Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1001,2,Mod(144,1001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1001, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1001.144");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1001 = 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1001.i (of order \(3\), 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: | \(7.99302524233\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Relative dimension: | \(25\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 144.17 | ||
Character | \(\chi\) | \(=\) | 1001.144 |
Dual form | 1001.2.i.d.716.17 |
$q$-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 \(\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(430\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.434546 | + | 0.752655i | 0.307270 | + | 0.532208i | 0.977764 | − | 0.209707i | \(-0.0672511\pi\) |
−0.670494 | + | 0.741915i | \(0.733918\pi\) | |||||||
\(3\) | 1.23247 | − | 2.13471i | 0.711570 | − | 1.23247i | −0.252698 | − | 0.967545i | \(-0.581318\pi\) |
0.964268 | − | 0.264930i | \(-0.0853487\pi\) | |||||||
\(4\) | 0.622340 | − | 1.07792i | 0.311170 | − | 0.538962i | ||||
\(5\) | 2.15910 | + | 3.73967i | 0.965580 | + | 1.67243i | 0.708050 | + | 0.706162i | \(0.249575\pi\) |
0.257530 | + | 0.966270i | \(0.417092\pi\) | |||||||
\(6\) | 2.14227 | 0.874577 | ||||||||
\(7\) | −1.52058 | + | 2.16514i | −0.574725 | + | 0.818346i | ||||
\(8\) | 2.81992 | 0.996994 | ||||||||
\(9\) | −1.53799 | − | 2.66387i | −0.512663 | − | 0.887958i | ||||
\(10\) | −1.87646 | + | 3.25012i | −0.593388 | + | 1.02778i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | −1.53404 | − | 2.65703i | −0.442838 | − | 0.767018i | ||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.29037 | − | 0.203620i | −0.612126 | − | 0.0544197i | ||||
\(15\) | 10.6442 | 2.74831 | ||||||||
\(16\) | −0.0192947 | − | 0.0334194i | −0.00482367 | − | 0.00835485i | ||||
\(17\) | 1.53679 | − | 2.66181i | 0.372727 | − | 0.645583i | −0.617257 | − | 0.786762i | \(-0.711756\pi\) |
0.989984 | + | 0.141179i | \(0.0450894\pi\) | |||||||
\(18\) | 1.33665 | − | 2.31515i | 0.315052 | − | 0.545686i | ||||
\(19\) | 3.03313 | + | 5.25354i | 0.695848 | + | 1.20524i | 0.969894 | + | 0.243528i | \(0.0783048\pi\) |
−0.274045 | + | 0.961717i | \(0.588362\pi\) | |||||||
\(20\) | 5.37478 | 1.20184 | ||||||||
\(21\) | 2.74787 | + | 5.91448i | 0.599634 | + | 1.29064i | ||||
\(22\) | −0.869091 | −0.185291 | ||||||||
\(23\) | −2.33356 | − | 4.04184i | −0.486580 | − | 0.842782i | 0.513301 | − | 0.858209i | \(-0.328423\pi\) |
−0.999881 | + | 0.0154270i | \(0.995089\pi\) | |||||||
\(24\) | 3.47548 | − | 6.01972i | 0.709430 | − | 1.22877i | ||||
\(25\) | −6.82344 | + | 11.8185i | −1.36469 | + | 2.36371i | ||||
\(26\) | −0.434546 | − | 0.752655i | −0.0852214 | − | 0.147608i | ||||
\(27\) | −0.187277 | −0.0360414 | ||||||||
\(28\) | 1.38754 | + | 2.98653i | 0.262221 | + | 0.564400i | ||||
\(29\) | 6.73380 | 1.25043 | 0.625217 | − | 0.780451i | \(-0.285010\pi\) | ||||
0.625217 | + | 0.780451i | \(0.285010\pi\) | |||||||
\(30\) | 4.62537 | + | 8.01138i | 0.844473 | + | 1.46267i | ||||
\(31\) | −1.30801 | + | 2.26554i | −0.234925 | + | 0.406903i | −0.959251 | − | 0.282555i | \(-0.908818\pi\) |
0.724326 | + | 0.689458i | \(0.242151\pi\) | |||||||
\(32\) | 2.83669 | − | 4.91330i | 0.501461 | − | 0.868556i | ||||
\(33\) | 1.23247 | + | 2.13471i | 0.214546 | + | 0.371605i | ||||
\(34\) | 2.67123 | 0.458112 | ||||||||
\(35\) | −11.3800 | − | 1.01171i | −1.92357 | − | 0.171011i | ||||
\(36\) | −3.82861 | −0.638101 | ||||||||
\(37\) | −4.45051 | − | 7.70850i | −0.731659 | − | 1.26727i | −0.956174 | − | 0.292799i | \(-0.905413\pi\) |
0.224515 | − | 0.974471i | \(-0.427920\pi\) | |||||||
\(38\) | −2.63607 | + | 4.56581i | −0.427627 | + | 0.740672i | ||||
\(39\) | −1.23247 | + | 2.13471i | −0.197354 | + | 0.341827i | ||||
\(40\) | 6.08850 | + | 10.5456i | 0.962677 | + | 1.66740i | ||||
\(41\) | 1.63987 | 0.256104 | 0.128052 | − | 0.991767i | \(-0.459128\pi\) | ||||
0.128052 | + | 0.991767i | \(0.459128\pi\) | |||||||
\(42\) | −3.25749 | + | 4.63831i | −0.502641 | + | 0.715707i | ||||
\(43\) | −3.16556 | −0.482743 | −0.241372 | − | 0.970433i | \(-0.577597\pi\) | ||||
−0.241372 | + | 0.970433i | \(0.577597\pi\) | |||||||
\(44\) | 0.622340 | + | 1.07792i | 0.0938213 | + | 0.162503i | ||||
\(45\) | 6.64134 | − | 11.5031i | 0.990033 | − | 1.71479i | ||||
\(46\) | 2.02807 | − | 3.51273i | 0.299023 | − | 0.517923i | ||||
\(47\) | −3.91671 | − | 6.78394i | −0.571310 | − | 0.989539i | −0.996432 | − | 0.0844023i | \(-0.973102\pi\) |
0.425121 | − | 0.905136i | \(-0.360231\pi\) | |||||||
\(48\) | −0.0951209 | −0.0137295 | ||||||||
\(49\) | −2.37567 | − | 6.58454i | −0.339382 | − | 0.940649i | ||||
\(50\) | −11.8604 | −1.67731 | ||||||||
\(51\) | −3.78812 | − | 6.56122i | −0.530443 | − | 0.918754i | ||||
\(52\) | −0.622340 | + | 1.07792i | −0.0863030 | + | 0.149481i | ||||
\(53\) | −0.187459 | + | 0.324688i | −0.0257495 | + | 0.0445994i | −0.878613 | − | 0.477535i | \(-0.841531\pi\) |
0.852864 | + | 0.522134i | \(0.174864\pi\) | |||||||
\(54\) | −0.0813802 | − | 0.140955i | −0.0110744 | − | 0.0191815i | ||||
\(55\) | −4.31820 | −0.582266 | ||||||||
\(56\) | −4.28792 | + | 6.10553i | −0.572997 | + | 0.815886i | ||||
\(57\) | 14.9530 | 1.98058 | ||||||||
\(58\) | 2.92614 | + | 5.06823i | 0.384221 | + | 0.665491i | ||||
\(59\) | −5.12480 | + | 8.87642i | −0.667193 | + | 1.15561i | 0.311493 | + | 0.950248i | \(0.399171\pi\) |
−0.978686 | + | 0.205363i | \(0.934162\pi\) | |||||||
\(60\) | 6.62428 | − | 11.4736i | 0.855191 | − | 1.48123i | ||||
\(61\) | −2.02221 | − | 3.50256i | −0.258917 | − | 0.448457i | 0.707035 | − | 0.707178i | \(-0.250032\pi\) |
−0.965952 | + | 0.258721i | \(0.916699\pi\) | |||||||
\(62\) | −2.27356 | −0.288742 | ||||||||
\(63\) | 8.10630 | + | 0.720672i | 1.02130 | + | 0.0907962i | ||||
\(64\) | 4.85351 | 0.606689 | ||||||||
\(65\) | −2.15910 | − | 3.73967i | −0.267804 | − | 0.463849i | ||||
\(66\) | −1.07113 | + | 1.85526i | −0.131847 | + | 0.228366i | ||||
\(67\) | 5.71278 | − | 9.89483i | 0.697927 | − | 1.20885i | −0.271257 | − | 0.962507i | \(-0.587439\pi\) |
0.969184 | − | 0.246338i | \(-0.0792275\pi\) | |||||||
\(68\) | −1.91282 | − | 3.31310i | −0.231963 | − | 0.401772i | ||||
\(69\) | −11.5042 | −1.38494 | ||||||||
\(70\) | −4.18366 | − | 9.00486i | −0.500043 | − | 1.07629i | ||||
\(71\) | −14.2444 | −1.69050 | −0.845249 | − | 0.534373i | \(-0.820548\pi\) | ||||
−0.845249 | + | 0.534373i | \(0.820548\pi\) | |||||||
\(72\) | −4.33701 | − | 7.51192i | −0.511121 | − | 0.885288i | ||||
\(73\) | 2.72448 | − | 4.71894i | 0.318876 | − | 0.552310i | −0.661377 | − | 0.750053i | \(-0.730028\pi\) |
0.980254 | + | 0.197743i | \(0.0633612\pi\) | |||||||
\(74\) | 3.86790 | − | 6.69939i | 0.449634 | − | 0.778789i | ||||
\(75\) | 16.8194 | + | 29.1321i | 1.94214 | + | 3.36389i | ||||
\(76\) | 7.55056 | 0.866109 | ||||||||
\(77\) | −1.11478 | − | 2.39943i | −0.127041 | − | 0.273441i | ||||
\(78\) | −2.14227 | −0.242564 | ||||||||
\(79\) | 4.84566 | + | 8.39293i | 0.545179 | + | 0.944278i | 0.998596 | + | 0.0529794i | \(0.0168718\pi\) |
−0.453416 | + | 0.891299i | \(0.649795\pi\) | |||||||
\(80\) | 0.0833184 | − | 0.144312i | 0.00931528 | − | 0.0161345i | ||||
\(81\) | 4.38315 | − | 7.59184i | 0.487017 | − | 0.843538i | ||||
\(82\) | 0.712597 | + | 1.23425i | 0.0786932 | + | 0.136301i | ||||
\(83\) | 4.95076 | 0.543417 | 0.271708 | − | 0.962380i | \(-0.412411\pi\) | ||||
0.271708 | + | 0.962380i | \(0.412411\pi\) | |||||||
\(84\) | 8.08547 | + | 0.718821i | 0.882197 | + | 0.0784298i | ||||
\(85\) | 13.2724 | 1.43959 | ||||||||
\(86\) | −1.37558 | − | 2.38258i | −0.148333 | − | 0.256920i | ||||
\(87\) | 8.29923 | − | 14.3747i | 0.889771 | − | 1.54113i | ||||
\(88\) | −1.40996 | + | 2.44213i | −0.150302 | + | 0.260331i | ||||
\(89\) | 0.609347 | + | 1.05542i | 0.0645906 | + | 0.111874i | 0.896512 | − | 0.443019i | \(-0.146093\pi\) |
−0.831922 | + | 0.554893i | \(0.812759\pi\) | |||||||
\(90\) | 11.5439 | 1.21683 | ||||||||
\(91\) | 1.52058 | − | 2.16514i | 0.159400 | − | 0.226968i | ||||
\(92\) | −5.80907 | −0.605637 | ||||||||
\(93\) | 3.22418 | + | 5.58444i | 0.334332 | + | 0.579079i | ||||
\(94\) | 3.40398 | − | 5.89586i | 0.351093 | − | 0.608111i | ||||
\(95\) | −13.0977 | + | 22.6859i | −1.34379 | + | 2.32752i | ||||
\(96\) | −6.99230 | − | 12.1110i | −0.713649 | − | 1.23608i | ||||
\(97\) | 7.28506 | 0.739686 | 0.369843 | − | 0.929094i | \(-0.379412\pi\) | ||||
0.369843 | + | 0.929094i | \(0.379412\pi\) | |||||||
\(98\) | 3.92355 | − | 4.64935i | 0.396339 | − | 0.469655i | ||||
\(99\) | 3.07598 | 0.309147 | ||||||||
\(100\) | 8.49300 | + | 14.7103i | 0.849300 | + | 1.47103i | ||||
\(101\) | 2.37473 | − | 4.11315i | 0.236294 | − | 0.409274i | −0.723354 | − | 0.690478i | \(-0.757400\pi\) |
0.959648 | + | 0.281204i | \(0.0907337\pi\) | |||||||
\(102\) | 3.29222 | − | 5.70230i | 0.325979 | − | 0.564611i | ||||
\(103\) | −7.96222 | − | 13.7910i | −0.784541 | − | 1.35887i | −0.929273 | − | 0.369394i | \(-0.879565\pi\) |
0.144732 | − | 0.989471i | \(-0.453768\pi\) | |||||||
\(104\) | −2.81992 | −0.276516 | ||||||||
\(105\) | −16.1853 | + | 23.0461i | −1.57952 | + | 2.24907i | ||||
\(106\) | −0.325838 | −0.0316482 | ||||||||
\(107\) | 6.82560 | + | 11.8223i | 0.659855 | + | 1.14290i | 0.980653 | + | 0.195755i | \(0.0627158\pi\) |
−0.320797 | + | 0.947148i | \(0.603951\pi\) | |||||||
\(108\) | −0.116550 | + | 0.201870i | −0.0112150 | + | 0.0194249i | ||||
\(109\) | −0.104953 | + | 0.181784i | −0.0100527 | + | 0.0174118i | −0.871008 | − | 0.491269i | \(-0.836533\pi\) |
0.860955 | + | 0.508681i | \(0.169867\pi\) | |||||||
\(110\) | −1.87646 | − | 3.25012i | −0.178913 | − | 0.309887i | ||||
\(111\) | −21.9405 | −2.08250 | ||||||||
\(112\) | 0.101697 | + | 0.00904113i | 0.00960945 | + | 0.000854307i | ||||
\(113\) | −8.16695 | −0.768282 | −0.384141 | − | 0.923274i | \(-0.625502\pi\) | ||||
−0.384141 | + | 0.923274i | \(0.625502\pi\) | |||||||
\(114\) | 6.49778 | + | 11.2545i | 0.608573 | + | 1.05408i | ||||
\(115\) | 10.0768 | − | 17.4535i | 0.939664 | − | 1.62755i | ||||
\(116\) | 4.19071 | − | 7.25852i | 0.389098 | − | 0.673937i | ||||
\(117\) | 1.53799 | + | 2.66387i | 0.142187 | + | 0.246275i | ||||
\(118\) | −8.90785 | −0.820034 | ||||||||
\(119\) | 3.42636 | + | 7.37486i | 0.314094 | + | 0.676053i | ||||
\(120\) | 30.0157 | 2.74005 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 1.75748 | − | 3.04405i | 0.159115 | − | 0.275595i | ||||
\(123\) | 2.02109 | − | 3.50064i | 0.182236 | − | 0.315642i | ||||
\(124\) | 1.62805 | + | 2.81987i | 0.146203 | + | 0.253232i | ||||
\(125\) | −37.3390 | −3.33970 | ||||||||
\(126\) | 2.98014 | + | 6.41441i | 0.265492 | + | 0.571441i | ||||
\(127\) | −7.88710 | −0.699867 | −0.349934 | − | 0.936775i | \(-0.613796\pi\) | ||||
−0.349934 | + | 0.936775i | \(0.613796\pi\) | |||||||
\(128\) | −3.56431 | − | 6.17357i | −0.315044 | − | 0.545672i | ||||
\(129\) | −3.90147 | + | 6.75755i | −0.343506 | + | 0.594969i | ||||
\(130\) | 1.87646 | − | 3.25012i | 0.164576 | − | 0.285054i | ||||
\(131\) | −8.76156 | − | 15.1755i | −0.765501 | − | 1.32589i | −0.939981 | − | 0.341226i | \(-0.889158\pi\) |
0.174480 | − | 0.984661i | \(-0.444175\pi\) | |||||||
\(132\) | 3.06807 | 0.267042 | ||||||||
\(133\) | −15.9868 | − | 1.42127i | −1.38623 | − | 0.123240i | ||||
\(134\) | 9.92986 | 0.857809 | ||||||||
\(135\) | −0.404349 | − | 0.700353i | −0.0348008 | − | 0.0602768i | ||||
\(136\) | 4.33364 | − | 7.50609i | 0.371607 | − | 0.643642i | ||||
\(137\) | 2.82834 | − | 4.89883i | 0.241641 | − | 0.418535i | −0.719541 | − | 0.694450i | \(-0.755648\pi\) |
0.961182 | + | 0.275915i | \(0.0889809\pi\) | |||||||
\(138\) | −4.99910 | − | 8.65870i | −0.425552 | − | 0.737077i | ||||
\(139\) | −3.47904 | −0.295088 | −0.147544 | − | 0.989055i | \(-0.547137\pi\) | ||||
−0.147544 | + | 0.989055i | \(0.547137\pi\) | |||||||
\(140\) | −8.17279 | + | 11.6372i | −0.690727 | + | 0.983520i | ||||
\(141\) | −19.3090 | −1.62611 | ||||||||
\(142\) | −6.18984 | − | 10.7211i | −0.519440 | − | 0.899696i | ||||
\(143\) | 0.500000 | − | 0.866025i | 0.0418121 | − | 0.0724207i | ||||
\(144\) | −0.0593500 | + | 0.102797i | −0.00494583 | + | 0.00856644i | ||||
\(145\) | 14.5389 | + | 25.1822i | 1.20739 | + | 2.09127i | ||||
\(146\) | 4.73565 | 0.391925 | ||||||||
\(147\) | −16.9840 | − | 3.04391i | −1.40082 | − | 0.251058i | ||||
\(148\) | −11.0789 | −0.910681 | ||||||||
\(149\) | −5.84324 | − | 10.1208i | −0.478696 | − | 0.829127i | 0.521005 | − | 0.853554i | \(-0.325557\pi\) |
−0.999702 | + | 0.0244269i | \(0.992224\pi\) | |||||||
\(150\) | −14.6176 | + | 25.3185i | −1.19352 | + | 2.06724i | ||||
\(151\) | −10.1493 | + | 17.5791i | −0.825937 | + | 1.43056i | 0.0752649 | + | 0.997164i | \(0.476020\pi\) |
−0.901201 | + | 0.433400i | \(0.857314\pi\) | |||||||
\(152\) | 8.55320 | + | 14.8146i | 0.693756 | + | 1.20162i | ||||
\(153\) | −9.45428 | −0.764333 | ||||||||
\(154\) | 1.32152 | − | 1.88171i | 0.106491 | − | 0.151632i | ||||
\(155\) | −11.2965 | −0.907356 | ||||||||
\(156\) | 1.53404 | + | 2.65703i | 0.122821 | + | 0.212733i | ||||
\(157\) | 0.928889 | − | 1.60888i | 0.0741334 | − | 0.128403i | −0.826576 | − | 0.562826i | \(-0.809714\pi\) |
0.900709 | + | 0.434423i | \(0.143048\pi\) | |||||||
\(158\) | −4.21132 | + | 7.29422i | −0.335035 | + | 0.580297i | ||||
\(159\) | 0.462077 | + | 0.800341i | 0.0366451 | + | 0.0634711i | ||||
\(160\) | 24.4988 | 1.93680 | ||||||||
\(161\) | 12.2995 | + | 1.09346i | 0.969337 | + | 0.0861768i | ||||
\(162\) | 7.61872 | 0.598583 | ||||||||
\(163\) | 0.389451 | + | 0.674550i | 0.0305042 | + | 0.0528348i | 0.880874 | − | 0.473350i | \(-0.156955\pi\) |
−0.850370 | + | 0.526185i | \(0.823622\pi\) | |||||||
\(164\) | 1.02055 | − | 1.76765i | 0.0796919 | − | 0.138030i | ||||
\(165\) | −5.32208 | + | 9.21811i | −0.414323 | + | 0.717629i | ||||
\(166\) | 2.15133 | + | 3.72622i | 0.166976 | + | 0.289210i | ||||
\(167\) | −4.83343 | −0.374022 | −0.187011 | − | 0.982358i | \(-0.559880\pi\) | ||||
−0.187011 | + | 0.982358i | \(0.559880\pi\) | |||||||
\(168\) | 7.74878 | + | 16.6784i | 0.597831 | + | 1.28676i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.76745 | + | 9.98952i | 0.442343 | + | 0.766161i | ||||
\(171\) | 9.32984 | − | 16.1598i | 0.713471 | − | 1.23577i | ||||
\(172\) | −1.97005 | + | 3.41224i | −0.150215 | + | 0.260180i | ||||
\(173\) | 12.2030 | + | 21.1362i | 0.927777 | + | 1.60696i | 0.787034 | + | 0.616910i | \(0.211616\pi\) |
0.140743 | + | 0.990046i | \(0.455051\pi\) | |||||||
\(174\) | 14.4256 | 1.09360 | ||||||||
\(175\) | −15.2132 | − | 32.7447i | −1.15001 | − | 2.47527i | ||||
\(176\) | 0.0385894 | 0.00290878 | ||||||||
\(177\) | 12.6324 | + | 21.8799i | 0.949508 | + | 1.64460i | ||||
\(178\) | −0.529578 | + | 0.917256i | −0.0396935 | + | 0.0687512i | ||||
\(179\) | 3.82502 | − | 6.62512i | 0.285895 | − | 0.495185i | −0.686931 | − | 0.726723i | \(-0.741042\pi\) |
0.972826 | + | 0.231538i | \(0.0743758\pi\) | |||||||
\(180\) | −8.26635 | − | 14.3177i | −0.616137 | − | 1.06718i | ||||
\(181\) | 9.31027 | 0.692027 | 0.346014 | − | 0.938229i | \(-0.387535\pi\) | ||||
0.346014 | + | 0.938229i | \(0.387535\pi\) | |||||||
\(182\) | 2.29037 | + | 0.203620i | 0.169773 | + | 0.0150933i | ||||
\(183\) | −9.96927 | −0.736950 | ||||||||
\(184\) | −6.58045 | − | 11.3977i | −0.485117 | − | 0.840248i | ||||
\(185\) | 19.2182 | − | 33.2869i | 1.41295 | − | 2.44730i | ||||
\(186\) | −2.80210 | + | 4.85339i | −0.205460 | + | 0.355868i | ||||
\(187\) | 1.53679 | + | 2.66181i | 0.112382 | + | 0.194650i | ||||
\(188\) | −9.75010 | −0.711099 | ||||||||
\(189\) | 0.284769 | − | 0.405480i | 0.0207139 | − | 0.0294943i | ||||
\(190\) | −22.7662 | −1.65163 | ||||||||
\(191\) | 2.59106 | + | 4.48785i | 0.187482 | + | 0.324729i | 0.944410 | − | 0.328769i | \(-0.106634\pi\) |
−0.756928 | + | 0.653499i | \(0.773301\pi\) | |||||||
\(192\) | 5.98183 | − | 10.3608i | 0.431701 | − | 0.747729i | ||||
\(193\) | −10.5474 | + | 18.2687i | −0.759222 | + | 1.31501i | 0.184026 | + | 0.982921i | \(0.441087\pi\) |
−0.943248 | + | 0.332089i | \(0.892246\pi\) | |||||||
\(194\) | 3.16569 | + | 5.48314i | 0.227283 | + | 0.393666i | ||||
\(195\) | −10.6442 | −0.762244 | ||||||||
\(196\) | −8.57612 | − | 1.53703i | −0.612580 | − | 0.109788i | ||||
\(197\) | −2.59763 | −0.185074 | −0.0925368 | − | 0.995709i | \(-0.529498\pi\) | ||||
−0.0925368 | + | 0.995709i | \(0.529498\pi\) | |||||||
\(198\) | 1.33665 | + | 2.31515i | 0.0949917 | + | 0.164530i | ||||
\(199\) | 1.66800 | − | 2.88907i | 0.118242 | − | 0.204801i | −0.800829 | − | 0.598893i | \(-0.795608\pi\) |
0.919071 | + | 0.394092i | \(0.128941\pi\) | |||||||
\(200\) | −19.2416 | + | 33.3274i | −1.36058 | + | 2.35660i | ||||
\(201\) | −14.0817 | − | 24.3902i | −0.993248 | − | 1.72036i | ||||
\(202\) | 4.12771 | 0.290425 | ||||||||
\(203\) | −10.2393 | + | 14.5796i | −0.718656 | + | 1.02329i | ||||
\(204\) | −9.42999 | −0.660232 | ||||||||
\(205\) | 3.54064 | + | 6.13257i | 0.247289 | + | 0.428317i | ||||
\(206\) | 6.91990 | − | 11.9856i | 0.482132 | − | 0.835077i | ||||
\(207\) | −7.17797 | + | 12.4326i | −0.498903 | + | 0.864125i | ||||
\(208\) | 0.0192947 | + | 0.0334194i | 0.00133785 | + | 0.00231722i | ||||
\(209\) | −6.06627 | −0.419612 | ||||||||
\(210\) | −24.3790 | − | 2.16736i | −1.68231 | − | 0.149562i | ||||
\(211\) | −13.5896 | −0.935547 | −0.467773 | − | 0.883848i | \(-0.654944\pi\) | ||||
−0.467773 | + | 0.883848i | \(0.654944\pi\) | |||||||
\(212\) | 0.233326 | + | 0.404133i | 0.0160249 | + | 0.0277560i | ||||
\(213\) | −17.5558 | + | 30.4076i | −1.20291 | + | 2.08350i | ||||
\(214\) | −5.93207 | + | 10.2746i | −0.405508 | + | 0.702360i | ||||
\(215\) | −6.83476 | − | 11.8382i | −0.466127 | − | 0.807356i | ||||
\(216\) | −0.528105 | −0.0359330 | ||||||||
\(217\) | −2.91628 | − | 6.27696i | −0.197970 | − | 0.426108i | ||||
\(218\) | −0.182428 | −0.0123556 | ||||||||
\(219\) | −6.71571 | − | 11.6319i | −0.453806 | − | 0.786014i | ||||
\(220\) | −2.68739 | + | 4.65470i | −0.181184 | + | 0.313820i | ||||
\(221\) | −1.53679 | + | 2.66181i | −0.103376 | + | 0.179052i | ||||
\(222\) | −9.53417 | − | 16.5137i | −0.639892 | − | 1.10832i | ||||
\(223\) | 17.8007 | 1.19202 | 0.596011 | − | 0.802976i | \(-0.296751\pi\) | ||||
0.596011 | + | 0.802976i | \(0.296751\pi\) | |||||||
\(224\) | 6.32456 | + | 13.6129i | 0.422577 | + | 0.909550i | ||||
\(225\) | 41.9775 | 2.79850 | ||||||||
\(226\) | −3.54891 | − | 6.14690i | −0.236070 | − | 0.408886i | ||||
\(227\) | 2.49387 | − | 4.31952i | 0.165524 | − | 0.286696i | −0.771317 | − | 0.636451i | \(-0.780402\pi\) |
0.936841 | + | 0.349755i | \(0.113735\pi\) | |||||||
\(228\) | 9.30588 | − | 16.1183i | 0.616297 | − | 1.06746i | ||||
\(229\) | 7.89196 | + | 13.6693i | 0.521516 | + | 0.903291i | 0.999687 | + | 0.0250248i | \(0.00796648\pi\) |
−0.478171 | + | 0.878267i | \(0.658700\pi\) | |||||||
\(230\) | 17.5153 | 1.15492 | ||||||||
\(231\) | −6.49602 | − | 0.577515i | −0.427407 | − | 0.0379977i | ||||
\(232\) | 18.9888 | 1.24668 | ||||||||
\(233\) | 1.75336 | + | 3.03690i | 0.114866 | + | 0.198954i | 0.917726 | − | 0.397213i | \(-0.130023\pi\) |
−0.802860 | + | 0.596168i | \(0.796689\pi\) | |||||||
\(234\) | −1.33665 | + | 2.31515i | −0.0873797 | + | 0.151346i | ||||
\(235\) | 16.9131 | − | 29.2944i | 1.10329 | − | 1.91096i | ||||
\(236\) | 6.37874 | + | 11.0483i | 0.415221 | + | 0.719184i | ||||
\(237\) | 23.8886 | 1.55173 | ||||||||
\(238\) | −4.06182 | + | 5.78359i | −0.263289 | + | 0.374894i | ||||
\(239\) | −14.3966 | −0.931239 | −0.465619 | − | 0.884985i | \(-0.654168\pi\) | ||||
−0.465619 | + | 0.884985i | \(0.654168\pi\) | |||||||
\(240\) | −0.205376 | − | 0.355721i | −0.0132569 | − | 0.0229617i | ||||
\(241\) | −5.20448 | + | 9.01443i | −0.335250 | + | 0.580671i | −0.983533 | − | 0.180729i | \(-0.942154\pi\) |
0.648283 | + | 0.761400i | \(0.275488\pi\) | |||||||
\(242\) | 0.434546 | − | 0.752655i | 0.0279337 | − | 0.0483825i | ||||
\(243\) | −11.0852 | − | 19.2001i | −0.711113 | − | 1.23168i | ||||
\(244\) | −5.03400 | −0.322269 | ||||||||
\(245\) | 19.4947 | − | 23.1009i | 1.24547 | − | 1.47586i | ||||
\(246\) | 3.51303 | 0.223983 | ||||||||
\(247\) | −3.03313 | − | 5.25354i | −0.192994 | − | 0.334275i | ||||
\(248\) | −3.68849 | + | 6.38864i | −0.234219 | + | 0.405679i | ||||
\(249\) | 6.10169 | − | 10.5684i | 0.386679 | − | 0.669747i | ||||
\(250\) | −16.2255 | − | 28.1034i | −1.02619 | − | 1.77741i | ||||
\(251\) | −21.0293 | −1.32736 | −0.663680 | − | 0.748017i | \(-0.731006\pi\) | ||||
−0.663680 | + | 0.748017i | \(0.731006\pi\) | |||||||
\(252\) | 5.82170 | − | 8.28947i | 0.366733 | − | 0.522188i | ||||
\(253\) | 4.66711 | 0.293419 | ||||||||
\(254\) | −3.42731 | − | 5.93627i | −0.215048 | − | 0.372475i | ||||
\(255\) | 16.3579 | − | 28.3327i | 1.02437 | − | 1.77426i | ||||
\(256\) | 7.95122 | − | 13.7719i | 0.496951 | − | 0.860745i | ||||
\(257\) | 8.92664 | + | 15.4614i | 0.556829 | + | 0.964456i | 0.997759 | + | 0.0669142i | \(0.0213154\pi\) |
−0.440930 | + | 0.897542i | \(0.645351\pi\) | |||||||
\(258\) | −6.78147 | −0.422196 | ||||||||
\(259\) | 23.4573 | + | 2.08542i | 1.45757 | + | 0.129582i | ||||
\(260\) | −5.37478 | −0.333330 | ||||||||
\(261\) | −10.3565 | − | 17.9380i | −0.641051 | − | 1.11033i | ||||
\(262\) | 7.61460 | − | 13.1889i | 0.470431 | − | 0.814811i | ||||
\(263\) | −12.1805 | + | 21.0972i | −0.751080 | + | 1.30091i | 0.196220 | + | 0.980560i | \(0.437133\pi\) |
−0.947300 | + | 0.320348i | \(0.896200\pi\) | |||||||
\(264\) | 3.47548 | + | 6.01972i | 0.213901 | + | 0.370488i | ||||
\(265\) | −1.61897 | −0.0994526 | ||||||||
\(266\) | −5.87726 | − | 12.6501i | −0.360358 | − | 0.775630i | ||||
\(267\) | 3.00402 | 0.183843 | ||||||||
\(268\) | −7.11059 | − | 12.3159i | −0.434348 | − | 0.752313i | ||||
\(269\) | 13.0996 | − | 22.6892i | 0.798699 | − | 1.38339i | −0.121764 | − | 0.992559i | \(-0.538855\pi\) |
0.920464 | − | 0.390828i | \(-0.127811\pi\) | |||||||
\(270\) | 0.351416 | − | 0.608671i | 0.0213865 | − | 0.0370425i | ||||
\(271\) | −2.97422 | − | 5.15151i | −0.180671 | − | 0.312932i | 0.761438 | − | 0.648238i | \(-0.224494\pi\) |
−0.942109 | + | 0.335306i | \(0.891160\pi\) | |||||||
\(272\) | −0.118608 | −0.00719166 | ||||||||
\(273\) | −2.74787 | − | 5.91448i | −0.166309 | − | 0.357960i | ||||
\(274\) | 4.91617 | 0.296997 | ||||||||
\(275\) | −6.82344 | − | 11.8185i | −0.411469 | − | 0.712685i | ||||
\(276\) | −7.15953 | + | 12.4007i | −0.430953 | + | 0.746432i | ||||
\(277\) | −3.82166 | + | 6.61932i | −0.229622 | + | 0.397716i | −0.957696 | − | 0.287782i | \(-0.907082\pi\) |
0.728074 | + | 0.685498i | \(0.240416\pi\) | |||||||
\(278\) | −1.51180 | − | 2.61852i | −0.0906718 | − | 0.157048i | ||||
\(279\) | 8.04681 | 0.481750 | ||||||||
\(280\) | −32.0907 | − | 2.85296i | −1.91779 | − | 0.170497i | ||||
\(281\) | −3.15916 | −0.188459 | −0.0942297 | − | 0.995550i | \(-0.530039\pi\) | ||||
−0.0942297 | + | 0.995550i | \(0.530039\pi\) | |||||||
\(282\) | −8.39063 | − | 14.5330i | −0.499655 | − | 0.865427i | ||||
\(283\) | 14.7591 | − | 25.5635i | 0.877339 | − | 1.51959i | 0.0230880 | − | 0.999733i | \(-0.492650\pi\) |
0.854251 | − | 0.519861i | \(-0.174016\pi\) | |||||||
\(284\) | −8.86485 | + | 15.3544i | −0.526032 | + | 0.911115i | ||||
\(285\) | 32.2851 | + | 55.9195i | 1.91241 | + | 3.31238i | ||||
\(286\) | 0.869091 | 0.0513904 | ||||||||
\(287\) | −2.49355 | + | 3.55054i | −0.147190 | + | 0.209582i | ||||
\(288\) | −17.4512 | −1.02832 | ||||||||
\(289\) | 3.77653 | + | 6.54114i | 0.222149 | + | 0.384773i | ||||
\(290\) | −12.6357 | + | 21.8856i | −0.741992 | + | 1.28517i | ||||
\(291\) | 8.97865 | − | 15.5515i | 0.526338 | − | 0.911644i | ||||
\(292\) | −3.39111 | − | 5.87357i | −0.198450 | − | 0.343725i | ||||
\(293\) | 28.9433 | 1.69088 | 0.845441 | − | 0.534068i | \(-0.179337\pi\) | ||||
0.845441 | + | 0.534068i | \(0.179337\pi\) | |||||||
\(294\) | −5.08932 | − | 14.1058i | −0.296815 | − | 0.822669i | ||||
\(295\) | −44.2599 | −2.57691 | ||||||||
\(296\) | −12.5501 | − | 21.7374i | −0.729459 | − | 1.26346i | ||||
\(297\) | 0.0936383 | − | 0.162186i | 0.00543344 | − | 0.00941100i | ||||
\(298\) | 5.07831 | − | 8.79588i | 0.294178 | − | 0.509532i | ||||
\(299\) | 2.33356 | + | 4.04184i | 0.134953 | + | 0.233746i | ||||
\(300\) | 41.8696 | 2.41734 | ||||||||
\(301\) | 4.81349 | − | 6.85388i | 0.277445 | − | 0.395051i | ||||
\(302\) | −17.6413 | −1.01514 | ||||||||
\(303\) | −5.85359 | − | 10.1387i | −0.336280 | − | 0.582454i | ||||
\(304\) | 0.117047 | − | 0.202731i | 0.00671309 | − | 0.0116274i | ||||
\(305\) | 8.73229 | − | 15.1248i | 0.500010 | − | 0.866042i | ||||
\(306\) | −4.10832 | − | 7.11581i | −0.234857 | − | 0.406784i | ||||
\(307\) | −1.67213 | −0.0954337 | −0.0477169 | − | 0.998861i | \(-0.515195\pi\) | ||||
−0.0477169 | + | 0.998861i | \(0.515195\pi\) | |||||||
\(308\) | −3.28018 | − | 0.291617i | −0.186905 | − | 0.0166164i | ||||
\(309\) | −39.2530 | −2.23302 | ||||||||
\(310\) | −4.90884 | − | 8.50237i | −0.278804 | − | 0.482902i | ||||
\(311\) | −14.7516 | + | 25.5505i | −0.836487 | + | 1.44884i | 0.0563276 | + | 0.998412i | \(0.482061\pi\) |
−0.892814 | + | 0.450425i | \(0.851272\pi\) | |||||||
\(312\) | −3.47548 | + | 6.01972i | −0.196761 | + | 0.340799i | ||||
\(313\) | −16.5589 | − | 28.6809i | −0.935967 | − | 1.62114i | −0.772900 | − | 0.634528i | \(-0.781195\pi\) |
−0.163067 | − | 0.986615i | \(-0.552139\pi\) | |||||||
\(314\) | 1.61458 | 0.0911159 | ||||||||
\(315\) | 14.8072 | + | 31.8709i | 0.834293 | + | 1.79572i | ||||
\(316\) | 12.0626 | 0.678574 | ||||||||
\(317\) | 7.23171 | + | 12.5257i | 0.406173 | + | 0.703513i | 0.994457 | − | 0.105142i | \(-0.0335296\pi\) |
−0.588284 | + | 0.808655i | \(0.700196\pi\) | |||||||
\(318\) | −0.401587 | + | 0.695569i | −0.0225199 | + | 0.0390056i | ||||
\(319\) | −3.36690 | + | 5.83164i | −0.188510 | + | 0.326509i | ||||
\(320\) | 10.4792 | + | 18.1505i | 0.585806 | + | 1.01465i | ||||
\(321\) | 33.6495 | 1.87813 | ||||||||
\(322\) | 4.52170 | + | 9.73245i | 0.251985 | + | 0.542368i | ||||
\(323\) | 18.6452 | 1.03745 | ||||||||
\(324\) | −5.45562 | − | 9.44941i | −0.303090 | − | 0.524967i | ||||
\(325\) | 6.82344 | − | 11.8185i | 0.378496 | − | 0.655575i | ||||
\(326\) | −0.338469 | + | 0.586245i | −0.0187461 | + | 0.0324691i | ||||
\(327\) | 0.258704 | + | 0.448089i | 0.0143064 | + | 0.0247794i | ||||
\(328\) | 4.62430 | 0.255334 | ||||||||
\(329\) | 20.6438 | + | 1.83530i | 1.13813 | + | 0.101183i | ||||
\(330\) | −9.25074 | −0.509236 | ||||||||
\(331\) | −3.35648 | − | 5.81359i | −0.184489 | − | 0.319544i | 0.758916 | − | 0.651189i | \(-0.225730\pi\) |
−0.943404 | + | 0.331646i | \(0.892396\pi\) | |||||||
\(332\) | 3.08106 | − | 5.33655i | 0.169095 | − | 0.292881i | ||||
\(333\) | −13.6896 | + | 23.7112i | −0.750188 | + | 1.29936i | ||||
\(334\) | −2.10035 | − | 3.63791i | −0.114926 | − | 0.199058i | ||||
\(335\) | 49.3379 | 2.69562 | ||||||||
\(336\) | 0.144639 | − | 0.205950i | 0.00789070 | − | 0.0112355i | ||||
\(337\) | 6.53587 | 0.356031 | 0.178016 | − | 0.984028i | \(-0.443032\pi\) | ||||
0.178016 | + | 0.984028i | \(0.443032\pi\) | |||||||
\(338\) | 0.434546 | + | 0.752655i | 0.0236362 | + | 0.0409390i | ||||
\(339\) | −10.0656 | + | 17.4341i | −0.546686 | + | 0.946889i | ||||
\(340\) | 8.25993 | − | 14.3066i | 0.447958 | − | 0.775886i | ||||
\(341\) | −1.30801 | − | 2.26554i | −0.0708327 | − | 0.122686i | ||||
\(342\) | 16.2170 | 0.876914 | ||||||||
\(343\) | 17.8689 | + | 4.86866i | 0.964828 | + | 0.262883i | ||||
\(344\) | −8.92664 | −0.481292 | ||||||||
\(345\) | −24.8387 | − | 43.0220i | −1.33727 | − | 2.31622i | ||||
\(346\) | −10.6055 | + | 18.3693i | −0.570156 | + | 0.987539i | ||||
\(347\) | −11.9032 | + | 20.6169i | −0.638996 | + | 1.10677i | 0.346657 | + | 0.937992i | \(0.387317\pi\) |
−0.985653 | + | 0.168782i | \(0.946017\pi\) | |||||||
\(348\) | −10.3299 | − | 17.8919i | −0.553740 | − | 0.959106i | ||||
\(349\) | 27.9522 | 1.49625 | 0.748123 | − | 0.663560i | \(-0.230955\pi\) | ||||
0.748123 | + | 0.663560i | \(0.230955\pi\) | |||||||
\(350\) | 18.0347 | − | 25.6794i | 0.963993 | − | 1.37262i | ||||
\(351\) | 0.187277 | 0.00999608 | ||||||||
\(352\) | 2.83669 | + | 4.91330i | 0.151196 | + | 0.261880i | ||||
\(353\) | −3.70093 | + | 6.41021i | −0.196981 | + | 0.341181i | −0.947548 | − | 0.319613i | \(-0.896447\pi\) |
0.750567 | + | 0.660794i | \(0.229780\pi\) | |||||||
\(354\) | −10.9787 | + | 19.0157i | −0.583511 | + | 1.01067i | ||||
\(355\) | −30.7551 | − | 53.2694i | −1.63231 | − | 2.82724i | ||||
\(356\) | 1.51688 | 0.0803947 | ||||||||
\(357\) | 19.9661 | + | 1.77504i | 1.05672 | + | 0.0939452i | ||||
\(358\) | 6.64858 | 0.351388 | ||||||||
\(359\) | −10.4751 | − | 18.1435i | −0.552857 | − | 0.957576i | −0.998067 | − | 0.0621500i | \(-0.980204\pi\) |
0.445210 | − | 0.895426i | \(-0.353129\pi\) | |||||||
\(360\) | 18.7281 | − | 32.4380i | 0.987057 | − | 1.70963i | ||||
\(361\) | −8.89979 | + | 15.4149i | −0.468410 | + | 0.811310i | ||||
\(362\) | 4.04574 | + | 7.00743i | 0.212639 | + | 0.368302i | ||||
\(363\) | −2.46495 | −0.129376 | ||||||||
\(364\) | −1.38754 | − | 2.98653i | −0.0727269 | − | 0.156536i | ||||
\(365\) | 23.5297 | 1.23160 | ||||||||
\(366\) | −4.33210 | − | 7.50342i | −0.226443 | − | 0.392210i | ||||
\(367\) | −5.22914 | + | 9.05713i | −0.272959 | + | 0.472779i | −0.969618 | − | 0.244624i | \(-0.921336\pi\) |
0.696659 | + | 0.717402i | \(0.254669\pi\) | |||||||
\(368\) | −0.0900505 | + | 0.155972i | −0.00469421 | + | 0.00813061i | ||||
\(369\) | −2.52209 | − | 4.36840i | −0.131295 | − | 0.227410i | ||||
\(370\) | 33.4047 | 1.73663 | ||||||||
\(371\) | −0.417950 | − | 0.899590i | −0.0216989 | − | 0.0467044i | ||||
\(372\) | 8.02614 | 0.416136 | ||||||||
\(373\) | 12.1764 | + | 21.0901i | 0.630468 | + | 1.09200i | 0.987456 | + | 0.157894i | \(0.0504705\pi\) |
−0.356988 | + | 0.934109i | \(0.616196\pi\) | |||||||
\(374\) | −1.33561 | + | 2.31335i | −0.0690630 | + | 0.119621i | ||||
\(375\) | −46.0193 | + | 79.7078i | −2.37643 | + | 4.11609i | ||||
\(376\) | −11.0448 | − | 19.1302i | −0.569593 | − | 0.986564i | ||||
\(377\) | −6.73380 | −0.346808 | ||||||||
\(378\) | 0.428932 | + | 0.0381332i | 0.0220619 | + | 0.00196136i | ||||
\(379\) | 22.1844 | 1.13954 | 0.569768 | − | 0.821805i | \(-0.307033\pi\) | ||||
0.569768 | + | 0.821805i | \(0.307033\pi\) | |||||||
\(380\) | 16.3024 | + | 28.2366i | 0.836297 | + | 1.44851i | ||||
\(381\) | −9.72065 | + | 16.8367i | −0.498004 | + | 0.862568i | ||||
\(382\) | −2.25187 | + | 3.90035i | −0.115216 | + | 0.199559i | ||||
\(383\) | 15.6926 | + | 27.1804i | 0.801855 | + | 1.38885i | 0.918394 | + | 0.395667i | \(0.129487\pi\) |
−0.116539 | + | 0.993186i | \(0.537180\pi\) | |||||||
\(384\) | −17.5717 | −0.896702 | ||||||||
\(385\) | 6.56617 | − | 9.34952i | 0.334643 | − | 0.476496i | ||||
\(386\) | −18.3334 | −0.933145 | ||||||||
\(387\) | 4.86859 | + | 8.43265i | 0.247484 | + | 0.428656i | ||||
\(388\) | 4.53378 | − | 7.85275i | 0.230168 | − | 0.398663i | ||||
\(389\) | 0.359796 | − | 0.623185i | 0.0182424 | − | 0.0315967i | −0.856760 | − | 0.515715i | \(-0.827526\pi\) |
0.875002 | + | 0.484118i | \(0.160860\pi\) | |||||||
\(390\) | −4.62537 | − | 8.01138i | −0.234215 | − | 0.405672i | ||||
\(391\) | −14.3448 | −0.725447 | ||||||||
\(392\) | −6.69921 | − | 18.5679i | −0.338361 | − | 0.937821i | ||||
\(393\) | −43.1936 | −2.17883 | ||||||||
\(394\) | −1.12879 | − | 1.95512i | −0.0568676 | − | 0.0984976i | ||||
\(395\) | −20.9245 | + | 36.2424i | −1.05283 | + | 1.82355i | ||||
\(396\) | 1.91430 | − | 3.31567i | 0.0961974 | − | 0.166619i | ||||
\(397\) | −2.30769 | − | 3.99703i | −0.115820 | − | 0.200605i | 0.802287 | − | 0.596938i | \(-0.203616\pi\) |
−0.918107 | + | 0.396332i | \(0.870283\pi\) | |||||||
\(398\) | 2.89930 | 0.145329 | ||||||||
\(399\) | −22.7373 | + | 32.3754i | −1.13829 | + | 1.62080i | ||||
\(400\) | 0.526625 | 0.0263312 | ||||||||
\(401\) | −9.47673 | − | 16.4142i | −0.473245 | − | 0.819685i | 0.526286 | − | 0.850308i | \(-0.323584\pi\) |
−0.999531 | + | 0.0306231i | \(0.990251\pi\) | |||||||
\(402\) | 12.2383 | − | 21.1974i | 0.610391 | − | 1.05723i | ||||
\(403\) | 1.30801 | − | 2.26554i | 0.0651566 | − | 0.112854i | ||||
\(404\) | −2.95578 | − | 5.11956i | −0.147055 | − | 0.254708i | ||||
\(405\) | 37.8547 | 1.88101 | ||||||||
\(406\) | −15.4229 | − | 1.37114i | −0.765424 | − | 0.0680483i | ||||
\(407\) | 8.90101 | 0.441207 | ||||||||
\(408\) | −10.6822 | − | 18.5021i | −0.528848 | − | 0.915992i | ||||
\(409\) | −5.80309 | + | 10.0513i | −0.286945 | + | 0.497002i | −0.973079 | − | 0.230472i | \(-0.925973\pi\) |
0.686134 | + | 0.727475i | \(0.259306\pi\) | |||||||
\(410\) | −3.07714 | + | 5.32976i | −0.151969 | + | 0.263218i | ||||
\(411\) | −6.97172 | − | 12.0754i | −0.343889 | − | 0.595634i | ||||
\(412\) | −19.8208 | −0.976503 | ||||||||
\(413\) | −11.4260 | − | 24.5932i | −0.562238 | − | 1.21015i | ||||
\(414\) | −12.4766 | −0.613192 | ||||||||
\(415\) | 10.6892 | + | 18.5142i | 0.524712 | + | 0.908828i | ||||
\(416\) | −2.83669 | + | 4.91330i | −0.139080 | + | 0.240894i | ||||
\(417\) | −4.28783 | + | 7.42673i | −0.209976 | + | 0.363689i | ||||
\(418\) | −2.63607 | − | 4.56581i | −0.128934 | − | 0.223321i | ||||
\(419\) | −12.0489 | −0.588626 | −0.294313 | − | 0.955709i | \(-0.595091\pi\) | ||||
−0.294313 | + | 0.955709i | \(0.595091\pi\) | |||||||
\(420\) | 14.7692 | + | 31.7890i | 0.720663 | + | 1.55115i | ||||
\(421\) | −18.9718 | −0.924630 | −0.462315 | − | 0.886716i | \(-0.652981\pi\) | ||||
−0.462315 | + | 0.886716i | \(0.652981\pi\) | |||||||
\(422\) | −5.90530 | − | 10.2283i | −0.287466 | − | 0.497905i | ||||
\(423\) | −12.0477 | + | 20.8672i | −0.585779 | + | 1.01460i | ||||
\(424\) | −0.528620 | + | 0.915597i | −0.0256721 | + | 0.0444653i | ||||
\(425\) | 20.9724 | + | 36.3253i | 1.01731 | + | 1.76204i | ||||
\(426\) | −30.5153 | −1.47847 | ||||||||
\(427\) | 10.6585 | + | 0.947568i | 0.515799 | + | 0.0458560i | ||||
\(428\) | 16.9914 | 0.821309 | ||||||||
\(429\) | −1.23247 | − | 2.13471i | −0.0595044 | − | 0.103065i | ||||
\(430\) | 5.94004 | − | 10.2884i | 0.286454 | − | 0.496153i | ||||
\(431\) | −4.08490 | + | 7.07525i | −0.196762 | + | 0.340803i | −0.947477 | − | 0.319824i | \(-0.896376\pi\) |
0.750714 | + | 0.660627i | \(0.229709\pi\) | |||||||
\(432\) | 0.00361344 | + | 0.00625867i | 0.000173852 | + | 0.000301120i | ||||
\(433\) | 29.4188 | 1.41378 | 0.706890 | − | 0.707324i | \(-0.250098\pi\) | ||||
0.706890 | + | 0.707324i | \(0.250098\pi\) | |||||||
\(434\) | 3.45713 | − | 4.92258i | 0.165947 | − | 0.236291i | ||||
\(435\) | 71.6755 | 3.43658 | ||||||||
\(436\) | 0.130633 | + | 0.226263i | 0.00625620 | + | 0.0108360i | ||||
\(437\) | 14.1560 | − | 24.5189i | 0.677172 | − | 1.17290i | ||||
\(438\) | 5.83656 | − | 10.1092i | 0.278882 | − | 0.483038i | ||||
\(439\) | −16.4896 | − | 28.5609i | −0.787007 | − | 1.36314i | −0.927792 | − | 0.373097i | \(-0.878296\pi\) |
0.140785 | − | 0.990040i | \(-0.455037\pi\) | |||||||
\(440\) | −12.1770 | −0.580516 | ||||||||
\(441\) | −13.8866 | + | 16.4554i | −0.661268 | + | 0.783592i | ||||
\(442\) | −2.67123 | −0.127057 | ||||||||
\(443\) | −12.6471 | − | 21.9054i | −0.600881 | − | 1.04076i | −0.992688 | − | 0.120709i | \(-0.961483\pi\) |
0.391807 | − | 0.920048i | \(-0.371850\pi\) | |||||||
\(444\) | −13.6545 | + | 23.6503i | −0.648013 | + | 1.12239i | ||||
\(445\) | −2.63128 | + | 4.55752i | −0.124735 | + | 0.216047i | ||||
\(446\) | 7.73521 | + | 13.3978i | 0.366273 | + | 0.634403i | ||||
\(447\) | −28.8066 | −1.36250 | ||||||||
\(448\) | −7.38015 | + | 10.5085i | −0.348679 | + | 0.496482i | ||||
\(449\) | −4.60539 | −0.217342 | −0.108671 | − | 0.994078i | \(-0.534659\pi\) | ||||
−0.108671 | + | 0.994078i | \(0.534659\pi\) | |||||||
\(450\) | 18.2411 | + | 31.5946i | 0.859895 | + | 1.48938i | ||||
\(451\) | −0.819933 | + | 1.42017i | −0.0386092 | + | 0.0668730i | ||||
\(452\) | −5.08262 | + | 8.80336i | −0.239066 | + | 0.414075i | ||||
\(453\) | 25.0175 | + | 43.3315i | 1.17542 | + | 2.03589i | ||||
\(454\) | 4.33481 | 0.203443 | ||||||||
\(455\) | 11.3800 | + | 1.01171i | 0.533503 | + | 0.0474299i | ||||
\(456\) | 42.1664 | 1.97462 | ||||||||
\(457\) | 1.20814 | + | 2.09256i | 0.0565144 | + | 0.0978858i | 0.892898 | − | 0.450258i | \(-0.148668\pi\) |
−0.836384 | + | 0.548144i | \(0.815335\pi\) | |||||||
\(458\) | −6.85884 | + | 11.8799i | −0.320492 | + | 0.555109i | ||||
\(459\) | −0.287805 | + | 0.498494i | −0.0134336 | + | 0.0232677i | ||||
\(460\) | −12.5424 | − | 21.7240i | −0.584791 | − | 1.01289i | ||||
\(461\) | −13.6537 | −0.635914 | −0.317957 | − | 0.948105i | \(-0.602997\pi\) | ||||
−0.317957 | + | 0.948105i | \(0.602997\pi\) | |||||||
\(462\) | −2.38815 | − | 5.14022i | −0.111107 | − | 0.239145i | ||||
\(463\) | −10.7298 | −0.498654 | −0.249327 | − | 0.968419i | \(-0.580209\pi\) | ||||
−0.249327 | + | 0.968419i | \(0.580209\pi\) | |||||||
\(464\) | −0.129927 | − | 0.225039i | −0.00603169 | − | 0.0104472i | ||||
\(465\) | −13.9226 | + | 24.1147i | −0.645647 | + | 1.11829i | ||||
\(466\) | −1.52383 | + | 2.63934i | −0.0705899 | + | 0.122265i | ||||
\(467\) | 1.00464 | + | 1.74008i | 0.0464891 | + | 0.0805215i | 0.888334 | − | 0.459199i | \(-0.151863\pi\) |
−0.841844 | + | 0.539720i | \(0.818530\pi\) | |||||||
\(468\) | 3.82861 | 0.176977 | ||||||||
\(469\) | 12.7370 | + | 27.4149i | 0.588138 | + | 1.26590i | ||||
\(470\) | 29.3981 | 1.35603 | ||||||||
\(471\) | −2.28966 | − | 3.96581i | −0.105502 | − | 0.182735i | ||||
\(472\) | −14.4516 | + | 25.0308i | −0.665187 | + | 1.15214i | ||||
\(473\) | 1.58278 | − | 2.74146i | 0.0727763 | − | 0.126052i | ||||
\(474\) | 10.3807 | + | 17.9799i | 0.476801 | + | 0.825844i | ||||
\(475\) | −82.7856 | −3.79846 | ||||||||
\(476\) | 10.0819 | + | 0.896310i | 0.462104 | + | 0.0410823i | ||||
\(477\) | 1.15324 | 0.0528032 | ||||||||
\(478\) | −6.25598 | − | 10.8357i | −0.286142 | − | 0.495612i | ||||
\(479\) | 7.24932 | − | 12.5562i | 0.331230 | − | 0.573707i | −0.651524 | − | 0.758628i | \(-0.725870\pi\) |
0.982753 | + | 0.184922i | \(0.0592032\pi\) | |||||||
\(480\) | 30.1942 | − | 52.2979i | 1.37817 | − | 2.38706i | ||||
\(481\) | 4.45051 | + | 7.70850i | 0.202926 | + | 0.351477i | ||||
\(482\) | −9.04634 | −0.412050 | ||||||||
\(483\) | 17.4931 | − | 24.9082i | 0.795962 | − | 1.13336i | ||||
\(484\) | −1.24468 | −0.0565764 | ||||||||
\(485\) | 15.7292 | + | 27.2437i | 0.714225 | + | 1.23707i | ||||
\(486\) | 9.63402 | − | 16.6866i | 0.437008 | − | 0.756920i | ||||
\(487\) | −15.4929 | + | 26.8346i | −0.702052 | + | 1.21599i | 0.265692 | + | 0.964058i | \(0.414399\pi\) |
−0.967745 | + | 0.251933i | \(0.918934\pi\) | |||||||
\(488\) | −5.70246 | − | 9.87696i | −0.258138 | − | 0.447109i | ||||
\(489\) | 1.91996 | 0.0868234 | ||||||||
\(490\) | 25.8584 | + | 4.63439i | 1.16816 | + | 0.209361i | ||||
\(491\) | −10.2575 | −0.462913 | −0.231457 | − | 0.972845i | \(-0.574349\pi\) | ||||
−0.231457 | + | 0.972845i | \(0.574349\pi\) | |||||||
\(492\) | −2.51562 | − | 4.35717i | −0.113413 | − | 0.196437i | ||||
\(493\) | 10.3485 | − | 17.9241i | 0.466071 | − | 0.807259i | ||||
\(494\) | 2.63607 | − | 4.56581i | 0.118602 | − | 0.205425i | ||||
\(495\) | 6.64134 | + | 11.5031i | 0.298506 | + | 0.517028i | ||||
\(496\) | 0.100951 | 0.00453281 | ||||||||
\(497\) | 21.6597 | − | 30.8411i | 0.971572 | − | 1.38341i | ||||
\(498\) | 10.6058 | 0.475259 | ||||||||
\(499\) | 18.5871 | + | 32.1939i | 0.832074 | + | 1.44120i | 0.896390 | + | 0.443265i | \(0.146180\pi\) |
−0.0643160 | + | 0.997930i | \(0.520487\pi\) | |||||||
\(500\) | −23.2375 | + | 40.2486i | −1.03921 | + | 1.79997i | ||||
\(501\) | −5.95709 | + | 10.3180i | −0.266143 | + | 0.460973i | ||||
\(502\) | −9.13821 | − | 15.8278i | −0.407858 | − | 0.706431i | ||||
\(503\) | 4.45664 | 0.198712 | 0.0993559 | − | 0.995052i | \(-0.468322\pi\) | ||||
0.0993559 | + | 0.995052i | \(0.468322\pi\) | |||||||
\(504\) | 22.8591 | + | 2.03224i | 1.01823 | + | 0.0905232i | ||||
\(505\) | 20.5091 | 0.912644 | ||||||||
\(506\) | 2.02807 | + | 3.51273i | 0.0901589 | + | 0.156160i | ||||
\(507\) | 1.23247 | − | 2.13471i | 0.0547361 | − | 0.0948057i | ||||
\(508\) | −4.90846 | + | 8.50170i | −0.217778 | + | 0.377202i | ||||
\(509\) | 10.2417 | + | 17.7392i | 0.453957 | + | 0.786277i | 0.998628 | − | 0.0523731i | \(-0.0166785\pi\) |
−0.544670 | + | 0.838650i | \(0.683345\pi\) | |||||||
\(510\) | 28.4330 | 1.25903 | ||||||||
\(511\) | 6.07438 | + | 13.0744i | 0.268715 | + | 0.578378i | ||||
\(512\) | −0.436571 | −0.0192939 | ||||||||
\(513\) | −0.568035 | − | 0.983865i | −0.0250793 | − | 0.0434387i | ||||
\(514\) | −7.75807 | + | 13.4374i | −0.342194 | + | 0.592697i | ||||
\(515\) | 34.3825 | − | 59.5522i | 1.51507 | − | 2.62418i | ||||
\(516\) | 4.85609 | + | 8.41099i | 0.213777 | + | 0.370273i | ||||
\(517\) | 7.83341 | 0.344513 | ||||||||
\(518\) | 8.62368 | + | 18.5615i | 0.378903 | + | 0.815546i | ||||
\(519\) | 60.1595 | 2.64071 | ||||||||
\(520\) | −6.08850 | − | 10.5456i | −0.266998 | − | 0.462455i | ||||
\(521\) | 2.92289 | − | 5.06260i | 0.128054 | − | 0.221796i | −0.794868 | − | 0.606782i | \(-0.792460\pi\) |
0.922923 | + | 0.384985i | \(0.125794\pi\) | |||||||
\(522\) | 9.00074 | − | 15.5897i | 0.393952 | − | 0.682344i | ||||
\(523\) | 5.71759 | + | 9.90316i | 0.250013 | + | 0.433035i | 0.963529 | − | 0.267604i | \(-0.0862318\pi\) |
−0.713516 | + | 0.700639i | \(0.752898\pi\) | |||||||
\(524\) | −21.8107 | −0.952804 | ||||||||
\(525\) | −88.6504 | − | 7.88127i | −3.86902 | − | 0.343967i | ||||
\(526\) | −21.1719 | −0.923138 | ||||||||
\(527\) | 4.02028 | + | 6.96333i | 0.175126 | + | 0.303327i | ||||
\(528\) | 0.0475604 | − | 0.0823771i | 0.00206980 | − | 0.00358500i | ||||
\(529\) | 0.609022 | − | 1.05486i | 0.0264792 | − | 0.0458633i | ||||
\(530\) | −0.703517 | − | 1.21853i | −0.0305588 | − | 0.0529294i | ||||
\(531\) | 31.5276 | 1.36818 | ||||||||
\(532\) | −11.4812 | + | 16.3480i | −0.497775 | + | 0.708777i | ||||
\(533\) | −1.63987 | −0.0710305 | ||||||||
\(534\) | 1.30538 | + | 2.26099i | 0.0564894 | + | 0.0978426i | ||||
\(535\) | −29.4743 | + | 51.0510i | −1.27429 | + | 2.20713i | ||||
\(536\) | 16.1096 | − | 27.9027i | 0.695829 | − | 1.20521i | ||||
\(537\) | −9.42847 | − | 16.3306i | −0.406869 | − | 0.704717i | ||||
\(538\) | 22.7696 | 0.981666 | ||||||||
\(539\) | 6.89022 | + | 1.23488i | 0.296783 | + | 0.0531900i | ||||
\(540\) | −1.00657 | −0.0433159 | ||||||||
\(541\) | 2.37445 | + | 4.11266i | 0.102085 | + | 0.176817i | 0.912544 | − | 0.408979i | \(-0.134115\pi\) |
−0.810458 | + | 0.585796i | \(0.800782\pi\) | |||||||
\(542\) | 2.58487 | − | 4.47713i | 0.111030 | − | 0.192309i | ||||
\(543\) | 11.4747 | − | 19.8747i | 0.492426 | − | 0.852906i | ||||
\(544\) | −8.71882 | − | 15.1014i | −0.373816 | − | 0.647469i | ||||
\(545\) | −0.906419 | −0.0388267 | ||||||||
\(546\) | 3.25749 | − | 4.63831i | 0.139408 | − | 0.198501i | ||||
\(547\) | 42.2663 | 1.80718 | 0.903589 | − | 0.428401i | \(-0.140923\pi\) | ||||
0.903589 | + | 0.428401i | \(0.140923\pi\) | |||||||
\(548\) | −3.52038 | − | 6.09748i | −0.150383 | − | 0.260471i | ||||
\(549\) | −6.22026 | + | 10.7738i | −0.265474 | + | 0.459814i | ||||
\(550\) | 5.93019 | − | 10.2714i | 0.252864 | − | 0.437974i | ||||
\(551\) | 20.4245 | + | 35.3763i | 0.870113 | + | 1.50708i | ||||
\(552\) | −32.4410 | −1.38078 | ||||||||
\(553\) | −25.5401 | − | 2.27059i | −1.08608 | − | 0.0965551i | ||||
\(554\) | −6.64275 | −0.282223 | ||||||||
\(555\) | −47.3719 | − | 82.0505i | −2.01082 | − | 3.48285i | ||||
\(556\) | −2.16514 | + | 3.75014i | −0.0918226 | + | 0.159041i | ||||
\(557\) | −8.57758 | + | 14.8568i | −0.363444 | + | 0.629503i | −0.988525 | − | 0.151057i | \(-0.951732\pi\) |
0.625081 | + | 0.780559i | \(0.285066\pi\) | |||||||
\(558\) | 3.49671 | + | 6.05647i | 0.148027 | + | 0.256391i | ||||
\(559\) | 3.16556 | 0.133889 | ||||||||
\(560\) | 0.185763 | + | 0.399834i | 0.00784991 | + | 0.0168961i | ||||
\(561\) | 7.57624 | 0.319869 | ||||||||
\(562\) | −1.37280 | − | 2.37776i | −0.0579080 | − | 0.100300i | ||||
\(563\) | 17.3190 | − | 29.9974i | 0.729910 | − | 1.26424i | −0.227011 | − | 0.973892i | \(-0.572895\pi\) |
0.956921 | − | 0.290349i | \(-0.0937714\pi\) | |||||||
\(564\) | −12.0167 | + | 20.8136i | −0.505996 | + | 0.876411i | ||||
\(565\) | −17.6333 | − | 30.5417i | −0.741838 | − | 1.28490i | ||||
\(566\) | 25.6540 | 1.07832 | ||||||||
\(567\) | 9.77247 | + | 21.0341i | 0.410405 | + | 0.883351i | ||||
\(568\) | −40.1681 | −1.68542 | ||||||||
\(569\) | 11.7736 | + | 20.3924i | 0.493573 | + | 0.854894i | 0.999973 | − | 0.00740537i | \(-0.00235722\pi\) |
−0.506400 | + | 0.862299i | \(0.669024\pi\) | |||||||
\(570\) | −28.0587 | + | 48.5991i | −1.17525 | + | 2.03559i | ||||
\(571\) | 9.22389 | − | 15.9763i | 0.386008 | − | 0.668585i | −0.605901 | − | 0.795540i | \(-0.707187\pi\) |
0.991908 | + | 0.126955i | \(0.0405204\pi\) | |||||||
\(572\) | −0.622340 | − | 1.07792i | −0.0260213 | − | 0.0450703i | ||||
\(573\) | 12.7737 | 0.533627 | ||||||||
\(574\) | −3.75589 | − | 0.333910i | −0.156768 | − | 0.0139371i | ||||
\(575\) | 63.6915 | 2.65612 | ||||||||
\(576\) | −7.46464 | − | 12.9291i | −0.311027 | − | 0.538714i | ||||
\(577\) | 11.9935 | − | 20.7734i | 0.499298 | − | 0.864809i | −0.500702 | − | 0.865620i | \(-0.666925\pi\) |
1.00000 | 0.000810545i | \(0.000258004\pi\) | ||||||||
\(578\) | −3.28215 | + | 5.68485i | −0.136519 | + | 0.236459i | ||||
\(579\) | 25.9989 | + | 45.0314i | 1.08048 | + | 1.87144i | ||||
\(580\) | 36.1927 | 1.50282 | ||||||||
\(581\) | −7.52803 | + | 10.7191i | −0.312315 | + | 0.444703i | ||||
\(582\) | 15.6065 | 0.646912 | ||||||||
\(583\) | −0.187459 | − | 0.324688i | −0.00776376 | − | 0.0134472i | ||||
\(584\) | 7.68283 | − | 13.3071i | 0.317918 | − | 0.550650i | ||||
\(585\) | −6.64134 | + | 11.5031i | −0.274586 | + | 0.475597i | ||||
\(586\) | 12.5772 | + | 21.7843i | 0.519558 | + | 0.899901i | ||||
\(587\) | 20.2547 | 0.836000 | 0.418000 | − | 0.908447i | \(-0.362731\pi\) | ||||
0.418000 | + | 0.908447i | \(0.362731\pi\) | |||||||
\(588\) | −13.8510 | + | 16.4132i | −0.571204 | + | 0.676867i | ||||
\(589\) | −15.8695 | −0.653890 | ||||||||
\(590\) | −19.2329 | − | 33.3124i | −0.791808 | − | 1.37145i | ||||
\(591\) | −3.20151 | + | 5.54519i | −0.131693 | + | 0.228098i | ||||
\(592\) | −0.171742 | + | 0.297466i | −0.00705856 | + | 0.0122258i | ||||
\(593\) | −20.3398 | − | 35.2296i | −0.835256 | − | 1.44671i | −0.893822 | − | 0.448422i | \(-0.851986\pi\) |
0.0585666 | − | 0.998284i | \(-0.481347\pi\) | |||||||
\(594\) | 0.162760 | 0.00667814 | ||||||||
\(595\) | −20.1817 | + | 28.7366i | −0.827370 | + | 1.17808i | ||||
\(596\) | −14.5459 | −0.595824 | ||||||||
\(597\) | −4.11155 | − | 7.12141i | −0.168274 | − | 0.291460i | ||||
\(598\) | −2.02807 | + | 3.51273i | −0.0829341 | + | 0.143646i | ||||
\(599\) | 10.2146 | − | 17.6923i | 0.417359 | − | 0.722886i | −0.578314 | − | 0.815814i | \(-0.696289\pi\) |
0.995673 | + | 0.0929277i | \(0.0296226\pi\) | |||||||
\(600\) | 47.4295 | + | 82.1503i | 1.93630 | + | 3.35377i | ||||
\(601\) | −14.7102 | −0.600042 | −0.300021 | − | 0.953933i | \(-0.596994\pi\) | ||||
−0.300021 | + | 0.953933i | \(0.596994\pi\) | |||||||
\(602\) | 7.25029 | + | 0.644571i | 0.295500 | + | 0.0262708i | ||||
\(603\) | −35.1448 | −1.43120 | ||||||||
\(604\) | 12.6326 | + | 21.8803i | 0.514013 | + | 0.890297i | ||||
\(605\) | 2.15910 | − | 3.73967i | 0.0877800 | − | 0.152039i | ||||
\(606\) | 5.08730 | − | 8.81146i | 0.206657 | − | 0.357941i | ||||
\(607\) | 0.814745 | + | 1.41118i | 0.0330695 | + | 0.0572780i | 0.882086 | − | 0.471088i | \(-0.156138\pi\) |
−0.849017 | + | 0.528366i | \(0.822805\pi\) | |||||||
\(608\) | 34.4163 | 1.39576 | ||||||||
\(609\) | 18.5036 | + | 39.8269i | 0.749803 | + | 1.61387i | ||||
\(610\) | 15.1783 | 0.614552 | ||||||||
\(611\) | 3.91671 | + | 6.78394i | 0.158453 | + | 0.274449i | ||||
\(612\) | −5.88378 | + | 10.1910i | −0.237838 | + | 0.411947i | ||||
\(613\) | 1.02097 | − | 1.76838i | 0.0412367 | − | 0.0714241i | −0.844670 | − | 0.535287i | \(-0.820204\pi\) |
0.885907 | + | 0.463863i | \(0.153537\pi\) | |||||||
\(614\) | −0.726618 | − | 1.25854i | −0.0293239 | − | 0.0507905i | ||||
\(615\) | 17.4550 | 0.703853 | ||||||||
\(616\) | −3.14359 | − | 6.76621i | −0.126659 | − | 0.272619i | ||||
\(617\) | −16.9937 | −0.684140 | −0.342070 | − | 0.939674i | \(-0.611128\pi\) | ||||
−0.342070 | + | 0.939674i | \(0.611128\pi\) | |||||||
\(618\) | −17.0572 | − | 29.5439i | −0.686141 | − | 1.18843i | ||||
\(619\) | 8.62453 | − | 14.9381i | 0.346649 | − | 0.600414i | −0.639003 | − | 0.769204i | \(-0.720653\pi\) |
0.985652 | + | 0.168790i | \(0.0539861\pi\) | |||||||
\(620\) | −7.03026 | + | 12.1768i | −0.282342 | + | 0.489031i | ||||
\(621\) | 0.437020 | + | 0.756942i | 0.0175370 | + | 0.0303750i | ||||
\(622\) | −25.6410 | −1.02811 | ||||||||
\(623\) | −3.21169 | − | 0.285528i | −0.128674 | − | 0.0114395i | ||||
\(624\) | 0.0951209 | 0.00380788 | ||||||||
\(625\) | −46.5014 | − | 80.5428i | −1.86006 | − | 3.22171i | ||||
\(626\) | 14.3912 | − | 24.9264i | 0.575190 | − | 0.996258i | ||||
\(627\) | −7.47652 | + | 12.9497i | −0.298583 | + | 0.517162i | ||||
\(628\) | −1.15617 | − | 2.00254i | −0.0461362 | − | 0.0799102i | ||||
\(629\) | −27.3580 | −1.09084 | ||||||||
\(630\) | −17.5534 | + | 24.9941i | −0.699343 | + | 0.995789i | ||||
\(631\) | 33.8602 | 1.34795 | 0.673976 | − | 0.738753i | \(-0.264585\pi\) | ||||
0.673976 | + | 0.738753i | \(0.264585\pi\) | |||||||
\(632\) | 13.6644 | + | 23.6674i | 0.543540 | + | 0.941439i | ||||
\(633\) | −16.7488 | + | 29.0098i | −0.665707 | + | 1.15304i | ||||
\(634\) | −6.28502 | + | 10.8860i | −0.249610 | + | 0.432337i | ||||
\(635\) | −17.0291 | − | 29.4952i | −0.675777 | − | 1.17048i | ||||
\(636\) | 1.15028 | 0.0456114 | ||||||||
\(637\) | 2.37567 | + | 6.58454i | 0.0941275 | + | 0.260889i | ||||
\(638\) | −5.85228 | −0.231694 | ||||||||
\(639\) | 21.9077 | + | 37.9452i | 0.866655 | + | 1.50109i | ||||
\(640\) | 15.3914 | − | 26.6587i | 0.608399 | − | 1.05378i | ||||
\(641\) | 18.8702 | − | 32.6842i | 0.745329 | − | 1.29095i | −0.204711 | − | 0.978822i | \(-0.565626\pi\) |
0.950041 | − | 0.312126i | \(-0.101041\pi\) | |||||||
\(642\) | 14.6222 | + | 25.3265i | 0.577094 | + | 0.999556i | ||||
\(643\) | −12.5479 | −0.494841 | −0.247420 | − | 0.968908i | \(-0.579583\pi\) | ||||
−0.247420 | + | 0.968908i | \(0.579583\pi\) | |||||||
\(644\) | 8.83315 | − | 12.5774i | 0.348075 | − | 0.495621i | ||||
\(645\) | −33.6947 | −1.32673 | ||||||||
\(646\) | 8.10219 | + | 14.0334i | 0.318776 | + | 0.552137i | ||||
\(647\) | −6.28305 | + | 10.8826i | −0.247012 | + | 0.427838i | −0.962695 | − | 0.270587i | \(-0.912782\pi\) |
0.715683 | + | 0.698425i | \(0.246115\pi\) | |||||||
\(648\) | 12.3601 | − | 21.4084i | 0.485552 | − | 0.841002i | ||||
\(649\) | −5.12480 | − | 8.87642i | −0.201166 | − | 0.348430i | ||||
\(650\) | 11.8604 | 0.465202 | ||||||||
\(651\) | −16.9937 | − | 1.51079i | −0.666036 | − | 0.0592125i | ||||
\(652\) | 0.969485 | 0.0379680 | ||||||||
\(653\) | −4.31018 | − | 7.46545i | −0.168670 | − | 0.292146i | 0.769282 | − | 0.638909i | \(-0.220614\pi\) |
−0.937953 | + | 0.346764i | \(0.887281\pi\) | |||||||
\(654\) | −0.224838 | + | 0.389430i | −0.00879185 | + | 0.0152279i | ||||
\(655\) | 37.8342 | − | 65.5307i | 1.47830 | − | 2.56050i | ||||
\(656\) | −0.0316407 | − | 0.0548033i | −0.00123536 | − | 0.00213971i | ||||
\(657\) | −16.7609 | −0.653904 | ||||||||
\(658\) | 7.58935 | + | 16.3352i | 0.295864 | + | 0.636813i | ||||
\(659\) | −26.1704 | −1.01946 | −0.509728 | − | 0.860336i | \(-0.670254\pi\) | ||||
−0.509728 | + | 0.860336i | \(0.670254\pi\) | |||||||
\(660\) | 6.62428 | + | 11.4736i | 0.257850 | + | 0.446609i | ||||
\(661\) | 10.1422 | − | 17.5667i | 0.394484 | − | 0.683266i | −0.598551 | − | 0.801085i | \(-0.704257\pi\) |
0.993035 | + | 0.117818i | \(0.0375900\pi\) | |||||||
\(662\) | 2.91708 | − | 5.05254i | 0.113376 | − | 0.196372i | ||||
\(663\) | 3.78812 | + | 6.56122i | 0.147118 | + | 0.254816i | ||||
\(664\) | 13.9608 | 0.541783 | ||||||||
\(665\) | −29.2020 | − | 62.8540i | −1.13240 | − | 2.43737i | ||||
\(666\) | −23.7951 | −0.922042 | ||||||||
\(667\) | −15.7137 | − | 27.2169i | −0.608437 | − | 1.05384i | ||||
\(668\) | −3.00804 | + | 5.21008i | −0.116385 | + | 0.201584i | ||||
\(669\) | 21.9389 | − | 37.9993i | 0.848207 | − | 1.46914i | ||||
\(670\) | 21.4396 | + | 37.1344i | 0.828283 | + | 1.43463i | ||||
\(671\) | 4.04441 | 0.156133 | ||||||||
\(672\) | 36.8544 | + | 3.27646i | 1.42169 | + | 0.126392i | ||||
\(673\) | 15.3876 | 0.593150 | 0.296575 | − | 0.955010i | \(-0.404156\pi\) | ||||
0.296575 | + | 0.955010i | \(0.404156\pi\) | |||||||
\(674\) | 2.84013 | + | 4.91925i | 0.109398 | + | 0.189483i | ||||
\(675\) | 1.27787 | − | 2.21334i | 0.0491852 | − | 0.0851913i | ||||
\(676\) | 0.622340 | − | 1.07792i | 0.0239362 | − | 0.0414586i | ||||
\(677\) | 1.96267 | + | 3.39944i | 0.0754314 | + | 0.130651i | 0.901274 | − | 0.433250i | \(-0.142633\pi\) |
−0.825842 | + | 0.563901i | \(0.809300\pi\) | |||||||
\(678\) | −17.4958 | −0.671922 | ||||||||
\(679\) | −11.0775 | + | 15.7732i | −0.425116 | + | 0.605319i | ||||
\(680\) | 37.4271 | 1.43526 | ||||||||
\(681\) | −6.14727 | − | 10.6474i | −0.235564 | − | 0.408009i | ||||
\(682\) | 1.13678 | − | 1.96896i | 0.0435295 | − | 0.0753954i | ||||
\(683\) | 22.3226 | − | 38.6640i | 0.854152 | − | 1.47944i | −0.0232767 | − | 0.999729i | \(-0.507410\pi\) |
0.877429 | − | 0.479706i | \(-0.159257\pi\) | |||||||
\(684\) | −11.6127 | − | 20.1137i | −0.444022 | − | 0.769068i | ||||
\(685\) | 24.4267 | 0.933296 | ||||||||
\(686\) | 4.10041 | + | 15.5647i | 0.156554 | + | 0.594265i | ||||
\(687\) | 38.9066 | 1.48438 | ||||||||
\(688\) | 0.0610785 | + | 0.105791i | 0.00232860 | + | 0.00403325i | ||||
\(689\) | 0.187459 | − | 0.324688i | 0.00714162 | − | 0.0123696i | ||||
\(690\) | 21.5871 | − | 37.3900i | 0.821808 | − | 1.42341i | ||||
\(691\) | 10.6370 | + | 18.4238i | 0.404649 | + | 0.700873i | 0.994281 | − | 0.106800i | \(-0.0340604\pi\) |
−0.589632 | + | 0.807672i | \(0.700727\pi\) | |||||||
\(692\) | 30.3777 | 1.15479 | ||||||||
\(693\) | −4.67727 | + | 6.65992i | −0.177675 | + | 0.252989i | ||||
\(694\) | −20.6899 | −0.785378 | ||||||||
\(695\) | −7.51159 | − | 13.0105i | −0.284931 | − | 0.493515i | ||||
\(696\) | 23.4032 | − | 40.5355i | 0.887096 | − | 1.53650i | ||||
\(697\) | 2.52014 | − | 4.36501i | 0.0954570 | − | 0.165336i | ||||
\(698\) | 12.1465 | + | 21.0384i | 0.459752 | + | 0.796314i | ||||
\(699\) | 8.64387 | 0.326941 | ||||||||
\(700\) | −44.7642 | − | 3.97966i | −1.69193 | − | 0.150417i | ||||
\(701\) | 4.24150 | 0.160199 | 0.0800996 | − | 0.996787i | \(-0.474476\pi\) | ||||
0.0800996 | + | 0.996787i | \(0.474476\pi\) | |||||||
\(702\) | 0.0813802 | + | 0.140955i | 0.00307150 | + | 0.00531999i | ||||
\(703\) | 26.9980 | − | 46.7618i | 1.01825 | − | 1.76366i | ||||
\(704\) | −2.42676 | + | 4.20326i | −0.0914618 | + | 0.158416i | ||||
\(705\) | −41.6900 | − | 72.2092i | −1.57014 | − | 2.71956i | ||||
\(706\) | −6.43290 | −0.242105 | ||||||||
\(707\) | 5.29459 | + | 11.3960i | 0.199123 | + | 0.428591i | ||||
\(708\) | 31.4466 | 1.18183 | ||||||||
\(709\) | 7.79957 | + | 13.5092i | 0.292919 | + | 0.507350i | 0.974499 | − | 0.224393i | \(-0.0720401\pi\) |
−0.681580 | + | 0.731744i | \(0.738707\pi\) | |||||||
\(710\) | 26.7290 | − | 46.2959i | 1.00312 | − | 1.73746i | ||||
\(711\) | 14.9051 | − | 25.8164i | 0.558986 | − | 0.968192i | ||||
\(712\) | 1.71831 | + | 2.97620i | 0.0643964 | + | 0.111538i | ||||
\(713\) | 12.2093 | 0.457240 | ||||||||
\(714\) | 7.34019 | + | 15.7989i | 0.274700 | + | 0.591260i | ||||
\(715\) | 4.31820 | 0.161492 | ||||||||
\(716\) | −4.76092 | − | 8.24616i | −0.177924 | − | 0.308173i | ||||
\(717\) | −17.7434 | + | 30.7326i | −0.662641 | + | 1.14773i | ||||
\(718\) | 9.10386 | − | 15.7683i | 0.339753 | − | 0.588469i | ||||
\(719\) | 12.6112 | + | 21.8432i | 0.470318 | + | 0.814614i | 0.999424 | − | 0.0339416i | \(-0.0108060\pi\) |
−0.529106 | + | 0.848556i | \(0.677473\pi\) | |||||||
\(720\) | −0.512571 | −0.0191024 | ||||||||
\(721\) | 41.9666 | + | 3.73095i | 1.56292 | + | 0.138948i | ||||
\(722\) | −15.4695 | −0.575714 | ||||||||
\(723\) | 12.8288 | + | 22.2201i | 0.477108 | + | 0.826375i | ||||
\(724\) | 5.79416 | − | 10.0358i | 0.215338 | − | 0.372977i | ||||
\(725\) | −45.9476 | + | 79.5836i | −1.70645 | + | 2.95566i | ||||
\(726\) | −1.07113 | − | 1.85526i | −0.0397535 | − | 0.0688550i | ||||
\(727\) | 2.90577 | 0.107769 | 0.0538844 | − | 0.998547i | \(-0.482840\pi\) | ||||
0.0538844 | + | 0.998547i | \(0.482840\pi\) | |||||||
\(728\) | 4.28792 | − | 6.10553i | 0.158921 | − | 0.226286i | ||||
\(729\) | −28.3498 | −1.04999 | ||||||||
\(730\) | 10.2247 | + | 17.7098i | 0.378435 | + | 0.655468i | ||||
\(731\) | −4.86481 | + | 8.42610i | −0.179932 | + | 0.311651i | ||||
\(732\) | −6.20428 | + | 10.7461i | −0.229317 | + | 0.397188i | ||||
\(733\) | −8.32294 | − | 14.4158i | −0.307415 | − | 0.532458i | 0.670381 | − | 0.742017i | \(-0.266131\pi\) |
−0.977796 | + | 0.209559i | \(0.932797\pi\) | |||||||
\(734\) | −9.08920 | −0.335488 | ||||||||
\(735\) | −25.2870 | − | 70.0869i | −0.932725 | − | 2.58519i | ||||
\(736\) | −26.4783 | −0.976004 | ||||||||
\(737\) | 5.71278 | + | 9.89483i | 0.210433 | + | 0.364481i | ||||
\(738\) | 2.19193 | − | 3.79654i | 0.0806861 | − | 0.139752i | ||||
\(739\) | −6.79770 | + | 11.7740i | −0.250057 | + | 0.433112i | −0.963541 | − | 0.267559i | \(-0.913783\pi\) |
0.713484 | + | 0.700672i | \(0.247116\pi\) | |||||||
\(740\) | −23.9205 | − | 41.4315i | −0.879335 | − | 1.52305i | ||||
\(741\) | −14.9530 | −0.549314 | ||||||||
\(742\) | 0.495463 | − | 0.705485i | 0.0181890 | − | 0.0258992i | ||||
\(743\) | −32.0224 | −1.17479 | −0.587394 | − | 0.809301i | \(-0.699846\pi\) | ||||
−0.587394 | + | 0.809301i | \(0.699846\pi\) | |||||||
\(744\) | 9.09193 | + | 15.7477i | 0.333326 | + | 0.577338i | ||||
\(745\) | 25.2323 | − | 43.7036i | 0.924439 | − | 1.60118i | ||||
\(746\) | −10.5824 | + | 18.3292i | −0.387448 | + | 0.671080i | ||||
\(747\) | −7.61421 | − | 13.1882i | −0.278589 | − | 0.482531i | ||||
\(748\) | 3.82563 | 0.139879 | ||||||||
\(749\) | −35.9758 | − | 3.19835i | −1.31453 | − | 0.116865i | ||||
\(750\) | −79.9900 | −2.92082 | ||||||||
\(751\) | −24.7409 | − | 42.8525i | −0.902808 | − | 1.56371i | −0.823833 | − | 0.566832i | \(-0.808169\pi\) |
−0.0789741 | − | 0.996877i | \(-0.525164\pi\) | |||||||
\(752\) | −0.151143 | + | 0.261788i | −0.00551163 | + | 0.00954642i | ||||
\(753\) | −25.9181 | + | 44.8915i | −0.944509 | + | 1.63594i | ||||
\(754\) | −2.92614 | − | 5.06823i | −0.106564 | − | 0.184574i | ||||
\(755\) | −87.6533 | −3.19003 | ||||||||
\(756\) | −0.259854 | − | 0.559306i | −0.00945079 | − | 0.0203418i | ||||
\(757\) | 4.26919 | 0.155166 | 0.0775832 | − | 0.996986i | \(-0.475280\pi\) | ||||
0.0775832 | + | 0.996986i | \(0.475280\pi\) | |||||||
\(758\) | 9.64014 | + | 16.6972i | 0.350146 | + | 0.606470i | ||||
\(759\) | 5.75210 | − | 9.96293i | 0.208788 | − | 0.361631i | ||||
\(760\) | −36.9345 | + | 63.9724i | −1.33975 | + | 2.32052i | ||||
\(761\) | 9.85280 | + | 17.0656i | 0.357164 | + | 0.618626i | 0.987486 | − | 0.157708i | \(-0.0504104\pi\) |
−0.630322 | + | 0.776334i | \(0.717077\pi\) | |||||||
\(762\) | −16.8963 | −0.612087 | ||||||||
\(763\) | −0.233999 | − | 0.503656i | −0.00847133 | − | 0.0182336i | ||||
\(764\) | 6.45008 | 0.233356 | ||||||||
\(765\) | −20.4128 | − | 35.3559i | −0.738025 | − | 1.27830i | ||||
\(766\) | −13.6383 | + | 23.6222i | −0.492772 | + | 0.853506i | ||||
\(767\) | 5.12480 | − | 8.87642i | 0.185046 | − | 0.320509i | ||||
\(768\) | −19.5994 | − | 33.9471i | −0.707231 | − | 1.22496i | ||||
\(769\) | 32.8588 | 1.18492 | 0.592459 | − | 0.805601i | \(-0.298157\pi\) | ||||
0.592459 | + | 0.805601i | \(0.298157\pi\) | |||||||
\(770\) | 9.89027 | + | 0.879272i | 0.356420 | + | 0.0316868i | ||||
\(771\) | 44.0075 | 1.58489 | ||||||||
\(772\) | 13.1282 | + | 22.7387i | 0.472494 | + | 0.818384i | ||||
\(773\) | −26.7680 | + | 46.3635i | −0.962777 | + | 1.66758i | −0.247305 | + | 0.968938i | \(0.579545\pi\) |
−0.715472 | + | 0.698641i | \(0.753788\pi\) | |||||||
\(774\) | −4.23125 | + | 7.32874i | −0.152089 | + | 0.263426i | ||||
\(775\) | −17.8502 | − | 30.9175i | −0.641199 | − | 1.11059i | ||||
\(776\) | 20.5433 | 0.737462 | ||||||||
\(777\) | 33.3624 | − | 47.5044i | 1.19687 | − | 1.70421i | ||||
\(778\) | 0.625391 | 0.0224213 | ||||||||
\(779\) | 4.97393 | + | 8.61511i | 0.178210 | + | 0.308668i | ||||
\(780\) | −6.62428 | + | 11.4736i | −0.237187 | + | 0.410821i | ||||
\(781\) | 7.12219 | − | 12.3360i | 0.254852 | − | 0.441417i | ||||
\(782\) | −6.23346 | − | 10.7967i | −0.222908 | − | 0.386088i | ||||
\(783\) | −1.26108 | −0.0450674 | ||||||||
\(784\) | −0.174213 | + | 0.206440i | −0.00622191 | + | 0.00737286i | ||||
\(785\) | 8.02226 | 0.286327 | ||||||||
\(786\) | −18.7696 | − | 32.5099i | −0.669489 | − | 1.15959i | ||||
\(787\) | 1.30773 | − | 2.26506i | 0.0466156 | − | 0.0807406i | −0.841776 | − | 0.539827i | \(-0.818490\pi\) |
0.888392 | + | 0.459086i | \(0.151823\pi\) | |||||||
\(788\) | −1.61661 | + | 2.80005i | −0.0575894 | + | 0.0997477i | ||||
\(789\) | 30.0242 | + | 52.0035i | 1.06889 | + | 1.85137i | ||||
\(790\) | −36.3707 | −1.29401 | ||||||||
\(791\) | 12.4185 | − | 17.6826i | 0.441551 | − | 0.628721i | ||||
\(792\) | 8.67402 | 0.308218 | ||||||||
\(793\) | 2.02221 | + | 3.50256i | 0.0718106 | + | 0.124380i | ||||
\(794\) | 2.00559 | − | 3.47379i | 0.0711758 | − | 0.123280i | ||||
\(795\) | −1.99534 | + | 3.45603i | −0.0707675 | + | 0.122573i | ||||
\(796\) | −2.07613 | − | 3.59597i | −0.0735866 | − | 0.127456i | ||||
\(797\) | −13.2158 | −0.468126 | −0.234063 | − | 0.972221i | \(-0.575202\pi\) | ||||
−0.234063 | + | 0.972221i | \(0.575202\pi\) | |||||||
\(798\) | −34.2479 | − | 3.04474i | −1.21236 | − | 0.107783i | ||||
\(799\) | −24.0767 | −0.851772 | ||||||||
\(800\) | 38.7120 | + | 67.0511i | 1.36868 | + | 2.37062i | ||||
\(801\) | 1.87434 | − | 3.24644i | 0.0662264 | − | 0.114707i | ||||
\(802\) | 8.23614 | − | 14.2654i | 0.290828 | − | 0.503729i | ||||
\(803\) | 2.72448 | + | 4.71894i | 0.0961449 | + | 0.166528i | ||||
\(804\) | −35.0545 | −1.23628 | ||||||||
\(805\) | 22.4667 | + | 48.3571i | 0.791847 | + | 1.70436i | ||||
\(806\) | 2.27356 | 0.0800827 | ||||||||
\(807\) | −32.2899 | − | 55.9278i | −1.13666 | − | 1.96875i | ||||
\(808\) | 6.69655 | − | 11.5988i | 0.235584 | − | 0.408043i | ||||
\(809\) | −9.40866 | + | 16.2963i | −0.330791 | + | 0.572946i | −0.982667 | − | 0.185379i | \(-0.940649\pi\) |
0.651876 | + | 0.758325i | \(0.273982\pi\) | |||||||
\(810\) | 16.4496 | + | 28.4915i | 0.577979 | + | 1.00109i | ||||
\(811\) | 6.22115 | 0.218454 | 0.109227 | − | 0.994017i | \(-0.465162\pi\) | ||||
0.109227 | + | 0.994017i | \(0.465162\pi\) | |||||||
\(812\) | 9.34342 | + | 20.1106i | 0.327890 | + | 0.705745i | ||||
\(813\) | −14.6626 | −0.514241 | ||||||||
\(814\) | 3.86790 | + | 6.69939i | 0.135570 | + | 0.234814i | ||||
\(815\) | −1.68173 | + | 2.91284i | −0.0589085 | + | 0.102032i | ||||
\(816\) | −0.146181 | + | 0.253193i | −0.00511737 | + | 0.00886354i | ||||
\(817\) | −9.60156 | − | 16.6304i | −0.335916 | − | 0.581824i | ||||
\(818\) | −10.0868 | −0.352678 | ||||||||
\(819\) | −8.10630 | − | 0.720672i | −0.283257 | − | 0.0251823i | ||||
\(820\) | 8.81392 | 0.307796 | ||||||||
\(821\) | 3.87601 | + | 6.71344i | 0.135274 | + | 0.234301i | 0.925702 | − | 0.378254i | \(-0.123475\pi\) |
−0.790428 | + | 0.612555i | \(0.790142\pi\) | |||||||
\(822\) | 6.05906 | − | 10.4946i | 0.211334 | − | 0.366041i | ||||
\(823\) | −7.49234 | + | 12.9771i | −0.261166 | + | 0.452354i | −0.966552 | − | 0.256470i | \(-0.917440\pi\) |
0.705386 | + | 0.708824i | \(0.250774\pi\) | |||||||
\(824\) | −22.4529 | − | 38.8895i | −0.782182 | − | 1.35478i | ||||
\(825\) | −33.6389 | −1.17115 | ||||||||
\(826\) | 13.5451 | − | 19.2867i | 0.471294 | − | 0.671072i | ||||
\(827\) | 0.496348 | 0.0172597 | 0.00862986 | − | 0.999963i | \(-0.497253\pi\) | ||||
0.00862986 | + | 0.999963i | \(0.497253\pi\) | |||||||
\(828\) | 8.93427 | + | 15.4746i | 0.310487 | + | 0.537780i | ||||
\(829\) | 10.8565 | − | 18.8040i | 0.377062 | − | 0.653091i | −0.613571 | − | 0.789639i | \(-0.710268\pi\) |
0.990633 | + | 0.136548i | \(0.0436009\pi\) | |||||||
\(830\) | −9.28989 | + | 16.0906i | −0.322457 | + | 0.558511i | ||||
\(831\) | 9.42021 | + | 16.3163i | 0.326783 | + | 0.566006i | ||||
\(832\) | −4.85351 | −0.168265 | ||||||||
\(833\) | −21.1777 | − | 3.79551i | −0.733763 | − | 0.131507i | ||||
\(834\) | −7.45302 | −0.258077 | ||||||||
\(835\) | −10.4359 | − | 18.0755i | −0.361148 | − | 0.625527i | ||||
\(836\) | −3.77528 | + | 6.53898i | −0.130571 | + | 0.226155i | ||||
\(837\) | 0.244959 | − | 0.424282i | 0.00846704 | − | 0.0146653i | ||||
\(838\) | −5.23579 | − | 9.06865i | −0.180867 | − | 0.313271i | ||||
\(839\) | −27.3078 | −0.942771 | −0.471386 | − | 0.881927i | \(-0.656246\pi\) | ||||
−0.471386 | + | 0.881927i | \(0.656246\pi\) | |||||||
\(840\) | −45.6413 | + | 64.9882i | −1.57477 | + | 2.24231i | ||||
\(841\) | 16.3440 | 0.563586 | ||||||||
\(842\) | −8.24412 | − | 14.2792i | −0.284111 | − | 0.492095i | ||||
\(843\) | −3.89358 | + | 6.74388i | −0.134102 | + | 0.232272i | ||||
\(844\) | −8.45736 | + | 14.6486i | −0.291114 | + | 0.504225i | ||||
\(845\) | 2.15910 | + | 3.73967i | 0.0742753 | + | 0.128649i | ||||
\(846\) | −20.9411 | −0.719970 | ||||||||
\(847\) | 2.63536 | + | 0.234291i | 0.0905519 | + | 0.00805032i | ||||
\(848\) | 0.0144679 | 0.000496828 | ||||||||
\(849\) | −36.3805 | − | 63.0128i | −1.24857 | − | 2.16260i | ||||
\(850\) | −18.2270 | + | 31.5700i | −0.625180 | + | 1.08284i | ||||
\(851\) | −20.7710 | + | 35.9765i | −0.712021 | + | 1.23326i | ||||
\(852\) | 21.8514 | + | 37.8478i | 0.748617 | + | 1.29664i | ||||
\(853\) | 4.39310 | 0.150417 | 0.0752084 | − | 0.997168i | \(-0.476038\pi\) | ||||
0.0752084 | + | 0.997168i | \(0.476038\pi\) | |||||||
\(854\) | 3.91840 | + | 8.43391i | 0.134085 | + | 0.288603i | ||||
\(855\) | 80.5763 | 2.75565 | ||||||||
\(856\) | 19.2477 | + | 33.3379i | 0.657872 | + | 1.13947i | ||||
\(857\) | 26.8932 | − | 46.5804i | 0.918654 | − | 1.59116i | 0.117193 | − | 0.993109i | \(-0.462610\pi\) |
0.801461 | − | 0.598047i | \(-0.204056\pi\) | |||||||
\(858\) | 1.07113 | − | 1.85526i | 0.0365679 | − | 0.0633374i | ||||
\(859\) | 24.6850 | + | 42.7556i | 0.842240 | + | 1.45880i | 0.887996 | + | 0.459850i | \(0.152097\pi\) |
−0.0457561 | + | 0.998953i | \(0.514570\pi\) | |||||||
\(860\) | −17.0142 | −0.580179 | ||||||||
\(861\) | 4.50614 | + | 9.69895i | 0.153569 | + | 0.330539i | ||||
\(862\) | −7.10029 | −0.241837 | ||||||||
\(863\) | −7.80233 | − | 13.5140i | −0.265595 | − | 0.460023i | 0.702125 | − | 0.712054i | \(-0.252235\pi\) |
−0.967719 | + | 0.252031i | \(0.918902\pi\) | |||||||
\(864\) | −0.531246 | + | 0.920145i | −0.0180734 | + | 0.0313040i | ||||
\(865\) | −52.6950 | + | 91.2704i | −1.79168 | + | 3.10329i | ||||
\(866\) | 12.7838 | + | 22.1422i | 0.434412 | + | 0.752424i | ||||
\(867\) | 18.6179 | 0.632297 | ||||||||
\(868\) | −8.58100 | − | 0.762875i | −0.291258 | − | 0.0258937i | ||||
\(869\) | −9.69132 | −0.328755 | ||||||||
\(870\) | 31.1463 | + | 53.9470i | 1.05596 | + | 1.82897i | ||||
\(871\) | −5.71278 | + | 9.89483i | −0.193570 | + | 0.335273i | ||||
\(872\) | −0.295960 | + | 0.512618i | −0.0100225 | + | 0.0173594i | ||||
\(873\) | −11.2043 | − | 19.4065i | −0.379209 | − | 0.656810i | ||||
\(874\) | 24.6057 | 0.832299 | ||||||||
\(875\) | 56.7769 | − | 80.8441i | 1.91941 | − | 2.73303i | ||||
\(876\) | −16.7178 | −0.564843 | ||||||||
\(877\) | −3.43438 | − | 5.94851i | −0.115971 | − | 0.200867i | 0.802197 | − | 0.597060i | \(-0.203665\pi\) |
−0.918167 | + | 0.396193i | \(0.870331\pi\) | |||||||
\(878\) | 14.3310 | − | 24.8220i | 0.483648 | − | 0.837703i | ||||
\(879\) | 35.6718 | − | 61.7854i | 1.20318 | − | 2.08397i | ||||
\(880\) | 0.0833184 | + | 0.144312i | 0.00280866 | + | 0.00486475i | ||||
\(881\) | 17.1117 | 0.576509 | 0.288255 | − | 0.957554i | \(-0.406925\pi\) | ||||
0.288255 | + | 0.957554i | \(0.406925\pi\) | |||||||
\(882\) | −18.4196 | − | 3.30121i | −0.620222 | − | 0.111157i | ||||
\(883\) | 10.0024 | 0.336606 | 0.168303 | − | 0.985735i | \(-0.446171\pi\) | ||||
0.168303 | + | 0.985735i | \(0.446171\pi\) | |||||||
\(884\) | 1.91282 | + | 3.31310i | 0.0643350 | + | 0.111431i | ||||
\(885\) | −54.5492 | + | 94.4820i | −1.83365 | + | 3.17598i | ||||
\(886\) | 10.9915 | − | 19.0378i | 0.369266 | − | 0.639587i | ||||
\(887\) | 11.4019 | + | 19.7487i | 0.382839 | + | 0.663096i | 0.991467 | − | 0.130360i | \(-0.0416132\pi\) |
−0.608628 | + | 0.793456i | \(0.708280\pi\) | |||||||
\(888\) | −61.8707 | −2.07624 | ||||||||
\(889\) | 11.9930 | − | 17.0767i | 0.402231 | − | 0.572734i | ||||
\(890\) | −4.57365 | −0.153309 | ||||||||
\(891\) | 4.38315 | + | 7.59184i | 0.146841 | + | 0.254336i | ||||
\(892\) | 11.0781 | − | 19.1878i | 0.370922 | − | 0.642455i | ||||
\(893\) | 23.7598 | − | 41.1532i | 0.795091 | − | 1.37714i | ||||
\(894\) | −12.5178 | − | 21.6814i | −0.418657 | − | 0.725135i | ||||
\(895\) | 33.0344 | 1.10422 | ||||||||
\(896\) | 18.7865 | + | 1.67017i | 0.627612 | + | 0.0557965i | ||||
\(897\) | 11.5042 | 0.384114 | ||||||||
\(898\) | −2.00125 | − | 3.46627i | −0.0667826 | − | 0.115671i | ||||
\(899\) | −8.80787 | + | 15.2557i | −0.293759 | + | 0.508805i | ||||
\(900\) | 26.1243 | − | 45.2485i | 0.870809 | − | 1.50828i | ||||
\(901\) | 0.576172 | + | 0.997958i | 0.0191951 | + | 0.0332468i | ||||
\(902\) | −1.42519 | −0.0474538 | ||||||||
\(903\) | −8.69854 | − | 18.7226i | −0.289469 | − | 0.623050i | ||||
\(904\) | −23.0302 | −0.765972 | ||||||||
\(905\) | 20.1018 | + | 34.8174i | 0.668207 | + | 1.15737i | ||||
\(906\) | −21.7425 | + | 37.6590i | −0.722345 | + | 1.25114i | ||||
\(907\) | 23.0726 | − | 39.9630i | 0.766114 | − | 1.32695i | −0.173541 | − | 0.984827i | \(-0.555521\pi\) |
0.939655 | − | 0.342122i | \(-0.111146\pi\) | |||||||
\(908\) | −3.10407 | − | 5.37641i | −0.103012 | − | 0.178423i | ||||
\(909\) | −14.6092 | −0.484557 | ||||||||
\(910\) | 4.18366 | + | 9.00486i | 0.138687 | + | 0.298508i | ||||
\(911\) | −49.7516 | −1.64835 | −0.824173 | − | 0.566338i | \(-0.808360\pi\) | ||||
−0.824173 | + | 0.566338i | \(0.808360\pi\) | |||||||
\(912\) | −0.288514 | − | 0.499721i | −0.00955366 | − | 0.0165474i | ||||
\(913\) | −2.47538 | + | 4.28749i | −0.0819231 | + | 0.141895i | ||||
\(914\) | −1.04998 | + | 1.81862i | −0.0347304 | + | 0.0601548i | ||||
\(915\) | −21.5247 | − | 37.2818i | −0.711583 | − | 1.23250i | ||||
\(916\) | 19.6459 | 0.649120 | ||||||||
\(917\) | 46.1797 | + | 4.10550i | 1.52499 | + | 0.135576i | ||||
\(918\) | −0.500258 | −0.0165110 | ||||||||
\(919\) | −3.91102 | − | 6.77408i | −0.129013 | − | 0.223456i | 0.794282 | − | 0.607550i | \(-0.207847\pi\) |
−0.923294 | + | 0.384093i | \(0.874514\pi\) | |||||||
\(920\) | 28.4157 | − | 49.2175i | 0.936839 | − | 1.62265i | ||||
\(921\) | −2.06086 | + | 3.56952i | −0.0679077 | + | 0.117620i | ||||
\(922\) | −5.93314 | − | 10.2765i | −0.195397 | − | 0.338438i | ||||
\(923\) | 14.2444 | 0.468860 | ||||||||
\(924\) | −4.66525 | + | 6.64281i | −0.153476 | + | 0.218532i | ||||
\(925\) | 121.471 | 3.99394 | ||||||||
\(926\) | −4.66257 | − | 8.07580i | −0.153221 | − | 0.265387i | ||||
\(927\) | −24.4916 | + | 42.4207i | −0.804410 | + | 1.39328i | ||||
\(928\) | 19.1017 | − | 33.0851i | 0.627044 | − | 1.08607i | ||||
\(929\) | 16.8475 | + | 29.1806i | 0.552747 | + | 0.957386i | 0.998075 | + | 0.0620185i | \(0.0197538\pi\) |
−0.445328 | + | 0.895368i | \(0.646913\pi\) | |||||||
\(930\) | −24.2001 | −0.793553 | ||||||||
\(931\) | 27.3864 | − | 32.4525i | 0.897554 | − | 1.06359i | ||||
\(932\) | 4.36474 | 0.142972 | ||||||||
\(933\) | 36.3620 | + | 62.9808i | 1.19044 | + | 2.06190i | ||||
\(934\) | −0.873122 | + | 1.51229i | −0.0285694 | + | 0.0494837i | ||||
\(935\) | −6.63619 | + | 11.4942i | −0.217027 | + | 0.375901i | ||||
\(936\) | 4.33701 | + | 7.51192i | 0.141760 | + | 0.245535i | ||||
\(937\) | 2.95506 | 0.0965376 | 0.0482688 | − | 0.998834i | \(-0.484630\pi\) | ||||
0.0482688 | + | 0.998834i | \(0.484630\pi\) | |||||||
\(938\) | −15.0991 | + | 21.4995i | −0.493005 | + | 0.701985i | ||||
\(939\) | −81.6339 | −2.66402 | ||||||||
\(940\) | −21.0514 | − | 36.4622i | −0.686622 | − | 1.18926i | ||||
\(941\) | −27.2236 | + | 47.1527i | −0.887465 | + | 1.53714i | −0.0446039 | + | 0.999005i | \(0.514203\pi\) |
−0.842862 | + | 0.538131i | \(0.819131\pi\) | |||||||
\(942\) | 1.98993 | − | 3.44665i | 0.0648353 | − | 0.112298i | ||||
\(943\) | −3.82672 | − | 6.62808i | −0.124615 | − | 0.215840i | ||||
\(944\) | 0.395526 | 0.0128733 | ||||||||
\(945\) | 2.13121 | + | 0.189470i | 0.0693282 | + | 0.00616347i | ||||
\(946\) | 2.75116 | 0.0894480 | ||||||||
\(947\) | 8.49825 | + | 14.7194i | 0.276156 | + | 0.478316i | 0.970426 | − | 0.241398i | \(-0.0776060\pi\) |
−0.694270 | + | 0.719715i | \(0.744273\pi\) | |||||||
\(948\) | 14.8668 | − | 25.7501i | 0.482853 | − | 0.836325i | ||||
\(949\) | −2.72448 | + | 4.71894i | −0.0884404 | + | 0.153183i | ||||
\(950\) | −35.9741 | − | 62.3090i | −1.16715 | − | 2.02157i | ||||
\(951\) | 35.6516 | 1.15608 | ||||||||
\(952\) | 9.66209 | + | 20.7966i | 0.313150 | + | 0.674020i | ||||
\(953\) | 51.8965 | 1.68109 | 0.840546 | − | 0.541739i | \(-0.182234\pi\) | ||||
0.840546 | + | 0.541739i | \(0.182234\pi\) | |||||||
\(954\) | 0.501135 | + | 0.867991i | 0.0162248 | + | 0.0281022i | ||||
\(955\) | −11.1887 | + | 19.3794i | −0.362058 | + | 0.627104i | ||||
\(956\) | −8.95958 | + | 15.5185i | −0.289774 | + | 0.501903i | ||||
\(957\) | 8.29923 | + | 14.3747i | 0.268276 | + | 0.464668i | ||||
\(958\) | 12.6006 | 0.407108 | ||||||||
\(959\) | 6.30594 | + | 13.5728i | 0.203629 | + | 0.438289i | ||||
\(960\) | 51.6615 | 1.66737 | ||||||||
\(961\) | 12.0782 | + | 20.9201i | 0.389620 | + | 0.674842i | ||||
\(962\) | −3.86790 | + | 6.69939i | −0.124706 | + | 0.215997i | ||||
\(963\) | 20.9954 | − | 36.3651i | 0.676566 | − | 1.17185i | ||||
\(964\) | 6.47792 | + | 11.2201i | 0.208640 | + | 0.361375i | ||||
\(965\) | −91.0920 | −2.93236 | ||||||||
\(966\) | 26.3488 | + | 2.34249i | 0.847760 | + | 0.0753682i | ||||
\(967\) | −7.32442 | −0.235537 | −0.117769 | − | 0.993041i | \(-0.537574\pi\) | ||||
−0.117769 | + | 0.993041i | \(0.537574\pi\) | |||||||
\(968\) | −1.40996 | − | 2.44213i | −0.0453179 | − | 0.0784929i | ||||
\(969\) | 22.9797 | − | 39.8021i | 0.738216 | − | 1.27863i | ||||
\(970\) | −13.6701 | + | 23.6773i | −0.438920 | + | 0.760232i | ||||
\(971\) | 13.5367 | + | 23.4462i | 0.434413 | + | 0.752426i | 0.997248 | − | 0.0741441i | \(-0.0236225\pi\) |
−0.562834 | + | 0.826570i | \(0.690289\pi\) | |||||||
\(972\) | −27.5950 | −0.885109 | ||||||||
\(973\) | 5.29016 | − | 7.53261i | 0.169595 | − | 0.241484i | ||||
\(974\) | −26.9296 | −0.862879 | ||||||||
\(975\) | −16.8194 | − | 29.1321i | −0.538653 | − | 0.932974i | ||||
\(976\) | −0.0780357 | + | 0.135162i | −0.00249786 | + | 0.00432642i | ||||
\(977\) | 4.26878 | − | 7.39374i | 0.136570 | − | 0.236547i | −0.789626 | − | 0.613589i | \(-0.789725\pi\) |
0.926196 | + | 0.377042i | \(0.123059\pi\) | |||||||
\(978\) | 0.834309 | + | 1.44507i | 0.0266783 | + | 0.0462081i | ||||
\(979\) | −1.21869 | −0.0389496 | ||||||||
\(980\) | −12.7687 | − | 35.3905i | −0.407882 | − | 1.13051i | ||||
\(981\) | 0.645667 | 0.0206146 | ||||||||
\(982\) | −4.45734 | − | 7.72034i | −0.142239 | − | 0.246366i | ||||
\(983\) | −20.1593 | + | 34.9170i | −0.642982 | + | 1.11368i | 0.341781 | + | 0.939780i | \(0.388970\pi\) |
−0.984764 | + | 0.173899i | \(0.944363\pi\) | |||||||
\(984\) | 5.69933 | − | 9.87153i | 0.181688 | − | 0.314693i | ||||
\(985\) | −5.60855 | − | 9.71429i | −0.178703 | − | 0.309523i | ||||
\(986\) | 17.9875 | 0.572839 | ||||||||
\(987\) | 29.3608 | − | 41.8066i | 0.934566 | − | 1.33072i | ||||
\(988\) | −7.55056 | −0.240215 | ||||||||
\(989\) | 7.38702 | + | 12.7947i | 0.234893 | + | 0.406847i | ||||
\(990\) | −5.77193 | + | 9.99728i | −0.183444 | + | 0.317735i | ||||
\(991\) | −12.9624 | + | 22.4515i | −0.411763 | + | 0.713195i | −0.995083 | − | 0.0990480i | \(-0.968420\pi\) |
0.583319 | + | 0.812243i | \(0.301754\pi\) | |||||||
\(992\) | 7.42084 | + | 12.8533i | 0.235612 | + | 0.408092i | ||||
\(993\) | −16.5471 | −0.525106 | ||||||||
\(994\) | 32.6249 | + | 2.90044i | 1.03480 | + | 0.0919964i | ||||
\(995\) | 14.4056 | 0.456687 | ||||||||
\(996\) | −7.59465 | − | 13.1543i | −0.240646 | − | 0.416811i | ||||
\(997\) | 6.66791 | − | 11.5492i | 0.211175 | − | 0.365766i | −0.740908 | − | 0.671607i | \(-0.765604\pi\) |
0.952082 | + | 0.305841i | \(0.0989377\pi\) | |||||||
\(998\) | −16.1539 | + | 27.9794i | −0.511343 | + | 0.885673i | ||||
\(999\) | 0.833475 | + | 1.44362i | 0.0263700 | + | 0.0456742i |
(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 | 1001.2.i.d.144.17 | ✓ | 50 | |
7.2 | even | 3 | inner | 1001.2.i.d.716.17 | yes | 50 | |
7.3 | odd | 6 | 7007.2.a.bi.1.9 | 25 | |||
7.4 | even | 3 | 7007.2.a.bh.1.9 | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1001.2.i.d.144.17 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1001.2.i.d.716.17 | yes | 50 | 7.2 | even | 3 | inner | |
7007.2.a.bh.1.9 | 25 | 7.4 | even | 3 | |||
7007.2.a.bi.1.9 | 25 | 7.3 | odd | 6 |