Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(68,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, 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("69.68");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.c (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: | \(11.0664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 68.13 | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.6.c.b.68.19 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.57119i | − | 0.277750i | −0.990310 | − | 0.138875i | \(-0.955651\pi\) | ||
0.990310 | − | 0.138875i | \(-0.0443487\pi\) | |||||||
\(3\) | −12.8969 | − | 8.75610i | −0.827338 | − | 0.561704i | ||||
\(4\) | 29.5314 | 0.922855 | ||||||||
\(5\) | −37.1969 | −0.665399 | −0.332699 | − | 0.943033i | \(-0.607959\pi\) | ||||
−0.332699 | + | 0.943033i | \(0.607959\pi\) | |||||||
\(6\) | −13.7575 | + | 20.2635i | −0.156013 | + | 0.229793i | ||||
\(7\) | − | 122.242i | − | 0.942923i | −0.881887 | − | 0.471461i | \(-0.843727\pi\) | ||
0.881887 | − | 0.471461i | \(-0.156273\pi\) | |||||||
\(8\) | − | 96.6776i | − | 0.534073i | ||||||
\(9\) | 89.6613 | + | 225.854i | 0.368976 | + | 0.929439i | ||||
\(10\) | 58.4435i | 0.184815i | ||||||||
\(11\) | −321.586 | −0.801337 | −0.400669 | − | 0.916223i | \(-0.631222\pi\) | ||||
−0.400669 | + | 0.916223i | \(0.631222\pi\) | |||||||
\(12\) | −380.864 | − | 258.580i | −0.763513 | − | 0.518372i | ||||
\(13\) | −207.773 | −0.340981 | −0.170491 | − | 0.985359i | \(-0.554535\pi\) | ||||
−0.170491 | + | 0.985359i | \(0.554535\pi\) | |||||||
\(14\) | −192.066 | −0.261897 | ||||||||
\(15\) | 479.726 | + | 325.700i | 0.550510 | + | 0.373757i | ||||
\(16\) | 793.104 | 0.774516 | ||||||||
\(17\) | −1644.37 | −1.38000 | −0.689999 | − | 0.723811i | \(-0.742389\pi\) | ||||
−0.689999 | + | 0.723811i | \(0.742389\pi\) | |||||||
\(18\) | 354.859 | − | 140.875i | 0.258152 | − | 0.102483i | ||||
\(19\) | 2885.27i | 1.83359i | 0.399357 | + | 0.916795i | \(0.369233\pi\) | ||||
−0.399357 | + | 0.916795i | \(0.630767\pi\) | |||||||
\(20\) | −1098.48 | −0.614066 | ||||||||
\(21\) | −1070.37 | + | 1576.55i | −0.529644 | + | 0.780116i | ||||
\(22\) | 505.273i | 0.222572i | ||||||||
\(23\) | −2534.43 | + | 114.122i | −0.998988 | + | 0.0449831i | ||||
\(24\) | −846.519 | + | 1246.84i | −0.299991 | + | 0.441859i | ||||
\(25\) | −1741.39 | −0.557245 | ||||||||
\(26\) | 326.451i | 0.0947076i | ||||||||
\(27\) | 821.243 | − | 3697.90i | 0.216801 | − | 0.976216i | ||||
\(28\) | − | 3609.98i | − | 0.870181i | ||||||
\(29\) | 2444.83i | 0.539827i | 0.962885 | + | 0.269913i | \(0.0869951\pi\) | ||||
−0.962885 | + | 0.269913i | \(0.913005\pi\) | |||||||
\(30\) | 511.737 | − | 753.742i | 0.103811 | − | 0.152904i | ||||
\(31\) | −244.199 | −0.0456394 | −0.0228197 | − | 0.999740i | \(-0.507264\pi\) | ||||
−0.0228197 | + | 0.999740i | \(0.507264\pi\) | |||||||
\(32\) | − | 4339.80i | − | 0.749195i | ||||||
\(33\) | 4147.47 | + | 2815.84i | 0.662977 | + | 0.450114i | ||||
\(34\) | 2583.63i | 0.383294i | ||||||||
\(35\) | 4547.03i | 0.627420i | ||||||||
\(36\) | 2647.82 | + | 6669.76i | 0.340512 | + | 0.857737i | ||||
\(37\) | − | 9937.02i | − | 1.19331i | −0.802499 | − | 0.596653i | \(-0.796497\pi\) | ||
0.802499 | − | 0.596653i | \(-0.203503\pi\) | |||||||
\(38\) | 4533.31 | 0.509280 | ||||||||
\(39\) | 2679.63 | + | 1819.28i | 0.282107 | + | 0.191531i | ||||
\(40\) | 3596.11i | 0.355372i | ||||||||
\(41\) | − | 17465.4i | − | 1.62263i | −0.584611 | − | 0.811313i | \(-0.698753\pi\) | ||
0.584611 | − | 0.811313i | \(-0.301247\pi\) | |||||||
\(42\) | 2477.06 | + | 1681.75i | 0.216677 | + | 0.147109i | ||||
\(43\) | − | 3358.44i | − | 0.276992i | −0.990363 | − | 0.138496i | \(-0.955773\pi\) | ||
0.990363 | − | 0.138496i | \(-0.0442268\pi\) | |||||||
\(44\) | −9496.87 | −0.739518 | ||||||||
\(45\) | −3335.12 | − | 8401.06i | −0.245516 | − | 0.618447i | ||||
\(46\) | 179.307 | + | 3982.07i | 0.0124941 | + | 0.277469i | ||||
\(47\) | 15047.0i | 0.993583i | 0.867870 | + | 0.496791i | \(0.165489\pi\) | ||||
−0.867870 | + | 0.496791i | \(0.834511\pi\) | |||||||
\(48\) | −10228.6 | − | 6944.50i | −0.640786 | − | 0.435049i | ||||
\(49\) | 1863.84 | 0.110896 | ||||||||
\(50\) | 2736.06i | 0.154775i | ||||||||
\(51\) | 21207.4 | + | 14398.3i | 1.14172 | + | 0.775150i | ||||
\(52\) | −6135.81 | −0.314676 | ||||||||
\(53\) | 7910.60 | 0.386830 | 0.193415 | − | 0.981117i | \(-0.438044\pi\) | ||||
0.193415 | + | 0.981117i | \(0.438044\pi\) | |||||||
\(54\) | −5810.11 | − | 1290.33i | −0.271144 | − | 0.0602166i | ||||
\(55\) | 11962.0 | 0.533209 | ||||||||
\(56\) | −11818.1 | −0.503590 | ||||||||
\(57\) | 25263.7 | − | 37211.1i | 1.02994 | − | 1.51700i | ||||
\(58\) | 3841.31 | 0.149937 | ||||||||
\(59\) | 11354.1i | 0.424640i | 0.977200 | + | 0.212320i | \(0.0681019\pi\) | ||||
−0.977200 | + | 0.212320i | \(0.931898\pi\) | |||||||
\(60\) | 14167.0 | + | 9618.37i | 0.508041 | + | 0.344924i | ||||
\(61\) | − | 25900.1i | − | 0.891204i | −0.895231 | − | 0.445602i | \(-0.852990\pi\) | ||
0.895231 | − | 0.445602i | \(-0.147010\pi\) | |||||||
\(62\) | 383.684i | 0.0126764i | ||||||||
\(63\) | 27608.8 | − | 10960.4i | 0.876389 | − | 0.347916i | ||||
\(64\) | 18560.7 | 0.566427 | ||||||||
\(65\) | 7728.51 | 0.226888 | ||||||||
\(66\) | 4424.22 | − | 6516.47i | 0.125019 | − | 0.184142i | ||||
\(67\) | − | 36948.4i | − | 1.00556i | −0.864414 | − | 0.502781i | \(-0.832310\pi\) | ||
0.864414 | − | 0.502781i | \(-0.167690\pi\) | |||||||
\(68\) | −48560.6 | −1.27354 | ||||||||
\(69\) | 33685.6 | + | 20719.9i | 0.851768 | + | 0.523920i | ||||
\(70\) | 7144.27 | 0.174266 | ||||||||
\(71\) | − | 52830.9i | − | 1.24378i | −0.783106 | − | 0.621888i | \(-0.786366\pi\) | ||
0.783106 | − | 0.621888i | \(-0.213634\pi\) | |||||||
\(72\) | 21835.0 | − | 8668.24i | 0.496388 | − | 0.197060i | ||||
\(73\) | −71803.2 | −1.57702 | −0.788510 | − | 0.615023i | \(-0.789147\pi\) | ||||
−0.788510 | + | 0.615023i | \(0.789147\pi\) | |||||||
\(74\) | −15613.0 | −0.331441 | ||||||||
\(75\) | 22458.6 | + | 15247.8i | 0.461030 | + | 0.313007i | ||||
\(76\) | 85205.9i | 1.69214i | ||||||||
\(77\) | 39311.4i | 0.755599i | ||||||||
\(78\) | 2858.44 | − | 4210.21i | 0.0531976 | − | 0.0783552i | ||||
\(79\) | 43369.5i | 0.781839i | 0.920425 | + | 0.390919i | \(0.127843\pi\) | ||||
−0.920425 | + | 0.390919i | \(0.872157\pi\) | |||||||
\(80\) | −29501.0 | −0.515362 | ||||||||
\(81\) | −42970.7 | + | 40500.7i | −0.727713 | + | 0.685882i | ||||
\(82\) | −27441.5 | −0.450685 | ||||||||
\(83\) | −107131. | −1.70694 | −0.853471 | − | 0.521140i | \(-0.825507\pi\) | ||||
−0.853471 | + | 0.521140i | \(0.825507\pi\) | |||||||
\(84\) | −31609.3 | + | 46557.6i | −0.488784 | + | 0.719934i | ||||
\(85\) | 61165.6 | 0.918248 | ||||||||
\(86\) | −5276.76 | −0.0769345 | ||||||||
\(87\) | 21407.2 | − | 31530.8i | 0.303223 | − | 0.446619i | ||||
\(88\) | 31090.1i | 0.427973i | ||||||||
\(89\) | 1120.11 | 0.0149895 | 0.00749474 | − | 0.999972i | \(-0.497614\pi\) | ||||
0.00749474 | + | 0.999972i | \(0.497614\pi\) | |||||||
\(90\) | −13199.7 | + | 5240.12i | −0.171774 | + | 0.0681923i | ||||
\(91\) | 25398.6i | 0.321519i | ||||||||
\(92\) | −74845.1 | + | 3370.17i | −0.921921 | + | 0.0415129i | ||||
\(93\) | 3149.42 | + | 2138.23i | 0.0377592 | + | 0.0256359i | ||||
\(94\) | 23641.7 | 0.275968 | ||||||||
\(95\) | − | 107323.i | − | 1.22007i | ||||||
\(96\) | −37999.8 | + | 55970.1i | −0.420826 | + | 0.619838i | ||||
\(97\) | − | 26716.2i | − | 0.288301i | −0.989556 | − | 0.144150i | \(-0.953955\pi\) | ||
0.989556 | − | 0.144150i | \(-0.0460449\pi\) | |||||||
\(98\) | − | 2928.45i | − | 0.0308015i | ||||||
\(99\) | −28833.8 | − | 72631.3i | −0.295675 | − | 0.744794i | ||||
\(100\) | −51425.6 | −0.514256 | ||||||||
\(101\) | 79301.9i | 0.773536i | 0.922177 | + | 0.386768i | \(0.126409\pi\) | ||||
−0.922177 | + | 0.386768i | \(0.873591\pi\) | |||||||
\(102\) | 22622.5 | − | 33320.8i | 0.215298 | − | 0.317114i | ||||
\(103\) | 79210.1i | 0.735678i | 0.929890 | + | 0.367839i | \(0.119902\pi\) | ||||
−0.929890 | + | 0.367839i | \(0.880098\pi\) | |||||||
\(104\) | 20087.0i | 0.182109i | ||||||||
\(105\) | 39814.3 | − | 58642.8i | 0.352424 | − | 0.519088i | ||||
\(106\) | − | 12429.1i | − | 0.107442i | ||||||
\(107\) | 191353. | 1.61576 | 0.807878 | − | 0.589350i | \(-0.200616\pi\) | ||||
0.807878 | + | 0.589350i | \(0.200616\pi\) | |||||||
\(108\) | 24252.4 | − | 109204.i | 0.200076 | − | 0.900905i | ||||
\(109\) | − | 123427.i | − | 0.995047i | −0.867451 | − | 0.497523i | \(-0.834243\pi\) | ||
0.867451 | − | 0.497523i | \(-0.165757\pi\) | |||||||
\(110\) | − | 18794.6i | − | 0.148099i | ||||||
\(111\) | −87009.5 | + | 128157.i | −0.670285 | + | 0.987267i | ||||
\(112\) | − | 96950.8i | − | 0.730309i | ||||||
\(113\) | 52135.8 | 0.384096 | 0.192048 | − | 0.981386i | \(-0.438487\pi\) | ||||
0.192048 | + | 0.981386i | \(0.438487\pi\) | |||||||
\(114\) | −58465.8 | − | 39694.2i | −0.421347 | − | 0.286065i | ||||
\(115\) | 94272.9 | − | 4244.98i | 0.664725 | − | 0.0299317i | ||||
\(116\) | 72199.3i | 0.498182i | ||||||||
\(117\) | −18629.2 | − | 46926.2i | −0.125814 | − | 0.316921i | ||||
\(118\) | 17839.4 | 0.117944 | ||||||||
\(119\) | 201012.i | 1.30123i | ||||||||
\(120\) | 31487.9 | − | 46378.7i | 0.199614 | − | 0.294013i | ||||
\(121\) | −57633.5 | −0.357859 | ||||||||
\(122\) | −40694.1 | −0.247532 | ||||||||
\(123\) | −152929. | + | 225250.i | −0.911437 | + | 1.34246i | ||||
\(124\) | −7211.53 | −0.0421185 | ||||||||
\(125\) | 181015. | 1.03619 | ||||||||
\(126\) | −17220.9 | − | 43378.8i | −0.0966338 | − | 0.243417i | ||||
\(127\) | −104033. | −0.572349 | −0.286174 | − | 0.958178i | \(-0.592384\pi\) | ||||
−0.286174 | + | 0.958178i | \(0.592384\pi\) | |||||||
\(128\) | − | 168036.i | − | 0.906520i | ||||||
\(129\) | −29406.9 | + | 43313.6i | −0.155588 | + | 0.229166i | ||||
\(130\) | − | 12143.0i | − | 0.0630183i | ||||||
\(131\) | − | 319871.i | − | 1.62853i | −0.580491 | − | 0.814267i | \(-0.697139\pi\) | ||
0.580491 | − | 0.814267i | \(-0.302861\pi\) | |||||||
\(132\) | 122480. | + | 83155.5i | 0.611831 | + | 0.415390i | ||||
\(133\) | 352702. | 1.72893 | ||||||||
\(134\) | −58053.1 | −0.279295 | ||||||||
\(135\) | −30547.7 | + | 137551.i | −0.144259 | + | 0.649573i | ||||
\(136\) | 158974.i | 0.737020i | ||||||||
\(137\) | 202011. | 0.919546 | 0.459773 | − | 0.888037i | \(-0.347931\pi\) | ||||
0.459773 | + | 0.888037i | \(0.347931\pi\) | |||||||
\(138\) | 32554.9 | − | 52926.5i | 0.145519 | − | 0.236579i | ||||
\(139\) | −197570. | −0.867330 | −0.433665 | − | 0.901074i | \(-0.642780\pi\) | ||||
−0.433665 | + | 0.901074i | \(0.642780\pi\) | |||||||
\(140\) | 134280.i | 0.579017i | ||||||||
\(141\) | 131753. | − | 194059.i | 0.558100 | − | 0.822029i | ||||
\(142\) | −83007.5 | −0.345459 | ||||||||
\(143\) | 66816.8 | 0.273241 | ||||||||
\(144\) | 71110.8 | + | 179125.i | 0.285778 | + | 0.719865i | ||||
\(145\) | − | 90940.3i | − | 0.359200i | ||||||
\(146\) | 112817.i | 0.438017i | ||||||||
\(147\) | −24037.8 | − | 16320.0i | −0.0917489 | − | 0.0622910i | ||||
\(148\) | − | 293454.i | − | 1.10125i | ||||||
\(149\) | 206334. | 0.761385 | 0.380692 | − | 0.924702i | \(-0.375686\pi\) | ||||
0.380692 | + | 0.924702i | \(0.375686\pi\) | |||||||
\(150\) | 23957.2 | − | 35286.7i | 0.0869377 | − | 0.128051i | ||||
\(151\) | −72590.0 | −0.259080 | −0.129540 | − | 0.991574i | \(-0.541350\pi\) | ||||
−0.129540 | + | 0.991574i | \(0.541350\pi\) | |||||||
\(152\) | 278941. | 0.979272 | ||||||||
\(153\) | −147437. | − | 371388.i | −0.509186 | − | 1.28262i | ||||
\(154\) | 61765.7 | 0.209868 | ||||||||
\(155\) | 9083.46 | 0.0303684 | ||||||||
\(156\) | 79133.1 | + | 53725.8i | 0.260343 | + | 0.176755i | ||||
\(157\) | − | 344412.i | − | 1.11514i | −0.830131 | − | 0.557569i | \(-0.811734\pi\) | ||
0.830131 | − | 0.557569i | \(-0.188266\pi\) | |||||||
\(158\) | 68141.9 | 0.217156 | ||||||||
\(159\) | −102022. | − | 69266.0i | −0.320039 | − | 0.217284i | ||||
\(160\) | 161427.i | 0.498514i | ||||||||
\(161\) | 13950.5 | + | 309814.i | 0.0424156 | + | 0.941968i | ||||
\(162\) | 63634.3 | + | 67515.2i | 0.190504 | + | 0.202122i | ||||
\(163\) | 52358.0 | 0.154353 | 0.0771764 | − | 0.997017i | \(-0.475410\pi\) | ||||
0.0771764 | + | 0.997017i | \(0.475410\pi\) | |||||||
\(164\) | − | 515777.i | − | 1.49745i | ||||||
\(165\) | −154273. | − | 104741.i | −0.441144 | − | 0.299506i | ||||
\(166\) | 168323.i | 0.474103i | ||||||||
\(167\) | 464676.i | 1.28931i | 0.764472 | + | 0.644657i | \(0.223000\pi\) | ||||
−0.764472 | + | 0.644657i | \(0.777000\pi\) | |||||||
\(168\) | 152417. | + | 103480.i | 0.416639 | + | 0.282869i | ||||
\(169\) | −328123. | −0.883732 | ||||||||
\(170\) | − | 96103.0i | − | 0.255044i | ||||||
\(171\) | −651649. | + | 258697.i | −1.70421 | + | 0.676552i | ||||
\(172\) | − | 99179.4i | − | 0.255623i | ||||||
\(173\) | 7055.13i | 0.0179221i | 0.999960 | + | 0.00896107i | \(0.00285243\pi\) | ||||
−0.999960 | + | 0.00896107i | \(0.997148\pi\) | |||||||
\(174\) | −49541.0 | − | 33634.9i | −0.124049 | − | 0.0842203i | ||||
\(175\) | 212871.i | 0.525439i | ||||||||
\(176\) | −255051. | −0.620648 | ||||||||
\(177\) | 99417.3 | − | 146432.i | 0.238522 | − | 0.351321i | ||||
\(178\) | − | 1759.91i | − | 0.00416333i | ||||||
\(179\) | − | 610113.i | − | 1.42324i | −0.702565 | − | 0.711619i | \(-0.747962\pi\) | ||
0.702565 | − | 0.711619i | \(-0.252038\pi\) | |||||||
\(180\) | −98490.7 | − | 248095.i | −0.226576 | − | 0.570737i | ||||
\(181\) | − | 58467.9i | − | 0.132654i | −0.997798 | − | 0.0663271i | \(-0.978872\pi\) | ||
0.997798 | − | 0.0663271i | \(-0.0211281\pi\) | |||||||
\(182\) | 39906.1 | 0.0893019 | ||||||||
\(183\) | −226784. | + | 334032.i | −0.500593 | + | 0.737327i | ||||
\(184\) | 11033.0 | + | 245022.i | 0.0240243 | + | 0.533533i | ||||
\(185\) | 369626.i | 0.794024i | ||||||||
\(186\) | 3359.58 | − | 4948.34i | 0.00712036 | − | 0.0104876i | ||||
\(187\) | 528807. | 1.10584 | ||||||||
\(188\) | 444357.i | 0.916932i | ||||||||
\(189\) | −452040. | − | 100391.i | −0.920496 | − | 0.204427i | ||||
\(190\) | −168625. | −0.338874 | ||||||||
\(191\) | −326167. | −0.646929 | −0.323464 | − | 0.946240i | \(-0.604848\pi\) | ||||
−0.323464 | + | 0.946240i | \(0.604848\pi\) | |||||||
\(192\) | −239376. | − | 162519.i | −0.468626 | − | 0.318164i | ||||
\(193\) | 196437. | 0.379603 | 0.189802 | − | 0.981822i | \(-0.439216\pi\) | ||||
0.189802 | + | 0.981822i | \(0.439216\pi\) | |||||||
\(194\) | −41976.4 | −0.0800757 | ||||||||
\(195\) | −99674.0 | − | 67671.6i | −0.187713 | − | 0.127444i | ||||
\(196\) | 55041.6 | 0.102341 | ||||||||
\(197\) | − | 66505.9i | − | 0.122094i | −0.998135 | − | 0.0610471i | \(-0.980556\pi\) | ||
0.998135 | − | 0.0610471i | \(-0.0194440\pi\) | |||||||
\(198\) | −114118. | + | 45303.4i | −0.206867 | + | 0.0821237i | ||||
\(199\) | 826467.i | 1.47942i | 0.672923 | + | 0.739712i | \(0.265038\pi\) | ||||
−0.672923 | + | 0.739712i | \(0.734962\pi\) | |||||||
\(200\) | 168353.i | 0.297609i | ||||||||
\(201\) | −323524. | + | 476521.i | −0.564829 | + | 0.831940i | ||||
\(202\) | 124599. | 0.214850 | ||||||||
\(203\) | 298862. | 0.509015 | ||||||||
\(204\) | 626282. | + | 425201.i | 1.05365 | + | 0.715351i | ||||
\(205\) | 649659.i | 1.07969i | ||||||||
\(206\) | 124454. | 0.204335 | ||||||||
\(207\) | −253015. | − | 562177.i | −0.410412 | − | 0.911900i | ||||
\(208\) | −164785. | −0.264095 | ||||||||
\(209\) | − | 927862.i | − | 1.46932i | ||||||
\(210\) | −92139.0 | − | 62555.9i | −0.144177 | − | 0.0978859i | ||||
\(211\) | 69431.8 | 0.107362 | 0.0536812 | − | 0.998558i | \(-0.482905\pi\) | ||||
0.0536812 | + | 0.998558i | \(0.482905\pi\) | |||||||
\(212\) | 233611. | 0.356988 | ||||||||
\(213\) | −462593. | + | 681356.i | −0.698635 | + | 1.02902i | ||||
\(214\) | − | 300652.i | − | 0.448776i | ||||||
\(215\) | 124924.i | 0.184310i | ||||||||
\(216\) | −357504. | − | 79395.8i | −0.521371 | − | 0.115788i | ||||
\(217\) | 29851.5i | 0.0430344i | ||||||||
\(218\) | −193927. | −0.276374 | ||||||||
\(219\) | 926041. | + | 628717.i | 1.30473 | + | 0.885818i | ||||
\(220\) | 353254. | 0.492074 | ||||||||
\(221\) | 341656. | 0.470553 | ||||||||
\(222\) | 201359. | + | 136709.i | 0.274214 | + | 0.186172i | ||||
\(223\) | −1.36980e6 | −1.84456 | −0.922282 | − | 0.386517i | \(-0.873678\pi\) | ||||
−0.922282 | + | 0.386517i | \(0.873678\pi\) | |||||||
\(224\) | −530507. | −0.706433 | ||||||||
\(225\) | −156135. | − | 393299.i | −0.205610 | − | 0.517925i | ||||
\(226\) | − | 81915.3i | − | 0.106683i | ||||||
\(227\) | −999585. | −1.28752 | −0.643762 | − | 0.765226i | \(-0.722627\pi\) | ||||
−0.643762 | + | 0.765226i | \(0.722627\pi\) | |||||||
\(228\) | 746072. | − | 1.09889e6i | 0.950481 | − | 1.39997i | ||||
\(229\) | − | 675351.i | − | 0.851022i | −0.904953 | − | 0.425511i | \(-0.860094\pi\) | ||
0.904953 | − | 0.425511i | \(-0.139906\pi\) | |||||||
\(230\) | −6669.69 | − | 148121.i | −0.00831354 | − | 0.184628i | ||||
\(231\) | 344214. | − | 506996.i | 0.424423 | − | 0.625136i | ||||
\(232\) | 236361. | 0.288307 | ||||||||
\(233\) | − | 537073.i | − | 0.648102i | −0.946040 | − | 0.324051i | \(-0.894955\pi\) | ||
0.946040 | − | 0.324051i | \(-0.105045\pi\) | |||||||
\(234\) | −73730.1 | + | 29270.0i | −0.0880249 | + | 0.0349449i | ||||
\(235\) | − | 559700.i | − | 0.661129i | ||||||
\(236\) | 335301.i | 0.391881i | ||||||||
\(237\) | 379748. | − | 559334.i | 0.439162 | − | 0.646845i | ||||
\(238\) | 315828. | 0.361417 | ||||||||
\(239\) | 1.04144e6i | 1.17934i | 0.807644 | + | 0.589670i | \(0.200742\pi\) | ||||
−0.807644 | + | 0.589670i | \(0.799258\pi\) | |||||||
\(240\) | 380473. | + | 258314.i | 0.426379 | + | 0.289481i | ||||
\(241\) | 993176.i | 1.10150i | 0.834671 | + | 0.550749i | \(0.185658\pi\) | ||||
−0.834671 | + | 0.550749i | \(0.814342\pi\) | |||||||
\(242\) | 90553.4i | 0.0993954i | ||||||||
\(243\) | 908818. | − | 146078.i | 0.987327 | − | 0.158697i | ||||
\(244\) | − | 764866.i | − | 0.822452i | ||||||
\(245\) | −69329.0 | −0.0737904 | ||||||||
\(246\) | 353911. | + | 240281.i | 0.372869 | + | 0.253152i | ||||
\(247\) | − | 599481.i | − | 0.625220i | ||||||
\(248\) | 23608.6i | 0.0243748i | ||||||||
\(249\) | 1.38166e6 | + | 938048.i | 1.41222 | + | 0.958797i | ||||
\(250\) | − | 284409.i | − | 0.287802i | ||||||
\(251\) | −648746. | −0.649966 | −0.324983 | − | 0.945720i | \(-0.605359\pi\) | ||||
−0.324983 | + | 0.945720i | \(0.605359\pi\) | |||||||
\(252\) | 815327. | − | 323675.i | 0.808780 | − | 0.321076i | ||||
\(253\) | 815036. | − | 36700.0i | 0.800526 | − | 0.0360466i | ||||
\(254\) | 163455.i | 0.158970i | ||||||||
\(255\) | −788848. | − | 535573.i | −0.759702 | − | 0.515784i | ||||
\(256\) | 329925. | 0.314641 | ||||||||
\(257\) | − | 950768.i | − | 0.897929i | −0.893550 | − | 0.448964i | \(-0.851793\pi\) | ||
0.893550 | − | 0.448964i | \(-0.148207\pi\) | |||||||
\(258\) | 68054.0 | + | 46203.9i | 0.0636509 | + | 0.0432145i | ||||
\(259\) | −1.21472e6 | −1.12520 | ||||||||
\(260\) | 228233. | 0.209385 | ||||||||
\(261\) | −552175. | + | 219207.i | −0.501736 | + | 0.199183i | ||||
\(262\) | −502579. | −0.452326 | ||||||||
\(263\) | 1.18331e6 | 1.05490 | 0.527450 | − | 0.849586i | \(-0.323148\pi\) | ||||
0.527450 | + | 0.849586i | \(0.323148\pi\) | |||||||
\(264\) | 272229. | − | 400967.i | 0.240394 | − | 0.354078i | ||||
\(265\) | −294250. | −0.257396 | ||||||||
\(266\) | − | 554162.i | − | 0.480212i | ||||||
\(267\) | −14446.0 | − | 9807.82i | −0.0124014 | − | 0.00841966i | ||||
\(268\) | − | 1.09114e6i | − | 0.927988i | ||||||
\(269\) | 1.60834e6i | 1.35518i | 0.735441 | + | 0.677588i | \(0.236975\pi\) | ||||
−0.735441 | + | 0.677588i | \(0.763025\pi\) | |||||||
\(270\) | 216118. | + | 47996.3i | 0.180419 | + | 0.0400681i | ||||
\(271\) | 453181. | 0.374842 | 0.187421 | − | 0.982280i | \(-0.439987\pi\) | ||||
0.187421 | + | 0.982280i | \(0.439987\pi\) | |||||||
\(272\) | −1.30416e6 | −1.06883 | ||||||||
\(273\) | 222393. | − | 327564.i | 0.180599 | − | 0.266005i | ||||
\(274\) | − | 317398.i | − | 0.255404i | ||||||
\(275\) | 560006. | 0.446541 | ||||||||
\(276\) | 994781. | + | 611886.i | 0.786058 | + | 0.483502i | ||||
\(277\) | 530675. | 0.415555 | 0.207778 | − | 0.978176i | \(-0.433377\pi\) | ||||
0.207778 | + | 0.978176i | \(0.433377\pi\) | |||||||
\(278\) | 310421.i | 0.240901i | ||||||||
\(279\) | −21895.2 | − | 55153.3i | −0.0168399 | − | 0.0424190i | ||||
\(280\) | 439596. | 0.335088 | ||||||||
\(281\) | 141938. | 0.107234 | 0.0536171 | − | 0.998562i | \(-0.482925\pi\) | ||||
0.0536171 | + | 0.998562i | \(0.482925\pi\) | |||||||
\(282\) | −304905. | − | 207009.i | −0.228319 | − | 0.155012i | ||||
\(283\) | 1.59400e6i | 1.18310i | 0.806268 | + | 0.591550i | \(0.201484\pi\) | ||||
−0.806268 | + | 0.591550i | \(0.798516\pi\) | |||||||
\(284\) | − | 1.56017e6i | − | 1.14783i | ||||||
\(285\) | −939733. | + | 1.38414e6i | −0.685318 | + | 1.00941i | ||||
\(286\) | − | 104982.i | − | 0.0758927i | ||||||
\(287\) | −2.13501e6 | −1.53001 | ||||||||
\(288\) | 980160. | − | 389112.i | 0.696331 | − | 0.276435i | ||||
\(289\) | 1.28411e6 | 0.904392 | ||||||||
\(290\) | −142885. | −0.0997679 | ||||||||
\(291\) | −233930. | + | 344557.i | −0.161940 | + | 0.238522i | ||||
\(292\) | −2.12045e6 | −1.45536 | ||||||||
\(293\) | 831087. | 0.565558 | 0.282779 | − | 0.959185i | \(-0.408744\pi\) | ||||
0.282779 | + | 0.959185i | \(0.408744\pi\) | |||||||
\(294\) | −25641.8 | + | 37767.9i | −0.0173013 | + | 0.0254833i | ||||
\(295\) | − | 422336.i | − | 0.282555i | ||||||
\(296\) | −960687. | −0.637313 | ||||||||
\(297\) | −264100. | + | 1.18919e6i | −0.173731 | + | 0.782278i | ||||
\(298\) | − | 324190.i | − | 0.211475i | ||||||
\(299\) | 526585. | − | 23711.4i | 0.340636 | − | 0.0153384i | ||||
\(300\) | 663232. | + | 450288.i | 0.425463 | + | 0.288860i | ||||
\(301\) | −410544. | −0.261182 | ||||||||
\(302\) | 114053.i | 0.0719596i | ||||||||
\(303\) | 694376. | − | 1.02275e6i | 0.434498 | − | 0.639975i | ||||
\(304\) | 2.28832e6i | 1.42015i | ||||||||
\(305\) | 963405.i | 0.593006i | ||||||||
\(306\) | −583521. | + | 231651.i | −0.356249 | + | 0.141427i | ||||
\(307\) | 1.41110e6 | 0.854499 | 0.427250 | − | 0.904134i | \(-0.359483\pi\) | ||||
0.427250 | + | 0.904134i | \(0.359483\pi\) | |||||||
\(308\) | 1.16092e6i | 0.697308i | ||||||||
\(309\) | 693572. | − | 1.02157e6i | 0.413233 | − | 0.608654i | ||||
\(310\) | − | 14271.9i | − | 0.00843483i | ||||||
\(311\) | − | 885448.i | − | 0.519113i | −0.965728 | − | 0.259557i | \(-0.916424\pi\) | ||
0.965728 | − | 0.259557i | \(-0.0835764\pi\) | |||||||
\(312\) | 175884. | − | 259060.i | 0.102291 | − | 0.150666i | ||||
\(313\) | − | 1.01876e6i | − | 0.587776i | −0.955840 | − | 0.293888i | \(-0.905051\pi\) | ||
0.955840 | − | 0.293888i | \(-0.0949492\pi\) | |||||||
\(314\) | −541137. | −0.309730 | ||||||||
\(315\) | −1.02696e6 | + | 407693.i | −0.583148 | + | 0.231503i | ||||
\(316\) | 1.28076e6i | 0.721524i | ||||||||
\(317\) | 75162.2i | 0.0420099i | 0.999779 | + | 0.0210049i | \(0.00668657\pi\) | ||||
−0.999779 | + | 0.0210049i | \(0.993313\pi\) | |||||||
\(318\) | −108830. | + | 160297.i | −0.0603506 | + | 0.0888909i | ||||
\(319\) | − | 786224.i | − | 0.432583i | ||||||
\(320\) | −690400. | −0.376900 | ||||||||
\(321\) | −2.46786e6 | − | 1.67551e6i | −1.33678 | − | 0.907577i | ||||
\(322\) | 486777. | − | 21918.9i | 0.261632 | − | 0.0117809i | ||||
\(323\) | − | 4.74446e6i | − | 2.53035i | ||||||
\(324\) | −1.26898e6 | + | 1.19604e6i | −0.671573 | + | 0.632970i | ||||
\(325\) | 361813. | 0.190010 | ||||||||
\(326\) | − | 82264.6i | − | 0.0428715i | ||||||
\(327\) | −1.08074e6 | + | 1.59183e6i | −0.558922 | + | 0.823240i | ||||
\(328\) | −1.68851e6 | −0.866602 | ||||||||
\(329\) | 1.83937e6 | 0.936872 | ||||||||
\(330\) | −164568. | + | 242393.i | −0.0831877 | + | 0.122528i | ||||
\(331\) | −574036. | −0.287985 | −0.143992 | − | 0.989579i | \(-0.545994\pi\) | ||||
−0.143992 | + | 0.989579i | \(0.545994\pi\) | |||||||
\(332\) | −3.16371e6 | −1.57526 | ||||||||
\(333\) | 2.24431e6 | − | 890966.i | 1.10910 | − | 0.440302i | ||||
\(334\) | 730095. | 0.358107 | ||||||||
\(335\) | 1.37437e6i | 0.669100i | ||||||||
\(336\) | −848912. | + | 1.25037e6i | −0.410218 | + | 0.604212i | ||||
\(337\) | 751869.i | 0.360635i | 0.983608 | + | 0.180317i | \(0.0577125\pi\) | ||||
−0.983608 | + | 0.180317i | \(0.942288\pi\) | |||||||
\(338\) | 515545.i | 0.245457i | ||||||||
\(339\) | −672391. | − | 456506.i | −0.317777 | − | 0.215748i | ||||
\(340\) | 1.80630e6 | 0.847410 | ||||||||
\(341\) | 78531.0 | 0.0365725 | ||||||||
\(342\) | 406463. | + | 1.02387e6i | 0.187912 | + | 0.473345i | ||||
\(343\) | − | 2.28236e6i | − | 1.04749i | ||||||
\(344\) | −324686. | −0.147934 | ||||||||
\(345\) | −1.25300e6 | − | 770716.i | −0.566765 | − | 0.348615i | ||||
\(346\) | 11085.0 | 0.00497788 | ||||||||
\(347\) | 4.25948e6i | 1.89903i | 0.313715 | + | 0.949517i | \(0.398426\pi\) | ||||
−0.313715 | + | 0.949517i | \(0.601574\pi\) | |||||||
\(348\) | 632184. | − | 931149.i | 0.279831 | − | 0.412165i | ||||
\(349\) | 918884. | 0.403829 | 0.201914 | − | 0.979403i | \(-0.435284\pi\) | ||||
0.201914 | + | 0.979403i | \(0.435284\pi\) | |||||||
\(350\) | 334462. | 0.145941 | ||||||||
\(351\) | −170632. | + | 768323.i | −0.0739252 | + | 0.332871i | ||||
\(352\) | 1.39562e6i | 0.600358i | ||||||||
\(353\) | 1.12183e6i | 0.479170i | 0.970875 | + | 0.239585i | \(0.0770114\pi\) | ||||
−0.970875 | + | 0.239585i | \(0.922989\pi\) | |||||||
\(354\) | −230073. | − | 156204.i | −0.0975795 | − | 0.0662496i | ||||
\(355\) | 1.96515e6i | 0.827607i | ||||||||
\(356\) | 33078.4 | 0.0138331 | ||||||||
\(357\) | 1.76008e6 | − | 2.59243e6i | 0.730907 | − | 1.07656i | ||||
\(358\) | −958605. | −0.395305 | ||||||||
\(359\) | −2.22040e6 | −0.909273 | −0.454636 | − | 0.890677i | \(-0.650231\pi\) | ||||
−0.454636 | + | 0.890677i | \(0.650231\pi\) | |||||||
\(360\) | −812194. | + | 322432.i | −0.330296 | + | 0.131124i | ||||
\(361\) | −5.84868e6 | −2.36206 | ||||||||
\(362\) | −91864.4 | −0.0368447 | ||||||||
\(363\) | 743295. | + | 504645.i | 0.296070 | + | 0.201011i | ||||
\(364\) | 750055.i | 0.296715i | ||||||||
\(365\) | 2.67086e6 | 1.04935 | ||||||||
\(366\) | 524828. | + | 356322.i | 0.204793 | + | 0.139040i | ||||
\(367\) | 4.35641e6i | 1.68835i | 0.536064 | + | 0.844177i | \(0.319910\pi\) | ||||
−0.536064 | + | 0.844177i | \(0.680090\pi\) | |||||||
\(368\) | −2.01006e6 | + | 90510.6i | −0.773732 | + | 0.0348401i | ||||
\(369\) | 3.94462e6 | − | 1.56597e6i | 1.50813 | − | 0.598711i | ||||
\(370\) | 580754. | 0.220540 | ||||||||
\(371\) | − | 967010.i | − | 0.364751i | ||||||
\(372\) | 93006.6 | + | 63144.9i | 0.0348463 | + | 0.0236582i | ||||
\(373\) | − | 4.60335e6i | − | 1.71318i | −0.516001 | − | 0.856588i | \(-0.672580\pi\) | ||
0.516001 | − | 0.856588i | \(-0.327420\pi\) | |||||||
\(374\) | − | 830858.i | − | 0.307148i | ||||||
\(375\) | −2.33453e6 | − | 1.58498e6i | −0.857278 | − | 0.582032i | ||||
\(376\) | 1.45470e6 | 0.530646 | ||||||||
\(377\) | − | 507970.i | − | 0.184071i | ||||||
\(378\) | −157733. | + | 710241.i | −0.0567797 | + | 0.255668i | ||||
\(379\) | − | 496941.i | − | 0.177708i | −0.996045 | − | 0.0888541i | \(-0.971680\pi\) | ||
0.996045 | − | 0.0888541i | \(-0.0283205\pi\) | |||||||
\(380\) | − | 3.16940e6i | − | 1.12595i | ||||||
\(381\) | 1.34170e6 | + | 910922.i | 0.473526 | + | 0.321491i | ||||
\(382\) | 512471.i | 0.179685i | ||||||||
\(383\) | 3.80492e6 | 1.32540 | 0.662702 | − | 0.748883i | \(-0.269410\pi\) | ||||
0.662702 | + | 0.748883i | \(0.269410\pi\) | |||||||
\(384\) | −1.47134e6 | + | 2.16715e6i | −0.509196 | + | 0.749999i | ||||
\(385\) | − | 1.46226e6i | − | 0.502775i | ||||||
\(386\) | − | 308640.i | − | 0.105435i | ||||||
\(387\) | 758517. | − | 301122.i | 0.257447 | − | 0.102204i | ||||
\(388\) | − | 788967.i | − | 0.266060i | ||||||
\(389\) | 1.45736e6 | 0.488306 | 0.244153 | − | 0.969737i | \(-0.421490\pi\) | ||||
0.244153 | + | 0.969737i | \(0.421490\pi\) | |||||||
\(390\) | −106325. | + | 156607.i | −0.0353976 | + | 0.0521374i | ||||
\(391\) | 4.16754e6 | − | 187659.i | 1.37860 | − | 0.0620766i | ||||
\(392\) | − | 180191.i | − | 0.0592268i | ||||||
\(393\) | −2.80082e6 | + | 4.12535e6i | −0.914755 | + | 1.34735i | ||||
\(394\) | −104494. | −0.0339117 | ||||||||
\(395\) | − | 1.61321e6i | − | 0.520234i | ||||||
\(396\) | −851501. | − | 2.14490e6i | −0.272865 | − | 0.687336i | ||||
\(397\) | −4.37853e6 | −1.39429 | −0.697144 | − | 0.716931i | \(-0.745546\pi\) | ||||
−0.697144 | + | 0.716931i | \(0.745546\pi\) | |||||||
\(398\) | 1.29854e6 | 0.410911 | ||||||||
\(399\) | −4.54877e6 | − | 3.08829e6i | −1.43041 | − | 0.971150i | ||||
\(400\) | −1.38110e6 | −0.431595 | ||||||||
\(401\) | 3.59017e6 | 1.11495 | 0.557473 | − | 0.830195i | \(-0.311771\pi\) | ||||
0.557473 | + | 0.830195i | \(0.311771\pi\) | |||||||
\(402\) | 748706. | + | 508319.i | 0.231071 | + | 0.156881i | ||||
\(403\) | 50737.9 | 0.0155622 | ||||||||
\(404\) | 2.34189e6i | 0.713861i | ||||||||
\(405\) | 1.59838e6 | − | 1.50650e6i | 0.484219 | − | 0.456385i | ||||
\(406\) | − | 469570.i | − | 0.141379i | ||||||
\(407\) | 3.19560e6i | 0.956240i | ||||||||
\(408\) | 1.39199e6 | − | 2.05028e6i | 0.413987 | − | 0.609764i | ||||
\(409\) | 6.32230e6 | 1.86882 | 0.934409 | − | 0.356202i | \(-0.115929\pi\) | ||||
0.934409 | + | 0.356202i | \(0.115929\pi\) | |||||||
\(410\) | 1.02074e6 | 0.299885 | ||||||||
\(411\) | −2.60532e6 | − | 1.76883e6i | −0.760775 | − | 0.516513i | ||||
\(412\) | 2.33918e6i | 0.678924i | ||||||||
\(413\) | 1.38795e6 | 0.400403 | ||||||||
\(414\) | −883288. | + | 397535.i | −0.253280 | + | 0.113992i | ||||
\(415\) | 3.98493e6 | 1.13580 | ||||||||
\(416\) | 901693.i | 0.255461i | ||||||||
\(417\) | 2.54805e6 | + | 1.72995e6i | 0.717575 | + | 0.487183i | ||||
\(418\) | −1.45785e6 | −0.408105 | ||||||||
\(419\) | 5.31646e6 | 1.47941 | 0.739704 | − | 0.672933i | \(-0.234966\pi\) | ||||
0.739704 | + | 0.672933i | \(0.234966\pi\) | |||||||
\(420\) | 1.17577e6 | − | 1.73180e6i | 0.325237 | − | 0.479043i | ||||
\(421\) | − | 5.94869e6i | − | 1.63575i | −0.575399 | − | 0.817873i | \(-0.695153\pi\) | ||
0.575399 | − | 0.817873i | \(-0.304847\pi\) | |||||||
\(422\) | − | 109091.i | − | 0.0298199i | ||||||
\(423\) | −3.39841e6 | + | 1.34913e6i | −0.923474 | + | 0.366609i | ||||
\(424\) | − | 764778.i | − | 0.206595i | ||||||
\(425\) | 2.86349e6 | 0.768996 | ||||||||
\(426\) | 1.07054e6 | + | 726823.i | 0.285811 | + | 0.194046i | ||||
\(427\) | −3.16609e6 | −0.840337 | ||||||||
\(428\) | 5.65091e6 | 1.49111 | ||||||||
\(429\) | −861731. | − | 585055.i | −0.226063 | − | 0.153481i | ||||
\(430\) | 196279. | 0.0511922 | ||||||||
\(431\) | −738404. | −0.191470 | −0.0957351 | − | 0.995407i | \(-0.530520\pi\) | ||||
−0.0957351 | + | 0.995407i | \(0.530520\pi\) | |||||||
\(432\) | 651331. | − | 2.93282e6i | 0.167916 | − | 0.756095i | ||||
\(433\) | 546533.i | 0.140087i | 0.997544 | + | 0.0700433i | \(0.0223137\pi\) | ||||
−0.997544 | + | 0.0700433i | \(0.977686\pi\) | |||||||
\(434\) | 46902.4 | 0.0119528 | ||||||||
\(435\) | −796283. | + | 1.17285e6i | −0.201764 | + | 0.297180i | ||||
\(436\) | − | 3.64496e6i | − | 0.918284i | ||||||
\(437\) | −329273. | − | 7.31251e6i | −0.0824806 | − | 1.83173i | ||||
\(438\) | 987835. | − | 1.45499e6i | 0.246036 | − | 0.362388i | ||||
\(439\) | −4.25006e6 | −1.05253 | −0.526264 | − | 0.850321i | \(-0.676408\pi\) | ||||
−0.526264 | + | 0.850321i | \(0.676408\pi\) | |||||||
\(440\) | − | 1.15646e6i | − | 0.284773i | ||||||
\(441\) | 167114. | + | 420954.i | 0.0409182 | + | 0.103071i | ||||
\(442\) | − | 536807.i | − | 0.130696i | ||||||
\(443\) | 4.67645e6i | 1.13216i | 0.824351 | + | 0.566079i | \(0.191540\pi\) | ||||
−0.824351 | + | 0.566079i | \(0.808460\pi\) | |||||||
\(444\) | −2.56951e6 | + | 3.78465e6i | −0.618576 | + | 0.911104i | ||||
\(445\) | −41664.7 | −0.00997398 | ||||||||
\(446\) | 2.15221e6i | 0.512328i | ||||||||
\(447\) | −2.66107e6 | − | 1.80668e6i | −0.629923 | − | 0.427673i | ||||
\(448\) | − | 2.26890e6i | − | 0.534097i | ||||||
\(449\) | 2.01589e6i | 0.471900i | 0.971765 | + | 0.235950i | \(0.0758202\pi\) | ||||
−0.971765 | + | 0.235950i | \(0.924180\pi\) | |||||||
\(450\) | −617948. | + | 245318.i | −0.143854 | + | 0.0571083i | ||||
\(451\) | 5.61662e6i | 1.30027i | ||||||||
\(452\) | 1.53964e6 | 0.354465 | ||||||||
\(453\) | 936188. | + | 635606.i | 0.214347 | + | 0.145527i | ||||
\(454\) | 1.57054e6i | 0.357610i | ||||||||
\(455\) | − | 944750.i | − | 0.213938i | ||||||
\(456\) | −3.59748e6 | − | 2.44244e6i | −0.810189 | − | 0.550061i | ||||
\(457\) | 8.34776e6i | 1.86973i | 0.355001 | + | 0.934866i | \(0.384481\pi\) | ||||
−0.355001 | + | 0.934866i | \(0.615519\pi\) | |||||||
\(458\) | −1.06111e6 | −0.236371 | ||||||||
\(459\) | −1.35043e6 | + | 6.08073e6i | −0.299185 | + | 1.34717i | ||||
\(460\) | 2.78401e6 | − | 125360.i | 0.613445 | − | 0.0276226i | ||||
\(461\) | − | 6.19226e6i | − | 1.35705i | −0.734576 | − | 0.678526i | \(-0.762619\pi\) | ||
0.734576 | − | 0.678526i | \(-0.237381\pi\) | |||||||
\(462\) | −796588. | − | 540827.i | −0.173632 | − | 0.117884i | ||||
\(463\) | 6.00846e6 | 1.30260 | 0.651300 | − | 0.758821i | \(-0.274224\pi\) | ||||
0.651300 | + | 0.758821i | \(0.274224\pi\) | |||||||
\(464\) | 1.93901e6i | 0.418105i | ||||||||
\(465\) | −117149. | − | 79535.7i | −0.0251249 | − | 0.0170581i | ||||
\(466\) | −843845. | −0.180010 | ||||||||
\(467\) | −5.16831e6 | −1.09662 | −0.548311 | − | 0.836275i | \(-0.684729\pi\) | ||||
−0.548311 | + | 0.836275i | \(0.684729\pi\) | |||||||
\(468\) | −550145. | − | 1.38580e6i | −0.116108 | − | 0.292472i | ||||
\(469\) | −4.51666e6 | −0.948168 | ||||||||
\(470\) | −879397. | −0.183629 | ||||||||
\(471\) | −3.01570e6 | + | 4.44185e6i | −0.626378 | + | 0.922596i | ||||
\(472\) | 1.09768e6 | 0.226789 | ||||||||
\(473\) | 1.08003e6i | 0.221964i | ||||||||
\(474\) | −878821. | − | 596657.i | −0.179661 | − | 0.121977i | ||||
\(475\) | − | 5.02438e6i | − | 1.02176i | ||||||
\(476\) | 5.93615e6i | 1.20085i | ||||||||
\(477\) | 709275. | + | 1.78664e6i | 0.142731 | + | 0.359535i | ||||
\(478\) | 1.63630e6 | 0.327562 | ||||||||
\(479\) | −7.21936e6 | −1.43767 | −0.718836 | − | 0.695180i | \(-0.755325\pi\) | ||||
−0.718836 | + | 0.695180i | \(0.755325\pi\) | |||||||
\(480\) | 1.41347e6 | − | 2.08192e6i | 0.280017 | − | 0.412439i | ||||
\(481\) | 2.06464e6i | 0.406895i | ||||||||
\(482\) | 1.56047e6 | 0.305941 | ||||||||
\(483\) | 2.53284e6 | − | 4.11780e6i | 0.494016 | − | 0.803151i | ||||
\(484\) | −1.70200e6 | −0.330252 | ||||||||
\(485\) | 993762.i | 0.191835i | ||||||||
\(486\) | −229516. | − | 1.42793e6i | −0.0440781 | − | 0.274230i | ||||
\(487\) | −1.69573e6 | −0.323991 | −0.161996 | − | 0.986791i | \(-0.551793\pi\) | ||||
−0.161996 | + | 0.986791i | \(0.551793\pi\) | |||||||
\(488\) | −2.50396e6 | −0.475968 | ||||||||
\(489\) | −675258. | − | 458452.i | −0.127702 | − | 0.0867006i | ||||
\(490\) | 108929.i | 0.0204953i | ||||||||
\(491\) | 1.97941e6i | 0.370537i | 0.982688 | + | 0.185269i | \(0.0593155\pi\) | ||||
−0.982688 | + | 0.185269i | \(0.940684\pi\) | |||||||
\(492\) | −4.51619e6 | + | 6.65193e6i | −0.841124 | + | 1.23890i | ||||
\(493\) | − | 4.02022e6i | − | 0.744960i | ||||||
\(494\) | −941899. | −0.173655 | ||||||||
\(495\) | 1.07253e6 | + | 2.70166e6i | 0.196741 | + | 0.495585i | ||||
\(496\) | −193675. | −0.0353484 | ||||||||
\(497\) | −6.45817e6 | −1.17279 | ||||||||
\(498\) | 1.47385e6 | − | 2.17085e6i | 0.266306 | − | 0.392244i | ||||
\(499\) | −5.04988e6 | −0.907882 | −0.453941 | − | 0.891032i | \(-0.649982\pi\) | ||||
−0.453941 | + | 0.891032i | \(0.649982\pi\) | |||||||
\(500\) | 5.34561e6 | 0.956252 | ||||||||
\(501\) | 4.06875e6 | − | 5.99289e6i | 0.724213 | − | 1.06670i | ||||
\(502\) | 1.01930e6i | 0.180528i | ||||||||
\(503\) | −1.44925e6 | −0.255402 | −0.127701 | − | 0.991813i | \(-0.540760\pi\) | ||||
−0.127701 | + | 0.991813i | \(0.540760\pi\) | |||||||
\(504\) | −1.05962e6 | − | 2.66916e6i | −0.185813 | − | 0.468056i | ||||
\(505\) | − | 2.94979e6i | − | 0.514710i | ||||||
\(506\) | −57662.7 | − | 1.28058e6i | −0.0100120 | − | 0.222346i | ||||
\(507\) | 4.23178e6 | + | 2.87308e6i | 0.731145 | + | 0.496396i | ||||
\(508\) | −3.07223e6 | −0.528195 | ||||||||
\(509\) | − | 1.18111e6i | − | 0.202068i | −0.994883 | − | 0.101034i | \(-0.967785\pi\) | ||
0.994883 | − | 0.101034i | \(-0.0322150\pi\) | |||||||
\(510\) | −841488. | + | 1.23943e6i | −0.143259 | + | 0.211007i | ||||
\(511\) | 8.77739e6i | 1.48701i | ||||||||
\(512\) | − | 5.89553e6i | − | 0.993912i | ||||||
\(513\) | 1.06694e7 | + | 2.36951e6i | 1.78998 | + | 0.397525i | ||||
\(514\) | −1.49384e6 | −0.249400 | ||||||||
\(515\) | − | 2.94637e6i | − | 0.489519i | ||||||
\(516\) | −868425. | + | 1.27911e6i | −0.143585 | + | 0.211487i | ||||
\(517\) | − | 4.83889e6i | − | 0.796195i | ||||||
\(518\) | 1.90856e6i | 0.312523i | ||||||||
\(519\) | 61775.4 | − | 90989.5i | 0.0100669 | − | 0.0148277i | ||||
\(520\) | − | 747174.i | − | 0.121175i | ||||||
\(521\) | −8.05639e6 | −1.30031 | −0.650154 | − | 0.759802i | \(-0.725296\pi\) | ||||
−0.650154 | + | 0.759802i | \(0.725296\pi\) | |||||||
\(522\) | 344416. | + | 867573.i | 0.0553232 | + | 0.139357i | ||||
\(523\) | 2.65776e6i | 0.424875i | 0.977175 | + | 0.212437i | \(0.0681401\pi\) | ||||
−0.977175 | + | 0.212437i | \(0.931860\pi\) | |||||||
\(524\) | − | 9.44623e6i | − | 1.50290i | ||||||
\(525\) | 1.86392e6 | − | 2.74538e6i | 0.295141 | − | 0.434715i | ||||
\(526\) | − | 1.85922e6i | − | 0.292998i | ||||||
\(527\) | 401555. | 0.0629822 | ||||||||
\(528\) | 3.28937e6 | + | 2.23325e6i | 0.513486 | + | 0.348621i | ||||
\(529\) | 6.41030e6 | − | 578467.i | 0.995953 | − | 0.0898752i | ||||
\(530\) | 462323.i | 0.0714918i | ||||||||
\(531\) | −2.56435e6 | + | 1.01802e6i | −0.394677 | + | 0.156682i | ||||
\(532\) | 1.04158e7 | 1.59556 | ||||||||
\(533\) | 3.62883e6i | 0.553285i | ||||||||
\(534\) | −15410.0 | + | 22697.5i | −0.00233856 | + | 0.00344448i | ||||
\(535\) | −7.11774e6 | −1.07512 | ||||||||
\(536\) | −3.57209e6 | −0.537044 | ||||||||
\(537\) | −5.34221e6 | + | 7.86858e6i | −0.799439 | + | 1.17750i | ||||
\(538\) | 2.52700e6 | 0.376401 | ||||||||
\(539\) | −599384. | −0.0888655 | ||||||||
\(540\) | −902115. | + | 4.06205e6i | −0.133130 | + | 0.599461i | ||||
\(541\) | −2.23163e6 | −0.327816 | −0.163908 | − | 0.986476i | \(-0.552410\pi\) | ||||
−0.163908 | + | 0.986476i | \(0.552410\pi\) | |||||||
\(542\) | − | 712035.i | − | 0.104113i | ||||||
\(543\) | −511951. | + | 754056.i | −0.0745125 | + | 0.109750i | ||||
\(544\) | 7.13626e6i | 1.03389i | ||||||||
\(545\) | 4.59110e6i | 0.662103i | ||||||||
\(546\) | −514666. | − | 349422.i | −0.0738829 | − | 0.0501613i | ||||
\(547\) | 7.42757e6 | 1.06140 | 0.530699 | − | 0.847560i | \(-0.321929\pi\) | ||||
0.530699 | + | 0.847560i | \(0.321929\pi\) | |||||||
\(548\) | 5.96565e6 | 0.848607 | ||||||||
\(549\) | 5.84964e6 | − | 2.32224e6i | 0.828320 | − | 0.328833i | ||||
\(550\) | − | 879877.i | − | 0.124027i | ||||||
\(551\) | −7.05401e6 | −0.989822 | ||||||||
\(552\) | 2.00315e6 | − | 3.25664e6i | 0.279811 | − | 0.454906i | ||||
\(553\) | 5.30159e6 | 0.737213 | ||||||||
\(554\) | − | 833792.i | − | 0.115421i | ||||||
\(555\) | 3.23649e6 | − | 4.76704e6i | 0.446007 | − | 0.656926i | ||||
\(556\) | −5.83452e6 | −0.800420 | ||||||||
\(557\) | −1.07965e7 | −1.47450 | −0.737252 | − | 0.675618i | \(-0.763877\pi\) | ||||
−0.737252 | + | 0.675618i | \(0.763877\pi\) | |||||||
\(558\) | −86656.4 | + | 34401.6i | −0.0117819 | + | 0.00467728i | ||||
\(559\) | 697793.i | 0.0944490i | ||||||||
\(560\) | 3.60627e6i | 0.485947i | ||||||||
\(561\) | −6.81999e6 | − | 4.63029e6i | −0.914906 | − | 0.621157i | ||||
\(562\) | − | 223012.i | − | 0.0297843i | ||||||
\(563\) | 995065. | 0.132306 | 0.0661531 | − | 0.997809i | \(-0.478927\pi\) | ||||
0.0661531 | + | 0.997809i | \(0.478927\pi\) | |||||||
\(564\) | 3.89084e6 | − | 5.73084e6i | 0.515045 | − | 0.758613i | ||||
\(565\) | −1.93929e6 | −0.255577 | ||||||||
\(566\) | 2.50448e6 | 0.328606 | ||||||||
\(567\) | 4.95089e6 | + | 5.25284e6i | 0.646734 | + | 0.686177i | ||||
\(568\) | −5.10757e6 | −0.664268 | ||||||||
\(569\) | −1.08672e7 | −1.40714 | −0.703568 | − | 0.710628i | \(-0.748411\pi\) | ||||
−0.703568 | + | 0.710628i | \(0.748411\pi\) | |||||||
\(570\) | 2.17475e6 | + | 1.47650e6i | 0.280364 | + | 0.190347i | ||||
\(571\) | 3.65300e6i | 0.468878i | 0.972131 | + | 0.234439i | \(0.0753253\pi\) | ||||
−0.972131 | + | 0.234439i | \(0.924675\pi\) | |||||||
\(572\) | 1.97319e6 | 0.252162 | ||||||||
\(573\) | 4.20655e6 | + | 2.85595e6i | 0.535229 | + | 0.363383i | ||||
\(574\) | 3.35451e6i | 0.424961i | ||||||||
\(575\) | 4.41342e6 | − | 198731.i | 0.556680 | − | 0.0250666i | ||||
\(576\) | 1.66417e6 | + | 4.19199e6i | 0.208998 | + | 0.526459i | ||||
\(577\) | −6.62252e6 | −0.828102 | −0.414051 | − | 0.910254i | \(-0.635886\pi\) | ||||
−0.414051 | + | 0.910254i | \(0.635886\pi\) | |||||||
\(578\) | − | 2.01758e6i | − | 0.251195i | ||||||
\(579\) | −2.53343e6 | − | 1.72002e6i | −0.314060 | − | 0.213225i | ||||
\(580\) | − | 2.68559e6i | − | 0.331490i | ||||||
\(581\) | 1.30959e7i | 1.60951i | ||||||||
\(582\) | 541366. | + | 367549.i | 0.0662496 | + | 0.0449788i | ||||
\(583\) | −2.54394e6 | −0.309981 | ||||||||
\(584\) | 6.94176e6i | 0.842244i | ||||||||
\(585\) | 692948. | + | 1.74551e6i | 0.0837165 | + | 0.210879i | ||||
\(586\) | − | 1.30580e6i | − | 0.157084i | ||||||
\(587\) | − | 2.94644e6i | − | 0.352941i | −0.984306 | − | 0.176471i | \(-0.943532\pi\) | ||
0.984306 | − | 0.176471i | \(-0.0564681\pi\) | |||||||
\(588\) | −709868. | − | 481950.i | −0.0846709 | − | 0.0574856i | ||||
\(589\) | − | 704581.i | − | 0.0836840i | ||||||
\(590\) | −663571. | −0.0784797 | ||||||||
\(591\) | −582333. | + | 857722.i | −0.0685808 | + | 0.101013i | ||||
\(592\) | − | 7.88109e6i | − | 0.924234i | ||||||
\(593\) | − | 6.52249e6i | − | 0.761687i | −0.924639 | − | 0.380844i | \(-0.875634\pi\) | ||
0.924639 | − | 0.380844i | \(-0.124366\pi\) | |||||||
\(594\) | 1.86845e6 | + | 414952.i | 0.217278 | + | 0.0482538i | ||||
\(595\) | − | 7.47702e6i | − | 0.865837i | ||||||
\(596\) | 6.09331e6 | 0.702648 | ||||||||
\(597\) | 7.23663e6 | − | 1.06589e7i | 0.830999 | − | 1.22398i | ||||
\(598\) | −37255.2 | − | 827366.i | −0.00426024 | − | 0.0946117i | ||||
\(599\) | − | 1.00980e7i | − | 1.14993i | −0.818179 | − | 0.574964i | \(-0.805016\pi\) | ||
0.818179 | − | 0.574964i | \(-0.194984\pi\) | |||||||
\(600\) | 1.47412e6 | − | 2.17124e6i | 0.167168 | − | 0.246224i | ||||
\(601\) | 1.44237e7 | 1.62889 | 0.814445 | − | 0.580240i | \(-0.197041\pi\) | ||||
0.814445 | + | 0.580240i | \(0.197041\pi\) | |||||||
\(602\) | 645043.i | 0.0725433i | ||||||||
\(603\) | 8.34494e6 | − | 3.31284e6i | 0.934609 | − | 0.371029i | ||||
\(604\) | −2.14368e6 | −0.239094 | ||||||||
\(605\) | 2.14379e6 | 0.238119 | ||||||||
\(606\) | −1.60694e6 | − | 1.09100e6i | −0.177753 | − | 0.120682i | ||||
\(607\) | 1.46050e6 | 0.160890 | 0.0804451 | − | 0.996759i | \(-0.474366\pi\) | ||||
0.0804451 | + | 0.996759i | \(0.474366\pi\) | |||||||
\(608\) | 1.25215e7 | 1.37372 | ||||||||
\(609\) | −3.85440e6 | − | 2.61687e6i | −0.421128 | − | 0.285916i | ||||
\(610\) | 1.51369e6 | 0.164708 | ||||||||
\(611\) | − | 3.12635e6i | − | 0.338793i | ||||||
\(612\) | −4.35400e6 | − | 1.09676e7i | −0.469905 | − | 1.18367i | ||||
\(613\) | 1.39592e6i | 0.150040i | 0.997182 | + | 0.0750202i | \(0.0239021\pi\) | ||||
−0.997182 | + | 0.0750202i | \(0.976098\pi\) | |||||||
\(614\) | − | 2.21711e6i | − | 0.237337i | ||||||
\(615\) | 5.68848e6 | − | 8.37860e6i | 0.606469 | − | 0.893272i | ||||
\(616\) | 3.80053e6 | 0.403545 | ||||||||
\(617\) | 1.33277e7 | 1.40943 | 0.704714 | − | 0.709492i | \(-0.251075\pi\) | ||||
0.704714 | + | 0.709492i | \(0.251075\pi\) | |||||||
\(618\) | −1.60508e6 | − | 1.08974e6i | −0.169054 | − | 0.114776i | ||||
\(619\) | − | 1.40755e7i | − | 1.47651i | −0.674519 | − | 0.738257i | \(-0.735649\pi\) | ||
0.674519 | − | 0.738257i | \(-0.264351\pi\) | |||||||
\(620\) | 268247. | 0.0280256 | ||||||||
\(621\) | −1.65937e6 | + | 9.46578e6i | −0.172669 | + | 0.984980i | ||||
\(622\) | −1.39121e6 | −0.144184 | ||||||||
\(623\) | − | 136925.i | − | 0.0141339i | ||||||
\(624\) | 2.12523e6 | + | 1.44288e6i | 0.218496 | + | 0.148343i | ||||
\(625\) | −1.29135e6 | −0.132234 | ||||||||
\(626\) | −1.60067e6 | −0.163255 | ||||||||
\(627\) | −8.12446e6 | + | 1.19666e7i | −0.825326 | + | 1.21563i | ||||
\(628\) | − | 1.01709e7i | − | 1.02911i | ||||||
\(629\) | 1.63402e7i | 1.64676i | ||||||||
\(630\) | 640564. | + | 1.61356e6i | 0.0643000 | + | 0.161970i | ||||
\(631\) | 9.75276e6i | 0.975112i | 0.873092 | + | 0.487556i | \(0.162111\pi\) | ||||
−0.873092 | + | 0.487556i | \(0.837889\pi\) | |||||||
\(632\) | 4.19286e6 | 0.417559 | ||||||||
\(633\) | −895457. | − | 607952.i | −0.0888250 | − | 0.0603060i | ||||
\(634\) | 118094. | 0.0116682 | ||||||||
\(635\) | 3.86970e6 | 0.380840 | ||||||||
\(636\) | −3.01286e6 | − | 2.04552e6i | −0.295349 | − | 0.200522i | ||||
\(637\) | −387255. | −0.0378136 | ||||||||
\(638\) | −1.23531e6 | −0.120150 | ||||||||
\(639\) | 1.19321e7 | − | 4.73689e6i | 1.15601 | − | 0.458924i | ||||
\(640\) | 6.25042e6i | 0.603197i | ||||||||
\(641\) | −1.64249e7 | −1.57891 | −0.789454 | − | 0.613810i | \(-0.789636\pi\) | ||||
−0.789454 | + | 0.613810i | \(0.789636\pi\) | |||||||
\(642\) | −2.63254e6 | + | 3.87749e6i | −0.252080 | + | 0.371290i | ||||
\(643\) | − | 6.63786e6i | − | 0.633141i | −0.948569 | − | 0.316571i | \(-0.897469\pi\) | ||
0.948569 | − | 0.316571i | \(-0.102531\pi\) | |||||||
\(644\) | 411978. | + | 9.14923e6i | 0.0391434 | + | 0.869300i | ||||
\(645\) | 1.09385e6 | − | 1.61113e6i | 0.103528 | − | 0.152487i | ||||
\(646\) | −7.45446e6 | −0.702805 | ||||||||
\(647\) | − | 1.25537e7i | − | 1.17899i | −0.807772 | − | 0.589495i | \(-0.799327\pi\) | ||
0.807772 | − | 0.589495i | \(-0.200673\pi\) | |||||||
\(648\) | 3.91551e6 | + | 4.15430e6i | 0.366311 | + | 0.388652i | ||||
\(649\) | − | 3.65130e6i | − | 0.340280i | ||||||
\(650\) | − | 568478.i | − | 0.0527753i | ||||||
\(651\) | 261382. | − | 384992.i | 0.0241726 | − | 0.0356040i | ||||
\(652\) | 1.54620e6 | 0.142445 | ||||||||
\(653\) | − | 9.03858e6i | − | 0.829502i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) | ||
0.909935 | − | 0.414751i | \(-0.136131\pi\) | |||||||
\(654\) | 2.50107e6 | + | 1.69805e6i | 0.228655 | + | 0.155241i | ||||
\(655\) | 1.18982e7i | 1.08362i | ||||||||
\(656\) | − | 1.38519e7i | − | 1.25675i | ||||||
\(657\) | −6.43797e6 | − | 1.62170e7i | −0.581883 | − | 1.46574i | ||||
\(658\) | − | 2.89001e6i | − | 0.260216i | ||||||
\(659\) | −658736. | −0.0590878 | −0.0295439 | − | 0.999563i | \(-0.509405\pi\) | ||||
−0.0295439 | + | 0.999563i | \(0.509405\pi\) | |||||||
\(660\) | −4.55589e6 | − | 3.09313e6i | −0.407112 | − | 0.276400i | ||||
\(661\) | 2.00503e7i | 1.78491i | 0.451132 | + | 0.892457i | \(0.351020\pi\) | ||||
−0.451132 | + | 0.892457i | \(0.648980\pi\) | |||||||
\(662\) | 901921.i | 0.0799878i | ||||||||
\(663\) | −4.40631e6 | − | 2.99158e6i | −0.389306 | − | 0.264312i | ||||
\(664\) | 1.03571e7i | 0.911632i | ||||||||
\(665\) | −1.31194e7 | −1.15043 | ||||||||
\(666\) | −1.39988e6 | − | 3.52624e6i | −0.122294 | − | 0.308054i | ||||
\(667\) | −279009. | − | 6.19625e6i | −0.0242831 | − | 0.539280i | ||||
\(668\) | 1.37225e7i | 1.18985i | ||||||||
\(669\) | 1.76662e7 | + | 1.19941e7i | 1.52608 | + | 1.03610i | ||||
\(670\) | 2.15940e6 | 0.185843 | ||||||||
\(671\) | 8.32911e6i | 0.714155i | ||||||||
\(672\) | 6.84191e6 | + | 4.64518e6i | 0.584459 | + | 0.396807i | ||||
\(673\) | −1.79212e7 | −1.52521 | −0.762604 | − | 0.646866i | \(-0.776079\pi\) | ||||
−0.762604 | + | 0.646866i | \(0.776079\pi\) | |||||||
\(674\) | 1.18133e6 | 0.100166 | ||||||||
\(675\) | −1.43010e6 | + | 6.43948e6i | −0.120811 | + | 0.543991i | ||||
\(676\) | −9.68993e6 | −0.815556 | ||||||||
\(677\) | −1.91825e7 | −1.60854 | −0.804271 | − | 0.594262i | \(-0.797444\pi\) | ||||
−0.804271 | + | 0.594262i | \(0.797444\pi\) | |||||||
\(678\) | −717259. | + | 1.05646e6i | −0.0599241 | + | 0.0882626i | ||||
\(679\) | −3.26585e6 | −0.271846 | ||||||||
\(680\) | − | 5.91335e6i | − | 0.490412i | ||||||
\(681\) | 1.28916e7 | + | 8.75247e6i | 1.06522 | + | 0.723207i | ||||
\(682\) | − | 123387.i | − | 0.0101580i | ||||||
\(683\) | − | 5.30024e6i | − | 0.434754i | −0.976088 | − | 0.217377i | \(-0.930250\pi\) | ||
0.976088 | − | 0.217377i | \(-0.0697502\pi\) | |||||||
\(684\) | −1.92441e7 | + | 7.63967e6i | −1.57274 | + | 0.624359i | ||||
\(685\) | −7.51418e6 | −0.611865 | ||||||||
\(686\) | −3.58603e6 | −0.290940 | ||||||||
\(687\) | −5.91344e6 | + | 8.70995e6i | −0.478023 | + | 0.704083i | ||||
\(688\) | − | 2.66360e6i | − | 0.214535i | ||||||
\(689\) | −1.64361e6 | −0.131902 | ||||||||
\(690\) | −1.21094e6 | + | 1.96870e6i | −0.0968280 | + | 0.157419i | ||||
\(691\) | 7.36822e6 | 0.587040 | 0.293520 | − | 0.955953i | \(-0.405173\pi\) | ||||
0.293520 | + | 0.955953i | \(0.405173\pi\) | |||||||
\(692\) | 208348.i | 0.0165395i | ||||||||
\(693\) | −8.87862e6 | + | 3.52471e6i | −0.702283 | + | 0.278798i | ||||
\(694\) | 6.69246e6 | 0.527457 | ||||||||
\(695\) | 7.34900e6 | 0.577120 | ||||||||
\(696\) | −3.04833e6 | − | 2.06960e6i | −0.238527 | − | 0.161943i | ||||
\(697\) | 2.87196e7i | 2.23922i | ||||||||
\(698\) | − | 1.44374e6i | − | 0.112163i | ||||||
\(699\) | −4.70267e6 | + | 6.92659e6i | −0.364042 | + | 0.536199i | ||||
\(700\) | 6.28638e6i | 0.484904i | ||||||||
\(701\) | −6.12013e6 | −0.470398 | −0.235199 | − | 0.971947i | \(-0.575574\pi\) | ||||
−0.235199 | + | 0.971947i | \(0.575574\pi\) | |||||||
\(702\) | 1.20718e6 | + | 268096.i | 0.0924550 | + | 0.0205327i | ||||
\(703\) | 2.86710e7 | 2.18803 | ||||||||
\(704\) | −5.96885e6 | −0.453899 | ||||||||
\(705\) | −4.90079e6 | + | 7.21841e6i | −0.371359 | + | 0.546977i | ||||
\(706\) | 1.76261e6 | 0.133090 | ||||||||
\(707\) | 9.69404e6 | 0.729384 | ||||||||
\(708\) | 2.93593e6 | − | 4.32435e6i | 0.220121 | − | 0.324218i | ||||
\(709\) | − | 1.54351e7i | − | 1.15317i | −0.817036 | − | 0.576587i | \(-0.804384\pi\) | ||
0.817036 | − | 0.576587i | \(-0.195616\pi\) | |||||||
\(710\) | 3.08762e6 | 0.229868 | ||||||||
\(711\) | −9.79517e6 | + | 3.88857e6i | −0.726671 | + | 0.288480i | ||||
\(712\) | − | 108290.i | − | 0.00800548i | ||||||
\(713\) | 618905. | − | 27868.5i | 0.0455932 | − | 0.00205300i | ||||
\(714\) | −4.07321e6 | − | 2.76543e6i | −0.299014 | − | 0.203010i | ||||
\(715\) | −2.48538e6 | −0.181814 | ||||||||
\(716\) | − | 1.80175e7i | − | 1.31344i | ||||||
\(717\) | 9.11894e6 | − | 1.34314e7i | 0.662440 | − | 0.975713i | ||||
\(718\) | 3.48867e6i | 0.252551i | ||||||||
\(719\) | 1.94171e7i | 1.40076i | 0.713772 | + | 0.700378i | \(0.246985\pi\) | ||||
−0.713772 | + | 0.700378i | \(0.753015\pi\) | |||||||
\(720\) | −2.64510e6 | − | 6.66292e6i | −0.190156 | − | 0.478997i | ||||
\(721\) | 9.68282e6 | 0.693688 | ||||||||
\(722\) | 9.18941e6i | 0.656061i | ||||||||
\(723\) | 8.69635e6 | − | 1.28089e7i | 0.618716 | − | 0.911311i | ||||
\(724\) | − | 1.72664e6i | − | 0.122421i | ||||||
\(725\) | − | 4.25741e6i | − | 0.300816i | ||||||
\(726\) | 792895. | − | 1.16786e6i | 0.0558308 | − | 0.0822336i | ||||
\(727\) | − | 1.77689e7i | − | 1.24688i | −0.781872 | − | 0.623439i | \(-0.785735\pi\) | ||
0.781872 | − | 0.623439i | \(-0.214265\pi\) | |||||||
\(728\) | 2.45548e6 | 0.171715 | ||||||||
\(729\) | −1.30000e7 | − | 6.07375e6i | −0.905994 | − | 0.423290i | ||||
\(730\) | − | 4.19643e6i | − | 0.291456i | ||||||
\(731\) | 5.52254e6i | 0.382248i | ||||||||
\(732\) | −6.69724e6 | + | 9.86441e6i | −0.461975 | + | 0.680446i | ||||
\(733\) | − | 5.47786e6i | − | 0.376575i | −0.982114 | − | 0.188287i | \(-0.939706\pi\) | ||
0.982114 | − | 0.188287i | \(-0.0602936\pi\) | |||||||
\(734\) | 6.84476e6 | 0.468941 | ||||||||
\(735\) | 894131. | + | 607052.i | 0.0610496 | + | 0.0414484i | ||||
\(736\) | 495267. | + | 1.09989e7i | 0.0337011 | + | 0.748437i | ||||
\(737\) | 1.18821e7i | 0.805794i | ||||||||
\(738\) | −2.46044e6 | − | 6.19776e6i | −0.166292 | − | 0.418884i | ||||
\(739\) | −5.18027e6 | −0.348933 | −0.174466 | − | 0.984663i | \(-0.555820\pi\) | ||||
−0.174466 | + | 0.984663i | \(0.555820\pi\) | |||||||
\(740\) | 1.09156e7i | 0.732769i | ||||||||
\(741\) | −5.24911e6 | + | 7.73146e6i | −0.351189 | + | 0.517268i | ||||
\(742\) | −1.51936e6 | −0.101310 | ||||||||
\(743\) | 1.14016e7 | 0.757697 | 0.378848 | − | 0.925459i | \(-0.376320\pi\) | ||||
0.378848 | + | 0.925459i | \(0.376320\pi\) | |||||||
\(744\) | 206719. | − | 304478.i | 0.0136914 | − | 0.0201662i | ||||
\(745\) | −7.67497e6 | −0.506625 | ||||||||
\(746\) | −7.23275e6 | −0.475835 | ||||||||
\(747\) | −9.60548e6 | − | 2.41959e7i | −0.629821 | − | 1.58650i | ||||
\(748\) | 1.56164e7 | 1.02053 | ||||||||
\(749\) | − | 2.33914e7i | − | 1.52353i | ||||||
\(750\) | −2.49031e6 | + | 3.66800e6i | −0.161659 | + | 0.238109i | ||||
\(751\) | − | 2.39349e7i | − | 1.54857i | −0.632836 | − | 0.774286i | \(-0.718109\pi\) | ||
0.632836 | − | 0.774286i | \(-0.281891\pi\) | |||||||
\(752\) | 1.19338e7i | 0.769545i | ||||||||
\(753\) | 8.36683e6 | + | 5.68049e6i | 0.537741 | + | 0.365089i | ||||
\(754\) | −798119. | −0.0511257 | ||||||||
\(755\) | 2.70013e6 | 0.172392 | ||||||||
\(756\) | −1.33493e7 | − | 2.96467e6i | −0.849484 | − | 0.188656i | ||||
\(757\) | 1.62210e7i | 1.02882i | 0.857546 | + | 0.514408i | \(0.171988\pi\) | ||||
−0.857546 | + | 0.514408i | \(0.828012\pi\) | |||||||
\(758\) | −780791. | −0.0493585 | ||||||||
\(759\) | −1.08328e7 | − | 6.66322e6i | −0.682553 | − | 0.419836i | ||||
\(760\) | −1.03757e7 | −0.651606 | ||||||||
\(761\) | − | 1.90740e7i | − | 1.19393i | −0.802265 | − | 0.596967i | \(-0.796372\pi\) | ||
0.802265 | − | 0.596967i | \(-0.203628\pi\) | |||||||
\(762\) | 1.43123e6 | − | 2.10807e6i | 0.0892941 | − | 0.131522i | ||||
\(763\) | −1.50880e7 | −0.938252 | ||||||||
\(764\) | −9.63215e6 | −0.597021 | ||||||||
\(765\) | 5.48419e6 | + | 1.38145e7i | 0.338812 | + | 0.853456i | ||||
\(766\) | − | 5.97825e6i | − | 0.368131i | ||||||
\(767\) | − | 2.35906e6i | − | 0.144794i | ||||||
\(768\) | −4.25501e6 | − | 2.88885e6i | −0.260314 | − | 0.176735i | ||||
\(769\) | − | 1.31501e7i | − | 0.801885i | −0.916103 | − | 0.400943i | \(-0.868683\pi\) | ||
0.916103 | − | 0.400943i | \(-0.131317\pi\) | |||||||
\(770\) | −2.29749e6 | −0.139646 | ||||||||
\(771\) | −8.32502e6 | + | 1.22620e7i | −0.504370 | + | 0.742891i | ||||
\(772\) | 5.80105e6 | 0.350318 | ||||||||
\(773\) | 4.24089e6 | 0.255275 | 0.127638 | − | 0.991821i | \(-0.459261\pi\) | ||||
0.127638 | + | 0.991821i | \(0.459261\pi\) | |||||||
\(774\) | −473121. | − | 1.19178e6i | −0.0283870 | − | 0.0715060i | ||||
\(775\) | 425246. | 0.0254323 | ||||||||
\(776\) | −2.58286e6 | −0.153974 | ||||||||
\(777\) | 1.56662e7 | + | 1.06362e7i | 0.930917 | + | 0.632027i | ||||
\(778\) | − | 2.28979e6i | − | 0.135627i | ||||||
\(779\) | 5.03924e7 | 2.97523 | ||||||||
\(780\) | −2.94351e6 | − | 1.99843e6i | −0.173232 | − | 0.117612i | ||||
\(781\) | 1.69897e7i | 0.996684i | ||||||||
\(782\) | −294848. | − | 6.54801e6i | −0.0172418 | − | 0.382906i | ||||
\(783\) | 9.04076e6 | + | 2.00780e6i | 0.526987 | + | 0.117035i | ||||
\(784\) | 1.47822e6 | 0.0858911 | ||||||||
\(785\) | 1.28111e7i | 0.742011i | ||||||||
\(786\) | 6.48172e6 | + | 4.40063e6i | 0.374226 | + | 0.254073i | ||||
\(787\) | − | 2.27264e6i | − | 0.130796i | −0.997859 | − | 0.0653980i | \(-0.979168\pi\) | ||
0.997859 | − | 0.0653980i | \(-0.0208317\pi\) | |||||||
\(788\) | − | 1.96401e6i | − | 0.112675i | ||||||
\(789\) | −1.52611e7 | − | 1.03612e7i | −0.872758 | − | 0.592541i | ||||
\(790\) | −2.53467e6 | −0.144495 | ||||||||
\(791\) | − | 6.37319e6i | − | 0.362173i | ||||||
\(792\) | −7.02182e6 | + | 2.78758e6i | −0.397774 | + | 0.157912i | ||||
\(793\) | 5.38134e6i | 0.303884i | ||||||||
\(794\) | 6.87952e6i | 0.387264i | ||||||||
\(795\) | 3.79492e6 | + | 2.57648e6i | 0.212954 | + | 0.144580i | ||||
\(796\) | 2.44067e7i | 1.36529i | ||||||||
\(797\) | 7.90668e6 | 0.440908 | 0.220454 | − | 0.975397i | \(-0.429246\pi\) | ||||
0.220454 | + | 0.975397i | \(0.429246\pi\) | |||||||
\(798\) | −4.85230e6 | + | 7.14699e6i | −0.269737 | + | 0.397298i | ||||
\(799\) | − | 2.47428e7i | − | 1.37114i | ||||||
\(800\) | 7.55728e6i | 0.417485i | ||||||||
\(801\) | 100431. | + | 252981.i | 0.00553077 | + | 0.0139318i | ||||
\(802\) | − | 5.64084e6i | − | 0.309676i | ||||||
\(803\) | 2.30909e7 | 1.26372 | ||||||||
\(804\) | −9.55411e6 | + | 1.40723e7i | −0.521255 | + | 0.767760i | ||||
\(805\) | −518916. | − | 1.15241e7i | −0.0282233 | − | 0.626785i | ||||
\(806\) | − | 79719.1i | − | 0.00432240i | ||||||
\(807\) | 1.40827e7 | − | 2.07426e7i | 0.761209 | − | 1.12119i | ||||
\(808\) | 7.66672e6 | 0.413125 | ||||||||
\(809\) | − | 8.57150e6i | − | 0.460453i | −0.973137 | − | 0.230227i | \(-0.926053\pi\) | ||
0.973137 | − | 0.230227i | \(-0.0739467\pi\) | |||||||
\(810\) | −2.36700e6 | − | 2.51136e6i | −0.126761 | − | 0.134492i | ||||
\(811\) | −1.32411e7 | −0.706921 | −0.353461 | − | 0.935449i | \(-0.614995\pi\) | ||||
−0.353461 | + | 0.935449i | \(0.614995\pi\) | |||||||
\(812\) | 8.82580e6 | 0.469747 | ||||||||
\(813\) | −5.84464e6 | − | 3.96810e6i | −0.310121 | − | 0.210551i | ||||
\(814\) | 5.02091e6 | 0.265596 | ||||||||
\(815\) | −1.94756e6 | −0.102706 | ||||||||
\(816\) | 1.68196e7 | + | 1.14194e7i | 0.884283 | + | 0.600366i | ||||
\(817\) | 9.69002e6 | 0.507890 | ||||||||
\(818\) | − | 9.93355e6i | − | 0.519064i | ||||||
\(819\) | −5.73637e6 | + | 2.27727e6i | −0.298832 | + | 0.118633i | ||||
\(820\) | 1.91853e7i | 0.996401i | ||||||||
\(821\) | 2.36284e7i | 1.22342i | 0.791080 | + | 0.611712i | \(0.209519\pi\) | ||||
−0.791080 | + | 0.611712i | \(0.790481\pi\) | |||||||
\(822\) | −2.77917e6 | + | 4.09346e6i | −0.143462 | + | 0.211305i | ||||
\(823\) | −2.96088e7 | −1.52378 | −0.761888 | − | 0.647709i | \(-0.775727\pi\) | ||||
−0.761888 | + | 0.647709i | \(0.775727\pi\) | |||||||
\(824\) | 7.65785e6 | 0.392906 | ||||||||
\(825\) | −7.22236e6 | − | 4.90347e6i | −0.369440 | − | 0.250824i | ||||
\(826\) | − | 2.18073e6i | − | 0.111212i | ||||||
\(827\) | 1.58750e7 | 0.807144 | 0.403572 | − | 0.914948i | \(-0.367768\pi\) | ||||
0.403572 | + | 0.914948i | \(0.367768\pi\) | |||||||
\(828\) | −7.47187e6 | − | 1.66019e7i | −0.378751 | − | 0.841551i | ||||
\(829\) | 1.94808e7 | 0.984509 | 0.492254 | − | 0.870451i | \(-0.336173\pi\) | ||||
0.492254 | + | 0.870451i | \(0.336173\pi\) | |||||||
\(830\) | − | 6.26110e6i | − | 0.315468i | ||||||
\(831\) | −6.84407e6 | − | 4.64664e6i | −0.343805 | − | 0.233419i | ||||
\(832\) | −3.85640e6 | −0.193141 | ||||||||
\(833\) | −3.06484e6 | −0.153037 | ||||||||
\(834\) | 2.71808e6 | − | 4.00347e6i | 0.135315 | − | 0.199307i | ||||
\(835\) | − | 1.72845e7i | − | 0.857908i | ||||||
\(836\) | − | 2.74010e7i | − | 1.35597i | ||||||
\(837\) | −200547. | + | 903024.i | −0.00989469 | + | 0.0445539i | ||||
\(838\) | − | 8.35319e6i | − | 0.410906i | ||||||
\(839\) | 3.57449e7 | 1.75311 | 0.876556 | − | 0.481299i | \(-0.159835\pi\) | ||||
0.876556 | + | 0.481299i | \(0.159835\pi\) | |||||||
\(840\) | −5.66944e6 | − | 3.84915e6i | −0.277231 | − | 0.188220i | ||||
\(841\) | 1.45339e7 | 0.708587 | ||||||||
\(842\) | −9.34653e6 | −0.454329 | ||||||||
\(843\) | −1.83057e6 | − | 1.24283e6i | −0.0887190 | − | 0.0602339i | ||||
\(844\) | 2.05042e6 | 0.0990800 | ||||||||
\(845\) | 1.22052e7 | 0.588034 | ||||||||
\(846\) | 2.11974e6 | + | 5.33955e6i | 0.101826 | + | 0.256495i | ||||
\(847\) | 7.04525e6i | 0.337433i | ||||||||
\(848\) | 6.27393e6 | 0.299606 | ||||||||
\(849\) | 1.39572e7 | − | 2.05577e7i | 0.664553 | − | 0.978824i | ||||
\(850\) | − | 4.49910e6i | − | 0.213589i | ||||||
\(851\) | 1.13403e6 | + | 2.51846e7i | 0.0536786 | + | 1.19210i | ||||
\(852\) | −1.36610e7 | + | 2.01214e7i | −0.644738 | + | 0.949639i | ||||
\(853\) | −2.25616e7 | −1.06169 | −0.530845 | − | 0.847469i | \(-0.678125\pi\) | ||||
−0.530845 | + | 0.847469i | \(0.678125\pi\) | |||||||
\(854\) | 4.97453e6i | 0.233404i | ||||||||
\(855\) | 2.42393e7 | − | 9.62273e6i | 1.13398 | − | 0.450177i | ||||
\(856\) | − | 1.84995e7i | − | 0.862932i | ||||||
\(857\) | − | 1.17266e7i | − | 0.545408i | −0.962098 | − | 0.272704i | \(-0.912082\pi\) | ||
0.962098 | − | 0.272704i | \(-0.0879180\pi\) | |||||||
\(858\) | −919234. | + | 1.35395e6i | −0.0426292 | + | 0.0627889i | ||||
\(859\) | 1.30115e7 | 0.601649 | 0.300824 | − | 0.953680i | \(-0.402738\pi\) | ||||
0.300824 | + | 0.953680i | \(0.402738\pi\) | |||||||
\(860\) | 3.68917e6i | 0.170091i | ||||||||
\(861\) | 2.75350e7 | + | 1.86944e7i | 1.26584 | + | 0.859414i | ||||
\(862\) | 1.16017e6i | 0.0531809i | ||||||||
\(863\) | 1.62440e7i | 0.742447i | 0.928544 | + | 0.371223i | \(0.121062\pi\) | ||||
−0.928544 | + | 0.371223i | \(0.878938\pi\) | |||||||
\(864\) | −1.60482e7 | − | 3.56403e6i | −0.731376 | − | 0.162427i | ||||
\(865\) | − | 262429.i | − | 0.0119254i | ||||||
\(866\) | 858708. | 0.0389091 | ||||||||
\(867\) | −1.65610e7 | − | 1.12438e7i | −0.748238 | − | 0.508001i | ||||
\(868\) | 881554.i | 0.0397145i | ||||||||
\(869\) | − | 1.39470e7i | − | 0.626516i | ||||||
\(870\) | 1.84277e6 | + | 1.25111e6i | 0.0825418 | + | 0.0560401i | ||||
\(871\) | 7.67688e6i | 0.342878i | ||||||||
\(872\) | −1.19326e7 | −0.531428 | ||||||||
\(873\) | 6.03396e6 | − | 2.39541e6i | 0.267958 | − | 0.106376i | ||||
\(874\) | −1.14894e7 | + | 517350.i | −0.508765 | + | 0.0229090i | ||||
\(875\) | − | 2.21276e7i | − | 0.977046i | ||||||
\(876\) | 2.73472e7 | + | 1.85669e7i | 1.20407 | + | 0.817482i | ||||
\(877\) | −5.44428e6 | −0.239024 | −0.119512 | − | 0.992833i | \(-0.538133\pi\) | ||||
−0.119512 | + | 0.992833i | \(0.538133\pi\) | |||||||
\(878\) | 6.67767e6i | 0.292340i | ||||||||
\(879\) | −1.07185e7 | − | 7.27708e6i | −0.467908 | − | 0.317677i | ||||
\(880\) | 9.48712e6 | 0.412979 | ||||||||
\(881\) | −2.73818e7 | −1.18856 | −0.594281 | − | 0.804258i | \(-0.702563\pi\) | ||||
−0.594281 | + | 0.804258i | \(0.702563\pi\) | |||||||
\(882\) | 661400. | − | 262568.i | 0.0286281 | − | 0.0113650i | ||||
\(883\) | 2.58182e7 | 1.11436 | 0.557179 | − | 0.830392i | \(-0.311884\pi\) | ||||
0.557179 | + | 0.830392i | \(0.311884\pi\) | |||||||
\(884\) | 1.00896e7 | 0.434252 | ||||||||
\(885\) | −3.69802e6 | + | 5.44684e6i | −0.158712 | + | 0.233769i | ||||
\(886\) | 7.34761e6 | 0.314457 | ||||||||
\(887\) | 4.06230e7i | 1.73366i | 0.498606 | + | 0.866828i | \(0.333845\pi\) | ||||
−0.498606 | + | 0.866828i | \(0.666155\pi\) | |||||||
\(888\) | 1.23899e7 | + | 8.41187e6i | 0.527273 | + | 0.357981i | ||||
\(889\) | 1.27172e7i | 0.539681i | ||||||||
\(890\) | 65463.3i | 0.00277028i | ||||||||
\(891\) | 1.38188e7 | − | 1.30244e7i | 0.583143 | − | 0.549623i | ||||
\(892\) | −4.04519e7 | −1.70227 | ||||||||
\(893\) | −4.34145e7 | −1.82182 | ||||||||
\(894\) | −2.83864e6 | + | 4.18105e6i | −0.118786 | + | 0.174961i | ||||
\(895\) | 2.26943e7i | 0.947021i | ||||||||
\(896\) | −2.05411e7 | −0.854779 | ||||||||
\(897\) | −6.99895e6 | − | 4.30503e6i | −0.290437 | − | 0.178647i | ||||
\(898\) | 3.16735e6 | 0.131070 | ||||||||
\(899\) | − | 597027.i | − | 0.0246374i | ||||||
\(900\) | −4.61088e6 | − | 1.16147e7i | −0.189748 | − | 0.477969i | ||||
\(901\) | −1.30080e7 | −0.533824 | ||||||||
\(902\) | 8.82479e6 | 0.361151 | ||||||||
\(903\) | 5.29475e6 | + | 3.59476e6i | 0.216086 | + | 0.146707i | ||||
\(904\) | − | 5.04036e6i | − | 0.205135i | ||||||
\(905\) | 2.17483e6i | 0.0882680i | ||||||||
\(906\) | 998659. | − | 1.47093e6i | 0.0404200 | − | 0.0595349i | ||||
\(907\) | − | 3.44711e6i | − | 0.139135i | −0.997577 | − | 0.0695675i | \(-0.977838\pi\) | ||
0.997577 | − | 0.0695675i | \(-0.0221619\pi\) | |||||||
\(908\) | −2.95191e7 | −1.18820 | ||||||||
\(909\) | −1.79106e7 | + | 7.11031e6i | −0.718954 | + | 0.285416i | ||||
\(910\) | −1.48438e6 | −0.0594214 | ||||||||
\(911\) | −1.14733e7 | −0.458030 | −0.229015 | − | 0.973423i | \(-0.573550\pi\) | ||||
−0.229015 | + | 0.973423i | \(0.573550\pi\) | |||||||
\(912\) | 2.00368e7 | − | 2.95123e7i | 0.797702 | − | 1.17494i | ||||
\(913\) | 3.44517e7 | 1.36784 | ||||||||
\(914\) | 1.31159e7 | 0.519318 | ||||||||
\(915\) | 8.43567e6 | − | 1.24250e7i | 0.333094 | − | 0.490617i | ||||
\(916\) | − | 1.99440e7i | − | 0.785370i | ||||||
\(917\) | −3.91018e7 | −1.53558 | ||||||||
\(918\) | 9.55400e6 | + | 2.12179e6i | 0.374178 | + | 0.0830988i | ||||
\(919\) | 7.12254e6i | 0.278193i | 0.990279 | + | 0.139096i | \(0.0444198\pi\) | ||||
−0.990279 | + | 0.139096i | \(0.955580\pi\) | |||||||
\(920\) | −410395. | − | 9.11407e6i | −0.0159857 | − | 0.355012i | ||||
\(921\) | −1.81988e7 | − | 1.23557e7i | −0.706960 | − | 0.479976i | ||||
\(922\) | −9.72923e6 | −0.376922 | ||||||||
\(923\) | 1.09768e7i | 0.424104i | ||||||||
\(924\) | 1.01651e7 | − | 1.49723e7i | 0.391681 | − | 0.576910i | ||||
\(925\) | 1.73042e7i | 0.664963i | ||||||||
\(926\) | − | 9.44045e6i | − | 0.361797i | ||||||
\(927\) | −1.78899e7 | + | 7.10208e6i | −0.683768 | + | 0.271448i | ||||
\(928\) | 1.06101e7 | 0.404436 | ||||||||
\(929\) | − | 1.96846e7i | − | 0.748319i | −0.927364 | − | 0.374160i | \(-0.877931\pi\) | ||
0.927364 | − | 0.374160i | \(-0.122069\pi\) | |||||||
\(930\) | −124966. | + | 184063.i | −0.00473788 | + | 0.00697846i | ||||
\(931\) | 5.37767e6i | 0.203339i | ||||||||
\(932\) | − | 1.58605e7i | − | 0.598104i | ||||||
\(933\) | −7.75307e6 | + | 1.14196e7i | −0.291588 | + | 0.429482i | ||||
\(934\) | 8.12041e6i | 0.304587i | ||||||||
\(935\) | −1.96700e7 | −0.735826 | ||||||||
\(936\) | −4.53672e6 | + | 1.80102e6i | −0.169259 | + | 0.0671939i | ||||
\(937\) | − | 6.94080e6i | − | 0.258262i | −0.991628 | − | 0.129131i | \(-0.958781\pi\) | ||
0.991628 | − | 0.129131i | \(-0.0412188\pi\) | |||||||
\(938\) | 7.09654e6i | 0.263354i | ||||||||
\(939\) | −8.92038e6 | + | 1.31389e7i | −0.330156 | + | 0.486289i | ||||
\(940\) | − | 1.65287e7i | − | 0.610126i | ||||||
\(941\) | −1.83924e7 | −0.677119 | −0.338559 | − | 0.940945i | \(-0.609940\pi\) | ||||
−0.338559 | + | 0.940945i | \(0.609940\pi\) | |||||||
\(942\) | 6.97900e6 | + | 4.73825e6i | 0.256251 | + | 0.173977i | ||||
\(943\) | 1.99318e6 | + | 4.42648e7i | 0.0729908 | + | 1.62098i | ||||
\(944\) | 9.00495e6i | 0.328891i | ||||||||
\(945\) | 1.68145e7 | + | 3.73422e6i | 0.612497 | + | 0.136026i | ||||
\(946\) | 1.69693e6 | 0.0616505 | ||||||||
\(947\) | − | 2.87108e7i | − | 1.04033i | −0.854066 | − | 0.520164i | \(-0.825871\pi\) | ||
0.854066 | − | 0.520164i | \(-0.174129\pi\) | |||||||
\(948\) | 1.12145e7 | − | 1.65179e7i | 0.405283 | − | 0.596944i | ||||
\(949\) | 1.49188e7 | 0.537734 | ||||||||
\(950\) | −7.89426e6 | −0.283794 | ||||||||
\(951\) | 658128. | − | 969361.i | 0.0235971 | − | 0.0347564i | ||||
\(952\) | 1.94333e7 | 0.694953 | ||||||||
\(953\) | −2.58238e7 | −0.921060 | −0.460530 | − | 0.887644i | \(-0.652341\pi\) | ||||
−0.460530 | + | 0.887644i | \(0.652341\pi\) | |||||||
\(954\) | 2.80715e6 | − | 1.11441e6i | 0.0998608 | − | 0.0396436i | ||||
\(955\) | 1.21324e7 | 0.430466 | ||||||||
\(956\) | 3.07551e7i | 1.08836i | ||||||||
\(957\) | −6.88426e6 | + | 1.01399e7i | −0.242984 | + | 0.357893i | ||||
\(958\) | 1.13430e7i | 0.399314i | ||||||||
\(959\) | − | 2.46943e7i | − | 0.867061i | ||||||
\(960\) | 8.90403e6 | + | 6.04521e6i | 0.311823 | + | 0.211706i | ||||
\(961\) | −2.85695e7 | −0.997917 | ||||||||
\(962\) | 3.24395e6 | 0.113015 | ||||||||
\(963\) | 1.71570e7 | + | 4.32178e7i | 0.596176 | + | 1.50175i | ||||
\(964\) | 2.93298e7i | 1.01652i | ||||||||
\(965\) | −7.30685e6 | −0.252587 | ||||||||
\(966\) | −6.46985e6 | − | 3.97959e6i | −0.223075 | − | 0.137213i | ||||
\(967\) | −2.62029e7 | −0.901121 | −0.450560 | − | 0.892746i | \(-0.648776\pi\) | ||||
−0.450560 | + | 0.892746i | \(0.648776\pi\) | |||||||
\(968\) | 5.57187e6i | 0.191123i | ||||||||
\(969\) | −4.15430e7 | + | 6.11890e7i | −1.42131 | + | 2.09345i | ||||
\(970\) | 1.56139e6 | 0.0532822 | ||||||||
\(971\) | 2.22674e7 | 0.757915 | 0.378958 | − | 0.925414i | \(-0.376283\pi\) | ||||
0.378958 | + | 0.925414i | \(0.376283\pi\) | |||||||
\(972\) | 2.68386e7 | − | 4.31388e6i | 0.911160 | − | 0.146454i | ||||
\(973\) | 2.41514e7i | 0.817825i | ||||||||
\(974\) | 2.66431e6i | 0.0899886i | ||||||||
\(975\) | −4.66628e6 | − | 3.16807e6i | −0.157202 | − | 0.106729i | ||||
\(976\) | − | 2.05415e7i | − | 0.690252i | ||||||
\(977\) | −1.24196e7 | −0.416267 | −0.208133 | − | 0.978100i | \(-0.566739\pi\) | ||||
−0.208133 | + | 0.978100i | \(0.566739\pi\) | |||||||
\(978\) | −720317. | + | 1.06096e6i | −0.0240811 | + | 0.0354692i | ||||
\(979\) | −360212. | −0.0120116 | ||||||||
\(980\) | −2.04738e6 | −0.0680978 | ||||||||
\(981\) | 2.78764e7 | − | 1.10666e7i | 0.924835 | − | 0.367149i | ||||
\(982\) | 3.11003e6 | 0.102917 | ||||||||
\(983\) | −4.07722e7 | −1.34580 | −0.672900 | − | 0.739733i | \(-0.734952\pi\) | ||||
−0.672900 | + | 0.739733i | \(0.734952\pi\) | |||||||
\(984\) | 2.17766e7 | + | 1.47848e7i | 0.716973 | + | 0.486774i | ||||
\(985\) | 2.47382e6i | 0.0812413i | ||||||||
\(986\) | −6.31654e6 | −0.206913 | ||||||||
\(987\) | −2.37223e7 | − | 1.61057e7i | −0.775110 | − | 0.526245i | ||||
\(988\) | − | 1.77035e7i | − | 0.576987i | ||||||
\(989\) | 383272. | + | 8.51173e6i | 0.0124600 | + | 0.276712i | ||||
\(990\) | 4.24483e6 | − | 1.68515e6i | 0.137649 | − | 0.0546450i | ||||
\(991\) | −4.46092e7 | −1.44291 | −0.721457 | − | 0.692459i | \(-0.756527\pi\) | ||||
−0.721457 | + | 0.692459i | \(0.756527\pi\) | |||||||
\(992\) | 1.05978e6i | 0.0341928i | ||||||||
\(993\) | 7.40330e6 | + | 5.02632e6i | 0.238261 | + | 0.161762i | ||||
\(994\) | 1.01470e7i | 0.325741i | ||||||||
\(995\) | − | 3.07420e7i | − | 0.984407i | ||||||
\(996\) | 4.08022e7 | + | 2.77018e7i | 1.30327 | + | 0.884830i | ||||
\(997\) | 8.22183e6 | 0.261957 | 0.130979 | − | 0.991385i | \(-0.458188\pi\) | ||||
0.130979 | + | 0.991385i | \(0.458188\pi\) | |||||||
\(998\) | 7.93433e6i | 0.252164i | ||||||||
\(999\) | −3.67461e7 | − | 8.16070e6i | −1.16492 | − | 0.258710i |
(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 | 69.6.c.b.68.13 | ✓ | 32 | |
3.2 | odd | 2 | inner | 69.6.c.b.68.20 | yes | 32 | |
23.22 | odd | 2 | inner | 69.6.c.b.68.14 | yes | 32 | |
69.68 | even | 2 | inner | 69.6.c.b.68.19 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.c.b.68.13 | ✓ | 32 | 1.1 | even | 1 | trivial | |
69.6.c.b.68.14 | yes | 32 | 23.22 | odd | 2 | inner | |
69.6.c.b.68.19 | yes | 32 | 69.68 | even | 2 | inner | |
69.6.c.b.68.20 | yes | 32 | 3.2 | odd | 2 | inner |