Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [936,2,Mod(181,936)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(936, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("936.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 936.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.47399762919\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.12 | ||
Root | \(-0.752864 + 0.902863i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 936.181 |
Dual form | 936.2.m.h.181.9 |
$q$-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 \(\left(\mathbb{Z}/936\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(469\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.831254 | + | 1.14412i | 0.587785 | + | 0.809017i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.618034 | + | 1.90211i | −0.309017 | + | 0.951057i | ||||
\(5\) | −2.68999 | −1.20300 | −0.601501 | − | 0.798872i | \(-0.705430\pi\) | ||||
−0.601501 | + | 0.798872i | \(0.705430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.15163i | 1.56917i | 0.620021 | + | 0.784585i | \(0.287124\pi\) | ||||
−0.620021 | + | 0.784585i | \(0.712876\pi\) | |||||||
\(8\) | −2.68999 | + | 0.874032i | −0.951057 | + | 0.309017i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.23607 | − | 3.07768i | −0.707107 | − | 0.973249i | ||||
\(11\) | 4.35250 | 1.31233 | 0.656164 | − | 0.754618i | \(-0.272178\pi\) | ||||
0.656164 | + | 0.754618i | \(0.272178\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.53159 | − | 0.726543i | 0.979487 | − | 0.201507i | ||||
\(14\) | −4.74998 | + | 3.45106i | −1.26949 | + | 0.922335i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.23607 | − | 2.35114i | −0.809017 | − | 0.587785i | ||||
\(17\) | −5.87130 | −1.42400 | −0.711999 | − | 0.702180i | \(-0.752210\pi\) | ||||
−0.711999 | + | 0.702180i | \(0.752210\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.71423 | −1.31094 | −0.655468 | − | 0.755223i | \(-0.727528\pi\) | ||||
−0.655468 | + | 0.755223i | \(0.727528\pi\) | |||||||
\(20\) | 1.66251 | − | 5.11667i | 0.371748 | − | 1.14412i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.61803 | + | 4.97980i | 0.771367 | + | 1.06170i | ||||
\(23\) | −3.62866 | −0.756628 | −0.378314 | − | 0.925677i | \(-0.623496\pi\) | ||||
−0.378314 | + | 0.925677i | \(0.623496\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.23607 | 0.447214 | ||||||||
\(26\) | 3.76690 | + | 3.43663i | 0.738750 | + | 0.673979i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.89688 | − | 2.56585i | −1.49237 | − | 0.484900i | ||||
\(29\) | − | 3.08672i | − | 0.573190i | −0.958052 | − | 0.286595i | \(-0.907477\pi\) | ||
0.958052 | − | 0.286595i | \(-0.0925234\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.28334i | 1.66734i | 0.552266 | + | 0.833668i | \(0.313763\pi\) | ||||
−0.552266 | + | 0.833668i | \(0.686237\pi\) | |||||||
\(32\) | − | 5.65685i | − | 1.00000i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.88054 | − | 6.71749i | −0.837006 | − | 1.15204i | ||||
\(35\) | − | 11.1679i | − | 1.88771i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.69790 | −0.443531 | −0.221766 | − | 0.975100i | \(-0.571182\pi\) | ||||
−0.221766 | + | 0.975100i | \(0.571182\pi\) | |||||||
\(38\) | −4.74998 | − | 6.53779i | −0.770548 | − | 1.06057i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.23607 | − | 2.35114i | 1.14412 | − | 0.371748i | ||||
\(41\) | − | 11.1074i | − | 1.73468i | −0.497715 | − | 0.867340i | \(-0.665828\pi\) | ||
0.497715 | − | 0.867340i | \(-0.334172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.80423i | − | 0.580139i | −0.957006 | − | 0.290070i | \(-0.906322\pi\) | ||
0.957006 | − | 0.290070i | \(-0.0936784\pi\) | |||||||
\(44\) | −2.68999 | + | 8.27895i | −0.405532 | + | 1.24810i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.01634 | − | 4.15163i | −0.444735 | − | 0.612125i | ||||
\(47\) | 4.91034i | 0.716247i | 0.933674 | + | 0.358123i | \(0.116583\pi\) | ||||
−0.933674 | + | 0.358123i | \(0.883417\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.2361 | −1.46230 | ||||||||
\(50\) | 1.85874 | + | 2.55834i | 0.262866 | + | 0.361803i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.800677 | + | 7.16651i | −0.111034 | + | 0.993817i | ||||
\(53\) | 1.17902i | 0.161951i | 0.996716 | + | 0.0809757i | \(0.0258036\pi\) | ||||
−0.996716 | + | 0.0809757i | \(0.974196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.7082 | −1.57873 | ||||||||
\(56\) | −3.62866 | − | 11.1679i | −0.484900 | − | 1.49237i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.53159 | − | 2.56585i | 0.463721 | − | 0.336913i | ||||
\(59\) | 2.29753 | 0.299113 | 0.149556 | − | 0.988753i | \(-0.452215\pi\) | ||||
0.149556 | + | 0.988753i | \(0.452215\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.05342i | 0.903098i | 0.892246 | + | 0.451549i | \(0.149128\pi\) | ||||
−0.892246 | + | 0.451549i | \(0.850872\pi\) | |||||||
\(62\) | −10.6213 | + | 7.71681i | −1.34890 | + | 0.980036i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.47214 | − | 4.70228i | 0.809017 | − | 0.587785i | ||||
\(65\) | −9.49996 | + | 1.95440i | −1.17832 | + | 0.242413i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0795 | 1.23141 | 0.615705 | − | 0.787977i | \(-0.288871\pi\) | ||||
0.615705 | + | 0.787977i | \(0.288871\pi\) | |||||||
\(68\) | 3.62866 | − | 11.1679i | 0.440040 | − | 1.35430i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 12.7774 | − | 9.28334i | 1.52719 | − | 1.10957i | ||||
\(71\) | 2.08191i | 0.247078i | 0.992340 | + | 0.123539i | \(0.0394244\pi\) | ||||
−0.992340 | + | 0.123539i | \(0.960576\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4350i | 1.57244i | 0.617944 | + | 0.786222i | \(0.287966\pi\) | ||||
−0.617944 | + | 0.786222i | \(0.712034\pi\) | |||||||
\(74\) | −2.24264 | − | 3.08672i | −0.260701 | − | 0.358824i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.53159 | − | 10.8691i | 0.405101 | − | 1.24677i | ||||
\(77\) | 18.0700i | 2.05927i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9443 | 1.23133 | 0.615663 | − | 0.788009i | \(-0.288888\pi\) | ||||
0.615663 | + | 0.788009i | \(0.288888\pi\) | |||||||
\(80\) | 8.70500 | + | 6.32456i | 0.973249 | + | 0.707107i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.7082 | − | 9.23305i | 1.40339 | − | 1.01962i | ||||
\(83\) | −9.73249 | −1.06828 | −0.534140 | − | 0.845396i | \(-0.679364\pi\) | ||||
−0.534140 | + | 0.845396i | \(0.679364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.7938 | 1.71307 | ||||||||
\(86\) | 4.35250 | − | 3.16228i | 0.469342 | − | 0.340997i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.7082 | + | 3.80423i | −1.24810 | + | 0.405532i | ||||
\(89\) | 12.1877i | 1.29190i | 0.763381 | + | 0.645949i | \(0.223538\pi\) | ||||
−0.763381 | + | 0.645949i | \(0.776462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.01634 | + | 14.6619i | 0.316198 | + | 1.53698i | ||||
\(92\) | 2.24264 | − | 6.90212i | 0.233811 | − | 0.719596i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.61803 | + | 4.08174i | −0.579456 | + | 0.420999i | ||||
\(95\) | 15.3713 | 1.57706 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.13170i | 0.521045i | 0.965468 | + | 0.260523i | \(0.0838949\pi\) | ||||
−0.965468 | + | 0.260523i | \(0.916105\pi\) | |||||||
\(98\) | −8.50877 | − | 11.7113i | −0.859516 | − | 1.18302i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.38197 | + | 4.25325i | −0.138197 | + | 0.425325i | ||||
\(101\) | 14.9833i | 1.49089i | 0.666566 | + | 0.745446i | \(0.267763\pi\) | ||||
−0.666566 | + | 0.745446i | \(0.732237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.70820 | 0.168314 | 0.0841572 | − | 0.996452i | \(-0.473180\pi\) | ||||
0.0841572 | + | 0.996452i | \(0.473180\pi\) | |||||||
\(104\) | −8.86494 | + | 5.04112i | −0.869279 | + | 0.494322i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.34895 | + | 0.980068i | −0.131021 | + | 0.0951926i | ||||
\(107\) | − | 4.99442i | − | 0.482829i | −0.970422 | − | 0.241415i | \(-0.922389\pi\) | ||
0.970422 | − | 0.241415i | \(-0.0776114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.73057 | −0.836237 | −0.418119 | − | 0.908392i | \(-0.637310\pi\) | ||||
−0.418119 | + | 0.908392i | \(0.637310\pi\) | |||||||
\(110\) | −9.73249 | − | 13.3956i | −0.927957 | − | 1.27722i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.76108 | − | 13.4350i | 0.922335 | − | 1.26949i | ||||
\(113\) | −5.87130 | −0.552325 | −0.276163 | − | 0.961111i | \(-0.589063\pi\) | ||||
−0.276163 | + | 0.961111i | \(0.589063\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.76108 | 0.910225 | ||||||||
\(116\) | 5.87130 | + | 1.90770i | 0.545136 | + | 0.177126i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.90983 | + | 2.62866i | 0.175814 | + | 0.241987i | ||||
\(119\) | − | 24.3755i | − | 2.23450i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.94427 | 0.722207 | ||||||||
\(122\) | −8.06998 | + | 5.86319i | −0.730622 | + | 0.530828i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −17.6580 | − | 5.73742i | −1.58573 | − | 0.515235i | ||||
\(125\) | 7.43496 | 0.665003 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00000 | −0.532414 | −0.266207 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(128\) | 10.7600 | + | 3.49613i | 0.951057 | + | 0.309017i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.1329 | − | 9.24452i | −0.888718 | − | 0.810798i | ||||
\(131\) | 8.80982i | 0.769718i | 0.922975 | + | 0.384859i | \(0.125750\pi\) | ||||
−0.922975 | + | 0.384859i | \(0.874250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 23.7234i | − | 2.05708i | ||||||
\(134\) | 8.37864 | + | 11.5322i | 0.723804 | + | 0.996231i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.7938 | − | 5.13170i | 1.35430 | − | 0.440040i | ||||
\(137\) | 10.4397i | 0.891922i | 0.895052 | + | 0.445961i | \(0.147138\pi\) | ||||
−0.895052 | + | 0.445961i | \(0.852862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.3188i | − | 1.21451i | −0.794507 | − | 0.607254i | \(-0.792271\pi\) | ||
0.794507 | − | 0.607254i | \(-0.207729\pi\) | |||||||
\(140\) | 21.2426 | + | 6.90212i | 1.79532 | + | 0.583336i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.38197 | + | 1.73060i | −0.199890 | + | 0.145229i | ||||
\(143\) | 15.3713 | − | 3.16228i | 1.28541 | − | 0.264443i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.30327i | 0.689549i | ||||||||
\(146\) | −15.3713 | + | 11.1679i | −1.27213 | + | 0.924260i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.66739 | − | 5.13170i | 0.137059 | − | 0.421823i | ||||
\(149\) | 0.635021 | 0.0520230 | 0.0260115 | − | 0.999662i | \(-0.491719\pi\) | ||||
0.0260115 | + | 0.999662i | \(0.491719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.15163i | − | 0.337855i | −0.985628 | − | 0.168928i | \(-0.945970\pi\) | ||
0.985628 | − | 0.168928i | \(-0.0540304\pi\) | |||||||
\(152\) | 15.3713 | − | 4.99442i | 1.24677 | − | 0.405101i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −20.6743 | + | 15.0208i | −1.66598 | + | 1.21041i | ||||
\(155\) | − | 24.9721i | − | 2.00581i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1150i | 1.28611i | 0.765818 | + | 0.643057i | \(0.222334\pi\) | ||||
−0.765818 | + | 0.643057i | \(0.777666\pi\) | |||||||
\(158\) | 9.09747 | + | 12.5216i | 0.723756 | + | 0.996164i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.2169i | 1.20300i | ||||||||
\(161\) | − | 15.0649i | − | 1.18728i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0795 | 0.789489 | 0.394745 | − | 0.918791i | \(-0.370833\pi\) | ||||
0.394745 | + | 0.918791i | \(0.370833\pi\) | |||||||
\(164\) | 21.1275 | + | 6.86474i | 1.64978 | + | 0.536046i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.09017 | − | 11.1352i | −0.627919 | − | 0.864256i | ||||
\(167\) | 24.2967i | 1.88013i | 0.340992 | + | 0.940066i | \(0.389237\pi\) | ||||
−0.340992 | + | 0.940066i | \(0.610763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9443 | − | 5.13170i | 0.918790 | − | 0.394746i | ||||
\(170\) | 13.1286 | + | 18.0700i | 1.00692 | + | 1.38591i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.23607 | + | 2.35114i | 0.551745 | + | 0.179273i | ||||
\(173\) | 1.17902i | 0.0896395i | 0.998995 | + | 0.0448198i | \(0.0142714\pi\) | ||||
−0.998995 | + | 0.0448198i | \(0.985729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.28334i | 0.701754i | ||||||||
\(176\) | −14.0850 | − | 10.2333i | −1.06170 | − | 0.771367i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.9443 | + | 10.1311i | −1.04517 | + | 0.759359i | ||||
\(179\) | − | 18.7987i | − | 1.40508i | −0.711645 | − | 0.702539i | \(-0.752049\pi\) | ||
0.711645 | − | 0.702539i | \(-0.247951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.2088i | − | 0.981802i | −0.871215 | − | 0.490901i | \(-0.836668\pi\) | ||
0.871215 | − | 0.490901i | \(-0.163332\pi\) | |||||||
\(182\) | −14.2676 | + | 15.6388i | −1.05759 | + | 1.15923i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.76108 | − | 3.17157i | 0.719596 | − | 0.233811i | ||||
\(185\) | 7.25732 | 0.533569 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.5548 | −1.86875 | ||||||||
\(188\) | −9.34003 | − | 3.03476i | −0.681191 | − | 0.221332i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.7774 | + | 17.5866i | 0.926971 | + | 1.27587i | ||||
\(191\) | 15.3713 | 1.11223 | 0.556113 | − | 0.831107i | \(-0.312292\pi\) | ||||
0.556113 | + | 0.831107i | \(0.312292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4350i | 0.967070i | 0.875325 | + | 0.483535i | \(0.160647\pi\) | ||||
−0.875325 | + | 0.483535i | \(0.839353\pi\) | |||||||
\(194\) | −5.87130 | + | 4.26575i | −0.421535 | + | 0.306263i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.32624 | − | 19.4702i | 0.451874 | − | 1.39073i | ||||
\(197\) | −10.6101 | −0.755936 | −0.377968 | − | 0.925819i | \(-0.623377\pi\) | ||||
−0.377968 | + | 0.925819i | \(0.623377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0000 | 1.27599 | 0.637993 | − | 0.770042i | \(-0.279765\pi\) | ||||
0.637993 | + | 0.770042i | \(0.279765\pi\) | |||||||
\(200\) | −6.01501 | + | 1.95440i | −0.425325 | + | 0.138197i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −17.1427 | + | 12.4549i | −1.20616 | + | 0.876324i | ||||
\(203\) | 12.8149 | 0.899433 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.8788i | 2.08682i | ||||||||
\(206\) | 1.41995 | + | 1.95440i | 0.0989327 | + | 0.136169i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.1367 | − | 5.95213i | −0.910864 | − | 0.412706i | ||||
\(209\) | −24.8712 | −1.72038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0130i | 1.17122i | 0.810591 | + | 0.585612i | \(0.199146\pi\) | ||||
−0.810591 | + | 0.585612i | \(0.800854\pi\) | |||||||
\(212\) | −2.24264 | − | 0.728677i | −0.154025 | − | 0.0500457i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.71423 | − | 4.15163i | 0.390617 | − | 0.283800i | ||||
\(215\) | 10.2333i | 0.697908i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38.5410 | −2.61633 | ||||||||
\(218\) | −7.25732 | − | 9.98885i | −0.491528 | − | 0.676530i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.23607 | − | 22.2703i | 0.487856 | − | 1.50147i | ||||
\(221\) | −20.7350 | + | 4.26575i | −1.39479 | + | 0.286945i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.28334i | − | 0.621658i | −0.950466 | − | 0.310829i | \(-0.899393\pi\) | ||
0.950466 | − | 0.310829i | \(-0.100607\pi\) | |||||||
\(224\) | 23.4852 | 1.56917 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.88054 | − | 6.71749i | −0.324649 | − | 0.446840i | ||||
\(227\) | 1.02749 | 0.0681967 | 0.0340983 | − | 0.999418i | \(-0.489144\pi\) | ||||
0.0340983 | + | 0.999418i | \(0.489144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4917 | −1.22196 | −0.610981 | − | 0.791645i | \(-0.709225\pi\) | ||||
−0.610981 | + | 0.791645i | \(0.709225\pi\) | |||||||
\(230\) | 8.11393 | + | 11.1679i | 0.535017 | + | 0.736388i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.69790 | + | 8.30327i | 0.177126 | + | 0.545136i | ||||
\(233\) | 7.25732 | 0.475443 | 0.237722 | − | 0.971333i | \(-0.423599\pi\) | ||||
0.237722 | + | 0.971333i | \(0.423599\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 13.2088i | − | 0.861646i | ||||||
\(236\) | −1.41995 | + | 4.37016i | −0.0924309 | + | 0.284473i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 27.8885 | − | 20.2622i | 1.80775 | − | 1.31340i | ||||
\(239\) | 7.07107i | 0.457389i | 0.973498 | + | 0.228695i | \(0.0734457\pi\) | ||||
−0.973498 | + | 0.228695i | \(0.926554\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.5667i | − | 1.19598i | −0.801502 | − | 0.597992i | \(-0.795965\pi\) | ||
0.801502 | − | 0.597992i | \(-0.204035\pi\) | |||||||
\(242\) | 6.60371 | + | 9.08922i | 0.424502 | + | 0.584277i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.4164 | − | 4.35926i | −0.858898 | − | 0.279073i | ||||
\(245\) | 27.5350 | 1.75914 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.1803 | + | 4.15163i | −1.28404 | + | 0.264162i | ||||
\(248\) | −8.11393 | − | 24.9721i | −0.515235 | − | 1.58573i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.18034 | + | 8.50651i | 0.390879 | + | 0.537999i | ||||
\(251\) | − | 2.35805i | − | 0.148839i | −0.997227 | − | 0.0744193i | \(-0.976290\pi\) | ||
0.997227 | − | 0.0744193i | \(-0.0237103\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.7938 | −0.992945 | ||||||||
\(254\) | −4.98752 | − | 6.86474i | −0.312945 | − | 0.430732i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.94427 | + | 15.2169i | 0.309017 | + | 0.951057i | ||||
\(257\) | 26.2572 | 1.63788 | 0.818941 | − | 0.573878i | \(-0.194562\pi\) | ||||
0.818941 | + | 0.573878i | \(0.194562\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 11.2007i | − | 0.695976i | ||||||
\(260\) | 2.15382 | − | 19.2779i | 0.133574 | − | 1.19556i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.0795 | + | 7.32320i | −0.622715 | + | 0.452429i | ||||
\(263\) | −7.25732 | −0.447506 | −0.223753 | − | 0.974646i | \(-0.571831\pi\) | ||||
−0.223753 | + | 0.974646i | \(0.571831\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.17157i | − | 0.194828i | ||||||
\(266\) | 27.1425 | − | 19.7202i | 1.66421 | − | 1.20912i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.22949 | + | 19.1724i | −0.380526 | + | 1.17114i | ||||
\(269\) | 19.2490i | 1.17363i | 0.809720 | + | 0.586817i | \(0.199619\pi\) | ||||
−0.809720 | + | 0.586817i | \(0.800381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.28334i | − | 0.563923i | −0.959426 | − | 0.281961i | \(-0.909015\pi\) | ||
0.959426 | − | 0.281961i | \(-0.0909850\pi\) | |||||||
\(272\) | 18.9999 | + | 13.8042i | 1.15204 | + | 0.837006i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.9443 | + | 8.67802i | −0.721580 | + | 0.524258i | ||||
\(275\) | 9.73249 | 0.586891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.7153i | − | 1.30475i | −0.757898 | − | 0.652373i | \(-0.773774\pi\) | ||
0.757898 | − | 0.652373i | \(-0.226226\pi\) | |||||||
\(278\) | 16.3825 | − | 11.9026i | 0.982558 | − | 0.713870i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.76108 | + | 30.0415i | 0.583336 | + | 1.79532i | ||||
\(281\) | − | 9.35931i | − | 0.558330i | −0.960243 | − | 0.279165i | \(-0.909942\pi\) | ||
0.960243 | − | 0.279165i | \(-0.0900576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.3107i | 0.731797i | 0.930655 | + | 0.365899i | \(0.119238\pi\) | ||||
−0.930655 | + | 0.365899i | \(0.880762\pi\) | |||||||
\(284\) | −3.96004 | − | 1.28669i | −0.234985 | − | 0.0763512i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.3955 | + | 14.9579i | 0.969483 | + | 0.884482i | ||||
\(287\) | 46.1138 | 2.72201 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.4721 | 1.02777 | ||||||||
\(290\) | −9.49996 | + | 6.90212i | −0.557857 | + | 0.405307i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −25.5548 | − | 8.30327i | −1.49548 | − | 0.485912i | ||||
\(293\) | −25.4800 | −1.48856 | −0.744278 | − | 0.667869i | \(-0.767206\pi\) | ||||
−0.744278 | + | 0.667869i | \(0.767206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.18034 | −0.359833 | ||||||||
\(296\) | 7.25732 | − | 2.35805i | 0.421823 | − | 0.137059i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.527864 | + | 0.726543i | 0.0305783 | + | 0.0420875i | ||||
\(299\) | −12.8149 | + | 2.63638i | −0.741108 | + | 0.152466i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.7938 | 0.910337 | ||||||||
\(302\) | 4.74998 | − | 3.45106i | 0.273331 | − | 0.198586i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.4917 | + | 13.4350i | 1.06057 | + | 0.770548i | ||||
\(305\) | − | 18.9737i | − | 1.08643i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.04684 | 0.230966 | 0.115483 | − | 0.993309i | \(-0.463158\pi\) | ||||
0.115483 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(308\) | −34.3712 | − | 11.1679i | −1.95848 | − | 0.636349i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 28.5712 | − | 20.7582i | 1.62273 | − | 1.17898i | ||||
\(311\) | −10.8860 | −0.617288 | −0.308644 | − | 0.951178i | \(-0.599875\pi\) | ||||
−0.308644 | + | 0.951178i | \(0.599875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47214 | −0.139733 | −0.0698667 | − | 0.997556i | \(-0.522257\pi\) | ||||
−0.0698667 | + | 0.997556i | \(0.522257\pi\) | |||||||
\(314\) | −18.4375 | + | 13.3956i | −1.04049 | + | 0.755959i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.76393 | + | 20.8172i | −0.380501 | + | 1.17106i | ||||
\(317\) | −14.2349 | −0.799512 | −0.399756 | − | 0.916622i | \(-0.630905\pi\) | ||||
−0.399756 | + | 0.916622i | \(0.630905\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 13.4350i | − | 0.752214i | ||||||
\(320\) | −17.4100 | + | 12.6491i | −0.973249 | + | 0.707107i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.2361 | − | 12.5227i | 0.960529 | − | 0.697865i | ||||
\(323\) | 33.5500 | 1.86677 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.89688 | − | 1.62460i | 0.438040 | − | 0.0901165i | ||||
\(326\) | 8.37864 | + | 11.5322i | 0.464050 | + | 0.638710i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.70820 | + | 29.8788i | 0.536046 | + | 1.64978i | ||||
\(329\) | −20.3859 | −1.12391 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.01634 | −0.165793 | −0.0828965 | − | 0.996558i | \(-0.526417\pi\) | ||||
−0.0828965 | + | 0.996558i | \(0.526417\pi\) | |||||||
\(332\) | 6.01501 | − | 18.5123i | 0.330117 | − | 1.01599i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −27.7984 | + | 20.1967i | −1.52106 | + | 1.10511i | ||||
\(335\) | −27.1139 | −1.48139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4721 | 0.788347 | 0.394174 | − | 0.919036i | \(-0.371031\pi\) | ||||
0.394174 | + | 0.919036i | \(0.371031\pi\) | |||||||
\(338\) | 15.8000 | + | 9.39997i | 0.859408 | + | 0.511291i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.76108 | + | 30.0415i | −0.529369 | + | 1.62923i | ||||
\(341\) | 40.4057i | 2.18809i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.4350i | − | 0.725420i | ||||||
\(344\) | 3.32502 | + | 10.2333i | 0.179273 | + | 0.551745i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.34895 | + | 0.980068i | −0.0725199 | + | 0.0526888i | ||||
\(347\) | 28.5092i | 1.53045i | 0.643761 | + | 0.765227i | \(0.277373\pi\) | ||||
−0.643761 | + | 0.765227i | \(0.722627\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.76108 | 0.522499 | 0.261249 | − | 0.965271i | \(-0.415866\pi\) | ||||
0.261249 | + | 0.965271i | \(0.415866\pi\) | |||||||
\(350\) | −10.6213 | + | 7.71681i | −0.567731 | + | 0.412481i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 24.6215i | − | 1.31233i | ||||||
\(353\) | 7.86629i | 0.418680i | 0.977843 | + | 0.209340i | \(0.0671316\pi\) | ||||
−0.977843 | + | 0.209340i | \(0.932868\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.60034i | − | 0.297235i | ||||||
\(356\) | −23.1825 | − | 7.53244i | −1.22867 | − | 0.399218i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.5080 | − | 15.6265i | 1.13673 | − | 0.825885i | ||||
\(359\) | − | 13.1406i | − | 0.693533i | −0.937951 | − | 0.346767i | \(-0.887280\pi\) | ||
0.937951 | − | 0.346767i | \(-0.112720\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.6525 | 0.718551 | ||||||||
\(362\) | 15.1125 | − | 10.9799i | 0.794294 | − | 0.577089i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −29.7527 | − | 3.32412i | −1.55947 | − | 0.174231i | ||||
\(365\) | − | 36.1400i | − | 1.89165i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.12461 | −0.476301 | −0.238150 | − | 0.971228i | \(-0.576541\pi\) | ||||
−0.238150 | + | 0.971228i | \(0.576541\pi\) | |||||||
\(368\) | 11.7426 | + | 8.53149i | 0.612125 | + | 0.444735i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.03268 | + | 8.30327i | 0.313624 | + | 0.431666i | ||||
\(371\) | −4.89487 | −0.254129 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.343027i | 0.0177613i | 0.999961 | + | 0.00888063i | \(0.00282683\pi\) | ||||
−0.999961 | + | 0.00888063i | \(0.997173\pi\) | |||||||
\(374\) | −21.2426 | − | 29.2379i | −1.09843 | − | 1.51185i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.29180 | − | 13.2088i | −0.221332 | − | 0.681191i | ||||
\(377\) | −2.24264 | − | 10.9010i | −0.115502 | − | 0.561432i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8101 | −0.966210 | −0.483105 | − | 0.875563i | \(-0.660491\pi\) | ||||
−0.483105 | + | 0.875563i | \(0.660491\pi\) | |||||||
\(380\) | −9.49996 | + | 29.2379i | −0.487338 | + | 1.49987i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.7774 | + | 17.5866i | 0.653750 | + | 0.899809i | ||||
\(383\) | 16.2241i | 0.829010i | 0.910047 | + | 0.414505i | \(0.136045\pi\) | ||||
−0.910047 | + | 0.414505i | \(0.863955\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 48.6082i | − | 2.47730i | ||||||
\(386\) | −15.3713 | + | 11.1679i | −0.782376 | + | 0.568430i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.76108 | − | 3.17157i | −0.495544 | − | 0.161012i | ||||
\(389\) | − | 11.6182i | − | 0.589067i | −0.955641 | − | 0.294534i | \(-0.904836\pi\) | ||
0.955641 | − | 0.294534i | \(-0.0951643\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.3050 | 1.07744 | ||||||||
\(392\) | 27.5350 | − | 8.94665i | 1.39073 | − | 0.451874i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.81966 | − | 12.1392i | −0.444328 | − | 0.611565i | ||||
\(395\) | −29.4400 | −1.48129 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.5243 | −1.23084 | −0.615420 | − | 0.788199i | \(-0.711014\pi\) | ||||
−0.615420 | + | 0.788199i | \(0.711014\pi\) | |||||||
\(398\) | 14.9626 | + | 20.5942i | 0.750006 | + | 1.03229i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.23607 | − | 5.25731i | −0.361803 | − | 0.262866i | ||||
\(401\) | 23.3438i | 1.16574i | 0.812567 | + | 0.582868i | \(0.198069\pi\) | ||||
−0.812567 | + | 0.582868i | \(0.801931\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.74474 | + | 32.7849i | 0.335979 | + | 1.63313i | ||||
\(404\) | −28.4999 | − | 9.26017i | −1.41792 | − | 0.460711i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.6525 | + | 14.6619i | 0.528673 | + | 0.727657i | ||||
\(407\) | −11.7426 | −0.582059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15.3951i | − | 0.761239i | −0.924732 | − | 0.380620i | \(-0.875711\pi\) | ||
0.924732 | − | 0.380620i | \(-0.124289\pi\) | |||||||
\(410\) | −34.1850 | + | 24.8369i | −1.68828 | + | 1.22660i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.05573 | + | 3.24920i | −0.0520120 | + | 0.160076i | ||||
\(413\) | 9.53850i | 0.469359i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.1803 | 1.28514 | ||||||||
\(416\) | −4.10995 | − | 19.9777i | −0.201507 | − | 0.979487i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.6743 | − | 28.4557i | −1.01121 | − | 1.39182i | ||||
\(419\) | − | 14.9833i | − | 0.731981i | −0.930619 | − | 0.365990i | \(-0.880730\pi\) | ||
0.930619 | − | 0.365990i | \(-0.119270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.7938 | 0.769741 | 0.384870 | − | 0.922971i | \(-0.374246\pi\) | ||||
0.384870 | + | 0.922971i | \(0.374246\pi\) | |||||||
\(422\) | −19.4650 | + | 14.1421i | −0.947540 | + | 0.688428i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.03050 | − | 3.17157i | −0.0500457 | − | 0.154025i | ||||
\(425\) | −13.1286 | −0.636832 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.2832 | −1.41711 | ||||||||
\(428\) | 9.49996 | + | 3.08672i | 0.459198 | + | 0.149202i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.7082 | + | 8.50651i | −0.564620 | + | 0.410220i | ||||
\(431\) | 20.8005i | 1.00193i | 0.865468 | + | 0.500963i | \(0.167021\pi\) | ||||
−0.865468 | + | 0.500963i | \(0.832979\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.1803 | 0.681464 | 0.340732 | − | 0.940161i | \(-0.389325\pi\) | ||||
0.340732 | + | 0.940161i | \(0.389325\pi\) | |||||||
\(434\) | −32.0374 | − | 44.0957i | −1.53784 | − | 2.11666i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.39579 | − | 16.6065i | 0.258412 | − | 0.795309i | ||||
\(437\) | 20.7350 | 0.991891 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.1803 | 1.15406 | 0.577032 | − | 0.816721i | \(-0.304211\pi\) | ||||
0.577032 | + | 0.816721i | \(0.304211\pi\) | |||||||
\(440\) | 31.4950 | − | 10.2333i | 1.50147 | − | 0.487856i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.1166 | − | 20.1775i | −1.05198 | − | 0.959745i | ||||
\(443\) | − | 1.17902i | − | 0.0560171i | −0.999608 | − | 0.0280086i | \(-0.991083\pi\) | ||
0.999608 | − | 0.0280086i | \(-0.00891656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 32.7849i | − | 1.55416i | ||||||
\(446\) | 10.6213 | − | 7.71681i | 0.502932 | − | 0.365402i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.5222 | + | 26.8699i | 0.922335 | + | 1.26949i | ||||
\(449\) | 33.3221i | 1.57257i | 0.617865 | + | 0.786284i | \(0.287998\pi\) | ||||
−0.617865 | + | 0.786284i | \(0.712002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 48.3449i | − | 2.27647i | ||||||
\(452\) | 3.62866 | − | 11.1679i | 0.170678 | − | 0.525293i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.854102 | + | 1.17557i | 0.0400850 | + | 0.0551723i | ||||
\(455\) | −8.11393 | − | 39.4404i | −0.380387 | − | 1.84899i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 38.3448i | − | 1.79369i | −0.442342 | − | 0.896847i | \(-0.645852\pi\) | ||
0.442342 | − | 0.896847i | \(-0.354148\pi\) | |||||||
\(458\) | −15.3713 | − | 21.1567i | −0.718252 | − | 0.988589i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.03268 | + | 18.5667i | −0.281275 | + | 0.865676i | ||||
\(461\) | 24.6951 | 1.15016 | 0.575082 | − | 0.818096i | \(-0.304970\pi\) | ||||
0.575082 | + | 0.818096i | \(0.304970\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.15163i | 0.192943i | 0.995336 | + | 0.0964714i | \(0.0307556\pi\) | ||||
−0.995336 | + | 0.0964714i | \(0.969244\pi\) | |||||||
\(464\) | −7.25732 | + | 9.98885i | −0.336913 | + | 0.463721i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.03268 | + | 8.30327i | 0.279458 | + | 0.384641i | ||||
\(467\) | 6.17345i | 0.285673i | 0.989746 | + | 0.142837i | \(0.0456223\pi\) | ||||
−0.989746 | + | 0.142837i | \(0.954378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.8465i | 1.93229i | ||||||||
\(470\) | 15.1125 | − | 10.9799i | 0.697087 | − | 0.506463i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.18034 | + | 2.00811i | −0.284473 | + | 0.0924309i | ||||
\(473\) | − | 16.5579i | − | 0.761333i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.7774 | −0.586268 | ||||||||
\(476\) | 46.3649 | + | 15.0649i | 2.12513 | + | 0.690497i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.09017 | + | 5.87785i | −0.370036 | + | 0.268847i | ||||
\(479\) | − | 10.3122i | − | 0.471174i | −0.971853 | − | 0.235587i | \(-0.924299\pi\) | ||
0.971853 | − | 0.235587i | \(-0.0757013\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.52786 | + | 1.96014i | −0.434433 | + | 0.0893745i | ||||
\(482\) | 21.2426 | − | 15.4336i | 0.967572 | − | 0.702982i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.90983 | + | 15.1109i | −0.223174 | + | 0.686859i | ||||
\(485\) | − | 13.8042i | − | 0.626819i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.5866i | − | 0.796925i | −0.917185 | − | 0.398463i | \(-0.869544\pi\) | ||
0.917185 | − | 0.398463i | \(-0.130456\pi\) | |||||||
\(488\) | −6.16492 | − | 18.9737i | −0.279073 | − | 0.858898i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 22.8885 | + | 31.5034i | 1.03400 | + | 1.42318i | ||||
\(491\) | − | 26.1511i | − | 1.18018i | −0.807336 | − | 0.590092i | \(-0.799091\pi\) | ||
0.807336 | − | 0.590092i | \(-0.200909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.1231i | 0.816222i | ||||||||
\(494\) | −21.5250 | − | 19.6377i | −0.968454 | − | 0.883543i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.8264 | − | 30.0415i | 0.980036 | − | 1.34890i | ||||
\(497\) | −8.64335 | −0.387707 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.3628 | 1.76212 | 0.881059 | − | 0.473006i | \(-0.156831\pi\) | ||||
0.881059 | + | 0.473006i | \(0.156831\pi\) | |||||||
\(500\) | −4.59506 | + | 14.1421i | −0.205497 | + | 0.632456i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.69790 | − | 1.96014i | 0.120413 | − | 0.0874851i | ||||
\(503\) | −18.9999 | −0.847164 | −0.423582 | − | 0.905858i | \(-0.639228\pi\) | ||||
−0.423582 | + | 0.905858i | \(0.639228\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 40.3049i | − | 1.79355i | ||||||
\(506\) | −13.1286 | − | 18.0700i | −0.583638 | − | 0.803309i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.70820 | − | 11.4127i | 0.164525 | − | 0.506356i | ||||
\(509\) | 27.5350 | 1.22047 | 0.610233 | − | 0.792222i | \(-0.291076\pi\) | ||||
0.610233 | + | 0.792222i | \(0.291076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −55.7771 | −2.46743 | ||||||||
\(512\) | −13.3001 | + | 18.3060i | −0.587785 | + | 0.809017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.8264 | + | 30.0415i | 0.962723 | + | 1.32507i | ||||
\(515\) | −4.59506 | −0.202482 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.3723i | 0.939951i | ||||||||
\(518\) | 12.8149 | − | 9.31061i | 0.563057 | − | 0.409085i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.8466 | − | 13.5606i | 1.04574 | − | 0.594671i | ||||
\(521\) | −24.8712 | −1.08963 | −0.544814 | − | 0.838557i | \(-0.683400\pi\) | ||||
−0.544814 | + | 0.838557i | \(0.683400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 21.9273i | − | 0.958814i | −0.877593 | − | 0.479407i | \(-0.840852\pi\) | ||
0.877593 | − | 0.479407i | \(-0.159148\pi\) | |||||||
\(524\) | −16.7573 | − | 5.44477i | −0.732045 | − | 0.237856i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.03268 | − | 8.30327i | −0.263037 | − | 0.362040i | ||||
\(527\) | − | 54.5052i | − | 2.37429i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.83282 | −0.427514 | ||||||||
\(530\) | 3.62866 | − | 2.63638i | 0.157619 | − | 0.114517i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 45.1246 | + | 14.6619i | 1.95640 | + | 0.635673i | ||||
\(533\) | −8.06998 | − | 39.2267i | −0.349550 | − | 1.69910i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.4350i | 0.580844i | ||||||||
\(536\) | −27.1139 | + | 8.80982i | −1.17114 | + | 0.380526i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.0232 | + | 16.0008i | −0.949489 | + | 0.689844i | ||||
\(539\) | −44.5525 | −1.91901 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.3486 | 1.77771 | 0.888857 | − | 0.458184i | \(-0.151500\pi\) | ||||
0.888857 | + | 0.458184i | \(0.151500\pi\) | |||||||
\(542\) | 10.6213 | − | 7.71681i | 0.456223 | − | 0.331465i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 33.2131i | 1.42400i | ||||||||
\(545\) | 23.4852 | 1.00600 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.212002i | 0.00906456i | 0.999990 | + | 0.00453228i | \(0.00144267\pi\) | ||||
−0.999990 | + | 0.00453228i | \(0.998557\pi\) | |||||||
\(548\) | −19.8574 | − | 6.45207i | −0.848268 | − | 0.275619i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.09017 | + | 11.1352i | 0.344966 | + | 0.474805i | ||||
\(551\) | 17.6383i | 0.751415i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45.4366i | 1.93216i | ||||||||
\(554\) | 24.8450 | − | 18.0509i | 1.05556 | − | 0.766910i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.2361 | + | 8.84953i | 1.15507 | + | 0.375304i | ||||
\(557\) | 3.47492 | 0.147237 | 0.0736186 | − | 0.997286i | \(-0.476545\pi\) | ||||
0.0736186 | + | 0.997286i | \(0.476545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.76393 | − | 13.4350i | −0.116902 | − | 0.568239i | ||||
\(560\) | −26.2572 | + | 36.1400i | −1.10957 | + | 1.52719i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.7082 | − | 7.77997i | 0.451698 | − | 0.328178i | ||||
\(563\) | 21.1567i | 0.891649i | 0.895120 | + | 0.445825i | \(0.147090\pi\) | ||||
−0.895120 | + | 0.445825i | \(0.852910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.7938 | 0.664448 | ||||||||
\(566\) | −14.0850 | + | 10.2333i | −0.592036 | + | 0.430140i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.81966 | − | 5.60034i | −0.0763512 | − | 0.234985i | ||||
\(569\) | 4.48527 | 0.188032 | 0.0940162 | − | 0.995571i | \(-0.470029\pi\) | ||||
0.0940162 | + | 0.995571i | \(0.470029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5.81234i | − | 0.243239i | −0.992577 | − | 0.121619i | \(-0.961191\pi\) | ||
0.992577 | − | 0.121619i | \(-0.0388087\pi\) | |||||||
\(572\) | −3.48495 | + | 31.1923i | −0.145713 | + | 1.30421i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 38.3323 | + | 52.7598i | 1.59996 | + | 2.20215i | ||||
\(575\) | −8.11393 | −0.338374 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6464i | 0.609738i | 0.952394 | + | 0.304869i | \(0.0986126\pi\) | ||||
−0.952394 | + | 0.304869i | \(0.901387\pi\) | |||||||
\(578\) | 14.5238 | + | 19.9903i | 0.604110 | + | 0.831486i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.7938 | − | 5.13170i | −0.655800 | − | 0.213082i | ||||
\(581\) | − | 40.4057i | − | 1.67631i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.13170i | 0.212533i | ||||||||
\(584\) | −11.7426 | − | 36.1400i | −0.485912 | − | 1.49548i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.1803 | − | 29.1522i | −0.874952 | − | 1.20427i | ||||
\(587\) | 25.0875 | 1.03547 | 0.517736 | − | 0.855540i | \(-0.326775\pi\) | ||||
0.517736 | + | 0.855540i | \(0.326775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 53.0472i | − | 2.18577i | ||||||
\(590\) | −5.13743 | − | 7.07107i | −0.211505 | − | 0.291111i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.73057 | + | 6.34313i | 0.358824 | + | 0.260701i | ||||
\(593\) | − | 17.1769i | − | 0.705370i | −0.935742 | − | 0.352685i | \(-0.885269\pi\) | ||
0.935742 | − | 0.352685i | \(-0.114731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 65.5699i | 2.68810i | ||||||||
\(596\) | −0.392465 | + | 1.20788i | −0.0160760 | + | 0.0494768i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.6688 | − | 12.4704i | −0.558959 | − | 0.509952i | ||||
\(599\) | −27.9705 | −1.14284 | −0.571421 | − | 0.820657i | \(-0.693608\pi\) | ||||
−0.571421 | + | 0.820657i | \(0.693608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.41641 | −0.302522 | −0.151261 | − | 0.988494i | \(-0.548333\pi\) | ||||
−0.151261 | + | 0.988494i | \(0.548333\pi\) | |||||||
\(602\) | 13.1286 | + | 18.0700i | 0.535083 | + | 0.736478i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.89688 | + | 2.56585i | 0.321319 | + | 0.104403i | ||||
\(605\) | −21.3700 | −0.868816 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.29180 | 0.0930211 | 0.0465106 | − | 0.998918i | \(-0.485190\pi\) | ||||
0.0465106 | + | 0.998918i | \(0.485190\pi\) | |||||||
\(608\) | 32.3246i | 1.31094i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.7082 | − | 15.7719i | 0.878939 | − | 0.638587i | ||||
\(611\) | 3.56757 | + | 17.3413i | 0.144329 | + | 0.701555i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2854 | −1.38477 | −0.692387 | − | 0.721526i | \(-0.743441\pi\) | ||||
−0.692387 | + | 0.721526i | \(0.743441\pi\) | |||||||
\(614\) | 3.36395 | + | 4.63009i | 0.135758 | + | 0.186855i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.7938 | − | 48.6082i | −0.636349 | − | 1.95848i | ||||
\(617\) | − | 6.53089i | − | 0.262924i | −0.991321 | − | 0.131462i | \(-0.958033\pi\) | ||
0.991321 | − | 0.131462i | \(-0.0419671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.2996 | −1.29823 | −0.649115 | − | 0.760691i | \(-0.724860\pi\) | ||||
−0.649115 | + | 0.760691i | \(0.724860\pi\) | |||||||
\(620\) | 47.4998 | + | 15.4336i | 1.90764 | + | 0.619829i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.04902 | − | 12.4549i | −0.362833 | − | 0.499396i | ||||
\(623\) | −50.5990 | −2.02721 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1803 | −1.24721 | ||||||||
\(626\) | −2.05497 | − | 2.82843i | −0.0821332 | − | 0.113047i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.6525 | − | 9.95959i | −1.22317 | − | 0.397431i | ||||
\(629\) | 15.8401 | 0.631588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.32320i | − | 0.291532i | −0.989319 | − | 0.145766i | \(-0.953435\pi\) | ||
0.989319 | − | 0.145766i | \(-0.0465647\pi\) | |||||||
\(632\) | −29.4400 | + | 9.56564i | −1.17106 | + | 0.380501i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.8328 | − | 16.2865i | −0.469941 | − | 0.646818i | ||||
\(635\) | 16.1400 | 0.640495 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.1496 | + | 7.43694i | −1.43230 | + | 0.294662i | ||||
\(638\) | 15.3713 | − | 11.1679i | 0.608554 | − | 0.442140i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28.9443 | − | 9.40456i | −1.14412 | − | 0.371748i | ||||
\(641\) | 27.6433 | 1.09184 | 0.545922 | − | 0.837836i | \(-0.316180\pi\) | ||||
0.545922 | + | 0.837836i | \(0.316180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.9691 | 1.53679 | 0.768396 | − | 0.639974i | \(-0.221055\pi\) | ||||
0.768396 | + | 0.639974i | \(0.221055\pi\) | |||||||
\(644\) | 28.6551 | + | 9.31061i | 1.12917 | + | 0.366889i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.8885 | + | 38.3853i | 1.09726 | + | 1.51025i | ||||
\(647\) | 16.2279 | 0.637983 | 0.318992 | − | 0.947758i | \(-0.396656\pi\) | ||||
0.318992 | + | 0.947758i | \(0.396656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | 0.392534 | ||||||||
\(650\) | 8.42305 | + | 7.68454i | 0.330379 | + | 0.301413i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.22949 | + | 19.1724i | −0.243966 | + | 0.750849i | ||||
\(653\) | − | 37.7694i | − | 1.47803i | −0.673689 | − | 0.739015i | \(-0.735291\pi\) | ||
0.673689 | − | 0.739015i | \(-0.264709\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 23.6984i | − | 0.925972i | ||||||
\(656\) | −26.1150 | + | 35.9442i | −1.01962 | + | 1.40339i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.9459 | − | 23.3240i | −0.660620 | − | 0.909265i | ||||
\(659\) | 1.45735i | 0.0567704i | 0.999597 | + | 0.0283852i | \(0.00903651\pi\) | ||||
−0.999597 | + | 0.0283852i | \(0.990963\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4938 | −0.913804 | −0.456902 | − | 0.889517i | \(-0.651041\pi\) | ||||
−0.456902 | + | 0.889517i | \(0.651041\pi\) | |||||||
\(662\) | −2.50734 | − | 3.45106i | −0.0974507 | − | 0.134129i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.1803 | − | 8.50651i | 1.01599 | − | 0.330117i | ||||
\(665\) | 63.8158i | 2.47467i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.2007i | 0.433692i | ||||||||
\(668\) | −46.2150 | − | 15.0162i | −1.78811 | − | 0.580993i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −22.5385 | − | 31.0216i | −0.870738 | − | 1.19847i | ||||
\(671\) | 30.7000i | 1.18516i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6525 | 0.719000 | 0.359500 | − | 0.933145i | \(-0.382947\pi\) | ||||
0.359500 | + | 0.933145i | \(0.382947\pi\) | |||||||
\(674\) | 12.0300 | + | 16.5579i | 0.463379 | + | 0.637787i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.37911 | + | 25.8909i | 0.0915043 | + | 0.995805i | ||||
\(677\) | 33.5036i | 1.28765i | 0.765173 | + | 0.643824i | \(0.222653\pi\) | ||||
−0.765173 | + | 0.643824i | \(0.777347\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.3050 | −0.817609 | ||||||||
\(680\) | −42.4851 | + | 13.8042i | −1.62923 | + | 0.529369i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −46.2291 | + | 33.5874i | −1.77020 | + | 1.28613i | ||||
\(683\) | 25.0875 | 0.959947 | 0.479974 | − | 0.877283i | \(-0.340646\pi\) | ||||
0.479974 | + | 0.877283i | \(0.340646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 28.0827i | − | 1.07298i | ||||||
\(686\) | 15.3713 | − | 11.1679i | 0.586877 | − | 0.426391i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.94427 | + | 12.3107i | −0.340997 | + | 0.469342i | ||||
\(689\) | 0.856611 | + | 4.16383i | 0.0326343 | + | 0.158629i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.34895 | 0.0513164 | 0.0256582 | − | 0.999671i | \(-0.491832\pi\) | ||||
0.0256582 | + | 0.999671i | \(0.491832\pi\) | |||||||
\(692\) | −2.24264 | − | 0.728677i | −0.0852522 | − | 0.0277001i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.6180 | + | 23.6984i | −1.23816 | + | 0.899578i | ||||
\(695\) | 38.5176i | 1.46106i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 65.2147i | 2.47018i | ||||||||
\(698\) | 8.11393 | + | 11.1679i | 0.307117 | + | 0.422710i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.6580 | − | 5.73742i | −0.667408 | − | 0.216854i | ||||
\(701\) | 5.44477i | 0.205646i | 0.994700 | + | 0.102823i | \(0.0327876\pi\) | ||||
−0.994700 | + | 0.102823i | \(0.967212\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.4164 | 0.581441 | ||||||||
\(704\) | 28.1700 | − | 20.4667i | 1.06170 | − | 0.771367i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 6.53888i | −0.338719 | + | 0.246094i | ||||
\(707\) | −62.2051 | −2.33946 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.7938 | −0.593147 | −0.296573 | − | 0.955010i | \(-0.595844\pi\) | ||||
−0.296573 | + | 0.955010i | \(0.595844\pi\) | |||||||
\(710\) | 6.40747 | − | 4.65530i | 0.240468 | − | 0.174710i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.6525 | − | 32.7849i | −0.399218 | − | 1.22867i | ||||
\(713\) | − | 33.6861i | − | 1.26155i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41.3486 | + | 8.50651i | −1.54635 | + | 0.318125i | ||||
\(716\) | 35.7572 | + | 11.6182i | 1.33631 | + | 0.434193i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.0344 | − | 10.9232i | 0.561080 | − | 0.407649i | ||||
\(719\) | 27.1139 | 1.01118 | 0.505588 | − | 0.862775i | \(-0.331276\pi\) | ||||
0.505588 | + | 0.862775i | \(0.331276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.09184i | 0.264114i | ||||||||
\(722\) | 11.3487 | + | 15.6201i | 0.422354 | + | 0.581320i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 25.1246 | + | 8.16348i | 0.933749 | + | 0.303393i | ||||
\(725\) | − | 6.90212i | − | 0.256338i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.3607 | 0.829312 | 0.414656 | − | 0.909978i | \(-0.363902\pi\) | ||||
0.414656 | + | 0.909978i | \(0.363902\pi\) | |||||||
\(728\) | −20.9289 | − | 36.8040i | −0.775676 | − | 1.36405i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 41.3486 | − | 30.0415i | 1.53038 | − | 1.11189i | ||||
\(731\) | 22.3357i | 0.826117i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.9179 | −0.920365 | −0.460183 | − | 0.887824i | \(-0.652216\pi\) | ||||
−0.460183 | + | 0.887824i | \(0.652216\pi\) | |||||||
\(734\) | −7.58487 | − | 10.4397i | −0.279963 | − | 0.385335i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.5268i | 0.756628i | ||||||||
\(737\) | 43.8711 | 1.61601 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.6017 | 1.08892 | 0.544458 | − | 0.838788i | \(-0.316736\pi\) | ||||
0.544458 | + | 0.838788i | \(0.316736\pi\) | |||||||
\(740\) | −4.48527 | + | 13.8042i | −0.164882 | + | 0.507454i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.06888 | − | 5.60034i | −0.149373 | − | 0.205595i | ||||
\(743\) | 3.31990i | 0.121795i | 0.998144 | + | 0.0608977i | \(0.0193963\pi\) | ||||
−0.998144 | + | 0.0608977i | \(0.980604\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.70820 | −0.0625837 | ||||||||
\(746\) | −0.392465 | + | 0.285142i | −0.0143692 | + | 0.0104398i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.7938 | − | 48.6082i | 0.577477 | − | 1.77729i | ||||
\(749\) | 20.7350 | 0.757641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5410 | 0.457628 | 0.228814 | − | 0.973470i | \(-0.426515\pi\) | ||||
0.228814 | + | 0.973470i | \(0.426515\pi\) | |||||||
\(752\) | 11.5449 | − | 15.8902i | 0.420999 | − | 0.579456i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.6079 | − | 11.6274i | 0.386318 | − | 0.423445i | ||||
\(755\) | 11.1679i | 0.406440i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.25731i | − | 0.191080i | −0.995426 | − | 0.0955401i | \(-0.969542\pi\) | ||
0.995426 | − | 0.0955401i | \(-0.0304578\pi\) | |||||||
\(758\) | −15.6360 | − | 21.5211i | −0.567924 | − | 0.781680i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −41.3486 | + | 13.4350i | −1.49987 | + | 0.487338i | ||||
\(761\) | − | 13.2681i | − | 0.480968i | −0.970653 | − | 0.240484i | \(-0.922694\pi\) | ||
0.970653 | − | 0.240484i | \(-0.0773062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 36.2461i | − | 1.31220i | ||||||
\(764\) | −9.49996 | + | 29.2379i | −0.343696 | + | 1.05779i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.5623 | + | 13.4863i | −0.670683 | + | 0.487280i | ||||
\(767\) | 8.11393 | − | 1.66925i | 0.292977 | − | 0.0602732i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.6480i | 1.68217i | 0.540902 | + | 0.841086i | \(0.318083\pi\) | ||||
−0.540902 | + | 0.841086i | \(0.681917\pi\) | |||||||
\(770\) | 55.6137 | − | 40.4057i | 2.00418 | − | 1.45612i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.5548 | − | 8.30327i | −0.919739 | − | 0.298841i | ||||
\(773\) | −37.0249 | −1.33169 | −0.665846 | − | 0.746089i | \(-0.731929\pi\) | ||||
−0.665846 | + | 0.746089i | \(0.731929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.7582i | 0.745656i | ||||||||
\(776\) | −4.48527 | − | 13.8042i | −0.161012 | − | 0.495544i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.2927 | − | 9.65769i | 0.476565 | − | 0.346245i | ||||
\(779\) | 63.4702i | 2.27405i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.06154i | 0.324247i | ||||||||
\(782\) | 17.7098 | + | 24.3755i | 0.633302 | + | 0.871665i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 33.1246 | + | 24.0664i | 1.18302 | + | 0.859516i | ||||
\(785\) | − | 43.3491i | − | 1.54720i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.07735 | 0.180988 | 0.0904940 | − | 0.995897i | \(-0.471155\pi\) | ||||
0.0904940 | + | 0.995897i | \(0.471155\pi\) | |||||||
\(788\) | 6.55738 | − | 20.1815i | 0.233597 | − | 0.718938i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −24.4721 | − | 33.6830i | −0.870680 | − | 1.19839i | ||||
\(791\) | − | 24.3755i | − | 0.866692i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.12461 | + | 24.9098i | 0.181980 | + | 0.884573i | ||||
\(794\) | −20.3859 | − | 28.0588i | −0.723470 | − | 0.995771i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.1246 | + | 34.2380i | −0.394301 | + | 1.21353i | ||||
\(797\) | − | 15.4336i | − | 0.546687i | −0.961917 | − | 0.273343i | \(-0.911870\pi\) | ||
0.961917 | − | 0.273343i | \(-0.0881295\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 28.8301i | − | 1.01993i | ||||||
\(800\) | − | 12.6491i | − | 0.447214i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.7082 | + | 19.4046i | −0.943099 | + | 0.685202i | ||||
\(803\) | 58.4757i | 2.06356i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.5244i | 1.42830i | ||||||||
\(806\) | −31.9034 | + | 34.9694i | −1.12375 | + | 1.23175i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.0959 | − | 40.3049i | −0.460711 | − | 1.41792i | ||||
\(809\) | 20.3859 | 0.716732 | 0.358366 | − | 0.933581i | \(-0.383334\pi\) | ||||
0.358366 | + | 0.933581i | \(0.383334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.6365 | 1.42694 | 0.713471 | − | 0.700685i | \(-0.247122\pi\) | ||||
0.713471 | + | 0.700685i | \(0.247122\pi\) | |||||||
\(812\) | −7.92007 | + | 24.3755i | −0.277940 | + | 0.855412i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.76108 | − | 13.4350i | −0.342126 | − | 0.470895i | ||||
\(815\) | −27.1139 | −0.949757 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.7382i | 0.760525i | ||||||||
\(818\) | 17.6139 | − | 12.7972i | 0.615855 | − | 0.447445i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −56.8328 | − | 18.4661i | −1.98469 | − | 0.644864i | ||||
\(821\) | −30.0750 | −1.04963 | −0.524813 | − | 0.851217i | \(-0.675865\pi\) | ||||
−0.524813 | + | 0.851217i | \(0.675865\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.18034 | −0.285149 | −0.142574 | − | 0.989784i | \(-0.545538\pi\) | ||||
−0.142574 | + | 0.989784i | \(0.545538\pi\) | |||||||
\(824\) | −4.59506 | + | 1.49302i | −0.160076 | + | 0.0520120i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.9132 | + | 7.92892i | −0.379719 | + | 0.275882i | ||||
\(827\) | 40.7424 | 1.41675 | 0.708376 | − | 0.705836i | \(-0.249428\pi\) | ||||
0.708376 | + | 0.705836i | \(0.249428\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.84953i | − | 0.307357i | −0.988121 | − | 0.153679i | \(-0.950888\pi\) | ||
0.988121 | − | 0.153679i | \(-0.0491120\pi\) | |||||||
\(830\) | 21.7625 | + | 29.9535i | 0.755388 | + | 1.03970i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.4405 | − | 21.3088i | 0.673979 | − | 0.738750i | ||||
\(833\) | 60.0990 | 2.08231 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 65.3579i | − | 2.26180i | ||||||
\(836\) | 15.3713 | − | 47.3079i | 0.531626 | − | 1.63618i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.1427 | − | 12.4549i | 0.592185 | − | 0.430247i | ||||
\(839\) | − | 30.8763i | − | 1.06597i | −0.846126 | − | 0.532984i | \(-0.821071\pi\) | ||
0.846126 | − | 0.532984i | \(-0.178929\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.4721 | 0.671453 | ||||||||
\(842\) | 13.1286 | + | 18.0700i | 0.452442 | + | 0.622733i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −32.3607 | − | 10.5146i | −1.11390 | − | 0.361928i | ||||
\(845\) | −32.1300 | + | 13.8042i | −1.10531 | + | 0.474881i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.9817i | 1.13327i | ||||||||
\(848\) | 2.77205 | − | 3.81540i | 0.0951926 | − | 0.131021i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.9132 | − | 15.0208i | −0.374320 | − | 0.515208i | ||||
\(851\) | 9.78975 | 0.335588 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.09369 | 0.277123 | 0.138561 | − | 0.990354i | \(-0.455752\pi\) | ||||
0.138561 | + | 0.990354i | \(0.455752\pi\) | |||||||
\(854\) | −24.3418 | − | 33.5036i | −0.832959 | − | 1.14647i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.36529 | + | 13.4350i | 0.149202 | + | 0.459198i | ||||
\(857\) | 37.9998 | 1.29805 | 0.649025 | − | 0.760767i | \(-0.275177\pi\) | ||||
0.649025 | + | 0.760767i | \(0.275177\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.49839i | 0.221722i | 0.993836 | + | 0.110861i | \(0.0353609\pi\) | ||||
−0.993836 | + | 0.110861i | \(0.964639\pi\) | |||||||
\(860\) | −19.4650 | − | 6.32456i | −0.663750 | − | 0.215666i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.7984 | + | 17.2905i | −0.810576 | + | 0.588918i | ||||
\(863\) | 24.7093i | 0.841115i | 0.907266 | + | 0.420558i | \(0.138166\pi\) | ||||
−0.907266 | + | 0.420558i | \(0.861834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 3.17157i | − | 0.107836i | ||||||
\(866\) | 11.7875 | + | 16.2241i | 0.400554 | + | 0.551316i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.8197 | − | 73.3094i | 0.808492 | − | 2.48828i | ||||
\(869\) | 47.6350 | 1.61591 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.5967 | − | 7.32320i | 1.20615 | − | 0.248137i | ||||
\(872\) | 23.4852 | − | 7.63080i | 0.795309 | − | 0.258412i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.2361 | + | 23.7234i | 0.583019 | + | 0.802456i | ||||
\(875\) | 30.8672i | 1.04350i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.4444 | 1.83846 | 0.919229 | − | 0.393723i | \(-0.128813\pi\) | ||||
0.919229 | + | 0.393723i | \(0.128813\pi\) | |||||||
\(878\) | 20.1000 | + | 27.6653i | 0.678342 | + | 0.933658i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 37.8885 | + | 27.5276i | 1.27722 | + | 0.927957i | ||||
\(881\) | −11.7426 | −0.395618 | −0.197809 | − | 0.980241i | \(-0.563383\pi\) | ||||
−0.197809 | + | 0.980241i | \(0.563383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.0130i | 0.572534i | 0.958150 | + | 0.286267i | \(0.0924144\pi\) | ||||
−0.958150 | + | 0.286267i | \(0.907586\pi\) | |||||||
\(884\) | 4.70102 | − | 42.0767i | 0.158112 | − | 1.41519i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.34895 | − | 0.980068i | 0.0453188 | − | 0.0329260i | ||||
\(887\) | 29.8859 | 1.00347 | 0.501735 | − | 0.865021i | \(-0.332695\pi\) | ||||
0.501735 | + | 0.865021i | \(0.332695\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 24.9098i | − | 0.835448i | ||||||
\(890\) | 37.5100 | − | 27.2526i | 1.25734 | − | 0.913510i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.6580 | + | 5.73742i | 0.591232 | + | 0.192103i | ||||
\(893\) | − | 28.0588i | − | 0.938953i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.5683i | 1.69031i | ||||||||
\(896\) | −14.5146 | + | 44.6715i | −0.484900 | + | 1.49237i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.1246 | + | 27.6992i | −1.27223 | + | 0.924333i | ||||
\(899\) | 28.6551 | 0.955701 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.92240i | − | 0.230619i | ||||||
\(902\) | 55.3125 | − | 40.1869i | 1.84170 | − | 1.33808i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.7938 | − | 5.13170i | 0.525293 | − | 0.170678i | ||||
\(905\) | 35.5316i | 1.18111i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.6215i | 0.817542i | 0.912637 | + | 0.408771i | \(0.134043\pi\) | ||||
−0.912637 | + | 0.408771i | \(0.865957\pi\) | |||||||
\(908\) | −0.635021 | + | 1.95440i | −0.0210739 | + | 0.0648589i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 38.3799 | − | 42.0683i | 1.27228 | − | 1.39455i | ||||
\(911\) | −18.1433 | −0.601115 | −0.300557 | − | 0.953764i | \(-0.597173\pi\) | ||||
−0.300557 | + | 0.953764i | \(0.597173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.3607 | −1.40193 | ||||||||
\(914\) | 43.8711 | − | 31.8742i | 1.45113 | − | 1.05431i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.4285 | − | 35.1732i | 0.377607 | − | 1.16216i | ||||
\(917\) | −36.5752 | −1.20782 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.4164 | −0.706462 | −0.353231 | − | 0.935536i | \(-0.614917\pi\) | ||||
−0.353231 | + | 0.935536i | \(0.614917\pi\) | |||||||
\(920\) | −26.2572 | + | 8.53149i | −0.865676 | + | 0.281275i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.5279 | + | 28.2542i | 0.676049 | + | 0.930502i | ||||
\(923\) | 1.51260 | + | 7.35247i | 0.0497878 | + | 0.242010i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.03268 | −0.198353 | ||||||||
\(926\) | −4.74998 | + | 3.45106i | −0.156094 | + | 0.113409i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.4611 | −0.573190 | ||||||||
\(929\) | − | 2.62210i | − | 0.0860282i | −0.999074 | − | 0.0430141i | \(-0.986304\pi\) | ||
0.999074 | − | 0.0430141i | \(-0.0136960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 58.4913 | 1.91697 | ||||||||
\(932\) | −4.48527 | + | 13.8042i | −0.146920 | + | 0.452173i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.06318 | + | 5.13170i | −0.231114 | + | 0.167914i | ||||
\(935\) | 68.7424 | 2.24812 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.652476 | 0.0213155 | 0.0106577 | − | 0.999943i | \(-0.496607\pi\) | ||||
0.0106577 | + | 0.999943i | \(0.496607\pi\) | |||||||
\(938\) | −47.8775 | + | 34.7851i | −1.56326 | + | 1.13577i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.1246 | + | 8.16348i | 0.819474 | + | 0.266263i | ||||
\(941\) | −10.9099 | −0.355652 | −0.177826 | − | 0.984062i | \(-0.556906\pi\) | ||||
−0.177826 | + | 0.984062i | \(0.556906\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.3049i | 1.31251i | ||||||||
\(944\) | −7.43496 | − | 5.40182i | −0.241987 | − | 0.175814i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.9443 | − | 13.7638i | 0.615931 | − | 0.447500i | ||||
\(947\) | 2.59735 | 0.0844024 | 0.0422012 | − | 0.999109i | \(-0.486563\pi\) | ||||
0.0422012 | + | 0.999109i | \(0.486563\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.76108 | + | 47.4468i | 0.316858 | + | 1.54019i | ||||
\(950\) | −10.6213 | − | 14.6189i | −0.344600 | − | 0.474301i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21.3050 | + | 65.5699i | 0.690497 | + | 2.12513i | ||||
\(953\) | −14.5146 | −0.470176 | −0.235088 | − | 0.971974i | \(-0.575538\pi\) | ||||
−0.235088 | + | 0.971974i | \(0.575538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −41.3486 | −1.33801 | ||||||||
\(956\) | −13.4500 | − | 4.37016i | −0.435003 | − | 0.141341i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.7984 | − | 8.57202i | 0.381188 | − | 0.276949i | ||||
\(959\) | −43.3417 | −1.39958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −55.1803 | −1.78001 | ||||||||
\(962\) | −10.1627 | − | 9.27168i | −0.327659 | − | 0.298931i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35.3159 | + | 11.4748i | 1.13745 | + | 0.369580i | ||||
\(965\) | − | 36.1400i | − | 1.16339i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.0216i | 0.997587i | 0.866721 | + | 0.498793i | \(0.166223\pi\) | ||||
−0.866721 | + | 0.498793i | \(0.833777\pi\) | |||||||
\(968\) | −21.3700 | + | 6.94355i | −0.686859 | + | 0.223174i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.7938 | − | 11.4748i | 0.507107 | − | 0.368435i | ||||
\(971\) | − | 52.3023i | − | 1.67846i | −0.543776 | − | 0.839230i | \(-0.683006\pi\) | ||
0.543776 | − | 0.839230i | \(-0.316994\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 59.4466 | 1.90577 | ||||||||
\(974\) | 20.1212 | − | 14.6189i | 0.644726 | − | 0.468421i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.5836 | − | 22.8254i | 0.530828 | − | 0.730622i | ||||
\(977\) | 44.8909i | 1.43619i | 0.695947 | + | 0.718093i | \(0.254985\pi\) | ||||
−0.695947 | + | 0.718093i | \(0.745015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53.0472i | 1.69539i | ||||||||
\(980\) | −17.0175 | + | 52.3746i | −0.543605 | + | 1.67305i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 29.9201 | − | 21.7382i | 0.954789 | − | 0.693695i | ||||
\(983\) | 43.4280i | 1.38514i | 0.721352 | + | 0.692568i | \(0.243521\pi\) | ||||
−0.721352 | + | 0.692568i | \(0.756479\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.5410 | 0.909393 | ||||||||
\(986\) | −20.7350 | + | 15.0649i | −0.660338 | + | 0.479763i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.57526 | − | 40.9511i | 0.145558 | − | 1.30283i | ||||
\(989\) | 13.8042i | 0.438950i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1803 | 0.386921 | 0.193461 | − | 0.981108i | \(-0.438029\pi\) | ||||
0.193461 | + | 0.981108i | \(0.438029\pi\) | |||||||
\(992\) | 52.5145 | 1.66734 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.18482 | − | 9.88905i | −0.227889 | − | 0.313662i | ||||
\(995\) | −48.4199 | −1.53501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 55.0553i | − | 1.74362i | −0.489846 | − | 0.871809i | \(-0.662947\pi\) | ||
0.489846 | − | 0.871809i | \(-0.337053\pi\) | |||||||
\(998\) | 32.7204 | + | 45.0358i | 1.03575 | + | 1.42558i | ||||
\(999\) | 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 | 936.2.m.h.181.12 | yes | 16 | |
3.2 | odd | 2 | inner | 936.2.m.h.181.6 | yes | 16 | |
4.3 | odd | 2 | 3744.2.m.h.1585.2 | 16 | |||
8.3 | odd | 2 | 3744.2.m.h.1585.13 | 16 | |||
8.5 | even | 2 | inner | 936.2.m.h.181.8 | yes | 16 | |
12.11 | even | 2 | 3744.2.m.h.1585.14 | 16 | |||
13.12 | even | 2 | inner | 936.2.m.h.181.5 | ✓ | 16 | |
24.5 | odd | 2 | inner | 936.2.m.h.181.10 | yes | 16 | |
24.11 | even | 2 | 3744.2.m.h.1585.1 | 16 | |||
39.38 | odd | 2 | inner | 936.2.m.h.181.11 | yes | 16 | |
52.51 | odd | 2 | 3744.2.m.h.1585.15 | 16 | |||
104.51 | odd | 2 | 3744.2.m.h.1585.4 | 16 | |||
104.77 | even | 2 | inner | 936.2.m.h.181.9 | yes | 16 | |
156.155 | even | 2 | 3744.2.m.h.1585.3 | 16 | |||
312.77 | odd | 2 | inner | 936.2.m.h.181.7 | yes | 16 | |
312.155 | even | 2 | 3744.2.m.h.1585.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
936.2.m.h.181.5 | ✓ | 16 | 13.12 | even | 2 | inner | |
936.2.m.h.181.6 | yes | 16 | 3.2 | odd | 2 | inner | |
936.2.m.h.181.7 | yes | 16 | 312.77 | odd | 2 | inner | |
936.2.m.h.181.8 | yes | 16 | 8.5 | even | 2 | inner | |
936.2.m.h.181.9 | yes | 16 | 104.77 | even | 2 | inner | |
936.2.m.h.181.10 | yes | 16 | 24.5 | odd | 2 | inner | |
936.2.m.h.181.11 | yes | 16 | 39.38 | odd | 2 | inner | |
936.2.m.h.181.12 | yes | 16 | 1.1 | even | 1 | trivial | |
3744.2.m.h.1585.1 | 16 | 24.11 | even | 2 | |||
3744.2.m.h.1585.2 | 16 | 4.3 | odd | 2 | |||
3744.2.m.h.1585.3 | 16 | 156.155 | even | 2 | |||
3744.2.m.h.1585.4 | 16 | 104.51 | odd | 2 | |||
3744.2.m.h.1585.13 | 16 | 8.3 | odd | 2 | |||
3744.2.m.h.1585.14 | 16 | 12.11 | even | 2 | |||
3744.2.m.h.1585.15 | 16 | 52.51 | odd | 2 | |||
3744.2.m.h.1585.16 | 16 | 312.155 | even | 2 |