Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.26 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.7 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.88981i | 1.33630i | 0.744026 | + | 0.668150i | \(0.232914\pi\) | ||||
−0.744026 | + | 0.668150i | \(0.767086\pi\) | |||||||
\(3\) | −0.327950 | −0.189342 | −0.0946711 | − | 0.995509i | \(-0.530180\pi\) | ||||
−0.0946711 | + | 0.995509i | \(0.530180\pi\) | |||||||
\(4\) | −1.57140 | −0.785699 | ||||||||
\(5\) | − | 1.75790i | − | 0.786158i | −0.919505 | − | 0.393079i | \(-0.871410\pi\) | ||
0.919505 | − | 0.393079i | \(-0.128590\pi\) | |||||||
\(6\) | − | 0.619765i | − | 0.253018i | ||||||
\(7\) | 0.652358i | 0.246568i | 0.992371 | + | 0.123284i | \(0.0393426\pi\) | ||||
−0.992371 | + | 0.123284i | \(0.960657\pi\) | |||||||
\(8\) | 0.809976i | 0.286370i | ||||||||
\(9\) | −2.89245 | −0.964150 | ||||||||
\(10\) | 3.32211 | 1.05054 | ||||||||
\(11\) | 4.04168i | 1.21861i | 0.792935 | + | 0.609306i | \(0.208552\pi\) | ||||
−0.792935 | + | 0.609306i | \(0.791448\pi\) | |||||||
\(12\) | 0.515341 | 0.148766 | ||||||||
\(13\) | −0.515318 | + | 3.56854i | −0.142923 | + | 0.989734i | ||||
\(14\) | −1.23284 | −0.329489 | ||||||||
\(15\) | 0.576505i | 0.148853i | ||||||||
\(16\) | −4.67350 | −1.16838 | ||||||||
\(17\) | −2.05056 | −0.497334 | −0.248667 | − | 0.968589i | \(-0.579992\pi\) | ||||
−0.248667 | + | 0.968589i | \(0.579992\pi\) | |||||||
\(18\) | − | 5.46619i | − | 1.28839i | ||||||
\(19\) | 7.52193i | 1.72565i | 0.505504 | + | 0.862824i | \(0.331307\pi\) | ||||
−0.505504 | + | 0.862824i | \(0.668693\pi\) | |||||||
\(20\) | 2.76237i | 0.617684i | ||||||||
\(21\) | − | 0.213941i | − | 0.0466857i | ||||||
\(22\) | −7.63802 | −1.62843 | ||||||||
\(23\) | −1.17786 | −0.245601 | −0.122801 | − | 0.992431i | \(-0.539188\pi\) | ||||
−0.122801 | + | 0.992431i | \(0.539188\pi\) | |||||||
\(24\) | − | 0.265632i | − | 0.0542219i | ||||||
\(25\) | 1.90978 | 0.381955 | ||||||||
\(26\) | −6.74387 | − | 0.973855i | −1.32258 | − | 0.190989i | ||||
\(27\) | 1.93243 | 0.371896 | ||||||||
\(28\) | − | 1.02511i | − | 0.193728i | ||||||
\(29\) | 6.42057 | 1.19227 | 0.596135 | − | 0.802884i | \(-0.296702\pi\) | ||||
0.596135 | + | 0.802884i | \(0.296702\pi\) | |||||||
\(30\) | −1.08949 | −0.198912 | ||||||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | − | 7.21210i | − | 1.27493i | ||||||
\(33\) | − | 1.32547i | − | 0.230735i | ||||||
\(34\) | − | 3.87518i | − | 0.664588i | ||||||
\(35\) | 1.14678 | 0.193842 | ||||||||
\(36\) | 4.54519 | 0.757532 | ||||||||
\(37\) | − | 4.69077i | − | 0.771158i | −0.922675 | − | 0.385579i | \(-0.874002\pi\) | ||
0.922675 | − | 0.385579i | \(-0.125998\pi\) | |||||||
\(38\) | −14.2150 | −2.30599 | ||||||||
\(39\) | 0.168999 | − | 1.17030i | 0.0270614 | − | 0.187398i | ||||
\(40\) | 1.42386 | 0.225132 | ||||||||
\(41\) | − | 5.09819i | − | 0.796204i | −0.917341 | − | 0.398102i | \(-0.869669\pi\) | ||
0.917341 | − | 0.398102i | \(-0.130331\pi\) | |||||||
\(42\) | 0.404309 | 0.0623862 | ||||||||
\(43\) | 2.44144 | 0.372317 | 0.186158 | − | 0.982520i | \(-0.440396\pi\) | ||||
0.186158 | + | 0.982520i | \(0.440396\pi\) | |||||||
\(44\) | − | 6.35109i | − | 0.957463i | ||||||
\(45\) | 5.08465i | 0.757974i | ||||||||
\(46\) | − | 2.22594i | − | 0.328197i | ||||||
\(47\) | − | 1.20893i | − | 0.176341i | −0.996105 | − | 0.0881703i | \(-0.971898\pi\) | ||
0.996105 | − | 0.0881703i | \(-0.0281020\pi\) | |||||||
\(48\) | 1.53268 | 0.221223 | ||||||||
\(49\) | 6.57443 | 0.939204 | ||||||||
\(50\) | 3.60912i | 0.510407i | ||||||||
\(51\) | 0.672482 | 0.0941663 | ||||||||
\(52\) | 0.809770 | − | 5.60759i | 0.112295 | − | 0.777633i | ||||
\(53\) | 0.419540 | 0.0576282 | 0.0288141 | − | 0.999585i | \(-0.490827\pi\) | ||||
0.0288141 | + | 0.999585i | \(0.490827\pi\) | |||||||
\(54\) | 3.65193i | 0.496965i | ||||||||
\(55\) | 7.10488 | 0.958022 | ||||||||
\(56\) | −0.528394 | −0.0706097 | ||||||||
\(57\) | − | 2.46682i | − | 0.326738i | ||||||
\(58\) | 12.1337i | 1.59323i | ||||||||
\(59\) | − | 10.2580i | − | 1.33548i | −0.744397 | − | 0.667738i | \(-0.767263\pi\) | ||
0.744397 | − | 0.667738i | \(-0.232737\pi\) | |||||||
\(60\) | − | 0.905919i | − | 0.116954i | ||||||
\(61\) | −12.7823 | −1.63661 | −0.818303 | − | 0.574788i | \(-0.805085\pi\) | ||||
−0.818303 | + | 0.574788i | \(0.805085\pi\) | |||||||
\(62\) | 1.88981 | 0.240007 | ||||||||
\(63\) | − | 1.88691i | − | 0.237728i | ||||||
\(64\) | 4.28253 | 0.535316 | ||||||||
\(65\) | 6.27314 | + | 0.905879i | 0.778087 | + | 0.112360i | ||||
\(66\) | 2.50489 | 0.308331 | ||||||||
\(67\) | 11.5333i | 1.40902i | 0.709693 | + | 0.704511i | \(0.248834\pi\) | ||||
−0.709693 | + | 0.704511i | \(0.751166\pi\) | |||||||
\(68\) | 3.22225 | 0.390755 | ||||||||
\(69\) | 0.386280 | 0.0465027 | ||||||||
\(70\) | 2.16721i | 0.259031i | ||||||||
\(71\) | − | 6.53421i | − | 0.775468i | −0.921771 | − | 0.387734i | \(-0.873258\pi\) | ||
0.921771 | − | 0.387734i | \(-0.126742\pi\) | |||||||
\(72\) | − | 2.34282i | − | 0.276103i | ||||||
\(73\) | 0.170013i | 0.0198985i | 0.999951 | + | 0.00994926i | \(0.00316700\pi\) | ||||
−0.999951 | + | 0.00994926i | \(0.996833\pi\) | |||||||
\(74\) | 8.86469 | 1.03050 | ||||||||
\(75\) | −0.626311 | −0.0723202 | ||||||||
\(76\) | − | 11.8200i | − | 1.35584i | ||||||
\(77\) | −2.63662 | −0.300471 | ||||||||
\(78\) | 2.21165 | + | 0.319376i | 0.250421 | + | 0.0361622i | ||||
\(79\) | 8.39155 | 0.944124 | 0.472062 | − | 0.881565i | \(-0.343510\pi\) | ||||
0.472062 | + | 0.881565i | \(0.343510\pi\) | |||||||
\(80\) | 8.21557i | 0.918528i | ||||||||
\(81\) | 8.04360 | 0.893734 | ||||||||
\(82\) | 9.63464 | 1.06397 | ||||||||
\(83\) | 13.1610i | 1.44461i | 0.691576 | + | 0.722304i | \(0.256917\pi\) | ||||
−0.691576 | + | 0.722304i | \(0.743083\pi\) | |||||||
\(84\) | 0.336186i | 0.0366810i | ||||||||
\(85\) | 3.60469i | 0.390983i | ||||||||
\(86\) | 4.61387i | 0.497527i | ||||||||
\(87\) | −2.10563 | −0.225747 | ||||||||
\(88\) | −3.27366 | −0.348974 | ||||||||
\(89\) | − | 7.61808i | − | 0.807515i | −0.914866 | − | 0.403758i | \(-0.867704\pi\) | ||
0.914866 | − | 0.403758i | \(-0.132296\pi\) | |||||||
\(90\) | −9.60904 | −1.01288 | ||||||||
\(91\) | −2.32796 | − | 0.336172i | −0.244037 | − | 0.0352404i | ||||
\(92\) | 1.85089 | 0.192969 | ||||||||
\(93\) | 0.327950i | 0.0340069i | ||||||||
\(94\) | 2.28465 | 0.235644 | ||||||||
\(95\) | 13.2228 | 1.35663 | ||||||||
\(96\) | 2.36521i | 0.241398i | ||||||||
\(97\) | 18.9945i | 1.92860i | 0.264812 | + | 0.964300i | \(0.414690\pi\) | ||||
−0.264812 | + | 0.964300i | \(0.585310\pi\) | |||||||
\(98\) | 12.4245i | 1.25506i | ||||||||
\(99\) | − | 11.6903i | − | 1.17492i | ||||||
\(100\) | −3.00102 | −0.300102 | ||||||||
\(101\) | −12.9992 | −1.29347 | −0.646733 | − | 0.762717i | \(-0.723865\pi\) | ||||
−0.646733 | + | 0.762717i | \(0.723865\pi\) | |||||||
\(102\) | 1.27087i | 0.125834i | ||||||||
\(103\) | −7.58987 | −0.747852 | −0.373926 | − | 0.927458i | \(-0.621989\pi\) | ||||
−0.373926 | + | 0.927458i | \(0.621989\pi\) | |||||||
\(104\) | −2.89043 | − | 0.417395i | −0.283430 | − | 0.0409290i | ||||
\(105\) | −0.376087 | −0.0367024 | ||||||||
\(106\) | 0.792853i | 0.0770087i | ||||||||
\(107\) | 14.5830 | 1.40979 | 0.704895 | − | 0.709312i | \(-0.250994\pi\) | ||||
0.704895 | + | 0.709312i | \(0.250994\pi\) | |||||||
\(108\) | −3.03662 | −0.292199 | ||||||||
\(109\) | 4.51756i | 0.432703i | 0.976315 | + | 0.216352i | \(0.0694158\pi\) | ||||
−0.976315 | + | 0.216352i | \(0.930584\pi\) | |||||||
\(110\) | 13.4269i | 1.28021i | ||||||||
\(111\) | 1.53834i | 0.146013i | ||||||||
\(112\) | − | 3.04880i | − | 0.288084i | ||||||
\(113\) | −12.3097 | −1.15800 | −0.578998 | − | 0.815329i | \(-0.696556\pi\) | ||||
−0.578998 | + | 0.815329i | \(0.696556\pi\) | |||||||
\(114\) | 4.66183 | 0.436620 | ||||||||
\(115\) | 2.07057i | 0.193082i | ||||||||
\(116\) | −10.0893 | −0.936766 | ||||||||
\(117\) | 1.49053 | − | 10.3218i | 0.137800 | − | 0.954251i | ||||
\(118\) | 19.3857 | 1.78460 | ||||||||
\(119\) | − | 1.33770i | − | 0.122627i | ||||||
\(120\) | −0.466955 | −0.0426270 | ||||||||
\(121\) | −5.33516 | −0.485015 | ||||||||
\(122\) | − | 24.1562i | − | 2.18700i | ||||||
\(123\) | 1.67195i | 0.150755i | ||||||||
\(124\) | 1.57140i | 0.141116i | ||||||||
\(125\) | − | 12.1467i | − | 1.08644i | ||||||
\(126\) | 3.56591 | 0.317677 | ||||||||
\(127\) | 20.8813 | 1.85292 | 0.926459 | − | 0.376396i | \(-0.122837\pi\) | ||||
0.926459 | + | 0.376396i | \(0.122837\pi\) | |||||||
\(128\) | − | 6.33102i | − | 0.559588i | ||||||
\(129\) | −0.800672 | −0.0704952 | ||||||||
\(130\) | −1.71194 | + | 11.8551i | −0.150147 | + | 1.03976i | ||||
\(131\) | 8.64964 | 0.755723 | 0.377861 | − | 0.925862i | \(-0.376660\pi\) | ||||
0.377861 | + | 0.925862i | \(0.376660\pi\) | |||||||
\(132\) | 2.08284i | 0.181288i | ||||||||
\(133\) | −4.90699 | −0.425490 | ||||||||
\(134\) | −21.7959 | −1.88288 | ||||||||
\(135\) | − | 3.39703i | − | 0.292369i | ||||||
\(136\) | − | 1.66091i | − | 0.142421i | ||||||
\(137\) | 14.7125i | 1.25697i | 0.777821 | + | 0.628486i | \(0.216325\pi\) | ||||
−0.777821 | + | 0.628486i | \(0.783675\pi\) | |||||||
\(138\) | 0.729998i | 0.0621416i | ||||||||
\(139\) | 15.5107 | 1.31560 | 0.657801 | − | 0.753192i | \(-0.271487\pi\) | ||||
0.657801 | + | 0.753192i | \(0.271487\pi\) | |||||||
\(140\) | −1.80205 | −0.152301 | ||||||||
\(141\) | 0.396469i | 0.0333887i | ||||||||
\(142\) | 12.3484 | 1.03626 | ||||||||
\(143\) | −14.4229 | − | 2.08275i | −1.20610 | − | 0.174168i | ||||
\(144\) | 13.5179 | 1.12649 | ||||||||
\(145\) | − | 11.2867i | − | 0.937313i | ||||||
\(146\) | −0.321293 | −0.0265904 | ||||||||
\(147\) | −2.15609 | −0.177831 | ||||||||
\(148\) | 7.37108i | 0.605899i | ||||||||
\(149\) | − | 1.96195i | − | 0.160729i | −0.996766 | − | 0.0803645i | \(-0.974392\pi\) | ||
0.996766 | − | 0.0803645i | \(-0.0256084\pi\) | |||||||
\(150\) | − | 1.18361i | − | 0.0966415i | ||||||
\(151\) | 3.06613i | 0.249518i | 0.992187 | + | 0.124759i | \(0.0398158\pi\) | ||||
−0.992187 | + | 0.124759i | \(0.960184\pi\) | |||||||
\(152\) | −6.09258 | −0.494174 | ||||||||
\(153\) | 5.93114 | 0.479504 | ||||||||
\(154\) | − | 4.98272i | − | 0.401519i | ||||||
\(155\) | −1.75790 | −0.141198 | ||||||||
\(156\) | −0.265564 | + | 1.83901i | −0.0212622 | + | 0.147239i | ||||
\(157\) | 9.92590 | 0.792173 | 0.396086 | − | 0.918213i | \(-0.370368\pi\) | ||||
0.396086 | + | 0.918213i | \(0.370368\pi\) | |||||||
\(158\) | 15.8585i | 1.26163i | ||||||||
\(159\) | −0.137588 | −0.0109115 | ||||||||
\(160\) | −12.6782 | −1.00230 | ||||||||
\(161\) | − | 0.768388i | − | 0.0605575i | ||||||
\(162\) | 15.2009i | 1.19430i | ||||||||
\(163\) | 9.23484i | 0.723328i | 0.932308 | + | 0.361664i | \(0.117791\pi\) | ||||
−0.932308 | + | 0.361664i | \(0.882209\pi\) | |||||||
\(164\) | 8.01129i | 0.625577i | ||||||||
\(165\) | −2.33005 | −0.181394 | ||||||||
\(166\) | −24.8718 | −1.93043 | ||||||||
\(167\) | − | 18.2427i | − | 1.41166i | −0.708379 | − | 0.705832i | \(-0.750573\pi\) | ||
0.708379 | − | 0.705832i | \(-0.249427\pi\) | |||||||
\(168\) | 0.173287 | 0.0133694 | ||||||||
\(169\) | −12.4689 | − | 3.67786i | −0.959146 | − | 0.282912i | ||||
\(170\) | −6.81219 | −0.522471 | ||||||||
\(171\) | − | 21.7568i | − | 1.66378i | ||||||
\(172\) | −3.83648 | −0.292529 | ||||||||
\(173\) | −0.0577833 | −0.00439318 | −0.00219659 | − | 0.999998i | \(-0.500699\pi\) | ||||
−0.00219659 | + | 0.999998i | \(0.500699\pi\) | |||||||
\(174\) | − | 3.97925i | − | 0.301666i | ||||||
\(175\) | 1.24586i | 0.0941779i | ||||||||
\(176\) | − | 18.8888i | − | 1.42380i | ||||||
\(177\) | 3.36411i | 0.252862i | ||||||||
\(178\) | 14.3968 | 1.07908 | ||||||||
\(179\) | 12.4809 | 0.932867 | 0.466433 | − | 0.884556i | \(-0.345539\pi\) | ||||
0.466433 | + | 0.884556i | \(0.345539\pi\) | |||||||
\(180\) | − | 7.99001i | − | 0.595540i | ||||||
\(181\) | 9.94653 | 0.739319 | 0.369660 | − | 0.929167i | \(-0.379474\pi\) | ||||
0.369660 | + | 0.929167i | \(0.379474\pi\) | |||||||
\(182\) | 0.635302 | − | 4.39942i | 0.0470917 | − | 0.326106i | ||||
\(183\) | 4.19196 | 0.309878 | ||||||||
\(184\) | − | 0.954041i | − | 0.0703329i | ||||||
\(185\) | −8.24593 | −0.606253 | ||||||||
\(186\) | −0.619765 | −0.0454434 | ||||||||
\(187\) | − | 8.28771i | − | 0.606057i | ||||||
\(188\) | 1.89971i | 0.138551i | ||||||||
\(189\) | 1.26064i | 0.0916978i | ||||||||
\(190\) | 24.9887i | 1.81287i | ||||||||
\(191\) | −26.3529 | −1.90683 | −0.953413 | − | 0.301669i | \(-0.902456\pi\) | ||||
−0.953413 | + | 0.301669i | \(0.902456\pi\) | |||||||
\(192\) | −1.40446 | −0.101358 | ||||||||
\(193\) | − | 0.942300i | − | 0.0678282i | −0.999425 | − | 0.0339141i | \(-0.989203\pi\) | ||
0.999425 | − | 0.0339141i | \(-0.0107973\pi\) | |||||||
\(194\) | −35.8961 | −2.57719 | ||||||||
\(195\) | −2.05728 | − | 0.297083i | −0.147325 | − | 0.0212746i | ||||
\(196\) | −10.3311 | −0.737932 | ||||||||
\(197\) | 10.5101i | 0.748812i | 0.927265 | + | 0.374406i | \(0.122153\pi\) | ||||
−0.927265 | + | 0.374406i | \(0.877847\pi\) | |||||||
\(198\) | 22.0926 | 1.57005 | ||||||||
\(199\) | 10.5659 | 0.748994 | 0.374497 | − | 0.927228i | \(-0.377815\pi\) | ||||
0.374497 | + | 0.927228i | \(0.377815\pi\) | |||||||
\(200\) | 1.54687i | 0.109380i | ||||||||
\(201\) | − | 3.78236i | − | 0.266787i | ||||||
\(202\) | − | 24.5660i | − | 1.72846i | ||||||
\(203\) | 4.18851i | 0.293976i | ||||||||
\(204\) | −1.05674 | −0.0739864 | ||||||||
\(205\) | −8.96213 | −0.625942 | ||||||||
\(206\) | − | 14.3435i | − | 0.999356i | ||||||
\(207\) | 3.40691 | 0.236796 | ||||||||
\(208\) | 2.40834 | − | 16.6776i | 0.166988 | − | 1.15638i | ||||
\(209\) | −30.4012 | −2.10290 | ||||||||
\(210\) | − | 0.710736i | − | 0.0490454i | ||||||
\(211\) | −0.214908 | −0.0147949 | −0.00739745 | − | 0.999973i | \(-0.502355\pi\) | ||||
−0.00739745 | + | 0.999973i | \(0.502355\pi\) | |||||||
\(212\) | −0.659265 | −0.0452785 | ||||||||
\(213\) | 2.14290i | 0.146829i | ||||||||
\(214\) | 27.5591i | 1.88390i | ||||||||
\(215\) | − | 4.29182i | − | 0.292700i | ||||||
\(216\) | 1.56522i | 0.106500i | ||||||||
\(217\) | 0.652358 | 0.0442849 | ||||||||
\(218\) | −8.53734 | −0.578222 | ||||||||
\(219\) | − | 0.0557558i | − | 0.00376763i | ||||||
\(220\) | −11.1646 | −0.752717 | ||||||||
\(221\) | 1.05669 | − | 7.31750i | 0.0710807 | − | 0.492228i | ||||
\(222\) | −2.90718 | −0.195117 | ||||||||
\(223\) | 7.54869i | 0.505497i | 0.967532 | + | 0.252749i | \(0.0813346\pi\) | ||||
−0.967532 | + | 0.252749i | \(0.918665\pi\) | |||||||
\(224\) | 4.70487 | 0.314357 | ||||||||
\(225\) | −5.52393 | −0.368262 | ||||||||
\(226\) | − | 23.2630i | − | 1.54743i | ||||||
\(227\) | − | 17.5811i | − | 1.16690i | −0.812149 | − | 0.583450i | \(-0.801702\pi\) | ||
0.812149 | − | 0.583450i | \(-0.198298\pi\) | |||||||
\(228\) | 3.87636i | 0.256718i | ||||||||
\(229\) | − | 2.48342i | − | 0.164109i | −0.996628 | − | 0.0820544i | \(-0.973852\pi\) | ||
0.996628 | − | 0.0820544i | \(-0.0261481\pi\) | |||||||
\(230\) | −3.91299 | −0.258015 | ||||||||
\(231\) | 0.864680 | 0.0568918 | ||||||||
\(232\) | 5.20051i | 0.341430i | ||||||||
\(233\) | −1.73165 | −0.113444 | −0.0567220 | − | 0.998390i | \(-0.518065\pi\) | ||||
−0.0567220 | + | 0.998390i | \(0.518065\pi\) | |||||||
\(234\) | 19.5063 | + | 2.81683i | 1.27517 | + | 0.184142i | ||||
\(235\) | −2.12518 | −0.138632 | ||||||||
\(236\) | 16.1194i | 1.04928i | ||||||||
\(237\) | −2.75201 | −0.178762 | ||||||||
\(238\) | 2.52800 | 0.163866 | ||||||||
\(239\) | 1.40954i | 0.0911755i | 0.998960 | + | 0.0455878i | \(0.0145161\pi\) | ||||
−0.998960 | + | 0.0455878i | \(0.985484\pi\) | |||||||
\(240\) | − | 2.69430i | − | 0.173916i | ||||||
\(241\) | 0.348571i | 0.0224534i | 0.999937 | + | 0.0112267i | \(0.00357365\pi\) | ||||
−0.999937 | + | 0.0112267i | \(0.996426\pi\) | |||||||
\(242\) | − | 10.0825i | − | 0.648125i | ||||||
\(243\) | −8.43519 | −0.541118 | ||||||||
\(244\) | 20.0861 | 1.28588 | ||||||||
\(245\) | − | 11.5572i | − | 0.738363i | ||||||
\(246\) | −3.15968 | −0.201454 | ||||||||
\(247\) | −26.8423 | − | 3.87618i | −1.70793 | − | 0.246636i | ||||
\(248\) | 0.809976 | 0.0514336 | ||||||||
\(249\) | − | 4.31615i | − | 0.273525i | ||||||
\(250\) | 22.9550 | 1.45180 | ||||||||
\(251\) | −7.54455 | −0.476208 | −0.238104 | − | 0.971240i | \(-0.576526\pi\) | ||||
−0.238104 | + | 0.971240i | \(0.576526\pi\) | |||||||
\(252\) | 2.96509i | 0.186783i | ||||||||
\(253\) | − | 4.76054i | − | 0.299293i | ||||||
\(254\) | 39.4618i | 2.47606i | ||||||||
\(255\) | − | 1.18216i | − | 0.0740296i | ||||||
\(256\) | 20.5295 | 1.28309 | ||||||||
\(257\) | −22.3905 | −1.39668 | −0.698341 | − | 0.715765i | \(-0.746078\pi\) | ||||
−0.698341 | + | 0.715765i | \(0.746078\pi\) | |||||||
\(258\) | − | 1.51312i | − | 0.0942028i | ||||||
\(259\) | 3.06006 | 0.190143 | ||||||||
\(260\) | −9.85761 | − | 1.42350i | −0.611343 | − | 0.0882816i | ||||
\(261\) | −18.5712 | −1.14953 | ||||||||
\(262\) | 16.3462i | 1.00987i | ||||||||
\(263\) | 19.5006 | 1.20246 | 0.601230 | − | 0.799076i | \(-0.294678\pi\) | ||||
0.601230 | + | 0.799076i | \(0.294678\pi\) | |||||||
\(264\) | 1.07360 | 0.0660755 | ||||||||
\(265\) | − | 0.737511i | − | 0.0453049i | ||||||
\(266\) | − | 9.27330i | − | 0.568582i | ||||||
\(267\) | 2.49835i | 0.152897i | ||||||||
\(268\) | − | 18.1235i | − | 1.10707i | ||||||
\(269\) | 22.4446 | 1.36847 | 0.684236 | − | 0.729261i | \(-0.260136\pi\) | ||||
0.684236 | + | 0.729261i | \(0.260136\pi\) | |||||||
\(270\) | 6.41975 | 0.390693 | ||||||||
\(271\) | 19.0371i | 1.15642i | 0.815887 | + | 0.578211i | \(0.196249\pi\) | ||||
−0.815887 | + | 0.578211i | \(0.803751\pi\) | |||||||
\(272\) | 9.58330 | 0.581073 | ||||||||
\(273\) | 0.763456 | + | 0.110248i | 0.0462064 | + | 0.00667249i | ||||
\(274\) | −27.8039 | −1.67969 | ||||||||
\(275\) | 7.71870i | 0.465455i | ||||||||
\(276\) | −0.607001 | −0.0365372 | ||||||||
\(277\) | 3.01871 | 0.181377 | 0.0906883 | − | 0.995879i | \(-0.471093\pi\) | ||||
0.0906883 | + | 0.995879i | \(0.471093\pi\) | |||||||
\(278\) | 29.3124i | 1.75804i | ||||||||
\(279\) | 2.89245i | 0.173166i | ||||||||
\(280\) | 0.928866i | 0.0555104i | ||||||||
\(281\) | 28.7820i | 1.71699i | 0.512820 | + | 0.858496i | \(0.328601\pi\) | ||||
−0.512820 | + | 0.858496i | \(0.671399\pi\) | |||||||
\(282\) | −0.749253 | −0.0446174 | ||||||||
\(283\) | −1.28804 | −0.0765662 | −0.0382831 | − | 0.999267i | \(-0.512189\pi\) | ||||
−0.0382831 | + | 0.999267i | \(0.512189\pi\) | |||||||
\(284\) | 10.2678i | 0.609285i | ||||||||
\(285\) | −4.33643 | −0.256868 | ||||||||
\(286\) | 3.93601 | − | 27.2566i | 0.232741 | − | 1.61171i | ||||
\(287\) | 3.32584 | 0.196318 | ||||||||
\(288\) | 20.8606i | 1.22922i | ||||||||
\(289\) | −12.7952 | −0.752659 | ||||||||
\(290\) | 21.3298 | 1.25253 | ||||||||
\(291\) | − | 6.22925i | − | 0.365165i | ||||||
\(292\) | − | 0.267158i | − | 0.0156343i | ||||||
\(293\) | 21.1020i | 1.23279i | 0.787436 | + | 0.616397i | \(0.211408\pi\) | ||||
−0.787436 | + | 0.616397i | \(0.788592\pi\) | |||||||
\(294\) | − | 4.07460i | − | 0.237636i | ||||||
\(295\) | −18.0325 | −1.04990 | ||||||||
\(296\) | 3.79942 | 0.220837 | ||||||||
\(297\) | 7.81026i | 0.453197i | ||||||||
\(298\) | 3.70772 | 0.214782 | ||||||||
\(299\) | 0.606974 | − | 4.20325i | 0.0351022 | − | 0.243080i | ||||
\(300\) | 0.984185 | 0.0568219 | ||||||||
\(301\) | 1.59269i | 0.0918014i | ||||||||
\(302\) | −5.79442 | −0.333431 | ||||||||
\(303\) | 4.26308 | 0.244908 | ||||||||
\(304\) | − | 35.1538i | − | 2.01621i | ||||||
\(305\) | 22.4700i | 1.28663i | ||||||||
\(306\) | 11.2088i | 0.640762i | ||||||||
\(307\) | − | 2.44457i | − | 0.139519i | −0.997564 | − | 0.0697595i | \(-0.977777\pi\) | ||
0.997564 | − | 0.0697595i | \(-0.0222232\pi\) | |||||||
\(308\) | 4.14318 | 0.236080 | ||||||||
\(309\) | 2.48910 | 0.141600 | ||||||||
\(310\) | − | 3.32211i | − | 0.188683i | ||||||
\(311\) | 19.4882 | 1.10508 | 0.552538 | − | 0.833487i | \(-0.313659\pi\) | ||||
0.552538 | + | 0.833487i | \(0.313659\pi\) | |||||||
\(312\) | 0.947917 | + | 0.136885i | 0.0536652 | + | 0.00774958i | ||||
\(313\) | 17.7760 | 1.00476 | 0.502380 | − | 0.864647i | \(-0.332458\pi\) | ||||
0.502380 | + | 0.864647i | \(0.332458\pi\) | |||||||
\(314\) | 18.7581i | 1.05858i | ||||||||
\(315\) | −3.31701 | −0.186892 | ||||||||
\(316\) | −13.1865 | −0.741797 | ||||||||
\(317\) | − | 2.03343i | − | 0.114209i | −0.998368 | − | 0.0571044i | \(-0.981813\pi\) | ||
0.998368 | − | 0.0571044i | \(-0.0181868\pi\) | |||||||
\(318\) | − | 0.260016i | − | 0.0145810i | ||||||
\(319\) | 25.9499i | 1.45291i | ||||||||
\(320\) | − | 7.52827i | − | 0.420843i | ||||||
\(321\) | −4.78249 | −0.266933 | ||||||||
\(322\) | 1.45211 | 0.0809230 | ||||||||
\(323\) | − | 15.4242i | − | 0.858224i | ||||||
\(324\) | −12.6397 | −0.702206 | ||||||||
\(325\) | −0.984141 | + | 6.81510i | −0.0545903 | + | 0.378034i | ||||
\(326\) | −17.4521 | −0.966584 | ||||||||
\(327\) | − | 1.48153i | − | 0.0819290i | ||||||
\(328\) | 4.12941 | 0.228009 | ||||||||
\(329\) | 0.788655 | 0.0434799 | ||||||||
\(330\) | − | 4.40336i | − | 0.242397i | ||||||
\(331\) | − | 18.5709i | − | 1.02075i | −0.859952 | − | 0.510376i | \(-0.829506\pi\) | ||
0.859952 | − | 0.510376i | \(-0.170494\pi\) | |||||||
\(332\) | − | 20.6812i | − | 1.13503i | ||||||
\(333\) | 13.5678i | 0.743512i | ||||||||
\(334\) | 34.4754 | 1.88641 | ||||||||
\(335\) | 20.2745 | 1.10771 | ||||||||
\(336\) | 0.999853i | 0.0545465i | ||||||||
\(337\) | 33.2525 | 1.81138 | 0.905689 | − | 0.423942i | \(-0.139354\pi\) | ||||
0.905689 | + | 0.423942i | \(0.139354\pi\) | |||||||
\(338\) | 6.95047 | − | 23.5639i | 0.378056 | − | 1.28171i | ||||
\(339\) | 4.03696 | 0.219258 | ||||||||
\(340\) | − | 5.66440i | − | 0.307195i | ||||||
\(341\) | 4.04168 | 0.218869 | ||||||||
\(342\) | 41.1163 | 2.22331 | ||||||||
\(343\) | 8.85538i | 0.478146i | ||||||||
\(344\) | 1.97751i | 0.106620i | ||||||||
\(345\) | − | 0.679044i | − | 0.0365585i | ||||||
\(346\) | − | 0.109200i | − | 0.00587061i | ||||||
\(347\) | 20.9692 | 1.12569 | 0.562843 | − | 0.826564i | \(-0.309708\pi\) | ||||
0.562843 | + | 0.826564i | \(0.309708\pi\) | |||||||
\(348\) | 3.30878 | 0.177369 | ||||||||
\(349\) | − | 30.4835i | − | 1.63175i | −0.578231 | − | 0.815873i | \(-0.696257\pi\) | ||
0.578231 | − | 0.815873i | \(-0.303743\pi\) | |||||||
\(350\) | −2.35444 | −0.125850 | ||||||||
\(351\) | −0.995816 | + | 6.89595i | −0.0531527 | + | 0.368078i | ||||
\(352\) | 29.1490 | 1.55365 | ||||||||
\(353\) | 10.5824i | 0.563243i | 0.959526 | + | 0.281621i | \(0.0908722\pi\) | ||||
−0.959526 | + | 0.281621i | \(0.909128\pi\) | |||||||
\(354\) | −6.35754 | −0.337899 | ||||||||
\(355\) | −11.4865 | −0.609640 | ||||||||
\(356\) | 11.9710i | 0.634464i | ||||||||
\(357\) | 0.438699i | 0.0232184i | ||||||||
\(358\) | 23.5866i | 1.24659i | ||||||||
\(359\) | − | 21.8192i | − | 1.15157i | −0.817600 | − | 0.575786i | \(-0.804696\pi\) | ||
0.817600 | − | 0.575786i | \(-0.195304\pi\) | |||||||
\(360\) | −4.11844 | −0.217061 | ||||||||
\(361\) | −37.5794 | −1.97786 | ||||||||
\(362\) | 18.7971i | 0.987953i | ||||||||
\(363\) | 1.74967 | 0.0918337 | ||||||||
\(364\) | 3.65816 | + | 0.528260i | 0.191740 | + | 0.0276883i | ||||
\(365\) | 0.298866 | 0.0156434 | ||||||||
\(366\) | 7.92202i | 0.414091i | ||||||||
\(367\) | −20.1551 | −1.05209 | −0.526044 | − | 0.850457i | \(-0.676325\pi\) | ||||
−0.526044 | + | 0.850457i | \(0.676325\pi\) | |||||||
\(368\) | 5.50475 | 0.286955 | ||||||||
\(369\) | 14.7463i | 0.767659i | ||||||||
\(370\) | − | 15.5833i | − | 0.810136i | ||||||
\(371\) | 0.273690i | 0.0142093i | ||||||||
\(372\) | − | 0.515341i | − | 0.0267192i | ||||||
\(373\) | −29.0660 | −1.50498 | −0.752491 | − | 0.658602i | \(-0.771148\pi\) | ||||
−0.752491 | + | 0.658602i | \(0.771148\pi\) | |||||||
\(374\) | 15.6622 | 0.809874 | ||||||||
\(375\) | 3.98352i | 0.205708i | ||||||||
\(376\) | 0.979205 | 0.0504986 | ||||||||
\(377\) | −3.30863 | + | 22.9120i | −0.170403 | + | 1.18003i | ||||
\(378\) | −2.38237 | −0.122536 | ||||||||
\(379\) | 12.4985i | 0.642003i | 0.947079 | + | 0.321002i | \(0.104019\pi\) | ||||
−0.947079 | + | 0.321002i | \(0.895981\pi\) | |||||||
\(380\) | −20.7783 | −1.06591 | ||||||||
\(381\) | −6.84804 | −0.350835 | ||||||||
\(382\) | − | 49.8020i | − | 2.54809i | ||||||
\(383\) | 5.69126i | 0.290810i | 0.989372 | + | 0.145405i | \(0.0464485\pi\) | ||||
−0.989372 | + | 0.145405i | \(0.953551\pi\) | |||||||
\(384\) | 2.07626i | 0.105954i | ||||||||
\(385\) | 4.63492i | 0.236218i | ||||||||
\(386\) | 1.78077 | 0.0906389 | ||||||||
\(387\) | −7.06175 | −0.358969 | ||||||||
\(388\) | − | 29.8479i | − | 1.51530i | ||||||
\(389\) | 23.5136 | 1.19219 | 0.596093 | − | 0.802915i | \(-0.296719\pi\) | ||||
0.596093 | + | 0.802915i | \(0.296719\pi\) | |||||||
\(390\) | 0.561432 | − | 3.88787i | 0.0284292 | − | 0.196870i | ||||
\(391\) | 2.41528 | 0.122146 | ||||||||
\(392\) | 5.32513i | 0.268960i | ||||||||
\(393\) | −2.83665 | −0.143090 | ||||||||
\(394\) | −19.8621 | −1.00064 | ||||||||
\(395\) | − | 14.7515i | − | 0.742231i | ||||||
\(396\) | 18.3702i | 0.923137i | ||||||||
\(397\) | − | 8.32867i | − | 0.418004i | −0.977915 | − | 0.209002i | \(-0.932979\pi\) | ||
0.977915 | − | 0.209002i | \(-0.0670215\pi\) | |||||||
\(398\) | 19.9675i | 1.00088i | ||||||||
\(399\) | 1.60925 | 0.0805632 | ||||||||
\(400\) | −8.92534 | −0.446267 | ||||||||
\(401\) | − | 32.6105i | − | 1.62849i | −0.580520 | − | 0.814246i | \(-0.697151\pi\) | ||
0.580520 | − | 0.814246i | \(-0.302849\pi\) | |||||||
\(402\) | 7.14797 | 0.356508 | ||||||||
\(403\) | 3.56854 | + | 0.515318i | 0.177761 | + | 0.0256698i | ||||
\(404\) | 20.4269 | 1.01628 | ||||||||
\(405\) | − | 14.1399i | − | 0.702616i | ||||||
\(406\) | −7.91550 | −0.392840 | ||||||||
\(407\) | 18.9586 | 0.939743 | ||||||||
\(408\) | 0.544694i | 0.0269664i | ||||||||
\(409\) | − | 22.2951i | − | 1.10242i | −0.834366 | − | 0.551211i | \(-0.814166\pi\) | ||
0.834366 | − | 0.551211i | \(-0.185834\pi\) | |||||||
\(410\) | − | 16.9368i | − | 0.836447i | ||||||
\(411\) | − | 4.82496i | − | 0.237998i | ||||||
\(412\) | 11.9267 | 0.587587 | ||||||||
\(413\) | 6.69187 | 0.329286 | ||||||||
\(414\) | 6.43842i | 0.316431i | ||||||||
\(415\) | 23.1358 | 1.13569 | ||||||||
\(416\) | 25.7366 | + | 3.71652i | 1.26184 | + | 0.182218i | ||||
\(417\) | −5.08674 | −0.249099 | ||||||||
\(418\) | − | 57.4527i | − | 2.81010i | ||||||
\(419\) | −30.9395 | −1.51149 | −0.755747 | − | 0.654864i | \(-0.772726\pi\) | ||||
−0.755747 | + | 0.654864i | \(0.772726\pi\) | |||||||
\(420\) | 0.590983 | 0.0288370 | ||||||||
\(421\) | 5.10402i | 0.248754i | 0.992235 | + | 0.124377i | \(0.0396933\pi\) | ||||
−0.992235 | + | 0.124377i | \(0.960307\pi\) | |||||||
\(422\) | − | 0.406137i | − | 0.0197704i | ||||||
\(423\) | 3.49677i | 0.170019i | ||||||||
\(424\) | 0.339817i | 0.0165030i | ||||||||
\(425\) | −3.91611 | −0.189959 | ||||||||
\(426\) | −4.04967 | −0.196207 | ||||||||
\(427\) | − | 8.33863i | − | 0.403534i | ||||||
\(428\) | −22.9157 | −1.10767 | ||||||||
\(429\) | 4.72999 | + | 0.683038i | 0.228366 | + | 0.0329774i | ||||
\(430\) | 8.11075 | 0.391135 | ||||||||
\(431\) | 24.6933i | 1.18944i | 0.803935 | + | 0.594718i | \(0.202736\pi\) | ||||
−0.803935 | + | 0.594718i | \(0.797264\pi\) | |||||||
\(432\) | −9.03122 | −0.434515 | ||||||||
\(433\) | −4.59601 | −0.220870 | −0.110435 | − | 0.993883i | \(-0.535224\pi\) | ||||
−0.110435 | + | 0.993883i | \(0.535224\pi\) | |||||||
\(434\) | 1.23284i | 0.0591780i | ||||||||
\(435\) | 3.70149i | 0.177473i | ||||||||
\(436\) | − | 7.09888i | − | 0.339975i | ||||||
\(437\) | − | 8.85980i | − | 0.423822i | ||||||
\(438\) | 0.105368 | 0.00503468 | ||||||||
\(439\) | −22.3774 | −1.06801 | −0.534007 | − | 0.845480i | \(-0.679314\pi\) | ||||
−0.534007 | + | 0.845480i | \(0.679314\pi\) | |||||||
\(440\) | 5.75479i | 0.274349i | ||||||||
\(441\) | −19.0162 | −0.905533 | ||||||||
\(442\) | 13.8287 | + | 1.99695i | 0.657765 | + | 0.0949852i | ||||
\(443\) | 27.0807 | 1.28664 | 0.643322 | − | 0.765596i | \(-0.277556\pi\) | ||||
0.643322 | + | 0.765596i | \(0.277556\pi\) | |||||||
\(444\) | − | 2.41735i | − | 0.114722i | ||||||
\(445\) | −13.3919 | −0.634835 | ||||||||
\(446\) | −14.2656 | −0.675497 | ||||||||
\(447\) | 0.643422i | 0.0304328i | ||||||||
\(448\) | 2.79374i | 0.131992i | ||||||||
\(449\) | − | 33.4114i | − | 1.57678i | −0.615175 | − | 0.788391i | \(-0.710915\pi\) | ||
0.615175 | − | 0.788391i | \(-0.289085\pi\) | |||||||
\(450\) | − | 10.4392i | − | 0.492108i | ||||||
\(451\) | 20.6052 | 0.970263 | ||||||||
\(452\) | 19.3434 | 0.909837 | ||||||||
\(453\) | − | 1.00554i | − | 0.0472443i | ||||||
\(454\) | 33.2251 | 1.55933 | ||||||||
\(455\) | −0.590957 | + | 4.09233i | −0.0277045 | + | 0.191851i | ||||
\(456\) | 1.99806 | 0.0935680 | ||||||||
\(457\) | 25.7519i | 1.20462i | 0.798262 | + | 0.602311i | \(0.205753\pi\) | ||||
−0.798262 | + | 0.602311i | \(0.794247\pi\) | |||||||
\(458\) | 4.69320 | 0.219299 | ||||||||
\(459\) | −3.96256 | −0.184957 | ||||||||
\(460\) | − | 3.25369i | − | 0.151704i | ||||||
\(461\) | 7.17831i | 0.334327i | 0.985929 | + | 0.167164i | \(0.0534608\pi\) | ||||
−0.985929 | + | 0.167164i | \(0.946539\pi\) | |||||||
\(462\) | 1.63409i | 0.0760245i | ||||||||
\(463\) | − | 2.14846i | − | 0.0998475i | −0.998753 | − | 0.0499238i | \(-0.984102\pi\) | ||
0.998753 | − | 0.0499238i | \(-0.0158978\pi\) | |||||||
\(464\) | −30.0065 | −1.39302 | ||||||||
\(465\) | 0.576505 | 0.0267348 | ||||||||
\(466\) | − | 3.27249i | − | 0.151595i | ||||||
\(467\) | −7.19142 | −0.332779 | −0.166390 | − | 0.986060i | \(-0.553211\pi\) | ||||
−0.166390 | + | 0.986060i | \(0.553211\pi\) | |||||||
\(468\) | −2.34222 | + | 16.2197i | −0.108269 | + | 0.749755i | ||||
\(469\) | −7.52387 | −0.347420 | ||||||||
\(470\) | − | 4.01620i | − | 0.185254i | ||||||
\(471\) | −3.25520 | −0.149992 | ||||||||
\(472\) | 8.30872 | 0.382440 | ||||||||
\(473\) | 9.86753i | 0.453709i | ||||||||
\(474\) | − | 5.20079i | − | 0.238880i | ||||||
\(475\) | 14.3652i | 0.659120i | ||||||||
\(476\) | 2.10206i | 0.0963477i | ||||||||
\(477\) | −1.21350 | −0.0555622 | ||||||||
\(478\) | −2.66377 | −0.121838 | ||||||||
\(479\) | − | 25.8734i | − | 1.18219i | −0.806603 | − | 0.591094i | \(-0.798696\pi\) | ||
0.806603 | − | 0.591094i | \(-0.201304\pi\) | |||||||
\(480\) | 4.15781 | 0.189777 | ||||||||
\(481\) | 16.7392 | + | 2.41724i | 0.763242 | + | 0.110217i | ||||
\(482\) | −0.658734 | −0.0300045 | ||||||||
\(483\) | 0.251993i | 0.0114661i | ||||||||
\(484\) | 8.38367 | 0.381076 | ||||||||
\(485\) | 33.3905 | 1.51618 | ||||||||
\(486\) | − | 15.9410i | − | 0.723096i | ||||||
\(487\) | 1.91760i | 0.0868946i | 0.999056 | + | 0.0434473i | \(0.0138341\pi\) | ||||
−0.999056 | + | 0.0434473i | \(0.986166\pi\) | |||||||
\(488\) | − | 10.3534i | − | 0.468674i | ||||||
\(489\) | − | 3.02857i | − | 0.136957i | ||||||
\(490\) | 21.8410 | 0.986675 | ||||||||
\(491\) | 5.36083 | 0.241931 | 0.120965 | − | 0.992657i | \(-0.461401\pi\) | ||||
0.120965 | + | 0.992657i | \(0.461401\pi\) | |||||||
\(492\) | − | 2.62731i | − | 0.118448i | ||||||
\(493\) | −13.1658 | −0.592956 | ||||||||
\(494\) | 7.32527 | − | 50.7269i | 0.329579 | − | 2.28231i | ||||
\(495\) | −20.5505 | −0.923676 | ||||||||
\(496\) | 4.67350i | 0.209846i | ||||||||
\(497\) | 4.26264 | 0.191206 | ||||||||
\(498\) | 8.15673 | 0.365512 | ||||||||
\(499\) | 22.3837i | 1.00203i | 0.865438 | + | 0.501016i | \(0.167040\pi\) | ||||
−0.865438 | + | 0.501016i | \(0.832960\pi\) | |||||||
\(500\) | 19.0873i | 0.853612i | ||||||||
\(501\) | 5.98271i | 0.267288i | ||||||||
\(502\) | − | 14.2578i | − | 0.636357i | ||||||
\(503\) | 1.51578 | 0.0675852 | 0.0337926 | − | 0.999429i | \(-0.489241\pi\) | ||||
0.0337926 | + | 0.999429i | \(0.489241\pi\) | |||||||
\(504\) | 1.52835 | 0.0680783 | ||||||||
\(505\) | 22.8513i | 1.01687i | ||||||||
\(506\) | 8.99654 | 0.399945 | ||||||||
\(507\) | 4.08918 | + | 1.20616i | 0.181607 | + | 0.0535672i | ||||
\(508\) | −32.8129 | −1.45584 | ||||||||
\(509\) | − | 15.8794i | − | 0.703842i | −0.936030 | − | 0.351921i | \(-0.885529\pi\) | ||
0.936030 | − | 0.351921i | \(-0.114471\pi\) | |||||||
\(510\) | 2.23406 | 0.0989258 | ||||||||
\(511\) | −0.110909 | −0.00490634 | ||||||||
\(512\) | 26.1349i | 1.15501i | ||||||||
\(513\) | 14.5356i | 0.641762i | ||||||||
\(514\) | − | 42.3139i | − | 1.86639i | ||||||
\(515\) | 13.3423i | 0.587930i | ||||||||
\(516\) | 1.25817 | 0.0553881 | ||||||||
\(517\) | 4.88611 | 0.214891 | ||||||||
\(518\) | 5.78295i | 0.254088i | ||||||||
\(519\) | 0.0189500 | 0.000831815 | ||||||||
\(520\) | −0.733741 | + | 5.08110i | −0.0321767 | + | 0.222821i | ||||
\(521\) | −15.5542 | −0.681440 | −0.340720 | − | 0.940165i | \(-0.610671\pi\) | ||||
−0.340720 | + | 0.940165i | \(0.610671\pi\) | |||||||
\(522\) | − | 35.0961i | − | 1.53611i | ||||||
\(523\) | −33.1558 | −1.44980 | −0.724901 | − | 0.688853i | \(-0.758115\pi\) | ||||
−0.724901 | + | 0.688853i | \(0.758115\pi\) | |||||||
\(524\) | −13.5920 | −0.593771 | ||||||||
\(525\) | − | 0.408579i | − | 0.0178319i | ||||||
\(526\) | 36.8525i | 1.60685i | ||||||||
\(527\) | 2.05056i | 0.0893238i | ||||||||
\(528\) | 6.19459i | 0.269585i | ||||||||
\(529\) | −21.6126 | −0.939680 | ||||||||
\(530\) | 1.39376 | 0.0605410 | ||||||||
\(531\) | 29.6707i | 1.28760i | ||||||||
\(532\) | 7.71084 | 0.334307 | ||||||||
\(533\) | 18.1931 | + | 2.62719i | 0.788030 | + | 0.113796i | ||||
\(534\) | −4.72142 | −0.204316 | ||||||||
\(535\) | − | 25.6355i | − | 1.10832i | ||||||
\(536\) | −9.34174 | −0.403502 | ||||||||
\(537\) | −4.09312 | −0.176631 | ||||||||
\(538\) | 42.4161i | 1.82869i | ||||||||
\(539\) | 26.5717i | 1.14453i | ||||||||
\(540\) | 5.33808i | 0.229715i | ||||||||
\(541\) | − | 38.6097i | − | 1.65996i | −0.557792 | − | 0.829981i | \(-0.688351\pi\) | ||
0.557792 | − | 0.829981i | \(-0.311649\pi\) | |||||||
\(542\) | −35.9766 | −1.54533 | ||||||||
\(543\) | −3.26197 | −0.139984 | ||||||||
\(544\) | 14.7889i | 0.634067i | ||||||||
\(545\) | 7.94143 | 0.340173 | ||||||||
\(546\) | −0.208347 | + | 1.44279i | −0.00891645 | + | 0.0617457i | ||||
\(547\) | −9.56630 | −0.409026 | −0.204513 | − | 0.978864i | \(-0.565561\pi\) | ||||
−0.204513 | + | 0.978864i | \(0.565561\pi\) | |||||||
\(548\) | − | 23.1192i | − | 0.987602i | ||||||
\(549\) | 36.9721 | 1.57793 | ||||||||
\(550\) | −14.5869 | −0.621988 | ||||||||
\(551\) | 48.2951i | 2.05744i | ||||||||
\(552\) | 0.312878i | 0.0133170i | ||||||||
\(553\) | 5.47430i | 0.232791i | ||||||||
\(554\) | 5.70480i | 0.242374i | ||||||||
\(555\) | 2.70425 | 0.114789 | ||||||||
\(556\) | −24.3735 | −1.03367 | ||||||||
\(557\) | − | 6.45936i | − | 0.273692i | −0.990592 | − | 0.136846i | \(-0.956303\pi\) | ||
0.990592 | − | 0.136846i | \(-0.0436965\pi\) | |||||||
\(558\) | −5.46619 | −0.231402 | ||||||||
\(559\) | −1.25812 | + | 8.71238i | −0.0532128 | + | 0.368494i | ||||
\(560\) | −5.35949 | −0.226480 | ||||||||
\(561\) | 2.71796i | 0.114752i | ||||||||
\(562\) | −54.3927 | −2.29442 | ||||||||
\(563\) | 3.68120 | 0.155144 | 0.0775721 | − | 0.996987i | \(-0.475283\pi\) | ||||
0.0775721 | + | 0.996987i | \(0.475283\pi\) | |||||||
\(564\) | − | 0.623011i | − | 0.0262335i | ||||||
\(565\) | 21.6392i | 0.910368i | ||||||||
\(566\) | − | 2.43416i | − | 0.102315i | ||||||
\(567\) | 5.24731i | 0.220366i | ||||||||
\(568\) | 5.29255 | 0.222071 | ||||||||
\(569\) | −27.0122 | −1.13241 | −0.566205 | − | 0.824265i | \(-0.691589\pi\) | ||||
−0.566205 | + | 0.824265i | \(0.691589\pi\) | |||||||
\(570\) | − | 8.19505i | − | 0.343253i | ||||||
\(571\) | 26.6613 | 1.11574 | 0.557870 | − | 0.829928i | \(-0.311619\pi\) | ||||
0.557870 | + | 0.829928i | \(0.311619\pi\) | |||||||
\(572\) | 22.6641 | + | 3.27283i | 0.947633 | + | 0.136844i | ||||
\(573\) | 8.64242 | 0.361042 | ||||||||
\(574\) | 6.28523i | 0.262340i | ||||||||
\(575\) | −2.24945 | −0.0938087 | ||||||||
\(576\) | −12.3870 | −0.516125 | ||||||||
\(577\) | 6.72496i | 0.279964i | 0.990154 | + | 0.139982i | \(0.0447044\pi\) | ||||
−0.990154 | + | 0.139982i | \(0.955296\pi\) | |||||||
\(578\) | − | 24.1806i | − | 1.00578i | ||||||
\(579\) | 0.309027i | 0.0128427i | ||||||||
\(580\) | 17.7360i | 0.736446i | ||||||||
\(581\) | −8.58568 | −0.356194 | ||||||||
\(582\) | 11.7721 | 0.487971 | ||||||||
\(583\) | 1.69565i | 0.0702265i | ||||||||
\(584\) | −0.137707 | −0.00569834 | ||||||||
\(585\) | −18.1447 | − | 2.62021i | −0.750193 | − | 0.108332i | ||||
\(586\) | −39.8789 | −1.64738 | ||||||||
\(587\) | 28.7519i | 1.18672i | 0.804938 | + | 0.593359i | \(0.202199\pi\) | ||||
−0.804938 | + | 0.593359i | \(0.797801\pi\) | |||||||
\(588\) | 3.38807 | 0.139722 | ||||||||
\(589\) | 7.52193 | 0.309936 | ||||||||
\(590\) | − | 34.0782i | − | 1.40298i | ||||||
\(591\) | − | 3.44678i | − | 0.141782i | ||||||
\(592\) | 21.9223i | 0.901003i | ||||||||
\(593\) | − | 1.97573i | − | 0.0811335i | −0.999177 | − | 0.0405668i | \(-0.987084\pi\) | ||
0.999177 | − | 0.0405668i | \(-0.0129163\pi\) | |||||||
\(594\) | −14.7599 | −0.605608 | ||||||||
\(595\) | −2.35155 | −0.0964040 | ||||||||
\(596\) | 3.08300i | 0.126285i | ||||||||
\(597\) | −3.46508 | −0.141816 | ||||||||
\(598\) | 7.94336 | + | 1.14707i | 0.324828 | + | 0.0469071i | ||||
\(599\) | 7.67011 | 0.313392 | 0.156696 | − | 0.987647i | \(-0.449916\pi\) | ||||
0.156696 | + | 0.987647i | \(0.449916\pi\) | |||||||
\(600\) | − | 0.507297i | − | 0.0207103i | ||||||
\(601\) | −34.0529 | −1.38905 | −0.694523 | − | 0.719470i | \(-0.744385\pi\) | ||||
−0.694523 | + | 0.719470i | \(0.744385\pi\) | |||||||
\(602\) | −3.00990 | −0.122674 | ||||||||
\(603\) | − | 33.3596i | − | 1.35851i | ||||||
\(604\) | − | 4.81811i | − | 0.196046i | ||||||
\(605\) | 9.37870i | 0.381298i | ||||||||
\(606\) | 8.05643i | 0.327270i | ||||||||
\(607\) | 32.5479 | 1.32108 | 0.660540 | − | 0.750791i | \(-0.270328\pi\) | ||||
0.660540 | + | 0.750791i | \(0.270328\pi\) | |||||||
\(608\) | 54.2489 | 2.20008 | ||||||||
\(609\) | − | 1.37362i | − | 0.0556620i | ||||||
\(610\) | −42.4642 | −1.71933 | ||||||||
\(611\) | 4.31411 | + | 0.622983i | 0.174530 | + | 0.0252032i | ||||
\(612\) | −9.32019 | −0.376746 | ||||||||
\(613\) | − | 17.8597i | − | 0.721348i | −0.932692 | − | 0.360674i | \(-0.882547\pi\) | ||
0.932692 | − | 0.360674i | \(-0.117453\pi\) | |||||||
\(614\) | 4.61978 | 0.186439 | ||||||||
\(615\) | 2.93913 | 0.118517 | ||||||||
\(616\) | − | 2.13560i | − | 0.0860458i | ||||||
\(617\) | − | 14.9164i | − | 0.600511i | −0.953859 | − | 0.300255i | \(-0.902928\pi\) | ||
0.953859 | − | 0.300255i | \(-0.0970719\pi\) | |||||||
\(618\) | 4.70394i | 0.189220i | ||||||||
\(619\) | − | 12.1473i | − | 0.488242i | −0.969745 | − | 0.244121i | \(-0.921501\pi\) | ||
0.969745 | − | 0.244121i | \(-0.0784994\pi\) | |||||||
\(620\) | 2.76237 | 0.110939 | ||||||||
\(621\) | −2.27614 | −0.0913383 | ||||||||
\(622\) | 36.8292i | 1.47671i | ||||||||
\(623\) | 4.96971 | 0.199107 | ||||||||
\(624\) | −0.789816 | + | 5.46941i | −0.0316179 | + | 0.218952i | ||||
\(625\) | −11.8039 | −0.472155 | ||||||||
\(626\) | 33.5934i | 1.34266i | ||||||||
\(627\) | 9.97009 | 0.398167 | ||||||||
\(628\) | −15.5975 | −0.622410 | ||||||||
\(629\) | 9.61872i | 0.383523i | ||||||||
\(630\) | − | 6.26853i | − | 0.249744i | ||||||
\(631\) | − | 18.8097i | − | 0.748800i | −0.927267 | − | 0.374400i | \(-0.877849\pi\) | ||
0.927267 | − | 0.374400i | \(-0.122151\pi\) | |||||||
\(632\) | 6.79696i | 0.270369i | ||||||||
\(633\) | 0.0704793 | 0.00280130 | ||||||||
\(634\) | 3.84281 | 0.152617 | ||||||||
\(635\) | − | 36.7073i | − | 1.45669i | ||||||
\(636\) | 0.216206 | 0.00857313 | ||||||||
\(637\) | −3.38792 | + | 23.4611i | −0.134234 | + | 0.929562i | ||||
\(638\) | −49.0404 | −1.94153 | ||||||||
\(639\) | 18.8999i | 0.747667i | ||||||||
\(640\) | −11.1293 | −0.439925 | ||||||||
\(641\) | −2.35909 | −0.0931783 | −0.0465892 | − | 0.998914i | \(-0.514835\pi\) | ||||
−0.0465892 | + | 0.998914i | \(0.514835\pi\) | |||||||
\(642\) | − | 9.03802i | − | 0.356702i | ||||||
\(643\) | − | 17.9916i | − | 0.709518i | −0.934958 | − | 0.354759i | \(-0.884563\pi\) | ||
0.934958 | − | 0.354759i | \(-0.115437\pi\) | |||||||
\(644\) | 1.20744i | 0.0475800i | ||||||||
\(645\) | 1.40750i | 0.0554204i | ||||||||
\(646\) | 29.1488 | 1.14684 | ||||||||
\(647\) | −43.8760 | −1.72494 | −0.862472 | − | 0.506105i | \(-0.831085\pi\) | ||||
−0.862472 | + | 0.506105i | \(0.831085\pi\) | |||||||
\(648\) | 6.51513i | 0.255938i | ||||||||
\(649\) | 41.4595 | 1.62743 | ||||||||
\(650\) | −12.8793 | − | 1.85984i | −0.505167 | − | 0.0729491i | ||||
\(651\) | −0.213941 | −0.00838500 | ||||||||
\(652\) | − | 14.5116i | − | 0.568319i | ||||||
\(653\) | −0.256698 | −0.0100454 | −0.00502269 | − | 0.999987i | \(-0.501599\pi\) | ||||
−0.00502269 | + | 0.999987i | \(0.501599\pi\) | |||||||
\(654\) | 2.79982 | 0.109482 | ||||||||
\(655\) | − | 15.2052i | − | 0.594118i | ||||||
\(656\) | 23.8264i | 0.930265i | ||||||||
\(657\) | − | 0.491754i | − | 0.0191851i | ||||||
\(658\) | 1.49041i | 0.0581023i | ||||||||
\(659\) | 8.42299 | 0.328113 | 0.164056 | − | 0.986451i | \(-0.447542\pi\) | ||||
0.164056 | + | 0.986451i | \(0.447542\pi\) | |||||||
\(660\) | 3.66143 | 0.142521 | ||||||||
\(661\) | − | 11.7394i | − | 0.456609i | −0.973590 | − | 0.228304i | \(-0.926682\pi\) | ||
0.973590 | − | 0.228304i | \(-0.0733181\pi\) | |||||||
\(662\) | 35.0956 | 1.36403 | ||||||||
\(663\) | −0.346542 | + | 2.39978i | −0.0134586 | + | 0.0931996i | ||||
\(664\) | −10.6601 | −0.413692 | ||||||||
\(665\) | 8.62601i | 0.334502i | ||||||||
\(666\) | −25.6407 | −0.993556 | ||||||||
\(667\) | −7.56255 | −0.292823 | ||||||||
\(668\) | 28.6666i | 1.10914i | ||||||||
\(669\) | − | 2.47559i | − | 0.0957120i | ||||||
\(670\) | 38.3151i | 1.48024i | ||||||||
\(671\) | − | 51.6619i | − | 1.99439i | ||||||
\(672\) | −1.54296 | −0.0595211 | ||||||||
\(673\) | −17.2708 | −0.665742 | −0.332871 | − | 0.942972i | \(-0.608017\pi\) | ||||
−0.332871 | + | 0.942972i | \(0.608017\pi\) | |||||||
\(674\) | 62.8410i | 2.42055i | ||||||||
\(675\) | 3.69051 | 0.142048 | ||||||||
\(676\) | 19.5936 | + | 5.77939i | 0.753600 | + | 0.222284i | ||||
\(677\) | 14.1990 | 0.545713 | 0.272857 | − | 0.962055i | \(-0.412032\pi\) | ||||
0.272857 | + | 0.962055i | \(0.412032\pi\) | |||||||
\(678\) | 7.62910i | 0.292994i | ||||||||
\(679\) | −12.3912 | −0.475531 | ||||||||
\(680\) | −2.91971 | −0.111966 | ||||||||
\(681\) | 5.76574i | 0.220943i | ||||||||
\(682\) | 7.63802i | 0.292475i | ||||||||
\(683\) | − | 10.1038i | − | 0.386611i | −0.981139 | − | 0.193305i | \(-0.938079\pi\) | ||
0.981139 | − | 0.193305i | \(-0.0619208\pi\) | |||||||
\(684\) | 34.1886i | 1.30723i | ||||||||
\(685\) | 25.8631 | 0.988179 | ||||||||
\(686\) | −16.7350 | −0.638947 | ||||||||
\(687\) | 0.814437i | 0.0310727i | ||||||||
\(688\) | −11.4101 | −0.435006 | ||||||||
\(689\) | −0.216196 | + | 1.49714i | −0.00823643 | + | 0.0570366i | ||||
\(690\) | 1.28327 | 0.0488531 | ||||||||
\(691\) | − | 9.41120i | − | 0.358019i | −0.983847 | − | 0.179009i | \(-0.942711\pi\) | ||
0.983847 | − | 0.179009i | \(-0.0572893\pi\) | |||||||
\(692\) | 0.0908006 | 0.00345172 | ||||||||
\(693\) | 7.62629 | 0.289699 | ||||||||
\(694\) | 39.6279i | 1.50426i | ||||||||
\(695\) | − | 27.2663i | − | 1.03427i | ||||||
\(696\) | − | 1.70551i | − | 0.0646471i | ||||||
\(697\) | 10.4542i | 0.395979i | ||||||||
\(698\) | 57.6082 | 2.18050 | ||||||||
\(699\) | 0.567894 | 0.0214797 | ||||||||
\(700\) | − | 1.95774i | − | 0.0739955i | ||||||
\(701\) | −22.3912 | −0.845703 | −0.422852 | − | 0.906199i | \(-0.638971\pi\) | ||||
−0.422852 | + | 0.906199i | \(0.638971\pi\) | |||||||
\(702\) | −13.0321 | − | 1.88191i | −0.491863 | − | 0.0710280i | ||||
\(703\) | 35.2837 | 1.33075 | ||||||||
\(704\) | 17.3086i | 0.652342i | ||||||||
\(705\) | 0.696954 | 0.0262488 | ||||||||
\(706\) | −19.9987 | −0.752662 | ||||||||
\(707\) | − | 8.48011i | − | 0.318927i | ||||||
\(708\) | − | 5.28636i | − | 0.198673i | ||||||
\(709\) | − | 20.3716i | − | 0.765072i | −0.923941 | − | 0.382536i | \(-0.875051\pi\) | ||
0.923941 | − | 0.382536i | \(-0.124949\pi\) | |||||||
\(710\) | − | 21.7074i | − | 0.814663i | ||||||
\(711\) | −24.2721 | −0.910276 | ||||||||
\(712\) | 6.17047 | 0.231248 | ||||||||
\(713\) | 1.17786i | 0.0441113i | ||||||||
\(714\) | −0.829059 | −0.0310268 | ||||||||
\(715\) | −3.66127 | + | 25.3540i | −0.136924 | + | 0.948187i | ||||
\(716\) | −19.6125 | −0.732953 | ||||||||
\(717\) | − | 0.462259i | − | 0.0172634i | ||||||
\(718\) | 41.2342 | 1.53885 | ||||||||
\(719\) | 14.9478 | 0.557459 | 0.278730 | − | 0.960370i | \(-0.410087\pi\) | ||||
0.278730 | + | 0.960370i | \(0.410087\pi\) | |||||||
\(720\) | − | 23.7631i | − | 0.885599i | ||||||
\(721\) | − | 4.95131i | − | 0.184396i | ||||||
\(722\) | − | 71.0181i | − | 2.64302i | ||||||
\(723\) | − | 0.114314i | − | 0.00425138i | ||||||
\(724\) | −15.6300 | −0.580883 | ||||||||
\(725\) | 12.2618 | 0.455393 | ||||||||
\(726\) | 3.30655i | 0.122717i | ||||||||
\(727\) | 27.0908 | 1.00474 | 0.502372 | − | 0.864652i | \(-0.332461\pi\) | ||||
0.502372 | + | 0.864652i | \(0.332461\pi\) | |||||||
\(728\) | 0.272291 | − | 1.88559i | 0.0100918 | − | 0.0698848i | ||||
\(729\) | −21.3645 | −0.791277 | ||||||||
\(730\) | 0.564802i | 0.0209043i | ||||||||
\(731\) | −5.00633 | −0.185166 | ||||||||
\(732\) | −6.58724 | −0.243471 | ||||||||
\(733\) | − | 16.9857i | − | 0.627382i | −0.949525 | − | 0.313691i | \(-0.898434\pi\) | ||
0.949525 | − | 0.313691i | \(-0.101566\pi\) | |||||||
\(734\) | − | 38.0894i | − | 1.40591i | ||||||
\(735\) | 3.79019i | 0.139803i | ||||||||
\(736\) | 8.49487i | 0.313125i | ||||||||
\(737\) | −46.6141 | −1.71705 | ||||||||
\(738\) | −27.8677 | −1.02582 | ||||||||
\(739\) | − | 4.03178i | − | 0.148311i | −0.997247 | − | 0.0741557i | \(-0.976374\pi\) | ||
0.997247 | − | 0.0741557i | \(-0.0236262\pi\) | |||||||
\(740\) | 12.9576 | 0.476332 | ||||||||
\(741\) | 8.80293 | + | 1.27120i | 0.323384 | + | 0.0466985i | ||||
\(742\) | −0.517224 | −0.0189879 | ||||||||
\(743\) | 5.56680i | 0.204226i | 0.994773 | + | 0.102113i | \(0.0325603\pi\) | ||||
−0.994773 | + | 0.102113i | \(0.967440\pi\) | |||||||
\(744\) | −0.265632 | −0.00973854 | ||||||||
\(745\) | −3.44892 | −0.126359 | ||||||||
\(746\) | − | 54.9294i | − | 2.01111i | ||||||
\(747\) | − | 38.0675i | − | 1.39282i | ||||||
\(748\) | 13.0233i | 0.476179i | ||||||||
\(749\) | 9.51332i | 0.347609i | ||||||||
\(750\) | −7.52811 | −0.274888 | ||||||||
\(751\) | −2.33856 | −0.0853354 | −0.0426677 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426677 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(752\) | 5.64994i | 0.206032i | ||||||||
\(753\) | 2.47424 | 0.0901662 | ||||||||
\(754\) | −43.2995 | − | 6.25270i | −1.57687 | − | 0.227710i | ||||
\(755\) | 5.38996 | 0.196161 | ||||||||
\(756\) | − | 1.98096i | − | 0.0720469i | ||||||
\(757\) | 8.27850 | 0.300887 | 0.150444 | − | 0.988619i | \(-0.451930\pi\) | ||||
0.150444 | + | 0.988619i | \(0.451930\pi\) | |||||||
\(758\) | −23.6198 | −0.857909 | ||||||||
\(759\) | 1.56122i | 0.0566687i | ||||||||
\(760\) | 10.7102i | 0.388499i | ||||||||
\(761\) | − | 26.7917i | − | 0.971199i | −0.874181 | − | 0.485600i | \(-0.838601\pi\) | ||
0.874181 | − | 0.485600i | \(-0.161399\pi\) | |||||||
\(762\) | − | 12.9415i | − | 0.468822i | ||||||
\(763\) | −2.94706 | −0.106691 | ||||||||
\(764\) | 41.4108 | 1.49819 | ||||||||
\(765\) | − | 10.4264i | − | 0.376966i | ||||||
\(766\) | −10.7554 | −0.388610 | ||||||||
\(767\) | 36.6060 | + | 5.28612i | 1.32177 | + | 0.190871i | ||||
\(768\) | −6.73266 | −0.242944 | ||||||||
\(769\) | − | 43.5055i | − | 1.56885i | −0.620224 | − | 0.784425i | \(-0.712958\pi\) | ||
0.620224 | − | 0.784425i | \(-0.287042\pi\) | |||||||
\(770\) | −8.75915 | −0.315658 | ||||||||
\(771\) | 7.34298 | 0.264451 | ||||||||
\(772\) | 1.48073i | 0.0532926i | ||||||||
\(773\) | 34.3969i | 1.23717i | 0.785718 | + | 0.618585i | \(0.212294\pi\) | ||||
−0.785718 | + | 0.618585i | \(0.787706\pi\) | |||||||
\(774\) | − | 13.3454i | − | 0.479690i | ||||||
\(775\) | − | 1.90978i | − | 0.0686012i | ||||||
\(776\) | −15.3851 | −0.552293 | ||||||||
\(777\) | −1.00355 | −0.0360021 | ||||||||
\(778\) | 44.4363i | 1.59312i | ||||||||
\(779\) | 38.3482 | 1.37397 | ||||||||
\(780\) | 3.23281 | + | 0.466836i | 0.115753 | + | 0.0167154i | ||||
\(781\) | 26.4092 | 0.944994 | ||||||||
\(782\) | 4.56443i | 0.163224i | ||||||||
\(783\) | 12.4073 | 0.443401 | ||||||||
\(784\) | −30.7256 | −1.09734 | ||||||||
\(785\) | − | 17.4488i | − | 0.622773i | ||||||
\(786\) | − | 5.36075i | − | 0.191212i | ||||||
\(787\) | 21.6617i | 0.772155i | 0.922466 | + | 0.386077i | \(0.126170\pi\) | ||||
−0.922466 | + | 0.386077i | \(0.873830\pi\) | |||||||
\(788\) | − | 16.5155i | − | 0.588341i | ||||||
\(789\) | −6.39523 | −0.227676 | ||||||||
\(790\) | 27.8777 | 0.991843 | ||||||||
\(791\) | − | 8.03031i | − | 0.285525i | ||||||
\(792\) | 9.46890 | 0.336463 | ||||||||
\(793\) | 6.58694 | − | 45.6141i | 0.233909 | − | 1.61980i | ||||
\(794\) | 15.7396 | 0.558579 | ||||||||
\(795\) | 0.241867i | 0.00857813i | ||||||||
\(796\) | −16.6032 | −0.588484 | ||||||||
\(797\) | 52.2693 | 1.85147 | 0.925736 | − | 0.378170i | \(-0.123447\pi\) | ||||
0.925736 | + | 0.378170i | \(0.123447\pi\) | |||||||
\(798\) | 3.04118i | 0.107657i | ||||||||
\(799\) | 2.47898i | 0.0877002i | ||||||||
\(800\) | − | 13.7735i | − | 0.486967i | ||||||
\(801\) | 22.0349i | 0.778565i | ||||||||
\(802\) | 61.6278 | 2.17615 | ||||||||
\(803\) | −0.687138 | −0.0242486 | ||||||||
\(804\) | 5.94360i | 0.209615i | ||||||||
\(805\) | −1.35075 | −0.0476078 | ||||||||
\(806\) | −0.973855 | + | 6.74387i | −0.0343026 | + | 0.237543i | ||||
\(807\) | −7.36071 | −0.259109 | ||||||||
\(808\) | − | 10.5290i | − | 0.370410i | ||||||
\(809\) | 29.6179 | 1.04131 | 0.520654 | − | 0.853768i | \(-0.325688\pi\) | ||||
0.520654 | + | 0.853768i | \(0.325688\pi\) | |||||||
\(810\) | 26.7218 | 0.938907 | ||||||||
\(811\) | − | 0.0929122i | − | 0.00326259i | −0.999999 | − | 0.00163129i | \(-0.999481\pi\) | ||
0.999999 | − | 0.00163129i | \(-0.000519257\pi\) | |||||||
\(812\) | − | 6.58182i | − | 0.230976i | ||||||
\(813\) | − | 6.24323i | − | 0.218960i | ||||||
\(814\) | 35.8282i | 1.25578i | ||||||||
\(815\) | 16.2339 | 0.568650 | ||||||||
\(816\) | −3.14285 | −0.110022 | ||||||||
\(817\) | 18.3644i | 0.642488i | ||||||||
\(818\) | 42.1336 | 1.47317 | ||||||||
\(819\) | 6.73351 | + | 0.972359i | 0.235288 | + | 0.0339770i | ||||
\(820\) | 14.0831 | 0.491802 | ||||||||
\(821\) | − | 22.6436i | − | 0.790267i | −0.918624 | − | 0.395133i | \(-0.870698\pi\) | ||
0.918624 | − | 0.395133i | \(-0.129302\pi\) | |||||||
\(822\) | 9.11828 | 0.318037 | ||||||||
\(823\) | −43.4443 | −1.51437 | −0.757187 | − | 0.653199i | \(-0.773427\pi\) | ||||
−0.757187 | + | 0.653199i | \(0.773427\pi\) | |||||||
\(824\) | − | 6.14762i | − | 0.214162i | ||||||
\(825\) | − | 2.53135i | − | 0.0881302i | ||||||
\(826\) | 12.6464i | 0.440025i | ||||||||
\(827\) | − | 32.1031i | − | 1.11633i | −0.829728 | − | 0.558167i | \(-0.811505\pi\) | ||
0.829728 | − | 0.558167i | \(-0.188495\pi\) | |||||||
\(828\) | −5.35361 | −0.186051 | ||||||||
\(829\) | 48.9477 | 1.70002 | 0.850011 | − | 0.526765i | \(-0.176595\pi\) | ||||
0.850011 | + | 0.526765i | \(0.176595\pi\) | |||||||
\(830\) | 43.7223i | 1.51762i | ||||||||
\(831\) | −0.989986 | −0.0343422 | ||||||||
\(832\) | −2.20686 | + | 15.2824i | −0.0765092 | + | 0.529820i | ||||
\(833\) | −13.4813 | −0.467098 | ||||||||
\(834\) | − | 9.61300i | − | 0.332871i | ||||||
\(835\) | −32.0690 | −1.10979 | ||||||||
\(836\) | 47.7724 | 1.65224 | ||||||||
\(837\) | − | 1.93243i | − | 0.0667946i | ||||||
\(838\) | − | 58.4699i | − | 2.01981i | ||||||
\(839\) | 26.2951i | 0.907808i | 0.891051 | + | 0.453904i | \(0.149969\pi\) | ||||
−0.891051 | + | 0.453904i | \(0.850031\pi\) | |||||||
\(840\) | − | 0.304622i | − | 0.0105105i | ||||||
\(841\) | 12.2237 | 0.421507 | ||||||||
\(842\) | −9.64564 | −0.332411 | ||||||||
\(843\) | − | 9.43908i | − | 0.325099i | ||||||
\(844\) | 0.337707 | 0.0116244 | ||||||||
\(845\) | −6.46532 | + | 21.9191i | −0.222414 | + | 0.754040i | ||||
\(846\) | −6.60824 | −0.227196 | ||||||||
\(847\) | − | 3.48043i | − | 0.119589i | ||||||
\(848\) | −1.96072 | −0.0673314 | ||||||||
\(849\) | 0.422414 | 0.0144972 | ||||||||
\(850\) | − | 7.40072i | − | 0.253843i | ||||||
\(851\) | 5.52509i | 0.189398i | ||||||||
\(852\) | − | 3.36734i | − | 0.115363i | ||||||
\(853\) | − | 40.0545i | − | 1.37144i | −0.727865 | − | 0.685720i | \(-0.759487\pi\) | ||
0.727865 | − | 0.685720i | \(-0.240513\pi\) | |||||||
\(854\) | 15.7585 | 0.539243 | ||||||||
\(855\) | −38.2463 | −1.30800 | ||||||||
\(856\) | 11.8119i | 0.403721i | ||||||||
\(857\) | −42.5354 | −1.45298 | −0.726491 | − | 0.687176i | \(-0.758850\pi\) | ||||
−0.726491 | + | 0.687176i | \(0.758850\pi\) | |||||||
\(858\) | −1.29082 | + | 8.93879i | −0.0440677 | + | 0.305165i | ||||
\(859\) | −26.3544 | −0.899201 | −0.449600 | − | 0.893230i | \(-0.648434\pi\) | ||||
−0.449600 | + | 0.893230i | \(0.648434\pi\) | |||||||
\(860\) | 6.74416i | 0.229974i | ||||||||
\(861\) | −1.09071 | −0.0371714 | ||||||||
\(862\) | −46.6658 | −1.58944 | ||||||||
\(863\) | − | 15.7514i | − | 0.536183i | −0.963394 | − | 0.268091i | \(-0.913607\pi\) | ||
0.963394 | − | 0.268091i | \(-0.0863929\pi\) | |||||||
\(864\) | − | 13.9369i | − | 0.474142i | ||||||
\(865\) | 0.101577i | 0.00345374i | ||||||||
\(866\) | − | 8.68560i | − | 0.295149i | ||||||
\(867\) | 4.19619 | 0.142510 | ||||||||
\(868\) | −1.02511 | −0.0347946 | ||||||||
\(869\) | 33.9160i | 1.15052i | ||||||||
\(870\) | −6.99513 | −0.237157 | ||||||||
\(871\) | −41.1572 | − | 5.94334i | −1.39456 | − | 0.201382i | ||||
\(872\) | −3.65911 | −0.123913 | ||||||||
\(873\) | − | 54.9406i | − | 1.85946i | ||||||
\(874\) | 16.7434 | 0.566353 | ||||||||
\(875\) | 7.92401 | 0.267880 | ||||||||
\(876\) | 0.0876146i | 0.00296022i | ||||||||
\(877\) | 33.1442i | 1.11920i | 0.828762 | + | 0.559601i | \(0.189045\pi\) | ||||
−0.828762 | + | 0.559601i | \(0.810955\pi\) | |||||||
\(878\) | − | 42.2891i | − | 1.42719i | ||||||
\(879\) | − | 6.92041i | − | 0.233420i | ||||||
\(880\) | −33.2047 | −1.11933 | ||||||||
\(881\) | 2.63745 | 0.0888580 | 0.0444290 | − | 0.999013i | \(-0.485853\pi\) | ||||
0.0444290 | + | 0.999013i | \(0.485853\pi\) | |||||||
\(882\) | − | 35.9371i | − | 1.21006i | ||||||
\(883\) | −22.2303 | −0.748109 | −0.374055 | − | 0.927407i | \(-0.622033\pi\) | ||||
−0.374055 | + | 0.927407i | \(0.622033\pi\) | |||||||
\(884\) | −1.66048 | + | 11.4987i | −0.0558481 | + | 0.386743i | ||||
\(885\) | 5.91378 | 0.198789 | ||||||||
\(886\) | 51.1776i | 1.71934i | ||||||||
\(887\) | −11.9865 | −0.402466 | −0.201233 | − | 0.979543i | \(-0.564495\pi\) | ||||
−0.201233 | + | 0.979543i | \(0.564495\pi\) | |||||||
\(888\) | −1.24602 | −0.0418137 | ||||||||
\(889\) | 13.6221i | 0.456870i | ||||||||
\(890\) | − | 25.3081i | − | 0.848330i | ||||||
\(891\) | 32.5097i | 1.08911i | ||||||||
\(892\) | − | 11.8620i | − | 0.397169i | ||||||
\(893\) | 9.09349 | 0.304302 | ||||||||
\(894\) | −1.21595 | −0.0406674 | ||||||||
\(895\) | − | 21.9402i | − | 0.733381i | ||||||
\(896\) | 4.13009 | 0.137977 | ||||||||
\(897\) | −0.199057 | + | 1.37846i | −0.00664633 | + | 0.0460253i | ||||
\(898\) | 63.1413 | 2.10705 | ||||||||
\(899\) | − | 6.42057i | − | 0.214138i | ||||||
\(900\) | 8.68029 | 0.289343 | ||||||||
\(901\) | −0.860292 | −0.0286605 | ||||||||
\(902\) | 38.9401i | 1.29656i | ||||||||
\(903\) | − | 0.522324i | − | 0.0173819i | ||||||
\(904\) | − | 9.97054i | − | 0.331615i | ||||||
\(905\) | − | 17.4850i | − | 0.581222i | ||||||
\(906\) | 1.90028 | 0.0631326 | ||||||||
\(907\) | 29.8644 | 0.991630 | 0.495815 | − | 0.868428i | \(-0.334869\pi\) | ||||
0.495815 | + | 0.868428i | \(0.334869\pi\) | |||||||
\(908\) | 27.6270i | 0.916833i | ||||||||
\(909\) | 37.5994 | 1.24709 | ||||||||
\(910\) | −7.73375 | − | 1.11680i | −0.256371 | − | 0.0370215i | ||||
\(911\) | 46.2206 | 1.53136 | 0.765678 | − | 0.643224i | \(-0.222404\pi\) | ||||
0.765678 | + | 0.643224i | \(0.222404\pi\) | |||||||
\(912\) | 11.5287i | 0.381753i | ||||||||
\(913\) | −53.1925 | −1.76042 | ||||||||
\(914\) | −48.6663 | −1.60974 | ||||||||
\(915\) | − | 7.36906i | − | 0.243613i | ||||||
\(916\) | 3.90244i | 0.128940i | ||||||||
\(917\) | 5.64266i | 0.186337i | ||||||||
\(918\) | − | 7.48851i | − | 0.247158i | ||||||
\(919\) | −20.0899 | −0.662705 | −0.331352 | − | 0.943507i | \(-0.607505\pi\) | ||||
−0.331352 | + | 0.943507i | \(0.607505\pi\) | |||||||
\(920\) | −1.67711 | −0.0552928 | ||||||||
\(921\) | 0.801698i | 0.0264168i | ||||||||
\(922\) | −13.5657 | −0.446762 | ||||||||
\(923\) | 23.3176 | + | 3.36719i | 0.767507 | + | 0.110833i | ||||
\(924\) | −1.35876 | −0.0446998 | ||||||||
\(925\) | − | 8.95832i | − | 0.294548i | ||||||
\(926\) | 4.06020 | 0.133426 | ||||||||
\(927\) | 21.9533 | 0.721042 | ||||||||
\(928\) | − | 46.3058i | − | 1.52006i | ||||||
\(929\) | − | 25.3137i | − | 0.830516i | −0.909704 | − | 0.415258i | \(-0.863691\pi\) | ||
0.909704 | − | 0.415258i | \(-0.136309\pi\) | |||||||
\(930\) | 1.08949i | 0.0357257i | ||||||||
\(931\) | 49.4524i | 1.62074i | ||||||||
\(932\) | 2.72111 | 0.0891328 | ||||||||
\(933\) | −6.39117 | −0.209238 | ||||||||
\(934\) | − | 13.5904i | − | 0.444693i | ||||||
\(935\) | −14.5690 | −0.476457 | ||||||||
\(936\) | 8.36042 | + | 1.20729i | 0.273269 | + | 0.0394617i | ||||
\(937\) | 33.0728 | 1.08044 | 0.540221 | − | 0.841523i | \(-0.318341\pi\) | ||||
0.540221 | + | 0.841523i | \(0.318341\pi\) | |||||||
\(938\) | − | 14.2187i | − | 0.464257i | ||||||
\(939\) | −5.82965 | −0.190243 | ||||||||
\(940\) | 3.33951 | 0.108923 | ||||||||
\(941\) | 33.7982i | 1.10179i | 0.834574 | + | 0.550895i | \(0.185714\pi\) | ||||
−0.834574 | + | 0.550895i | \(0.814286\pi\) | |||||||
\(942\) | − | 6.15173i | − | 0.200434i | ||||||
\(943\) | 6.00497i | 0.195549i | ||||||||
\(944\) | 47.9407i | 1.56034i | ||||||||
\(945\) | 2.21608 | 0.0720890 | ||||||||
\(946\) | −18.6478 | −0.606292 | ||||||||
\(947\) | 30.3168i | 0.985163i | 0.870266 | + | 0.492581i | \(0.163947\pi\) | ||||
−0.870266 | + | 0.492581i | \(0.836053\pi\) | |||||||
\(948\) | 4.32451 | 0.140454 | ||||||||
\(949\) | −0.606698 | − | 0.0876107i | −0.0196942 | − | 0.00284397i | ||||
\(950\) | −27.1475 | −0.880783 | ||||||||
\(951\) | 0.666864i | 0.0216246i | ||||||||
\(952\) | 1.08350 | 0.0351166 | ||||||||
\(953\) | 19.2346 | 0.623068 | 0.311534 | − | 0.950235i | \(-0.399157\pi\) | ||||
0.311534 | + | 0.950235i | \(0.399157\pi\) | |||||||
\(954\) | − | 2.29329i | − | 0.0742479i | ||||||
\(955\) | 46.3258i | 1.49907i | ||||||||
\(956\) | − | 2.21495i | − | 0.0716365i | ||||||
\(957\) | − | 8.51027i | − | 0.275098i | ||||||
\(958\) | 48.8960 | 1.57976 | ||||||||
\(959\) | −9.59780 | −0.309929 | ||||||||
\(960\) | 2.46890i | 0.0796834i | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −4.56813 | + | 31.6340i | −0.147283 | + | 1.01992i | ||||
\(963\) | −42.1805 | −1.35925 | ||||||||
\(964\) | − | 0.547744i | − | 0.0176416i | ||||||
\(965\) | −1.65647 | −0.0533237 | ||||||||
\(966\) | −0.476220 | −0.0153221 | ||||||||
\(967\) | 42.6693i | 1.37215i | 0.727530 | + | 0.686076i | \(0.240668\pi\) | ||||
−0.727530 | + | 0.686076i | \(0.759332\pi\) | |||||||
\(968\) | − | 4.32135i | − | 0.138894i | ||||||
\(969\) | 5.05836i | 0.162498i | ||||||||
\(970\) | 63.1019i | 2.02608i | ||||||||
\(971\) | 50.8279 | 1.63114 | 0.815572 | − | 0.578656i | \(-0.196423\pi\) | ||||
0.815572 | + | 0.578656i | \(0.196423\pi\) | |||||||
\(972\) | 13.2551 | 0.425156 | ||||||||
\(973\) | 10.1185i | 0.324385i | ||||||||
\(974\) | −3.62390 | −0.116117 | ||||||||
\(975\) | 0.322749 | − | 2.23501i | 0.0103363 | − | 0.0715777i | ||||
\(976\) | 59.7381 | 1.91217 | ||||||||
\(977\) | − | 12.8260i | − | 0.410340i | −0.978726 | − | 0.205170i | \(-0.934225\pi\) | ||
0.978726 | − | 0.205170i | \(-0.0657748\pi\) | |||||||
\(978\) | 5.72343 | 0.183015 | ||||||||
\(979\) | 30.7898 | 0.984047 | ||||||||
\(980\) | 18.1610i | 0.580132i | ||||||||
\(981\) | − | 13.0668i | − | 0.417191i | ||||||
\(982\) | 10.1310i | 0.323293i | ||||||||
\(983\) | − | 33.5024i | − | 1.06856i | −0.845307 | − | 0.534280i | \(-0.820583\pi\) | ||
0.845307 | − | 0.534280i | \(-0.179417\pi\) | |||||||
\(984\) | −1.35424 | −0.0431717 | ||||||||
\(985\) | 18.4757 | 0.588685 | ||||||||
\(986\) | − | 24.8809i | − | 0.792368i | ||||||
\(987\) | −0.258640 | −0.00823259 | ||||||||
\(988\) | 42.1799 | + | 6.09103i | 1.34192 | + | 0.193782i | ||||
\(989\) | −2.87569 | −0.0914415 | ||||||||
\(990\) | − | 38.8366i | − | 1.23431i | ||||||
\(991\) | 42.9474 | 1.36427 | 0.682134 | − | 0.731227i | \(-0.261052\pi\) | ||||
0.682134 | + | 0.731227i | \(0.261052\pi\) | |||||||
\(992\) | −7.21210 | −0.228984 | ||||||||
\(993\) | 6.09035i | 0.193271i | ||||||||
\(994\) | 8.05560i | 0.255508i | ||||||||
\(995\) | − | 18.5738i | − | 0.588828i | ||||||
\(996\) | 6.78240i | 0.214909i | ||||||||
\(997\) | 38.7880 | 1.22843 | 0.614214 | − | 0.789139i | \(-0.289473\pi\) | ||||
0.614214 | + | 0.789139i | \(0.289473\pi\) | |||||||
\(998\) | −42.3010 | −1.33902 | ||||||||
\(999\) | − | 9.06459i | − | 0.286791i |
(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 | 403.2.c.b.311.26 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.l.1.13 | 16 | |||
13.8 | odd | 4 | 5239.2.a.k.1.4 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.7 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.7 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.26 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.4 | 16 | 13.8 | odd | 4 | |||
5239.2.a.l.1.13 | 16 | 13.5 | odd | 4 |