Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,9,Mod(12,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.12");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.8139796918\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Relative dimension: | \(19\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 12.10 | ||
Character | \(\chi\) | \(=\) | 29.12 |
Dual form | 29.9.c.a.17.10 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.384989 | + | 0.384989i | 0.0240618 | + | 0.0240618i | 0.719035 | − | 0.694974i | \(-0.244584\pi\) |
−0.694974 | + | 0.719035i | \(0.744584\pi\) | |||||||
\(3\) | 93.7530 | + | 93.7530i | 1.15744 | + | 1.15744i | 0.985023 | + | 0.172421i | \(0.0551590\pi\) |
0.172421 | + | 0.985023i | \(0.444841\pi\) | |||||||
\(4\) | − | 255.704i | − | 0.998842i | ||||||
\(5\) | 802.752i | 1.28440i | 0.766536 | + | 0.642201i | \(0.221979\pi\) | ||||
−0.766536 | + | 0.642201i | \(0.778021\pi\) | |||||||
\(6\) | 72.1877i | 0.0557004i | ||||||||
\(7\) | 2726.98 | 1.13577 | 0.567884 | − | 0.823108i | \(-0.307762\pi\) | ||||
0.567884 | + | 0.823108i | \(0.307762\pi\) | |||||||
\(8\) | 197.000 | − | 197.000i | 0.0480957 | − | 0.0480957i | ||||
\(9\) | 11018.2i | 1.67935i | ||||||||
\(10\) | −309.050 | + | 309.050i | −0.0309050 | + | 0.0309050i | ||||
\(11\) | −10332.7 | − | 10332.7i | −0.705737 | − | 0.705737i | 0.259899 | − | 0.965636i | \(-0.416311\pi\) |
−0.965636 | + | 0.259899i | \(0.916311\pi\) | |||||||
\(12\) | 23973.0 | − | 23973.0i | 1.15610 | − | 1.15610i | ||||
\(13\) | 21024.9i | 0.736140i | 0.929798 | + | 0.368070i | \(0.119981\pi\) | ||||
−0.929798 | + | 0.368070i | \(0.880019\pi\) | |||||||
\(14\) | 1049.86 | + | 1049.86i | 0.0273286 | + | 0.0273286i | ||||
\(15\) | −75260.4 | + | 75260.4i | −1.48662 | + | 1.48662i | ||||
\(16\) | −65308.4 | −0.996528 | ||||||||
\(17\) | 75820.3 | + | 75820.3i | 0.907799 | + | 0.907799i | 0.996094 | − | 0.0882951i | \(-0.0281418\pi\) |
−0.0882951 | + | 0.996094i | \(0.528142\pi\) | |||||||
\(18\) | −4241.90 | + | 4241.90i | −0.0404083 | + | 0.0404083i | ||||
\(19\) | 49482.1 | + | 49482.1i | 0.379694 | + | 0.379694i | 0.870992 | − | 0.491298i | \(-0.163477\pi\) |
−0.491298 | + | 0.870992i | \(0.663477\pi\) | |||||||
\(20\) | 205266. | 1.28292 | ||||||||
\(21\) | 255663. | + | 255663.i | 1.31459 | + | 1.31459i | ||||
\(22\) | − | 7955.94i | − | 0.0339626i | ||||||
\(23\) | −10519.0 | −0.0375893 | −0.0187947 | − | 0.999823i | \(-0.505983\pi\) | ||||
−0.0187947 | + | 0.999823i | \(0.505983\pi\) | |||||||
\(24\) | 36938.7 | 0.111336 | ||||||||
\(25\) | −253785. | −0.649691 | ||||||||
\(26\) | −8094.35 | + | 8094.35i | −0.0177129 | + | 0.0177129i | ||||
\(27\) | −417880. | + | 417880.i | −0.786316 | + | 0.786316i | ||||
\(28\) | − | 697299.i | − | 1.13445i | ||||||
\(29\) | −290625. | + | 644813.i | −0.410905 | + | 0.911678i | ||||
\(30\) | −57948.8 | −0.0715417 | ||||||||
\(31\) | −1.05254e6 | − | 1.05254e6i | −1.13970 | − | 1.13970i | −0.988504 | − | 0.151195i | \(-0.951688\pi\) |
−0.151195 | − | 0.988504i | \(-0.548312\pi\) | |||||||
\(32\) | −75575.1 | − | 75575.1i | −0.0720740 | − | 0.0720740i | ||||
\(33\) | − | 1.93744e6i | − | 1.63370i | ||||||
\(34\) | 58379.9i | 0.0436866i | ||||||||
\(35\) | 2.18909e6i | 1.45878i | ||||||||
\(36\) | 2.81741e6 | 1.67741 | ||||||||
\(37\) | 2.43856e6 | − | 2.43856e6i | 1.30115 | − | 1.30115i | 0.373533 | − | 0.927617i | \(-0.378146\pi\) |
0.927617 | − | 0.373533i | \(-0.121854\pi\) | |||||||
\(38\) | 38100.1i | 0.0182722i | ||||||||
\(39\) | −1.97115e6 | + | 1.97115e6i | −0.852041 | + | 0.852041i | ||||
\(40\) | 158142. | + | 158142.i | 0.0617743 | + | 0.0617743i | ||||
\(41\) | 3.64219e6 | − | 3.64219e6i | 1.28892 | − | 1.28892i | 0.353484 | − | 0.935441i | \(-0.384997\pi\) |
0.935441 | − | 0.353484i | \(-0.115003\pi\) | |||||||
\(42\) | 196855.i | 0.0632628i | ||||||||
\(43\) | −2.65043e6 | − | 2.65043e6i | −0.775252 | − | 0.775252i | 0.203767 | − | 0.979019i | \(-0.434681\pi\) |
−0.979019 | + | 0.203767i | \(0.934681\pi\) | |||||||
\(44\) | −2.64211e6 | + | 2.64211e6i | −0.704920 | + | 0.704920i | ||||
\(45\) | −8.84492e6 | −2.15697 | ||||||||
\(46\) | −4049.71 | − | 4049.71i | −0.000904467 | − | 0.000904467i | ||||
\(47\) | 2.80524e6 | − | 2.80524e6i | 0.574882 | − | 0.574882i | −0.358607 | − | 0.933489i | \(-0.616748\pi\) |
0.933489 | + | 0.358607i | \(0.116748\pi\) | |||||||
\(48\) | −6.12286e6 | − | 6.12286e6i | −1.15343 | − | 1.15343i | ||||
\(49\) | 1.67162e6 | 0.289971 | ||||||||
\(50\) | −97704.5 | − | 97704.5i | −0.0156327 | − | 0.0156327i | ||||
\(51\) | 1.42168e7i | 2.10145i | ||||||||
\(52\) | 5.37614e6 | 0.735288 | ||||||||
\(53\) | 5.48448e6 | 0.695075 | 0.347538 | − | 0.937666i | \(-0.387018\pi\) | ||||
0.347538 | + | 0.937666i | \(0.387018\pi\) | |||||||
\(54\) | −321759. | −0.0378403 | ||||||||
\(55\) | 8.29459e6 | − | 8.29459e6i | 0.906450 | − | 0.906450i | ||||
\(56\) | 537216. | − | 537216.i | 0.0546257 | − | 0.0546257i | ||||
\(57\) | 9.27819e6i | 0.878949i | ||||||||
\(58\) | −360133. | + | 136358.i | −0.0318237 | + | 0.0120495i | ||||
\(59\) | −4.51198e6 | −0.372357 | −0.186178 | − | 0.982516i | \(-0.559610\pi\) | ||||
−0.186178 | + | 0.982516i | \(0.559610\pi\) | |||||||
\(60\) | 1.92443e7 | + | 1.92443e7i | 1.48490 | + | 1.48490i | ||||
\(61\) | −9.36984e6 | − | 9.36984e6i | −0.676726 | − | 0.676726i | 0.282532 | − | 0.959258i | \(-0.408826\pi\) |
−0.959258 | + | 0.282532i | \(0.908826\pi\) | |||||||
\(62\) | − | 810429.i | − | 0.0548464i | ||||||
\(63\) | 3.00466e7i | 1.90736i | ||||||||
\(64\) | 1.66608e7i | 0.993059i | ||||||||
\(65\) | −1.68778e7 | −0.945500 | ||||||||
\(66\) | 745893. | − | 745893.i | 0.0393098 | − | 0.0393098i | ||||
\(67\) | − | 9.67617e6i | − | 0.480180i | −0.970751 | − | 0.240090i | \(-0.922823\pi\) | ||
0.970751 | − | 0.240090i | \(-0.0771770\pi\) | |||||||
\(68\) | 1.93875e7 | − | 1.93875e7i | 0.906748 | − | 0.906748i | ||||
\(69\) | −986191. | − | 986191.i | −0.0435076 | − | 0.0435076i | ||||
\(70\) | −842775. | + | 842775.i | −0.0351010 | + | 0.0351010i | ||||
\(71\) | − | 5.43326e6i | − | 0.213809i | −0.994269 | − | 0.106905i | \(-0.965906\pi\) | ||
0.994269 | − | 0.106905i | \(-0.0340940\pi\) | |||||||
\(72\) | 2.17060e6 | + | 2.17060e6i | 0.0807698 | + | 0.0807698i | ||||
\(73\) | −1.88608e7 | + | 1.88608e7i | −0.664154 | + | 0.664154i | −0.956356 | − | 0.292202i | \(-0.905612\pi\) |
0.292202 | + | 0.956356i | \(0.405612\pi\) | |||||||
\(74\) | 1.87764e6 | 0.0626160 | ||||||||
\(75\) | −2.37931e7 | − | 2.37931e7i | −0.751981 | − | 0.751981i | ||||
\(76\) | 1.26527e7 | − | 1.26527e7i | 0.379254 | − | 0.379254i | ||||
\(77\) | −2.81771e7 | − | 2.81771e7i | −0.801554 | − | 0.801554i | ||||
\(78\) | −1.51774e6 | −0.0410033 | ||||||||
\(79\) | 7.39724e6 | + | 7.39724e6i | 0.189916 | + | 0.189916i | 0.795660 | − | 0.605744i | \(-0.207124\pi\) |
−0.605744 | + | 0.795660i | \(0.707124\pi\) | |||||||
\(80\) | − | 5.24265e7i | − | 1.27994i | ||||||
\(81\) | −6.06434e6 | −0.140878 | ||||||||
\(82\) | 2.80441e6 | 0.0620277 | ||||||||
\(83\) | 6.15697e7 | 1.29734 | 0.648671 | − | 0.761069i | \(-0.275325\pi\) | ||||
0.648671 | + | 0.761069i | \(0.275325\pi\) | |||||||
\(84\) | 6.53738e7 | − | 6.53738e7i | 1.31307 | − | 1.31307i | ||||
\(85\) | −6.08649e7 | + | 6.08649e7i | −1.16598 | + | 1.16598i | ||||
\(86\) | − | 2.04077e6i | − | 0.0373079i | ||||||
\(87\) | −8.77001e7 | + | 3.32061e7i | −1.53082 | + | 0.579617i | ||||
\(88\) | −4.07108e6 | −0.0678859 | ||||||||
\(89\) | 5.11006e7 | + | 5.11006e7i | 0.814454 | + | 0.814454i | 0.985298 | − | 0.170844i | \(-0.0546496\pi\) |
−0.170844 | + | 0.985298i | \(0.554650\pi\) | |||||||
\(90\) | −3.40519e6 | − | 3.40519e6i | −0.0519005 | − | 0.0519005i | ||||
\(91\) | 5.73345e7i | 0.836085i | ||||||||
\(92\) | 2.68976e6i | 0.0375458i | ||||||||
\(93\) | − | 1.97357e8i | − | 2.63828i | ||||||
\(94\) | 2.15997e6 | 0.0276654 | ||||||||
\(95\) | −3.97218e7 | + | 3.97218e7i | −0.487680 | + | 0.487680i | ||||
\(96\) | − | 1.41708e7i | − | 0.166843i | ||||||
\(97\) | 6.15776e7 | − | 6.15776e7i | 0.695562 | − | 0.695562i | −0.267888 | − | 0.963450i | \(-0.586326\pi\) |
0.963450 | + | 0.267888i | \(0.0863257\pi\) | |||||||
\(98\) | 643557. | + | 643557.i | 0.00697722 | + | 0.00697722i | ||||
\(99\) | 1.13848e8 | − | 1.13848e8i | 1.18518 | − | 1.18518i | ||||
\(100\) | 6.48938e7i | 0.648938i | ||||||||
\(101\) | 3.53918e7 | + | 3.53918e7i | 0.340108 | + | 0.340108i | 0.856408 | − | 0.516300i | \(-0.172691\pi\) |
−0.516300 | + | 0.856408i | \(0.672691\pi\) | |||||||
\(102\) | −5.47329e6 | + | 5.47329e6i | −0.0505648 | + | 0.0505648i | ||||
\(103\) | −1.06856e8 | −0.949406 | −0.474703 | − | 0.880146i | \(-0.657444\pi\) | ||||
−0.474703 | + | 0.880146i | \(0.657444\pi\) | |||||||
\(104\) | 4.14191e6 | + | 4.14191e6i | 0.0354052 | + | 0.0354052i | ||||
\(105\) | −2.05234e8 | + | 2.05234e8i | −1.68846 | + | 1.68846i | ||||
\(106\) | 2.11146e6 | + | 2.11146e6i | 0.0167248 | + | 0.0167248i | ||||
\(107\) | −2.30440e8 | −1.75802 | −0.879008 | − | 0.476807i | \(-0.841794\pi\) | ||||
−0.879008 | + | 0.476807i | \(0.841794\pi\) | |||||||
\(108\) | 1.06853e8 | + | 1.06853e8i | 0.785405 | + | 0.785405i | ||||
\(109\) | − | 1.37188e8i | − | 0.971873i | −0.873994 | − | 0.485936i | \(-0.838479\pi\) | ||
0.873994 | − | 0.485936i | \(-0.161521\pi\) | |||||||
\(110\) | 6.38665e6 | 0.0436217 | ||||||||
\(111\) | 4.57245e8 | 3.01202 | ||||||||
\(112\) | −1.78095e8 | −1.13182 | ||||||||
\(113\) | −8.21417e7 | + | 8.21417e7i | −0.503790 | + | 0.503790i | −0.912614 | − | 0.408823i | \(-0.865939\pi\) |
0.408823 | + | 0.912614i | \(0.365939\pi\) | |||||||
\(114\) | −3.57200e6 | + | 3.57200e6i | −0.0211491 | + | 0.0211491i | ||||
\(115\) | − | 8.44418e6i | − | 0.0482799i | ||||||
\(116\) | 1.64881e8 | + | 7.43139e7i | 0.910623 | + | 0.410429i | ||||
\(117\) | −2.31658e8 | −1.23624 | ||||||||
\(118\) | −1.73706e6 | − | 1.73706e6i | −0.00895958 | − | 0.00895958i | ||||
\(119\) | 2.06761e8 | + | 2.06761e8i | 1.03105 | + | 1.03105i | ||||
\(120\) | 2.96526e7i | 0.143001i | ||||||||
\(121\) | − | 829827.i | − | 0.00387120i | ||||||
\(122\) | − | 7.21457e6i | − | 0.0325665i | ||||||
\(123\) | 6.82933e8 | 2.98372 | ||||||||
\(124\) | −2.69137e8 | + | 2.69137e8i | −1.13838 | + | 1.13838i | ||||
\(125\) | 1.09848e8i | 0.449938i | ||||||||
\(126\) | −1.15676e7 | + | 1.15676e7i | −0.0458945 | + | 0.0458945i | ||||
\(127\) | 5.82442e7 | + | 5.82442e7i | 0.223892 | + | 0.223892i | 0.810135 | − | 0.586243i | \(-0.199394\pi\) |
−0.586243 | + | 0.810135i | \(0.699394\pi\) | |||||||
\(128\) | −2.57614e7 | + | 2.57614e7i | −0.0959688 | + | 0.0959688i | ||||
\(129\) | − | 4.96972e8i | − | 1.79462i | ||||||
\(130\) | −6.49776e6 | − | 6.49776e6i | −0.0227504 | − | 0.0227504i | ||||
\(131\) | −4.54145e7 | + | 4.54145e7i | −0.154209 | + | 0.154209i | −0.779995 | − | 0.625786i | \(-0.784778\pi\) |
0.625786 | + | 0.779995i | \(0.284778\pi\) | |||||||
\(132\) | −4.95411e8 | −1.63181 | ||||||||
\(133\) | 1.34937e8 | + | 1.34937e8i | 0.431245 | + | 0.431245i | ||||
\(134\) | 3.72522e6 | − | 3.72522e6i | 0.0115540 | − | 0.0115540i | ||||
\(135\) | −3.35454e8 | − | 3.35454e8i | −1.00995 | − | 1.00995i | ||||
\(136\) | 2.98732e7 | 0.0873226 | ||||||||
\(137\) | −2.83150e8 | − | 2.83150e8i | −0.803775 | − | 0.803775i | 0.179909 | − | 0.983683i | \(-0.442420\pi\) |
−0.983683 | + | 0.179909i | \(0.942420\pi\) | |||||||
\(138\) | − | 759345.i | − | 0.00209374i | ||||||
\(139\) | −4.91187e8 | −1.31579 | −0.657897 | − | 0.753108i | \(-0.728554\pi\) | ||||
−0.657897 | + | 0.753108i | \(0.728554\pi\) | |||||||
\(140\) | 5.59758e8 | 1.45710 | ||||||||
\(141\) | 5.26000e8 | 1.33079 | ||||||||
\(142\) | 2.09174e6 | − | 2.09174e6i | 0.00514464 | − | 0.00514464i | ||||
\(143\) | 2.17244e8 | − | 2.17244e8i | 0.519521 | − | 0.519521i | ||||
\(144\) | − | 7.19584e8i | − | 1.67352i | ||||||
\(145\) | −5.17625e8 | − | 2.33300e8i | −1.17096 | − | 0.527767i | ||||
\(146\) | −1.45224e7 | −0.0319615 | ||||||||
\(147\) | 1.56720e8 | + | 1.56720e8i | 0.335625 | + | 0.335625i | ||||
\(148\) | −6.23549e8 | − | 6.23549e8i | −1.29964 | − | 1.29964i | ||||
\(149\) | 3.37753e8i | 0.685259i | 0.939471 | + | 0.342629i | \(0.111318\pi\) | ||||
−0.939471 | + | 0.342629i | \(0.888682\pi\) | |||||||
\(150\) | − | 1.83202e7i | − | 0.0361880i | ||||||
\(151\) | 4.47050e8i | 0.859900i | 0.902853 | + | 0.429950i | \(0.141469\pi\) | ||||
−0.902853 | + | 0.429950i | \(0.858531\pi\) | |||||||
\(152\) | 1.94960e7 | 0.0365233 | ||||||||
\(153\) | −8.35407e8 | + | 8.35407e8i | −1.52452 | + | 1.52452i | ||||
\(154\) | − | 2.16957e7i | − | 0.0385737i | ||||||
\(155\) | 8.44925e8 | − | 8.44925e8i | 1.46383 | − | 1.46383i | ||||
\(156\) | 5.04029e8 | + | 5.04029e8i | 0.851055 | + | 0.851055i | ||||
\(157\) | 4.12641e8 | − | 4.12641e8i | 0.679162 | − | 0.679162i | −0.280649 | − | 0.959811i | \(-0.590550\pi\) |
0.959811 | + | 0.280649i | \(0.0905496\pi\) | |||||||
\(158\) | 5.69571e6i | 0.00913944i | ||||||||
\(159\) | 5.14186e8 | + | 5.14186e8i | 0.804511 | + | 0.804511i | ||||
\(160\) | 6.06680e7 | − | 6.06680e7i | 0.0925720 | − | 0.0925720i | ||||
\(161\) | −2.86852e7 | −0.0426928 | ||||||||
\(162\) | −2.33470e6 | − | 2.33470e6i | −0.00338978 | − | 0.00338978i | ||||
\(163\) | −8.01327e8 | + | 8.01327e8i | −1.13517 | + | 1.13517i | −0.145861 | + | 0.989305i | \(0.546595\pi\) |
−0.989305 | + | 0.145861i | \(0.953405\pi\) | |||||||
\(164\) | −9.31322e8 | − | 9.31322e8i | −1.28743 | − | 1.28743i | ||||
\(165\) | 1.55528e9 | 2.09833 | ||||||||
\(166\) | 2.37037e7 | + | 2.37037e7i | 0.0312164 | + | 0.0312164i | ||||
\(167\) | − | 8.76082e8i | − | 1.12636i | −0.826333 | − | 0.563182i | \(-0.809577\pi\) | ||
0.826333 | − | 0.563182i | \(-0.190423\pi\) | |||||||
\(168\) | 1.00731e8 | 0.126452 | ||||||||
\(169\) | 3.73684e8 | 0.458098 | ||||||||
\(170\) | −4.68646e7 | −0.0561112 | ||||||||
\(171\) | −5.45206e8 | + | 5.45206e8i | −0.637641 | + | 0.637641i | ||||
\(172\) | −6.77725e8 | + | 6.77725e8i | −0.774355 | + | 0.774355i | ||||
\(173\) | 9.38376e7i | 0.104759i | 0.998627 | + | 0.0523796i | \(0.0166806\pi\) | ||||
−0.998627 | + | 0.0523796i | \(0.983319\pi\) | |||||||
\(174\) | −4.65476e7 | − | 2.09796e7i | −0.0507808 | − | 0.0228876i | ||||
\(175\) | −6.92068e8 | −0.737898 | ||||||||
\(176\) | 6.74812e8 | + | 6.74812e8i | 0.703286 | + | 0.703286i | ||||
\(177\) | −4.23012e8 | − | 4.23012e8i | −0.430982 | − | 0.430982i | ||||
\(178\) | 3.93464e7i | 0.0391944i | ||||||||
\(179\) | − | 5.27432e8i | − | 0.513753i | −0.966444 | − | 0.256877i | \(-0.917307\pi\) | ||
0.966444 | − | 0.256877i | \(-0.0826934\pi\) | |||||||
\(180\) | 2.26168e9i | 2.15447i | ||||||||
\(181\) | 1.00453e8 | 0.0935939 | 0.0467969 | − | 0.998904i | \(-0.485099\pi\) | ||||
0.0467969 | + | 0.998904i | \(0.485099\pi\) | |||||||
\(182\) | −2.20731e7 | + | 2.20731e7i | −0.0201177 | + | 0.0201177i | ||||
\(183\) | − | 1.75690e9i | − | 1.56654i | ||||||
\(184\) | −2.07225e6 | + | 2.07225e6i | −0.00180789 | + | 0.00180789i | ||||
\(185\) | 1.95756e9 | + | 1.95756e9i | 1.67120 | + | 1.67120i | ||||
\(186\) | 7.59802e7 | − | 7.59802e7i | 0.0634817 | − | 0.0634817i | ||||
\(187\) | − | 1.56686e9i | − | 1.28133i | ||||||
\(188\) | −7.17310e8 | − | 7.17310e8i | −0.574217 | − | 0.574217i | ||||
\(189\) | −1.13955e9 | + | 1.13955e9i | −0.893073 | + | 0.893073i | ||||
\(190\) | −3.05849e7 | −0.0234689 | ||||||||
\(191\) | −3.80660e7 | − | 3.80660e7i | −0.0286025 | − | 0.0286025i | 0.692661 | − | 0.721263i | \(-0.256438\pi\) |
−0.721263 | + | 0.692661i | \(0.756438\pi\) | |||||||
\(192\) | −1.56200e9 | + | 1.56200e9i | −1.14941 | + | 1.14941i | ||||
\(193\) | 1.91551e9 | + | 1.91551e9i | 1.38056 | + | 1.38056i | 0.843627 | + | 0.536930i | \(0.180416\pi\) |
0.536930 | + | 0.843627i | \(0.319584\pi\) | |||||||
\(194\) | 4.74134e7 | 0.0334730 | ||||||||
\(195\) | −1.58234e9 | − | 1.58234e9i | −1.09436 | − | 1.09436i | ||||
\(196\) | − | 4.27440e8i | − | 0.289635i | ||||||
\(197\) | 1.51393e9 | 1.00517 | 0.502586 | − | 0.864527i | \(-0.332382\pi\) | ||||
0.502586 | + | 0.864527i | \(0.332382\pi\) | |||||||
\(198\) | 8.76605e7 | 0.0570353 | ||||||||
\(199\) | −2.13226e9 | −1.35965 | −0.679827 | − | 0.733372i | \(-0.737945\pi\) | ||||
−0.679827 | + | 0.733372i | \(0.737945\pi\) | |||||||
\(200\) | −4.99958e7 | + | 4.99958e7i | −0.0312474 | + | 0.0312474i | ||||
\(201\) | 9.07170e8 | − | 9.07170e8i | 0.555782 | − | 0.555782i | ||||
\(202\) | 2.72509e7i | 0.0163672i | ||||||||
\(203\) | −7.92529e8 | + | 1.75839e9i | −0.466693 | + | 1.03546i | ||||
\(204\) | 3.63528e9 | 2.09902 | ||||||||
\(205\) | 2.92378e9 | + | 2.92378e9i | 1.65550 | + | 1.65550i | ||||
\(206\) | −4.11385e7 | − | 4.11385e7i | −0.0228444 | − | 0.0228444i | ||||
\(207\) | − | 1.15901e8i | − | 0.0631259i | ||||||
\(208\) | − | 1.37310e9i | − | 0.733584i | ||||||
\(209\) | − | 1.02257e9i | − | 0.535928i | ||||||
\(210\) | −1.58025e8 | −0.0812549 | ||||||||
\(211\) | 5.04224e8 | − | 5.04224e8i | 0.254387 | − | 0.254387i | −0.568380 | − | 0.822766i | \(-0.692430\pi\) |
0.822766 | + | 0.568380i | \(0.192430\pi\) | |||||||
\(212\) | − | 1.40240e9i | − | 0.694271i | ||||||
\(213\) | 5.09384e8 | − | 5.09384e8i | 0.247473 | − | 0.247473i | ||||
\(214\) | −8.87168e7 | − | 8.87168e7i | −0.0423010 | − | 0.0423010i | ||||
\(215\) | 2.12764e9 | − | 2.12764e9i | 0.995736 | − | 0.995736i | ||||
\(216\) | 1.64645e8i | 0.0756369i | ||||||||
\(217\) | −2.87025e9 | − | 2.87025e9i | −1.29443 | − | 1.29443i | ||||
\(218\) | 5.28158e7 | − | 5.28158e7i | 0.0233850 | − | 0.0233850i | ||||
\(219\) | −3.53651e9 | −1.53744 | ||||||||
\(220\) | −2.12096e9 | − | 2.12096e9i | −0.905401 | − | 0.905401i | ||||
\(221\) | −1.59411e9 | + | 1.59411e9i | −0.668268 | + | 0.668268i | ||||
\(222\) | 1.76034e8 | + | 1.76034e8i | 0.0724746 | + | 0.0724746i | ||||
\(223\) | −4.05878e9 | −1.64126 | −0.820628 | − | 0.571463i | \(-0.806376\pi\) | ||||
−0.820628 | + | 0.571463i | \(0.806376\pi\) | |||||||
\(224\) | −2.06092e8 | − | 2.06092e8i | −0.0818594 | − | 0.0818594i | ||||
\(225\) | − | 2.79627e9i | − | 1.09106i | ||||||
\(226\) | −6.32473e7 | −0.0242442 | ||||||||
\(227\) | −1.26056e9 | −0.474744 | −0.237372 | − | 0.971419i | \(-0.576286\pi\) | ||||
−0.237372 | + | 0.971419i | \(0.576286\pi\) | |||||||
\(228\) | 2.37247e9 | 0.877931 | ||||||||
\(229\) | −3.83854e9 | + | 3.83854e9i | −1.39580 | + | 1.39580i | −0.584178 | + | 0.811626i | \(0.698583\pi\) |
−0.811626 | + | 0.584178i | \(0.801417\pi\) | |||||||
\(230\) | 3.25091e6 | − | 3.25091e6i | 0.00116170 | − | 0.00116170i | ||||
\(231\) | − | 5.28337e9i | − | 1.85551i | ||||||
\(232\) | 6.97750e7 | + | 1.84281e8i | 0.0240851 | + | 0.0636106i | ||||
\(233\) | 2.44354e9 | 0.829079 | 0.414539 | − | 0.910031i | \(-0.363943\pi\) | ||||
0.414539 | + | 0.910031i | \(0.363943\pi\) | |||||||
\(234\) | −8.91856e7 | − | 8.91856e7i | −0.0297462 | − | 0.0297462i | ||||
\(235\) | 2.25191e9 | + | 2.25191e9i | 0.738380 | + | 0.738380i | ||||
\(236\) | 1.15373e9i | 0.371926i | ||||||||
\(237\) | 1.38703e9i | 0.439634i | ||||||||
\(238\) | 1.59201e8i | 0.0496179i | ||||||||
\(239\) | 3.12903e8 | 0.0958999 | 0.0479499 | − | 0.998850i | \(-0.484731\pi\) | ||||
0.0479499 | + | 0.998850i | \(0.484731\pi\) | |||||||
\(240\) | 4.91514e9 | − | 4.91514e9i | 1.48146 | − | 1.48146i | ||||
\(241\) | − | 2.35690e9i | − | 0.698671i | −0.936998 | − | 0.349336i | \(-0.886407\pi\) | ||
0.936998 | − | 0.349336i | \(-0.113593\pi\) | |||||||
\(242\) | 319474. | − | 319474.i | 9.31481e−5 | − | 9.31481e-5i | ||||
\(243\) | 2.17316e9 | + | 2.17316e9i | 0.623257 | + | 0.623257i | ||||
\(244\) | −2.39590e9 | + | 2.39590e9i | −0.675942 | + | 0.675942i | ||||
\(245\) | 1.34190e9i | 0.372439i | ||||||||
\(246\) | 2.62922e8 | + | 2.62922e8i | 0.0717936 | + | 0.0717936i | ||||
\(247\) | −1.04036e9 | + | 1.04036e9i | −0.279508 | + | 0.279508i | ||||
\(248\) | −4.14700e8 | −0.109629 | ||||||||
\(249\) | 5.77234e9 | + | 5.77234e9i | 1.50160 | + | 1.50160i | ||||
\(250\) | −4.22904e7 | + | 4.22904e7i | −0.0108263 | + | 0.0108263i | ||||
\(251\) | 1.52610e9 | + | 1.52610e9i | 0.384492 | + | 0.384492i | 0.872717 | − | 0.488226i | \(-0.162356\pi\) |
−0.488226 | + | 0.872717i | \(0.662356\pi\) | |||||||
\(252\) | 7.68301e9 | 1.90515 | ||||||||
\(253\) | 1.08690e8 | + | 1.08690e8i | 0.0265282 | + | 0.0265282i | ||||
\(254\) | 4.48467e7i | 0.0107745i | ||||||||
\(255\) | −1.14125e10 | −2.69911 | ||||||||
\(256\) | 4.24532e9 | 0.988441 | ||||||||
\(257\) | 1.14264e9 | 0.261924 | 0.130962 | − | 0.991387i | \(-0.458193\pi\) | ||||
0.130962 | + | 0.991387i | \(0.458193\pi\) | |||||||
\(258\) | 1.91329e8 | − | 1.91329e8i | 0.0431819 | − | 0.0431819i | ||||
\(259\) | 6.64992e9 | − | 6.64992e9i | 1.47781 | − | 1.47781i | ||||
\(260\) | 4.31571e9i | 0.944406i | ||||||||
\(261\) | −7.10471e9 | − | 3.20218e9i | −1.53103 | − | 0.690055i | ||||
\(262\) | −3.49681e7 | −0.00742108 | ||||||||
\(263\) | −3.38727e9 | − | 3.38727e9i | −0.707989 | − | 0.707989i | 0.258123 | − | 0.966112i | \(-0.416896\pi\) |
−0.966112 | + | 0.258123i | \(0.916896\pi\) | |||||||
\(264\) | −3.81676e8 | − | 3.81676e8i | −0.0785741 | − | 0.0785741i | ||||
\(265\) | 4.40268e9i | 0.892757i | ||||||||
\(266\) | 1.03898e8i | 0.0207530i | ||||||||
\(267\) | 9.58168e9i | 1.88537i | ||||||||
\(268\) | −2.47423e9 | −0.479624 | ||||||||
\(269\) | −6.36007e9 | + | 6.36007e9i | −1.21466 | + | 1.21466i | −0.245177 | + | 0.969478i | \(0.578846\pi\) |
−0.969478 | + | 0.245177i | \(0.921154\pi\) | |||||||
\(270\) | − | 2.58292e8i | − | 0.0486022i | ||||||
\(271\) | −2.36975e9 | + | 2.36975e9i | −0.439366 | + | 0.439366i | −0.891798 | − | 0.452433i | \(-0.850556\pi\) |
0.452433 | + | 0.891798i | \(0.350556\pi\) | |||||||
\(272\) | −4.95170e9 | − | 4.95170e9i | −0.904647 | − | 0.904647i | ||||
\(273\) | −5.37528e9 | + | 5.37528e9i | −0.967722 | + | 0.967722i | ||||
\(274\) | − | 2.18019e8i | − | 0.0386805i | ||||||
\(275\) | 2.62229e9 | + | 2.62229e9i | 0.458511 | + | 0.458511i | ||||
\(276\) | −2.52173e8 | + | 2.52173e8i | −0.0434572 | + | 0.0434572i | ||||
\(277\) | 4.94342e9 | 0.839670 | 0.419835 | − | 0.907600i | \(-0.362088\pi\) | ||||
0.419835 | + | 0.907600i | \(0.362088\pi\) | |||||||
\(278\) | −1.89102e8 | − | 1.89102e8i | −0.0316604 | − | 0.0316604i | ||||
\(279\) | 1.15971e10 | − | 1.15971e10i | 1.91396 | − | 1.91396i | ||||
\(280\) | 4.31251e8 | + | 4.31251e8i | 0.0701613 | + | 0.0701613i | ||||
\(281\) | −8.54127e9 | −1.36993 | −0.684963 | − | 0.728577i | \(-0.740182\pi\) | ||||
−0.684963 | + | 0.728577i | \(0.740182\pi\) | |||||||
\(282\) | 2.02504e8 | + | 2.02504e8i | 0.0320212 | + | 0.0320212i | ||||
\(283\) | − | 3.36436e9i | − | 0.524513i | −0.964998 | − | 0.262257i | \(-0.915533\pi\) | ||
0.964998 | − | 0.262257i | \(-0.0844667\pi\) | |||||||
\(284\) | −1.38930e9 | −0.213562 | ||||||||
\(285\) | −7.44808e9 | −1.12892 | ||||||||
\(286\) | 1.67273e8 | 0.0250012 | ||||||||
\(287\) | 9.93219e9 | − | 9.93219e9i | 1.46392 | − | 1.46392i | ||||
\(288\) | 8.32705e8 | − | 8.32705e8i | 0.121038 | − | 0.121038i | ||||
\(289\) | 4.52168e9i | 0.648199i | ||||||||
\(290\) | −1.09462e8 | − | 2.89098e8i | −0.0154764 | − | 0.0408745i | ||||
\(291\) | 1.15462e10 | 1.61015 | ||||||||
\(292\) | 4.82278e9 | + | 4.82278e9i | 0.663385 | + | 0.663385i | ||||
\(293\) | 6.59250e9 | + | 6.59250e9i | 0.894499 | + | 0.894499i | 0.994943 | − | 0.100444i | \(-0.0320263\pi\) |
−0.100444 | + | 0.994943i | \(0.532026\pi\) | |||||||
\(294\) | 1.20671e8i | 0.0161515i | ||||||||
\(295\) | − | 3.62200e9i | − | 0.478256i | ||||||
\(296\) | − | 9.60795e8i | − | 0.125160i | ||||||
\(297\) | 8.63566e9 | 1.10986 | ||||||||
\(298\) | −1.30031e8 | + | 1.30031e8i | −0.0164886 | + | 0.0164886i | ||||
\(299\) | − | 2.21162e8i | − | 0.0276710i | ||||||
\(300\) | −6.08399e9 | + | 6.08399e9i | −0.751110 | + | 0.751110i | ||||
\(301\) | −7.22768e9 | − | 7.22768e9i | −0.880508 | − | 0.880508i | ||||
\(302\) | −1.72109e8 | + | 1.72109e8i | −0.0206908 | + | 0.0206908i | ||||
\(303\) | 6.63618e9i | 0.787313i | ||||||||
\(304\) | −3.23160e9 | − | 3.23160e9i | −0.378375 | − | 0.378375i | ||||
\(305\) | 7.52165e9 | − | 7.52165e9i | 0.869188 | − | 0.869188i | ||||
\(306\) | −6.43245e8 | −0.0733653 | ||||||||
\(307\) | 1.92561e9 | + | 1.92561e9i | 0.216778 | + | 0.216778i | 0.807139 | − | 0.590361i | \(-0.201015\pi\) |
−0.590361 | + | 0.807139i | \(0.701015\pi\) | |||||||
\(308\) | −7.20497e9 | + | 7.20497e9i | −0.800626 | + | 0.800626i | ||||
\(309\) | −1.00181e10 | − | 1.00181e10i | −1.09888 | − | 1.09888i | ||||
\(310\) | 6.50574e8 | 0.0704449 | ||||||||
\(311\) | −5.70463e9 | − | 5.70463e9i | −0.609798 | − | 0.609798i | 0.333095 | − | 0.942893i | \(-0.391907\pi\) |
−0.942893 | + | 0.333095i | \(0.891907\pi\) | |||||||
\(312\) | 7.76633e8i | 0.0819591i | ||||||||
\(313\) | 1.73518e10 | 1.80787 | 0.903933 | − | 0.427674i | \(-0.140667\pi\) | ||||
0.903933 | + | 0.427674i | \(0.140667\pi\) | |||||||
\(314\) | 3.17724e8 | 0.0326837 | ||||||||
\(315\) | −2.41199e10 | −2.44982 | ||||||||
\(316\) | 1.89150e9 | − | 1.89150e9i | 0.189696 | − | 0.189696i | ||||
\(317\) | −5.25464e9 | + | 5.25464e9i | −0.520363 | + | 0.520363i | −0.917681 | − | 0.397318i | \(-0.869941\pi\) |
0.397318 | + | 0.917681i | \(0.369941\pi\) | |||||||
\(318\) | 3.95912e8i | 0.0387160i | ||||||||
\(319\) | 9.66559e9 | − | 3.65971e9i | 0.933396 | − | 0.353414i | ||||
\(320\) | −1.33745e10 | −1.27549 | ||||||||
\(321\) | −2.16044e10 | − | 2.16044e10i | −2.03481 | − | 2.03481i | ||||
\(322\) | −1.10435e7 | − | 1.10435e7i | −0.00102727 | − | 0.00102727i | ||||
\(323\) | 7.50349e9i | 0.689372i | ||||||||
\(324\) | 1.55067e9i | 0.140715i | ||||||||
\(325\) | − | 5.33581e9i | − | 0.478263i | ||||||
\(326\) | −6.17004e8 | −0.0546283 | ||||||||
\(327\) | 1.28618e10 | − | 1.28618e10i | 1.12489 | − | 1.12489i | ||||
\(328\) | − | 1.43503e9i | − | 0.123984i | ||||||
\(329\) | 7.64984e9 | − | 7.64984e9i | 0.652933 | − | 0.652933i | ||||
\(330\) | 5.98767e8 | + | 5.98767e8i | 0.0504896 | + | 0.0504896i | ||||
\(331\) | 8.71393e8 | − | 8.71393e8i | 0.0725942 | − | 0.0725942i | −0.669877 | − | 0.742472i | \(-0.733653\pi\) |
0.742472 | + | 0.669877i | \(0.233653\pi\) | |||||||
\(332\) | − | 1.57436e10i | − | 1.29584i | ||||||
\(333\) | 2.68687e10 | + | 2.68687e10i | 2.18509 | + | 2.18509i | ||||
\(334\) | 3.37282e8 | − | 3.37282e8i | 0.0271024 | − | 0.0271024i | ||||
\(335\) | 7.76756e9 | 0.616745 | ||||||||
\(336\) | −1.66969e10 | − | 1.66969e10i | −1.31002 | − | 1.31002i | ||||
\(337\) | 5.79665e9 | − | 5.79665e9i | 0.449426 | − | 0.449426i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(338\) | 1.43864e8 | + | 1.43864e8i | 0.0110227 | + | 0.0110227i | ||||
\(339\) | −1.54021e10 | −1.16622 | ||||||||
\(340\) | 1.55634e10 | + | 1.55634e10i | 1.16463 | + | 1.16463i | ||||
\(341\) | 2.17511e10i | 1.60866i | ||||||||
\(342\) | −4.19796e8 | −0.0306856 | ||||||||
\(343\) | −1.11620e10 | −0.806429 | ||||||||
\(344\) | −1.04427e9 | −0.0745727 | ||||||||
\(345\) | 7.91667e8 | − | 7.91667e8i | 0.0558813 | − | 0.0558813i | ||||
\(346\) | −3.61264e7 | + | 3.61264e7i | −0.00252070 | + | 0.00252070i | ||||
\(347\) | 1.44331e10i | 0.995500i | 0.867321 | + | 0.497750i | \(0.165840\pi\) | ||||
−0.867321 | + | 0.497750i | \(0.834160\pi\) | |||||||
\(348\) | 8.49093e9 | + | 2.24252e10i | 0.578946 | + | 1.52904i | ||||
\(349\) | 4.35187e8 | 0.0293342 | 0.0146671 | − | 0.999892i | \(-0.495331\pi\) | ||||
0.0146671 | + | 0.999892i | \(0.495331\pi\) | |||||||
\(350\) | −2.66438e8 | − | 2.66438e8i | −0.0177552 | − | 0.0177552i | ||||
\(351\) | −8.78589e9 | − | 8.78589e9i | −0.578838 | − | 0.578838i | ||||
\(352\) | 1.56179e9i | 0.101731i | ||||||||
\(353\) | 4.34810e9i | 0.280028i | 0.990150 | + | 0.140014i | \(0.0447147\pi\) | ||||
−0.990150 | + | 0.140014i | \(0.955285\pi\) | |||||||
\(354\) | − | 3.25710e8i | − | 0.0207404i | ||||||
\(355\) | 4.36156e9 | 0.274617 | ||||||||
\(356\) | 1.30666e10 | − | 1.30666e10i | 0.813510 | − | 0.813510i | ||||
\(357\) | 3.87688e10i | 2.38677i | ||||||||
\(358\) | 2.03056e8 | − | 2.03056e8i | 0.0123618 | − | 0.0123618i | ||||
\(359\) | −5.31301e9 | − | 5.31301e9i | −0.319862 | − | 0.319862i | 0.528852 | − | 0.848714i | \(-0.322623\pi\) |
−0.848714 | + | 0.528852i | \(0.822623\pi\) | |||||||
\(360\) | −1.74245e9 | + | 1.74245e9i | −0.103741 | + | 0.103741i | ||||
\(361\) | − | 1.20866e10i | − | 0.711665i | ||||||
\(362\) | 3.86732e7 | + | 3.86732e7i | 0.00225204 | + | 0.00225204i | ||||
\(363\) | 7.77987e7 | − | 7.77987e7i | 0.00448070 | − | 0.00448070i | ||||
\(364\) | 1.46606e10 | 0.835117 | ||||||||
\(365\) | −1.51405e10 | − | 1.51405e10i | −0.853041 | − | 0.853041i | ||||
\(366\) | 6.76387e8 | − | 6.76387e8i | 0.0376939 | − | 0.0376939i | ||||
\(367\) | 8.06359e9 | + | 8.06359e9i | 0.444492 | + | 0.444492i | 0.893519 | − | 0.449026i | \(-0.148229\pi\) |
−0.449026 | + | 0.893519i | \(0.648229\pi\) | |||||||
\(368\) | 6.86982e8 | 0.0374588 | ||||||||
\(369\) | 4.01306e10 | + | 4.01306e10i | 2.16456 | + | 2.16456i | ||||
\(370\) | 1.50728e9i | 0.0804242i | ||||||||
\(371\) | 1.49561e10 | 0.789445 | ||||||||
\(372\) | −5.04648e10 | −2.63522 | ||||||||
\(373\) | −9.26204e9 | −0.478488 | −0.239244 | − | 0.970959i | \(-0.576900\pi\) | ||||
−0.239244 | + | 0.970959i | \(0.576900\pi\) | |||||||
\(374\) | 6.03222e8 | − | 6.03222e8i | 0.0308312 | − | 0.0308312i | ||||
\(375\) | −1.02986e10 | + | 1.02986e10i | −0.520779 | + | 0.520779i | ||||
\(376\) | − | 1.10527e9i | − | 0.0552988i | ||||||
\(377\) | −1.35571e10 | − | 6.11037e9i | −0.671123 | − | 0.302484i | ||||
\(378\) | −8.77429e8 | −0.0429779 | ||||||||
\(379\) | 4.45713e9 | + | 4.45713e9i | 0.216022 | + | 0.216022i | 0.806820 | − | 0.590797i | \(-0.201187\pi\) |
−0.590797 | + | 0.806820i | \(0.701187\pi\) | |||||||
\(380\) | 1.01570e10 | + | 1.01570e10i | 0.487115 | + | 0.487115i | ||||
\(381\) | 1.09211e10i | 0.518284i | ||||||||
\(382\) | − | 2.93100e7i | − | 0.00137646i | ||||||
\(383\) | − | 2.49677e10i | − | 1.16033i | −0.814498 | − | 0.580167i | \(-0.802987\pi\) | ||
0.814498 | − | 0.580167i | \(-0.197013\pi\) | |||||||
\(384\) | −4.83042e9 | −0.222157 | ||||||||
\(385\) | 2.26192e10 | − | 2.26192e10i | 1.02952 | − | 1.02952i | ||||
\(386\) | 1.47490e9i | 0.0664374i | ||||||||
\(387\) | 2.92031e10 | − | 2.92031e10i | 1.30192 | − | 1.30192i | ||||
\(388\) | −1.57456e10 | − | 1.57456e10i | −0.694757 | − | 0.694757i | ||||
\(389\) | −1.83603e10 | + | 1.83603e10i | −0.801829 | + | 0.801829i | −0.983381 | − | 0.181553i | \(-0.941888\pi\) |
0.181553 | + | 0.983381i | \(0.441888\pi\) | |||||||
\(390\) | − | 1.21837e9i | − | 0.0526648i | ||||||
\(391\) | −7.97557e8 | − | 7.97557e8i | −0.0341236 | − | 0.0341236i | ||||
\(392\) | 3.29310e8 | − | 3.29310e8i | 0.0139464 | − | 0.0139464i | ||||
\(393\) | −8.51548e9 | −0.356976 | ||||||||
\(394\) | 5.82846e8 | + | 5.82846e8i | 0.0241863 | + | 0.0241863i | ||||
\(395\) | −5.93815e9 | + | 5.93815e9i | −0.243929 | + | 0.243929i | ||||
\(396\) | −2.91114e10 | − | 2.91114e10i | −1.18381 | − | 1.18381i | ||||
\(397\) | 1.00393e9 | 0.0404151 | 0.0202075 | − | 0.999796i | \(-0.493567\pi\) | ||||
0.0202075 | + | 0.999796i | \(0.493567\pi\) | |||||||
\(398\) | −8.20898e8 | − | 8.20898e8i | −0.0327158 | − | 0.0327158i | ||||
\(399\) | 2.53014e10i | 0.998283i | ||||||||
\(400\) | 1.65743e10 | 0.647435 | ||||||||
\(401\) | 6.28405e9 | 0.243031 | 0.121516 | − | 0.992590i | \(-0.461225\pi\) | ||||
0.121516 | + | 0.992590i | \(0.461225\pi\) | |||||||
\(402\) | 6.98501e8 | 0.0267462 | ||||||||
\(403\) | 2.21295e10 | − | 2.21295e10i | 0.838978 | − | 0.838978i | ||||
\(404\) | 9.04981e9 | − | 9.04981e9i | 0.339715 | − | 0.339715i | ||||
\(405\) | − | 4.86816e9i | − | 0.180944i | ||||||
\(406\) | −9.82076e8 | + | 3.71846e8i | −0.0361444 | + | 0.0136855i | ||||
\(407\) | −5.03939e10 | −1.83654 | ||||||||
\(408\) | 2.80070e9 | + | 2.80070e9i | 0.101071 | + | 0.101071i | ||||
\(409\) | 1.83804e9 | + | 1.83804e9i | 0.0656845 | + | 0.0656845i | 0.739186 | − | 0.673501i | \(-0.235210\pi\) |
−0.673501 | + | 0.739186i | \(0.735210\pi\) | |||||||
\(410\) | 2.25124e9i | 0.0796686i | ||||||||
\(411\) | − | 5.30923e10i | − | 1.86065i | ||||||
\(412\) | 2.73236e10i | 0.948306i | ||||||||
\(413\) | −1.23041e10 | −0.422911 | ||||||||
\(414\) | 4.46207e7 | − | 4.46207e7i | 0.00151892 | − | 0.00151892i | ||||
\(415\) | 4.94252e10i | 1.66631i | ||||||||
\(416\) | 1.58896e9 | − | 1.58896e9i | 0.0530566 | − | 0.0530566i | ||||
\(417\) | −4.60503e10 | − | 4.60503e10i | −1.52296 | − | 1.52296i | ||||
\(418\) | 3.93677e8 | − | 3.93677e8i | 0.0128954 | − | 0.0128954i | ||||
\(419\) | − | 2.03704e10i | − | 0.660911i | −0.943822 | − | 0.330455i | \(-0.892798\pi\) | ||
0.943822 | − | 0.330455i | \(-0.107202\pi\) | |||||||
\(420\) | 5.24790e10 | + | 5.24790e10i | 1.68651 | + | 1.68651i | ||||
\(421\) | 1.07169e10 | − | 1.07169e10i | 0.341147 | − | 0.341147i | −0.515652 | − | 0.856798i | \(-0.672450\pi\) |
0.856798 | + | 0.515652i | \(0.172450\pi\) | |||||||
\(422\) | 3.88242e8 | 0.0122420 | ||||||||
\(423\) | 3.09089e10 | + | 3.09089e10i | 0.965431 | + | 0.965431i | ||||
\(424\) | 1.08044e9 | − | 1.08044e9i | 0.0334302 | − | 0.0334302i | ||||
\(425\) | −1.92421e10 | − | 1.92421e10i | −0.589789 | − | 0.589789i | ||||
\(426\) | 3.92214e8 | 0.0119093 | ||||||||
\(427\) | −2.55514e10 | − | 2.55514e10i | −0.768604 | − | 0.768604i | ||||
\(428\) | 5.89243e10i | 1.75598i | ||||||||
\(429\) | 4.07345e10 | 1.20263 | ||||||||
\(430\) | 1.63824e9 | 0.0479184 | ||||||||
\(431\) | 2.98922e10 | 0.866261 | 0.433130 | − | 0.901331i | \(-0.357409\pi\) | ||||
0.433130 | + | 0.901331i | \(0.357409\pi\) | |||||||
\(432\) | 2.72911e10 | − | 2.72911e10i | 0.783585 | − | 0.783585i | ||||
\(433\) | 3.95905e10 | − | 3.95905e10i | 1.12626 | − | 1.12626i | 0.135483 | − | 0.990780i | \(-0.456741\pi\) |
0.990780 | − | 0.135483i | \(-0.0432586\pi\) | |||||||
\(434\) | − | 2.21003e9i | − | 0.0622929i | ||||||
\(435\) | −2.66563e10 | − | 7.04014e10i | −0.744462 | − | 1.96618i | ||||
\(436\) | −3.50794e10 | −0.970747 | ||||||||
\(437\) | −5.20504e8 | − | 5.20504e8i | −0.0142724 | − | 0.0142724i | ||||
\(438\) | −1.36152e9 | − | 1.36152e9i | −0.0369936 | − | 0.0369936i | ||||
\(439\) | 4.59391e9i | 0.123687i | 0.998086 | + | 0.0618435i | \(0.0196980\pi\) | ||||
−0.998086 | + | 0.0618435i | \(0.980302\pi\) | |||||||
\(440\) | − | 3.26807e9i | − | 0.0871928i | ||||||
\(441\) | 1.84184e10i | 0.486964i | ||||||||
\(442\) | −1.22743e9 | −0.0321594 | ||||||||
\(443\) | 7.38201e9 | − | 7.38201e9i | 0.191672 | − | 0.191672i | −0.604746 | − | 0.796418i | \(-0.706725\pi\) |
0.796418 | + | 0.604746i | \(0.206725\pi\) | |||||||
\(444\) | − | 1.16919e11i | − | 3.00853i | ||||||
\(445\) | −4.10211e10 | + | 4.10211e10i | −1.04609 | + | 1.04609i | ||||
\(446\) | −1.56259e9 | − | 1.56259e9i | −0.0394916 | − | 0.0394916i | ||||
\(447\) | −3.16654e10 | + | 3.16654e10i | −0.793149 | + | 0.793149i | ||||
\(448\) | 4.54336e10i | 1.12789i | ||||||||
\(449\) | 3.68491e10 | + | 3.68491e10i | 0.906654 | + | 0.906654i | 0.996001 | − | 0.0893470i | \(-0.0284780\pi\) |
−0.0893470 | + | 0.996001i | \(0.528478\pi\) | |||||||
\(450\) | 1.07653e9 | − | 1.07653e9i | 0.0262529 | − | 0.0262529i | ||||
\(451\) | −7.52673e10 | −1.81928 | ||||||||
\(452\) | 2.10039e10 | + | 2.10039e10i | 0.503207 | + | 0.503207i | ||||
\(453\) | −4.19123e10 | + | 4.19123e10i | −0.995287 | + | 0.995287i | ||||
\(454\) | −4.85301e8 | − | 4.85301e8i | −0.0114232 | − | 0.0114232i | ||||
\(455\) | −4.60254e10 | −1.07387 | ||||||||
\(456\) | 1.82780e9 | + | 1.82780e9i | 0.0422737 | + | 0.0422737i | ||||
\(457\) | − | 6.58821e10i | − | 1.51044i | −0.655473 | − | 0.755218i | \(-0.727531\pi\) | ||
0.655473 | − | 0.755218i | \(-0.272469\pi\) | |||||||
\(458\) | −2.95559e9 | −0.0671711 | ||||||||
\(459\) | −6.33676e10 | −1.42763 | ||||||||
\(460\) | −2.15921e9 | −0.0482240 | ||||||||
\(461\) | −2.82917e10 | + | 2.82917e10i | −0.626405 | + | 0.626405i | −0.947162 | − | 0.320756i | \(-0.896063\pi\) |
0.320756 | + | 0.947162i | \(0.396063\pi\) | |||||||
\(462\) | 2.03404e9 | − | 2.03404e9i | 0.0446469 | − | 0.0446469i | ||||
\(463\) | 4.28979e10i | 0.933494i | 0.884391 | + | 0.466747i | \(0.154574\pi\) | ||||
−0.884391 | + | 0.466747i | \(0.845426\pi\) | |||||||
\(464\) | 1.89803e10 | − | 4.21117e10i | 0.409478 | − | 0.908512i | ||||
\(465\) | 1.58429e11 | 3.38861 | ||||||||
\(466\) | 9.40736e8 | + | 9.40736e8i | 0.0199491 | + | 0.0199491i | ||||
\(467\) | 2.73491e10 | + | 2.73491e10i | 0.575011 | + | 0.575011i | 0.933525 | − | 0.358513i | \(-0.116716\pi\) |
−0.358513 | + | 0.933525i | \(0.616716\pi\) | |||||||
\(468\) | 5.92357e10i | 1.23481i | ||||||||
\(469\) | − | 2.63867e10i | − | 0.545374i | ||||||
\(470\) | 1.73392e9i | 0.0355335i | ||||||||
\(471\) | 7.73726e10 | 1.57218 | ||||||||
\(472\) | −8.88861e8 | + | 8.88861e8i | −0.0179088 | + | 0.0179088i | ||||
\(473\) | 5.47722e10i | 1.09425i | ||||||||
\(474\) | −5.33990e8 | + | 5.33990e8i | −0.0105784 | + | 0.0105784i | ||||
\(475\) | −1.25578e10 | − | 1.25578e10i | −0.246684 | − | 0.246684i | ||||
\(476\) | 5.28694e10 | − | 5.28694e10i | 1.02986 | − | 1.02986i | ||||
\(477\) | 6.04293e10i | 1.16728i | ||||||||
\(478\) | 1.20464e8 | + | 1.20464e8i | 0.00230752 | + | 0.00230752i | ||||
\(479\) | −6.03446e10 | + | 6.03446e10i | −1.14630 | + | 1.14630i | −0.159020 | + | 0.987275i | \(0.550834\pi\) |
−0.987275 | + | 0.159020i | \(0.949166\pi\) | |||||||
\(480\) | 1.13756e10 | 0.214294 | ||||||||
\(481\) | 5.12706e10 | + | 5.12706e10i | 0.957828 | + | 0.957828i | ||||
\(482\) | 9.07380e8 | − | 9.07380e8i | 0.0168113 | − | 0.0168113i | ||||
\(483\) | −2.68933e9 | − | 2.68933e9i | −0.0494145 | − | 0.0494145i | ||||
\(484\) | −2.12190e8 | −0.00386672 | ||||||||
\(485\) | 4.94315e10 | + | 4.94315e10i | 0.893382 | + | 0.893382i | ||||
\(486\) | 1.67329e9i | 0.0299934i | ||||||||
\(487\) | −4.88736e10 | −0.868878 | −0.434439 | − | 0.900701i | \(-0.643053\pi\) | ||||
−0.434439 | + | 0.900701i | \(0.643053\pi\) | |||||||
\(488\) | −3.69172e9 | −0.0650953 | ||||||||
\(489\) | −1.50254e11 | −2.62778 | ||||||||
\(490\) | −5.16616e8 | + | 5.16616e8i | −0.00896157 | + | 0.00896157i | ||||
\(491\) | 3.31464e10 | − | 3.31464e10i | 0.570310 | − | 0.570310i | −0.361905 | − | 0.932215i | \(-0.617874\pi\) |
0.932215 | + | 0.361905i | \(0.117874\pi\) | |||||||
\(492\) | − | 1.74628e11i | − | 2.98026i | ||||||
\(493\) | −7.09252e10 | + | 2.68546e10i | −1.20064 | + | 0.454602i | ||||
\(494\) | −8.01051e8 | −0.0134509 | ||||||||
\(495\) | 9.13918e10 | + | 9.13918e10i | 1.52225 | + | 1.52225i | ||||
\(496\) | 6.87395e10 | + | 6.87395e10i | 1.13574 | + | 1.13574i | ||||
\(497\) | − | 1.48164e10i | − | 0.242838i | ||||||
\(498\) | 4.44458e9i | 0.0722625i | ||||||||
\(499\) | − | 2.25994e10i | − | 0.364497i | −0.983252 | − | 0.182249i | \(-0.941662\pi\) | ||
0.983252 | − | 0.182249i | \(-0.0583376\pi\) | |||||||
\(500\) | 2.80886e10 | 0.449417 | ||||||||
\(501\) | 8.21353e10 | − | 8.21353e10i | 1.30370 | − | 1.30370i | ||||
\(502\) | 1.17506e9i | 0.0185031i | ||||||||
\(503\) | 2.07414e10 | − | 2.07414e10i | 0.324015 | − | 0.324015i | −0.526290 | − | 0.850305i | \(-0.676417\pi\) |
0.850305 | + | 0.526290i | \(0.176417\pi\) | |||||||
\(504\) | 5.91918e9 | + | 5.91918e9i | 0.0917359 | + | 0.0917359i | ||||
\(505\) | −2.84108e10 | + | 2.84108e10i | −0.436836 | + | 0.436836i | ||||
\(506\) | 8.36889e7i | 0.00127663i | ||||||||
\(507\) | 3.50340e10 | + | 3.50340e10i | 0.530223 | + | 0.530223i | ||||
\(508\) | 1.48933e10 | − | 1.48933e10i | 0.223632 | − | 0.223632i | ||||
\(509\) | −8.66687e10 | −1.29119 | −0.645596 | − | 0.763679i | \(-0.723391\pi\) | ||||
−0.645596 | + | 0.763679i | \(0.723391\pi\) | |||||||
\(510\) | −4.39370e9 | − | 4.39370e9i | −0.0649455 | − | 0.0649455i | ||||
\(511\) | −5.14331e10 | + | 5.14331e10i | −0.754325 | + | 0.754325i | ||||
\(512\) | 8.22933e9 | + | 8.22933e9i | 0.119752 | + | 0.119752i | ||||
\(513\) | −4.13552e10 | −0.597118 | ||||||||
\(514\) | 4.39902e8 | + | 4.39902e8i | 0.00630236 | + | 0.00630236i | ||||
\(515\) | − | 8.57792e10i | − | 1.21942i | ||||||
\(516\) | −1.27078e11 | −1.79254 | ||||||||
\(517\) | −5.79714e10 | −0.811431 | ||||||||
\(518\) | 5.12029e9 | 0.0711173 | ||||||||
\(519\) | −8.79756e9 | + | 8.79756e9i | −0.121253 | + | 0.121253i | ||||
\(520\) | −3.32492e9 | + | 3.32492e9i | −0.0454746 | + | 0.0454746i | ||||
\(521\) | − | 1.21697e11i | − | 1.65169i | −0.563900 | − | 0.825843i | \(-0.690700\pi\) | ||
0.563900 | − | 0.825843i | \(-0.309300\pi\) | |||||||
\(522\) | −1.50243e9 | − | 3.96804e9i | −0.0202354 | − | 0.0534433i | ||||
\(523\) | 5.55302e10 | 0.742203 | 0.371101 | − | 0.928592i | \(-0.378980\pi\) | ||||
0.371101 | + | 0.928592i | \(0.378980\pi\) | |||||||
\(524\) | 1.16126e10 | + | 1.16126e10i | 0.154030 | + | 0.154030i | ||||
\(525\) | −6.48834e10 | − | 6.48834e10i | −0.854076 | − | 0.854076i | ||||
\(526\) | − | 2.60812e9i | − | 0.0340710i | ||||||
\(527\) | − | 1.59607e11i | − | 2.06924i | ||||||
\(528\) | 1.26531e11i | 1.62803i | ||||||||
\(529\) | −7.82003e10 | −0.998587 | ||||||||
\(530\) | −1.69498e9 | + | 1.69498e9i | −0.0214813 | + | 0.0214813i | ||||
\(531\) | − | 4.97141e10i | − | 0.625319i | ||||||
\(532\) | 3.45038e10 | − | 3.45038e10i | 0.430745 | − | 0.430745i | ||||
\(533\) | 7.65767e10 | + | 7.65767e10i | 0.948829 | + | 0.948829i | ||||
\(534\) | −3.68884e9 | + | 3.68884e9i | −0.0453654 | + | 0.0453654i | ||||
\(535\) | − | 1.84986e11i | − | 2.25800i | ||||||
\(536\) | −1.90621e9 | − | 1.90621e9i | −0.0230946 | − | 0.0230946i | ||||
\(537\) | 4.94483e10 | − | 4.94483e10i | 0.594641 | − | 0.594641i | ||||
\(538\) | −4.89711e9 | −0.0584536 | ||||||||
\(539\) | −1.72724e10 | − | 1.72724e10i | −0.204643 | − | 0.204643i | ||||
\(540\) | −8.57768e10 | + | 8.57768e10i | −1.00878 | + | 1.00878i | ||||
\(541\) | 2.00767e9 | + | 2.00767e9i | 0.0234370 | + | 0.0234370i | 0.718728 | − | 0.695291i | \(-0.244725\pi\) |
−0.695291 | + | 0.718728i | \(0.744725\pi\) | |||||||
\(542\) | −1.82466e9 | −0.0211439 | ||||||||
\(543\) | 9.41775e9 | + | 9.41775e9i | 0.108330 | + | 0.108330i | ||||
\(544\) | − | 1.14602e10i | − | 0.130857i | ||||||
\(545\) | 1.10128e11 | 1.24828 | ||||||||
\(546\) | −4.13885e9 | −0.0465703 | ||||||||
\(547\) | 4.07148e10 | 0.454782 | 0.227391 | − | 0.973804i | \(-0.426980\pi\) | ||||
0.227391 | + | 0.973804i | \(0.426980\pi\) | |||||||
\(548\) | −7.24025e10 | + | 7.24025e10i | −0.802844 | + | 0.802844i | ||||
\(549\) | 1.03239e11 | − | 1.03239e11i | 1.13646 | − | 1.13646i | ||||
\(550\) | 2.01910e9i | 0.0220652i | ||||||||
\(551\) | −4.62874e10 | + | 1.75259e10i | −0.502177 | + | 0.190141i | ||||
\(552\) | −3.88560e8 | −0.00418506 | ||||||||
\(553\) | 2.01721e10 | + | 2.01721e10i | 0.215701 | + | 0.215701i | ||||
\(554\) | 1.90316e9 | + | 1.90316e9i | 0.0202040 | + | 0.0202040i | ||||
\(555\) | 3.67054e11i | 3.86864i | ||||||||
\(556\) | 1.25598e11i | 1.31427i | ||||||||
\(557\) | 9.69776e10i | 1.00751i | 0.863846 | + | 0.503756i | \(0.168049\pi\) | ||||
−0.863846 | + | 0.503756i | \(0.831951\pi\) | |||||||
\(558\) | 8.92951e9 | 0.0921066 | ||||||||
\(559\) | 5.57251e10 | − | 5.57251e10i | 0.570694 | − | 0.570694i | ||||
\(560\) | − | 1.42966e11i | − | 1.45372i | ||||||
\(561\) | 1.46897e11 | − | 1.46897e11i | 1.48307 | − | 1.48307i | ||||
\(562\) | −3.28830e9 | − | 3.28830e9i | −0.0329629 | − | 0.0329629i | ||||
\(563\) | 5.73948e10 | − | 5.73948e10i | 0.571266 | − | 0.571266i | −0.361216 | − | 0.932482i | \(-0.617638\pi\) |
0.932482 | + | 0.361216i | \(0.117638\pi\) | |||||||
\(564\) | − | 1.34500e11i | − | 1.32925i | ||||||
\(565\) | −6.59394e10 | − | 6.59394e10i | −0.647070 | − | 0.647070i | ||||
\(566\) | 1.29524e9 | − | 1.29524e9i | 0.0126207 | − | 0.0126207i | ||||
\(567\) | −1.65373e10 | −0.160005 | ||||||||
\(568\) | −1.07035e9 | − | 1.07035e9i | −0.0102833 | − | 0.0102833i | ||||
\(569\) | −8.28425e10 | + | 8.28425e10i | −0.790322 | + | 0.790322i | −0.981546 | − | 0.191224i | \(-0.938754\pi\) |
0.191224 | + | 0.981546i | \(0.438754\pi\) | |||||||
\(570\) | −2.86743e9 | − | 2.86743e9i | −0.0271640 | − | 0.0271640i | ||||
\(571\) | −2.04986e10 | −0.192832 | −0.0964162 | − | 0.995341i | \(-0.530738\pi\) | ||||
−0.0964162 | + | 0.995341i | \(0.530738\pi\) | |||||||
\(572\) | −5.55500e10 | − | 5.55500e10i | −0.518920 | − | 0.518920i | ||||
\(573\) | − | 7.13761e9i | − | 0.0662117i | ||||||
\(574\) | 7.64757e9 | 0.0704491 | ||||||||
\(575\) | 2.66958e9 | 0.0244214 | ||||||||
\(576\) | −1.83572e11 | −1.66770 | ||||||||
\(577\) | 6.21525e10 | − | 6.21525e10i | 0.560732 | − | 0.560732i | −0.368783 | − | 0.929515i | \(-0.620226\pi\) |
0.929515 | + | 0.368783i | \(0.120226\pi\) | |||||||
\(578\) | −1.74080e9 | + | 1.74080e9i | −0.0155968 | + | 0.0155968i | ||||
\(579\) | 3.59169e11i | 3.19584i | ||||||||
\(580\) | −5.96556e10 | + | 1.32358e11i | −0.527156 | + | 1.16961i | ||||
\(581\) | 1.67899e11 | 1.47348 | ||||||||
\(582\) | 4.44515e9 | + | 4.44515e9i | 0.0387431 | + | 0.0387431i | ||||
\(583\) | −5.66694e10 | − | 5.66694e10i | −0.490540 | − | 0.490540i | ||||
\(584\) | 7.43116e9i | 0.0638860i | ||||||||
\(585\) | − | 1.85963e11i | − | 1.58783i | ||||||
\(586\) | 5.07608e9i | 0.0430465i | ||||||||
\(587\) | 1.35471e11 | 1.14102 | 0.570512 | − | 0.821289i | \(-0.306745\pi\) | ||||
0.570512 | + | 0.821289i | \(0.306745\pi\) | |||||||
\(588\) | 4.00738e10 | − | 4.00738e10i | 0.335237 | − | 0.335237i | ||||
\(589\) | − | 1.04163e11i | − | 0.865474i | ||||||
\(590\) | 1.39443e9 | − | 1.39443e9i | 0.0115077 | − | 0.0115077i | ||||
\(591\) | 1.41935e11 | + | 1.41935e11i | 1.16343 | + | 1.16343i | ||||
\(592\) | −1.59259e11 | + | 1.59259e11i | −1.29663 | + | 1.29663i | ||||
\(593\) | − | 1.26193e10i | − | 0.102050i | −0.998697 | − | 0.0510252i | \(-0.983751\pi\) | ||
0.998697 | − | 0.0510252i | \(-0.0162489\pi\) | |||||||
\(594\) | 3.32463e9 | + | 3.32463e9i | 0.0267053 | + | 0.0267053i | ||||
\(595\) | −1.65977e11 | + | 1.65977e11i | −1.32428 | + | 1.32428i | ||||
\(596\) | 8.63648e10 | 0.684465 | ||||||||
\(597\) | −1.99906e11 | − | 1.99906e11i | −1.57372 | − | 1.57372i | ||||
\(598\) | 8.51448e7 | − | 8.51448e7i | 0.000665815 | − | 0.000665815i | ||||
\(599\) | −5.38002e10 | − | 5.38002e10i | −0.417904 | − | 0.417904i | 0.466577 | − | 0.884481i | \(-0.345487\pi\) |
−0.884481 | + | 0.466577i | \(0.845487\pi\) | |||||||
\(600\) | −9.37450e9 | −0.0723341 | ||||||||
\(601\) | −1.01554e11 | − | 1.01554e11i | −0.778397 | − | 0.778397i | 0.201161 | − | 0.979558i | \(-0.435529\pi\) |
−0.979558 | + | 0.201161i | \(0.935529\pi\) | |||||||
\(602\) | − | 5.56515e9i | − | 0.0423732i | ||||||
\(603\) | 1.06614e11 | 0.806393 | ||||||||
\(604\) | 1.14312e11 | 0.858905 | ||||||||
\(605\) | 6.66145e8 | 0.00497218 | ||||||||
\(606\) | −2.55485e9 | + | 2.55485e9i | −0.0189442 | + | 0.0189442i | ||||
\(607\) | 7.32554e10 | − | 7.32554e10i | 0.539616 | − | 0.539616i | −0.383800 | − | 0.923416i | \(-0.625385\pi\) |
0.923416 | + | 0.383800i | \(0.125385\pi\) | |||||||
\(608\) | − | 7.47922e9i | − | 0.0547321i | ||||||
\(609\) | −2.39157e11 | + | 9.05525e10i | −1.73865 | + | 0.658311i | ||||
\(610\) | 5.79151e9 | 0.0418285 | ||||||||
\(611\) | 5.89799e10 | + | 5.89799e10i | 0.423194 | + | 0.423194i | ||||
\(612\) | 2.13617e11 | + | 2.13617e11i | 1.52275 | + | 1.52275i | ||||
\(613\) | 4.76968e10i | 0.337791i | 0.985634 | + | 0.168895i | \(0.0540200\pi\) | ||||
−0.985634 | + | 0.168895i | \(0.945980\pi\) | |||||||
\(614\) | 1.48268e9i | 0.0104322i | ||||||||
\(615\) | 5.48226e11i | 3.83229i | ||||||||
\(616\) | −1.11018e10 | −0.0771027 | ||||||||
\(617\) | −1.21988e11 | + | 1.21988e11i | −0.841739 | + | 0.841739i | −0.989085 | − | 0.147346i | \(-0.952927\pi\) |
0.147346 | + | 0.989085i | \(0.452927\pi\) | |||||||
\(618\) | − | 7.71372e9i | − | 0.0528823i | ||||||
\(619\) | 6.31992e10 | − | 6.31992e10i | 0.430476 | − | 0.430476i | −0.458314 | − | 0.888790i | \(-0.651547\pi\) |
0.888790 | + | 0.458314i | \(0.151547\pi\) | |||||||
\(620\) | −2.16050e11 | − | 2.16050e11i | −1.46214 | − | 1.46214i | ||||
\(621\) | 4.39570e9 | − | 4.39570e9i | 0.0295571 | − | 0.0295571i | ||||
\(622\) | − | 4.39244e9i | − | 0.0293457i | ||||||
\(623\) | 1.39350e11 | + | 1.39350e11i | 0.925031 | + | 0.925031i | ||||
\(624\) | 1.28733e11 | − | 1.28733e11i | 0.849083 | − | 0.849083i | ||||
\(625\) | −1.87316e11 | −1.22759 | ||||||||
\(626\) | 6.68024e9 | + | 6.68024e9i | 0.0435005 | + | 0.0435005i | ||||
\(627\) | 9.58687e10 | − | 9.58687e10i | 0.620307 | − | 0.620307i | ||||
\(628\) | −1.05514e11 | − | 1.05514e11i | −0.678375 | − | 0.678375i | ||||
\(629\) | 3.69785e11 | 2.36237 | ||||||||
\(630\) | −9.28590e9 | − | 9.28590e9i | −0.0589470 | − | 0.0589470i | ||||
\(631\) | − | 1.01804e11i | − | 0.642167i | −0.947051 | − | 0.321083i | \(-0.895953\pi\) | ||
0.947051 | − | 0.321083i | \(-0.104047\pi\) | |||||||
\(632\) | 2.91452e9 | 0.0182683 | ||||||||
\(633\) | 9.45451e10 | 0.588876 | ||||||||
\(634\) | −4.04596e9 | −0.0250417 | ||||||||
\(635\) | −4.67556e10 | + | 4.67556e10i | −0.287567 | + | 0.287567i | ||||
\(636\) | 1.31479e11 | − | 1.31479e11i | 0.803579 | − | 0.803579i | ||||
\(637\) | 3.51457e10i | 0.213459i | ||||||||
\(638\) | 5.13009e9 | + | 2.31220e9i | 0.0309630 | + | 0.0139554i | ||||
\(639\) | 5.98650e10 | 0.359062 | ||||||||
\(640\) | −2.06800e10 | − | 2.06800e10i | −0.123263 | − | 0.123263i | ||||
\(641\) | −1.41113e11 | − | 1.41113e11i | −0.835866 | − | 0.835866i | 0.152446 | − | 0.988312i | \(-0.451285\pi\) |
−0.988312 | + | 0.152446i | \(0.951285\pi\) | |||||||
\(642\) | − | 1.66349e10i | − | 0.0979222i | ||||||
\(643\) | 1.87106e11i | 1.09457i | 0.836947 | + | 0.547284i | \(0.184338\pi\) | ||||
−0.836947 | + | 0.547284i | \(0.815662\pi\) | |||||||
\(644\) | 7.33491e9i | 0.0426434i | ||||||||
\(645\) | 3.98945e11 | 2.30502 | ||||||||
\(646\) | −2.88876e9 | + | 2.88876e9i | −0.0165875 | + | 0.0165875i | ||||
\(647\) | 3.07155e10i | 0.175283i | 0.996152 | + | 0.0876417i | \(0.0279331\pi\) | ||||
−0.996152 | + | 0.0876417i | \(0.972067\pi\) | |||||||
\(648\) | −1.19468e9 | + | 1.19468e9i | −0.00677563 | + | 0.00677563i | ||||
\(649\) | 4.66209e10 | + | 4.66209e10i | 0.262786 | + | 0.262786i | ||||
\(650\) | 2.05423e9 | − | 2.05423e9i | 0.0115079 | − | 0.0115079i | ||||
\(651\) | − | 5.38188e11i | − | 2.99647i | ||||||
\(652\) | 2.04902e11 | + | 2.04902e11i | 1.13385 | + | 1.13385i | ||||
\(653\) | −1.12901e11 | + | 1.12901e11i | −0.620934 | + | 0.620934i | −0.945770 | − | 0.324836i | \(-0.894691\pi\) |
0.324836 | + | 0.945770i | \(0.394691\pi\) | |||||||
\(654\) | 9.90327e9 | 0.0541337 | ||||||||
\(655\) | −3.64565e10 | − | 3.64565e10i | −0.198066 | − | 0.198066i | ||||
\(656\) | −2.37866e11 | + | 2.37866e11i | −1.28445 | + | 1.28445i | ||||
\(657\) | −2.07813e11 | − | 2.07813e11i | −1.11535 | − | 1.11535i | ||||
\(658\) | 5.89021e9 | 0.0314215 | ||||||||
\(659\) | 1.50790e11 | + | 1.50790e11i | 0.799522 | + | 0.799522i | 0.983020 | − | 0.183498i | \(-0.0587421\pi\) |
−0.183498 | + | 0.983020i | \(0.558742\pi\) | |||||||
\(660\) | − | 3.97692e11i | − | 2.09590i | ||||||
\(661\) | −2.80608e11 | −1.46992 | −0.734962 | − | 0.678109i | \(-0.762800\pi\) | ||||
−0.734962 | + | 0.678109i | \(0.762800\pi\) | |||||||
\(662\) | 6.70953e8 | 0.00349349 | ||||||||
\(663\) | −2.98906e11 | −1.54696 | ||||||||
\(664\) | 1.21292e10 | − | 1.21292e10i | 0.0623967 | − | 0.0623967i | ||||
\(665\) | −1.08321e11 | + | 1.08321e11i | −0.553892 | + | 0.553892i | ||||
\(666\) | 2.06883e10i | 0.105155i | ||||||||
\(667\) | 3.05710e9 | − | 6.78281e9i | 0.0154456 | − | 0.0342694i | ||||
\(668\) | −2.24017e11 | −1.12506 | ||||||||
\(669\) | −3.80523e11 | − | 3.80523e11i | −1.89966 | − | 1.89966i | ||||
\(670\) | 2.99042e9 | + | 2.99042e9i | 0.0148400 | + | 0.0148400i | ||||
\(671\) | 1.93631e11i | 0.955180i | ||||||||
\(672\) | − | 3.86434e10i | − | 0.189495i | ||||||
\(673\) | − | 1.05430e11i | − | 0.513930i | −0.966421 | − | 0.256965i | \(-0.917277\pi\) | ||
0.966421 | − | 0.256965i | \(-0.0827226\pi\) | |||||||
\(674\) | 4.46329e9 | 0.0216280 | ||||||||
\(675\) | 1.06052e11 | − | 1.06052e11i | 0.510862 | − | 0.510862i | ||||
\(676\) | − | 9.55524e10i | − | 0.457567i | ||||||
\(677\) | −2.99102e9 | + | 2.99102e9i | −0.0142385 | + | 0.0142385i | −0.714190 | − | 0.699952i | \(-0.753205\pi\) |
0.699952 | + | 0.714190i | \(0.253205\pi\) | |||||||
\(678\) | −5.92962e9 | − | 5.92962e9i | −0.0280613 | − | 0.0280613i | ||||
\(679\) | 1.67921e11 | − | 1.67921e11i | 0.789998 | − | 0.789998i | ||||
\(680\) | 2.39808e10i | 0.112157i | ||||||||
\(681\) | −1.18181e11 | − | 1.18181e11i | −0.549489 | − | 0.549489i | ||||
\(682\) | −8.37392e9 | + | 8.37392e9i | −0.0387072 | + | 0.0387072i | ||||
\(683\) | 1.49572e9 | 0.00687333 | 0.00343666 | − | 0.999994i | \(-0.498906\pi\) | ||||
0.00343666 | + | 0.999994i | \(0.498906\pi\) | |||||||
\(684\) | 1.39411e11 | + | 1.39411e11i | 0.636902 | + | 0.636902i | ||||
\(685\) | 2.27299e11 | − | 2.27299e11i | 1.03237 | − | 1.03237i | ||||
\(686\) | −4.29725e9 | − | 4.29725e9i | −0.0194041 | − | 0.0194041i | ||||
\(687\) | −7.19749e11 | −3.23113 | ||||||||
\(688\) | 1.73096e11 | + | 1.73096e11i | 0.772560 | + | 0.772560i | ||||
\(689\) | 1.15311e11i | 0.511673i | ||||||||
\(690\) | 6.09566e8 | 0.00268921 | ||||||||
\(691\) | −2.43095e11 | −1.06626 | −0.533132 | − | 0.846032i | \(-0.678985\pi\) | ||||
−0.533132 | + | 0.846032i | \(0.678985\pi\) | |||||||
\(692\) | 2.39946e10 | 0.104638 | ||||||||
\(693\) | 3.10462e11 | − | 3.10462e11i | 1.34609 | − | 1.34609i | ||||
\(694\) | −5.55658e9 | + | 5.55658e9i | −0.0239535 | + | 0.0239535i | ||||
\(695\) | − | 3.94302e11i | − | 1.69001i | ||||||
\(696\) | −1.07353e10 | + | 2.38186e10i | −0.0457486 | + | 0.101503i | ||||
\(697\) | 5.52304e11 | 2.34017 | ||||||||
\(698\) | 1.67542e8 | + | 1.67542e8i | 0.000705833 | + | 0.000705833i | ||||
\(699\) | 2.29089e11 | + | 2.29089e11i | 0.959612 | + | 0.959612i | ||||
\(700\) | 1.76964e11i | 0.737044i | ||||||||
\(701\) | − | 3.29493e9i | − | 0.0136450i | −0.999977 | − | 0.00682250i | \(-0.997828\pi\) | ||
0.999977 | − | 0.00682250i | \(-0.00217169\pi\) | |||||||
\(702\) | − | 6.76494e9i | − | 0.0278558i | ||||||
\(703\) | 2.41330e11 | 0.988077 | ||||||||
\(704\) | 1.72151e11 | − | 1.72151e11i | 0.700838 | − | 0.700838i | ||||
\(705\) | 4.22247e11i | 1.70927i | ||||||||
\(706\) | −1.67397e9 | + | 1.67397e9i | −0.00673797 | + | 0.00673797i | ||||
\(707\) | 9.65128e10 | + | 9.65128e10i | 0.386284 | + | 0.386284i | ||||
\(708\) | −1.08166e11 | + | 1.08166e11i | −0.430483 | + | 0.430483i | ||||
\(709\) | 4.66187e11i | 1.84491i | 0.386107 | + | 0.922454i | \(0.373820\pi\) | ||||
−0.386107 | + | 0.922454i | \(0.626180\pi\) | |||||||
\(710\) | 1.67915e9 | + | 1.67915e9i | 0.00660779 | + | 0.00660779i | ||||
\(711\) | −8.15047e10 | + | 8.15047e10i | −0.318936 | + | 0.318936i | ||||
\(712\) | 2.01337e10 | 0.0783435 | ||||||||
\(713\) | 1.10717e10 | + | 1.10717e10i | 0.0428405 | + | 0.0428405i | ||||
\(714\) | −1.49256e10 | + | 1.49256e10i | −0.0574299 | + | 0.0574299i | ||||
\(715\) | 1.74393e11 | + | 1.74393e11i | 0.667274 | + | 0.667274i | ||||
\(716\) | −1.34866e11 | −0.513158 | ||||||||
\(717\) | 2.93356e10 | + | 2.93356e10i | 0.110999 | + | 0.110999i | ||||
\(718\) | − | 4.09090e9i | − | 0.0153929i | ||||||
\(719\) | −2.67420e11 | −1.00064 | −0.500320 | − | 0.865841i | \(-0.666784\pi\) | ||||
−0.500320 | + | 0.865841i | \(0.666784\pi\) | |||||||
\(720\) | 5.77648e11 | 2.14948 | ||||||||
\(721\) | −2.91396e11 | −1.07831 | ||||||||
\(722\) | 4.65321e9 | − | 4.65321e9i | 0.0171239 | − | 0.0171239i | ||||
\(723\) | 2.20966e11 | − | 2.20966e11i | 0.808673 | − | 0.808673i | ||||
\(724\) | − | 2.56861e10i | − | 0.0934855i | ||||||
\(725\) | 7.37564e10 | − | 1.63644e11i | 0.266961 | − | 0.592309i | ||||
\(726\) | 5.99033e7 | 0.000215628 | ||||||||
\(727\) | 1.53119e11 | + | 1.53119e11i | 0.548141 | + | 0.548141i | 0.925903 | − | 0.377762i | \(-0.123306\pi\) |
−0.377762 | + | 0.925903i | \(0.623306\pi\) | |||||||
\(728\) | 1.12949e10 | + | 1.12949e10i | 0.0402121 | + | 0.0402121i | ||||
\(729\) | 4.47269e11i | 1.58365i | ||||||||
\(730\) | − | 1.16579e10i | − | 0.0410514i | ||||||
\(731\) | − | 4.01913e11i | − | 1.40755i | ||||||
\(732\) | −4.49246e11 | −1.56473 | ||||||||
\(733\) | −1.52946e10 | + | 1.52946e10i | −0.0529811 | + | 0.0529811i | −0.733101 | − | 0.680120i | \(-0.761928\pi\) |
0.680120 | + | 0.733101i | \(0.261928\pi\) | |||||||
\(734\) | 6.20879e9i | 0.0213906i | ||||||||
\(735\) | −1.25807e11 | + | 1.25807e11i | −0.431078 | + | 0.431078i | ||||
\(736\) | 7.94977e8 | + | 7.94977e8i | 0.00270921 | + | 0.00270921i | ||||
\(737\) | −9.99809e10 | + | 9.99809e10i | −0.338881 | + | 0.338881i | ||||
\(738\) | 3.08997e10i | 0.104167i | ||||||||
\(739\) | −1.00402e10 | − | 1.00402e10i | −0.0336641 | − | 0.0336641i | 0.690074 | − | 0.723738i | \(-0.257578\pi\) |
−0.723738 | + | 0.690074i | \(0.757578\pi\) | |||||||
\(740\) | 5.00555e11 | − | 5.00555e11i | 1.66927 | − | 1.66927i | ||||
\(741\) | −1.95073e11 | −0.647030 | ||||||||
\(742\) | 5.75792e9 | + | 5.75792e9i | 0.0189955 | + | 0.0189955i | ||||
\(743\) | −1.39158e11 | + | 1.39158e11i | −0.456618 | + | 0.456618i | −0.897544 | − | 0.440926i | \(-0.854650\pi\) |
0.440926 | + | 0.897544i | \(0.354650\pi\) | |||||||
\(744\) | −3.88793e10 | − | 3.88793e10i | −0.126890 | − | 0.126890i | ||||
\(745\) | −2.71132e11 | −0.880148 | ||||||||
\(746\) | −3.56578e9 | − | 3.56578e9i | −0.0115133 | − | 0.0115133i | ||||
\(747\) | 6.78390e11i | 2.17870i | ||||||||
\(748\) | −4.00651e11 | −1.27985 | ||||||||
\(749\) | −6.28406e11 | −1.99670 | ||||||||
\(750\) | −7.92969e9 | −0.0250618 | ||||||||
\(751\) | 2.94916e11 | − | 2.94916e11i | 0.927125 | − | 0.927125i | −0.0703940 | − | 0.997519i | \(-0.522426\pi\) |
0.997519 | + | 0.0703940i | \(0.0224257\pi\) | |||||||
\(752\) | −1.83206e11 | + | 1.83206e11i | −0.572886 | + | 0.572886i | ||||
\(753\) | 2.86152e11i | 0.890056i | ||||||||
\(754\) | −2.86692e9 | − | 7.57176e9i | −0.00887013 | − | 0.0234267i | ||||
\(755\) | −3.58870e11 | −1.10446 | ||||||||
\(756\) | 2.91387e11 | + | 2.91387e11i | 0.892039 | + | 0.892039i | ||||
\(757\) | 1.92054e11 | + | 1.92054e11i | 0.584844 | + | 0.584844i | 0.936231 | − | 0.351386i | \(-0.114290\pi\) |
−0.351386 | + | 0.936231i | \(0.614290\pi\) | |||||||
\(758\) | 3.43189e9i | 0.0103958i | ||||||||
\(759\) | 2.03800e10i | 0.0614098i | ||||||||
\(760\) | 1.56504e10i | 0.0469107i | ||||||||
\(761\) | 8.05148e10 | 0.240070 | 0.120035 | − | 0.992770i | \(-0.461699\pi\) | ||||
0.120035 | + | 0.992770i | \(0.461699\pi\) | |||||||
\(762\) | −4.20452e9 | + | 4.20452e9i | −0.0124709 | + | 0.0124709i | ||||
\(763\) | − | 3.74108e11i | − | 1.10382i | ||||||
\(764\) | −9.73362e9 | + | 9.73362e9i | −0.0285694 | + | 0.0285694i | ||||
\(765\) | −6.70624e11 | − | 6.70624e11i | −1.95809 | − | 1.95809i | ||||
\(766\) | 9.61227e9 | − | 9.61227e9i | 0.0279197 | − | 0.0279197i | ||||
\(767\) | − | 9.48640e10i | − | 0.274107i | ||||||
\(768\) | 3.98012e11 | + | 3.98012e11i | 1.14407 | + | 1.14407i | ||||
\(769\) | −5.67272e10 | + | 5.67272e10i | −0.162213 | + | 0.162213i | −0.783546 | − | 0.621333i | \(-0.786591\pi\) |
0.621333 | + | 0.783546i | \(0.286591\pi\) | |||||||
\(770\) | 1.74163e10 | 0.0495441 | ||||||||
\(771\) | 1.07125e11 | + | 1.07125e11i | 0.303162 | + | 0.303162i | ||||
\(772\) | 4.89802e11 | − | 4.89802e11i | 1.37896 | − | 1.37896i | ||||
\(773\) | −2.20080e10 | − | 2.20080e10i | −0.0616399 | − | 0.0616399i | 0.675615 | − | 0.737255i | \(-0.263878\pi\) |
−0.737255 | + | 0.675615i | \(0.763878\pi\) | |||||||
\(774\) | 2.24858e10 | 0.0626533 | ||||||||
\(775\) | 2.67118e11 | + | 2.67118e11i | 0.740452 | + | 0.740452i | ||||
\(776\) | − | 2.42616e10i | − | 0.0669071i | ||||||
\(777\) | 1.24690e12 | 3.42095 | ||||||||
\(778\) | −1.41370e10 | −0.0385869 | ||||||||
\(779\) | 3.60447e11 | 0.978794 | ||||||||
\(780\) | −4.04610e11 | + | 4.04610e11i | −1.09310 | + | 1.09310i | ||||
\(781\) | −5.61402e10 | + | 5.61402e10i | −0.150893 | + | 0.150893i | ||||
\(782\) | − | 6.14101e8i | − | 0.00164215i | ||||||
\(783\) | −1.48008e11 | − | 3.90901e11i | −0.393766 | − | 1.03997i | ||||
\(784\) | −1.09171e11 | −0.288964 | ||||||||
\(785\) | 3.31248e11 | + | 3.31248e11i | 0.872317 | + | 0.872317i | ||||
\(786\) | −3.27837e9 | − | 3.27837e9i | −0.00858949 | − | 0.00858949i | ||||
\(787\) | − | 6.14633e11i | − | 1.60220i | −0.598530 | − | 0.801101i | \(-0.704248\pi\) | ||
0.598530 | − | 0.801101i | \(-0.295752\pi\) | |||||||
\(788\) | − | 3.87117e11i | − | 1.00401i | ||||||
\(789\) | − | 6.35133e11i | − | 1.63892i | ||||||
\(790\) | −4.57224e9 | −0.0117387 | ||||||||
\(791\) | −2.23999e11 | + | 2.23999e11i | −0.572189 | + | 0.572189i | ||||
\(792\) | − | 4.48562e10i | − | 0.114004i | ||||||
\(793\) | 1.97000e11 | − | 1.97000e11i | 0.498165 | − | 0.498165i | ||||
\(794\) | 3.86504e8 | + | 3.86504e8i | 0.000972460 | + | 0.000972460i | ||||
\(795\) | −4.12764e11 | + | 4.12764e11i | −1.03332 | + | 1.03332i | ||||
\(796\) | 5.45228e11i | 1.35808i | ||||||||
\(797\) | 2.44620e11 | + | 2.44620e11i | 0.606259 | + | 0.606259i | 0.941966 | − | 0.335707i | \(-0.108975\pi\) |
−0.335707 | + | 0.941966i | \(0.608975\pi\) | |||||||
\(798\) | −9.74077e9 | + | 9.74077e9i | −0.0240205 | + | 0.0240205i | ||||
\(799\) | 4.25389e11 | 1.04376 | ||||||||
\(800\) | 1.91798e10 | + | 1.91798e10i | 0.0468258 | + | 0.0468258i | ||||
\(801\) | −5.63040e11 | + | 5.63040e11i | −1.36776 | + | 1.36776i | ||||
\(802\) | 2.41929e9 | + | 2.41929e9i | 0.00584777 | + | 0.00584777i | ||||
\(803\) | 3.89766e11 | 0.937436 | ||||||||
\(804\) | −2.31967e11 | − | 2.31967e11i | −0.555138 | − | 0.555138i | ||||
\(805\) | − | 2.30271e10i | − | 0.0548348i | ||||||
\(806\) | 1.70392e10 | 0.0403747 | ||||||||
\(807\) | −1.19255e12 | −2.81179 | ||||||||
\(808\) | 1.39444e10 | 0.0327155 | ||||||||
\(809\) | 2.32790e11 | − | 2.32790e11i | 0.543463 | − | 0.543463i | −0.381080 | − | 0.924542i | \(-0.624448\pi\) |
0.924542 | + | 0.381080i | \(0.124448\pi\) | |||||||
\(810\) | 1.87419e9 | − | 1.87419e9i | 0.00435384 | − | 0.00435384i | ||||
\(811\) | − | 5.46311e9i | − | 0.0126286i | −0.999980 | − | 0.00631432i | \(-0.997990\pi\) | ||
0.999980 | − | 0.00631432i | \(-0.00200992\pi\) | |||||||
\(812\) | 4.49627e11 | + | 2.02653e11i | 1.03426 | + | 0.466153i | ||||
\(813\) | −4.44343e11 | −1.01708 | ||||||||
\(814\) | −1.94011e10 | − | 1.94011e10i | −0.0441904 | − | 0.0441904i | ||||
\(815\) | −6.43267e11 | − | 6.43267e11i | −1.45801 | − | 1.45801i | ||||
\(816\) | − | 9.28474e11i | − | 2.09416i | ||||||
\(817\) | − | 2.62298e11i | − | 0.588717i | ||||||
\(818\) | 1.41525e9i | 0.00316097i | ||||||||
\(819\) | −6.31726e11 | −1.40408 | ||||||||
\(820\) | 7.47620e11 | − | 7.47620e11i | 1.65358 | − | 1.65358i | ||||
\(821\) | 3.30921e11i | 0.728369i | 0.931327 | + | 0.364185i | \(0.118652\pi\) | ||||
−0.931327 | + | 0.364185i | \(0.881348\pi\) | |||||||
\(822\) | 2.04400e10 | − | 2.04400e10i | 0.0447706 | − | 0.0447706i | ||||
\(823\) | −2.87737e11 | − | 2.87737e11i | −0.627186 | − | 0.627186i | 0.320173 | − | 0.947359i | \(-0.396259\pi\) |
−0.947359 | + | 0.320173i | \(0.896259\pi\) | |||||||
\(824\) | −2.10507e10 | + | 2.10507e10i | −0.0456624 | + | 0.0456624i | ||||
\(825\) | 4.91694e11i | 1.06140i | ||||||||
\(826\) | −4.73694e9 | − | 4.73694e9i | −0.0101760 | − | 0.0101760i | ||||
\(827\) | −4.78666e11 | + | 4.78666e11i | −1.02332 | + | 1.02332i | −0.0235963 | + | 0.999722i | \(0.507512\pi\) |
−0.999722 | + | 0.0235963i | \(0.992488\pi\) | |||||||
\(828\) | −2.96364e10 | −0.0630528 | ||||||||
\(829\) | 1.00884e11 | + | 1.00884e11i | 0.213602 | + | 0.213602i | 0.805796 | − | 0.592193i | \(-0.201738\pi\) |
−0.592193 | + | 0.805796i | \(0.701738\pi\) | |||||||
\(830\) | −1.90281e10 | + | 1.90281e10i | −0.0400944 | + | 0.0400944i | ||||
\(831\) | 4.63461e11 | + | 4.63461e11i | 0.971871 | + | 0.971871i | ||||
\(832\) | −3.50291e11 | −0.731031 | ||||||||
\(833\) | 1.26743e11 | + | 1.26743e11i | 0.263235 | + | 0.263235i | ||||
\(834\) | − | 3.54577e10i | − | 0.0732903i | ||||||
\(835\) | 7.03277e11 | 1.44671 | ||||||||
\(836\) | −2.61474e11 | −0.535307 | ||||||||
\(837\) | 8.79668e11 | 1.79233 | ||||||||
\(838\) | 7.84237e9 | − | 7.84237e9i | 0.0159027 | − | 0.0159027i | ||||
\(839\) | 3.47996e11 | − | 3.47996e11i | 0.702306 | − | 0.702306i | −0.262599 | − | 0.964905i | \(-0.584580\pi\) |
0.964905 | + | 0.262599i | \(0.0845798\pi\) | |||||||
\(840\) | 8.08621e10i | 0.162416i | ||||||||
\(841\) | −3.31320e11 | − | 3.74798e11i | −0.662314 | − | 0.749226i | ||||
\(842\) | 8.25178e9 | 0.0164172 | ||||||||
\(843\) | −8.00770e11 | − | 8.00770e11i | −1.58561 | − | 1.58561i | ||||
\(844\) | −1.28932e11 | − | 1.28932e11i | −0.254092 | − | 0.254092i | ||||
\(845\) | 2.99976e11i | 0.588382i | ||||||||
\(846\) | 2.37991e10i | 0.0464600i | ||||||||
\(847\) | − | 2.26292e9i | − | 0.00439679i | ||||||
\(848\) | −3.58183e11 | −0.692662 | ||||||||
\(849\) | 3.15419e11 | − | 3.15419e11i | 0.607095 | − | 0.607095i | ||||
\(850\) | − | 1.48160e10i | − | 0.0283828i | ||||||
\(851\) | −2.56514e10 | + | 2.56514e10i | −0.0489094 | + | 0.0489094i | ||||
\(852\) | −1.30251e11 | − | 1.30251e11i | −0.247186 | − | 0.247186i | ||||
\(853\) | 5.53587e11 | − | 5.53587e11i | 1.04566 | − | 1.04566i | 0.0467510 | − | 0.998907i | \(-0.485113\pi\) |
0.998907 | − | 0.0467510i | \(-0.0148867\pi\) | |||||||
\(854\) | − | 1.96740e10i | − | 0.0369880i | ||||||
\(855\) | −4.37665e11 | − | 4.37665e11i | −0.818988 | − | 0.818988i | ||||
\(856\) | −4.53967e10 | + | 4.53967e10i | −0.0845531 | + | 0.0845531i | ||||
\(857\) | −4.23255e11 | −0.784656 | −0.392328 | − | 0.919825i | \(-0.628330\pi\) | ||||
−0.392328 | + | 0.919825i | \(0.628330\pi\) | |||||||
\(858\) | 1.56823e10 | + | 1.56823e10i | 0.0289375 | + | 0.0289375i | ||||
\(859\) | 3.43252e11 | − | 3.43252e11i | 0.630435 | − | 0.630435i | −0.317742 | − | 0.948177i | \(-0.602925\pi\) |
0.948177 | + | 0.317742i | \(0.102925\pi\) | |||||||
\(860\) | −5.44045e11 | − | 5.44045e11i | −0.994583 | − | 0.994583i | ||||
\(861\) | 1.86235e12 | 3.38881 | ||||||||
\(862\) | 1.15082e10 | + | 1.15082e10i | 0.0208438 | + | 0.0208438i | ||||
\(863\) | 8.57111e11i | 1.54523i | 0.634874 | + | 0.772616i | \(0.281052\pi\) | ||||
−0.634874 | + | 0.772616i | \(0.718948\pi\) | |||||||
\(864\) | 6.31627e10 | 0.113346 | ||||||||
\(865\) | −7.53283e10 | −0.134553 | ||||||||
\(866\) | 3.04838e10 | 0.0541998 | ||||||||
\(867\) | −4.23921e11 | + | 4.23921e11i | −0.750254 | + | 0.750254i | ||||
\(868\) | −7.33932e11 | + | 7.33932e11i | −1.29294 | + | 1.29294i | ||||
\(869\) | − | 1.52867e11i | − | 0.268061i | ||||||
\(870\) | 1.68414e10 | − | 3.73661e10i | 0.0293969 | − | 0.0652231i | ||||
\(871\) | 2.03440e11 | 0.353480 | ||||||||
\(872\) | −2.70260e10 | − | 2.70260e10i | −0.0467429 | − | 0.0467429i | ||||
\(873\) | 6.78477e11 | + | 6.78477e11i | 1.16810 | + | 1.16810i | ||||
\(874\) | − | 4.00777e8i | − | 0.000686842i | ||||||
\(875\) | 2.99554e11i | 0.511026i | ||||||||
\(876\) | 9.04299e11i | 1.53566i | ||||||||
\(877\) | −5.33654e11 | −0.902114 | −0.451057 | − | 0.892495i | \(-0.648953\pi\) | ||||
−0.451057 | + | 0.892495i | \(0.648953\pi\) | |||||||
\(878\) | −1.76860e9 | + | 1.76860e9i | −0.00297613 | + | 0.00297613i | ||||
\(879\) | 1.23613e12i | 2.07067i | ||||||||
\(880\) | −5.41706e11 | + | 5.41706e11i | −0.903303 | + | 0.903303i | ||||
\(881\) | 2.27315e10 | + | 2.27315e10i | 0.0377333 | + | 0.0377333i | 0.725722 | − | 0.687988i | \(-0.241506\pi\) |
−0.687988 | + | 0.725722i | \(0.741506\pi\) | |||||||
\(882\) | −7.09087e9 | + | 7.09087e9i | −0.0117172 | + | 0.0117172i | ||||
\(883\) | − | 3.04160e11i | − | 0.500333i | −0.968203 | − | 0.250167i | \(-0.919515\pi\) | ||
0.968203 | − | 0.250167i | \(-0.0804854\pi\) | |||||||
\(884\) | 4.07621e11 | + | 4.07621e11i | 0.667494 | + | 0.667494i | ||||
\(885\) | 3.39573e11 | − | 3.39573e11i | 0.553555 | − | 0.553555i | ||||
\(886\) | 5.68398e9 | 0.00922397 | ||||||||
\(887\) | −2.74403e11 | − | 2.74403e11i | −0.443296 | − | 0.443296i | 0.449822 | − | 0.893118i | \(-0.351487\pi\) |
−0.893118 | + | 0.449822i | \(0.851487\pi\) | |||||||
\(888\) | 9.00774e10 | − | 9.00774e10i | 0.144865 | − | 0.144865i | ||||
\(889\) | 1.58831e11 | + | 1.58831e11i | 0.254289 | + | 0.254289i | ||||
\(890\) | −3.15854e10 | −0.0503415 | ||||||||
\(891\) | 6.26609e10 | + | 6.26609e10i | 0.0994228 | + | 0.0994228i | ||||
\(892\) | 1.03785e12i | 1.63936i | ||||||||
\(893\) | 2.77618e11 | 0.436559 | ||||||||
\(894\) | −2.43816e10 | −0.0381692 | ||||||||
\(895\) | 4.23397e11 | 0.659866 | ||||||||
\(896\) | −7.02509e10 | + | 7.02509e10i | −0.108998 | + | 0.108998i | ||||
\(897\) | 2.07346e10 | − | 2.07346e10i | 0.0320277 | − | 0.0320277i | ||||
\(898\) | 2.83730e10i | 0.0436314i | ||||||||
\(899\) | 9.84582e11 | − | 3.72795e11i | 1.50735 | − | 0.570731i | ||||
\(900\) | −7.15016e11 | −1.08980 | ||||||||
\(901\) | 4.15835e11 | + | 4.15835e11i | 0.630989 | + | 0.630989i | ||||
\(902\) | −2.89771e10 | − | 2.89771e10i | −0.0437752 | − | 0.0437752i | ||||
\(903\) | − | 1.35523e12i | − | 2.03828i | ||||||
\(904\) | 3.23638e10i | 0.0484603i | ||||||||
\(905\) | 8.06386e10i | 0.120212i | ||||||||
\(906\) | −3.22715e10 | −0.0478968 | ||||||||
\(907\) | 5.12278e10 | − | 5.12278e10i | 0.0756966 | − | 0.0756966i | −0.668245 | − | 0.743941i | \(-0.732954\pi\) |
0.743941 | + | 0.668245i | \(0.232954\pi\) | |||||||
\(908\) | 3.22329e11i | 0.474194i | ||||||||
\(909\) | −3.89956e11 | + | 3.89956e11i | −0.571163 | + | 0.571163i | ||||
\(910\) | −1.77193e10 | − | 1.77193e10i | −0.0258393 | − | 0.0258393i | ||||
\(911\) | −1.66277e11 | + | 1.66277e11i | −0.241412 | + | 0.241412i | −0.817434 | − | 0.576022i | \(-0.804604\pi\) |
0.576022 | + | 0.817434i | \(0.304604\pi\) | |||||||
\(912\) | − | 6.05944e11i | − | 0.875897i | ||||||
\(913\) | −6.36181e11 | − | 6.36181e11i | −0.915582 | − | 0.915582i | ||||
\(914\) | 2.53639e10 | − | 2.53639e10i | 0.0363438 | − | 0.0363438i | ||||
\(915\) | 1.41035e12 | 2.01207 | ||||||||
\(916\) | 9.81529e11 | + | 9.81529e11i | 1.39419 | + | 1.39419i | ||||
\(917\) | −1.23844e11 | + | 1.23844e11i | −0.175145 | + | 0.175145i | ||||
\(918\) | −2.43958e10 | − | 2.43958e10i | −0.0343514 | − | 0.0343514i | ||||
\(919\) | −1.25364e12 | −1.75756 | −0.878779 | − | 0.477229i | \(-0.841641\pi\) | ||||
−0.878779 | + | 0.477229i | \(0.841641\pi\) | |||||||
\(920\) | −1.66350e9 | − | 1.66350e9i | −0.00232206 | − | 0.00232206i | ||||
\(921\) | 3.61064e11i | 0.501818i | ||||||||
\(922\) | −2.17840e10 | −0.0301449 | ||||||||
\(923\) | 1.14234e11 | 0.157394 | ||||||||
\(924\) | −1.35098e12 | −1.85336 | ||||||||
\(925\) | −6.18872e11 | + | 6.18872e11i | −0.845345 | + | 0.845345i | ||||
\(926\) | −1.65152e10 | + | 1.65152e10i | −0.0224616 | + | 0.0224616i | ||||
\(927\) | − | 1.17737e12i | − | 1.59439i | ||||||
\(928\) | 7.06958e10 | − | 2.67677e10i | 0.0953239 | − | 0.0360927i | ||||
\(929\) | −7.21060e11 | −0.968075 | −0.484037 | − | 0.875047i | \(-0.660830\pi\) | ||||
−0.484037 | + | 0.875047i | \(0.660830\pi\) | |||||||
\(930\) | 6.09932e10 | + | 6.09932e10i | 0.0815361 | + | 0.0815361i | ||||
\(931\) | 8.27155e10 | + | 8.27155e10i | 0.110100 | + | 0.110100i | ||||
\(932\) | − | 6.24822e11i | − | 0.828119i | ||||||
\(933\) | − | 1.06965e12i | − | 1.41161i | ||||||
\(934\) | 2.10582e10i | 0.0276716i | ||||||||
\(935\) | 1.25780e12 | 1.64575 | ||||||||
\(936\) | −4.56366e10 | + | 4.56366e10i | −0.0594579 | + | 0.0594579i | ||||
\(937\) | 3.37163e11i | 0.437402i | 0.975792 | + | 0.218701i | \(0.0701820\pi\) | ||||
−0.975792 | + | 0.218701i | \(0.929818\pi\) | |||||||
\(938\) | 1.01586e10 | − | 1.01586e10i | 0.0131227 | − | 0.0131227i | ||||
\(939\) | 1.62678e12 | + | 1.62678e12i | 2.09250 | + | 2.09250i | ||||
\(940\) | 5.75822e11 | − | 5.75822e11i | 0.737525 | − | 0.737525i | ||||
\(941\) | − | 2.70865e11i | − | 0.345457i | −0.984969 | − | 0.172729i | \(-0.944742\pi\) | ||
0.984969 | − | 0.172729i | \(-0.0552584\pi\) | |||||||
\(942\) | 2.97876e10 | + | 2.97876e10i | 0.0378296 | + | 0.0378296i | ||||
\(943\) | −3.83124e10 | + | 3.83124e10i | −0.0484498 | + | 0.0484498i | ||||
\(944\) | 2.94670e11 | 0.371064 | ||||||||
\(945\) | −9.14777e11 | − | 9.14777e11i | −1.14707 | − | 1.14707i | ||||
\(946\) | −2.10867e10 | + | 2.10867e10i | −0.0263296 | + | 0.0263296i | ||||
\(947\) | 1.60874e11 | + | 1.60874e11i | 0.200025 | + | 0.200025i | 0.800011 | − | 0.599986i | \(-0.204827\pi\) |
−0.599986 | + | 0.800011i | \(0.704827\pi\) | |||||||
\(948\) | 3.54668e11 | 0.439125 | ||||||||
\(949\) | −3.96547e11 | − | 3.96547e11i | −0.488910 | − | 0.488910i | ||||
\(950\) | − | 9.66925e9i | − | 0.0118713i | ||||||
\(951\) | −9.85277e11 | −1.20458 | ||||||||
\(952\) | 8.14637e10 | 0.0991783 | ||||||||
\(953\) | −3.75674e11 | −0.455449 | −0.227724 | − | 0.973726i | \(-0.573129\pi\) | ||||
−0.227724 | + | 0.973726i | \(0.573129\pi\) | |||||||
\(954\) | −2.32646e10 | + | 2.32646e10i | −0.0280868 | + | 0.0280868i | ||||
\(955\) | 3.05576e10 | − | 3.05576e10i | 0.0367372 | − | 0.0367372i | ||||
\(956\) | − | 8.00104e10i | − | 0.0957888i | ||||||
\(957\) | 1.24929e12 | + | 5.63069e11i | 1.48941 | + | 0.671296i | ||||
\(958\) | −4.64640e10 | −0.0551639 | ||||||||
\(959\) | −7.72145e11 | − | 7.72145e11i | −0.912902 | − | 0.912902i | ||||
\(960\) | −1.25390e12 | − | 1.25390e12i | −1.47631 | − | 1.47631i | ||||
\(961\) | 1.36277e12i | 1.59783i | ||||||||
\(962\) | 3.94772e10i | 0.0460942i | ||||||||
\(963\) | − | 2.53904e12i | − | 2.95233i | ||||||
\(964\) | −6.02668e11 | −0.697862 | ||||||||
\(965\) | −1.53768e12 | + | 1.53768e12i | −1.77319 | + | 1.77319i | ||||
\(966\) | − | 2.07072e9i | − | 0.00237801i | ||||||
\(967\) | −5.07328e11 | + | 5.07328e11i | −0.580207 | + | 0.580207i | −0.934960 | − | 0.354753i | \(-0.884565\pi\) |
0.354753 | + | 0.934960i | \(0.384565\pi\) | |||||||
\(968\) | −1.63476e8 | − | 1.63476e8i | −0.000186188 | − | 0.000186188i | ||||
\(969\) | −7.03475e11 | + | 7.03475e11i | −0.797909 | + | 0.797909i | ||||
\(970\) | 3.80612e10i | 0.0429928i | ||||||||
\(971\) | −1.17516e11 | − | 1.17516e11i | −0.132197 | − | 0.132197i | 0.637912 | − | 0.770109i | \(-0.279798\pi\) |
−0.770109 | + | 0.637912i | \(0.779798\pi\) | |||||||
\(972\) | 5.55686e11 | − | 5.55686e11i | 0.622535 | − | 0.622535i | ||||
\(973\) | −1.33946e12 | −1.49444 | ||||||||
\(974\) | −1.88158e10 | − | 1.88158e10i | −0.0209068 | − | 0.0209068i | ||||
\(975\) | 5.00248e11 | − | 5.00248e11i | 0.553563 | − | 0.553563i | ||||
\(976\) | 6.11929e11 | + | 6.11929e11i | 0.674376 | + | 0.674376i | ||||
\(977\) | 1.61586e11 | 0.177348 | 0.0886739 | − | 0.996061i | \(-0.471737\pi\) | ||||
0.0886739 | + | 0.996061i | \(0.471737\pi\) | |||||||
\(978\) | −5.78460e10 | − | 5.78460e10i | −0.0632292 | − | 0.0632292i | ||||
\(979\) | − | 1.05601e12i | − | 1.14958i | ||||||
\(980\) | 3.43129e11 | 0.372008 | ||||||||
\(981\) | 1.51157e12 | 1.63212 | ||||||||
\(982\) | 2.55220e10 | 0.0274454 | ||||||||
\(983\) | 1.22639e12 | − | 1.22639e12i | 1.31345 | − | 1.31345i | 0.394598 | − | 0.918854i | \(-0.370884\pi\) |
0.918854 | − | 0.394598i | \(-0.129116\pi\) | |||||||
\(984\) | 1.34538e11 | − | 1.34538e11i | 0.143504 | − | 0.143504i | ||||
\(985\) | 1.21531e12i | 1.29105i | ||||||||
\(986\) | −3.76441e10 | − | 1.69667e10i | −0.0398281 | − | 0.0179510i | ||||
\(987\) | 1.43439e12 | 1.51147 | ||||||||
\(988\) | 2.66023e11 | + | 2.66023e11i | 0.279184 | + | 0.279184i | ||||
\(989\) | 2.78800e10 | + | 2.78800e10i | 0.0291412 | + | 0.0291412i | ||||
\(990\) | 7.03697e10i | 0.0732562i | ||||||||
\(991\) | 1.40982e12i | 1.46174i | 0.682519 | + | 0.730868i | \(0.260884\pi\) | ||||
−0.682519 | + | 0.730868i | \(0.739116\pi\) | |||||||
\(992\) | 1.59091e11i | 0.164285i | ||||||||
\(993\) | 1.63391e11 | 0.168047 | ||||||||
\(994\) | 5.70415e9 | − | 5.70415e9i | 0.00584312 | − | 0.00584312i | ||||
\(995\) | − | 1.71168e12i | − | 1.74634i | ||||||
\(996\) | 1.47601e12 | − | 1.47601e12i | 1.49986 | − | 1.49986i | ||||
\(997\) | −6.96211e11 | − | 6.96211e11i | −0.704629 | − | 0.704629i | 0.260772 | − | 0.965401i | \(-0.416023\pi\) |
−0.965401 | + | 0.260772i | \(0.916023\pi\) | |||||||
\(998\) | 8.70051e9 | − | 8.70051e9i | 0.00877046 | − | 0.00877046i | ||||
\(999\) | 2.03806e12i | 2.04623i |
(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 | 29.9.c.a.12.10 | ✓ | 38 | |
29.17 | odd | 4 | inner | 29.9.c.a.17.10 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.9.c.a.12.10 | ✓ | 38 | 1.1 | even | 1 | trivial | |
29.9.c.a.17.10 | yes | 38 | 29.17 | odd | 4 | inner |