Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.4 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.23 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 8.57523i | − | 1.51590i | −0.652312 | − | 0.757950i | \(-0.726201\pi\) | ||
0.652312 | − | 0.757950i | \(-0.273799\pi\) | |||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | −41.5346 | −1.29796 | ||||||||
\(5\) | −51.2624 | − | 22.2971i | −0.917010 | − | 0.398863i | ||||
\(6\) | 77.1771 | 0.875206 | ||||||||
\(7\) | − | 178.462i | − | 1.37658i | −0.725435 | − | 0.688290i | \(-0.758362\pi\) | ||
0.725435 | − | 0.688290i | \(-0.241638\pi\) | |||||||
\(8\) | 81.7612i | 0.451671i | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | −191.203 | + | 439.587i | −0.604637 | + | 1.39010i | ||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | − | 373.811i | − | 0.749375i | ||||||
\(13\) | − | 361.980i | − | 0.594054i | −0.954869 | − | 0.297027i | \(-0.904005\pi\) | ||
0.954869 | − | 0.297027i | \(-0.0959951\pi\) | |||||||
\(14\) | −1530.36 | −2.08676 | ||||||||
\(15\) | 200.674 | − | 461.362i | 0.230284 | − | 0.529436i | ||||
\(16\) | −627.985 | −0.613267 | ||||||||
\(17\) | − | 934.004i | − | 0.783838i | −0.920000 | − | 0.391919i | \(-0.871811\pi\) | ||
0.920000 | − | 0.391919i | \(-0.128189\pi\) | |||||||
\(18\) | 694.594i | 0.505300i | ||||||||
\(19\) | −753.929 | −0.479122 | −0.239561 | − | 0.970881i | \(-0.577004\pi\) | ||||
−0.239561 | + | 0.970881i | \(0.577004\pi\) | |||||||
\(20\) | 2129.16 | + | 926.102i | 1.19024 | + | 0.517707i | ||||
\(21\) | 1606.16 | 0.794769 | ||||||||
\(22\) | − | 1037.60i | − | 0.457061i | ||||||
\(23\) | 3231.01i | 1.27356i | 0.771046 | + | 0.636780i | \(0.219734\pi\) | ||||
−0.771046 | + | 0.636780i | \(0.780266\pi\) | |||||||
\(24\) | −735.851 | −0.260773 | ||||||||
\(25\) | 2130.68 | + | 2286.01i | 0.681816 | + | 0.731523i | ||||
\(26\) | −3104.06 | −0.900527 | ||||||||
\(27\) | − | 729.000i | − | 0.192450i | ||||||
\(28\) | 7412.36i | 1.78674i | ||||||||
\(29\) | −2606.34 | −0.575488 | −0.287744 | − | 0.957707i | \(-0.592905\pi\) | ||||
−0.287744 | + | 0.957707i | \(0.592905\pi\) | |||||||
\(30\) | −3956.29 | − | 1720.83i | −0.802573 | − | 0.349087i | ||||
\(31\) | 662.215 | 0.123764 | 0.0618821 | − | 0.998083i | \(-0.480290\pi\) | ||||
0.0618821 | + | 0.998083i | \(0.480290\pi\) | |||||||
\(32\) | 8001.48i | 1.38132i | ||||||||
\(33\) | 1089.00i | 0.174078i | ||||||||
\(34\) | −8009.30 | −1.18822 | ||||||||
\(35\) | −3979.20 | + | 9148.42i | −0.549067 | + | 1.26234i | ||||
\(36\) | 3364.30 | 0.432652 | ||||||||
\(37\) | 12924.2i | 1.55203i | 0.630717 | + | 0.776013i | \(0.282761\pi\) | ||||
−0.630717 | + | 0.776013i | \(0.717239\pi\) | |||||||
\(38\) | 6465.11i | 0.726302i | ||||||||
\(39\) | 3257.82 | 0.342977 | ||||||||
\(40\) | 1823.04 | − | 4191.28i | 0.180155 | − | 0.414187i | ||||
\(41\) | −2538.56 | −0.235846 | −0.117923 | − | 0.993023i | \(-0.537624\pi\) | ||||
−0.117923 | + | 0.993023i | \(0.537624\pi\) | |||||||
\(42\) | − | 13773.2i | − | 1.20479i | ||||||
\(43\) | 22022.8i | 1.81636i | 0.418583 | + | 0.908178i | \(0.362527\pi\) | ||||
−0.418583 | + | 0.908178i | \(0.637473\pi\) | |||||||
\(44\) | −5025.68 | −0.391348 | ||||||||
\(45\) | 4152.26 | + | 1806.07i | 0.305670 | + | 0.132954i | ||||
\(46\) | 27706.7 | 1.93059 | ||||||||
\(47\) | − | 20835.4i | − | 1.37581i | −0.725802 | − | 0.687903i | \(-0.758531\pi\) | ||
0.725802 | − | 0.687903i | \(-0.241469\pi\) | |||||||
\(48\) | − | 5651.87i | − | 0.354070i | ||||||
\(49\) | −15041.8 | −0.894974 | ||||||||
\(50\) | 19603.1 | − | 18271.0i | 1.10892 | − | 1.03357i | ||||
\(51\) | 8406.03 | 0.452549 | ||||||||
\(52\) | 15034.7i | 0.771056i | ||||||||
\(53\) | − | 27450.5i | − | 1.34233i | −0.741307 | − | 0.671166i | \(-0.765794\pi\) | ||
0.741307 | − | 0.671166i | \(-0.234206\pi\) | |||||||
\(54\) | −6251.34 | −0.291735 | ||||||||
\(55\) | −6202.76 | − | 2697.95i | −0.276489 | − | 0.120262i | ||||
\(56\) | 14591.3 | 0.621762 | ||||||||
\(57\) | − | 6785.36i | − | 0.276621i | ||||||
\(58\) | 22350.0i | 0.872383i | ||||||||
\(59\) | −7759.71 | −0.290212 | −0.145106 | − | 0.989416i | \(-0.546352\pi\) | ||||
−0.145106 | + | 0.989416i | \(0.546352\pi\) | |||||||
\(60\) | −8334.92 | + | 19162.5i | −0.298898 | + | 0.687185i | ||||
\(61\) | 38469.2 | 1.32370 | 0.661849 | − | 0.749638i | \(-0.269772\pi\) | ||||
0.661849 | + | 0.749638i | \(0.269772\pi\) | |||||||
\(62\) | − | 5678.65i | − | 0.187614i | ||||||
\(63\) | 14455.5i | 0.458860i | ||||||||
\(64\) | 48519.0 | 1.48068 | ||||||||
\(65\) | −8071.11 | + | 18556.0i | −0.236946 | + | 0.544754i | ||||
\(66\) | 9338.43 | 0.263884 | ||||||||
\(67\) | − | 35521.3i | − | 0.966723i | −0.875421 | − | 0.483362i | \(-0.839416\pi\) | ||
0.875421 | − | 0.483362i | \(-0.160584\pi\) | |||||||
\(68\) | 38793.4i | 1.01739i | ||||||||
\(69\) | −29079.1 | −0.735290 | ||||||||
\(70\) | 78449.8 | + | 34122.5i | 1.91358 | + | 0.832332i | ||||
\(71\) | −62677.1 | −1.47558 | −0.737790 | − | 0.675030i | \(-0.764131\pi\) | ||||
−0.737790 | + | 0.675030i | \(0.764131\pi\) | |||||||
\(72\) | − | 6622.66i | − | 0.150557i | ||||||
\(73\) | 68950.2i | 1.51436i | 0.653208 | + | 0.757179i | \(0.273423\pi\) | ||||
−0.653208 | + | 0.757179i | \(0.726577\pi\) | |||||||
\(74\) | 110828. | 2.35272 | ||||||||
\(75\) | −20574.1 | + | 19176.1i | −0.422345 | + | 0.393647i | ||||
\(76\) | 31314.1 | 0.621879 | ||||||||
\(77\) | − | 21594.0i | − | 0.415055i | ||||||
\(78\) | − | 27936.5i | − | 0.519919i | ||||||
\(79\) | 17313.8 | 0.312123 | 0.156061 | − | 0.987747i | \(-0.450120\pi\) | ||||
0.156061 | + | 0.987747i | \(0.450120\pi\) | |||||||
\(80\) | 32192.1 | + | 14002.3i | 0.562372 | + | 0.244610i | ||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 21768.7i | 0.357518i | ||||||||
\(83\) | − | 89017.9i | − | 1.41835i | −0.705035 | − | 0.709173i | \(-0.749069\pi\) | ||
0.705035 | − | 0.709173i | \(-0.250931\pi\) | |||||||
\(84\) | −66711.2 | −1.03158 | ||||||||
\(85\) | −20825.6 | + | 47879.3i | −0.312644 | + | 0.718787i | ||||
\(86\) | 188850. | 2.75342 | ||||||||
\(87\) | − | 23457.1i | − | 0.332258i | ||||||
\(88\) | 9893.11i | 0.136184i | ||||||||
\(89\) | −129627. | −1.73468 | −0.867341 | − | 0.497714i | \(-0.834173\pi\) | ||||
−0.867341 | + | 0.497714i | \(0.834173\pi\) | |||||||
\(90\) | 15487.4 | − | 35606.6i | 0.201546 | − | 0.463366i | ||||
\(91\) | −64599.8 | −0.817763 | ||||||||
\(92\) | − | 134199.i | − | 1.65302i | ||||||
\(93\) | 5959.94i | 0.0714553i | ||||||||
\(94\) | −178668. | −2.08559 | ||||||||
\(95\) | 38648.2 | + | 16810.4i | 0.439360 | + | 0.191104i | ||||
\(96\) | −72013.3 | −0.797507 | ||||||||
\(97\) | 136732.i | 1.47551i | 0.675069 | + | 0.737755i | \(0.264114\pi\) | ||||
−0.675069 | + | 0.737755i | \(0.735886\pi\) | |||||||
\(98\) | 128987.i | 1.35669i | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | −88496.7 | − | 94948.5i | −0.884967 | − | 0.949485i | ||||
\(101\) | 51376.9 | 0.501146 | 0.250573 | − | 0.968098i | \(-0.419381\pi\) | ||||
0.250573 | + | 0.968098i | \(0.419381\pi\) | |||||||
\(102\) | − | 72083.7i | − | 0.686019i | ||||||
\(103\) | − | 94899.7i | − | 0.881398i | −0.897655 | − | 0.440699i | \(-0.854731\pi\) | ||
0.897655 | − | 0.440699i | \(-0.145269\pi\) | |||||||
\(104\) | 29595.9 | 0.268317 | ||||||||
\(105\) | −82335.8 | − | 35812.8i | −0.728812 | − | 0.317004i | ||||
\(106\) | −235394. | −2.03484 | ||||||||
\(107\) | 52232.6i | 0.441045i | 0.975382 | + | 0.220522i | \(0.0707762\pi\) | ||||
−0.975382 | + | 0.220522i | \(0.929224\pi\) | |||||||
\(108\) | 30278.7i | 0.249792i | ||||||||
\(109\) | −138553. | −1.11699 | −0.558496 | − | 0.829507i | \(-0.688622\pi\) | ||||
−0.558496 | + | 0.829507i | \(0.688622\pi\) | |||||||
\(110\) | −23135.6 | + | 53190.1i | −0.182305 | + | 0.419130i | ||||
\(111\) | −116318. | −0.896063 | ||||||||
\(112\) | 112072.i | 0.844211i | ||||||||
\(113\) | − | 136642.i | − | 1.00667i | −0.864091 | − | 0.503336i | \(-0.832106\pi\) | ||
0.864091 | − | 0.503336i | \(-0.167894\pi\) | |||||||
\(114\) | −58186.0 | −0.419330 | ||||||||
\(115\) | 72042.3 | − | 165630.i | 0.507976 | − | 1.16787i | ||||
\(116\) | 108253. | 0.746958 | ||||||||
\(117\) | 29320.4i | 0.198018i | ||||||||
\(118\) | 66541.3i | 0.439933i | ||||||||
\(119\) | −166685. | −1.07902 | ||||||||
\(120\) | 37721.5 | + | 16407.4i | 0.239131 | + | 0.104013i | ||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | − | 329882.i | − | 2.00659i | ||||||
\(123\) | − | 22847.0i | − | 0.136165i | ||||||
\(124\) | −27504.8 | −0.160640 | ||||||||
\(125\) | −58252.2 | − | 164694.i | −0.333455 | − | 0.942766i | ||||
\(126\) | 123959. | 0.695587 | ||||||||
\(127\) | − | 23888.8i | − | 0.131427i | −0.997839 | − | 0.0657136i | \(-0.979068\pi\) | ||
0.997839 | − | 0.0657136i | \(-0.0209324\pi\) | |||||||
\(128\) | − | 160014.i | − | 0.863244i | ||||||
\(129\) | −198205. | −1.04867 | ||||||||
\(130\) | 159122. | + | 69211.6i | 0.825793 | + | 0.359187i | ||||
\(131\) | 67597.5 | 0.344154 | 0.172077 | − | 0.985084i | \(-0.444952\pi\) | ||||
0.172077 | + | 0.985084i | \(0.444952\pi\) | |||||||
\(132\) | − | 45231.2i | − | 0.225945i | ||||||
\(133\) | 134548.i | 0.659550i | ||||||||
\(134\) | −304604. | −1.46546 | ||||||||
\(135\) | −16254.6 | + | 37370.3i | −0.0767613 | + | 0.176479i | ||||
\(136\) | 76365.3 | 0.354037 | ||||||||
\(137\) | 205843.i | 0.936991i | 0.883466 | + | 0.468496i | \(0.155204\pi\) | ||||
−0.883466 | + | 0.468496i | \(0.844796\pi\) | |||||||
\(138\) | 249360.i | 1.11463i | ||||||||
\(139\) | −43495.6 | −0.190945 | −0.0954724 | − | 0.995432i | \(-0.530436\pi\) | ||||
−0.0954724 | + | 0.995432i | \(0.530436\pi\) | |||||||
\(140\) | 165274. | − | 379976.i | 0.712665 | − | 1.63846i | ||||
\(141\) | 187519. | 0.794323 | ||||||||
\(142\) | 537470.i | 2.23683i | ||||||||
\(143\) | − | 43799.6i | − | 0.179114i | ||||||
\(144\) | 50866.8 | 0.204422 | ||||||||
\(145\) | 133607. | + | 58113.9i | 0.527728 | + | 0.229541i | ||||
\(146\) | 591264. | 2.29562 | ||||||||
\(147\) | − | 135376.i | − | 0.516713i | ||||||
\(148\) | − | 536801.i | − | 2.01446i | ||||||
\(149\) | −219355. | −0.809436 | −0.404718 | − | 0.914442i | \(-0.632630\pi\) | ||||
−0.404718 | + | 0.914442i | \(0.632630\pi\) | |||||||
\(150\) | 164439. | + | 176428.i | 0.596730 | + | 0.640234i | ||||
\(151\) | −32928.1 | −0.117523 | −0.0587616 | − | 0.998272i | \(-0.518715\pi\) | ||||
−0.0587616 | + | 0.998272i | \(0.518715\pi\) | |||||||
\(152\) | − | 61642.1i | − | 0.216406i | ||||||
\(153\) | 75654.3i | 0.261279i | ||||||||
\(154\) | −185173. | −0.629182 | ||||||||
\(155\) | −33946.8 | − | 14765.5i | −0.113493 | − | 0.0493650i | ||||
\(156\) | −135312. | −0.445169 | ||||||||
\(157\) | − | 457292.i | − | 1.48062i | −0.672265 | − | 0.740311i | \(-0.734678\pi\) | ||
0.672265 | − | 0.740311i | \(-0.265322\pi\) | |||||||
\(158\) | − | 148470.i | − | 0.473147i | ||||||
\(159\) | 247054. | 0.774996 | ||||||||
\(160\) | 178410. | − | 410175.i | 0.550959 | − | 1.26669i | ||||
\(161\) | 576614. | 1.75316 | ||||||||
\(162\) | − | 56262.1i | − | 0.168433i | ||||||
\(163\) | − | 52822.0i | − | 0.155721i | −0.996964 | − | 0.0778603i | \(-0.975191\pi\) | ||
0.996964 | − | 0.0778603i | \(-0.0248088\pi\) | |||||||
\(164\) | 105438. | 0.306117 | ||||||||
\(165\) | 24281.6 | − | 55824.8i | 0.0694332 | − | 0.159631i | ||||
\(166\) | −763349. | −2.15007 | ||||||||
\(167\) | 327606.i | 0.908993i | 0.890748 | + | 0.454497i | \(0.150181\pi\) | ||||
−0.890748 | + | 0.454497i | \(0.849819\pi\) | |||||||
\(168\) | 131322.i | 0.358974i | ||||||||
\(169\) | 240264. | 0.647100 | ||||||||
\(170\) | 410576. | + | 178584.i | 1.08961 | + | 0.473937i | ||||
\(171\) | 61068.2 | 0.159707 | ||||||||
\(172\) | − | 914707.i | − | 2.35755i | ||||||
\(173\) | 246387.i | 0.625897i | 0.949770 | + | 0.312949i | \(0.101317\pi\) | ||||
−0.949770 | + | 0.312949i | \(0.898683\pi\) | |||||||
\(174\) | −201150. | −0.503670 | ||||||||
\(175\) | 407967. | − | 380246.i | 1.00700 | − | 0.938575i | ||||
\(176\) | −75986.2 | −0.184907 | ||||||||
\(177\) | − | 69837.4i | − | 0.167554i | ||||||
\(178\) | 1.11158e6i | 2.62961i | ||||||||
\(179\) | −302341. | −0.705285 | −0.352643 | − | 0.935758i | \(-0.614717\pi\) | ||||
−0.352643 | + | 0.935758i | \(0.614717\pi\) | |||||||
\(180\) | −172462. | − | 75014.3i | −0.396746 | − | 0.172569i | ||||
\(181\) | −465374. | −1.05586 | −0.527929 | − | 0.849288i | \(-0.677031\pi\) | ||||
−0.527929 | + | 0.849288i | \(0.677031\pi\) | |||||||
\(182\) | 553958.i | 1.23965i | ||||||||
\(183\) | 346223.i | 0.764237i | ||||||||
\(184\) | −264172. | −0.575230 | ||||||||
\(185\) | 288172. | − | 662526.i | 0.619046 | − | 1.42322i | ||||
\(186\) | 51107.8 | 0.108319 | ||||||||
\(187\) | − | 113014.i | − | 0.236336i | ||||||
\(188\) | 865390.i | 1.78574i | ||||||||
\(189\) | −130099. | −0.264923 | ||||||||
\(190\) | 144153. | − | 331417.i | 0.289695 | − | 0.666026i | ||||
\(191\) | 294182. | 0.583489 | 0.291745 | − | 0.956496i | \(-0.405764\pi\) | ||||
0.291745 | + | 0.956496i | \(0.405764\pi\) | |||||||
\(192\) | 436671.i | 0.854872i | ||||||||
\(193\) | − | 280529.i | − | 0.542106i | −0.962564 | − | 0.271053i | \(-0.912628\pi\) | ||
0.962564 | − | 0.271053i | \(-0.0873718\pi\) | |||||||
\(194\) | 1.17251e6 | 2.23673 | ||||||||
\(195\) | −167004. | − | 72640.0i | −0.314514 | − | 0.136801i | ||||
\(196\) | 624756. | 1.16164 | ||||||||
\(197\) | 241625.i | 0.443585i | 0.975094 | + | 0.221792i | \(0.0711907\pi\) | ||||
−0.975094 | + | 0.221792i | \(0.928809\pi\) | |||||||
\(198\) | 84045.8i | 0.152354i | ||||||||
\(199\) | −621763. | −1.11299 | −0.556496 | − | 0.830850i | \(-0.687855\pi\) | ||||
−0.556496 | + | 0.830850i | \(0.687855\pi\) | |||||||
\(200\) | −186907. | + | 174207.i | −0.330408 | + | 0.307957i | ||||
\(201\) | 319692. | 0.558138 | ||||||||
\(202\) | − | 440569.i | − | 0.759688i | ||||||
\(203\) | 465134.i | 0.792205i | ||||||||
\(204\) | −349141. | −0.587389 | ||||||||
\(205\) | 130133. | + | 56602.6i | 0.216273 | + | 0.0940701i | ||||
\(206\) | −813787. | −1.33611 | ||||||||
\(207\) | − | 261712.i | − | 0.424520i | ||||||
\(208\) | 227318.i | 0.364314i | ||||||||
\(209\) | −91225.4 | −0.144461 | ||||||||
\(210\) | −307103. | + | 706048.i | −0.480547 | + | 1.10481i | ||||
\(211\) | −446582. | −0.690550 | −0.345275 | − | 0.938502i | \(-0.612214\pi\) | ||||
−0.345275 | + | 0.938502i | \(0.612214\pi\) | |||||||
\(212\) | 1.14014e6i | 1.74229i | ||||||||
\(213\) | − | 564094.i | − | 0.851927i | ||||||
\(214\) | 447907. | 0.668580 | ||||||||
\(215\) | 491045. | − | 1.12894e6i | 0.724478 | − | 1.66562i | ||||
\(216\) | 59603.9 | 0.0869242 | ||||||||
\(217\) | − | 118181.i | − | 0.170371i | ||||||
\(218\) | 1.18813e6i | 1.69325i | ||||||||
\(219\) | −620552. | −0.874314 | ||||||||
\(220\) | 257629. | + | 112058.i | 0.358871 | + | 0.156094i | ||||
\(221\) | −338090. | −0.465642 | ||||||||
\(222\) | 997451.i | 1.35834i | ||||||||
\(223\) | 29867.7i | 0.0402198i | 0.999798 | + | 0.0201099i | \(0.00640161\pi\) | ||||
−0.999798 | + | 0.0201099i | \(0.993598\pi\) | |||||||
\(224\) | 1.42796e6 | 1.90150 | ||||||||
\(225\) | −172585. | − | 185167.i | −0.227272 | − | 0.243841i | ||||
\(226\) | −1.17174e6 | −1.52602 | ||||||||
\(227\) | − | 425464.i | − | 0.548022i | −0.961726 | − | 0.274011i | \(-0.911649\pi\) | ||
0.961726 | − | 0.274011i | \(-0.0883505\pi\) | |||||||
\(228\) | 281827.i | 0.359042i | ||||||||
\(229\) | 1.31835e6 | 1.66127 | 0.830637 | − | 0.556814i | \(-0.187977\pi\) | ||||
0.830637 | + | 0.556814i | \(0.187977\pi\) | |||||||
\(230\) | −1.42031e6 | − | 617780.i | −1.77037 | − | 0.770041i | ||||
\(231\) | 194346. | 0.239632 | ||||||||
\(232\) | − | 213098.i | − | 0.259931i | ||||||
\(233\) | − | 320062.i | − | 0.386228i | −0.981176 | − | 0.193114i | \(-0.938141\pi\) | ||
0.981176 | − | 0.193114i | \(-0.0618588\pi\) | |||||||
\(234\) | 251429. | 0.300176 | ||||||||
\(235\) | −464570. | + | 1.06807e6i | −0.548759 | + | 1.26163i | ||||
\(236\) | 322296. | 0.376683 | ||||||||
\(237\) | 155825.i | 0.180204i | ||||||||
\(238\) | 1.42936e6i | 1.63568i | ||||||||
\(239\) | −1.25534e6 | −1.42156 | −0.710781 | − | 0.703414i | \(-0.751658\pi\) | ||||
−0.710781 | + | 0.703414i | \(0.751658\pi\) | |||||||
\(240\) | −126020. | + | 289728.i | −0.141225 | + | 0.324686i | ||||
\(241\) | −1.07813e6 | −1.19572 | −0.597859 | − | 0.801601i | \(-0.703982\pi\) | ||||
−0.597859 | + | 0.801601i | \(0.703982\pi\) | |||||||
\(242\) | − | 125550.i | − | 0.137809i | ||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | −1.59780e6 | −1.71810 | ||||||||
\(245\) | 771081. | + | 335390.i | 0.820700 | + | 0.356972i | ||||
\(246\) | −195919. | −0.206413 | ||||||||
\(247\) | 272907.i | 0.284624i | ||||||||
\(248\) | 54143.5i | 0.0559007i | ||||||||
\(249\) | 801161. | 0.818882 | ||||||||
\(250\) | −1.41229e6 | + | 499526.i | −1.42914 | + | 0.505485i | ||||
\(251\) | −918775. | −0.920502 | −0.460251 | − | 0.887789i | \(-0.652241\pi\) | ||||
−0.460251 | + | 0.887789i | \(0.652241\pi\) | |||||||
\(252\) | − | 600401.i | − | 0.595580i | ||||||
\(253\) | 390953.i | 0.383993i | ||||||||
\(254\) | −204852. | −0.199231 | ||||||||
\(255\) | −430914. | − | 187430.i | −0.414992 | − | 0.180505i | ||||
\(256\) | 180449. | 0.172089 | ||||||||
\(257\) | − | 797355.i | − | 0.753041i | −0.926408 | − | 0.376521i | \(-0.877120\pi\) | ||
0.926408 | − | 0.376521i | \(-0.122880\pi\) | |||||||
\(258\) | 1.69965e6i | 1.58969i | ||||||||
\(259\) | 2.30648e6 | 2.13649 | ||||||||
\(260\) | 335230. | − | 770714.i | 0.307546 | − | 0.707066i | ||||
\(261\) | 211114. | 0.191829 | ||||||||
\(262\) | − | 579664.i | − | 0.521703i | ||||||
\(263\) | − | 980563.i | − | 0.874150i | −0.899425 | − | 0.437075i | \(-0.856014\pi\) | ||
0.899425 | − | 0.437075i | \(-0.143986\pi\) | |||||||
\(264\) | −89038.0 | −0.0786259 | ||||||||
\(265\) | −612067. | + | 1.40718e6i | −0.535407 | + | 1.23093i | ||||
\(266\) | 1.15378e6 | 0.999813 | ||||||||
\(267\) | − | 1.16664e6i | − | 1.00152i | ||||||
\(268\) | 1.47536e6i | 1.25476i | ||||||||
\(269\) | 1.32137e6 | 1.11338 | 0.556691 | − | 0.830719i | \(-0.312071\pi\) | ||||
0.556691 | + | 0.830719i | \(0.312071\pi\) | |||||||
\(270\) | 320459. | + | 139387.i | 0.267524 | + | 0.116362i | ||||
\(271\) | −62864.5 | −0.0519975 | −0.0259987 | − | 0.999662i | \(-0.508277\pi\) | ||||
−0.0259987 | + | 0.999662i | \(0.508277\pi\) | |||||||
\(272\) | 586540.i | 0.480702i | ||||||||
\(273\) | − | 581398.i | − | 0.472136i | ||||||
\(274\) | 1.76515e6 | 1.42039 | ||||||||
\(275\) | 257812. | + | 276607.i | 0.205575 | + | 0.220563i | ||||
\(276\) | 1.20779e6 | 0.954374 | ||||||||
\(277\) | − | 1.44313e6i | − | 1.13007i | −0.825066 | − | 0.565037i | \(-0.808862\pi\) | ||
0.825066 | − | 0.565037i | \(-0.191138\pi\) | |||||||
\(278\) | 372984.i | 0.289453i | ||||||||
\(279\) | −53639.4 | −0.0412547 | ||||||||
\(280\) | −747986. | − | 325344.i | −0.570162 | − | 0.247998i | ||||
\(281\) | −143939. | −0.108746 | −0.0543731 | − | 0.998521i | \(-0.517316\pi\) | ||||
−0.0543731 | + | 0.998521i | \(0.517316\pi\) | |||||||
\(282\) | − | 1.60802e6i | − | 1.20411i | ||||||
\(283\) | − | 9060.12i | − | 0.00672462i | −0.999994 | − | 0.00336231i | \(-0.998930\pi\) | ||
0.999994 | − | 0.00336231i | \(-0.00107026\pi\) | |||||||
\(284\) | 2.60327e6 | 1.91524 | ||||||||
\(285\) | −151294. | + | 347834.i | −0.110334 | + | 0.253665i | ||||
\(286\) | −375591. | −0.271519 | ||||||||
\(287\) | 453037.i | 0.324660i | ||||||||
\(288\) | − | 648120.i | − | 0.460441i | ||||||
\(289\) | 547494. | 0.385598 | ||||||||
\(290\) | 498340. | − | 1.14571e6i | 0.347961 | − | 0.799984i | ||||
\(291\) | −1.23059e6 | −0.851886 | ||||||||
\(292\) | − | 2.86382e6i | − | 1.96557i | ||||||
\(293\) | − | 1.85674e6i | − | 1.26352i | −0.775165 | − | 0.631759i | \(-0.782333\pi\) | ||
0.775165 | − | 0.631759i | \(-0.217667\pi\) | |||||||
\(294\) | −1.16088e6 | −0.783286 | ||||||||
\(295\) | 397782. | + | 173019.i | 0.266128 | + | 0.115755i | ||||
\(296\) | −1.05670e6 | −0.701006 | ||||||||
\(297\) | − | 88209.0i | − | 0.0580259i | ||||||
\(298\) | 1.88102e6i | 1.22703i | ||||||||
\(299\) | 1.16956e6 | 0.756563 | ||||||||
\(300\) | 854536. | − | 796471.i | 0.548185 | − | 0.510936i | ||||
\(301\) | 3.93024e6 | 2.50036 | ||||||||
\(302\) | 282366.i | 0.178154i | ||||||||
\(303\) | 462392.i | 0.289337i | ||||||||
\(304\) | 473456. | 0.293830 | ||||||||
\(305\) | −1.97203e6 | − | 857753.i | −1.21384 | − | 0.527974i | ||||
\(306\) | 648753. | 0.396074 | ||||||||
\(307\) | 504688.i | 0.305617i | 0.988256 | + | 0.152808i | \(0.0488318\pi\) | ||||
−0.988256 | + | 0.152808i | \(0.951168\pi\) | |||||||
\(308\) | 896896.i | 0.538723i | ||||||||
\(309\) | 854097. | 0.508875 | ||||||||
\(310\) | −126618. | + | 291101.i | −0.0748324 | + | 0.172044i | ||||
\(311\) | −448511. | −0.262950 | −0.131475 | − | 0.991320i | \(-0.541971\pi\) | ||||
−0.131475 | + | 0.991320i | \(0.541971\pi\) | |||||||
\(312\) | 266363.i | 0.154913i | ||||||||
\(313\) | 825146.i | 0.476069i | 0.971257 | + | 0.238035i | \(0.0765031\pi\) | ||||
−0.971257 | + | 0.238035i | \(0.923497\pi\) | |||||||
\(314\) | −3.92138e6 | −2.24448 | ||||||||
\(315\) | 322315. | − | 741022.i | 0.183022 | − | 0.420780i | ||||
\(316\) | −719123. | −0.405122 | ||||||||
\(317\) | − | 3.26266e6i | − | 1.82358i | −0.410659 | − | 0.911789i | \(-0.634701\pi\) | ||
0.410659 | − | 0.911789i | \(-0.365299\pi\) | |||||||
\(318\) | − | 2.11855e6i | − | 1.17482i | ||||||
\(319\) | −315367. | −0.173516 | ||||||||
\(320\) | −2.48720e6 | − | 1.08183e6i | −1.35780 | − | 0.590589i | ||||
\(321\) | −470094. | −0.254637 | ||||||||
\(322\) | − | 4.94460e6i | − | 2.65761i | ||||||
\(323\) | 704172.i | 0.375554i | ||||||||
\(324\) | −272508. | −0.144217 | ||||||||
\(325\) | 827490. | − | 771262.i | 0.434564 | − | 0.405036i | ||||
\(326\) | −452961. | −0.236057 | ||||||||
\(327\) | − | 1.24698e6i | − | 0.644896i | ||||||
\(328\) | − | 207556.i | − | 0.106525i | ||||||
\(329\) | −3.71834e6 | −1.89391 | ||||||||
\(330\) | −478711. | − | 208220.i | −0.241985 | − | 0.105254i | ||||
\(331\) | −3.48175e6 | −1.74674 | −0.873369 | − | 0.487059i | \(-0.838070\pi\) | ||||
−0.873369 | + | 0.487059i | \(0.838070\pi\) | |||||||
\(332\) | 3.69732e6i | 1.84095i | ||||||||
\(333\) | − | 1.04686e6i | − | 0.517342i | ||||||
\(334\) | 2.80930e6 | 1.37794 | ||||||||
\(335\) | −792024. | + | 1.82091e6i | −0.385590 | + | 0.886495i | ||||
\(336\) | −1.00865e6 | −0.487406 | ||||||||
\(337\) | 1.52759e6i | 0.732710i | 0.930475 | + | 0.366355i | \(0.119394\pi\) | ||||
−0.930475 | + | 0.366355i | \(0.880606\pi\) | |||||||
\(338\) | − | 2.06032e6i | − | 0.980939i | ||||||
\(339\) | 1.22978e6 | 0.581203 | ||||||||
\(340\) | 864982. | − | 1.98865e6i | 0.405798 | − | 0.932954i | ||||
\(341\) | 80128.0 | 0.0373163 | ||||||||
\(342\) | − | 523674.i | − | 0.242101i | ||||||
\(343\) | − | 315017.i | − | 0.144577i | ||||||
\(344\) | −1.80061e6 | −0.820396 | ||||||||
\(345\) | 1.49067e6 | + | 648381.i | 0.674268 | + | 0.293280i | ||||
\(346\) | 2.11283e6 | 0.948798 | ||||||||
\(347\) | 4.01479e6i | 1.78994i | 0.446122 | + | 0.894972i | \(0.352805\pi\) | ||||
−0.446122 | + | 0.894972i | \(0.647195\pi\) | |||||||
\(348\) | 974279.i | 0.431256i | ||||||||
\(349\) | 511478. | 0.224783 | 0.112391 | − | 0.993664i | \(-0.464149\pi\) | ||||
0.112391 | + | 0.993664i | \(0.464149\pi\) | |||||||
\(350\) | −3.26069e6 | − | 3.49841e6i | −1.42279 | − | 1.52651i | ||||
\(351\) | −263883. | −0.114326 | ||||||||
\(352\) | 968179.i | 0.416485i | ||||||||
\(353\) | − | 722636.i | − | 0.308662i | −0.988019 | − | 0.154331i | \(-0.950678\pi\) | ||
0.988019 | − | 0.154331i | \(-0.0493221\pi\) | |||||||
\(354\) | −598872. | −0.253995 | ||||||||
\(355\) | 3.21298e6 | + | 1.39752e6i | 1.35312 | + | 0.588555i | ||||
\(356\) | 5.38400e6 | 2.25154 | ||||||||
\(357\) | − | 1.50016e6i | − | 0.622970i | ||||||
\(358\) | 2.59264e6i | 1.06914i | ||||||||
\(359\) | −393345. | −0.161078 | −0.0805392 | − | 0.996751i | \(-0.525664\pi\) | ||||
−0.0805392 | + | 0.996751i | \(0.525664\pi\) | |||||||
\(360\) | −147666. | + | 339494.i | −0.0600517 | + | 0.138062i | ||||
\(361\) | −1.90769e6 | −0.770442 | ||||||||
\(362\) | 3.99069e6i | 1.60058i | ||||||||
\(363\) | 131769.i | 0.0524864i | ||||||||
\(364\) | 2.68312e6 | 1.06142 | ||||||||
\(365\) | 1.53739e6 | − | 3.53455e6i | 0.604021 | − | 1.38868i | ||||
\(366\) | 2.96894e6 | 1.15851 | ||||||||
\(367\) | 2.87578e6i | 1.11453i | 0.830336 | + | 0.557264i | \(0.188149\pi\) | ||||
−0.830336 | + | 0.557264i | \(0.811851\pi\) | |||||||
\(368\) | − | 2.02903e6i | − | 0.781032i | ||||||
\(369\) | 205623. | 0.0786152 | ||||||||
\(370\) | −5.68131e6 | − | 2.47114e6i | −2.15747 | − | 0.938413i | ||||
\(371\) | −4.89888e6 | −1.84783 | ||||||||
\(372\) | − | 247543.i | − | 0.0927458i | ||||||
\(373\) | 3.86030e6i | 1.43665i | 0.695710 | + | 0.718323i | \(0.255090\pi\) | ||||
−0.695710 | + | 0.718323i | \(0.744910\pi\) | |||||||
\(374\) | −969125. | −0.358262 | ||||||||
\(375\) | 1.48225e6 | − | 524270.i | 0.544306 | − | 0.192520i | ||||
\(376\) | 1.70353e6 | 0.621412 | ||||||||
\(377\) | 943443.i | 0.341871i | ||||||||
\(378\) | 1.11563e6i | 0.401597i | ||||||||
\(379\) | 1.63355e6 | 0.584162 | 0.292081 | − | 0.956394i | \(-0.405652\pi\) | ||||
0.292081 | + | 0.956394i | \(0.405652\pi\) | |||||||
\(380\) | −1.60524e6 | − | 698215.i | −0.570270 | − | 0.248045i | ||||
\(381\) | 214999. | 0.0758795 | ||||||||
\(382\) | − | 2.52268e6i | − | 0.884512i | ||||||
\(383\) | 3.86858e6i | 1.34758i | 0.738923 | + | 0.673790i | \(0.235335\pi\) | ||||
−0.738923 | + | 0.673790i | \(0.764665\pi\) | |||||||
\(384\) | 1.44013e6 | 0.498394 | ||||||||
\(385\) | −481483. | + | 1.10696e6i | −0.165550 | + | 0.380609i | ||||
\(386\) | −2.40560e6 | −0.821779 | ||||||||
\(387\) | − | 1.78385e6i | − | 0.605452i | ||||||
\(388\) | − | 5.67912e6i | − | 1.91515i | ||||||
\(389\) | 10040.7 | 0.00336428 | 0.00168214 | − | 0.999999i | \(-0.499465\pi\) | ||||
0.00168214 | + | 0.999999i | \(0.499465\pi\) | |||||||
\(390\) | −622905. | + | 1.43210e6i | −0.207377 | + | 0.476772i | ||||
\(391\) | 3.01778e6 | 0.998264 | ||||||||
\(392\) | − | 1.22984e6i | − | 0.404234i | ||||||
\(393\) | 608378.i | 0.198697i | ||||||||
\(394\) | 2.07199e6 | 0.672431 | ||||||||
\(395\) | −887550. | − | 386049.i | −0.286220 | − | 0.124494i | ||||
\(396\) | 407080. | 0.130449 | ||||||||
\(397\) | 3.77944e6i | 1.20352i | 0.798679 | + | 0.601758i | \(0.205533\pi\) | ||||
−0.798679 | + | 0.601758i | \(0.794467\pi\) | |||||||
\(398\) | 5.33176e6i | 1.68719i | ||||||||
\(399\) | −1.21093e6 | −0.380791 | ||||||||
\(400\) | −1.33803e6 | − | 1.43558e6i | −0.418135 | − | 0.448619i | ||||
\(401\) | −5.77840e6 | −1.79451 | −0.897256 | − | 0.441510i | \(-0.854443\pi\) | ||||
−0.897256 | + | 0.441510i | \(0.854443\pi\) | |||||||
\(402\) | − | 2.74143e6i | − | 0.846082i | ||||||
\(403\) | − | 239708.i | − | 0.0735226i | ||||||
\(404\) | −2.13392e6 | −0.650465 | ||||||||
\(405\) | −336333. | − | 146291.i | −0.101890 | − | 0.0443181i | ||||
\(406\) | 3.98863e6 | 1.20090 | ||||||||
\(407\) | 1.56383e6i | 0.467954i | ||||||||
\(408\) | 687287.i | 0.204403i | ||||||||
\(409\) | −4.93158e6 | −1.45773 | −0.728866 | − | 0.684656i | \(-0.759952\pi\) | ||||
−0.728866 | + | 0.684656i | \(0.759952\pi\) | |||||||
\(410\) | 485380. | − | 1.11592e6i | 0.142601 | − | 0.327848i | ||||
\(411\) | −1.85259e6 | −0.540972 | ||||||||
\(412\) | 3.94162e6i | 1.14401i | ||||||||
\(413\) | 1.38482e6i | 0.399501i | ||||||||
\(414\) | −2.24424e6 | −0.643530 | ||||||||
\(415\) | −1.98484e6 | + | 4.56327e6i | −0.565726 | + | 1.30064i | ||||
\(416\) | 2.89637e6 | 0.820580 | ||||||||
\(417\) | − | 391460.i | − | 0.110242i | ||||||
\(418\) | 782278.i | 0.218988i | ||||||||
\(419\) | 4.38879e6 | 1.22126 | 0.610632 | − | 0.791914i | \(-0.290915\pi\) | ||||
0.610632 | + | 0.791914i | \(0.290915\pi\) | |||||||
\(420\) | 3.41978e6 | + | 1.48747e6i | 0.945965 | + | 0.411457i | ||||
\(421\) | −6.32905e6 | −1.74034 | −0.870169 | − | 0.492754i | \(-0.835990\pi\) | ||||
−0.870169 | + | 0.492754i | \(0.835990\pi\) | |||||||
\(422\) | 3.82954e6i | 1.04681i | ||||||||
\(423\) | 1.68767e6i | 0.458602i | ||||||||
\(424\) | 2.24438e6 | 0.606293 | ||||||||
\(425\) | 2.13514e6 | − | 1.99006e6i | 0.573396 | − | 0.534433i | ||||
\(426\) | −4.83723e6 | −1.29144 | ||||||||
\(427\) | − | 6.86531e6i | − | 1.82218i | ||||||
\(428\) | − | 2.16946e6i | − | 0.572456i | ||||||
\(429\) | 394196. | 0.103412 | ||||||||
\(430\) | −9.68094e6 | − | 4.21082e6i | −2.52491 | − | 1.09824i | ||||
\(431\) | −4.39779e6 | −1.14036 | −0.570179 | − | 0.821520i | \(-0.693126\pi\) | ||||
−0.570179 | + | 0.821520i | \(0.693126\pi\) | |||||||
\(432\) | 457801.i | 0.118023i | ||||||||
\(433\) | − | 1.57360e6i | − | 0.403344i | −0.979453 | − | 0.201672i | \(-0.935362\pi\) | ||
0.979453 | − | 0.201672i | \(-0.0646375\pi\) | |||||||
\(434\) | −1.01343e6 | −0.258266 | ||||||||
\(435\) | −523025. | + | 1.20247e6i | −0.132526 | + | 0.304684i | ||||
\(436\) | 5.75475e6 | 1.44981 | ||||||||
\(437\) | − | 2.43595e6i | − | 0.610190i | ||||||
\(438\) | 5.32137e6i | 1.32537i | ||||||||
\(439\) | 7.89299e6 | 1.95470 | 0.977351 | − | 0.211626i | \(-0.0678759\pi\) | ||||
0.977351 | + | 0.211626i | \(0.0678759\pi\) | |||||||
\(440\) | 220588. | − | 507145.i | 0.0543188 | − | 0.124882i | ||||
\(441\) | 1.21839e6 | 0.298325 | ||||||||
\(442\) | 2.89920e6i | 0.705867i | ||||||||
\(443\) | − | 557226.i | − | 0.134903i | −0.997723 | − | 0.0674516i | \(-0.978513\pi\) | ||
0.997723 | − | 0.0674516i | \(-0.0214868\pi\) | |||||||
\(444\) | 4.83121e6 | 1.16305 | ||||||||
\(445\) | 6.64499e6 | + | 2.89031e6i | 1.59072 | + | 0.691901i | ||||
\(446\) | 256123. | 0.0609693 | ||||||||
\(447\) | − | 1.97420e6i | − | 0.467328i | ||||||
\(448\) | − | 8.65881e6i | − | 2.03828i | ||||||
\(449\) | −2.27558e6 | −0.532691 | −0.266346 | − | 0.963878i | \(-0.585816\pi\) | ||||
−0.266346 | + | 0.963878i | \(0.585816\pi\) | |||||||
\(450\) | −1.58785e6 | + | 1.47995e6i | −0.369639 | + | 0.344522i | ||||
\(451\) | −307166. | −0.0711101 | ||||||||
\(452\) | 5.67537e6i | 1.30662i | ||||||||
\(453\) | − | 296352.i | − | 0.0678521i | ||||||
\(454\) | −3.64845e6 | −0.830748 | ||||||||
\(455\) | 3.31154e6 | + | 1.44039e6i | 0.749897 | + | 0.326176i | ||||
\(456\) | 554779. | 0.124942 | ||||||||
\(457\) | − | 7.50427e6i | − | 1.68081i | −0.541961 | − | 0.840404i | \(-0.682318\pi\) | ||
0.541961 | − | 0.840404i | \(-0.317682\pi\) | |||||||
\(458\) | − | 1.13051e7i | − | 2.51833i | ||||||
\(459\) | −680889. | −0.150850 | ||||||||
\(460\) | −2.99225e6 | + | 6.87936e6i | −0.659330 | + | 1.51584i | ||||
\(461\) | 436978. | 0.0957652 | 0.0478826 | − | 0.998853i | \(-0.484753\pi\) | ||||
0.0478826 | + | 0.998853i | \(0.484753\pi\) | |||||||
\(462\) | − | 1.66656e6i | − | 0.363258i | ||||||
\(463\) | − | 3.11651e6i | − | 0.675642i | −0.941210 | − | 0.337821i | \(-0.890310\pi\) | ||
0.941210 | − | 0.337821i | \(-0.109690\pi\) | |||||||
\(464\) | 1.63674e6 | 0.352928 | ||||||||
\(465\) | 132889. | − | 305521.i | 0.0285009 | − | 0.0655252i | ||||
\(466\) | −2.74460e6 | −0.585484 | ||||||||
\(467\) | 1.89749e6i | 0.402613i | 0.979528 | + | 0.201307i | \(0.0645187\pi\) | ||||
−0.979528 | + | 0.201307i | \(0.935481\pi\) | |||||||
\(468\) | − | 1.21781e6i | − | 0.257019i | ||||||
\(469\) | −6.33922e6 | −1.33077 | ||||||||
\(470\) | 9.15898e6 | + | 3.98379e6i | 1.91251 | + | 0.831864i | ||||
\(471\) | 4.11562e6 | 0.854837 | ||||||||
\(472\) | − | 634444.i | − | 0.131081i | ||||||
\(473\) | 2.66476e6i | 0.547652i | ||||||||
\(474\) | 1.33623e6 | 0.273172 | ||||||||
\(475\) | −1.60638e6 | − | 1.72349e6i | −0.326673 | − | 0.350489i | ||||
\(476\) | 6.92317e6 | 1.40051 | ||||||||
\(477\) | 2.22349e6i | 0.447444i | ||||||||
\(478\) | 1.07648e7i | 2.15495i | ||||||||
\(479\) | 6.10287e6 | 1.21533 | 0.607666 | − | 0.794193i | \(-0.292106\pi\) | ||||
0.607666 | + | 0.794193i | \(0.292106\pi\) | |||||||
\(480\) | 3.69158e6 | + | 1.60569e6i | 0.731322 | + | 0.318096i | ||||
\(481\) | 4.67830e6 | 0.921987 | ||||||||
\(482\) | 9.24522e6i | 1.81259i | ||||||||
\(483\) | 5.18953e6i | 1.01219i | ||||||||
\(484\) | −608108. | −0.117996 | ||||||||
\(485\) | 3.04874e6 | − | 7.00924e6i | 0.588527 | − | 1.35306i | ||||
\(486\) | 506359. | 0.0972451 | ||||||||
\(487\) | 7.30170e6i | 1.39509i | 0.716542 | + | 0.697544i | \(0.245724\pi\) | ||||
−0.716542 | + | 0.697544i | \(0.754276\pi\) | |||||||
\(488\) | 3.14529e6i | 0.597876i | ||||||||
\(489\) | 475398. | 0.0899053 | ||||||||
\(490\) | 2.87604e6 | − | 6.61220e6i | 0.541134 | − | 1.24410i | ||||
\(491\) | 4.40884e6 | 0.825317 | 0.412658 | − | 0.910886i | \(-0.364600\pi\) | ||||
0.412658 | + | 0.910886i | \(0.364600\pi\) | |||||||
\(492\) | 948942.i | 0.176737i | ||||||||
\(493\) | 2.43433e6i | 0.451089i | ||||||||
\(494\) | 2.34024e6 | 0.431462 | ||||||||
\(495\) | 502423. | + | 218534.i | 0.0921630 | + | 0.0400873i | ||||
\(496\) | −415861. | −0.0759004 | ||||||||
\(497\) | 1.11855e7i | 2.03125i | ||||||||
\(498\) | − | 6.87014e6i | − | 1.24134i | ||||||
\(499\) | −3.45620e6 | −0.621367 | −0.310683 | − | 0.950513i | \(-0.600558\pi\) | ||||
−0.310683 | + | 0.950513i | \(0.600558\pi\) | |||||||
\(500\) | 2.41948e6 | + | 6.84051e6i | 0.432810 | + | 1.22367i | ||||
\(501\) | −2.94845e6 | −0.524808 | ||||||||
\(502\) | 7.87871e6i | 1.39539i | ||||||||
\(503\) | 5.07651e6i | 0.894634i | 0.894375 | + | 0.447317i | \(0.147620\pi\) | ||||
−0.894375 | + | 0.447317i | \(0.852380\pi\) | |||||||
\(504\) | −1.18190e6 | −0.207254 | ||||||||
\(505\) | −2.63370e6 | − | 1.14556e6i | −0.459556 | − | 0.199889i | ||||
\(506\) | 3.35251e6 | 0.582095 | ||||||||
\(507\) | 2.16237e6i | 0.373603i | ||||||||
\(508\) | 992212.i | 0.170587i | ||||||||
\(509\) | −7.63894e6 | −1.30689 | −0.653445 | − | 0.756974i | \(-0.726677\pi\) | ||||
−0.653445 | + | 0.756974i | \(0.726677\pi\) | |||||||
\(510\) | −1.60726e6 | + | 3.69518e6i | −0.273628 | + | 0.629087i | ||||
\(511\) | 1.23050e7 | 2.08463 | ||||||||
\(512\) | − | 6.66784e6i | − | 1.12411i | ||||||
\(513\) | 549614.i | 0.0922071i | ||||||||
\(514\) | −6.83750e6 | −1.14154 | ||||||||
\(515\) | −2.11599e6 | + | 4.86479e6i | −0.351557 | + | 0.808251i | ||||
\(516\) | 8.23237e6 | 1.36113 | ||||||||
\(517\) | − | 2.52109e6i | − | 0.414821i | ||||||
\(518\) | − | 1.97786e7i | − | 3.23871i | ||||||
\(519\) | −2.21748e6 | −0.361362 | ||||||||
\(520\) | −1.51716e6 | − | 659904.i | −0.246050 | − | 0.107022i | ||||
\(521\) | −9.46786e6 | −1.52812 | −0.764060 | − | 0.645145i | \(-0.776797\pi\) | ||||
−0.764060 | + | 0.645145i | \(0.776797\pi\) | |||||||
\(522\) | − | 1.81035e6i | − | 0.290794i | ||||||
\(523\) | − | 1.12533e6i | − | 0.179898i | −0.995946 | − | 0.0899490i | \(-0.971330\pi\) | ||
0.995946 | − | 0.0899490i | \(-0.0286704\pi\) | |||||||
\(524\) | −2.80764e6 | −0.446696 | ||||||||
\(525\) | 3.42221e6 | + | 3.67170e6i | 0.541887 | + | 0.581392i | ||||
\(526\) | −8.40855e6 | −1.32512 | ||||||||
\(527\) | − | 618511.i | − | 0.0970110i | ||||||
\(528\) | − | 683876.i | − | 0.106756i | ||||||
\(529\) | −4.00311e6 | −0.621953 | ||||||||
\(530\) | 1.20669e7 | + | 5.24861e6i | 1.86597 | + | 0.811624i | ||||
\(531\) | 628537. | 0.0967374 | ||||||||
\(532\) | − | 5.58839e6i | − | 0.856067i | ||||||
\(533\) | 918907.i | 0.140105i | ||||||||
\(534\) | −1.00042e7 | −1.51820 | ||||||||
\(535\) | 1.16464e6 | − | 2.67757e6i | 0.175916 | − | 0.404442i | ||||
\(536\) | 2.90427e6 | 0.436641 | ||||||||
\(537\) | − | 2.72107e6i | − | 0.407196i | ||||||
\(538\) | − | 1.13311e7i | − | 1.68778i | ||||||
\(539\) | −1.82006e6 | −0.269845 | ||||||||
\(540\) | 675128. | − | 1.55216e6i | 0.0996327 | − | 0.229062i | ||||
\(541\) | 1.05433e7 | 1.54876 | 0.774379 | − | 0.632722i | \(-0.218062\pi\) | ||||
0.774379 | + | 0.632722i | \(0.218062\pi\) | |||||||
\(542\) | 539078.i | 0.0788230i | ||||||||
\(543\) | − | 4.18837e6i | − | 0.609600i | ||||||
\(544\) | 7.47341e6 | 1.08273 | ||||||||
\(545\) | 7.10258e6 | + | 3.08934e6i | 1.02429 | + | 0.445527i | ||||
\(546\) | −4.98562e6 | −0.715711 | ||||||||
\(547\) | − | 9.65329e6i | − | 1.37945i | −0.724070 | − | 0.689727i | \(-0.757731\pi\) | ||
0.724070 | − | 0.689727i | \(-0.242269\pi\) | |||||||
\(548\) | − | 8.54962e6i | − | 1.21617i | ||||||
\(549\) | −3.11601e6 | −0.441232 | ||||||||
\(550\) | 2.37197e6 | − | 2.21080e6i | 0.334351 | − | 0.311632i | ||||
\(551\) | 1.96499e6 | 0.275729 | ||||||||
\(552\) | − | 2.37754e6i | − | 0.332109i | ||||||
\(553\) | − | 3.08987e6i | − | 0.429662i | ||||||
\(554\) | −1.23752e7 | −1.71308 | ||||||||
\(555\) | 5.96273e6 | + | 2.59355e6i | 0.821699 | + | 0.357406i | ||||
\(556\) | 1.80657e6 | 0.247838 | ||||||||
\(557\) | − | 4.21289e6i | − | 0.575363i | −0.957726 | − | 0.287682i | \(-0.907115\pi\) | ||
0.957726 | − | 0.287682i | \(-0.0928845\pi\) | |||||||
\(558\) | 459970.i | 0.0625381i | ||||||||
\(559\) | 7.97180e6 | 1.07901 | ||||||||
\(560\) | 2.49888e6 | − | 5.74507e6i | 0.336725 | − | 0.774150i | ||||
\(561\) | 1.01713e6 | 0.136449 | ||||||||
\(562\) | 1.23431e6i | 0.164848i | ||||||||
\(563\) | 9.59902e6i | 1.27631i | 0.769908 | + | 0.638155i | \(0.220302\pi\) | ||||
−0.769908 | + | 0.638155i | \(0.779698\pi\) | |||||||
\(564\) | −7.78851e6 | −1.03100 | ||||||||
\(565\) | −3.04673e6 | + | 7.00461e6i | −0.401525 | + | 0.923129i | ||||
\(566\) | −77692.6 | −0.0101939 | ||||||||
\(567\) | − | 1.17089e6i | − | 0.152953i | ||||||
\(568\) | − | 5.12455e6i | − | 0.666477i | ||||||
\(569\) | −4.20682e6 | −0.544720 | −0.272360 | − | 0.962195i | \(-0.587804\pi\) | ||||
−0.272360 | + | 0.962195i | \(0.587804\pi\) | |||||||
\(570\) | 2.98276e6 | + | 1.29738e6i | 0.384530 | + | 0.167255i | ||||
\(571\) | −1.22447e7 | −1.57165 | −0.785826 | − | 0.618447i | \(-0.787762\pi\) | ||||
−0.785826 | + | 0.618447i | \(0.787762\pi\) | |||||||
\(572\) | 1.81920e6i | 0.232482i | ||||||||
\(573\) | 2.64764e6i | 0.336878i | ||||||||
\(574\) | 3.88490e6 | 0.492153 | ||||||||
\(575\) | −7.38613e6 | + | 6.88424e6i | −0.931638 | + | 0.868334i | ||||
\(576\) | −3.93004e6 | −0.493561 | ||||||||
\(577\) | − | 5.32012e6i | − | 0.665245i | −0.943060 | − | 0.332623i | \(-0.892066\pi\) | ||
0.943060 | − | 0.332623i | \(-0.107934\pi\) | |||||||
\(578\) | − | 4.69489e6i | − | 0.584529i | ||||||
\(579\) | 2.52476e6 | 0.312985 | ||||||||
\(580\) | −5.54933e6 | − | 2.41374e6i | −0.684968 | − | 0.297934i | ||||
\(581\) | −1.58863e7 | −1.95247 | ||||||||
\(582\) | 1.05526e7i | 1.29137i | ||||||||
\(583\) | − | 3.32151e6i | − | 0.404728i | ||||||
\(584\) | −5.63745e6 | −0.683992 | ||||||||
\(585\) | 653760. | − | 1.50303e6i | 0.0789821 | − | 0.181585i | ||||
\(586\) | −1.59220e7 | −1.91537 | ||||||||
\(587\) | 5.70534e6i | 0.683418i | 0.939806 | + | 0.341709i | \(0.111006\pi\) | ||||
−0.939806 | + | 0.341709i | \(0.888994\pi\) | |||||||
\(588\) | 5.62280e6i | 0.670671i | ||||||||
\(589\) | −499263. | −0.0592981 | ||||||||
\(590\) | 1.48368e6 | − | 3.41107e6i | 0.175473 | − | 0.403423i | ||||
\(591\) | −2.17463e6 | −0.256104 | ||||||||
\(592\) | − | 8.11620e6i | − | 0.951806i | ||||||
\(593\) | 2.15575e6i | 0.251746i | 0.992046 | + | 0.125873i | \(0.0401731\pi\) | ||||
−0.992046 | + | 0.125873i | \(0.959827\pi\) | |||||||
\(594\) | −756413. | −0.0879615 | ||||||||
\(595\) | 8.54466e6 | + | 3.71659e6i | 0.989469 | + | 0.430380i | ||||
\(596\) | 9.11083e6 | 1.05061 | ||||||||
\(597\) | − | 5.59587e6i | − | 0.642587i | ||||||
\(598\) | − | 1.00293e7i | − | 1.14687i | ||||||
\(599\) | −5.13968e6 | −0.585287 | −0.292643 | − | 0.956222i | \(-0.594535\pi\) | ||||
−0.292643 | + | 0.956222i | \(0.594535\pi\) | |||||||
\(600\) | −1.56786e6 | − | 1.68216e6i | −0.177799 | − | 0.190761i | ||||
\(601\) | −7.48666e6 | −0.845478 | −0.422739 | − | 0.906252i | \(-0.638931\pi\) | ||||
−0.422739 | + | 0.906252i | \(0.638931\pi\) | |||||||
\(602\) | − | 3.37027e7i | − | 3.79030i | ||||||
\(603\) | 2.87723e6i | 0.322241i | ||||||||
\(604\) | 1.36765e6 | 0.152540 | ||||||||
\(605\) | −750533. | − | 326452.i | −0.0833646 | − | 0.0362603i | ||||
\(606\) | 3.96512e6 | 0.438606 | ||||||||
\(607\) | 8.62794e6i | 0.950464i | 0.879861 | + | 0.475232i | \(0.157636\pi\) | ||||
−0.879861 | + | 0.475232i | \(0.842364\pi\) | |||||||
\(608\) | − | 6.03254e6i | − | 0.661822i | ||||||
\(609\) | −4.18620e6 | −0.457380 | ||||||||
\(610\) | −7.35543e6 | + | 1.69106e7i | −0.800356 | + | 1.84007i | ||||
\(611\) | −7.54200e6 | −0.817304 | ||||||||
\(612\) | − | 3.14227e6i | − | 0.339129i | ||||||
\(613\) | − | 1.44646e7i | − | 1.55473i | −0.629047 | − | 0.777367i | \(-0.716555\pi\) | ||
0.629047 | − | 0.777367i | \(-0.283445\pi\) | |||||||
\(614\) | 4.32782e6 | 0.463285 | ||||||||
\(615\) | −509423. | + | 1.17119e6i | −0.0543114 | + | 0.124865i | ||||
\(616\) | 1.76555e6 | 0.187468 | ||||||||
\(617\) | − | 5.82746e6i | − | 0.616264i | −0.951344 | − | 0.308132i | \(-0.900296\pi\) | ||
0.951344 | − | 0.308132i | \(-0.0997038\pi\) | |||||||
\(618\) | − | 7.32408e6i | − | 0.771404i | ||||||
\(619\) | 2.32647e6 | 0.244045 | 0.122023 | − | 0.992527i | \(-0.461062\pi\) | ||||
0.122023 | + | 0.992527i | \(0.461062\pi\) | |||||||
\(620\) | 1.40996e6 | + | 613279.i | 0.147309 | + | 0.0640735i | ||||
\(621\) | 2.35541e6 | 0.245097 | ||||||||
\(622\) | 3.84609e6i | 0.398605i | ||||||||
\(623\) | 2.31335e7i | 2.38793i | ||||||||
\(624\) | −2.04586e6 | −0.210337 | ||||||||
\(625\) | −686064. | + | 9.74150e6i | −0.0702529 | + | 0.997529i | ||||
\(626\) | 7.07582e6 | 0.721674 | ||||||||
\(627\) | − | 821028.i | − | 0.0834044i | ||||||
\(628\) | 1.89934e7i | 1.92178i | ||||||||
\(629\) | 1.20712e7 | 1.21654 | ||||||||
\(630\) | −6.35443e6 | − | 2.76393e6i | −0.637860 | − | 0.277444i | ||||
\(631\) | −398154. | −0.0398087 | −0.0199043 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199043 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 1.41560e6i | 0.140977i | ||||||||
\(633\) | − | 4.01924e6i | − | 0.398689i | ||||||
\(634\) | −2.79781e7 | −2.76436 | ||||||||
\(635\) | −532652. | + | 1.22460e6i | −0.0524215 | + | 0.120520i | ||||
\(636\) | −1.02613e7 | −1.00591 | ||||||||
\(637\) | 5.44484e6i | 0.531663i | ||||||||
\(638\) | 2.70435e6i | 0.263033i | ||||||||
\(639\) | 5.07684e6 | 0.491860 | ||||||||
\(640\) | −3.56786e6 | + | 8.20272e6i | −0.344316 | + | 0.791604i | ||||
\(641\) | 1.81586e7 | 1.74557 | 0.872784 | − | 0.488107i | \(-0.162312\pi\) | ||||
0.872784 | + | 0.488107i | \(0.162312\pi\) | |||||||
\(642\) | 4.03116e6i | 0.386005i | ||||||||
\(643\) | − | 4.48264e6i | − | 0.427569i | −0.976881 | − | 0.213784i | \(-0.931421\pi\) | ||
0.976881 | − | 0.213784i | \(-0.0685790\pi\) | |||||||
\(644\) | −2.39494e7 | −2.27552 | ||||||||
\(645\) | 1.01605e7 | + | 4.41940e6i | 0.961645 | + | 0.418277i | ||||
\(646\) | 6.03844e6 | 0.569303 | ||||||||
\(647\) | − | 1.75122e7i | − | 1.64467i | −0.569003 | − | 0.822336i | \(-0.692671\pi\) | ||
0.569003 | − | 0.822336i | \(-0.307329\pi\) | |||||||
\(648\) | 536435.i | 0.0501857i | ||||||||
\(649\) | −938925. | −0.0875023 | ||||||||
\(650\) | −6.61375e6 | − | 7.09591e6i | −0.613994 | − | 0.658757i | ||||
\(651\) | 1.06362e6 | 0.0983639 | ||||||||
\(652\) | 2.19394e6i | 0.202118i | ||||||||
\(653\) | − | 1.89639e7i | − | 1.74039i | −0.492711 | − | 0.870193i | \(-0.663994\pi\) | ||
0.492711 | − | 0.870193i | \(-0.336006\pi\) | |||||||
\(654\) | −1.06931e7 | −0.977599 | ||||||||
\(655\) | −3.46521e6 | − | 1.50723e6i | −0.315593 | − | 0.137270i | ||||
\(656\) | 1.59418e6 | 0.144636 | ||||||||
\(657\) | − | 5.58496e6i | − | 0.504786i | ||||||
\(658\) | 3.18856e7i | 2.87098i | ||||||||
\(659\) | −23732.7 | −0.00212879 | −0.00106440 | − | 0.999999i | \(-0.500339\pi\) | ||||
−0.00106440 | + | 0.999999i | \(0.500339\pi\) | |||||||
\(660\) | −1.00852e6 | + | 2.31866e6i | −0.0901212 | + | 0.207194i | ||||
\(661\) | 1.09938e7 | 0.978686 | 0.489343 | − | 0.872091i | \(-0.337237\pi\) | ||||
0.489343 | + | 0.872091i | \(0.337237\pi\) | |||||||
\(662\) | 2.98568e7i | 2.64788i | ||||||||
\(663\) | − | 3.04281e6i | − | 0.268839i | ||||||
\(664\) | 7.27821e6 | 0.640626 | ||||||||
\(665\) | 3.00003e6 | − | 6.89725e6i | 0.263070 | − | 0.604814i | ||||
\(666\) | −8.97706e6 | −0.784239 | ||||||||
\(667\) | − | 8.42112e6i | − | 0.732918i | ||||||
\(668\) | − | 1.36070e7i | − | 1.17983i | ||||||
\(669\) | −268810. | −0.0232209 | ||||||||
\(670\) | 1.56147e7 | + | 6.79179e6i | 1.34384 | + | 0.584517i | ||||
\(671\) | 4.65477e6 | 0.399110 | ||||||||
\(672\) | 1.28517e7i | 1.09783i | ||||||||
\(673\) | 1.19040e6i | 0.101310i | 0.998716 | + | 0.0506552i | \(0.0161310\pi\) | ||||
−0.998716 | + | 0.0506552i | \(0.983869\pi\) | |||||||
\(674\) | 1.30994e7 | 1.11072 | ||||||||
\(675\) | 1.66650e6 | − | 1.55326e6i | 0.140782 | − | 0.131216i | ||||
\(676\) | −9.97925e6 | −0.839907 | ||||||||
\(677\) | 2.03890e7i | 1.70972i | 0.518859 | + | 0.854860i | \(0.326357\pi\) | ||||
−0.518859 | + | 0.854860i | \(0.673643\pi\) | |||||||
\(678\) | − | 1.05456e7i | − | 0.881046i | ||||||
\(679\) | 2.44016e7 | 2.03116 | ||||||||
\(680\) | −3.91467e6 | − | 1.70273e6i | −0.324656 | − | 0.141212i | ||||
\(681\) | 3.82918e6 | 0.316401 | ||||||||
\(682\) | − | 687116.i | − | 0.0565678i | ||||||
\(683\) | − | 2.37020e7i | − | 1.94416i | −0.234640 | − | 0.972082i | \(-0.575391\pi\) | ||
0.234640 | − | 0.972082i | \(-0.424609\pi\) | |||||||
\(684\) | −2.53644e6 | −0.207293 | ||||||||
\(685\) | 4.58972e6 | − | 1.05520e7i | 0.373731 | − | 0.859231i | ||||
\(686\) | −2.70134e6 | −0.219164 | ||||||||
\(687\) | 1.18651e7i | 0.959137i | ||||||||
\(688\) | − | 1.38300e7i | − | 1.11391i | ||||||
\(689\) | −9.93651e6 | −0.797418 | ||||||||
\(690\) | 5.56002e6 | − | 1.27828e7i | 0.444583 | − | 1.02212i | ||||
\(691\) | −1.32012e7 | −1.05176 | −0.525881 | − | 0.850558i | \(-0.676264\pi\) | ||||
−0.525881 | + | 0.850558i | \(0.676264\pi\) | |||||||
\(692\) | − | 1.02336e7i | − | 0.812387i | ||||||
\(693\) | 1.74911e6i | 0.138352i | ||||||||
\(694\) | 3.44278e7 | 2.71338 | ||||||||
\(695\) | 2.22969e6 | + | 969826.i | 0.175098 | + | 0.0761608i | ||||
\(696\) | 1.91788e6 | 0.150071 | ||||||||
\(697\) | 2.37102e6i | 0.184865i | ||||||||
\(698\) | − | 4.38604e6i | − | 0.340749i | ||||||
\(699\) | 2.88056e6 | 0.222989 | ||||||||
\(700\) | −1.69447e7 | + | 1.57933e7i | −1.30704 | + | 1.21823i | ||||
\(701\) | 9.76550e6 | 0.750584 | 0.375292 | − | 0.926907i | \(-0.377542\pi\) | ||||
0.375292 | + | 0.926907i | \(0.377542\pi\) | |||||||
\(702\) | 2.26286e6i | 0.173306i | ||||||||
\(703\) | − | 9.74392e6i | − | 0.743610i | ||||||
\(704\) | 5.87080e6 | 0.446442 | ||||||||
\(705\) | −9.61267e6 | − | 4.18113e6i | −0.728402 | − | 0.316826i | ||||
\(706\) | −6.19677e6 | −0.467900 | ||||||||
\(707\) | − | 9.16884e6i | − | 0.689868i | ||||||
\(708\) | 2.90067e6i | 0.217478i | ||||||||
\(709\) | 6.77780e6 | 0.506376 | 0.253188 | − | 0.967417i | \(-0.418521\pi\) | ||||
0.253188 | + | 0.967417i | \(0.418521\pi\) | |||||||
\(710\) | 1.19840e7 | − | 2.75520e7i | 0.892190 | − | 2.05120i | ||||
\(711\) | −1.40242e6 | −0.104041 | ||||||||
\(712\) | − | 1.05985e7i | − | 0.783506i | ||||||
\(713\) | 2.13963e6i | 0.157621i | ||||||||
\(714\) | −1.28642e7 | −0.944361 | ||||||||
\(715\) | −976604. | + | 2.24527e6i | −0.0714420 | + | 0.164249i | ||||
\(716\) | 1.25576e7 | 0.915429 | ||||||||
\(717\) | − | 1.12980e7i | − | 0.820739i | ||||||
\(718\) | 3.37302e6i | 0.244179i | ||||||||
\(719\) | 9.77686e6 | 0.705305 | 0.352653 | − | 0.935754i | \(-0.385280\pi\) | ||||
0.352653 | + | 0.935754i | \(0.385280\pi\) | |||||||
\(720\) | −2.60756e6 | − | 1.13418e6i | −0.187457 | − | 0.0815365i | ||||
\(721\) | −1.69360e7 | −1.21331 | ||||||||
\(722\) | 1.63589e7i | 1.16791i | ||||||||
\(723\) | − | 9.70317e6i | − | 0.690348i | ||||||
\(724\) | 1.93291e7 | 1.37046 | ||||||||
\(725\) | −5.55327e6 | − | 5.95812e6i | −0.392377 | − | 0.420983i | ||||
\(726\) | 1.12995e6 | 0.0795642 | ||||||||
\(727\) | 1.13969e7i | 0.799745i | 0.916571 | + | 0.399873i | \(0.130946\pi\) | ||||
−0.916571 | + | 0.399873i | \(0.869054\pi\) | |||||||
\(728\) | − | 5.28176e6i | − | 0.369360i | ||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | −3.03096e7 | − | 1.31835e7i | −2.10510 | − | 0.915636i | ||||
\(731\) | 2.05694e7 | 1.42373 | ||||||||
\(732\) | − | 1.43802e7i | − | 0.991946i | ||||||
\(733\) | − | 6.58492e6i | − | 0.452679i | −0.974048 | − | 0.226340i | \(-0.927324\pi\) | ||
0.974048 | − | 0.226340i | \(-0.0726759\pi\) | |||||||
\(734\) | 2.46605e7 | 1.68951 | ||||||||
\(735\) | −3.01851e6 | + | 6.93973e6i | −0.206098 | + | 0.473832i | ||||
\(736\) | −2.58529e7 | −1.75920 | ||||||||
\(737\) | − | 4.29808e6i | − | 0.291478i | ||||||
\(738\) | − | 1.76327e6i | − | 0.119173i | ||||||
\(739\) | 1.51924e7 | 1.02333 | 0.511664 | − | 0.859186i | \(-0.329029\pi\) | ||||
0.511664 | + | 0.859186i | \(0.329029\pi\) | |||||||
\(740\) | −1.19691e7 | + | 2.75177e7i | −0.803494 | + | 1.84728i | ||||
\(741\) | −2.45616e6 | −0.164328 | ||||||||
\(742\) | 4.20090e7i | 2.80112i | ||||||||
\(743\) | − | 6.92543e6i | − | 0.460230i | −0.973163 | − | 0.230115i | \(-0.926090\pi\) | ||
0.973163 | − | 0.230115i | \(-0.0739102\pi\) | |||||||
\(744\) | −487292. | −0.0322743 | ||||||||
\(745\) | 1.12447e7 | + | 4.89100e6i | 0.742261 | + | 0.322854i | ||||
\(746\) | 3.31030e7 | 2.17781 | ||||||||
\(747\) | 7.21045e6i | 0.472782i | ||||||||
\(748\) | 4.69401e6i | 0.306754i | ||||||||
\(749\) | 9.32156e6 | 0.607133 | ||||||||
\(750\) | −4.49573e6 | − | 1.27106e7i | −0.291842 | − | 0.825114i | ||||
\(751\) | −1.53073e7 | −0.990370 | −0.495185 | − | 0.868788i | \(-0.664900\pi\) | ||||
−0.495185 | + | 0.868788i | \(0.664900\pi\) | |||||||
\(752\) | 1.30843e7i | 0.843737i | ||||||||
\(753\) | − | 8.26898e6i | − | 0.531452i | ||||||
\(754\) | 8.09024e6 | 0.518242 | ||||||||
\(755\) | 1.68797e6 | + | 734201.i | 0.107770 | + | 0.0468757i | ||||
\(756\) | 5.40361e6 | 0.343858 | ||||||||
\(757\) | − | 9.00842e6i | − | 0.571359i | −0.958325 | − | 0.285679i | \(-0.907781\pi\) | ||
0.958325 | − | 0.285679i | \(-0.0922193\pi\) | |||||||
\(758\) | − | 1.40080e7i | − | 0.885531i | ||||||
\(759\) | −3.51857e6 | −0.221698 | ||||||||
\(760\) | −1.37444e6 | + | 3.15993e6i | −0.0863162 | + | 0.198446i | ||||
\(761\) | 1.62103e7 | 1.01468 | 0.507339 | − | 0.861746i | \(-0.330629\pi\) | ||||
0.507339 | + | 0.861746i | \(0.330629\pi\) | |||||||
\(762\) | − | 1.84367e6i | − | 0.115026i | ||||||
\(763\) | 2.47265e7i | 1.53763i | ||||||||
\(764\) | −1.22187e7 | −0.757343 | ||||||||
\(765\) | 1.68687e6 | − | 3.87822e6i | 0.104215 | − | 0.239596i | ||||
\(766\) | 3.31740e7 | 2.04280 | ||||||||
\(767\) | 2.80886e6i | 0.172402i | ||||||||
\(768\) | 1.62404e6i | 0.0993558i | ||||||||
\(769\) | −1.67909e7 | −1.02390 | −0.511950 | − | 0.859015i | \(-0.671077\pi\) | ||||
−0.511950 | + | 0.859015i | \(0.671077\pi\) | |||||||
\(770\) | 9.49243e6 | + | 4.12883e6i | 0.576966 | + | 0.250957i | ||||
\(771\) | 7.17619e6 | 0.434768 | ||||||||
\(772\) | 1.16516e7i | 0.703629i | ||||||||
\(773\) | 1.62605e7i | 0.978780i | 0.872065 | + | 0.489390i | \(0.162781\pi\) | ||||
−0.872065 | + | 0.489390i | \(0.837219\pi\) | |||||||
\(774\) | −1.52969e7 | −0.917806 | ||||||||
\(775\) | 1.41097e6 | + | 1.51383e6i | 0.0843844 | + | 0.0905364i | ||||
\(776\) | −1.11794e7 | −0.666445 | ||||||||
\(777\) | 2.07583e7i | 1.23350i | ||||||||
\(778\) | − | 86101.7i | − | 0.00509991i | ||||||
\(779\) | 1.91389e6 | 0.112999 | ||||||||
\(780\) | 6.93643e6 | + | 3.01707e6i | 0.408225 | + | 0.177562i | ||||
\(781\) | −7.58393e6 | −0.444904 | ||||||||
\(782\) | − | 2.58781e7i | − | 1.51327i | ||||||
\(783\) | 1.90002e6i | 0.110753i | ||||||||
\(784\) | 9.44604e6 | 0.548858 | ||||||||
\(785\) | −1.01963e7 | + | 2.34419e7i | −0.590565 | + | 1.35775i | ||||
\(786\) | 5.21698e6 | 0.301205 | ||||||||
\(787\) | 5.01128e6i | 0.288411i | 0.989548 | + | 0.144206i | \(0.0460626\pi\) | ||||
−0.989548 | + | 0.144206i | \(0.953937\pi\) | |||||||
\(788\) | − | 1.00358e7i | − | 0.575753i | ||||||
\(789\) | 8.82506e6 | 0.504691 | ||||||||
\(790\) | −3.31046e6 | + | 7.61094e6i | −0.188721 | + | 0.433881i | ||||
\(791\) | −2.43855e7 | −1.38577 | ||||||||
\(792\) | − | 801342.i | − | 0.0453947i | ||||||
\(793\) | − | 1.39251e7i | − | 0.786348i | ||||||
\(794\) | 3.24096e7 | 1.82441 | ||||||||
\(795\) | −1.26646e7 | − | 5.50860e6i | −0.710679 | − | 0.309117i | ||||
\(796\) | 2.58247e7 | 1.44461 | ||||||||
\(797\) | − | 3.07160e7i | − | 1.71285i | −0.516273 | − | 0.856424i | \(-0.672681\pi\) | ||
0.516273 | − | 0.856424i | \(-0.327319\pi\) | |||||||
\(798\) | 1.03840e7i | 0.577242i | ||||||||
\(799\) | −1.94604e7 | −1.07841 | ||||||||
\(800\) | −1.82915e7 | + | 1.70486e7i | −1.01047 | + | 0.941809i | ||||
\(801\) | 1.04998e7 | 0.578227 | ||||||||
\(802\) | 4.95511e7i | 2.72030i | ||||||||
\(803\) | 8.34297e6i | 0.456596i | ||||||||
\(804\) | −1.32783e7 | −0.724438 | ||||||||
\(805\) | −2.95587e7 | − | 1.28568e7i | −1.60766 | − | 0.699270i | ||||
\(806\) | −2.05556e6 | −0.111453 | ||||||||
\(807\) | 1.18924e7i | 0.642812i | ||||||||
\(808\) | 4.20064e6i | 0.226353i | ||||||||
\(809\) | −6.14509e6 | −0.330108 | −0.165054 | − | 0.986284i | \(-0.552780\pi\) | ||||
−0.165054 | + | 0.986284i | \(0.552780\pi\) | |||||||
\(810\) | −1.25448e6 | + | 2.88413e6i | −0.0671819 | + | 0.154455i | ||||
\(811\) | −1.46687e7 | −0.783138 | −0.391569 | − | 0.920149i | \(-0.628068\pi\) | ||||
−0.391569 | + | 0.920149i | \(0.628068\pi\) | |||||||
\(812\) | − | 1.93191e7i | − | 1.02825i | ||||||
\(813\) | − | 565780.i | − | 0.0300208i | ||||||
\(814\) | 1.34102e7 | 0.709371 | ||||||||
\(815\) | −1.17778e6 | + | 2.70779e6i | −0.0621112 | + | 0.142797i | ||||
\(816\) | −5.27886e6 | −0.277533 | ||||||||
\(817\) | − | 1.66036e7i | − | 0.870257i | ||||||
\(818\) | 4.22894e7i | 2.20978i | ||||||||
\(819\) | 5.23258e6 | 0.272588 | ||||||||
\(820\) | −5.40501e6 | − | 2.35096e6i | −0.280713 | − | 0.122099i | ||||
\(821\) | −1.54951e7 | −0.802300 | −0.401150 | − | 0.916012i | \(-0.631389\pi\) | ||||
−0.401150 | + | 0.916012i | \(0.631389\pi\) | |||||||
\(822\) | 1.58864e7i | 0.820060i | ||||||||
\(823\) | 2.53285e7i | 1.30349i | 0.758436 | + | 0.651747i | \(0.225964\pi\) | ||||
−0.758436 | + | 0.651747i | \(0.774036\pi\) | |||||||
\(824\) | 7.75912e6 | 0.398102 | ||||||||
\(825\) | −2.48947e6 | + | 2.32031e6i | −0.127342 | + | 0.118689i | ||||
\(826\) | 1.18751e7 | 0.605603 | ||||||||
\(827\) | 6.01962e6i | 0.306059i | 0.988222 | + | 0.153030i | \(0.0489030\pi\) | ||||
−0.988222 | + | 0.153030i | \(0.951097\pi\) | |||||||
\(828\) | 1.08701e7i | 0.551008i | ||||||||
\(829\) | 2.70703e7 | 1.36807 | 0.684033 | − | 0.729451i | \(-0.260225\pi\) | ||||
0.684033 | + | 0.729451i | \(0.260225\pi\) | |||||||
\(830\) | 3.91311e7 | + | 1.70205e7i | 1.97164 | + | 0.857584i | ||||
\(831\) | 1.29882e7 | 0.652449 | ||||||||
\(832\) | − | 1.75629e7i | − | 0.879605i | ||||||
\(833\) | 1.40491e7i | 0.701514i | ||||||||
\(834\) | −3.35686e6 | −0.167116 | ||||||||
\(835\) | 7.30467e6 | − | 1.67939e7i | 0.362564 | − | 0.833556i | ||||
\(836\) | 3.78901e6 | 0.187504 | ||||||||
\(837\) | − | 482755.i | − | 0.0238184i | ||||||
\(838\) | − | 3.76349e7i | − | 1.85132i | ||||||
\(839\) | −2.29868e7 | −1.12739 | −0.563694 | − | 0.825984i | \(-0.690620\pi\) | ||||
−0.563694 | + | 0.825984i | \(0.690620\pi\) | |||||||
\(840\) | 2.92810e6 | − | 6.73187e6i | 0.143182 | − | 0.329183i | ||||
\(841\) | −1.37181e7 | −0.668814 | ||||||||
\(842\) | 5.42731e7i | 2.63818i | ||||||||
\(843\) | − | 1.29546e6i | − | 0.0627847i | ||||||
\(844\) | 1.85486e7 | 0.896303 | ||||||||
\(845\) | −1.23165e7 | − | 5.35719e6i | −0.593397 | − | 0.258104i | ||||
\(846\) | 1.44721e7 | 0.695196 | ||||||||
\(847\) | − | 2.61287e6i | − | 0.125144i | ||||||
\(848\) | 1.72385e7i | 0.823208i | ||||||||
\(849\) | 81541.1 | 0.00388246 | ||||||||
\(850\) | −1.70652e7 | − | 1.83093e7i | −0.810148 | − | 0.869211i | ||||
\(851\) | −4.17582e7 | −1.97660 | ||||||||
\(852\) | 2.34294e7i | 1.10576i | ||||||||
\(853\) | − | 3.27587e7i | − | 1.54154i | −0.637116 | − | 0.770768i | \(-0.719873\pi\) | ||
0.637116 | − | 0.770768i | \(-0.280127\pi\) | |||||||
\(854\) | −5.88716e7 | −2.76224 | ||||||||
\(855\) | −3.13051e6 | − | 1.36165e6i | −0.146453 | − | 0.0637014i | ||||
\(856\) | −4.27060e6 | −0.199207 | ||||||||
\(857\) | 5.91710e6i | 0.275205i | 0.990488 | + | 0.137603i | \(0.0439397\pi\) | ||||
−0.990488 | + | 0.137603i | \(0.956060\pi\) | |||||||
\(858\) | − | 3.38032e6i | − | 0.156762i | ||||||
\(859\) | 3.88859e7 | 1.79808 | 0.899041 | − | 0.437865i | \(-0.144265\pi\) | ||||
0.899041 | + | 0.437865i | \(0.144265\pi\) | |||||||
\(860\) | −2.03953e7 | + | 4.68901e7i | −0.940340 | + | 2.16190i | ||||
\(861\) | −4.07734e6 | −0.187443 | ||||||||
\(862\) | 3.77121e7i | 1.72867i | ||||||||
\(863\) | 7.21944e6i | 0.329972i | 0.986296 | + | 0.164986i | \(0.0527579\pi\) | ||||
−0.986296 | + | 0.164986i | \(0.947242\pi\) | |||||||
\(864\) | 5.83308e6 | 0.265836 | ||||||||
\(865\) | 5.49373e6 | − | 1.26304e7i | 0.249647 | − | 0.573954i | ||||
\(866\) | −1.34940e7 | −0.611430 | ||||||||
\(867\) | 4.92745e6i | 0.222625i | ||||||||
\(868\) | 4.90858e6i | 0.221134i | ||||||||
\(869\) | 2.09497e6 | 0.0941086 | ||||||||
\(870\) | 1.03114e7 | + | 4.48506e6i | 0.461871 | + | 0.200896i | ||||
\(871\) | −1.28580e7 | −0.574286 | ||||||||
\(872\) | − | 1.13283e7i | − | 0.504514i | ||||||
\(873\) | − | 1.10753e7i | − | 0.491837i | ||||||
\(874\) | −2.08889e7 | −0.924988 | ||||||||
\(875\) | −2.93918e7 | + | 1.03958e7i | −1.29779 | + | 0.459028i | ||||
\(876\) | 2.57744e7 | 1.13482 | ||||||||
\(877\) | − | 2.38159e7i | − | 1.04561i | −0.852453 | − | 0.522803i | \(-0.824886\pi\) | ||
0.852453 | − | 0.522803i | \(-0.175114\pi\) | |||||||
\(878\) | − | 6.76842e7i | − | 2.96313i | ||||||
\(879\) | 1.67106e7 | 0.729493 | ||||||||
\(880\) | 3.89524e6 | + | 1.69427e6i | 0.169562 | + | 0.0737525i | ||||
\(881\) | −9.82240e6 | −0.426361 | −0.213181 | − | 0.977013i | \(-0.568382\pi\) | ||||
−0.213181 | + | 0.977013i | \(0.568382\pi\) | |||||||
\(882\) | − | 1.04480e7i | − | 0.452231i | ||||||
\(883\) | − | 175255.i | − | 0.00756430i | −0.999993 | − | 0.00378215i | \(-0.998796\pi\) | ||
0.999993 | − | 0.00378215i | \(-0.00120390\pi\) | |||||||
\(884\) | 1.40424e7 | 0.604383 | ||||||||
\(885\) | −1.55717e6 | + | 3.58004e6i | −0.0668312 | + | 0.153649i | ||||
\(886\) | −4.77834e6 | −0.204500 | ||||||||
\(887\) | − | 4.60415e7i | − | 1.96490i | −0.186524 | − | 0.982450i | \(-0.559722\pi\) | ||
0.186524 | − | 0.982450i | \(-0.440278\pi\) | |||||||
\(888\) | − | 9.51028e6i | − | 0.404726i | ||||||
\(889\) | −4.26325e6 | −0.180920 | ||||||||
\(890\) | 2.47850e7 | − | 5.69823e7i | 1.04885 | − | 2.41138i | ||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | − | 1.24054e6i | − | 0.0522035i | ||||||
\(893\) | 1.57084e7i | 0.659179i | ||||||||
\(894\) | −1.69292e7 | −0.708423 | ||||||||
\(895\) | 1.54987e7 | + | 6.74134e6i | 0.646754 | + | 0.281312i | ||||
\(896\) | −2.85565e7 | −1.18833 | ||||||||
\(897\) | 1.05261e7i | 0.436802i | ||||||||
\(898\) | 1.95136e7i | 0.807507i | ||||||||
\(899\) | −1.72596e6 | −0.0712248 | ||||||||
\(900\) | 7.16824e6 | + | 7.69083e6i | 0.294989 | + | 0.316495i | ||||
\(901\) | −2.56388e7 | −1.05217 | ||||||||
\(902\) | 2.63402e6i | 0.107796i | ||||||||
\(903\) | 3.53722e7i | 1.44358i | ||||||||
\(904\) | 1.11720e7 | 0.454685 | ||||||||
\(905\) | 2.38562e7 | + | 1.03765e7i | 0.968234 | + | 0.421143i | ||||
\(906\) | −2.54129e6 | −0.102857 | ||||||||
\(907\) | − | 3.68866e7i | − | 1.48885i | −0.667706 | − | 0.744425i | \(-0.732724\pi\) | ||
0.667706 | − | 0.744425i | \(-0.267276\pi\) | |||||||
\(908\) | 1.76715e7i | 0.711309i | ||||||||
\(909\) | −4.16153e6 | −0.167049 | ||||||||
\(910\) | 1.23517e7 | − | 2.83972e7i | 0.494450 | − | 1.13677i | ||||
\(911\) | −3.44197e7 | −1.37408 | −0.687038 | − | 0.726622i | \(-0.741089\pi\) | ||||
−0.687038 | + | 0.726622i | \(0.741089\pi\) | |||||||
\(912\) | 4.26110e6i | 0.169643i | ||||||||
\(913\) | − | 1.07712e7i | − | 0.427647i | ||||||
\(914\) | −6.43509e7 | −2.54794 | ||||||||
\(915\) | 7.71978e6 | − | 1.77482e7i | 0.304826 | − | 0.700813i | ||||
\(916\) | −5.47570e7 | −2.15626 | ||||||||
\(917\) | − | 1.20636e7i | − | 0.473755i | ||||||
\(918\) | 5.83878e6i | 0.228673i | ||||||||
\(919\) | 1.33270e7 | 0.520527 | 0.260263 | − | 0.965538i | \(-0.416191\pi\) | ||||
0.260263 | + | 0.965538i | \(0.416191\pi\) | |||||||
\(920\) | 1.35421e7 | + | 5.89027e6i | 0.527492 | + | 0.229438i | ||||
\(921\) | −4.54220e6 | −0.176448 | ||||||||
\(922\) | − | 3.74719e6i | − | 0.145171i | ||||||
\(923\) | 2.26878e7i | 0.876574i | ||||||||
\(924\) | −8.07206e6 | −0.311032 | ||||||||
\(925\) | −2.95448e7 | + | 2.75373e7i | −1.13534 | + | 1.05820i | ||||
\(926\) | −2.67248e7 | −1.02421 | ||||||||
\(927\) | 7.68688e6i | 0.293799i | ||||||||
\(928\) | − | 2.08546e7i | − | 0.794935i | ||||||
\(929\) | −2.43196e7 | −0.924521 | −0.462260 | − | 0.886744i | \(-0.652961\pi\) | ||||
−0.462260 | + | 0.886744i | \(0.652961\pi\) | |||||||
\(930\) | −2.61991e6 | − | 1.13956e6i | −0.0993298 | − | 0.0432045i | ||||
\(931\) | 1.13405e7 | 0.428802 | ||||||||
\(932\) | 1.32936e7i | 0.501307i | ||||||||
\(933\) | − | 4.03660e6i | − | 0.151814i | ||||||
\(934\) | 1.62714e7 | 0.610322 | ||||||||
\(935\) | −2.51990e6 | + | 5.79340e6i | −0.0942657 | + | 0.216723i | ||||
\(936\) | −2.39727e6 | −0.0894390 | ||||||||
\(937\) | − | 3.18520e7i | − | 1.18519i | −0.805501 | − | 0.592595i | \(-0.798104\pi\) | ||
0.805501 | − | 0.592595i | \(-0.201896\pi\) | |||||||
\(938\) | 5.43603e7i | 2.01732i | ||||||||
\(939\) | −7.42631e6 | −0.274859 | ||||||||
\(940\) | 1.92957e7 | − | 4.43620e7i | 0.712264 | − | 1.63754i | ||||
\(941\) | 5.35961e7 | 1.97315 | 0.986573 | − | 0.163318i | \(-0.0522197\pi\) | ||||
0.986573 | + | 0.163318i | \(0.0522197\pi\) | |||||||
\(942\) | − | 3.52924e7i | − | 1.29585i | ||||||
\(943\) | − | 8.20212e6i | − | 0.300363i | ||||||
\(944\) | 4.87299e6 | 0.177978 | ||||||||
\(945\) | 6.66920e6 | + | 2.90084e6i | 0.242937 | + | 0.105668i | ||||
\(946\) | 2.28509e7 | 0.830186 | ||||||||
\(947\) | − | 1.82063e7i | − | 0.659700i | −0.944033 | − | 0.329850i | \(-0.893002\pi\) | ||
0.944033 | − | 0.329850i | \(-0.106998\pi\) | |||||||
\(948\) | − | 6.47211e6i | − | 0.233897i | ||||||
\(949\) | 2.49586e7 | 0.899610 | ||||||||
\(950\) | −1.47793e7 | + | 1.37751e7i | −0.531307 | + | 0.495204i | ||||
\(951\) | 2.93640e7 | 1.05284 | ||||||||
\(952\) | − | 1.36283e7i | − | 0.487360i | ||||||
\(953\) | − | 1.33257e6i | − | 0.0475289i | −0.999718 | − | 0.0237645i | \(-0.992435\pi\) | ||
0.999718 | − | 0.0237645i | \(-0.00756518\pi\) | |||||||
\(954\) | 1.90669e7 | 0.678281 | ||||||||
\(955\) | −1.50805e7 | − | 6.55942e6i | −0.535066 | − | 0.232732i | ||||
\(956\) | 5.21399e7 | 1.84512 | ||||||||
\(957\) | − | 2.83830e6i | − | 0.100180i | ||||||
\(958\) | − | 5.23335e7i | − | 1.84232i | ||||||
\(959\) | 3.67353e7 | 1.28984 | ||||||||
\(960\) | 9.73651e6 | − | 2.23848e7i | 0.340977 | − | 0.783927i | ||||
\(961\) | −2.81906e7 | −0.984682 | ||||||||
\(962\) | − | 4.01175e7i | − | 1.39764i | ||||||
\(963\) | − | 4.23084e6i | − | 0.147015i | ||||||
\(964\) | 4.47797e7 | 1.55199 | ||||||||
\(965\) | −6.25499e6 | + | 1.43806e7i | −0.216226 | + | 0.497117i | ||||
\(966\) | 4.45014e7 | 1.53437 | ||||||||
\(967\) | 5.74029e7i | 1.97409i | 0.160429 | + | 0.987047i | \(0.448712\pi\) | ||||
−0.160429 | + | 0.987047i | \(0.551288\pi\) | |||||||
\(968\) | 1.19707e6i | 0.0410610i | ||||||||
\(969\) | −6.33755e6 | −0.216826 | ||||||||
\(970\) | −6.01058e7 | − | 2.61437e7i | −2.05110 | − | 0.892148i | ||||
\(971\) | 3.56758e7 | 1.21430 | 0.607149 | − | 0.794588i | \(-0.292313\pi\) | ||||
0.607149 | + | 0.794588i | \(0.292313\pi\) | |||||||
\(972\) | − | 2.45258e6i | − | 0.0832639i | ||||||
\(973\) | 7.76232e6i | 0.262851i | ||||||||
\(974\) | 6.26137e7 | 2.11481 | ||||||||
\(975\) | 6.94135e6 | + | 7.44741e6i | 0.233847 | + | 0.250896i | ||||
\(976\) | −2.41581e7 | −0.811780 | ||||||||
\(977\) | − | 5.30033e7i | − | 1.77651i | −0.459354 | − | 0.888253i | \(-0.651919\pi\) | ||
0.459354 | − | 0.888253i | \(-0.348081\pi\) | |||||||
\(978\) | − | 4.07665e6i | − | 0.136288i | ||||||
\(979\) | −1.56848e7 | −0.523026 | ||||||||
\(980\) | −3.20265e7 | − | 1.39303e7i | −1.06523 | − | 0.463334i | ||||
\(981\) | 1.12228e7 | 0.372331 | ||||||||
\(982\) | − | 3.78068e7i | − | 1.25110i | ||||||
\(983\) | 2.40146e7i | 0.792667i | 0.918107 | + | 0.396333i | \(0.129718\pi\) | ||||
−0.918107 | + | 0.396333i | \(0.870282\pi\) | |||||||
\(984\) | 1.86800e6 | 0.0615020 | ||||||||
\(985\) | 5.38755e6 | − | 1.23863e7i | 0.176930 | − | 0.406772i | ||||
\(986\) | 2.08750e7 | 0.683806 | ||||||||
\(987\) | − | 3.34650e7i | − | 1.09345i | ||||||
\(988\) | − | 1.13351e7i | − | 0.369430i | ||||||
\(989\) | −7.11559e7 | −2.31324 | ||||||||
\(990\) | 1.87398e6 | − | 4.30839e6i | 0.0607683 | − | 0.139710i | ||||
\(991\) | 5.40921e7 | 1.74964 | 0.874822 | − | 0.484444i | \(-0.160978\pi\) | ||||
0.874822 | + | 0.484444i | \(0.160978\pi\) | |||||||
\(992\) | 5.29870e6i | 0.170958i | ||||||||
\(993\) | − | 3.13358e7i | − | 1.00848i | ||||||
\(994\) | 9.59182e7 | 3.07918 | ||||||||
\(995\) | 3.18731e7 | + | 1.38635e7i | 1.02063 | + | 0.443932i | ||||
\(996\) | −3.32759e7 | −1.06287 | ||||||||
\(997\) | − | 4.73500e7i | − | 1.50863i | −0.656513 | − | 0.754314i | \(-0.727969\pi\) | ||
0.656513 | − | 0.754314i | \(-0.272031\pi\) | |||||||
\(998\) | 2.96378e7i | 0.941931i | ||||||||
\(999\) | 9.42174e6 | 0.298688 |
(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 | 165.6.c.b.34.4 | ✓ | 26 | |
5.2 | odd | 4 | 825.6.a.y.1.11 | 13 | |||
5.3 | odd | 4 | 825.6.a.v.1.3 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.23 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.4 | ✓ | 26 | 1.1 | even | 1 | trivial | |
165.6.c.b.34.23 | yes | 26 | 5.4 | even | 2 | inner | |
825.6.a.v.1.3 | 13 | 5.3 | odd | 4 | |||
825.6.a.y.1.11 | 13 | 5.2 | odd | 4 |