Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,7,Mod(22,69)]
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([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.22");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.8737317698\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.9 | ||
Character | \(\chi\) | \(=\) | 69.22 |
Dual form | 69.7.d.a.22.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.73591 | −0.591988 | −0.295994 | − | 0.955190i | \(-0.595651\pi\) | ||||
−0.295994 | + | 0.955190i | \(0.595651\pi\) | |||||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | −41.5712 | −0.649550 | ||||||||
\(5\) | − | 38.4146i | − | 0.307317i | −0.988124 | − | 0.153659i | \(-0.950894\pi\) | ||
0.988124 | − | 0.153659i | \(-0.0491056\pi\) | |||||||
\(6\) | 73.8255 | 0.341785 | ||||||||
\(7\) | 655.803i | 1.91196i | 0.293429 | + | 0.955981i | \(0.405203\pi\) | ||||
−0.293429 | + | 0.955981i | \(0.594797\pi\) | |||||||
\(8\) | 499.975 | 0.976514 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 181.928i | 0.181928i | ||||||||
\(11\) | 589.638i | 0.443004i | 0.975160 | + | 0.221502i | \(0.0710959\pi\) | ||||
−0.975160 | + | 0.221502i | \(0.928904\pi\) | |||||||
\(12\) | 648.031 | 0.375018 | ||||||||
\(13\) | −3173.89 | −1.44465 | −0.722325 | − | 0.691554i | \(-0.756926\pi\) | ||||
−0.722325 | + | 0.691554i | \(0.756926\pi\) | |||||||
\(14\) | − | 3105.82i | − | 1.13186i | ||||||
\(15\) | 598.825i | 0.177430i | ||||||||
\(16\) | 292.721 | 0.0714650 | ||||||||
\(17\) | 909.300i | 0.185080i | 0.995709 | + | 0.0925402i | \(0.0294987\pi\) | ||||
−0.995709 | + | 0.0925402i | \(0.970501\pi\) | |||||||
\(18\) | −1150.83 | −0.197329 | ||||||||
\(19\) | − | 3910.57i | − | 0.570138i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||
0.958507 | − | 0.285069i | \(-0.0920165\pi\) | |||||||
\(20\) | 1596.94i | 0.199618i | ||||||||
\(21\) | − | 10223.0i | − | 1.10387i | ||||||
\(22\) | − | 2792.47i | − | 0.262253i | ||||||
\(23\) | 2677.23 | − | 11868.8i | 0.220040 | − | 0.975491i | ||||
\(24\) | −7793.84 | −0.563791 | ||||||||
\(25\) | 14149.3 | 0.905556 | ||||||||
\(26\) | 15031.3 | 0.855216 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | − | 27262.5i | − | 1.24191i | ||||||
\(29\) | −38085.2 | −1.56157 | −0.780786 | − | 0.624799i | \(-0.785181\pi\) | ||||
−0.780786 | + | 0.624799i | \(0.785181\pi\) | |||||||
\(30\) | − | 2835.98i | − | 0.105036i | ||||||
\(31\) | −12573.1 | −0.422044 | −0.211022 | − | 0.977481i | \(-0.567679\pi\) | ||||
−0.211022 | + | 0.977481i | \(0.567679\pi\) | |||||||
\(32\) | −33384.7 | −1.01882 | ||||||||
\(33\) | − | 9191.55i | − | 0.255768i | ||||||
\(34\) | − | 4306.36i | − | 0.109565i | ||||||
\(35\) | 25192.4 | 0.587579 | ||||||||
\(36\) | −10101.8 | −0.216517 | ||||||||
\(37\) | − | 80835.5i | − | 1.59587i | −0.602745 | − | 0.797934i | \(-0.705927\pi\) | ||
0.602745 | − | 0.797934i | \(-0.294073\pi\) | |||||||
\(38\) | 18520.1i | 0.337515i | ||||||||
\(39\) | 49476.1 | 0.834069 | ||||||||
\(40\) | − | 19206.4i | − | 0.300100i | ||||||
\(41\) | 35231.0 | 0.511179 | 0.255589 | − | 0.966785i | \(-0.417730\pi\) | ||||
0.255589 | + | 0.966785i | \(0.417730\pi\) | |||||||
\(42\) | 48414.9i | 0.653479i | ||||||||
\(43\) | − | 46800.8i | − | 0.588637i | −0.955707 | − | 0.294318i | \(-0.904907\pi\) | ||
0.955707 | − | 0.294318i | \(-0.0950926\pi\) | |||||||
\(44\) | − | 24512.0i | − | 0.287753i | ||||||
\(45\) | − | 9334.76i | − | 0.102439i | ||||||
\(46\) | −12679.1 | + | 56209.5i | −0.130261 | + | 0.577479i | ||||
\(47\) | 147162. | 1.41743 | 0.708714 | − | 0.705495i | \(-0.249275\pi\) | ||||
0.708714 | + | 0.705495i | \(0.249275\pi\) | |||||||
\(48\) | −4563.06 | −0.0412603 | ||||||||
\(49\) | −312428. | −2.65560 | ||||||||
\(50\) | −67009.8 | −0.536079 | ||||||||
\(51\) | − | 14174.6i | − | 0.106856i | ||||||
\(52\) | 131943. | 0.938372 | ||||||||
\(53\) | 254361.i | 1.70853i | 0.519836 | + | 0.854266i | \(0.325993\pi\) | ||||
−0.519836 | + | 0.854266i | \(0.674007\pi\) | |||||||
\(54\) | 17939.6 | 0.113928 | ||||||||
\(55\) | 22650.7 | 0.136143 | ||||||||
\(56\) | 327885.i | 1.86706i | ||||||||
\(57\) | 60959.8i | 0.329169i | ||||||||
\(58\) | 180368. | 0.924432 | ||||||||
\(59\) | −98850.5 | −0.481308 | −0.240654 | − | 0.970611i | \(-0.577362\pi\) | ||||
−0.240654 | + | 0.970611i | \(0.577362\pi\) | |||||||
\(60\) | − | 24893.9i | − | 0.115249i | ||||||
\(61\) | − | 149261.i | − | 0.657591i | −0.944401 | − | 0.328796i | \(-0.893357\pi\) | ||
0.944401 | − | 0.328796i | \(-0.106643\pi\) | |||||||
\(62\) | 59545.0 | 0.249845 | ||||||||
\(63\) | 159360.i | 0.637321i | ||||||||
\(64\) | 139373. | 0.531665 | ||||||||
\(65\) | 121924.i | 0.443966i | ||||||||
\(66\) | 43530.3i | 0.151412i | ||||||||
\(67\) | − | 331116.i | − | 1.10092i | −0.834861 | − | 0.550460i | \(-0.814452\pi\) | ||
0.834861 | − | 0.550460i | \(-0.185548\pi\) | |||||||
\(68\) | − | 37800.7i | − | 0.120219i | ||||||
\(69\) | −41733.8 | + | 185016.i | −0.127040 | + | 0.563200i | ||||
\(70\) | −119309. | −0.347840 | ||||||||
\(71\) | 371128. | 1.03693 | 0.518464 | − | 0.855100i | \(-0.326504\pi\) | ||||
0.518464 | + | 0.855100i | \(0.326504\pi\) | |||||||
\(72\) | 121494. | 0.325505 | ||||||||
\(73\) | 31506.8 | 0.0809907 | 0.0404954 | − | 0.999180i | \(-0.487106\pi\) | ||||
0.0404954 | + | 0.999180i | \(0.487106\pi\) | |||||||
\(74\) | 382829.i | 0.944735i | ||||||||
\(75\) | −220566. | −0.522823 | ||||||||
\(76\) | 162567.i | 0.370333i | ||||||||
\(77\) | −386686. | −0.847006 | ||||||||
\(78\) | −234314. | −0.493759 | ||||||||
\(79\) | 242806.i | 0.492469i | 0.969210 | + | 0.246234i | \(0.0791933\pi\) | ||||
−0.969210 | + | 0.246234i | \(0.920807\pi\) | |||||||
\(80\) | − | 11244.8i | − | 0.0219624i | ||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −166851. | −0.302612 | ||||||||
\(83\) | − | 827839.i | − | 1.44781i | −0.689900 | − | 0.723905i | \(-0.742345\pi\) | ||
0.689900 | − | 0.723905i | \(-0.257655\pi\) | |||||||
\(84\) | 424980.i | 0.717020i | ||||||||
\(85\) | 34930.4 | 0.0568784 | ||||||||
\(86\) | 221644.i | 0.348466i | ||||||||
\(87\) | 593689. | 0.901574 | ||||||||
\(88\) | 294804.i | 0.432599i | ||||||||
\(89\) | − | 1.03994e6i | − | 1.47515i | −0.675265 | − | 0.737576i | \(-0.735971\pi\) | ||
0.675265 | − | 0.737576i | \(-0.264029\pi\) | |||||||
\(90\) | 44208.5i | 0.0606427i | ||||||||
\(91\) | − | 2.08145e6i | − | 2.76211i | ||||||
\(92\) | −111295. | + | 493400.i | −0.142927 | + | 0.633630i | ||||
\(93\) | 195995. | 0.243667 | ||||||||
\(94\) | −696944. | −0.839101 | ||||||||
\(95\) | −150223. | −0.175213 | ||||||||
\(96\) | 520416. | 0.588216 | ||||||||
\(97\) | 833514.i | 0.913267i | 0.889655 | + | 0.456633i | \(0.150945\pi\) | ||||
−0.889655 | + | 0.456633i | \(0.849055\pi\) | |||||||
\(98\) | 1.47963e6 | 1.57208 | ||||||||
\(99\) | 143282.i | 0.147668i | ||||||||
\(100\) | −588204. | −0.588204 | ||||||||
\(101\) | −365591. | −0.354839 | −0.177420 | − | 0.984135i | \(-0.556775\pi\) | ||||
−0.177420 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(102\) | 67129.5i | 0.0632576i | ||||||||
\(103\) | − | 1.37353e6i | − | 1.25698i | −0.777819 | − | 0.628489i | \(-0.783674\pi\) | ||
0.777819 | − | 0.628489i | \(-0.216326\pi\) | |||||||
\(104\) | −1.58687e6 | −1.41072 | ||||||||
\(105\) | −392711. | −0.339239 | ||||||||
\(106\) | − | 1.20463e6i | − | 1.01143i | ||||||
\(107\) | 1.26985e6i | 1.03657i | 0.855207 | + | 0.518287i | \(0.173430\pi\) | ||||
−0.855207 | + | 0.518287i | \(0.826570\pi\) | |||||||
\(108\) | 157471. | 0.125006 | ||||||||
\(109\) | − | 1.06233e6i | − | 0.820315i | −0.912015 | − | 0.410157i | \(-0.865474\pi\) | ||
0.912015 | − | 0.410157i | \(-0.134526\pi\) | |||||||
\(110\) | −107272. | −0.0805949 | ||||||||
\(111\) | 1.26010e6i | 0.921374i | ||||||||
\(112\) | 191967.i | 0.136638i | ||||||||
\(113\) | − | 1.24438e6i | − | 0.862415i | −0.902253 | − | 0.431207i | \(-0.858088\pi\) | ||
0.902253 | − | 0.431207i | \(-0.141912\pi\) | |||||||
\(114\) | − | 288700.i | − | 0.194864i | ||||||
\(115\) | −455936. | − | 102845.i | −0.299785 | − | 0.0676220i | ||||
\(116\) | 1.58325e6 | 1.01432 | ||||||||
\(117\) | −771256. | −0.481550 | ||||||||
\(118\) | 468147. | 0.284928 | ||||||||
\(119\) | −596321. | −0.353867 | ||||||||
\(120\) | 299398.i | 0.173263i | ||||||||
\(121\) | 1.42389e6 | 0.803748 | ||||||||
\(122\) | 706885.i | 0.389286i | ||||||||
\(123\) | −549196. | −0.295129 | ||||||||
\(124\) | 522679. | 0.274138 | ||||||||
\(125\) | − | 1.14377e6i | − | 0.585610i | ||||||
\(126\) | − | 754714.i | − | 0.377286i | ||||||
\(127\) | −874087. | −0.426721 | −0.213360 | − | 0.976974i | \(-0.568441\pi\) | ||||
−0.213360 | + | 0.976974i | \(0.568441\pi\) | |||||||
\(128\) | 1.47657e6 | 0.704081 | ||||||||
\(129\) | 729552.i | 0.339850i | ||||||||
\(130\) | − | 577421.i | − | 0.262822i | ||||||
\(131\) | −1.81535e6 | −0.807509 | −0.403754 | − | 0.914867i | \(-0.632295\pi\) | ||||
−0.403754 | + | 0.914867i | \(0.632295\pi\) | |||||||
\(132\) | 382104.i | 0.166134i | ||||||||
\(133\) | 2.56457e6 | 1.09008 | ||||||||
\(134\) | 1.56814e6i | 0.651732i | ||||||||
\(135\) | 145514.i | 0.0591432i | ||||||||
\(136\) | 454627.i | 0.180734i | ||||||||
\(137\) | − | 269246.i | − | 0.104710i | −0.998629 | − | 0.0523549i | \(-0.983327\pi\) | ||
0.998629 | − | 0.0523549i | \(-0.0166727\pi\) | |||||||
\(138\) | 197647. | − | 876220.i | 0.0752062 | − | 0.333408i | ||||
\(139\) | −1.01592e6 | −0.378282 | −0.189141 | − | 0.981950i | \(-0.560570\pi\) | ||||
−0.189141 | + | 0.981950i | \(0.560570\pi\) | |||||||
\(140\) | −1.04728e6 | −0.381662 | ||||||||
\(141\) | −2.29402e6 | −0.818353 | ||||||||
\(142\) | −1.75763e6 | −0.613849 | ||||||||
\(143\) | − | 1.87145e6i | − | 0.639985i | ||||||
\(144\) | 71131.1 | 0.0238217 | ||||||||
\(145\) | 1.46303e6i | 0.479898i | ||||||||
\(146\) | −149213. | −0.0479456 | ||||||||
\(147\) | 4.87028e6 | 1.53321 | ||||||||
\(148\) | 3.36043e6i | 1.03660i | ||||||||
\(149\) | 5.31546e6i | 1.60688i | 0.595388 | + | 0.803438i | \(0.296998\pi\) | ||||
−0.595388 | + | 0.803438i | \(0.703002\pi\) | |||||||
\(150\) | 1.04458e6 | 0.309505 | ||||||||
\(151\) | −4.02808e6 | −1.16995 | −0.584975 | − | 0.811051i | \(-0.698896\pi\) | ||||
−0.584975 | + | 0.811051i | \(0.698896\pi\) | |||||||
\(152\) | − | 1.95519e6i | − | 0.556748i | ||||||
\(153\) | 220960.i | 0.0616935i | ||||||||
\(154\) | 1.83131e6 | 0.501418 | ||||||||
\(155\) | 482991.i | 0.129701i | ||||||||
\(156\) | −2.05678e6 | −0.541769 | ||||||||
\(157\) | − | 2.80608e6i | − | 0.725107i | −0.931963 | − | 0.362553i | \(-0.881905\pi\) | ||
0.931963 | − | 0.362553i | \(-0.118095\pi\) | |||||||
\(158\) | − | 1.14991e6i | − | 0.291536i | ||||||
\(159\) | − | 3.96510e6i | − | 0.986421i | ||||||
\(160\) | 1.28246e6i | 0.313101i | ||||||||
\(161\) | 7.78359e6 | + | 1.75573e6i | 1.86510 | + | 0.420708i | ||||
\(162\) | −279651. | −0.0657765 | ||||||||
\(163\) | −1.69615e6 | −0.391652 | −0.195826 | − | 0.980639i | \(-0.562739\pi\) | ||||
−0.195826 | + | 0.980639i | \(0.562739\pi\) | |||||||
\(164\) | −1.46459e6 | −0.332036 | ||||||||
\(165\) | −353090. | −0.0786020 | ||||||||
\(166\) | 3.92057e6i | 0.857087i | ||||||||
\(167\) | 4.14358e6 | 0.889665 | 0.444832 | − | 0.895614i | \(-0.353263\pi\) | ||||
0.444832 | + | 0.895614i | \(0.353263\pi\) | |||||||
\(168\) | − | 5.11122e6i | − | 1.07795i | ||||||
\(169\) | 5.24680e6 | 1.08701 | ||||||||
\(170\) | −165427. | −0.0336713 | ||||||||
\(171\) | − | 950270.i | − | 0.190046i | ||||||
\(172\) | 1.94556e6i | 0.382349i | ||||||||
\(173\) | −3.49007e6 | −0.674056 | −0.337028 | − | 0.941495i | \(-0.609422\pi\) | ||||
−0.337028 | + | 0.941495i | \(0.609422\pi\) | |||||||
\(174\) | −2.81166e6 | −0.533721 | ||||||||
\(175\) | 9.27916e6i | 1.73139i | ||||||||
\(176\) | 172599.i | 0.0316593i | ||||||||
\(177\) | 1.54093e6 | 0.277883 | ||||||||
\(178\) | 4.92504e6i | 0.873272i | ||||||||
\(179\) | −4.02563e6 | −0.701899 | −0.350949 | − | 0.936394i | \(-0.614141\pi\) | ||||
−0.350949 | + | 0.936394i | \(0.614141\pi\) | |||||||
\(180\) | 388057.i | 0.0665393i | ||||||||
\(181\) | 9.09130e6i | 1.53317i | 0.642143 | + | 0.766585i | \(0.278046\pi\) | ||||
−0.642143 | + | 0.766585i | \(0.721954\pi\) | |||||||
\(182\) | 9.85755e6i | 1.63514i | ||||||||
\(183\) | 2.32674e6i | 0.379660i | ||||||||
\(184\) | 1.33855e6 | − | 5.93411e6i | 0.214872 | − | 0.952581i | ||||
\(185\) | −3.10527e6 | −0.490437 | ||||||||
\(186\) | −928215. | −0.144248 | ||||||||
\(187\) | −536158. | −0.0819913 | ||||||||
\(188\) | −6.11769e6 | −0.920691 | ||||||||
\(189\) | − | 2.48418e6i | − | 0.367957i | ||||||
\(190\) | 711444. | 0.103724 | ||||||||
\(191\) | − | 91981.9i | − | 0.0132009i | −0.999978 | − | 0.00660043i | \(-0.997899\pi\) | ||
0.999978 | − | 0.00660043i | \(-0.00210100\pi\) | |||||||
\(192\) | −2.17261e6 | −0.306957 | ||||||||
\(193\) | 1.89895e6 | 0.264145 | 0.132073 | − | 0.991240i | \(-0.457837\pi\) | ||||
0.132073 | + | 0.991240i | \(0.457837\pi\) | |||||||
\(194\) | − | 3.94744e6i | − | 0.540643i | ||||||
\(195\) | − | 1.90061e6i | − | 0.256324i | ||||||
\(196\) | 1.29880e7 | 1.72494 | ||||||||
\(197\) | −2.32424e6 | −0.304006 | −0.152003 | − | 0.988380i | \(-0.548572\pi\) | ||||
−0.152003 | + | 0.988380i | \(0.548572\pi\) | |||||||
\(198\) | − | 678570.i | − | 0.0874177i | ||||||
\(199\) | − | 6.58139e6i | − | 0.835138i | −0.908645 | − | 0.417569i | \(-0.862882\pi\) | ||
0.908645 | − | 0.417569i | \(-0.137118\pi\) | |||||||
\(200\) | 7.07431e6 | 0.884288 | ||||||||
\(201\) | 5.16159e6i | 0.635617i | ||||||||
\(202\) | 1.73141e6 | 0.210061 | ||||||||
\(203\) | − | 2.49764e7i | − | 2.98566i | ||||||
\(204\) | 589254.i | 0.0694084i | ||||||||
\(205\) | − | 1.35339e6i | − | 0.157094i | ||||||
\(206\) | 6.50492e6i | 0.744116i | ||||||||
\(207\) | 650566. | − | 2.88412e6i | 0.0733466 | − | 0.325164i | ||||
\(208\) | −929065. | −0.103242 | ||||||||
\(209\) | 2.30582e6 | 0.252573 | ||||||||
\(210\) | 1.85984e6 | 0.200825 | ||||||||
\(211\) | −9.49872e6 | −1.01115 | −0.505577 | − | 0.862781i | \(-0.668720\pi\) | ||||
−0.505577 | + | 0.862781i | \(0.668720\pi\) | |||||||
\(212\) | − | 1.05741e7i | − | 1.10978i | ||||||
\(213\) | −5.78531e6 | −0.598670 | ||||||||
\(214\) | − | 6.01388e6i | − | 0.613639i | ||||||
\(215\) | −1.79783e6 | −0.180898 | ||||||||
\(216\) | −1.89390e6 | −0.187930 | ||||||||
\(217\) | − | 8.24547e6i | − | 0.806931i | ||||||
\(218\) | 5.03110e6i | 0.485617i | ||||||||
\(219\) | −491142. | −0.0467600 | ||||||||
\(220\) | −941618. | −0.0884315 | ||||||||
\(221\) | − | 2.88602e6i | − | 0.267376i | ||||||
\(222\) | − | 5.96772e6i | − | 0.545443i | ||||||
\(223\) | −1.00094e7 | −0.902596 | −0.451298 | − | 0.892373i | \(-0.649039\pi\) | ||||
−0.451298 | + | 0.892373i | \(0.649039\pi\) | |||||||
\(224\) | − | 2.18938e7i | − | 1.94795i | ||||||
\(225\) | 3.43828e6 | 0.301852 | ||||||||
\(226\) | 5.89324e6i | 0.510539i | ||||||||
\(227\) | − | 1.06382e7i | − | 0.909479i | −0.890625 | − | 0.454739i | \(-0.849732\pi\) | ||
0.890625 | − | 0.454739i | \(-0.150268\pi\) | |||||||
\(228\) | − | 2.53417e6i | − | 0.213812i | ||||||
\(229\) | 1.56747e7i | 1.30525i | 0.757682 | + | 0.652624i | \(0.226332\pi\) | ||||
−0.757682 | + | 0.652624i | \(0.773668\pi\) | |||||||
\(230\) | 2.15927e6 | + | 487063.i | 0.177469 | + | 0.0400314i | ||||
\(231\) | 6.02784e6 | 0.489019 | ||||||||
\(232\) | −1.90416e7 | −1.52490 | ||||||||
\(233\) | −1.75407e7 | −1.38669 | −0.693345 | − | 0.720605i | \(-0.743864\pi\) | ||||
−0.693345 | + | 0.720605i | \(0.743864\pi\) | |||||||
\(234\) | 3.65260e6 | 0.285072 | ||||||||
\(235\) | − | 5.65317e6i | − | 0.435600i | ||||||
\(236\) | 4.10933e6 | 0.312633 | ||||||||
\(237\) | − | 3.78498e6i | − | 0.284327i | ||||||
\(238\) | 2.82412e6 | 0.209485 | ||||||||
\(239\) | 1.76748e7 | 1.29468 | 0.647339 | − | 0.762202i | \(-0.275882\pi\) | ||||
0.647339 | + | 0.762202i | \(0.275882\pi\) | |||||||
\(240\) | 175288.i | 0.0126800i | ||||||||
\(241\) | − | 1.74693e7i | − | 1.24803i | −0.781413 | − | 0.624015i | \(-0.785501\pi\) | ||
0.781413 | − | 0.624015i | \(-0.214499\pi\) | |||||||
\(242\) | −6.74340e6 | −0.475809 | ||||||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | 6.20495e6i | 0.427138i | ||||||||
\(245\) | 1.20018e7i | 0.816110i | ||||||||
\(246\) | 2.60094e6 | 0.174713 | ||||||||
\(247\) | 1.24118e7i | 0.823649i | ||||||||
\(248\) | −6.28624e6 | −0.412132 | ||||||||
\(249\) | 1.29047e7i | 0.835894i | ||||||||
\(250\) | 5.41679e6i | 0.346674i | ||||||||
\(251\) | 2.77630e7i | 1.75568i | 0.478957 | + | 0.877839i | \(0.341015\pi\) | ||||
−0.478957 | + | 0.877839i | \(0.658985\pi\) | |||||||
\(252\) | − | 6.62479e6i | − | 0.413971i | ||||||
\(253\) | 6.99829e6 | + | 1.57859e6i | 0.432146 | + | 0.0974785i | ||||
\(254\) | 4.13960e6 | 0.252614 | ||||||||
\(255\) | −544512. | −0.0328387 | ||||||||
\(256\) | −1.59127e7 | −0.948473 | ||||||||
\(257\) | 2.30184e7 | 1.35605 | 0.678026 | − | 0.735038i | \(-0.262836\pi\) | ||||
0.678026 | + | 0.735038i | \(0.262836\pi\) | |||||||
\(258\) | − | 3.45509e6i | − | 0.201187i | ||||||
\(259\) | 5.30121e7 | 3.05124 | ||||||||
\(260\) | − | 5.06853e6i | − | 0.288378i | ||||||
\(261\) | −9.25470e6 | −0.520524 | ||||||||
\(262\) | 8.59734e6 | 0.478036 | ||||||||
\(263\) | − | 1.22401e7i | − | 0.672849i | −0.941710 | − | 0.336424i | \(-0.890782\pi\) | ||
0.941710 | − | 0.336424i | \(-0.109218\pi\) | |||||||
\(264\) | − | 4.59555e6i | − | 0.249761i | ||||||
\(265\) | 9.77119e6 | 0.525061 | ||||||||
\(266\) | −1.21455e7 | −0.645315 | ||||||||
\(267\) | 1.62110e7i | 0.851679i | ||||||||
\(268\) | 1.37649e7i | 0.715103i | ||||||||
\(269\) | −2.04992e7 | −1.05312 | −0.526562 | − | 0.850136i | \(-0.676519\pi\) | ||||
−0.526562 | + | 0.850136i | \(0.676519\pi\) | |||||||
\(270\) | − | 689143.i | − | 0.0350121i | ||||||
\(271\) | −1.50443e7 | −0.755898 | −0.377949 | − | 0.925826i | \(-0.623371\pi\) | ||||
−0.377949 | + | 0.925826i | \(0.623371\pi\) | |||||||
\(272\) | 266171.i | 0.0132268i | ||||||||
\(273\) | 3.24466e7i | 1.59471i | ||||||||
\(274\) | 1.27512e6i | 0.0619870i | ||||||||
\(275\) | 8.34297e6i | 0.401165i | ||||||||
\(276\) | 1.73492e6 | − | 7.69135e6i | 0.0825189 | − | 0.365826i | ||||
\(277\) | −3.89399e7 | −1.83213 | −0.916063 | − | 0.401034i | \(-0.868651\pi\) | ||||
−0.916063 | + | 0.401034i | \(0.868651\pi\) | |||||||
\(278\) | 4.81131e6 | 0.223939 | ||||||||
\(279\) | −3.05526e6 | −0.140681 | ||||||||
\(280\) | 1.25956e7 | 0.573779 | ||||||||
\(281\) | 2.98207e7i | 1.34400i | 0.740553 | + | 0.671998i | \(0.234564\pi\) | ||||
−0.740553 | + | 0.671998i | \(0.765436\pi\) | |||||||
\(282\) | 1.08643e7 | 0.484455 | ||||||||
\(283\) | − | 8.12480e6i | − | 0.358470i | −0.983806 | − | 0.179235i | \(-0.942638\pi\) | ||
0.983806 | − | 0.179235i | \(-0.0573623\pi\) | |||||||
\(284\) | −1.54282e7 | −0.673536 | ||||||||
\(285\) | 2.34175e6 | 0.101159 | ||||||||
\(286\) | 8.86301e6i | 0.378864i | ||||||||
\(287\) | 2.31046e7i | 0.977355i | ||||||||
\(288\) | −8.11249e6 | −0.339607 | ||||||||
\(289\) | 2.33107e7 | 0.965745 | ||||||||
\(290\) | − | 6.92876e6i | − | 0.284094i | ||||||
\(291\) | − | 1.29932e7i | − | 0.527275i | ||||||
\(292\) | −1.30977e6 | −0.0526075 | ||||||||
\(293\) | − | 3.59566e6i | − | 0.142947i | −0.997442 | − | 0.0714736i | \(-0.977230\pi\) | ||
0.997442 | − | 0.0714736i | \(-0.0227702\pi\) | |||||||
\(294\) | −2.30652e7 | −0.907642 | ||||||||
\(295\) | 3.79731e6i | 0.147914i | ||||||||
\(296\) | − | 4.04157e7i | − | 1.55839i | ||||||
\(297\) | − | 2.23355e6i | − | 0.0852561i | ||||||
\(298\) | − | 2.51735e7i | − | 0.951252i | ||||||
\(299\) | −8.49723e6 | + | 3.76703e7i | −0.317881 | + | 1.40924i | ||||
\(300\) | 9.16919e6 | 0.339600 | ||||||||
\(301\) | 3.06921e7 | 1.12545 | ||||||||
\(302\) | 1.90766e7 | 0.692597 | ||||||||
\(303\) | 5.69900e6 | 0.204866 | ||||||||
\(304\) | − | 1.14471e6i | − | 0.0407449i | ||||||
\(305\) | −5.73380e6 | −0.202089 | ||||||||
\(306\) | − | 1.04645e6i | − | 0.0365218i | ||||||
\(307\) | −3.56413e7 | −1.23179 | −0.615897 | − | 0.787826i | \(-0.711206\pi\) | ||||
−0.615897 | + | 0.787826i | \(0.711206\pi\) | |||||||
\(308\) | 1.60750e7 | 0.550173 | ||||||||
\(309\) | 2.14113e7i | 0.725716i | ||||||||
\(310\) | − | 2.28740e6i | − | 0.0767816i | ||||||
\(311\) | 2.80618e7 | 0.932899 | 0.466450 | − | 0.884548i | \(-0.345533\pi\) | ||||
0.466450 | + | 0.884548i | \(0.345533\pi\) | |||||||
\(312\) | 2.47368e7 | 0.814480 | ||||||||
\(313\) | − | 1.51413e7i | − | 0.493777i | −0.969044 | − | 0.246889i | \(-0.920592\pi\) | ||
0.969044 | − | 0.246889i | \(-0.0794082\pi\) | |||||||
\(314\) | 1.32894e7i | 0.429255i | ||||||||
\(315\) | 6.12176e6 | 0.195860 | ||||||||
\(316\) | − | 1.00938e7i | − | 0.319883i | ||||||
\(317\) | 2.13859e7 | 0.671351 | 0.335676 | − | 0.941978i | \(-0.391035\pi\) | ||||
0.335676 | + | 0.941978i | \(0.391035\pi\) | |||||||
\(318\) | 1.87783e7i | 0.583950i | ||||||||
\(319\) | − | 2.24565e7i | − | 0.691782i | ||||||
\(320\) | − | 5.35395e6i | − | 0.163390i | ||||||
\(321\) | − | 1.97950e7i | − | 0.598466i | ||||||
\(322\) | −3.68624e7 | − | 8.31498e6i | −1.10412 | − | 0.249054i | ||||
\(323\) | 3.55589e6 | 0.105521 | ||||||||
\(324\) | −2.45474e6 | −0.0721722 | ||||||||
\(325\) | −4.49084e7 | −1.30821 | ||||||||
\(326\) | 8.03279e6 | 0.231853 | ||||||||
\(327\) | 1.65601e7i | 0.473609i | ||||||||
\(328\) | 1.76146e7 | 0.499174 | ||||||||
\(329\) | 9.65091e7i | 2.71007i | ||||||||
\(330\) | 1.67220e6 | 0.0465315 | ||||||||
\(331\) | −2.67122e7 | −0.736591 | −0.368295 | − | 0.929709i | \(-0.620059\pi\) | ||||
−0.368295 | + | 0.929709i | \(0.620059\pi\) | |||||||
\(332\) | 3.44143e7i | 0.940425i | ||||||||
\(333\) | − | 1.96430e7i | − | 0.531956i | ||||||
\(334\) | −1.96236e7 | −0.526671 | ||||||||
\(335\) | −1.27197e7 | −0.338332 | ||||||||
\(336\) | − | 2.99247e6i | − | 0.0788882i | ||||||
\(337\) | − | 4.34797e7i | − | 1.13605i | −0.823011 | − | 0.568025i | \(-0.807708\pi\) | ||
0.823011 | − | 0.568025i | \(-0.192292\pi\) | |||||||
\(338\) | −2.48484e7 | −0.643498 | ||||||||
\(339\) | 1.93979e7i | 0.497915i | ||||||||
\(340\) | −1.45210e6 | −0.0369453 | ||||||||
\(341\) | − | 7.41358e6i | − | 0.186967i | ||||||
\(342\) | 4.50039e6i | 0.112505i | ||||||||
\(343\) | − | 1.27737e8i | − | 3.16544i | ||||||
\(344\) | − | 2.33992e7i | − | 0.574812i | ||||||
\(345\) | 7.10733e6 | + | 1.60319e6i | 0.173081 | + | 0.0390416i | ||||
\(346\) | 1.65286e7 | 0.399033 | ||||||||
\(347\) | 1.79683e7 | 0.430049 | 0.215024 | − | 0.976609i | \(-0.431017\pi\) | ||||
0.215024 | + | 0.976609i | \(0.431017\pi\) | |||||||
\(348\) | −2.46804e7 | −0.585617 | ||||||||
\(349\) | −1.98878e7 | −0.467855 | −0.233927 | − | 0.972254i | \(-0.575158\pi\) | ||||
−0.233927 | + | 0.972254i | \(0.575158\pi\) | |||||||
\(350\) | − | 4.39452e7i | − | 1.02496i | ||||||
\(351\) | 1.20227e7 | 0.278023 | ||||||||
\(352\) | − | 1.96849e7i | − | 0.451341i | ||||||
\(353\) | 2.64567e7 | 0.601467 | 0.300733 | − | 0.953708i | \(-0.402769\pi\) | ||||
0.300733 | + | 0.953708i | \(0.402769\pi\) | |||||||
\(354\) | −7.29768e6 | −0.164504 | ||||||||
\(355\) | − | 1.42567e7i | − | 0.318665i | ||||||
\(356\) | 4.32314e7i | 0.958184i | ||||||||
\(357\) | 9.29573e6 | 0.204305 | ||||||||
\(358\) | 1.90650e7 | 0.415516 | ||||||||
\(359\) | − | 5.31179e7i | − | 1.14804i | −0.818841 | − | 0.574020i | \(-0.805383\pi\) | ||
0.818841 | − | 0.574020i | \(-0.194617\pi\) | |||||||
\(360\) | − | 4.66715e6i | − | 0.100033i | ||||||
\(361\) | 3.17533e7 | 0.674943 | ||||||||
\(362\) | − | 4.30555e7i | − | 0.907618i | ||||||
\(363\) | −2.21962e7 | −0.464044 | ||||||||
\(364\) | 8.65283e7i | 1.79413i | ||||||||
\(365\) | − | 1.21032e6i | − | 0.0248898i | ||||||
\(366\) | − | 1.10192e7i | − | 0.224754i | ||||||
\(367\) | 1.02909e7i | 0.208188i | 0.994567 | + | 0.104094i | \(0.0331942\pi\) | ||||
−0.994567 | + | 0.104094i | \(0.966806\pi\) | |||||||
\(368\) | 783679. | − | 3.47424e6i | 0.0157252 | − | 0.0697135i | ||||
\(369\) | 8.56112e6 | 0.170393 | ||||||||
\(370\) | 1.47062e7 | 0.290333 | ||||||||
\(371\) | −1.66811e8 | −3.26665 | ||||||||
\(372\) | −8.14776e6 | −0.158274 | ||||||||
\(373\) | 2.28746e7i | 0.440785i | 0.975411 | + | 0.220392i | \(0.0707338\pi\) | ||||
−0.975411 | + | 0.220392i | \(0.929266\pi\) | |||||||
\(374\) | 2.53919e6 | 0.0485379 | ||||||||
\(375\) | 1.78296e7i | 0.338102i | ||||||||
\(376\) | 7.35772e7 | 1.38414 | ||||||||
\(377\) | 1.20878e8 | 2.25592 | ||||||||
\(378\) | 1.17648e7i | 0.217826i | ||||||||
\(379\) | − | 8.53493e7i | − | 1.56777i | −0.620906 | − | 0.783885i | \(-0.713235\pi\) | ||
0.620906 | − | 0.783885i | \(-0.286765\pi\) | |||||||
\(380\) | 6.24496e6 | 0.113810 | ||||||||
\(381\) | 1.36257e7 | 0.246367 | ||||||||
\(382\) | 435618.i | 0.00781475i | ||||||||
\(383\) | − | 5.06708e7i | − | 0.901906i | −0.892548 | − | 0.450953i | \(-0.851084\pi\) | ||
0.892548 | − | 0.450953i | \(-0.148916\pi\) | |||||||
\(384\) | −2.30174e7 | −0.406502 | ||||||||
\(385\) | 1.48544e7i | 0.260300i | ||||||||
\(386\) | −8.99327e6 | −0.156371 | ||||||||
\(387\) | − | 1.13726e7i | − | 0.196212i | ||||||
\(388\) | − | 3.46502e7i | − | 0.593212i | ||||||
\(389\) | 4.61864e7i | 0.784630i | 0.919831 | + | 0.392315i | \(0.128326\pi\) | ||||
−0.919831 | + | 0.392315i | \(0.871674\pi\) | |||||||
\(390\) | 9.00110e6i | 0.151741i | ||||||||
\(391\) | 1.07923e7 | + | 2.43440e6i | 0.180544 | + | 0.0407251i | ||||
\(392\) | −1.56206e8 | −2.59323 | ||||||||
\(393\) | 2.82986e7 | 0.466215 | ||||||||
\(394\) | 1.10074e7 | 0.179968 | ||||||||
\(395\) | 9.32732e6 | 0.151344 | ||||||||
\(396\) | − | 5.95641e6i | − | 0.0959177i | ||||||
\(397\) | −6.30551e7 | −1.00774 | −0.503870 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503870 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(398\) | 3.11688e7i | 0.494392i | ||||||||
\(399\) | −3.99776e7 | −0.629359 | ||||||||
\(400\) | 4.14180e6 | 0.0647156 | ||||||||
\(401\) | − | 6.06571e7i | − | 0.940695i | −0.882481 | − | 0.470347i | \(-0.844129\pi\) | ||
0.882481 | − | 0.470347i | \(-0.155871\pi\) | |||||||
\(402\) | − | 2.44448e7i | − | 0.376278i | ||||||
\(403\) | 3.99057e7 | 0.609705 | ||||||||
\(404\) | 1.51981e7 | 0.230486 | ||||||||
\(405\) | − | 2.26835e6i | − | 0.0341463i | ||||||
\(406\) | 1.18286e8i | 1.76748i | ||||||||
\(407\) | 4.76637e7 | 0.706975 | ||||||||
\(408\) | − | 7.08694e6i | − | 0.104347i | ||||||
\(409\) | −8.56293e7 | −1.25156 | −0.625781 | − | 0.779998i | \(-0.715220\pi\) | ||||
−0.625781 | + | 0.779998i | \(0.715220\pi\) | |||||||
\(410\) | 6.40950e6i | 0.0929978i | ||||||||
\(411\) | 4.19713e6i | 0.0604542i | ||||||||
\(412\) | 5.70994e7i | 0.816470i | ||||||||
\(413\) | − | 6.48264e7i | − | 0.920242i | ||||||
\(414\) | −3.08102e6 | + | 1.36589e7i | −0.0434203 | + | 0.192493i | ||||
\(415\) | −3.18011e7 | −0.444937 | ||||||||
\(416\) | 1.05960e8 | 1.47184 | ||||||||
\(417\) | 1.58367e7 | 0.218401 | ||||||||
\(418\) | −1.09202e7 | −0.149520 | ||||||||
\(419\) | 4.27680e7i | 0.581403i | 0.956814 | + | 0.290701i | \(0.0938886\pi\) | ||||
−0.956814 | + | 0.290701i | \(0.906111\pi\) | |||||||
\(420\) | 1.63255e7 | 0.220352 | ||||||||
\(421\) | 1.37696e7i | 0.184534i | 0.995734 | + | 0.0922668i | \(0.0294113\pi\) | ||||
−0.995734 | + | 0.0922668i | \(0.970589\pi\) | |||||||
\(422\) | 4.49850e7 | 0.598592 | ||||||||
\(423\) | 3.57603e7 | 0.472476 | ||||||||
\(424\) | 1.27174e8i | 1.66841i | ||||||||
\(425\) | 1.28660e7i | 0.167601i | ||||||||
\(426\) | 2.73987e7 | 0.354406 | ||||||||
\(427\) | 9.78856e7 | 1.25729 | ||||||||
\(428\) | − | 5.27891e7i | − | 0.673306i | ||||||
\(429\) | 2.91730e7i | 0.369496i | ||||||||
\(430\) | 8.51437e6 | 0.107090 | ||||||||
\(431\) | 1.76722e7i | 0.220729i | 0.993891 | + | 0.110365i | \(0.0352018\pi\) | ||||
−0.993891 | + | 0.110365i | \(0.964798\pi\) | |||||||
\(432\) | −1.10882e6 | −0.0137534 | ||||||||
\(433\) | − | 6.14430e7i | − | 0.756848i | −0.925632 | − | 0.378424i | \(-0.876466\pi\) | ||
0.925632 | − | 0.378424i | \(-0.123534\pi\) | |||||||
\(434\) | 3.90498e7i | 0.477694i | ||||||||
\(435\) | − | 2.28063e7i | − | 0.277069i | ||||||
\(436\) | 4.41624e7i | 0.532835i | ||||||||
\(437\) | −4.64138e7 | − | 1.04695e7i | −0.556164 | − | 0.125453i | ||||
\(438\) | 2.32600e6 | 0.0276814 | ||||||||
\(439\) | −4.41260e7 | −0.521556 | −0.260778 | − | 0.965399i | \(-0.583979\pi\) | ||||
−0.260778 | + | 0.965399i | \(0.583979\pi\) | |||||||
\(440\) | 1.13248e7 | 0.132945 | ||||||||
\(441\) | −7.59201e7 | −0.885199 | ||||||||
\(442\) | 1.36679e7i | 0.158284i | ||||||||
\(443\) | 3.93587e7 | 0.452719 | 0.226360 | − | 0.974044i | \(-0.427318\pi\) | ||||
0.226360 | + | 0.974044i | \(0.427318\pi\) | |||||||
\(444\) | − | 5.23839e7i | − | 0.598479i | ||||||
\(445\) | −3.99488e7 | −0.453339 | ||||||||
\(446\) | 4.74036e7 | 0.534326 | ||||||||
\(447\) | − | 8.28599e7i | − | 0.927730i | ||||||
\(448\) | 9.14010e7i | 1.01652i | ||||||||
\(449\) | −9.04011e7 | −0.998699 | −0.499349 | − | 0.866401i | \(-0.666428\pi\) | ||||
−0.499349 | + | 0.866401i | \(0.666428\pi\) | |||||||
\(450\) | −1.62834e7 | −0.178693 | ||||||||
\(451\) | 2.07735e7i | 0.226454i | ||||||||
\(452\) | 5.17302e7i | 0.560181i | ||||||||
\(453\) | 6.27916e7 | 0.675471 | ||||||||
\(454\) | 5.03817e7i | 0.538401i | ||||||||
\(455\) | −7.99581e7 | −0.848845 | ||||||||
\(456\) | 3.04784e7i | 0.321438i | ||||||||
\(457\) | 4.88645e7i | 0.511970i | 0.966681 | + | 0.255985i | \(0.0823998\pi\) | ||||
−0.966681 | + | 0.255985i | \(0.917600\pi\) | |||||||
\(458\) | − | 7.42340e7i | − | 0.772692i | ||||||
\(459\) | − | 3.44442e6i | − | 0.0356187i | ||||||
\(460\) | 1.89538e7 | + | 4.27538e6i | 0.194725 | + | 0.0439239i | ||||
\(461\) | −5.13497e7 | −0.524125 | −0.262063 | − | 0.965051i | \(-0.584403\pi\) | ||||
−0.262063 | + | 0.965051i | \(0.584403\pi\) | |||||||
\(462\) | −2.85473e7 | −0.289494 | ||||||||
\(463\) | −9.15812e7 | −0.922706 | −0.461353 | − | 0.887217i | \(-0.652636\pi\) | ||||
−0.461353 | + | 0.887217i | \(0.652636\pi\) | |||||||
\(464\) | −1.11483e7 | −0.111598 | ||||||||
\(465\) | − | 7.52909e6i | − | 0.0748830i | ||||||
\(466\) | 8.30712e7 | 0.820905 | ||||||||
\(467\) | − | 1.65064e8i | − | 1.62070i | −0.585948 | − | 0.810349i | \(-0.699278\pi\) | ||
0.585948 | − | 0.810349i | \(-0.300722\pi\) | |||||||
\(468\) | 3.20621e7 | 0.312791 | ||||||||
\(469\) | 2.17147e8 | 2.10492 | ||||||||
\(470\) | 2.67729e7i | 0.257870i | ||||||||
\(471\) | 4.37425e7i | 0.418640i | ||||||||
\(472\) | −4.94228e7 | −0.470004 | ||||||||
\(473\) | 2.75955e7 | 0.260768 | ||||||||
\(474\) | 1.79253e7i | 0.168318i | ||||||||
\(475\) | − | 5.53320e7i | − | 0.516292i | ||||||
\(476\) | 2.47898e7 | 0.229854 | ||||||||
\(477\) | 6.18098e7i | 0.569511i | ||||||||
\(478\) | −8.37064e7 | −0.766434 | ||||||||
\(479\) | − | 5.12647e7i | − | 0.466457i | −0.972422 | − | 0.233228i | \(-0.925071\pi\) | ||
0.972422 | − | 0.233228i | \(-0.0749290\pi\) | |||||||
\(480\) | − | 1.99916e7i | − | 0.180769i | ||||||
\(481\) | 2.56563e8i | 2.30547i | ||||||||
\(482\) | 8.27330e7i | 0.738819i | ||||||||
\(483\) | −1.21334e8 | − | 2.73692e7i | −1.07682 | − | 0.242896i | ||||
\(484\) | −5.91927e7 | −0.522074 | ||||||||
\(485\) | 3.20191e7 | 0.280663 | ||||||||
\(486\) | 4.35932e6 | 0.0379761 | ||||||||
\(487\) | 1.00852e8 | 0.873168 | 0.436584 | − | 0.899664i | \(-0.356188\pi\) | ||||
0.436584 | + | 0.899664i | \(0.356188\pi\) | |||||||
\(488\) | − | 7.46266e7i | − | 0.642147i | ||||||
\(489\) | 2.64403e7 | 0.226120 | ||||||||
\(490\) | − | 5.68395e7i | − | 0.483128i | ||||||
\(491\) | 4.28499e7 | 0.361998 | 0.180999 | − | 0.983483i | \(-0.442067\pi\) | ||||
0.180999 | + | 0.983483i | \(0.442067\pi\) | |||||||
\(492\) | 2.28308e7 | 0.191701 | ||||||||
\(493\) | − | 3.46308e7i | − | 0.289016i | ||||||
\(494\) | − | 5.87809e7i | − | 0.487591i | ||||||
\(495\) | 5.50413e6 | 0.0453809 | ||||||||
\(496\) | −3.68041e6 | −0.0301613 | ||||||||
\(497\) | 2.43387e8i | 1.98256i | ||||||||
\(498\) | − | 6.11156e7i | − | 0.494839i | ||||||
\(499\) | 2.43539e8 | 1.96005 | 0.980024 | − | 0.198877i | \(-0.0637295\pi\) | ||||
0.980024 | + | 0.198877i | \(0.0637295\pi\) | |||||||
\(500\) | 4.75479e7i | 0.380383i | ||||||||
\(501\) | −6.45920e7 | −0.513648 | ||||||||
\(502\) | − | 1.31483e8i | − | 1.03934i | ||||||
\(503\) | 2.71475e7i | 0.213317i | 0.994296 | + | 0.106659i | \(0.0340152\pi\) | ||||
−0.994296 | + | 0.106659i | \(0.965985\pi\) | |||||||
\(504\) | 7.96761e7i | 0.622352i | ||||||||
\(505\) | 1.40441e7i | 0.109048i | ||||||||
\(506\) | −3.31433e7 | − | 7.47607e6i | −0.255825 | − | 0.0577061i | ||||
\(507\) | −8.17895e7 | −0.627587 | ||||||||
\(508\) | 3.63369e7 | 0.277176 | ||||||||
\(509\) | 1.63613e8 | 1.24069 | 0.620347 | − | 0.784327i | \(-0.286992\pi\) | ||||
0.620347 | + | 0.784327i | \(0.286992\pi\) | |||||||
\(510\) | 2.57876e6 | 0.0194401 | ||||||||
\(511\) | 2.06622e7i | 0.154851i | ||||||||
\(512\) | −1.91390e7 | −0.142597 | ||||||||
\(513\) | 1.48132e7i | 0.109723i | ||||||||
\(514\) | −1.09013e8 | −0.802766 | ||||||||
\(515\) | −5.27638e7 | −0.386291 | ||||||||
\(516\) | − | 3.03283e7i | − | 0.220749i | ||||||
\(517\) | 8.67722e7i | 0.627926i | ||||||||
\(518\) | −2.51060e8 | −1.80630 | ||||||||
\(519\) | 5.44048e7 | 0.389166 | ||||||||
\(520\) | 6.09590e7i | 0.433539i | ||||||||
\(521\) | − | 3.82670e7i | − | 0.270590i | −0.990805 | − | 0.135295i | \(-0.956802\pi\) | ||
0.990805 | − | 0.135295i | \(-0.0431982\pi\) | |||||||
\(522\) | 4.38294e7 | 0.308144 | ||||||||
\(523\) | − | 1.69427e8i | − | 1.18434i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) | ||
0.805812 | − | 0.592172i | \(-0.201729\pi\) | |||||||
\(524\) | 7.54664e7 | 0.524517 | ||||||||
\(525\) | − | 1.44648e8i | − | 0.999618i | ||||||
\(526\) | 5.79679e7i | 0.398319i | ||||||||
\(527\) | − | 1.14327e7i | − | 0.0781120i | ||||||
\(528\) | − | 2.69056e6i | − | 0.0182785i | ||||||
\(529\) | −1.33701e8 | − | 6.35509e7i | −0.903165 | − | 0.429294i | ||||
\(530\) | −4.62754e7 | −0.310830 | ||||||||
\(531\) | −2.40207e7 | −0.160436 | ||||||||
\(532\) | −1.06612e8 | −0.708062 | ||||||||
\(533\) | −1.11819e8 | −0.738474 | ||||||||
\(534\) | − | 7.67737e7i | − | 0.504184i | ||||||
\(535\) | 4.87807e7 | 0.318557 | ||||||||
\(536\) | − | 1.65550e8i | − | 1.07506i | ||||||
\(537\) | 6.27533e7 | 0.405241 | ||||||||
\(538\) | 9.70822e7 | 0.623438 | ||||||||
\(539\) | − | 1.84220e8i | − | 1.17644i | ||||||
\(540\) | − | 6.04921e6i | − | 0.0384165i | ||||||
\(541\) | −1.41458e8 | −0.893378 | −0.446689 | − | 0.894689i | \(-0.647397\pi\) | ||||
−0.446689 | + | 0.894689i | \(0.647397\pi\) | |||||||
\(542\) | 7.12483e7 | 0.447483 | ||||||||
\(543\) | − | 1.41719e8i | − | 0.885176i | ||||||
\(544\) | − | 3.03567e7i | − | 0.188564i | ||||||
\(545\) | −4.08091e7 | −0.252097 | ||||||||
\(546\) | − | 1.53664e8i | − | 0.944048i | ||||||
\(547\) | −5.97977e7 | −0.365361 | −0.182681 | − | 0.983172i | \(-0.558477\pi\) | ||||
−0.182681 | + | 0.983172i | \(0.558477\pi\) | |||||||
\(548\) | 1.11929e7i | 0.0680142i | ||||||||
\(549\) | − | 3.62703e7i | − | 0.219197i | ||||||
\(550\) | − | 3.95115e7i | − | 0.237485i | ||||||
\(551\) | 1.48935e8i | 0.890311i | ||||||||
\(552\) | −2.08659e7 | + | 9.25035e7i | −0.124056 | + | 0.549973i | ||||
\(553\) | −1.59233e8 | −0.941582 | ||||||||
\(554\) | 1.84416e8 | 1.08460 | ||||||||
\(555\) | 4.84063e7 | 0.283154 | ||||||||
\(556\) | 4.22331e7 | 0.245713 | ||||||||
\(557\) | 3.31067e7i | 0.191580i | 0.995402 | + | 0.0957900i | \(0.0305377\pi\) | ||||
−0.995402 | + | 0.0957900i | \(0.969462\pi\) | |||||||
\(558\) | 1.44694e7 | 0.0832816 | ||||||||
\(559\) | 1.48541e8i | 0.850374i | ||||||||
\(560\) | 7.37435e6 | 0.0419913 | ||||||||
\(561\) | 8.35787e6 | 0.0473377 | ||||||||
\(562\) | − | 1.41228e8i | − | 0.795630i | ||||||
\(563\) | − | 2.07541e8i | − | 1.16299i | −0.813548 | − | 0.581497i | \(-0.802467\pi\) | ||
0.813548 | − | 0.581497i | \(-0.197533\pi\) | |||||||
\(564\) | 9.53653e7 | 0.531561 | ||||||||
\(565\) | −4.78022e7 | −0.265035 | ||||||||
\(566\) | 3.84783e7i | 0.212210i | ||||||||
\(567\) | 3.87245e7i | 0.212440i | ||||||||
\(568\) | 1.85555e8 | 1.01257 | ||||||||
\(569\) | 2.45063e8i | 1.33027i | 0.746723 | + | 0.665136i | \(0.231626\pi\) | ||||
−0.746723 | + | 0.665136i | \(0.768374\pi\) | |||||||
\(570\) | −1.10903e7 | −0.0598851 | ||||||||
\(571\) | − | 1.57184e8i | − | 0.844307i | −0.906524 | − | 0.422153i | \(-0.861274\pi\) | ||
0.906524 | − | 0.422153i | \(-0.138726\pi\) | |||||||
\(572\) | 7.77984e7i | 0.415702i | ||||||||
\(573\) | 1.43386e6i | 0.00762152i | ||||||||
\(574\) | − | 1.09421e8i | − | 0.578582i | ||||||
\(575\) | 3.78809e7 | − | 1.67935e8i | 0.199258 | − | 0.883362i | ||||
\(576\) | 3.38676e7 | 0.177222 | ||||||||
\(577\) | 7.78829e7 | 0.405429 | 0.202715 | − | 0.979238i | \(-0.435024\pi\) | ||||
0.202715 | + | 0.979238i | \(0.435024\pi\) | |||||||
\(578\) | −1.10397e8 | −0.571710 | ||||||||
\(579\) | −2.96018e7 | −0.152504 | ||||||||
\(580\) | − | 6.08198e7i | − | 0.311717i | ||||||
\(581\) | 5.42899e8 | 2.76816 | ||||||||
\(582\) | 6.15346e7i | 0.312141i | ||||||||
\(583\) | −1.49981e8 | −0.756886 | ||||||||
\(584\) | 1.57526e7 | 0.0790886 | ||||||||
\(585\) | 2.96275e7i | 0.147989i | ||||||||
\(586\) | 1.70287e7i | 0.0846231i | ||||||||
\(587\) | −1.75136e7 | −0.0865888 | −0.0432944 | − | 0.999062i | \(-0.513785\pi\) | ||||
−0.0432944 | + | 0.999062i | \(0.513785\pi\) | |||||||
\(588\) | −2.02463e8 | −0.995896 | ||||||||
\(589\) | 4.91680e7i | 0.240623i | ||||||||
\(590\) | − | 1.79837e7i | − | 0.0875634i | ||||||
\(591\) | 3.62313e7 | 0.175518 | ||||||||
\(592\) | − | 2.36622e7i | − | 0.114049i | ||||||
\(593\) | −3.78225e8 | −1.81379 | −0.906893 | − | 0.421361i | \(-0.861553\pi\) | ||||
−0.906893 | + | 0.421361i | \(0.861553\pi\) | |||||||
\(594\) | 1.05779e7i | 0.0504706i | ||||||||
\(595\) | 2.29075e7i | 0.108749i | ||||||||
\(596\) | − | 2.20970e8i | − | 1.04375i | ||||||
\(597\) | 1.02594e8i | 0.482167i | ||||||||
\(598\) | 4.02421e7 | − | 1.78403e8i | 0.188182 | − | 0.834255i | ||||
\(599\) | −6.74384e7 | −0.313781 | −0.156891 | − | 0.987616i | \(-0.550147\pi\) | ||||
−0.156891 | + | 0.987616i | \(0.550147\pi\) | |||||||
\(600\) | −1.10278e8 | −0.510544 | ||||||||
\(601\) | −1.98091e8 | −0.912516 | −0.456258 | − | 0.889847i | \(-0.650811\pi\) | ||||
−0.456258 | + | 0.889847i | \(0.650811\pi\) | |||||||
\(602\) | −1.45355e8 | −0.666254 | ||||||||
\(603\) | − | 8.04612e7i | − | 0.366974i | ||||||
\(604\) | 1.67452e8 | 0.759941 | ||||||||
\(605\) | − | 5.46981e7i | − | 0.247005i | ||||||
\(606\) | −2.69899e7 | −0.121279 | ||||||||
\(607\) | −3.35592e7 | −0.150053 | −0.0750267 | − | 0.997182i | \(-0.523904\pi\) | ||||
−0.0750267 | + | 0.997182i | \(0.523904\pi\) | |||||||
\(608\) | 1.30553e8i | 0.580868i | ||||||||
\(609\) | 3.89343e8i | 1.72377i | ||||||||
\(610\) | 2.71547e7 | 0.119634 | ||||||||
\(611\) | −4.67076e8 | −2.04769 | ||||||||
\(612\) | − | 9.18557e6i | − | 0.0400730i | ||||||
\(613\) | − | 6.44452e7i | − | 0.279775i | −0.990167 | − | 0.139888i | \(-0.955326\pi\) | ||
0.990167 | − | 0.139888i | \(-0.0446741\pi\) | |||||||
\(614\) | 1.68794e8 | 0.729208 | ||||||||
\(615\) | 2.10972e7i | 0.0906983i | ||||||||
\(616\) | −1.93334e8 | −0.827114 | ||||||||
\(617\) | 3.01733e8i | 1.28460i | 0.766453 | + | 0.642300i | \(0.222020\pi\) | ||||
−0.766453 | + | 0.642300i | \(0.777980\pi\) | |||||||
\(618\) | − | 1.01402e8i | − | 0.429616i | ||||||
\(619\) | − | 6.36803e7i | − | 0.268493i | −0.990948 | − | 0.134246i | \(-0.957139\pi\) | ||
0.990948 | − | 0.134246i | \(-0.0428614\pi\) | |||||||
\(620\) | − | 2.00785e7i | − | 0.0842474i | ||||||
\(621\) | −1.01413e7 | + | 4.49589e7i | −0.0423467 | + | 0.187733i | ||||
\(622\) | −1.32898e8 | −0.552265 | ||||||||
\(623\) | 6.81993e8 | 2.82043 | ||||||||
\(624\) | 1.44827e7 | 0.0596067 | ||||||||
\(625\) | 1.77146e8 | 0.725588 | ||||||||
\(626\) | 7.17080e7i | 0.292310i | ||||||||
\(627\) | −3.59442e7 | −0.145823 | ||||||||
\(628\) | 1.16652e8i | 0.470993i | ||||||||
\(629\) | 7.35037e7 | 0.295364 | ||||||||
\(630\) | −2.89921e7 | −0.115947 | ||||||||
\(631\) | 1.83010e8i | 0.728427i | 0.931315 | + | 0.364214i | \(0.118662\pi\) | ||||
−0.931315 | + | 0.364214i | \(0.881338\pi\) | |||||||
\(632\) | 1.21397e8i | 0.480903i | ||||||||
\(633\) | 1.48070e8 | 0.583790 | ||||||||
\(634\) | −1.01282e8 | −0.397432 | ||||||||
\(635\) | 3.35778e7i | 0.131139i | ||||||||
\(636\) | 1.64834e8i | 0.640730i | ||||||||
\(637\) | 9.91615e8 | 3.83641 | ||||||||
\(638\) | 1.06352e8i | 0.409527i | ||||||||
\(639\) | 9.01840e7 | 0.345642 | ||||||||
\(640\) | − | 5.67217e7i | − | 0.216376i | ||||||
\(641\) | 3.89706e8i | 1.47967i | 0.672791 | + | 0.739833i | \(0.265095\pi\) | ||||
−0.672791 | + | 0.739833i | \(0.734905\pi\) | |||||||
\(642\) | 9.37470e7i | 0.354285i | ||||||||
\(643\) | 2.85643e8i | 1.07446i | 0.843436 | + | 0.537230i | \(0.180529\pi\) | ||||
−0.843436 | + | 0.537230i | \(0.819471\pi\) | |||||||
\(644\) | −3.23573e8 | − | 7.29879e7i | −1.21148 | − | 0.273271i | ||||
\(645\) | 2.80255e7 | 0.104442 | ||||||||
\(646\) | −1.68403e7 | −0.0624674 | ||||||||
\(647\) | −4.43292e8 | −1.63673 | −0.818365 | − | 0.574699i | \(-0.805119\pi\) | ||||
−0.818365 | + | 0.574699i | \(0.805119\pi\) | |||||||
\(648\) | 2.95230e7 | 0.108502 | ||||||||
\(649\) | − | 5.82860e7i | − | 0.213221i | ||||||
\(650\) | 2.12682e8 | 0.774446 | ||||||||
\(651\) | 1.28534e8i | 0.465882i | ||||||||
\(652\) | 7.05108e7 | 0.254398 | ||||||||
\(653\) | 1.53784e8 | 0.552294 | 0.276147 | − | 0.961115i | \(-0.410942\pi\) | ||||
0.276147 | + | 0.961115i | \(0.410942\pi\) | |||||||
\(654\) | − | 7.84271e7i | − | 0.280371i | ||||||
\(655\) | 6.97361e7i | 0.248161i | ||||||||
\(656\) | 1.03128e7 | 0.0365314 | ||||||||
\(657\) | 7.65614e6 | 0.0269969 | ||||||||
\(658\) | − | 4.57058e8i | − | 1.60433i | ||||||
\(659\) | 1.40657e8i | 0.491481i | 0.969336 | + | 0.245740i | \(0.0790311\pi\) | ||||
−0.969336 | + | 0.245740i | \(0.920969\pi\) | |||||||
\(660\) | 1.46784e7 | 0.0510559 | ||||||||
\(661\) | − | 1.20638e8i | − | 0.417713i | −0.977946 | − | 0.208857i | \(-0.933026\pi\) | ||
0.977946 | − | 0.208857i | \(-0.0669742\pi\) | |||||||
\(662\) | 1.26507e8 | 0.436053 | ||||||||
\(663\) | 4.49886e7i | 0.154370i | ||||||||
\(664\) | − | 4.13899e8i | − | 1.41381i | ||||||
\(665\) | − | 9.85169e7i | − | 0.335001i | ||||||
\(666\) | 9.30275e7i | 0.314912i | ||||||||
\(667\) | −1.01963e8 | + | 4.52025e8i | −0.343608 | + | 1.52330i | ||||
\(668\) | −1.72254e8 | −0.577882 | ||||||||
\(669\) | 1.56031e8 | 0.521114 | ||||||||
\(670\) | 6.02393e7 | 0.200288 | ||||||||
\(671\) | 8.80098e7 | 0.291315 | ||||||||
\(672\) | 3.41290e8i | 1.12465i | ||||||||
\(673\) | −4.99233e8 | −1.63779 | −0.818895 | − | 0.573943i | \(-0.805413\pi\) | ||||
−0.818895 | + | 0.573943i | \(0.805413\pi\) | |||||||
\(674\) | 2.05916e8i | 0.672528i | ||||||||
\(675\) | −5.35975e7 | −0.174274 | ||||||||
\(676\) | −2.18116e8 | −0.706069 | ||||||||
\(677\) | 5.75205e8i | 1.85377i | 0.375342 | + | 0.926886i | \(0.377525\pi\) | ||||
−0.375342 | + | 0.926886i | \(0.622475\pi\) | |||||||
\(678\) | − | 9.18666e7i | − | 0.294760i | ||||||
\(679\) | −5.46621e8 | −1.74613 | ||||||||
\(680\) | 1.74644e7 | 0.0555425 | ||||||||
\(681\) | 1.65834e8i | 0.525088i | ||||||||
\(682\) | 3.51100e7i | 0.110682i | ||||||||
\(683\) | 3.10528e8 | 0.974626 | 0.487313 | − | 0.873227i | \(-0.337977\pi\) | ||||
0.487313 | + | 0.873227i | \(0.337977\pi\) | |||||||
\(684\) | 3.95038e7i | 0.123444i | ||||||||
\(685\) | −1.03430e7 | −0.0321791 | ||||||||
\(686\) | 6.04950e8i | 1.87390i | ||||||||
\(687\) | − | 2.44345e8i | − | 0.753585i | ||||||
\(688\) | − | 1.36995e7i | − | 0.0420669i | ||||||
\(689\) | − | 8.07315e8i | − | 2.46823i | ||||||
\(690\) | −3.36597e7 | − | 7.59255e6i | −0.102462 | − | 0.0231122i | ||||
\(691\) | 3.16160e7 | 0.0958237 | 0.0479119 | − | 0.998852i | \(-0.484743\pi\) | ||||
0.0479119 | + | 0.998852i | \(0.484743\pi\) | |||||||
\(692\) | 1.45086e8 | 0.437833 | ||||||||
\(693\) | −9.39648e7 | −0.282335 | ||||||||
\(694\) | −8.50960e7 | −0.254584 | ||||||||
\(695\) | 3.90263e7i | 0.116253i | ||||||||
\(696\) | 2.96830e8 | 0.880399 | ||||||||
\(697\) | 3.20355e7i | 0.0946092i | ||||||||
\(698\) | 9.41869e7 | 0.276964 | ||||||||
\(699\) | 2.73433e8 | 0.800606 | ||||||||
\(700\) | − | 3.85746e8i | − | 1.12462i | ||||||
\(701\) | − | 6.49293e8i | − | 1.88489i | −0.334355 | − | 0.942447i | \(-0.608519\pi\) | ||
0.334355 | − | 0.942447i | \(-0.391481\pi\) | |||||||
\(702\) | −5.69384e7 | −0.164586 | ||||||||
\(703\) | −3.16113e8 | −0.909864 | ||||||||
\(704\) | 8.21795e7i | 0.235530i | ||||||||
\(705\) | 8.81241e7i | 0.251494i | ||||||||
\(706\) | −1.25296e8 | −0.356061 | ||||||||
\(707\) | − | 2.39756e8i | − | 0.678439i | ||||||
\(708\) | −6.40582e7 | −0.180499 | ||||||||
\(709\) | 2.76124e8i | 0.774757i | 0.921921 | + | 0.387379i | \(0.126619\pi\) | ||||
−0.921921 | + | 0.387379i | \(0.873381\pi\) | |||||||
\(710\) | 6.75186e7i | 0.188646i | ||||||||
\(711\) | 5.90020e7i | 0.164156i | ||||||||
\(712\) | − | 5.19942e8i | − | 1.44051i | ||||||
\(713\) | −3.36610e7 | + | 1.49228e8i | −0.0928664 | + | 0.411700i | ||||
\(714\) | −4.40237e7 | −0.120946 | ||||||||
\(715\) | −7.18911e7 | −0.196678 | ||||||||
\(716\) | 1.67350e8 | 0.455918 | ||||||||
\(717\) | −2.75524e8 | −0.747483 | ||||||||
\(718\) | 2.51561e8i | 0.679627i | ||||||||
\(719\) | −1.67972e7 | −0.0451907 | −0.0225953 | − | 0.999745i | \(-0.507193\pi\) | ||||
−0.0225953 | + | 0.999745i | \(0.507193\pi\) | |||||||
\(720\) | − | 2.73248e6i | − | 0.00732081i | ||||||
\(721\) | 9.00767e8 | 2.40329 | ||||||||
\(722\) | −1.50381e8 | −0.399558 | ||||||||
\(723\) | 2.72320e8i | 0.720550i | ||||||||
\(724\) | − | 3.77936e8i | − | 0.995870i | ||||||
\(725\) | −5.38879e8 | −1.41409 | ||||||||
\(726\) | 1.05119e8 | 0.274709 | ||||||||
\(727\) | − | 1.40934e8i | − | 0.366786i | −0.983040 | − | 0.183393i | \(-0.941292\pi\) | ||
0.983040 | − | 0.183393i | \(-0.0587082\pi\) | |||||||
\(728\) | − | 1.04067e9i | − | 2.69724i | ||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 5.73197e6i | 0.0147345i | ||||||||
\(731\) | 4.25559e7 | 0.108945 | ||||||||
\(732\) | − | 9.67255e7i | − | 0.246608i | ||||||
\(733\) | − | 4.60922e8i | − | 1.17035i | −0.810907 | − | 0.585175i | \(-0.801026\pi\) | ||
0.810907 | − | 0.585175i | \(-0.198974\pi\) | |||||||
\(734\) | − | 4.87367e7i | − | 0.123245i | ||||||
\(735\) | − | 1.87090e8i | − | 0.471182i | ||||||
\(736\) | −8.93784e7 | + | 3.96236e8i | −0.224181 | + | 0.993850i | ||||
\(737\) | 1.95239e8 | 0.487712 | ||||||||
\(738\) | −4.05447e7 | −0.100871 | ||||||||
\(739\) | −2.18814e8 | −0.542177 | −0.271088 | − | 0.962554i | \(-0.587384\pi\) | ||||
−0.271088 | + | 0.962554i | \(0.587384\pi\) | |||||||
\(740\) | 1.29090e8 | 0.318564 | ||||||||
\(741\) | − | 1.93480e8i | − | 0.475534i | ||||||
\(742\) | 7.90000e8 | 1.93382 | ||||||||
\(743\) | − | 6.03913e8i | − | 1.47234i | −0.676797 | − | 0.736170i | \(-0.736632\pi\) | ||
0.676797 | − | 0.736170i | \(-0.263368\pi\) | |||||||
\(744\) | 9.79928e7 | 0.237944 | ||||||||
\(745\) | 2.04192e8 | 0.493821 | ||||||||
\(746\) | − | 1.08332e8i | − | 0.260939i | ||||||
\(747\) | − | 2.01165e8i | − | 0.482603i | ||||||
\(748\) | 2.22887e7 | 0.0532574 | ||||||||
\(749\) | −8.32769e8 | −1.98189 | ||||||||
\(750\) | − | 8.44393e7i | − | 0.200152i | ||||||
\(751\) | 3.51109e8i | 0.828938i | 0.910063 | + | 0.414469i | \(0.136033\pi\) | ||||
−0.910063 | + | 0.414469i | \(0.863967\pi\) | |||||||
\(752\) | 4.30773e7 | 0.101297 | ||||||||
\(753\) | − | 4.32782e8i | − | 1.01364i | ||||||
\(754\) | −5.72468e8 | −1.33548 | ||||||||
\(755\) | 1.54737e8i | 0.359546i | ||||||||
\(756\) | 1.03270e8i | 0.239007i | ||||||||
\(757\) | − | 3.44892e8i | − | 0.795051i | −0.917591 | − | 0.397526i | \(-0.869869\pi\) | ||
0.917591 | − | 0.397526i | \(-0.130131\pi\) | |||||||
\(758\) | 4.04206e8i | 0.928101i | ||||||||
\(759\) | −1.09093e8 | − | 2.46078e7i | −0.249500 | − | 0.0562792i | ||||
\(760\) | −7.51079e7 | −0.171098 | ||||||||
\(761\) | −6.29042e8 | −1.42733 | −0.713667 | − | 0.700485i | \(-0.752967\pi\) | ||||
−0.713667 | + | 0.700485i | \(0.752967\pi\) | |||||||
\(762\) | −6.45299e7 | −0.145847 | ||||||||
\(763\) | 6.96680e8 | 1.56841 | ||||||||
\(764\) | 3.82380e6i | 0.00857462i | ||||||||
\(765\) | 8.48809e6 | 0.0189595 | ||||||||
\(766\) | 2.39972e8i | 0.533918i | ||||||||
\(767\) | 3.13741e8 | 0.695321 | ||||||||
\(768\) | 2.48055e8 | 0.547601 | ||||||||
\(769\) | − | 7.77114e6i | − | 0.0170886i | −0.999963 | − | 0.00854428i | \(-0.997280\pi\) | ||
0.999963 | − | 0.00854428i | \(-0.00271976\pi\) | |||||||
\(770\) | − | 7.03491e7i | − | 0.154094i | ||||||
\(771\) | −3.58822e8 | −0.782916 | ||||||||
\(772\) | −7.89418e7 | −0.171575 | ||||||||
\(773\) | − | 3.82987e8i | − | 0.829174i | −0.910010 | − | 0.414587i | \(-0.863926\pi\) | ||
0.910010 | − | 0.414587i | \(-0.136074\pi\) | |||||||
\(774\) | 5.38595e7i | 0.116155i | ||||||||
\(775\) | −1.77901e8 | −0.382184 | ||||||||
\(776\) | 4.16736e8i | 0.891818i | ||||||||
\(777\) | −8.26377e8 | −1.76163 | ||||||||
\(778\) | − | 2.18734e8i | − | 0.464492i | ||||||
\(779\) | − | 1.37773e8i | − | 0.291442i | ||||||
\(780\) | 7.90105e7i | 0.166495i | ||||||||
\(781\) | 2.18831e8i | 0.459363i | ||||||||
\(782\) | −5.11113e7 | − | 1.15291e7i | −0.106880 | − | 0.0241088i | ||||
\(783\) | 1.44266e8 | 0.300525 | ||||||||
\(784\) | −9.14542e7 | −0.189782 | ||||||||
\(785\) | −1.07795e8 | −0.222838 | ||||||||
\(786\) | −1.34019e8 | −0.275994 | ||||||||
\(787\) | − | 3.06974e8i | − | 0.629763i | −0.949131 | − | 0.314881i | \(-0.898035\pi\) | ||
0.949131 | − | 0.314881i | \(-0.101965\pi\) | |||||||
\(788\) | 9.66215e7 | 0.197467 | ||||||||
\(789\) | 1.90804e8i | 0.388469i | ||||||||
\(790\) | −4.41733e7 | −0.0895940 | ||||||||
\(791\) | 8.16065e8 | 1.64890 | ||||||||
\(792\) | 7.16375e7i | 0.144200i | ||||||||
\(793\) | 4.73738e8i | 0.949989i | ||||||||
\(794\) | 2.98623e8 | 0.596571 | ||||||||
\(795\) | −1.52318e8 | −0.303144 | ||||||||
\(796\) | 2.73596e8i | 0.542464i | ||||||||
\(797\) | 8.04892e8i | 1.58987i | 0.606692 | + | 0.794937i | \(0.292496\pi\) | ||||
−0.606692 | + | 0.794937i | \(0.707504\pi\) | |||||||
\(798\) | 1.89330e8 | 0.372573 | ||||||||
\(799\) | 1.33814e8i | 0.262338i | ||||||||
\(800\) | −4.72371e8 | −0.922599 | ||||||||
\(801\) | − | 2.52704e8i | − | 0.491717i | ||||||
\(802\) | 2.87266e8i | 0.556880i | ||||||||
\(803\) | 1.85776e7i | 0.0358792i | ||||||||
\(804\) | − | 2.14573e8i | − | 0.412865i | ||||||
\(805\) | 6.74458e7 | − | 2.99004e8i | 0.129291 | − | 0.573178i | ||||
\(806\) | −1.88990e8 | −0.360938 | ||||||||
\(807\) | 3.19551e8 | 0.608022 | ||||||||
\(808\) | −1.82787e8 | −0.346505 | ||||||||
\(809\) | 6.07169e8 | 1.14674 | 0.573368 | − | 0.819298i | \(-0.305636\pi\) | ||||
0.573368 | + | 0.819298i | \(0.305636\pi\) | |||||||
\(810\) | 1.07427e7i | 0.0202142i | ||||||||
\(811\) | 8.35320e8 | 1.56600 | 0.782998 | − | 0.622025i | \(-0.213690\pi\) | ||||
0.782998 | + | 0.622025i | \(0.213690\pi\) | |||||||
\(812\) | 1.03830e9i | 1.93934i | ||||||||
\(813\) | 2.34517e8 | 0.436418 | ||||||||
\(814\) | −2.25731e8 | −0.418521 | ||||||||
\(815\) | 6.51568e7i | 0.120361i | ||||||||
\(816\) | − | 4.14919e6i | − | 0.00763648i | ||||||
\(817\) | −1.83018e8 | −0.335604 | ||||||||
\(818\) | 4.05532e8 | 0.740910 | ||||||||
\(819\) | − | 5.05792e8i | − | 0.920705i | ||||||
\(820\) | 5.62618e7i | 0.102040i | ||||||||
\(821\) | 3.94342e8 | 0.712596 | 0.356298 | − | 0.934372i | \(-0.384039\pi\) | ||||
0.356298 | + | 0.934372i | \(0.384039\pi\) | |||||||
\(822\) | − | 1.98772e7i | − | 0.0357882i | ||||||
\(823\) | −3.08910e8 | −0.554156 | −0.277078 | − | 0.960847i | \(-0.589366\pi\) | ||||
−0.277078 | + | 0.960847i | \(0.589366\pi\) | |||||||
\(824\) | − | 6.86733e8i | − | 1.22746i | ||||||
\(825\) | − | 1.30054e8i | − | 0.231613i | ||||||
\(826\) | 3.07012e8i | 0.544772i | ||||||||
\(827\) | 9.23533e7i | 0.163281i | 0.996662 | + | 0.0816405i | \(0.0260159\pi\) | ||||
−0.996662 | + | 0.0816405i | \(0.973984\pi\) | |||||||
\(828\) | −2.70448e7 | + | 1.19896e8i | −0.0476423 | + | 0.211210i | ||||
\(829\) | −9.68038e8 | −1.69914 | −0.849569 | − | 0.527477i | \(-0.823138\pi\) | ||||
−0.849569 | + | 0.527477i | \(0.823138\pi\) | |||||||
\(830\) | 1.50607e8 | 0.263397 | ||||||||
\(831\) | 6.07013e8 | 1.05778 | ||||||||
\(832\) | −4.42354e8 | −0.768069 | ||||||||
\(833\) | − | 2.84091e8i | − | 0.491499i | ||||||
\(834\) | −7.50009e7 | −0.129291 | ||||||||
\(835\) | − | 1.59174e8i | − | 0.273409i | ||||||
\(836\) | −9.58558e7 | −0.164059 | ||||||||
\(837\) | 4.76268e7 | 0.0812223 | ||||||||
\(838\) | − | 2.02545e8i | − | 0.344184i | ||||||
\(839\) | 3.10762e8i | 0.526190i | 0.964770 | + | 0.263095i | \(0.0847432\pi\) | ||||
−0.964770 | + | 0.263095i | \(0.915257\pi\) | |||||||
\(840\) | −1.96346e8 | −0.331271 | ||||||||
\(841\) | 8.55656e8 | 1.43851 | ||||||||
\(842\) | − | 6.52116e7i | − | 0.109242i | ||||||
\(843\) | − | 4.64858e8i | − | 0.775957i | ||||||
\(844\) | 3.94873e8 | 0.656795 | ||||||||
\(845\) | − | 2.01554e8i | − | 0.334057i | ||||||
\(846\) | −1.69357e8 | −0.279700 | ||||||||
\(847\) | 9.33790e8i | 1.53673i | ||||||||
\(848\) | 7.44568e7i | 0.122100i | ||||||||
\(849\) | 1.26653e8i | 0.206963i | ||||||||
\(850\) | − | 6.09320e7i | − | 0.0992176i | ||||||
\(851\) | −9.59420e8 | − | 2.16415e8i | −1.55675 | − | 0.351154i | ||||
\(852\) | 2.40502e8 | 0.388866 | ||||||||
\(853\) | −7.92172e8 | −1.27636 | −0.638179 | − | 0.769888i | \(-0.720312\pi\) | ||||
−0.638179 | + | 0.769888i | \(0.720312\pi\) | |||||||
\(854\) | −4.63577e8 | −0.744300 | ||||||||
\(855\) | −3.65043e7 | −0.0584044 | ||||||||
\(856\) | 6.34892e8i | 1.01223i | ||||||||
\(857\) | −1.82412e8 | −0.289809 | −0.144905 | − | 0.989446i | \(-0.546287\pi\) | ||||
−0.144905 | + | 0.989446i | \(0.546287\pi\) | |||||||
\(858\) | − | 1.38161e8i | − | 0.218737i | ||||||
\(859\) | 7.83080e8 | 1.23545 | 0.617727 | − | 0.786393i | \(-0.288054\pi\) | ||||
0.617727 | + | 0.786393i | \(0.288054\pi\) | |||||||
\(860\) | 7.47381e7 | 0.117502 | ||||||||
\(861\) | − | 3.60165e8i | − | 0.564276i | ||||||
\(862\) | − | 8.36940e7i | − | 0.130669i | ||||||
\(863\) | −2.77850e8 | −0.432293 | −0.216147 | − | 0.976361i | \(-0.569349\pi\) | ||||
−0.216147 | + | 0.976361i | \(0.569349\pi\) | |||||||
\(864\) | 1.26461e8 | 0.196072 | ||||||||
\(865\) | 1.34070e8i | 0.207149i | ||||||||
\(866\) | 2.90988e8i | 0.448045i | ||||||||
\(867\) | −3.63379e8 | −0.557573 | ||||||||
\(868\) | 3.42774e8i | 0.524142i | ||||||||
\(869\) | −1.43168e8 | −0.218166 | ||||||||
\(870\) | 1.08009e8i | 0.164022i | ||||||||
\(871\) | 1.05093e9i | 1.59044i | ||||||||
\(872\) | − | 5.31139e8i | − | 0.801049i | ||||||
\(873\) | 2.02544e8i | 0.304422i | ||||||||
\(874\) | 2.19811e8 | + | 4.95825e7i | 0.329243 | + | 0.0742667i | ||||
\(875\) | 7.50087e8 | 1.11966 | ||||||||
\(876\) | 2.04174e7 | 0.0303730 | ||||||||
\(877\) | −3.26734e8 | −0.484390 | −0.242195 | − | 0.970228i | \(-0.577867\pi\) | ||||
−0.242195 | + | 0.970228i | \(0.577867\pi\) | |||||||
\(878\) | 2.08976e8 | 0.308755 | ||||||||
\(879\) | 5.60508e7i | 0.0825307i | ||||||||
\(880\) | 6.63034e6 | 0.00972944 | ||||||||
\(881\) | − | 5.55927e8i | − | 0.812999i | −0.913651 | − | 0.406499i | \(-0.866749\pi\) | ||
0.913651 | − | 0.406499i | \(-0.133251\pi\) | |||||||
\(882\) | 3.59550e8 | 0.524027 | ||||||||
\(883\) | −1.18410e8 | −0.171991 | −0.0859953 | − | 0.996296i | \(-0.527407\pi\) | ||||
−0.0859953 | + | 0.996296i | \(0.527407\pi\) | |||||||
\(884\) | 1.19975e8i | 0.173674i | ||||||||
\(885\) | − | 5.91941e7i | − | 0.0853982i | ||||||
\(886\) | −1.86399e8 | −0.268005 | ||||||||
\(887\) | −6.88323e8 | −0.986327 | −0.493164 | − | 0.869937i | \(-0.664160\pi\) | ||||
−0.493164 | + | 0.869937i | \(0.664160\pi\) | |||||||
\(888\) | 6.30019e8i | 0.899735i | ||||||||
\(889\) | − | 5.73229e8i | − | 0.815873i | ||||||
\(890\) | 1.89194e8 | 0.268372 | ||||||||
\(891\) | 3.48175e7i | 0.0492226i | ||||||||
\(892\) | 4.16103e8 | 0.586281 | ||||||||
\(893\) | − | 5.75487e8i | − | 0.808130i | ||||||
\(894\) | 3.92417e8i | 0.549206i | ||||||||
\(895\) | 1.54643e8i | 0.215705i | ||||||||
\(896\) | 9.68336e8i | 1.34618i | ||||||||
\(897\) | 1.32459e8 | − | 5.87222e8i | 0.183528 | − | 0.813626i | ||||
\(898\) | 4.28131e8 | 0.591218 | ||||||||
\(899\) | 4.78849e8 | 0.659051 | ||||||||
\(900\) | −1.42934e8 | −0.196068 | ||||||||
\(901\) | −2.31291e8 | −0.316216 | ||||||||
\(902\) | − | 9.83814e7i | − | 0.134058i | ||||||
\(903\) | −4.78442e8 | −0.649780 | ||||||||
\(904\) | − | 6.22157e8i | − | 0.842160i | ||||||
\(905\) | 3.49239e8 | 0.471169 | ||||||||
\(906\) | −2.97375e8 | −0.399871 | ||||||||
\(907\) | 3.43780e8i | 0.460743i | 0.973103 | + | 0.230372i | \(0.0739942\pi\) | ||||
−0.973103 | + | 0.230372i | \(0.926006\pi\) | |||||||
\(908\) | 4.42245e8i | 0.590752i | ||||||||
\(909\) | −8.88386e7 | −0.118280 | ||||||||
\(910\) | 3.78674e8 | 0.502506 | ||||||||
\(911\) | 8.52295e8i | 1.12729i | 0.826018 | + | 0.563644i | \(0.190601\pi\) | ||||
−0.826018 | + | 0.563644i | \(0.809399\pi\) | |||||||
\(912\) | 1.78442e7i | 0.0235241i | ||||||||
\(913\) | 4.88125e8 | 0.641385 | ||||||||
\(914\) | − | 2.31418e8i | − | 0.303080i | ||||||
\(915\) | 8.93810e7 | 0.116676 | ||||||||
\(916\) | − | 6.51617e8i | − | 0.847824i | ||||||
\(917\) | − | 1.19051e9i | − | 1.54393i | ||||||
\(918\) | 1.63125e7i | 0.0210859i | ||||||||
\(919\) | 1.19920e9i | 1.54505i | 0.634982 | + | 0.772527i | \(0.281008\pi\) | ||||
−0.634982 | + | 0.772527i | \(0.718992\pi\) | |||||||
\(920\) | −2.27957e8 | − | 5.14198e7i | −0.292744 | − | 0.0660339i | ||||
\(921\) | 5.55593e8 | 0.711177 | ||||||||
\(922\) | 2.43187e8 | 0.310276 | ||||||||
\(923\) | −1.17792e9 | −1.49800 | ||||||||
\(924\) | −2.50585e8 | −0.317642 | ||||||||
\(925\) | − | 1.14377e9i | − | 1.44515i | ||||||
\(926\) | 4.33720e8 | 0.546231 | ||||||||
\(927\) | − | 3.33769e8i | − | 0.418993i | ||||||
\(928\) | 1.27146e9 | 1.59096 | ||||||||
\(929\) | 1.19275e8 | 0.148765 | 0.0743825 | − | 0.997230i | \(-0.476301\pi\) | ||||
0.0743825 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(930\) | 3.56570e7i | 0.0443299i | ||||||||
\(931\) | 1.22177e9i | 1.51406i | ||||||||
\(932\) | 7.29189e8 | 0.900725 | ||||||||
\(933\) | −4.37441e8 | −0.538610 | ||||||||
\(934\) | 7.81728e8i | 0.959434i | ||||||||
\(935\) | 2.05963e7i | 0.0251973i | ||||||||
\(936\) | −3.85609e8 | −0.470240 | ||||||||
\(937\) | 4.74435e8i | 0.576711i | 0.957523 | + | 0.288356i | \(0.0931085\pi\) | ||||
−0.957523 | + | 0.288356i | \(0.906891\pi\) | |||||||
\(938\) | −1.02839e9 | −1.24609 | ||||||||
\(939\) | 2.36030e8i | 0.285083i | ||||||||
\(940\) | 2.35009e8i | 0.282944i | ||||||||
\(941\) | 1.43051e9i | 1.71681i | 0.512975 | + | 0.858404i | \(0.328543\pi\) | ||||
−0.512975 | + | 0.858404i | \(0.671457\pi\) | |||||||
\(942\) | − | 2.07161e8i | − | 0.247830i | ||||||
\(943\) | 9.43212e7 | − | 4.18149e8i | 0.112480 | − | 0.498650i | ||||
\(944\) | −2.89356e7 | −0.0343967 | ||||||||
\(945\) | −9.54288e7 | −0.113080 | ||||||||
\(946\) | −1.30690e8 | −0.154372 | ||||||||
\(947\) | 5.63569e8 | 0.663586 | 0.331793 | − | 0.943352i | \(-0.392346\pi\) | ||||
0.331793 | + | 0.943352i | \(0.392346\pi\) | |||||||
\(948\) | 1.57346e8i | 0.184685i | ||||||||
\(949\) | −9.99992e7 | −0.117003 | ||||||||
\(950\) | 2.62047e8i | 0.305639i | ||||||||
\(951\) | −3.33373e8 | −0.387605 | ||||||||
\(952\) | −2.98146e8 | −0.345556 | ||||||||
\(953\) | − | 1.28750e9i | − | 1.48754i | −0.668433 | − | 0.743772i | \(-0.733035\pi\) | ||
0.668433 | − | 0.743772i | \(-0.266965\pi\) | |||||||
\(954\) | − | 2.92725e8i | − | 0.337144i | ||||||
\(955\) | −3.53345e6 | −0.00405685 | ||||||||
\(956\) | −7.34764e8 | −0.840958 | ||||||||
\(957\) | 3.50062e8i | 0.399401i | ||||||||
\(958\) | 2.42785e8i | 0.276137i | ||||||||
\(959\) | 1.76572e8 | 0.200201 | ||||||||
\(960\) | 8.34599e7i | 0.0943331i | ||||||||
\(961\) | −7.29421e8 | −0.821879 | ||||||||
\(962\) | − | 1.21506e9i | − | 1.36481i | ||||||
\(963\) | 3.08573e8i | 0.345524i | ||||||||
\(964\) | 7.26220e8i | 0.810657i | ||||||||
\(965\) | − | 7.29477e7i | − | 0.0811763i | ||||||
\(966\) | 5.74627e8 | + | 1.29618e8i | 0.637463 | + | 0.143791i | ||||
\(967\) | −1.14839e9 | −1.27002 | −0.635010 | − | 0.772504i | \(-0.719004\pi\) | ||||
−0.635010 | + | 0.772504i | \(0.719004\pi\) | |||||||
\(968\) | 7.11909e8 | 0.784871 | ||||||||
\(969\) | −5.54308e7 | −0.0609228 | ||||||||
\(970\) | −1.51640e8 | −0.166149 | ||||||||
\(971\) | 7.06658e8i | 0.771883i | 0.922523 | + | 0.385942i | \(0.126123\pi\) | ||||
−0.922523 | + | 0.385942i | \(0.873877\pi\) | |||||||
\(972\) | 3.82656e7 | 0.0416686 | ||||||||
\(973\) | − | 6.66244e8i | − | 0.723261i | ||||||
\(974\) | −4.77626e8 | −0.516905 | ||||||||
\(975\) | 7.00053e8 | 0.755296 | ||||||||
\(976\) | − | 4.36917e7i | − | 0.0469948i | ||||||
\(977\) | 3.80874e8i | 0.408411i | 0.978928 | + | 0.204206i | \(0.0654611\pi\) | ||||
−0.978928 | + | 0.204206i | \(0.934539\pi\) | |||||||
\(978\) | −1.25219e8 | −0.133861 | ||||||||
\(979\) | 6.13186e8 | 0.653498 | ||||||||
\(980\) | − | 4.98930e8i | − | 0.530104i | ||||||
\(981\) | − | 2.58147e8i | − | 0.273438i | ||||||
\(982\) | −2.02933e8 | −0.214298 | ||||||||
\(983\) | − | 1.51176e9i | − | 1.59155i | −0.605590 | − | 0.795777i | \(-0.707063\pi\) | ||
0.605590 | − | 0.795777i | \(-0.292937\pi\) | |||||||
\(984\) | −2.74585e8 | −0.288198 | ||||||||
\(985\) | 8.92849e7i | 0.0934264i | ||||||||
\(986\) | 1.64008e8i | 0.171094i | ||||||||
\(987\) | − | 1.50443e9i | − | 1.56466i | ||||||
\(988\) | − | 5.15971e8i | − | 0.535001i | ||||||
\(989\) | −5.55469e8 | − | 1.25296e8i | −0.574210 | − | 0.129524i | ||||
\(990\) | −2.60670e7 | −0.0268650 | ||||||||
\(991\) | 4.20133e8 | 0.431684 | 0.215842 | − | 0.976428i | \(-0.430750\pi\) | ||||
0.215842 | + | 0.976428i | \(0.430750\pi\) | |||||||
\(992\) | 4.19749e8 | 0.429987 | ||||||||
\(993\) | 4.16403e8 | 0.425271 | ||||||||
\(994\) | − | 1.15266e9i | − | 1.17365i | ||||||
\(995\) | −2.52822e8 | −0.256652 | ||||||||
\(996\) | − | 5.36465e8i | − | 0.542955i | ||||||
\(997\) | −3.88505e8 | −0.392023 | −0.196011 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196011 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(998\) | −1.15338e9 | −1.16033 | ||||||||
\(999\) | 3.06204e8i | 0.307125i |
(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 | 69.7.d.a.22.9 | ✓ | 24 | |
3.2 | odd | 2 | 207.7.d.e.91.16 | 24 | |||
23.22 | odd | 2 | inner | 69.7.d.a.22.10 | yes | 24 | |
69.68 | even | 2 | 207.7.d.e.91.15 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.7.d.a.22.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
69.7.d.a.22.10 | yes | 24 | 23.22 | odd | 2 | inner | |
207.7.d.e.91.15 | 24 | 69.68 | even | 2 | |||
207.7.d.e.91.16 | 24 | 3.2 | odd | 2 |