\(500\) | 4.67590e6i | 0.836450i | ||||||||
\(501\) | 3.07789e6 | + | 3.20085e6i | 0.547846 | + | 0.569733i | ||||
\(502\) | 8.25085e6i | 1.46130i | ||||||||
\(503\) | 8.08256e6 | 1.42439 | 0.712195 | − | 0.701982i | \(-0.247701\pi\) | ||||
0.712195 | + | 0.701982i | \(0.247701\pi\) | |||||||
\(504\) | 44372.8 | − | 1.13243e6i | 0.00778109 | − | 0.198580i | ||||
\(505\) | − | 3.77414e6i | − | 0.658551i | ||||||
\(506\) | −2.27293e6 | −0.394647 | ||||||||
\(507\) | 4.07989e6 | − | 3.92316e6i | 0.704903 | − | 0.677823i | ||||
\(508\) | −4.03904e6 | −0.694414 | ||||||||
\(509\) | 1.08452e6 | 0.185542 | 0.0927709 | − | 0.995687i | \(-0.470428\pi\) | ||||
0.0927709 | + | 0.995687i | \(0.470428\pi\) | |||||||
\(510\) | −3.36870e6 | + | 3.23928e6i | −0.573504 | + | 0.551472i | ||||
\(511\) | − | 3.44655e6i | − | 0.583891i | ||||||
\(512\) | −6.87327e6 | −1.15875 | ||||||||
\(513\) | −6.24267e6 | − | 7.02286e6i | −1.04731 | − | 1.17820i | ||||
\(514\) | 35911.4i | 0.00599549i | ||||||||
\(515\) | 5.41962e6 | 0.900432 | ||||||||
\(516\) | 1.73528e6 | + | 1.80461e6i | 0.286910 | + | 0.298372i | ||||
\(517\) | −1.89387e7 | −3.11619 | ||||||||
\(518\) | 7.19879e6i | 1.17879i | ||||||||
\(519\) | 3.72324e6 | − | 3.58021e6i | 0.606740 | − | 0.583432i | ||||
\(520\) | 239028. | 0.0387651 | ||||||||
\(521\) | 2.94176e6i | 0.474802i | 0.971412 | + | 0.237401i | \(0.0762956\pi\) | ||||
−0.971412 | + | 0.237401i | \(0.923704\pi\) | |||||||
\(522\) | −1.25700e7 | − | 492539.i | −2.01911 | − | 0.0791160i | ||||
\(523\) | −7.68801e6 | −1.22902 | −0.614511 | − | 0.788908i | \(-0.710647\pi\) | ||||
−0.614511 | + | 0.788908i | \(0.710647\pi\) | |||||||
\(524\) | 426263. | 0.0678186 | ||||||||
\(525\) | 497325. | − | 478219.i | 0.0787484 | − | 0.0757232i | ||||
\(526\) | 3.78827e6i | 0.597003i | ||||||||
\(527\) | 812436. | 0.127427 | ||||||||
\(528\) | 9.16683e6 | − | 8.81468e6i | 1.43098 | − | 1.37601i | ||||
\(529\) | −6.24246e6 | −0.969877 | ||||||||
\(530\) | −1.01510e7 | −1.56971 | ||||||||
\(531\) | −5.52225e6 | − | 3.42350e6i | −0.849923 | − | 0.526906i | ||||
\(532\) | 5.67139e6 | 0.868781 | ||||||||
\(533\) | −1.50689e6 | −0.229755 | ||||||||
\(534\) | 4.39785e6 | − | 4.22890e6i | 0.667402 | − | 0.641763i | ||||
\(535\) | 1.05465e7 | 1.59303 | ||||||||
\(536\) | − | 3.75978e6i | − | 0.565263i | ||||||
\(537\) | −3.19258e6 | + | 3.06994e6i | −0.477757 | + | 0.459403i | ||||
\(538\) | 1.39542e7 | 2.07849 | ||||||||
\(539\) | 5.85409e6 | 0.867936 | ||||||||
\(540\) | 3.66416e6 | − | 3.25710e6i | 0.540742 | − | 0.480670i | ||||
\(541\) | − | 5.59453e6i | − | 0.821809i | −0.911678 | − | 0.410904i | \(-0.865213\pi\) | ||
0.911678 | − | 0.410904i | \(-0.134787\pi\) | |||||||
\(542\) | −3.15662e6 | −0.461556 | ||||||||
\(543\) | 3.96857e6 | − | 3.81611e6i | 0.577610 | − | 0.555420i | ||||
\(544\) | − | 5.70844e6i | − | 0.827029i | ||||||
\(545\) | −820409. | −0.118315 | ||||||||
\(546\) | 671203. | + | 698019.i | 0.0963546 | + | 0.100204i | ||||
\(547\) | 8.95135e6 | 1.27915 | 0.639573 | − | 0.768730i | \(-0.279111\pi\) | ||||
0.639573 | + | 0.768730i | \(0.279111\pi\) | |||||||
\(548\) | − | 3.15111e6i | − | 0.448241i | ||||||
\(549\) | 2.28322e6 | + | 89464.9i | 0.323309 | + | 0.0126684i | ||||
\(550\) | 2.51848e6 | 0.355002 | ||||||||
\(551\) | 1.69787e7i | 2.38247i | ||||||||
\(552\) | −254356. | + | 244585.i | −0.0355299 | + | 0.0341650i | ||||
\(553\) | −1.69425e6 | −0.235595 | ||||||||
\(554\) | −381613. | −0.0528261 | ||||||||
\(555\) | 6.05412e6 | − | 5.82154e6i | 0.834293 | − | 0.802242i | ||||
\(556\) | −2.14609e6 | −0.294416 | ||||||||
\(557\) | 3.54159e6i | 0.483683i | 0.970316 | + | 0.241841i | \(0.0777513\pi\) | ||||
−0.970316 | + | 0.241841i | \(0.922249\pi\) | |||||||
\(558\) | −1.93290e6 | − | 75737.9i | −0.262799 | − | 0.0102974i | ||||
\(559\) | 576961. | 0.0780938 | ||||||||
\(560\) | − | 5.56850e6i | − | 0.750357i | ||||||
\(561\) | 5.69229e6 | + | 5.91970e6i | 0.763624 | + | 0.794132i | ||||
\(562\) | 2.18995e6i | 0.292478i | ||||||||
\(563\) | 5.89504e6 | 0.783818 | 0.391909 | − | 0.920004i | \(-0.371815\pi\) | ||||
0.391909 | + | 0.920004i | \(0.371815\pi\) | |||||||
\(564\) | 7.85803e6 | − | 7.55615e6i | 1.04020 | − | 1.00024i | ||||
\(565\) | 9.60846e6i | 1.26629i | ||||||||
\(566\) | − | 1.37855e7i | − | 1.80876i | ||||||
\(567\) | −5.34037e6 | − | 419153.i | −0.697612 | − | 0.0547539i | ||||
\(568\) | 2.24942e6i | 0.292550i | ||||||||
\(569\) | 1.23342e7 | 1.59710 | 0.798548 | − | 0.601931i | \(-0.205602\pi\) | ||||
0.798548 | + | 0.601931i | \(0.205602\pi\) | |||||||
\(570\) | −1.04097e7 | − | 1.08256e7i | −1.34199 | − | 1.39561i | ||||
\(571\) | − | 1.24034e7i | − | 1.59203i | −0.605276 | − | 0.796015i | \(-0.706937\pi\) | ||
0.605276 | − | 0.796015i | \(-0.293063\pi\) | |||||||
\(572\) | 1.55738e6i | 0.199024i | ||||||||
\(573\) | 4.60102e6 | − | 4.42427e6i | 0.585420 | − | 0.562930i | ||||
\(574\) | 1.14195e7i | 1.44666i | ||||||||
\(575\) | −214826. | −0.0270967 | ||||||||
\(576\) | −168238. | + | 4.29358e6i | −0.0211284 | + | 0.539216i | ||||
\(577\) | 9.28511e6 | 1.16104 | 0.580520 | − | 0.814246i | \(-0.302849\pi\) | ||||
0.580520 | + | 0.814246i | \(0.302849\pi\) | |||||||
\(578\) | −6.23231e6 | −0.775943 | ||||||||
\(579\) | −871444. | + | 837966.i | −0.108030 | + | 0.103880i | ||||
\(580\) | −8.85863e6 | −1.09344 | ||||||||
\(581\) | 9.87476e6 | 1.21363 | ||||||||
\(582\) | 7.42889e6 | + | 7.72568e6i | 0.909110 | + | 0.945430i | ||||
\(583\) | 1.78380e7i | 2.17358i | ||||||||
\(584\) | − | 1.95316e6i | − | 0.236977i | ||||||
\(585\) | 44236.4 | − | 1.12895e6i | 0.00534429 | − | 0.136391i | ||||
\(586\) | − | 2.02954e7i | − | 2.44148i | ||||||
\(587\) | −2.94212e6 | −0.352423 | −0.176212 | − | 0.984352i | \(-0.556384\pi\) | ||||
−0.176212 | + | 0.984352i | \(0.556384\pi\) | |||||||
\(588\) | −2.42898e6 | + | 2.33567e6i | −0.289721 | + | 0.278591i | ||||
\(589\) | 2.61083e6i | 0.310091i | ||||||||
\(590\) | −9.03385e6 | − | 5.12209e6i | −1.06842 | − | 0.605784i | ||||
\(591\) | −7.19868e6 | − | 7.48627e6i | −0.847781 | − | 0.881651i | ||||
\(592\) | 1.25412e7i | 1.47074i | ||||||||
\(593\) | 185695.i | 0.0216852i | 0.999941 | + | 0.0108426i | \(0.00345137\pi\) | ||||
−0.999941 | + | 0.0108426i | \(0.996549\pi\) | |||||||
\(594\) | −1.29909e7 | − | 1.46144e7i | −1.51068 | − | 1.69948i | ||||
\(595\) | 3.59599e6 | 0.416415 | ||||||||
\(596\) | 4.03708e6 | 0.465534 | ||||||||
\(597\) | −1.70054e6 | + | 1.63521e6i | −0.195277 | + | 0.187775i | ||||
\(598\) | − | 301518.i | − | 0.0344795i | ||||||
\(599\) | 7.69736e6i | 0.876547i | 0.898842 | + | 0.438273i | \(0.144410\pi\) | ||||
−0.898842 | + | 0.438273i | \(0.855590\pi\) | |||||||
\(600\) | 281834. | − | 271007.i | 0.0319607 | − | 0.0307329i | ||||
\(601\) | 4.64907e6i | 0.525025i | 0.964929 | + | 0.262513i | \(0.0845511\pi\) | ||||
−0.964929 | + | 0.262513i | \(0.915449\pi\) | |||||||
\(602\) | − | 4.37229e6i | − | 0.491720i | ||||||
\(603\) | −1.77578e7 | − | 695813.i | −1.98882 | − | 0.0779291i | ||||
\(604\) | 6.85066e6i | 0.764082i | ||||||||
\(605\) | 1.56509e7i | 1.73840i | ||||||||
\(606\) | 6.24582e6 | − | 6.00588e6i | 0.690889 | − | 0.664347i | ||||
\(607\) | 4.50819e6 | 0.496628 | 0.248314 | − | 0.968680i | \(-0.420124\pi\) | ||||
0.248314 | + | 0.968680i | \(0.420124\pi\) | |||||||
\(608\) | 1.83445e7 | 2.01255 | ||||||||
\(609\) | 6.70909e6 | + | 6.97712e6i | 0.733027 | + | 0.762312i | ||||
\(610\) | 3.65214e6 | 0.397396 | ||||||||
\(611\) | − | 2.51233e6i | − | 0.272254i | ||||||
\(612\) | −4.72368e6 | − | 185091.i | −0.509803 | − | 0.0199759i | ||||
\(613\) | − | 1.23655e7i | − | 1.32911i | −0.747240 | − | 0.664554i | \(-0.768621\pi\) | ||
0.747240 | − | 0.664554i | \(-0.231379\pi\) | |||||||
\(614\) | −3.85057e6 | −0.412196 | ||||||||
\(615\) | 9.60366e6 | − | 9.23473e6i | 1.02388 | − | 0.984547i | ||||
\(616\) | −3.18310e6 | −0.337986 | ||||||||
\(617\) | − | 8.93156e6i | − | 0.944527i | −0.881457 | − | 0.472264i | \(-0.843437\pi\) | ||
0.881457 | − | 0.472264i | \(-0.156563\pi\) | |||||||
\(618\) | 8.62438e6 | + | 8.96893e6i | 0.908357 | + | 0.944647i | ||||
\(619\) | 9.58850e6 | 1.00583 | 0.502914 | − | 0.864336i | \(-0.332261\pi\) | ||||
0.502914 | + | 0.864336i | \(0.332261\pi\) | |||||||
\(620\) | −1.36219e6 | −0.142318 | ||||||||
\(621\) | 1.10812e6 | + | 1.24661e6i | 0.115308 | + | 0.129719i | ||||
\(622\) | 1.04533e7i | 1.08337i | ||||||||
\(623\) | −4.69459e6 | −0.484593 | ||||||||
\(624\) | 1.16932e6 | + | 1.21604e6i | 0.120219 | + | 0.125022i | ||||
\(625\) | −8.00294e6 | −0.819502 | ||||||||
\(626\) | 1.43862e7i | 1.46727i | ||||||||
\(627\) | −1.90234e7 | + | 1.82926e7i | −1.93250 | + | 1.85826i | ||||
\(628\) | 2.93203e6i | 0.296668i | ||||||||
\(629\) | −8.09878e6 | −0.816194 | ||||||||
\(630\) | −8.55536e6 | − | 335230.i | −0.858790 | − | 0.0336505i | ||||
\(631\) | −1.05488e7 | −1.05470 | −0.527350 | − | 0.849648i | \(-0.676814\pi\) | ||||
−0.527350 | + | 0.849648i | \(0.676814\pi\) | |||||||
\(632\) | −960135. | −0.0956180 | ||||||||
\(633\) | −2.72542e6 | − | 2.83430e6i | −0.270349 | − | 0.281149i | ||||
\(634\) | − | 2.27776e7i | − | 2.25053i | ||||||
\(635\) | − | 8.22993e6i | − | 0.809956i | ||||||
\(636\) | −7.11701e6 | − | 7.40135e6i | −0.697678 | − | 0.725551i | ||||
\(637\) | 776582.i | 0.0758296i | ||||||||
\(638\) | 3.53325e7i | 3.43655i | ||||||||
\(639\) | 1.06242e7 | + | 416295.i | 1.02931 | + | 0.0403319i | ||||
\(640\) | − | 5.28483e6i | − | 0.510013i | ||||||
\(641\) | 1.11258e7i | 1.06952i | 0.845005 | + | 0.534758i | \(0.179597\pi\) | ||||
−0.845005 | + | 0.534758i | \(0.820403\pi\) | |||||||
\(642\) | 1.67829e7 | + | 1.74534e7i | 1.60705 | + | 1.67125i | ||||
\(643\) | −909665. | −0.0867669 | −0.0433834 | − | 0.999058i | \(-0.513814\pi\) | ||||
−0.0433834 | + | 0.999058i | \(0.513814\pi\) | |||||||
\(644\) | −1.00671e6 | −0.0956515 | ||||||||
\(645\) | −3.67706e6 | + | 3.53580e6i | −0.348018 | + | 0.334648i | ||||
\(646\) | 1.44817e7i | 1.36533i | ||||||||
\(647\) | − | 557807.i | − | 0.0523869i | −0.999657 | − | 0.0261935i | \(-0.991661\pi\) | ||
0.999657 | − | 0.0261935i | \(-0.00833859\pi\) | |||||||
\(648\) | −3.02640e6 | − | 237535.i | −0.283132 | − | 0.0222223i | ||||
\(649\) | −9.00089e6 | + | 1.58749e7i | −0.838830 | + | 1.47945i | ||||
\(650\) | 334091.i | 0.0310157i | ||||||||
\(651\) | 1.03166e6 | + | 1.07287e6i | 0.0954077 | + | 0.0992193i | ||||
\(652\) | −3.96996e6 | −0.365736 | ||||||||
\(653\) | 5.96299e6i | 0.547244i | 0.961837 | + | 0.273622i | \(0.0882217\pi\) | ||||
−0.961837 | + | 0.273622i | \(0.911778\pi\) | |||||||
\(654\) | −1.30554e6 | − | 1.35769e6i | −0.119356 | − | 0.124125i | ||||
\(655\) | 868551.i | 0.0791028i | ||||||||
\(656\) | 1.98942e7i | 1.80495i | ||||||||
\(657\) | −9.22496e6 | − | 361467.i | −0.833779 | − | 0.0326705i | ||||
\(658\) | −1.90388e7 | −1.71425 | ||||||||
\(659\) | −92952.4 | −0.00833772 | −0.00416886 | − | 0.999991i | \(-0.501327\pi\) | ||||
−0.00416886 | + | 0.999991i | \(0.501327\pi\) | |||||||
\(660\) | −9.54413e6 | − | 9.92543e6i | −0.852858 | − | 0.886930i | ||||
\(661\) | 934288. | 0.0831720 | 0.0415860 | − | 0.999135i | \(-0.486759\pi\) | ||||
0.0415860 | + | 0.999135i | \(0.486759\pi\) | |||||||
\(662\) | 1.70652e7 | 1.51344 | ||||||||
\(663\) | −785285. | + | 755118.i | −0.0693815 | + | 0.0667161i | ||||
\(664\) | 5.59604e6 | 0.492562 | ||||||||
\(665\) | 1.15560e7i | 1.01334i | ||||||||
\(666\) | 1.92681e7 | + | 754995.i | 1.68327 | + | 0.0659566i | ||||
\(667\) | − | 3.01386e6i | − | 0.262306i | ||||||
\(668\) | 7.17933e6i | 0.622505i | ||||||||
\(669\) | 3.12466e6 | − | 3.00462e6i | 0.269922 | − | 0.259552i | ||||
\(670\) | −2.84046e7 | −2.44456 | ||||||||
\(671\) | − | 6.41779e6i | − | 0.550275i | ||||||
\(672\) | 7.53837e6 | − | 7.24877e6i | 0.643953 | − | 0.619215i | ||||
\(673\) | 8.53811e6i | 0.726648i | 0.931663 | + | 0.363324i | \(0.118358\pi\) | ||||
−0.931663 | + | 0.363324i | \(0.881642\pi\) | |||||||
\(674\) | − | 6.75994e6i | − | 0.573183i | ||||||
\(675\) | −1.22783e6 | − | 1.38128e6i | −0.103724 | − | 0.116687i | ||||
\(676\) | 9.15098e6 | 0.770195 | ||||||||
\(677\) | 1.23950e7i | 1.03938i | 0.854356 | + | 0.519689i | \(0.173952\pi\) | ||||
−0.854356 | + | 0.519689i | \(0.826048\pi\) | |||||||
\(678\) | −1.59010e7 | + | 1.52902e7i | −1.32847 | + | 1.27743i | ||||
\(679\) | − | 8.24695e6i | − | 0.686466i | ||||||
\(680\) | 2.03785e6 | 0.169005 | ||||||||
\(681\) | −1.27768e7 | + | 1.22860e7i | −1.05573 | + | 1.01518i | ||||
\(682\) | 5.43308e6i | 0.447286i | ||||||||
\(683\) | −2.08318e7 | −1.70874 | −0.854369 | − | 0.519667i | \(-0.826056\pi\) | ||||
−0.854369 | + | 0.519667i | \(0.826056\pi\) | |||||||
\(684\) | 594804. | − | 1.51799e7i | 0.0486109 | − | 1.24059i | ||||
\(685\) | 6.42068e6 | 0.522823 | ||||||||
\(686\) | 1.74167e7 | 1.41304 | ||||||||
\(687\) | 6.01504e6 | + | 6.25535e6i | 0.486235 | + | 0.505661i | ||||
\(688\) | − | 7.61709e6i | − | 0.613505i | ||||||
\(689\) | −2.36633e6 | −0.189901 | ||||||||
\(690\) | 1.84780e6 | + | 1.92162e6i | 0.147752 | + | 0.153654i | ||||
\(691\) | 2.11131e7i | 1.68212i | 0.540945 | + | 0.841058i | \(0.318067\pi\) | ||||
−0.540945 | + | 0.841058i | \(0.681933\pi\) | |||||||
\(692\) | 8.35102e6 | 0.662940 | ||||||||
\(693\) | −589088. | + | 1.50341e7i | −0.0465959 | + | 1.18917i | ||||
\(694\) | −1.57697e6 | −0.124287 | ||||||||
\(695\) | − | 4.37286e6i | − | 0.343403i | ||||||
\(696\) | 3.80205e6 | + | 3.95394e6i | 0.297505 | + | 0.309391i | ||||
\(697\) | −1.28471e7 | −1.00167 | ||||||||
\(698\) | − | 2.73674e7i | − | 2.12616i | ||||||
\(699\) | 1.14385e7 | − | 1.09991e7i | 0.885477 | − | 0.851460i | ||||
\(700\) | 1.11547e6 | 0.0860425 | ||||||||
\(701\) | 4.36551e6 | 0.335537 | 0.167768 | − | 0.985826i | \(-0.446344\pi\) | ||||
0.167768 | + | 0.985826i | \(0.446344\pi\) | |||||||
\(702\) | 1.93870e6 | − | 1.72332e6i | 0.148480 | − | 0.131985i | ||||
\(703\) | − | 2.60261e7i | − | 1.98619i | ||||||
\(704\) | 1.20686e7 | 0.917751 | ||||||||
\(705\) | 1.53964e7 | + | 1.60115e7i | 1.16666 | + | 1.21327i | ||||
\(706\) | 6.96277e6 | 0.525739 | ||||||||
\(707\) | −6.66724e6 | −0.501646 | ||||||||
\(708\) | −2.59912e6 | − | 1.01780e7i | −0.194869 | − | 0.763095i | ||||
\(709\) | −1.32319e7 | −0.988567 | −0.494284 | − | 0.869301i | \(-0.664570\pi\) | ||||
−0.494284 | + | 0.869301i | \(0.664570\pi\) | |||||||
\(710\) | 1.69940e7 | 1.26517 | ||||||||
\(711\) | −177690. | + | 4.53481e6i | −0.0131822 | + | 0.336422i | ||||
\(712\) | −2.66043e6 | −0.196676 | ||||||||
\(713\) | − | 463442.i | − | 0.0341406i | ||||||
\(714\) | 5.72239e6 | + | 5.95100e6i | 0.420080 | + | 0.436862i | ||||
\(715\) | −3.17331e6 | −0.232139 | ||||||||
\(716\) | −7.16079e6 | −0.522009 | ||||||||
\(717\) | 1.52721e6 | + | 1.58822e6i | 0.110943 | + | 0.115376i | ||||
\(718\) | − | 2.55378e7i | − | 1.84872i | ||||||
\(719\) | 9.06635e6 | 0.654049 | 0.327024 | − | 0.945016i | \(-0.393954\pi\) | ||||
0.327024 | + | 0.945016i | \(0.393954\pi\) | |||||||
\(720\) | −1.49045e7 | − | 584013.i | −1.07149 | − | 0.0419847i | ||||
\(721\) | − | 9.57408e6i | − | 0.685897i | ||||||
\(722\) | −2.78107e7 | −1.98550 | ||||||||
\(723\) | 4.55522e6 | − | 4.38022e6i | 0.324088 | − | 0.311638i | ||||
\(724\) | 8.90128e6 | 0.631112 | ||||||||
\(725\) | 3.33945e6i | 0.235955i | ||||||||
\(726\) | −2.59007e7 | + | 2.49057e7i | −1.82377 | + | 1.75371i | ||||
\(727\) | −8.46504e6 | −0.594009 | −0.297004 | − | 0.954876i | \(-0.595988\pi\) | ||||
−0.297004 | + | 0.954876i | \(0.595988\pi\) | |||||||
\(728\) | − | 422258.i | − | 0.0295290i | ||||||
\(729\) | −1.68199e6 | + | 1.42500e7i | −0.117221 | + | 0.993106i | ||||
\(730\) | −1.47558e7 | −1.02484 | ||||||||
\(731\) | 4.91892e6 | 0.340468 | ||||||||
\(732\) | 2.56057e6 | + | 2.66287e6i | 0.176628 | + | 0.183684i | ||||
\(733\) | 1.86428e7 | 1.28159 | 0.640797 | − | 0.767710i | \(-0.278604\pi\) | ||||
0.640797 | + | 0.767710i | \(0.278604\pi\) | |||||||
\(734\) | 5.68997e6i | 0.389825i | ||||||||
\(735\) | −4.75914e6 | − | 4.94927e6i | −0.324945 | − | 0.337927i | ||||
\(736\) | −3.25629e6 | −0.221579 | ||||||||
\(737\) | 4.99144e7i | 3.38499i | ||||||||
\(738\) | 3.05651e7 | + | 1.19765e6i | 2.06578 | + | 0.0809448i | ||||
\(739\) | − | 1.79550e7i | − | 1.20941i | −0.796449 | − | 0.604705i | \(-0.793291\pi\) | ||
0.796449 | − | 0.604705i | \(-0.206709\pi\) | |||||||
\(740\) | 1.35790e7 | 0.911570 | ||||||||
\(741\) | −2.42663e6 | − | 2.52358e6i | −0.162352 | − | 0.168838i | ||||
\(742\) | 1.79323e7i | 1.19571i | ||||||||
\(743\) | − | 6.34797e6i | − | 0.421854i | −0.977502 | − | 0.210927i | \(-0.932352\pi\) | ||
0.977502 | − | 0.210927i | \(-0.0676483\pi\) | |||||||
\(744\) | 584642. | + | 607999.i | 0.0387220 | + | 0.0402690i | ||||
\(745\) | 8.22593e6i | 0.542993i | ||||||||
\(746\) | 2.53454e7 | 1.66745 | ||||||||
\(747\) | 1.03565e6 | − | 2.64306e7i | 0.0679062 | − | 1.73303i | ||||
\(748\) | 1.32776e7i | 0.867689i | ||||||||
\(749\) | − | 1.86310e7i | − | 1.21348i | ||||||
\(750\) | −1.51615e7 | − | 1.57672e7i | −0.984212 | − | 1.02353i | ||||
\(751\) | 1.02347e7i | 0.662177i | 0.943600 | + | 0.331089i | \(0.107416\pi\) | ||||
−0.943600 | + | 0.331089i | \(0.892584\pi\) | |||||||
\(752\) | −3.31681e7 | −2.13883 | ||||||||
\(753\) | −1.17871e7 | − | 1.22580e7i | −0.757562 | − | 0.787827i | ||||
\(754\) | −4.68707e6 | −0.300243 | ||||||||
\(755\) | −1.39589e7 | −0.891216 | ||||||||
\(756\) | −5.75387e6 | − | 6.47296e6i | −0.366147 | − | 0.411906i | ||||
\(757\) | 6.04589e6 | 0.383460 | 0.191730 | − | 0.981448i | \(-0.438590\pi\) | ||||
0.191730 | + | 0.981448i | \(0.438590\pi\) | |||||||
\(758\) | 1.05423e7 | 0.666439 | ||||||||
\(759\) | 3.37680e6 | − | 3.24708e6i | 0.212765 | − | 0.204592i | ||||
\(760\) | 6.54879e6i | 0.411270i | ||||||||
\(761\) | 3.64475e6i | 0.228142i | 0.993473 | + | 0.114071i | \(0.0363892\pi\) | ||||
−0.993473 | + | 0.114071i | \(0.963611\pi\) | |||||||
\(762\) | 1.36197e7 | − | 1.30965e7i | 0.849729 | − | 0.817085i | ||||
\(763\) | 1.44930e6i | 0.0901254i | ||||||||
\(764\) | 1.03198e7 | 0.639645 | ||||||||
\(765\) | 377140. | − | 9.62496e6i | 0.0232996 | − | 0.594628i | ||||
\(766\) | − | 3.84542e7i | − | 2.36795i | ||||||
\(767\) | −2.10590e6 | − | 1.19402e6i | −0.129256 | − | 0.0732866i | ||||
\(768\) | 1.51039e7 | − | 1.45237e7i | 0.924031 | − | 0.888533i | ||||
\(769\) | − | 1.02131e7i | − | 0.622790i | −0.950281 | − | 0.311395i | \(-0.899204\pi\) | ||
0.950281 | − | 0.311395i | \(-0.100796\pi\) | |||||||
\(770\) | 2.40478e7i | 1.46167i | ||||||||
\(771\) | −51302.6 | − | 53352.2i | −0.00310816 | − | 0.00323234i | ||||
\(772\) | −1.95460e6 | −0.118036 | ||||||||
\(773\) | 1.74197e7 | 1.04856 | 0.524278 | − | 0.851547i | \(-0.324335\pi\) | ||||
0.524278 | + | 0.851547i | \(0.324335\pi\) | |||||||
\(774\) | −1.17028e7 | − | 458557.i | −0.702162 | − | 0.0275132i | ||||
\(775\) | 513508.i | 0.0307109i | ||||||||
\(776\) | − | 4.67356e6i | − | 0.278608i | ||||||
\(777\) | −1.02841e7 | − | 1.06950e7i | −0.611102 | − | 0.635516i | ||||
\(778\) | − | 1.01021e6i | − | 0.0598358i | ||||||
\(779\) | − | 4.12852e7i | − | 2.43754i | ||||||
\(780\) | 1.31667e6 | − | 1.26609e6i | 0.0774891 | − | 0.0745122i | ||||
\(781\) | − | 2.98631e7i | − | 1.75189i | ||||||
\(782\) | − | 2.57061e6i | − | 0.150321i | ||||||
\(783\) | 1.93785e7 | − | 1.72257e7i | 1.12957 | − | 1.00409i | ||||
\(784\) | 1.02525e7 | 0.595717 | ||||||||
\(785\) | −5.97430e6 | −0.346029 | ||||||||
\(786\) | −1.43736e6 | + | 1.38215e6i | −0.0829871 | + | 0.0797991i | ||||
\(787\) | 3.39441e7 | 1.95356 | 0.976781 | − | 0.214240i | \(-0.0687274\pi\) | ||||
0.976781 | + | 0.214240i | \(0.0687274\pi\) | |||||||
\(788\) | − | 1.67913e7i | − | 0.963315i | ||||||
\(789\) | −5.41187e6 | − | 5.62808e6i | −0.309496 | − | 0.321861i | ||||
\(790\) | 7.25368e6i | 0.413514i | ||||||||
\(791\) | 1.69739e7 | 0.964586 | ||||||||
\(792\) | −333837. | + | 8.51982e6i | −0.0189113 | + | 0.482633i | ||||
\(793\) | 851360. | 0.0480762 | ||||||||
\(794\) | − | 3.14078e7i | − | 1.76802i | ||||||
\(795\) | 1.50809e7 | − | 1.45016e7i | 0.846274 | − | 0.813763i | ||||
\(796\) | −3.81422e6 | −0.213365 | ||||||||
\(797\) | −1.74467e7 | −0.972899 | −0.486450 | − | 0.873709i | \(-0.661708\pi\) | ||||
−0.486450 | + | 0.873709i | \(0.661708\pi\) | |||||||
\(798\) | −1.91240e7 | + | 1.83893e7i | −1.06309 | + | 1.02225i | ||||
\(799\) | − | 2.14191e7i | − | 1.18695i | ||||||
\(800\) | 3.60808e6 | 0.199320 | ||||||||
\(801\) | −492359. | + | 1.25654e7i | −0.0271144 | + | 0.691985i | ||||
\(802\) | 2.16529e7 | 1.18872 | ||||||||
\(803\) | 2.59300e7i | 1.41910i | ||||||||
\(804\) | −1.99149e7 | − | 2.07105e7i | −1.08652 | − | 1.12993i | ||||
\(805\) | − | 2.05128e6i | − | 0.111567i | ||||||
\(806\) | −720733. | −0.0390784 | ||||||||
\(807\) | −2.07312e7 | + | 1.99347e7i | −1.12057 | + | 1.07752i | ||||
\(808\) | −3.77833e6 | −0.203597 | ||||||||
\(809\) | 2.11906e7 | 1.13834 | 0.569171 | − | 0.822219i | \(-0.307264\pi\) | ||||
0.569171 | + | 0.822219i | \(0.307264\pi\) | |||||||
\(810\) | −1.79454e6 | + | 2.28640e7i | −0.0961037 | + | 1.22444i | ||||
\(811\) | 5.25984e6i | 0.280815i | 0.990094 | + | 0.140407i | \(0.0448412\pi\) | ||||
−0.990094 | + | 0.140407i | \(0.955159\pi\) | |||||||
\(812\) | 1.56493e7i | 0.832923i | ||||||||
\(813\) | 4.68967e6 | − | 4.50951e6i | 0.248838 | − | 0.239278i | ||||
\(814\) | − | 5.41598e7i | − | 2.86494i | ||||||
\(815\) | − | 8.08917e6i | − | 0.426589i | ||||||
\(816\) | 9.96913e6 | + | 1.03674e7i | 0.524121 | + | 0.545061i | ||||
\(817\) | 1.58073e7i | 0.828520i | ||||||||
\(818\) | 8.45965e6i | 0.442048i | ||||||||
\(819\) | −1.99436e6 | − | 78146.2i | −0.103895 | − | 0.00407097i | ||||
\(820\) | 2.15405e7 | 1.11872 | ||||||||
\(821\) | −6.62750e6 | −0.343156 | −0.171578 | − | 0.985171i | \(-0.554887\pi\) | ||||
−0.171578 | + | 0.985171i | \(0.554887\pi\) | |||||||
\(822\) | 1.02174e7 | + | 1.06256e7i | 0.527425 | + | 0.548496i | ||||
\(823\) | − | 2.39642e7i | − | 1.23328i | −0.787244 | − | 0.616642i | \(-0.788493\pi\) | ||
0.787244 | − | 0.616642i | \(-0.211507\pi\) | |||||||
\(824\) | − | 5.42564e6i | − | 0.278377i | ||||||
\(825\) | −3.74160e6 | + | 3.59786e6i | −0.191392 | + | 0.184039i | ||||
\(826\) | −9.04849e6 | + | 1.59588e7i | −0.461451 | + | 0.813862i | ||||
\(827\) | − | 1.92579e7i | − | 0.979142i | −0.871963 | − | 0.489571i | \(-0.837153\pi\) | ||
0.871963 | − | 0.489571i | \(-0.162847\pi\) | |||||||
\(828\) | −105582. | + | 2.69455e6i | −0.00535199 | + | 0.136587i | ||||
\(829\) | −1.23458e7 | −0.623925 | −0.311962 | − | 0.950094i | \(-0.600986\pi\) | ||||
−0.311962 | + | 0.950094i | \(0.600986\pi\) | |||||||
\(830\) | − | 4.22772e7i | − | 2.13016i | ||||||
\(831\) | 566948. | − | 545168.i | 0.0284800 | − | 0.0273859i | ||||
\(832\) | 1.60097e6i | 0.0801818i | ||||||||
\(833\) | 6.62080e6i | 0.330596i | ||||||||
\(834\) | 7.23665e6 | − | 6.95865e6i | 0.360265 | − | 0.346425i | ||||
\(835\) | −1.46286e7 | −0.726082 | ||||||||
\(836\) | −4.26685e7 | −2.11150 | ||||||||
\(837\) | 2.97983e6 | − | 2.64880e6i | 0.147021 | − | 0.130688i | ||||
\(838\) | −1.69265e7 | −0.832638 | ||||||||
\(839\) | −1.97118e7 | −0.966768 | −0.483384 | − | 0.875408i | \(-0.660592\pi\) | ||||
−0.483384 | + | 0.875408i | \(0.660592\pi\) | |||||||
\(840\) | 2.58773e6 | + | 2.69111e6i | 0.126538 | + | 0.131593i | ||||
\(841\) | −2.63390e7 | −1.28413 | ||||||||
\(842\) | − | 4.20258e7i | − | 2.04285i | ||||||
\(843\) | −3.12854e6 | − | 3.25353e6i | −0.151626 | − | 0.157683i | ||||
\(844\) | − | 6.35719e6i | − | 0.307191i | ||||||
\(845\) | 1.86460e7i | 0.898346i | ||||||||
\(846\) | −1.99675e6 | + | 5.09589e7i | −0.0959177 | + | 2.44790i | ||||
\(847\) | 2.76483e7 | 1.32422 | ||||||||
\(848\) | 3.12404e7i | 1.49186i | ||||||||
\(849\) | 1.96938e7 | + | 2.04806e7i | 0.937691 | + | 0.975152i | ||||
\(850\) | 2.84832e6i | 0.135220i | ||||||||
\(851\) | 4.61983e6i | 0.218676i | ||||||||
\(852\) | 1.19148e7 | + | 1.23908e7i | 0.562324 | + | 0.584789i | ||||
\(853\) | 1.73670e7 | 0.817247 | 0.408623 | − | 0.912703i | \(-0.366009\pi\) | ||||
0.408623 | + | 0.912703i | \(0.366009\pi\) | |||||||
\(854\) | − | 6.45173e6i | − | 0.302713i | ||||||
\(855\) | 3.09305e7 | + | 1.21197e6i | 1.44701 | + | 0.0566991i | ||||
\(856\) | − | 1.05582e7i | − | 0.492500i | ||||||
\(857\) | −1.02414e7 | −0.476328 | −0.238164 | − | 0.971225i | \(-0.576546\pi\) | ||||
−0.238164 | + | 0.971225i | \(0.576546\pi\) | |||||||
\(858\) | −5.04977e6 | − | 5.25152e6i | −0.234182 | − | 0.243538i | ||||
\(859\) | 7.65375e6i | 0.353909i | 0.984219 | + | 0.176954i | \(0.0566245\pi\) | ||||
−0.984219 | + | 0.176954i | \(0.943375\pi\) | |||||||
\(860\) | −8.24744e6 | −0.380253 | ||||||||
\(861\) | −1.63137e7 | − | 1.69654e7i | −0.749971 | − | 0.779933i | ||||
\(862\) | 3.49651e7 | 1.60275 | ||||||||
\(863\) | 4.64967e6 | 0.212518 | 0.106259 | − | 0.994339i | \(-0.466113\pi\) | ||||
0.106259 | + | 0.994339i | \(0.466113\pi\) | |||||||
\(864\) | −1.86113e7 | − | 2.09373e7i | −0.848189 | − | 0.954193i | ||||
\(865\) | 1.70160e7i | 0.773245i | ||||||||
\(866\) | −9.09789e6 | −0.412236 | ||||||||
\(867\) | 9.25911e6 | − | 8.90341e6i | 0.418332 | − | 0.402262i | ||||
\(868\) | 2.40640e6i | 0.108410i | ||||||||
\(869\) | 1.27467e7 | 0.572594 | ||||||||
\(870\) | 2.98714e7 | − | 2.87239e7i | 1.33801 | − | 1.28660i | ||||
\(871\) | −6.62146e6 | −0.295739 | ||||||||
\(872\) | 821320.i | 0.0365781i | ||||||||
\(873\) | −2.20736e7 | − | 864924.i | −0.980253 | − | 0.0384098i | ||||
\(874\) | 8.26086e6 | 0.365803 | ||||||||
\(875\) | 1.68311e7i | 0.743175i | ||||||||
\(876\) | −1.03455e7 | − | 1.07589e7i | −0.455505 | − | 0.473702i | ||||
\(877\) | −1.47835e7 | −0.649049 | −0.324525 | − | 0.945877i | \(-0.605204\pi\) | ||||
−0.324525 | + | 0.945877i | \(0.605204\pi\) | |||||||
\(878\) | −1.37098e7 | −0.600198 | ||||||||
\(879\) | 2.89937e7 | + | 3.01520e7i | 1.26570 | + | 1.31627i | ||||
\(880\) | 4.18944e7i | 1.82368i | ||||||||
\(881\) | 4.18565e7 | 1.81687 | 0.908434 | − | 0.418028i | \(-0.137278\pi\) | ||||
0.908434 | + | 0.418028i | \(0.137278\pi\) | |||||||
\(882\) | 617212. | − | 1.57518e7i | 0.0267155 | − | 0.681803i | ||||
\(883\) | 1.06724e7 | 0.460639 | 0.230320 | − | 0.973115i | \(-0.426023\pi\) | ||||
0.230320 | + | 0.973115i | \(0.426023\pi\) | |||||||
\(884\) | −1.76135e6 | −0.0758080 | ||||||||
\(885\) | 2.07386e7 | − | 5.29595e6i | 0.890064 | − | 0.227293i | ||||
\(886\) | 3.48005e7 | 1.48936 | ||||||||
\(887\) | −2.45260e7 | −1.04669 | −0.523345 | − | 0.852121i | \(-0.675316\pi\) | ||||
−0.523345 | + | 0.852121i | \(0.675316\pi\) | |||||||
\(888\) | −5.82801e6 | − | 6.06085e6i | −0.248021 | − | 0.257929i | ||||
\(889\) | −1.45387e7 | −0.616978 | ||||||||
\(890\) | 2.00991e7i | 0.850554i | ||||||||
\(891\) | 4.01781e7 | + | 3.15348e6i | 1.69549 | + | 0.133075i | ||||
\(892\) | 7.00844e6 | 0.294923 | ||||||||
\(893\) | 6.88318e7 | 2.88842 | ||||||||
\(894\) | −1.36131e7 | + | 1.30901e7i | −0.569656 | + | 0.547772i | ||||
\(895\) | − | 1.45908e7i | − | 0.608865i | ||||||
\(896\) | −9.33597e6 | −0.388499 | ||||||||
\(897\) | 430745. | + | 447954.i | 0.0178747 | + | 0.0185888i | ||||
\(898\) | 2.98484e7i | 1.23518i | ||||||||
\(899\) | −7.20416e6 | −0.297293 | ||||||||
\(900\) | 116988. | − | 2.98565e6i | 0.00481434 | − | 0.122866i | ||||
\(901\) | −2.01743e7 | −0.827915 | ||||||||
\(902\) | − | 8.59138e7i | − | 3.51598i | ||||||
\(903\) | 6.24620e6 | + | 6.49574e6i | 0.254916 | + | 0.265100i | ||||
\(904\) | 9.61914e6 | 0.391485 | ||||||||
\(905\) | 1.81372e7i | 0.736121i | ||||||||
\(906\) | −2.22131e7 | − | 2.31005e7i | −0.899060 | − | 0.934978i | ||||
\(907\) | 2.48597e7 | 1.00341 | 0.501704 | − | 0.865039i | \(-0.332707\pi\) | ||||
0.501704 | + | 0.865039i | \(0.332707\pi\) | |||||||
\(908\) | −2.86576e7 | −1.15352 | ||||||||
\(909\) | −699247. | + | 1.78454e7i | −0.0280686 | + | 0.716336i | ||||
\(910\) | −3.19009e6 | −0.127703 | ||||||||
\(911\) | − | 2.17026e7i | − | 0.866394i | −0.901299 | − | 0.433197i | \(-0.857385\pi\) | ||
0.901299 | − | 0.433197i | \(-0.142615\pi\) | |||||||
\(912\) | −3.33165e7 | + | 3.20366e7i | −1.32639 | + | 1.27544i | ||||
\(913\) | −7.42924e7 | −2.94963 | ||||||||
\(914\) | 1.11982e7i | 0.443386i | ||||||||
\(915\) | −5.42585e6 | + | 5.21741e6i | −0.214247 | + | 0.206017i | ||||
\(916\) | 1.40304e7i | 0.552498i | ||||||||
\(917\) | 1.53435e6 | 0.0602560 | ||||||||
\(918\) | 1.65285e7 | − | 1.46923e7i | 0.647331 | − | 0.575418i | ||||
\(919\) | − | 3.10147e7i | − | 1.21138i | −0.795702 | − | 0.605688i | \(-0.792898\pi\) | ||
0.795702 | − | 0.605688i | \(-0.207102\pi\) | |||||||
\(920\) | − | 1.16246e6i | − | 0.0452802i | ||||||
\(921\) | 5.72065e6 | − | 5.50088e6i | 0.222227 | − | 0.213689i | ||||
\(922\) | − | 8.20013e6i | − | 0.317683i | ||||||
\(923\) | 3.96152e6 | 0.153059 | ||||||||
\(924\) | −1.75339e7 | + | 1.68603e7i | −0.675613 | + | 0.649658i | ||||
\(925\) | − | 5.11891e6i | − | 0.196709i | ||||||
\(926\) | 4.49275e7i | 1.72181i | ||||||||
\(927\) | −2.56258e7 | − | 1.00411e6i | −0.979441 | − | 0.0383780i | ||||
\(928\) | 5.06188e7i | 1.92949i | ||||||||
\(929\) | −4.97769e7 | −1.89229 | −0.946147 | − | 0.323738i | \(-0.895060\pi\) | ||||
−0.946147 | + | 0.323738i | \(0.895060\pi\) | |||||||
\(930\) | 4.59334e6 | − | 4.41688e6i | 0.174149 | − | 0.167459i | ||||
\(931\) | −2.12765e7 | −0.804498 | ||||||||
\(932\) | 2.56560e7 | 0.967495 | ||||||||
\(933\) | −1.49334e7 | − | 1.55301e7i | −0.561637 | − | 0.584075i | ||||
\(934\) | 3.23230e7 | 1.21240 | ||||||||
\(935\) | −2.70543e7 | −1.01206 | ||||||||
\(936\) | −1.13021e6 | − | 44285.6i | −0.0421666 | − | 0.00165224i | ||||
\(937\) | 4.77907e7i | 1.77826i | 0.457659 | + | 0.889128i | \(0.348688\pi\) | ||||
−0.457659 | + | 0.889128i | \(0.651312\pi\) | |||||||
\(938\) | 5.01784e7i | 1.86213i | ||||||||
\(939\) | −2.05520e7 | − | 2.13730e7i | −0.760658 | − | 0.791047i | ||||
\(940\) | 3.59129e7i | 1.32565i | ||||||||
\(941\) | −2.53175e7 | −0.932068 | −0.466034 | − | 0.884767i | \(-0.654318\pi\) | ||||
−0.466034 | + | 0.884767i | \(0.654318\pi\) | |||||||
\(942\) | −9.50705e6 | − | 9.88687e6i | −0.349075 | − | 0.363021i | ||||
\(943\) | 7.32844e6i | 0.268369i | ||||||||
\(944\) | −1.57636e7 | + | 2.78023e7i | −0.575739 | + | 1.01543i | ||||
\(945\) | 1.31893e7 | − | 1.17240e7i | 0.480443 | − | 0.427069i | ||||
\(946\) | 3.28948e7i | 1.19509i | ||||||||
\(947\) | − | 2.19876e7i | − | 0.796713i | −0.917231 | − | 0.398357i | \(-0.869581\pi\) | ||
0.917231 | − | 0.398357i | \(-0.130419\pi\) | |||||||
\(948\) | −5.28884e6 | + | 5.08566e6i | −0.191135 | + | 0.183792i | ||||
\(949\) | −3.43977e6 | −0.123984 | ||||||||
\(950\) | −9.15329e6 | −0.329055 | ||||||||
\(951\) | 3.25398e7 | + | 3.38398e7i | 1.16671 | + | 1.21332i | ||||
\(952\) | − | 3.59999e6i | − | 0.128739i | ||||||
\(953\) | − | 1.62711e7i | − | 0.580343i | −0.956975 | − | 0.290171i | \(-0.906288\pi\) | ||
0.956975 | − | 0.290171i | \(-0.0937123\pi\) | |||||||
\(954\) | 4.79974e7 | + | 1.88071e6i | 1.70744 | + | 0.0669038i | ||||
\(955\) | 2.10276e7i | 0.746074i | ||||||||
\(956\) | 3.56230e6i | 0.126062i | ||||||||
\(957\) | −5.04756e7 | − | 5.24921e7i | −1.78156 | − | 1.85274i | ||||
\(958\) | 6.47936e7i | 2.28096i | ||||||||
\(959\) | − | 1.13425e7i | − | 0.398257i | ||||||
\(960\) | −9.81128e6 | − | 1.02032e7i | −0.343596 | − | 0.357323i | ||||
\(961\) | 2.75214e7 | 0.961306 | ||||||||
\(962\) | 7.18464e6 | 0.250304 | ||||||||
\(963\) | −4.98674e7 | − | 1.95398e6i | −1.73281 | − | 0.0678977i | ||||
\(964\) | 1.02171e7 | 0.354107 | ||||||||
\(965\) | − | 3.98268e6i | − | 0.137676i | ||||||
\(966\) | 3.39466e6 | − | 3.26425e6i | 0.117045 | − | 0.112549i | ||||
\(967\) | − | 1.46175e7i | − | 0.502697i | −0.967897 | − | 0.251348i | \(-0.919126\pi\) | ||
0.967897 | − | 0.251348i | \(-0.0808740\pi\) | |||||||
\(968\) | 1.56683e7 | 0.537444 | ||||||||
\(969\) | −2.06884e7 | − | 2.15149e7i | −0.707811 | − | 0.736088i | ||||
\(970\) | −3.53080e7 | −1.20488 | ||||||||
\(971\) | 4.75451e6i | 0.161830i | 0.996721 | + | 0.0809148i | \(0.0257842\pi\) | ||||
−0.996721 | + | 0.0809148i | \(0.974216\pi\) | |||||||
\(972\) | −1.79289e7 | + | 1.47218e7i | −0.608677 | + | 0.499799i | ||||
\(973\) | −7.72492e6 | −0.261585 | ||||||||
\(974\) | −4.83798e7 | −1.63405 | ||||||||
\(975\) | −477279. | − | 496347.i | −0.0160791 | − | 0.0167214i | ||||
\(976\) | − | 1.12397e7i | − | 0.377687i | ||||||
\(977\) | −7.34779e6 | −0.246275 | −0.123137 | − | 0.992390i | \(-0.539296\pi\) | ||||
−0.123137 | + | 0.992390i | \(0.539296\pi\) | |||||||
\(978\) | 1.33868e7 | − | 1.28725e7i | 0.447537 | − | 0.430344i | ||||
\(979\) | 3.53195e7 | 1.17776 | ||||||||
\(980\) | − | 1.11009e7i | − | 0.369228i | ||||||
\(981\) | 3.87917e6 | + | 152000.i | 0.128696 | + | 0.00504279i | ||||
\(982\) | − | 2.68954e6i | − | 0.0890019i | ||||||
\(983\) | −1.79483e6 | −0.0592433 | −0.0296217 | − | 0.999561i | \(-0.509430\pi\) | ||||
−0.0296217 | + | 0.999561i | \(0.509430\pi\) | |||||||
\(984\) | −9.24499e6 | − | 9.61434e6i | −0.304382 | − | 0.316542i | ||||
\(985\) | 3.42138e7 | 1.12360 | ||||||||
\(986\) | −3.99600e7 | −1.30898 | ||||||||
\(987\) | 2.82852e7 | − | 2.71986e7i | 0.924202 | − | 0.888698i | ||||
\(988\) | − | 5.66024e6i | − | 0.184477i | ||||||
\(989\) | − | 2.80592e6i | − | 0.0912188i | ||||||
\(990\) | 6.43659e7 | + | 2.52209e6i | 2.08722 | + | 0.0817847i | ||||
\(991\) | − | 2.51297e7i | − | 0.812835i | −0.913687 | − | 0.406418i | \(-0.866778\pi\) | ||
0.913687 | − | 0.406418i | \(-0.133222\pi\) | |||||||
\(992\) | 7.78367e6i | 0.251134i | ||||||||
\(993\) | −2.53530e7 | + | 2.43791e7i | −0.815938 | + | 0.784592i | ||||
\(994\) | − | 3.00210e7i | − | 0.963738i | ||||||
\(995\) | − | 7.77184e6i | − | 0.248866i | ||||||
\(996\) | 3.08254e7 | − | 2.96412e7i | 0.984601 | − | 0.946776i | ||||
\(997\) | 5.76794e7 | 1.83774 | 0.918868 | − | 0.394565i | \(-0.129105\pi\) | ||||
0.918868 | + | 0.394565i | \(0.129105\pi\) | |||||||
\(998\) | 4.76791e7 | 1.51531 | ||||||||
\(999\) | −2.97045e7 | + | 2.64046e7i | −0.941691 | + | 0.837077i |
(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 | 177.6.d.b.176.18 | yes | 92 | |
3.2 | odd | 2 | inner | 177.6.d.b.176.75 | yes | 92 | |
59.58 | odd | 2 | inner | 177.6.d.b.176.76 | yes | 92 | |
177.176 | even | 2 | inner | 177.6.d.b.176.17 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.d.b.176.17 | ✓ | 92 | 177.176 | even | 2 | inner | |
177.6.d.b.176.18 | yes | 92 | 1.1 | even | 1 | trivial | |
177.6.d.b.176.75 | yes | 92 | 3.2 | odd | 2 | inner | |
177.6.d.b.176.76 | yes | 92 | 59.58 | odd | 2 | inner |