Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(989,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.989");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 989.6 | ||
Character | \(\chi\) | \(=\) | 1386.989 |
Dual form | 1386.2.ba.b.1187.6 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.42385 | − | 0.822059i | −0.636764 | − | 0.367636i | 0.146603 | − | 0.989195i | \(-0.453166\pi\) |
−0.783367 | + | 0.621559i | \(0.786499\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.58759 | − | 0.551706i | 0.978017 | − | 0.208525i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.42385 | + | 0.822059i | −0.450260 | + | 0.259958i | ||||
\(11\) | −2.53893 | − | 2.13397i | −0.765516 | − | 0.643417i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.29335i | 0.358711i | 0.983784 | + | 0.179355i | \(0.0574012\pi\) | ||||
−0.983784 | + | 0.179355i | \(0.942599\pi\) | |||||||
\(14\) | 0.816004 | − | 2.51677i | 0.218086 | − | 0.672635i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.68534 | − | 2.91910i | −0.408756 | − | 0.707986i | 0.585995 | − | 0.810315i | \(-0.300704\pi\) |
−0.994751 | + | 0.102329i | \(0.967371\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.340140 | − | 0.196380i | −0.0780335 | − | 0.0450527i | 0.460476 | − | 0.887672i | \(-0.347679\pi\) |
−0.538509 | + | 0.842620i | \(0.681012\pi\) | |||||||
\(20\) | 1.64412i | 0.367636i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.11754 | + | 1.13179i | −0.664661 | + | 0.241299i | ||||
\(23\) | −0.455476 | − | 0.262969i | −0.0949733 | − | 0.0548329i | 0.451761 | − | 0.892139i | \(-0.350796\pi\) |
−0.546734 | + | 0.837306i | \(0.684129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.14844 | − | 1.98915i | −0.229687 | − | 0.397830i | ||||
\(26\) | 1.12007 | + | 0.646675i | 0.219665 | + | 0.126823i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.77159 | − | 1.96507i | −0.334798 | − | 0.371362i | ||||
\(29\) | 1.33002 | 0.246979 | 0.123490 | − | 0.992346i | \(-0.460591\pi\) | ||||
0.123490 | + | 0.992346i | \(0.460591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.86951 | − | 4.97013i | −0.515379 | − | 0.892662i | −0.999841 | − | 0.0178500i | \(-0.994318\pi\) |
0.484462 | − | 0.874812i | \(-0.339015\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.37069 | −0.578068 | ||||||||
\(35\) | −4.13787 | − | 1.34161i | −0.699428 | − | 0.226773i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50973 | − | 2.61493i | 0.248198 | − | 0.429892i | −0.714828 | − | 0.699300i | \(-0.753495\pi\) |
0.963026 | + | 0.269409i | \(0.0868283\pi\) | |||||||
\(38\) | −0.340140 | + | 0.196380i | −0.0551780 | + | 0.0318570i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.42385 | + | 0.822059i | 0.225130 | + | 0.129979i | ||||
\(41\) | −10.9253 | −1.70624 | −0.853120 | − | 0.521714i | \(-0.825293\pi\) | ||||
−0.853120 | + | 0.521714i | \(0.825293\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5847i | 1.61416i | 0.590444 | + | 0.807079i | \(0.298953\pi\) | ||||
−0.590444 | + | 0.807079i | \(0.701047\pi\) | |||||||
\(44\) | −0.578609 | + | 3.26576i | −0.0872286 | + | 0.492332i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.455476 | + | 0.262969i | −0.0671563 | + | 0.0387727i | ||||
\(47\) | −4.48768 | − | 2.59096i | −0.654595 | − | 0.377931i | 0.135619 | − | 0.990761i | \(-0.456698\pi\) |
−0.790215 | + | 0.612830i | \(0.790031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.39124 | − | 2.85518i | 0.913034 | − | 0.407882i | ||||
\(50\) | −2.29687 | −0.324827 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.12007 | − | 0.646675i | 0.155326 | − | 0.0896777i | ||||
\(53\) | −1.43915 | + | 0.830895i | −0.197683 | + | 0.114132i | −0.595574 | − | 0.803300i | \(-0.703075\pi\) |
0.397891 | + | 0.917433i | \(0.369742\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.86080 | + | 5.12560i | 0.250910 | + | 0.691136i | ||||
\(56\) | −2.58759 | + | 0.551706i | −0.345781 | + | 0.0737248i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.665012 | − | 1.15183i | 0.0873203 | − | 0.151243i | ||||
\(59\) | 8.26233 | − | 4.77026i | 1.07566 | − | 0.621035i | 0.145941 | − | 0.989293i | \(-0.453379\pi\) |
0.929724 | + | 0.368258i | \(0.120046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.32010 | − | 1.91686i | −0.425095 | − | 0.245429i | 0.272160 | − | 0.962252i | \(-0.412262\pi\) |
−0.697255 | + | 0.716823i | \(0.745595\pi\) | |||||||
\(62\) | −5.73902 | −0.728856 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.06321 | − | 1.84153i | 0.131875 | − | 0.228414i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.80137 | − | 11.7803i | −0.830919 | − | 1.43919i | −0.897310 | − | 0.441401i | \(-0.854482\pi\) |
0.0663907 | − | 0.997794i | \(-0.478852\pi\) | |||||||
\(68\) | −1.68534 | + | 2.91910i | −0.204378 | + | 0.353993i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.23080 | + | 2.91270i | −0.386155 | + | 0.348134i | ||||
\(71\) | 1.62169i | 0.192459i | 0.995359 | + | 0.0962296i | \(0.0306783\pi\) | ||||
−0.995359 | + | 0.0962296i | \(0.969322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.82651 | + | 5.09599i | −1.03307 | + | 0.596440i | −0.917861 | − | 0.396901i | \(-0.870085\pi\) |
−0.115204 | + | 0.993342i | \(0.536752\pi\) | |||||||
\(74\) | −1.50973 | − | 2.61493i | −0.175503 | − | 0.303979i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.392760i | 0.0450527i | ||||||||
\(77\) | −7.74703 | − | 4.12110i | −0.882856 | − | 0.469643i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.22793 | + | 4.17305i | 0.813206 | + | 0.469505i | 0.848068 | − | 0.529887i | \(-0.177766\pi\) |
−0.0348619 | + | 0.999392i | \(0.511099\pi\) | |||||||
\(80\) | 1.42385 | − | 0.822059i | 0.159191 | − | 0.0919090i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.46264 | + | 9.46156i | −0.603247 | + | 1.04485i | ||||
\(83\) | −5.98532 | −0.656975 | −0.328487 | − | 0.944508i | \(-0.606539\pi\) | ||||
−0.328487 | + | 0.944508i | \(0.606539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.54181i | 0.601094i | ||||||||
\(86\) | 9.16665 | + | 5.29237i | 0.988466 | + | 0.570691i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.53893 | + | 2.13397i | 0.270651 | + | 0.227482i | ||||
\(89\) | −8.32280 | − | 4.80517i | −0.882215 | − | 0.509347i | −0.0108269 | − | 0.999941i | \(-0.503446\pi\) |
−0.871388 | + | 0.490594i | \(0.836780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.713549 | + | 3.34666i | 0.0748003 | + | 0.350825i | ||||
\(92\) | 0.525938i | 0.0548329i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.48768 | + | 2.59096i | −0.462869 | + | 0.267237i | ||||
\(95\) | 0.322872 | + | 0.559231i | 0.0331260 | + | 0.0573759i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.31783 | 0.844548 | 0.422274 | − | 0.906468i | \(-0.361232\pi\) | ||||
0.422274 | + | 0.906468i | \(0.361232\pi\) | |||||||
\(98\) | 0.722965 | − | 6.96257i | 0.0730305 | − | 0.703325i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.14844 | + | 1.98915i | −0.114844 | + | 0.198915i | ||||
\(101\) | 2.53452 | + | 4.38992i | 0.252194 | + | 0.436813i | 0.964130 | − | 0.265432i | \(-0.0855145\pi\) |
−0.711935 | + | 0.702245i | \(0.752181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.64472 | + | 6.31283i | −0.359124 | + | 0.622022i | −0.987815 | − | 0.155634i | \(-0.950258\pi\) |
0.628690 | + | 0.777656i | \(0.283591\pi\) | |||||||
\(104\) | − | 1.29335i | − | 0.126823i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.66179i | 0.161407i | ||||||||
\(107\) | −2.16028 | + | 3.74171i | −0.208842 | + | 0.361725i | −0.951350 | − | 0.308112i | \(-0.900303\pi\) |
0.742508 | + | 0.669837i | \(0.233636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.84618 | + | 3.37529i | −0.559962 | + | 0.323294i | −0.753130 | − | 0.657871i | \(-0.771457\pi\) |
0.193168 | + | 0.981166i | \(0.438124\pi\) | |||||||
\(110\) | 5.36930 | + | 0.951302i | 0.511943 | + | 0.0907030i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.816004 | + | 2.51677i | −0.0771051 | + | 0.237813i | ||||
\(113\) | − | 18.2771i | − | 1.71936i | −0.510831 | − | 0.859681i | \(-0.670662\pi\) | ||
0.510831 | − | 0.859681i | \(-0.329338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.432353 | + | 0.748857i | 0.0403171 | + | 0.0698312i | ||||
\(116\) | −0.665012 | − | 1.15183i | −0.0617448 | − | 0.106945i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 9.54052i | − | 0.878276i | ||||||
\(119\) | −5.97146 | − | 6.62362i | −0.547403 | − | 0.607186i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.89233 | + | 10.8360i | 0.172030 | + | 0.985092i | ||||
\(122\) | −3.32010 | + | 1.91686i | −0.300588 | + | 0.173544i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.86951 | + | 4.97013i | −0.257689 | + | 0.446331i | ||||
\(125\) | 11.9969i | 1.07304i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.84411i | − | 0.873524i | −0.899577 | − | 0.436762i | \(-0.856125\pi\) | ||
0.899577 | − | 0.436762i | \(-0.143875\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.06321 | − | 1.84153i | −0.0932497 | − | 0.161513i | ||||
\(131\) | 3.20488 | − | 5.55101i | 0.280011 | − | 0.484994i | −0.691376 | − | 0.722495i | \(-0.742995\pi\) |
0.971387 | + | 0.237501i | \(0.0763284\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.988487 | − | 0.320494i | −0.0857127 | − | 0.0277903i | ||||
\(134\) | −13.6027 | −1.17510 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.68534 | + | 2.91910i | 0.144517 | + | 0.250311i | ||||
\(137\) | 14.4951 | − | 8.36876i | 1.23840 | − | 0.714992i | 0.269634 | − | 0.962963i | \(-0.413097\pi\) |
0.968767 | + | 0.247971i | \(0.0797639\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.66143i | − | 0.310559i | −0.987871 | − | 0.155279i | \(-0.950372\pi\) | ||
0.987871 | − | 0.155279i | \(-0.0496278\pi\) | |||||||
\(140\) | 0.907070 | + | 4.25430i | 0.0766614 | + | 0.359554i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.40442 | + | 0.810845i | 0.117857 | + | 0.0680446i | ||||
\(143\) | 2.75997 | − | 3.28373i | 0.230801 | − | 0.274599i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.89375 | − | 1.09336i | −0.157268 | − | 0.0907984i | ||||
\(146\) | 10.1920i | 0.843494i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.01946 | −0.248198 | ||||||||
\(149\) | 7.35277 | − | 12.7354i | 0.602363 | − | 1.04332i | −0.390100 | − | 0.920773i | \(-0.627559\pi\) |
0.992462 | − | 0.122550i | \(-0.0391072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.55083 | − | 4.93683i | 0.695857 | − | 0.401753i | −0.109946 | − | 0.993938i | \(-0.535068\pi\) |
0.805802 | + | 0.592184i | \(0.201734\pi\) | |||||||
\(152\) | 0.340140 | + | 0.196380i | 0.0275890 | + | 0.0159285i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.44249 | + | 4.64858i | −0.599733 | + | 0.374593i | ||||
\(155\) | 9.43562i | 0.757887i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.33551 | + | 7.50933i | 0.346012 | + | 0.599310i | 0.985537 | − | 0.169460i | \(-0.0542025\pi\) |
−0.639525 | + | 0.768770i | \(0.720869\pi\) | |||||||
\(158\) | 7.22793 | − | 4.17305i | 0.575024 | − | 0.331990i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.64412i | − | 0.129979i | ||||||
\(161\) | −1.32367 | − | 0.429168i | −0.104320 | − | 0.0338232i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.06457 | − | 10.5041i | 0.475014 | − | 0.822748i | −0.524577 | − | 0.851363i | \(-0.675776\pi\) |
0.999591 | + | 0.0286150i | \(0.00910968\pi\) | |||||||
\(164\) | 5.46264 | + | 9.46156i | 0.426560 | + | 0.738824i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.99266 | + | 5.18344i | −0.232276 | + | 0.402313i | ||||
\(167\) | −1.42411 | −0.110201 | −0.0551006 | − | 0.998481i | \(-0.517548\pi\) | ||||
−0.0551006 | + | 0.998481i | \(0.517548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3272 | 0.871327 | ||||||||
\(170\) | 4.79935 | + | 2.77090i | 0.368093 | + | 0.212519i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.16665 | − | 5.29237i | 0.698951 | − | 0.403539i | ||||
\(173\) | −2.13167 | + | 3.69216i | −0.162068 | + | 0.280709i | −0.935610 | − | 0.353035i | \(-0.885150\pi\) |
0.773542 | + | 0.633745i | \(0.218483\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.06911 | − | 4.51351i | −0.307596 | − | 0.341189i | ||||
\(176\) | 3.11754 | − | 1.13179i | 0.234993 | − | 0.0853120i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.32280 | + | 4.80517i | −0.623820 | + | 0.360163i | ||||
\(179\) | −1.32093 | + | 0.762640i | −0.0987311 | + | 0.0570024i | −0.548553 | − | 0.836116i | \(-0.684821\pi\) |
0.449821 | + | 0.893118i | \(0.351488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.7414 | 1.46736 | 0.733682 | − | 0.679493i | \(-0.237800\pi\) | ||||
0.733682 | + | 0.679493i | \(0.237800\pi\) | |||||||
\(182\) | 3.25507 | + | 1.05538i | 0.241282 | + | 0.0782299i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.455476 | + | 0.262969i | 0.0335781 | + | 0.0193864i | ||||
\(185\) | −4.29925 | + | 2.48217i | −0.316087 | + | 0.182493i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.95031 | + | 11.0079i | −0.142621 | + | 0.804975i | ||||
\(188\) | 5.18193i | 0.377931i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.645744 | 0.0468472 | ||||||||
\(191\) | 12.9424 | + | 7.47229i | 0.936478 | + | 0.540676i | 0.888854 | − | 0.458190i | \(-0.151502\pi\) |
0.0476233 | + | 0.998865i | \(0.484835\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.47593 | − | 2.00683i | 0.250203 | − | 0.144455i | −0.369654 | − | 0.929169i | \(-0.620524\pi\) |
0.619857 | + | 0.784715i | \(0.287190\pi\) | |||||||
\(194\) | 4.15892 | − | 7.20346i | 0.298593 | − | 0.517178i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.66828 | − | 4.10739i | −0.404877 | − | 0.293385i | ||||
\(197\) | 21.4340 | 1.52711 | 0.763554 | − | 0.645744i | \(-0.223453\pi\) | ||||
0.763554 | + | 0.645744i | \(0.223453\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7097 | − | 20.2818i | −0.830079 | − | 1.43774i | −0.897975 | − | 0.440047i | \(-0.854962\pi\) |
0.0678951 | − | 0.997692i | \(-0.478372\pi\) | |||||||
\(200\) | 1.14844 | + | 1.98915i | 0.0812068 | + | 0.140654i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.06904 | 0.356656 | ||||||||
\(203\) | 3.44156 | − | 0.733782i | 0.241550 | − | 0.0515014i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.5559 | + | 8.98122i | 1.08647 | + | 0.627276i | ||||
\(206\) | 3.64472 | + | 6.31283i | 0.253939 | + | 0.439836i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.12007 | − | 0.646675i | −0.0776632 | − | 0.0448389i | ||||
\(209\) | 0.444523 | + | 1.22444i | 0.0307483 | + | 0.0846966i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.15572i | 0.148406i | 0.997243 | + | 0.0742028i | \(0.0236412\pi\) | ||||
−0.997243 | + | 0.0742028i | \(0.976359\pi\) | |||||||
\(212\) | 1.43915 | + | 0.830895i | 0.0988414 | + | 0.0570661i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.16028 | + | 3.74171i | 0.147674 | + | 0.255778i | ||||
\(215\) | 8.70128 | − | 15.0711i | 0.593423 | − | 1.02784i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1672 | − | 11.2775i | −0.690192 | − | 0.765569i | ||||
\(218\) | 6.75058i | 0.457207i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.50850 | − | 4.17430i | 0.236543 | − | 0.281431i | ||||
\(221\) | 3.77542 | − | 2.17974i | 0.253962 | − | 0.146625i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.01103 | 0.469493 | 0.234747 | − | 0.972057i | \(-0.424574\pi\) | ||||
0.234747 | + | 0.972057i | \(0.424574\pi\) | |||||||
\(224\) | 1.77159 | + | 1.96507i | 0.118369 | + | 0.131296i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.8284 | − | 9.13854i | −1.05289 | − | 0.607886i | ||||
\(227\) | 10.0653 | + | 17.4337i | 0.668060 | + | 1.15711i | 0.978446 | + | 0.206503i | \(0.0662082\pi\) |
−0.310387 | + | 0.950610i | \(0.600458\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.19825 | − | 7.27158i | 0.277428 | − | 0.480520i | −0.693317 | − | 0.720633i | \(-0.743851\pi\) |
0.970745 | + | 0.240113i | \(0.0771846\pi\) | |||||||
\(230\) | 0.864705 | 0.0570170 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.33002 | −0.0873203 | ||||||||
\(233\) | −6.15876 | + | 10.6673i | −0.403474 | + | 0.698838i | −0.994143 | − | 0.108077i | \(-0.965531\pi\) |
0.590669 | + | 0.806914i | \(0.298864\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.25985 | + | 7.37828i | 0.277882 | + | 0.481306i | ||||
\(236\) | −8.26233 | − | 4.77026i | −0.537832 | − | 0.310518i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.72196 | + | 1.85963i | −0.565360 | + | 0.120542i | ||||
\(239\) | 6.66725 | 0.431268 | 0.215634 | − | 0.976474i | \(-0.430818\pi\) | ||||
0.215634 | + | 0.976474i | \(0.430818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.40382 | − | 2.54255i | 0.283675 | − | 0.163780i | −0.351411 | − | 0.936221i | \(-0.614298\pi\) |
0.635086 | + | 0.772441i | \(0.280965\pi\) | |||||||
\(242\) | 10.3304 | + | 3.77920i | 0.664065 | + | 0.242936i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.83372i | 0.245429i | ||||||||
\(245\) | −11.4473 | − | 1.18864i | −0.731340 | − | 0.0759394i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.253988 | − | 0.439920i | 0.0161609 | − | 0.0279915i | ||||
\(248\) | 2.86951 | + | 4.97013i | 0.182214 | + | 0.315604i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.3896 | + | 5.99846i | 0.657099 | + | 0.379376i | ||||
\(251\) | 15.5033i | 0.978563i | 0.872126 | + | 0.489281i | \(0.162741\pi\) | ||||
−0.872126 | + | 0.489281i | \(0.837259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.595253 | + | 1.63963i | 0.0374232 | + | 0.103083i | ||||
\(254\) | −8.52525 | − | 4.92206i | −0.534922 | − | 0.308837i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −11.4588 | − | 6.61574i | −0.714780 | − | 0.412678i | 0.0980485 | − | 0.995182i | \(-0.468740\pi\) |
−0.812828 | + | 0.582503i | \(0.802073\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.46389 | − | 7.59929i | 0.153099 | − | 0.472197i | ||||
\(260\) | −2.12642 | −0.131875 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.20488 | − | 5.55101i | −0.197998 | − | 0.342942i | ||||
\(263\) | −2.38841 | − | 4.13684i | −0.147275 | − | 0.255088i | 0.782944 | − | 0.622092i | \(-0.213717\pi\) |
−0.930220 | + | 0.367004i | \(0.880384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.73218 | 0.167837 | ||||||||
\(266\) | −0.771799 | + | 0.695808i | −0.0473220 | + | 0.0426627i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.80137 | + | 11.7803i | −0.415460 | + | 0.719597i | ||||
\(269\) | 9.14107 | − | 5.27760i | 0.557341 | − | 0.321781i | −0.194737 | − | 0.980856i | \(-0.562385\pi\) |
0.752077 | + | 0.659075i | \(0.229052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.4275 | − | 12.3712i | −1.30163 | − | 0.751496i | −0.320946 | − | 0.947098i | \(-0.604001\pi\) |
−0.980683 | + | 0.195602i | \(0.937334\pi\) | |||||||
\(272\) | 3.37069 | 0.204378 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 16.7375i | − | 1.01115i | ||||||
\(275\) | −1.32899 | + | 7.50105i | −0.0801412 | + | 0.452330i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2245 | − | 5.90312i | 0.614331 | − | 0.354684i | −0.160328 | − | 0.987064i | \(-0.551255\pi\) |
0.774659 | + | 0.632380i | \(0.217922\pi\) | |||||||
\(278\) | −3.17089 | − | 1.83072i | −0.190178 | − | 0.109799i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.13787 | + | 1.34161i | 0.247285 | + | 0.0801763i | ||||
\(281\) | 16.1488 | 0.963359 | 0.481680 | − | 0.876347i | \(-0.340027\pi\) | ||||
0.481680 | + | 0.876347i | \(0.340027\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.4555 | + | 6.61385i | −0.680960 | + | 0.393153i | −0.800217 | − | 0.599711i | \(-0.795282\pi\) |
0.119257 | + | 0.992863i | \(0.461949\pi\) | |||||||
\(284\) | 1.40442 | − | 0.810845i | 0.0833373 | − | 0.0481148i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.46380 | − | 4.03207i | −0.0865565 | − | 0.238421i | ||||
\(287\) | −28.2701 | + | 6.02754i | −1.66873 | + | 0.355794i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.81923 | − | 4.88306i | 0.165837 | − | 0.287239i | ||||
\(290\) | −1.89375 | + | 1.09336i | −0.111205 | + | 0.0642042i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.82651 | + | 5.09599i | 0.516533 | + | 0.298220i | ||||
\(293\) | 14.9415 | 0.872894 | 0.436447 | − | 0.899730i | \(-0.356237\pi\) | ||||
0.436447 | + | 0.899730i | \(0.356237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.6857 | −0.913260 | ||||||||
\(296\) | −1.50973 | + | 2.61493i | −0.0877513 | + | 0.151990i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.35277 | − | 12.7354i | −0.425935 | − | 0.737741i | ||||
\(299\) | 0.340111 | − | 0.589090i | 0.0196691 | − | 0.0340680i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.83966 | + | 27.3890i | 0.336593 | + | 1.57867i | ||||
\(302\) | − | 9.87365i | − | 0.568165i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.340140 | − | 0.196380i | 0.0195084 | − | 0.0112632i | ||||
\(305\) | 3.15154 | + | 5.45863i | 0.180457 | + | 0.312561i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 32.9465i | − | 1.88036i | −0.340683 | − | 0.940178i | \(-0.610658\pi\) | ||
0.340683 | − | 0.940178i | \(-0.389342\pi\) | |||||||
\(308\) | 0.304539 | + | 8.76968i | 0.0173527 | + | 0.499699i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.17149 | + | 4.71781i | 0.464109 | + | 0.267954i | ||||
\(311\) | −16.8425 | + | 9.72400i | −0.955049 | + | 0.551398i | −0.894646 | − | 0.446776i | \(-0.852572\pi\) |
−0.0604031 | + | 0.998174i | \(0.519239\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.28905 | + | 7.42885i | −0.242431 | + | 0.419904i | −0.961406 | − | 0.275132i | \(-0.911278\pi\) |
0.718975 | + | 0.695036i | \(0.244612\pi\) | |||||||
\(314\) | 8.67102 | 0.489334 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 8.34610i | − | 0.469505i | ||||||
\(317\) | −1.74470 | − | 1.00730i | −0.0979923 | − | 0.0565759i | 0.450203 | − | 0.892926i | \(-0.351352\pi\) |
−0.548195 | + | 0.836350i | \(0.684685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.37684 | − | 2.83823i | −0.189067 | − | 0.158911i | ||||
\(320\) | −1.42385 | − | 0.822059i | −0.0795955 | − | 0.0459545i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.03350 | + | 0.931745i | −0.0575949 | + | 0.0519241i | ||||
\(323\) | 1.32387i | 0.0736622i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.57267 | − | 1.48533i | 0.142706 | − | 0.0823914i | ||||
\(326\) | −6.06457 | − | 10.5041i | −0.335886 | − | 0.581771i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.9253 | 0.603247 | ||||||||
\(329\) | −13.0417 | − | 4.22847i | −0.719013 | − | 0.233123i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.13936 | − | 15.8298i | 0.502345 | − | 0.870086i | −0.497652 | − | 0.867377i | \(-0.665804\pi\) |
0.999996 | − | 0.00270934i | \(-0.000862412\pi\) | |||||||
\(332\) | 2.99266 | + | 5.18344i | 0.164244 | + | 0.284478i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.712056 | + | 1.23332i | −0.0389620 | + | 0.0674841i | ||||
\(335\) | 22.3645i | 1.22190i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.04529i | − | 0.0569406i | −0.999595 | − | 0.0284703i | \(-0.990936\pi\) | ||
0.999595 | − | 0.0284703i | \(-0.00906361\pi\) | |||||||
\(338\) | 5.66362 | − | 9.80968i | 0.308060 | − | 0.533576i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.79935 | − | 2.77090i | 0.260281 | − | 0.150273i | ||||
\(341\) | −3.32065 | + | 18.7423i | −0.179823 | + | 1.01495i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.9627 | − | 10.9141i | 0.807909 | − | 0.589307i | ||||
\(344\) | − | 10.5847i | − | 0.570691i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.13167 | + | 3.69216i | 0.114599 | + | 0.198492i | ||||
\(347\) | 12.0831 | + | 20.9286i | 0.648657 | + | 1.12351i | 0.983444 | + | 0.181212i | \(0.0580022\pi\) |
−0.334787 | + | 0.942294i | \(0.608664\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.8063i | 1.64902i | 0.565846 | + | 0.824511i | \(0.308550\pi\) | ||||
−0.565846 | + | 0.824511i | \(0.691450\pi\) | |||||||
\(350\) | −5.94337 | + | 1.26720i | −0.317686 | + | 0.0677346i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.578609 | − | 3.26576i | 0.0308400 | − | 0.174066i | ||||
\(353\) | −8.94782 | + | 5.16602i | −0.476244 | + | 0.274960i | −0.718850 | − | 0.695165i | \(-0.755331\pi\) |
0.242606 | + | 0.970125i | \(0.421998\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.33313 | − | 2.30904i | 0.0707549 | − | 0.122551i | ||||
\(356\) | 9.61034i | 0.509347i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.52528i | 0.0806136i | ||||||||
\(359\) | 10.1350 | − | 17.5542i | 0.534902 | − | 0.926478i | −0.464266 | − | 0.885696i | \(-0.653682\pi\) |
0.999168 | − | 0.0407819i | \(-0.0129849\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.42287 | − | 16.3209i | −0.495941 | − | 0.858994i | ||||
\(362\) | 9.87068 | − | 17.0965i | 0.518792 | − | 0.898573i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.54152 | − | 2.29128i | 0.133212 | − | 0.120096i | ||||
\(365\) | 16.7568 | 0.877092 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.97708 | − | 8.62055i | −0.259801 | − | 0.449989i | 0.706387 | − | 0.707826i | \(-0.250324\pi\) |
−0.966189 | + | 0.257836i | \(0.916990\pi\) | |||||||
\(368\) | 0.455476 | − | 0.262969i | 0.0237433 | − | 0.0137082i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.96435i | 0.258084i | ||||||||
\(371\) | −3.26553 | + | 2.94401i | −0.169538 | + | 0.152845i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3112 | + | 5.95317i | 0.533894 | + | 0.308244i | 0.742601 | − | 0.669735i | \(-0.233592\pi\) |
−0.208707 | + | 0.977978i | \(0.566925\pi\) | |||||||
\(374\) | 8.55794 | + | 7.19295i | 0.442520 | + | 0.371939i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.48768 | + | 2.59096i | 0.231434 | + | 0.133619i | ||||
\(377\) | 1.72019i | 0.0885941i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.3862 | −0.944437 | −0.472218 | − | 0.881482i | \(-0.656547\pi\) | ||||
−0.472218 | + | 0.881482i | \(0.656547\pi\) | |||||||
\(380\) | 0.322872 | − | 0.559231i | 0.0165630 | − | 0.0286879i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.9424 | − | 7.47229i | 0.662190 | − | 0.382315i | ||||
\(383\) | −33.5005 | − | 19.3415i | −1.71180 | − | 0.988306i | −0.932141 | − | 0.362096i | \(-0.882061\pi\) |
−0.779655 | − | 0.626209i | \(-0.784606\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.64281 | + | 12.2363i | 0.389514 | + | 0.623622i | ||||
\(386\) | − | 4.01366i | − | 0.204290i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.15892 | − | 7.20346i | −0.211137 | − | 0.365700i | ||||
\(389\) | 27.7566 | − | 16.0253i | 1.40731 | − | 0.812513i | 0.412185 | − | 0.911100i | \(-0.364766\pi\) |
0.995128 | + | 0.0985872i | \(0.0314323\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.77277i | 0.0896530i | ||||||||
\(392\) | −6.39124 | + | 2.85518i | −0.322806 | + | 0.144208i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.7170 | − | 18.5624i | 0.539914 | − | 0.935159i | ||||
\(395\) | −6.86099 | − | 11.8836i | −0.345214 | − | 0.597928i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4657 | − | 28.5193i | 0.826387 | − | 1.43134i | −0.0744670 | − | 0.997223i | \(-0.523726\pi\) |
0.900854 | − | 0.434121i | \(-0.142941\pi\) | |||||||
\(398\) | −23.4194 | −1.17391 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.29687 | 0.114844 | ||||||||
\(401\) | 8.94782 | + | 5.16602i | 0.446833 | + | 0.257979i | 0.706492 | − | 0.707721i | \(-0.250277\pi\) |
−0.259659 | + | 0.965700i | \(0.583610\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.42812 | − | 3.71128i | 0.320208 | − | 0.184872i | ||||
\(404\) | 2.53452 | − | 4.38992i | 0.126097 | − | 0.218407i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.08530 | − | 3.34736i | 0.0538627 | − | 0.166127i | ||||
\(407\) | −9.41328 | + | 3.41740i | −0.466599 | + | 0.169394i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.7011 | − | 7.91033i | 0.677476 | − | 0.391141i | −0.121428 | − | 0.992600i | \(-0.538747\pi\) |
0.798903 | + | 0.601459i | \(0.205414\pi\) | |||||||
\(410\) | 15.5559 | − | 8.98122i | 0.768253 | − | 0.443551i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.28943 | 0.359124 | ||||||||
\(413\) | 18.7478 | − | 16.9019i | 0.922516 | − | 0.831686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.52220 | + | 4.92029i | 0.418338 | + | 0.241528i | ||||
\(416\) | −1.12007 | + | 0.646675i | −0.0549162 | + | 0.0317059i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.28266 | + | 0.227254i | 0.0627370 | + | 0.0111154i | ||||
\(419\) | 32.3275i | 1.57930i | 0.613556 | + | 0.789651i | \(0.289739\pi\) | ||||
−0.613556 | + | 0.789651i | \(0.710261\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8176 | −0.527217 | −0.263609 | − | 0.964630i | \(-0.584913\pi\) | ||||
−0.263609 | + | 0.964630i | \(0.584913\pi\) | |||||||
\(422\) | 1.86691 | + | 1.07786i | 0.0908795 | + | 0.0524693i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.43915 | − | 0.830895i | 0.0698914 | − | 0.0403518i | ||||
\(425\) | −3.87102 | + | 6.70481i | −0.187772 | + | 0.325231i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.64859 | − | 3.12833i | −0.466928 | − | 0.151390i | ||||
\(428\) | 4.32056 | 0.208842 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.70128 | − | 15.0711i | −0.419613 | − | 0.726791i | ||||
\(431\) | 17.9409 | + | 31.0745i | 0.864183 | + | 1.49681i | 0.867856 | + | 0.496815i | \(0.165497\pi\) |
−0.00367384 | + | 0.999993i | \(0.501169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.8240 | 1.14491 | 0.572454 | − | 0.819937i | \(-0.305991\pi\) | ||||
0.572454 | + | 0.819937i | \(0.305991\pi\) | |||||||
\(434\) | −14.8502 | + | 3.16625i | −0.712833 | + | 0.151985i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.84618 | + | 3.37529i | 0.279981 | + | 0.161647i | ||||
\(437\) | 0.103284 | + | 0.178893i | 0.00494074 | + | 0.00855760i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.4555 | − | 10.6553i | −0.880834 | − | 0.508550i | −0.00990091 | − | 0.999951i | \(-0.503152\pi\) |
−0.870933 | + | 0.491401i | \(0.836485\pi\) | |||||||
\(440\) | −1.86080 | − | 5.12560i | −0.0887102 | − | 0.244354i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 4.35948i | − | 0.207359i | ||||||
\(443\) | 27.1827 | + | 15.6939i | 1.29149 | + | 0.745642i | 0.978918 | − | 0.204252i | \(-0.0654763\pi\) |
0.312571 | + | 0.949894i | \(0.398810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.90027 | + | 13.6837i | 0.374509 | + | 0.648668i | ||||
\(446\) | 3.50552 | − | 6.07173i | 0.165991 | − | 0.287505i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.58759 | − | 0.551706i | 0.122252 | − | 0.0260657i | ||||
\(449\) | 20.7653i | 0.979973i | 0.871730 | + | 0.489987i | \(0.162998\pi\) | ||||
−0.871730 | + | 0.489987i | \(0.837002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.7385 | + | 23.3142i | 1.30616 | + | 1.09782i | ||||
\(452\) | −15.8284 | + | 9.13854i | −0.744506 | + | 0.429841i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.1307 | 0.944779 | ||||||||
\(455\) | 1.73517 | − | 5.35172i | 0.0813459 | − | 0.250892i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.43048 | + | 1.98059i | 0.160471 | + | 0.0926479i | 0.578085 | − | 0.815977i | \(-0.303800\pi\) |
−0.417614 | + | 0.908625i | \(0.637134\pi\) | |||||||
\(458\) | −4.19825 | − | 7.27158i | −0.196171 | − | 0.339779i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.432353 | − | 0.748857i | 0.0201585 | − | 0.0349156i | ||||
\(461\) | −4.46540 | −0.207975 | −0.103987 | − | 0.994579i | \(-0.533160\pi\) | ||||
−0.103987 | + | 0.994579i | \(0.533160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.8033 | −1.57097 | −0.785486 | − | 0.618879i | \(-0.787587\pi\) | ||||
−0.785486 | + | 0.618879i | \(0.787587\pi\) | |||||||
\(464\) | −0.665012 | + | 1.15183i | −0.0308724 | + | 0.0534726i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.15876 | + | 10.6673i | 0.285299 | + | 0.494153i | ||||
\(467\) | −2.67151 | − | 1.54240i | −0.123623 | − | 0.0713735i | 0.436914 | − | 0.899504i | \(-0.356072\pi\) |
−0.560536 | + | 0.828130i | \(0.689405\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.0984 | − | 26.7303i | −1.11276 | − | 1.23429i | ||||
\(470\) | 8.51970 | 0.392984 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.26233 | + | 4.77026i | −0.380305 | + | 0.219569i | ||||
\(473\) | 22.5875 | − | 26.8739i | 1.03858 | − | 1.23566i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.902120i | 0.0413921i | ||||||||
\(476\) | −2.75049 | + | 8.48325i | −0.126069 | + | 0.388829i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.33362 | − | 5.77400i | 0.152476 | − | 0.264097i | ||||
\(479\) | −7.85049 | − | 13.5974i | −0.358698 | − | 0.621283i | 0.629046 | − | 0.777368i | \(-0.283446\pi\) |
−0.987744 | + | 0.156085i | \(0.950113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.38202 | + | 1.95261i | 0.154207 | + | 0.0890313i | ||||
\(482\) | − | 5.08510i | − | 0.231620i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.43809 | − | 7.05681i | 0.383550 | − | 0.320764i | ||||
\(485\) | −11.8433 | − | 6.83775i | −0.537778 | − | 0.310486i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.0970 | − | 24.4167i | −0.638795 | − | 1.10643i | −0.985698 | − | 0.168524i | \(-0.946100\pi\) |
0.346903 | − | 0.937901i | \(-0.387233\pi\) | |||||||
\(488\) | 3.32010 | + | 1.91686i | 0.150294 | + | 0.0867722i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.75303 | + | 9.31932i | −0.305071 | + | 0.421004i | ||||
\(491\) | 14.6613 | 0.661655 | 0.330828 | − | 0.943691i | \(-0.392672\pi\) | ||||
0.330828 | + | 0.943691i | \(0.392672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.24155 | − | 3.88247i | −0.100954 | − | 0.174858i | ||||
\(494\) | −0.253988 | − | 0.439920i | −0.0114275 | − | 0.0197930i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.73902 | 0.257689 | ||||||||
\(497\) | 0.894696 | + | 4.19627i | 0.0401326 | + | 0.188228i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.5576 | + | 33.8747i | −0.875517 | + | 1.51644i | −0.0193055 | + | 0.999814i | \(0.506146\pi\) |
−0.856211 | + | 0.516626i | \(0.827188\pi\) | |||||||
\(500\) | 10.3896 | − | 5.99846i | 0.464639 | − | 0.268259i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.4263 | + | 7.75167i | 0.599245 | + | 0.345974i | ||||
\(503\) | −39.2496 | −1.75005 | −0.875027 | − | 0.484074i | \(-0.839156\pi\) | ||||
−0.875027 | + | 0.484074i | \(0.839156\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.33410i | − | 0.370863i | ||||||
\(506\) | 1.71759 | + | 0.304313i | 0.0763562 | + | 0.0135283i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.52525 | + | 4.92206i | −0.378247 | + | 0.218381i | ||||
\(509\) | 3.76989 | + | 2.17655i | 0.167098 | + | 0.0964738i | 0.581217 | − | 0.813749i | \(-0.302577\pi\) |
−0.414119 | + | 0.910223i | \(0.635910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.0279 | + | 18.0560i | −0.885982 | + | 0.798749i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.4588 | + | 6.61574i | −0.505426 | + | 0.291808i | ||||
\(515\) | 10.3790 | − | 5.99234i | 0.457355 | − | 0.264054i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.86486 | + | 16.1549i | 0.257936 | + | 0.710490i | ||||
\(518\) | −5.34923 | − | 5.93344i | −0.235032 | − | 0.260700i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.06321 | + | 1.84153i | −0.0466249 | + | 0.0807566i | ||||
\(521\) | 17.8760 | − | 10.3207i | 0.783161 | − | 0.452158i | −0.0543883 | − | 0.998520i | \(-0.517321\pi\) |
0.837549 | + | 0.546362i | \(0.183988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.0273 | − | 13.2948i | −1.00691 | − | 0.581343i | −0.0966280 | − | 0.995321i | \(-0.530806\pi\) |
−0.910287 | + | 0.413978i | \(0.864139\pi\) | |||||||
\(524\) | −6.40975 | −0.280011 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.77681 | −0.208279 | ||||||||
\(527\) | −9.67221 | + | 16.7528i | −0.421328 | + | 0.729762i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3617 | − | 19.6790i | −0.493987 | − | 0.855610i | ||||
\(530\) | 1.36609 | − | 2.36614i | 0.0593392 | − | 0.102778i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.216688 | + | 1.01630i | 0.00939462 | + | 0.0440623i | ||||
\(533\) | − | 14.1302i | − | 0.612047i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.15182 | − | 3.55175i | 0.265966 | − | 0.153556i | ||||
\(536\) | 6.80137 | + | 11.7803i | 0.293774 | + | 0.508832i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10.5552i | − | 0.455067i | ||||||
\(539\) | −22.3198 | − | 6.38963i | −0.961381 | − | 0.275221i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.7295 | − | 13.1229i | −0.977218 | − | 0.564197i | −0.0757888 | − | 0.997124i | \(-0.524147\pi\) |
−0.901429 | + | 0.432927i | \(0.857481\pi\) | |||||||
\(542\) | −21.4275 | + | 12.3712i | −0.920391 | + | 0.531388i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.68534 | − | 2.91910i | 0.0722585 | − | 0.125155i | ||||
\(545\) | 11.0988 | 0.475419 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.4556i | 1.60149i | 0.599008 | + | 0.800743i | \(0.295562\pi\) | ||||
−0.599008 | + | 0.800743i | \(0.704438\pi\) | |||||||
\(548\) | −14.4951 | − | 8.36876i | −0.619201 | − | 0.357496i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.83160 | + | 4.90146i | 0.248660 | + | 0.208999i | ||||
\(551\) | −0.452394 | − | 0.261190i | −0.0192727 | − | 0.0111271i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.0052 | + | 6.81045i | 0.893233 | + | 0.289610i | ||||
\(554\) | − | 11.8062i | − | 0.501599i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.17089 | + | 1.83072i | −0.134476 | + | 0.0776397i | ||||
\(557\) | 6.80146 | + | 11.7805i | 0.288187 | + | 0.499155i | 0.973377 | − | 0.229210i | \(-0.0736141\pi\) |
−0.685190 | + | 0.728365i | \(0.740281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6898 | −0.579016 | ||||||||
\(560\) | 3.23080 | − | 2.91270i | 0.136526 | − | 0.123084i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.07442 | − | 13.9853i | 0.340599 | − | 0.589935i | ||||
\(563\) | −6.85190 | − | 11.8678i | −0.288773 | − | 0.500170i | 0.684744 | − | 0.728784i | \(-0.259914\pi\) |
−0.973517 | + | 0.228614i | \(0.926581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.0248 | + | 26.0238i | −0.632100 | + | 1.09483i | ||||
\(566\) | 13.2277i | 0.556002i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.62169i | − | 0.0680446i | ||||||
\(569\) | 16.1147 | − | 27.9115i | 0.675565 | − | 1.17011i | −0.300738 | − | 0.953707i | \(-0.597233\pi\) |
0.976303 | − | 0.216406i | \(-0.0694336\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.5520 | + | 15.3298i | −1.11117 | + | 0.641532i | −0.939131 | − | 0.343558i | \(-0.888368\pi\) |
−0.172035 | + | 0.985091i | \(0.555034\pi\) | |||||||
\(572\) | −4.22378 | − | 0.748344i | −0.176605 | − | 0.0312898i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.91506 | + | 27.4964i | −0.372107 | + | 1.14768i | ||||
\(575\) | 1.20801i | 0.0503777i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.7360 | + | 30.7197i | 0.738360 | + | 1.27888i | 0.953233 | + | 0.302235i | \(0.0977329\pi\) |
−0.214873 | + | 0.976642i | \(0.568934\pi\) | |||||||
\(578\) | −2.81923 | − | 4.88306i | −0.117265 | − | 0.203108i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.18672i | 0.0907984i | ||||||||
\(581\) | −15.4876 | + | 3.30214i | −0.642532 | + | 0.136996i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.42702 | + | 0.961527i | 0.224764 | + | 0.0398224i | ||||
\(584\) | 8.82651 | − | 5.09599i | 0.365244 | − | 0.210874i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.47077 | − | 12.9398i | 0.308615 | − | 0.534536i | ||||
\(587\) | − | 17.6758i | − | 0.729557i | −0.931094 | − | 0.364778i | \(-0.881145\pi\) | ||
0.931094 | − | 0.364778i | \(-0.118855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.25406i | 0.0928768i | ||||||||
\(590\) | −7.84287 | + | 13.5843i | −0.322886 | + | 0.559255i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.50973 | + | 2.61493i | 0.0620495 | + | 0.107473i | ||||
\(593\) | 1.53418 | − | 2.65729i | 0.0630014 | − | 0.109122i | −0.832804 | − | 0.553568i | \(-0.813266\pi\) |
0.895806 | + | 0.444446i | \(0.146599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.05745 | + | 14.3399i | 0.125343 | + | 0.587880i | ||||
\(596\) | −14.7055 | −0.602363 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.340111 | − | 0.589090i | −0.0139082 | − | 0.0240897i | ||||
\(599\) | −1.84155 | + | 1.06322i | −0.0752436 | + | 0.0434419i | −0.537150 | − | 0.843487i | \(-0.680499\pi\) |
0.461906 | + | 0.886929i | \(0.347166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.74930i | − | 0.152937i | −0.997072 | − | 0.0764686i | \(-0.975635\pi\) | ||
0.997072 | − | 0.0764686i | \(-0.0243645\pi\) | |||||||
\(602\) | 26.6394 | + | 8.63718i | 1.08574 | + | 0.352025i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.55083 | − | 4.93683i | −0.347928 | − | 0.200877i | ||||
\(605\) | 6.21345 | − | 16.9844i | 0.252613 | − | 0.690516i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2817 | + | 9.40025i | 0.660855 | + | 0.381545i | 0.792602 | − | 0.609739i | \(-0.208726\pi\) |
−0.131748 | + | 0.991283i | \(0.542059\pi\) | |||||||
\(608\) | − | 0.392760i | − | 0.0159285i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.30309 | 0.255205 | ||||||||
\(611\) | 3.35102 | − | 5.80414i | 0.135568 | − | 0.234810i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.7160 | + | 10.2283i | −0.715542 | + | 0.413118i | −0.813110 | − | 0.582110i | \(-0.802227\pi\) |
0.0975676 | + | 0.995229i | \(0.468894\pi\) | |||||||
\(614\) | −28.5325 | − | 16.4733i | −1.15148 | − | 0.664806i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.74703 | + | 4.12110i | 0.312137 | + | 0.166044i | ||||
\(617\) | − | 29.3351i | − | 1.18099i | −0.807043 | − | 0.590493i | \(-0.798933\pi\) | ||
0.807043 | − | 0.590493i | \(-0.201067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.16332 | − | 10.6752i | −0.247725 | − | 0.429072i | 0.715169 | − | 0.698951i | \(-0.246350\pi\) |
−0.962894 | + | 0.269879i | \(0.913016\pi\) | |||||||
\(620\) | 8.17149 | − | 4.71781i | 0.328175 | − | 0.189472i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.4480i | 0.779794i | ||||||||
\(623\) | −24.1870 | − | 7.84207i | −0.969033 | − | 0.314186i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.12000 | − | 7.13605i | 0.164800 | − | 0.285442i | ||||
\(626\) | 4.28905 | + | 7.42885i | 0.171425 | + | 0.296917i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.33551 | − | 7.50933i | 0.173006 | − | 0.299655i | ||||
\(629\) | −10.1777 | −0.405810 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7738 | −0.588136 | −0.294068 | − | 0.955784i | \(-0.595009\pi\) | ||||
−0.294068 | + | 0.955784i | \(0.595009\pi\) | |||||||
\(632\) | −7.22793 | − | 4.17305i | −0.287512 | − | 0.165995i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.74470 | + | 1.00730i | −0.0692910 | + | 0.0400052i | ||||
\(635\) | −8.09244 | + | 14.0165i | −0.321139 | + | 0.556229i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.69274 | + | 8.26611i | 0.146312 | + | 0.327515i | ||||
\(638\) | −4.14640 | + | 1.50531i | −0.164158 | + | 0.0595958i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.42385 | + | 0.822059i | −0.0562826 | + | 0.0324947i | ||||
\(641\) | 17.1907 | − | 9.92508i | 0.678994 | − | 0.392017i | −0.120482 | − | 0.992716i | \(-0.538444\pi\) |
0.799476 | + | 0.600698i | \(0.205111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.60504 | 0.102733 | 0.0513664 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513664 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(644\) | 0.290163 | + | 1.36091i | 0.0114340 | + | 0.0536275i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.14651 | + | 0.661936i | 0.0451087 | + | 0.0260435i | ||||
\(647\) | −11.2756 | + | 6.50996i | −0.443289 | + | 0.255933i | −0.704992 | − | 0.709216i | \(-0.749049\pi\) |
0.261703 | + | 0.965149i | \(0.415716\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.1571 | − | 5.52023i | −1.22302 | − | 0.216688i | ||||
\(650\) | − | 2.97066i | − | 0.116519i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.1291 | −0.475014 | ||||||||
\(653\) | 34.0245 | + | 19.6441i | 1.33148 | + | 0.768732i | 0.985527 | − | 0.169518i | \(-0.0542212\pi\) |
0.345956 | + | 0.938251i | \(0.387554\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.12652 | + | 5.26920i | −0.356602 | + | 0.205885i | ||||
\(656\) | 5.46264 | − | 9.46156i | 0.213280 | − | 0.369412i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.1828 | + | 9.18023i | −0.396968 | + | 0.357883i | ||||
\(659\) | −21.8725 | −0.852033 | −0.426017 | − | 0.904715i | \(-0.640083\pi\) | ||||
−0.426017 | + | 0.904715i | \(0.640083\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6974 | − | 25.4567i | −0.571665 | − | 0.990152i | −0.996395 | − | 0.0848322i | \(-0.972965\pi\) |
0.424731 | − | 0.905320i | \(-0.360369\pi\) | |||||||
\(662\) | −9.13936 | − | 15.8298i | −0.355211 | − | 0.615244i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.98532 | 0.232276 | ||||||||
\(665\) | 1.14399 | + | 1.26893i | 0.0443621 | + | 0.0492070i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.605794 | − | 0.349755i | −0.0234564 | − | 0.0135426i | ||||
\(668\) | 0.712056 | + | 1.23332i | 0.0275503 | + | 0.0477185i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19.3682 | + | 11.1823i | 0.748260 | + | 0.432008i | ||||
\(671\) | 4.33897 | + | 11.9518i | 0.167504 | + | 0.461393i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0026i | 0.693949i | 0.937875 | + | 0.346975i | \(0.112791\pi\) | ||||
−0.937875 | + | 0.346975i | \(0.887209\pi\) | |||||||
\(674\) | −0.905249 | − | 0.522645i | −0.0348689 | − | 0.0201316i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.66362 | − | 9.80968i | −0.217832 | − | 0.377295i | ||||
\(677\) | −17.7248 | + | 30.7003i | −0.681219 | + | 1.17991i | 0.293390 | + | 0.955993i | \(0.405217\pi\) |
−0.974609 | + | 0.223914i | \(0.928117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.5231 | − | 4.58900i | 0.825982 | − | 0.176110i | ||||
\(680\) | − | 5.54181i | − | 0.212519i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.5710 | + | 12.2469i | 0.557951 | + | 0.468958i | ||||
\(683\) | −4.85527 | + | 2.80319i | −0.185782 | + | 0.107261i | −0.590006 | − | 0.807399i | \(-0.700875\pi\) |
0.404225 | + | 0.914660i | \(0.367541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.5185 | −1.05143 | ||||||||
\(686\) | −1.97055 | − | 18.4151i | −0.0752360 | − | 0.703093i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.16665 | − | 5.29237i | −0.349475 | − | 0.201770i | ||||
\(689\) | −1.07464 | − | 1.86133i | −0.0409405 | − | 0.0709110i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.7993 | + | 29.0972i | −0.639074 | + | 1.10691i | 0.346562 | + | 0.938027i | \(0.387349\pi\) |
−0.985636 | + | 0.168882i | \(0.945984\pi\) | |||||||
\(692\) | 4.26333 | 0.162068 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.1663 | 0.917339 | ||||||||
\(695\) | −3.00992 | + | 5.21333i | −0.114173 | + | 0.197753i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.4128 | + | 31.8920i | 0.697436 | + | 1.20799i | ||||
\(698\) | 26.6790 | + | 15.4031i | 1.00982 | + | 0.583017i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.87426 | + | 5.78071i | −0.0708403 | + | 0.218490i | ||||
\(701\) | −43.4126 | −1.63967 | −0.819835 | − | 0.572600i | \(-0.805935\pi\) | ||||
−0.819835 | + | 0.572600i | \(0.805935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.02704 | + | 0.592962i | −0.0387355 | + | 0.0223640i | ||||
\(704\) | −2.53893 | − | 2.13397i | −0.0956895 | − | 0.0804271i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3320i | 0.388852i | ||||||||
\(707\) | 8.98024 | + | 9.96100i | 0.337737 | + | 0.374622i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.34801 | + | 2.33482i | −0.0506255 | + | 0.0876859i | −0.890228 | − | 0.455516i | \(-0.849455\pi\) |
0.839602 | + | 0.543202i | \(0.182788\pi\) | |||||||
\(710\) | −1.33313 | − | 2.30904i | −0.0500313 | − | 0.0866567i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.32280 | + | 4.80517i | 0.311910 | + | 0.180081i | ||||
\(713\) | 3.01837i | 0.113039i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.62920 | + | 2.40667i | −0.247918 | + | 0.0900042i | ||||
\(716\) | 1.32093 | + | 0.762640i | 0.0493655 | + | 0.0285012i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.1350 | − | 17.5542i | −0.378233 | − | 0.655119i | ||||
\(719\) | −6.61138 | − | 3.81708i | −0.246563 | − | 0.142353i | 0.371627 | − | 0.928382i | \(-0.378800\pi\) |
−0.618189 | + | 0.786029i | \(0.712134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.94820 | + | 18.3458i | −0.221523 | + | 0.683234i | ||||
\(722\) | −18.8457 | −0.701366 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.87068 | − | 17.0965i | −0.366841 | − | 0.635387i | ||||
\(725\) | −1.52745 | − | 2.64562i | −0.0567280 | − | 0.0982558i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.8096 | 0.623435 | 0.311717 | − | 0.950175i | \(-0.399096\pi\) | ||||
0.311717 | + | 0.950175i | \(0.399096\pi\) | |||||||
\(728\) | −0.713549 | − | 3.34666i | −0.0264459 | − | 0.124035i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.37841 | − | 14.5118i | 0.310099 | − | 0.537107i | ||||
\(731\) | 30.8979 | − | 17.8389i | 1.14280 | − | 0.659796i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.28623 | + | 1.31996i | 0.0844440 | + | 0.0487537i | 0.541627 | − | 0.840619i | \(-0.317808\pi\) |
−0.457183 | + | 0.889372i | \(0.651142\pi\) | |||||||
\(734\) | −9.95416 | −0.367415 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 0.525938i | − | 0.0193864i | ||||||
\(737\) | −7.87066 | + | 44.4233i | −0.289920 | + | 1.63635i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.14077 | + | 1.23598i | −0.0787496 | + | 0.0454661i | −0.538858 | − | 0.842397i | \(-0.681144\pi\) |
0.460108 | + | 0.887863i | \(0.347811\pi\) | |||||||
\(740\) | 4.29925 | + | 2.48217i | 0.158044 | + | 0.0912465i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.916820 | + | 4.30003i | 0.0336575 | + | 0.157859i | ||||
\(743\) | −9.82643 | −0.360497 | −0.180248 | − | 0.983621i | \(-0.557690\pi\) | ||||
−0.180248 | + | 0.983621i | \(0.557690\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.9385 | + | 12.0888i | −0.767126 | + | 0.442901i | ||||
\(746\) | 10.3112 | − | 5.95317i | 0.377520 | − | 0.217961i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.5082 | − | 3.81492i | 0.384220 | − | 0.139487i | ||||
\(749\) | −3.52559 | + | 10.8739i | −0.128822 | + | 0.397322i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.78977 | + | 10.0282i | −0.211272 | + | 0.365934i | −0.952113 | − | 0.305747i | \(-0.901094\pi\) |
0.740841 | + | 0.671680i | \(0.234427\pi\) | |||||||
\(752\) | 4.48768 | − | 2.59096i | 0.163649 | − | 0.0944827i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.48973 | + | 0.860093i | 0.0542526 | + | 0.0313227i | ||||
\(755\) | −16.2335 | −0.590796 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.5191 | 0.927507 | 0.463753 | − | 0.885964i | \(-0.346502\pi\) | ||||
0.463753 | + | 0.885964i | \(0.346502\pi\) | |||||||
\(758\) | −9.19311 | + | 15.9229i | −0.333909 | + | 0.578347i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.322872 | − | 0.559231i | −0.0117118 | − | 0.0202854i | ||||
\(761\) | −5.09089 | + | 8.81767i | −0.184544 | + | 0.319640i | −0.943423 | − | 0.331592i | \(-0.892414\pi\) |
0.758878 | + | 0.651232i | \(0.225748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.2653 | + | 11.9592i | −0.480237 | + | 0.432954i | ||||
\(764\) | − | 14.9446i | − | 0.540676i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.5005 | + | 19.3415i | −1.21042 | + | 0.698838i | ||||
\(767\) | 6.16962 | + | 10.6861i | 0.222772 | + | 0.385852i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.7648i | 0.820921i | 0.911878 | + | 0.410461i | \(0.134632\pi\) | ||||
−0.911878 | + | 0.410461i | \(0.865368\pi\) | |||||||
\(770\) | 14.4184 | − | 0.500698i | 0.519603 | − | 0.0180439i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.47593 | − | 2.00683i | −0.125102 | − | 0.0722274i | ||||
\(773\) | −1.09140 | + | 0.630122i | −0.0392551 | + | 0.0226639i | −0.519499 | − | 0.854471i | \(-0.673881\pi\) |
0.480244 | + | 0.877135i | \(0.340548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.59090 | + | 11.4158i | −0.236752 | + | 0.410067i | ||||
\(776\) | −8.31783 | −0.298593 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 32.0505i | − | 1.14907i | ||||||
\(779\) | 3.71612 | + | 2.14551i | 0.133144 | + | 0.0768707i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.46064 | − | 4.11736i | 0.123831 | − | 0.147331i | ||||
\(782\) | 1.53527 | + | 0.886387i | 0.0549010 | + | 0.0316971i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.722965 | + | 6.96257i | −0.0258202 | + | 0.248663i | ||||
\(785\) | − | 14.2562i | − | 0.508825i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.6470 | − | 22.8902i | 1.41326 | − | 0.815948i | 0.417568 | − | 0.908646i | \(-0.362882\pi\) |
0.995694 | + | 0.0926980i | \(0.0295491\pi\) | |||||||
\(788\) | −10.7170 | − | 18.5624i | −0.381777 | − | 0.661257i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.7220 | −0.488206 | ||||||||
\(791\) | −10.0836 | − | 47.2936i | −0.358530 | − | 1.68157i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.47917 | − | 4.29405i | 0.0880379 | − | 0.152486i | ||||
\(794\) | −16.4657 | − | 28.5193i | −0.584344 | − | 1.01211i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.7097 | + | 20.2818i | −0.415040 | + | 0.718870i | ||||
\(797\) | 2.29098i | 0.0811508i | 0.999176 | + | 0.0405754i | \(0.0129191\pi\) | ||||
−0.999176 | + | 0.0405754i | \(0.987081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.4666i | 0.617926i | ||||||||
\(800\) | 1.14844 | − | 1.98915i | 0.0406034 | − | 0.0703271i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.94782 | − | 5.16602i | 0.315958 | − | 0.182419i | ||||
\(803\) | 33.2846 | + | 5.89717i | 1.17459 | + | 0.208107i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.53190 | + | 1.69920i | 0.0539924 | + | 0.0598890i | ||||
\(806\) | − | 7.42256i | − | 0.261448i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.53452 | − | 4.38992i | −0.0891641 | − | 0.154437i | ||||
\(809\) | −12.5840 | − | 21.7961i | −0.442430 | − | 0.766311i | 0.555439 | − | 0.831557i | \(-0.312550\pi\) |
−0.997869 | + | 0.0652458i | \(0.979217\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.0031i | − | 0.421487i | −0.977541 | − | 0.210744i | \(-0.932411\pi\) | ||
0.977541 | − | 0.210744i | \(-0.0675885\pi\) | |||||||
\(812\) | −2.35625 | − | 2.61358i | −0.0826882 | − | 0.0917188i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.74709 | + | 9.86084i | −0.0612353 | + | 0.345622i | ||||
\(815\) | −17.2701 | + | 9.97088i | −0.604944 | + | 0.349265i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.07863 | − | 3.60029i | 0.0727221 | − | 0.125958i | ||||
\(818\) | − | 15.8207i | − | 0.553157i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 17.9624i | − | 0.627276i | ||||||
\(821\) | −5.69313 | + | 9.86078i | −0.198691 | + | 0.344144i | −0.948104 | − | 0.317959i | \(-0.897003\pi\) |
0.749413 | + | 0.662103i | \(0.230336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.8850 | − | 48.2982i | −0.972010 | − | 1.68357i | −0.689469 | − | 0.724315i | \(-0.742156\pi\) |
−0.282540 | − | 0.959255i | \(-0.591177\pi\) | |||||||
\(824\) | 3.64472 | − | 6.31283i | 0.126970 | − | 0.219918i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.26356 | − | 24.6870i | −0.183143 | − | 0.858969i | ||||
\(827\) | 13.7158 | 0.476946 | 0.238473 | − | 0.971149i | \(-0.423353\pi\) | ||||
0.238473 | + | 0.971149i | \(0.423353\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2816 | + | 35.1287i | 0.704408 | + | 1.22007i | 0.966905 | + | 0.255137i | \(0.0821207\pi\) |
−0.262497 | + | 0.964933i | \(0.584546\pi\) | |||||||
\(830\) | 8.52220 | − | 4.92029i | 0.295810 | − | 0.170786i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.29335i | 0.0448389i | ||||||||
\(833\) | −19.1060 | − | 13.8447i | −0.661983 | − | 0.479691i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.02772 | + | 1.17071i | 0.0701722 | + | 0.0405139i | ||||
\(836\) | 0.838139 | − | 0.997190i | 0.0289876 | − | 0.0344885i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.9965 | + | 16.1638i | 0.967121 | + | 0.558368i | ||||
\(839\) | 38.8580i | 1.34153i | 0.741672 | + | 0.670763i | \(0.234033\pi\) | ||||
−0.741672 | + | 0.670763i | \(0.765967\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2310 | −0.939001 | ||||||||
\(842\) | −5.40880 | + | 9.36831i | −0.186399 | + | 0.322853i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.86691 | − | 1.07786i | 0.0642615 | − | 0.0371014i | ||||
\(845\) | −16.1283 | − | 9.31167i | −0.554830 | − | 0.320331i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.8749 | + | 26.9951i | 0.373665 | + | 0.927564i | ||||
\(848\) | − | 1.66179i | − | 0.0570661i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.87102 | + | 6.70481i | 0.132775 | + | 0.229973i | ||||
\(851\) | −1.37529 | + | 0.794025i | −0.0471444 | + | 0.0272188i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.3490i | 1.75816i | 0.476677 | + | 0.879078i | \(0.341841\pi\) | ||||
−0.476677 | + | 0.879078i | \(0.658159\pi\) | |||||||
\(854\) | −7.53351 | + | 6.79176i | −0.257791 | + | 0.232409i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.16028 | − | 3.74171i | 0.0738368 | − | 0.127889i | ||||
\(857\) | 20.2462 | + | 35.0674i | 0.691596 | + | 1.19788i | 0.971315 | + | 0.237797i | \(0.0764253\pi\) |
−0.279719 | + | 0.960082i | \(0.590241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.6853 | − | 18.5075i | 0.364577 | − | 0.631467i | −0.624131 | − | 0.781320i | \(-0.714547\pi\) |
0.988708 | + | 0.149853i | \(0.0478801\pi\) | |||||||
\(860\) | −17.4026 | −0.593423 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.8818 | 1.22214 | ||||||||
\(863\) | −18.8633 | − | 10.8907i | −0.642113 | − | 0.370724i | 0.143315 | − | 0.989677i | \(-0.454224\pi\) |
−0.785428 | + | 0.618953i | \(0.787557\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.07034 | − | 3.50471i | 0.206398 | − | 0.119164i | ||||
\(866\) | 11.9120 | − | 20.6322i | 0.404786 | − | 0.701110i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.68306 | + | 14.4438i | −0.158953 | + | 0.490254i | ||||
\(869\) | −9.44605 | − | 26.0193i | −0.320435 | − | 0.882644i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2361 | − | 8.79655i | 0.516255 | − | 0.298060i | ||||
\(872\) | 5.84618 | − | 3.37529i | 0.197977 | − | 0.114302i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.206568 | 0.00698725 | ||||||||
\(875\) | 6.61877 | + | 31.0431i | 0.223755 | + | 1.04945i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.1630 | − | 5.86760i | −0.343180 | − | 0.198135i | 0.318498 | − | 0.947924i | \(-0.396822\pi\) |
−0.661677 | + | 0.749789i | \(0.730155\pi\) | |||||||
\(878\) | −18.4555 | + | 10.6553i | −0.622844 | + | 0.359599i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.36930 | − | 0.951302i | −0.180999 | − | 0.0320684i | ||||
\(881\) | 9.90728i | 0.333785i | 0.985975 | + | 0.166892i | \(0.0533732\pi\) | ||||
−0.985975 | + | 0.166892i | \(0.946627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.62510 | 0.290258 | 0.145129 | − | 0.989413i | \(-0.453640\pi\) | ||||
0.145129 | + | 0.989413i | \(0.453640\pi\) | |||||||
\(884\) | −3.77542 | − | 2.17974i | −0.126981 | − | 0.0733126i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.1827 | − | 15.6939i | 0.913221 | − | 0.527248i | ||||
\(887\) | 3.00576 | − | 5.20614i | 0.100924 | − | 0.174805i | −0.811142 | − | 0.584850i | \(-0.801154\pi\) |
0.912065 | + | 0.410045i | \(0.134487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.43106 | − | 25.4725i | −0.182152 | − | 0.854321i | ||||
\(890\) | 15.8005 | 0.529635 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.50552 | − | 6.07173i | −0.117373 | − | 0.203297i | ||||
\(893\) | 1.01763 | + | 1.76258i | 0.0340536 | + | 0.0589825i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.50774 | 0.0838246 | ||||||||
\(896\) | 0.816004 | − | 2.51677i | 0.0272608 | − | 0.0840794i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.9832 | + | 10.3826i | 0.600109 | + | 0.346473i | ||||
\(899\) | −3.81651 | − | 6.61039i | −0.127288 | − | 0.220469i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.85093 | + | 2.80069i | 0.161608 | + | 0.0933045i | ||||
\(902\) | 34.0600 | − | 12.3651i | 1.13407 | − | 0.411714i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.2771i | 0.607886i | ||||||||
\(905\) | −28.1087 | − | 16.2286i | −0.934365 | − | 0.539456i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.3959 | + | 19.7383i | 0.378395 | + | 0.655400i | 0.990829 | − | 0.135122i | \(-0.0431426\pi\) |
−0.612434 | + | 0.790522i | \(0.709809\pi\) | |||||||
\(908\) | 10.0653 | − | 17.4337i | 0.334030 | − | 0.578557i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.76714 | − | 4.17856i | −0.124879 | − | 0.138518i | ||||
\(911\) | − | 8.07918i | − | 0.267675i | −0.991003 | − | 0.133838i | \(-0.957270\pi\) | ||
0.991003 | − | 0.133838i | \(-0.0427300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.1963 | + | 12.7725i | 0.502925 | + | 0.422709i | ||||
\(914\) | 3.43048 | − | 1.98059i | 0.113470 | − | 0.0655120i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.39650 | −0.277428 | ||||||||
\(917\) | 5.23038 | − | 16.1319i | 0.172722 | − | 0.532722i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.9595 | − | 20.7612i | −1.18619 | − | 0.684850i | −0.228755 | − | 0.973484i | \(-0.573466\pi\) |
−0.957440 | + | 0.288634i | \(0.906799\pi\) | |||||||
\(920\) | −0.432353 | − | 0.748857i | −0.0142542 | − | 0.0246891i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.23270 | + | 3.86715i | −0.0735301 | + | 0.127358i | ||||
\(923\) | −2.09741 | −0.0690372 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.93532 | −0.228032 | ||||||||
\(926\) | −16.9017 | + | 29.2745i | −0.555423 | + | 0.962020i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.665012 | + | 1.15183i | 0.0218301 | + | 0.0378108i | ||||
\(929\) | −18.1293 | − | 10.4670i | −0.594803 | − | 0.343410i | 0.172191 | − | 0.985064i | \(-0.444915\pi\) |
−0.766994 | + | 0.641654i | \(0.778249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.73462 | − | 0.283952i | −0.0896235 | − | 0.00930614i | ||||
\(932\) | 12.3175 | 0.403474 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.67151 | + | 1.54240i | −0.0874144 | + | 0.0504687i | ||||
\(935\) | 11.8261 | − | 14.0703i | 0.386754 | − | 0.460147i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.24085i | − | 0.236548i | −0.992981 | − | 0.118274i | \(-0.962264\pi\) | ||
0.992981 | − | 0.118274i | \(-0.0377362\pi\) | |||||||
\(938\) | −35.1983 | + | 7.50471i | −1.14927 | + | 0.245037i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.25985 | − | 7.37828i | 0.138941 | − | 0.240653i | ||||
\(941\) | −27.6924 | − | 47.9646i | −0.902745 | − | 1.56360i | −0.823916 | − | 0.566713i | \(-0.808215\pi\) |
−0.0788298 | − | 0.996888i | \(-0.525118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.97620 | + | 2.87301i | 0.162047 | + | 0.0935581i | ||||
\(944\) | 9.54052i | 0.310518i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.9797 | − | 32.9983i | −0.389494 | − | 1.07287i | ||||
\(947\) | −16.0090 | − | 9.24283i | −0.520224 | − | 0.300352i | 0.216802 | − | 0.976216i | \(-0.430437\pi\) |
−0.737026 | + | 0.675864i | \(0.763771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.59090 | − | 11.4158i | −0.213950 | − | 0.370572i | ||||
\(950\) | 0.781259 | + | 0.451060i | 0.0253474 | + | 0.0146343i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.97146 | + | 6.62362i | 0.193536 | + | 0.214673i | ||||
\(953\) | 42.1993 | 1.36697 | 0.683485 | − | 0.729964i | \(-0.260463\pi\) | ||||
0.683485 | + | 0.729964i | \(0.260463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.2853 | − | 21.2788i | −0.397544 | − | 0.688566i | ||||
\(956\) | −3.33362 | − | 5.77400i | −0.107817 | − | 0.186745i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.7010 | −0.507275 | ||||||||
\(959\) | 32.8903 | − | 29.6520i | 1.06208 | − | 0.957512i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.968154 | + | 1.67689i | −0.0312308 | + | 0.0540933i | ||||
\(962\) | 3.38202 | − | 1.95261i | 0.109041 | − | 0.0629547i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.40382 | − | 2.54255i | −0.141838 | − | 0.0818900i | ||||
\(965\) | −6.59894 | −0.212427 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.8707i | 0.928420i | 0.885725 | + | 0.464210i | \(0.153662\pi\) | ||||
−0.885725 | + | 0.464210i | \(0.846338\pi\) | |||||||
\(968\) | −1.89233 | − | 10.8360i | −0.0608218 | − | 0.348283i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.8433 | + | 6.83775i | −0.380267 | + | 0.219547i | ||||
\(971\) | 33.5960 | + | 19.3967i | 1.07815 | + | 0.622469i | 0.930396 | − | 0.366556i | \(-0.119463\pi\) |
0.147752 | + | 0.989024i | \(0.452796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.02003 | − | 9.47429i | −0.0647593 | − | 0.303732i | ||||
\(974\) | −28.1940 | −0.903393 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.32010 | − | 1.91686i | 0.106274 | − | 0.0613572i | ||||
\(977\) | −51.7993 | + | 29.9064i | −1.65721 | + | 0.956789i | −0.683212 | + | 0.730220i | \(0.739418\pi\) |
−0.973995 | + | 0.226569i | \(0.927249\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.8769 | + | 29.9606i | 0.347627 | + | 0.957545i | ||||
\(980\) | 4.69425 | + | 10.5080i | 0.149952 | + | 0.335664i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.33065 | − | 12.6971i | 0.233931 | − | 0.405180i | ||||
\(983\) | 26.0949 | − | 15.0659i | 0.832298 | − | 0.480528i | −0.0223406 | − | 0.999750i | \(-0.507112\pi\) |
0.854639 | + | 0.519223i | \(0.173779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.5187 | − | 17.6200i | −0.972408 | − | 0.561420i | ||||
\(986\) | −4.48309 | −0.142771 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.507976 | −0.0161609 | ||||||||
\(989\) | 2.78346 | − | 4.82110i | 0.0885089 | − | 0.153302i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.6850 | − | 42.7557i | −0.784146 | − | 1.35818i | −0.929508 | − | 0.368802i | \(-0.879768\pi\) |
0.145362 | − | 0.989379i | \(-0.453565\pi\) | |||||||
\(992\) | 2.86951 | − | 4.97013i | 0.0911070 | − | 0.157802i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.08142 | + | 1.32330i | 0.129455 | + | 0.0419727i | ||||
\(995\) | 38.5043i | 1.22067i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.8425 | − | 24.1578i | 1.32517 | − | 0.765085i | 0.340618 | − | 0.940202i | \(-0.389364\pi\) |
0.984548 | + | 0.175117i | \(0.0560302\pi\) | |||||||
\(998\) | 19.5576 | + | 33.8747i | 0.619084 | + | 1.07228i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.ba.b.989.6 | yes | 32 | |
3.2 | odd | 2 | 1386.2.ba.a.989.11 | yes | 32 | ||
7.4 | even | 3 | inner | 1386.2.ba.b.1187.11 | yes | 32 | |
11.10 | odd | 2 | 1386.2.ba.a.989.6 | ✓ | 32 | ||
21.11 | odd | 6 | 1386.2.ba.a.1187.6 | yes | 32 | ||
33.32 | even | 2 | inner | 1386.2.ba.b.989.11 | yes | 32 | |
77.32 | odd | 6 | 1386.2.ba.a.1187.11 | yes | 32 | ||
231.32 | even | 6 | inner | 1386.2.ba.b.1187.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.ba.a.989.6 | ✓ | 32 | 11.10 | odd | 2 | ||
1386.2.ba.a.989.11 | yes | 32 | 3.2 | odd | 2 | ||
1386.2.ba.a.1187.6 | yes | 32 | 21.11 | odd | 6 | ||
1386.2.ba.a.1187.11 | yes | 32 | 77.32 | odd | 6 | ||
1386.2.ba.b.989.6 | yes | 32 | 1.1 | even | 1 | trivial | |
1386.2.ba.b.989.11 | yes | 32 | 33.32 | even | 2 | inner | |
1386.2.ba.b.1187.6 | yes | 32 | 231.32 | even | 6 | inner | |
1386.2.ba.b.1187.11 | yes | 32 | 7.4 | even | 3 | inner |