Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(49,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.bb (of order \(12\), degree \(4\), not 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 49.16 | ||
Character | \(\chi\) | \(=\) | 576.49 |
Dual form | 576.2.bb.e.529.16 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.64464 | + | 0.543291i | 0.949532 | + | 0.313669i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.60558 | + | 0.430214i | −0.718037 | + | 0.192397i | −0.599296 | − | 0.800528i | \(-0.704553\pi\) |
−0.118741 | + | 0.992925i | \(0.537886\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.62762 | + | 2.09441i | −1.37111 | + | 0.791611i | −0.991068 | − | 0.133358i | \(-0.957424\pi\) |
−0.380043 | + | 0.924969i | \(0.624091\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.40967 | + | 1.78703i | 0.803223 | + | 0.595678i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.24125 | + | 4.63241i | −0.374251 | + | 1.39673i | 0.480184 | + | 0.877168i | \(0.340570\pi\) |
−0.854436 | + | 0.519557i | \(0.826097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.879738 | − | 3.28323i | −0.243995 | − | 0.910603i | −0.973886 | − | 0.227039i | \(-0.927096\pi\) |
0.729890 | − | 0.683564i | \(-0.239571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.87433 | − | 0.164751i | −0.742148 | − | 0.0425384i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.14142 | −0.519370 | −0.259685 | − | 0.965693i | \(-0.583619\pi\) | ||||
−0.259685 | + | 0.965693i | \(0.583619\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.03156 | + | 1.03156i | −0.236656 | + | 0.236656i | −0.815464 | − | 0.578808i | \(-0.803518\pi\) |
0.578808 | + | 0.815464i | \(0.303518\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.10399 | + | 1.47369i | −1.55022 | + | 0.321585i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.405884 | + | 0.234337i | 0.0846327 | + | 0.0488627i | 0.541719 | − | 0.840560i | \(-0.317774\pi\) |
−0.457086 | + | 0.889422i | \(0.651107\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.93733 | + | 1.11852i | −0.387465 | + | 0.223703i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.99216 | + | 4.24818i | 0.575841 | + | 0.817562i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.55186 | + | 1.75557i | 1.21665 | + | 0.326000i | 0.809368 | − | 0.587302i | \(-0.199810\pi\) |
0.407282 | + | 0.913302i | \(0.366477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.18054 | + | 5.50886i | −0.571242 | + | 0.989421i | 0.425196 | + | 0.905101i | \(0.360205\pi\) |
−0.996439 | + | 0.0843198i | \(0.973128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.55816 | + | 6.94428i | −0.793473 | + | 1.20884i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.92339 | − | 4.92339i | 0.832204 | − | 0.832204i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.728237 | − | 0.728237i | −0.119721 | − | 0.119721i | 0.644708 | − | 0.764429i | \(-0.276979\pi\) |
−0.764429 | + | 0.644708i | \(0.776979\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.336896 | − | 5.87767i | 0.0539466 | − | 0.941181i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.52351 | + | 1.45695i | 0.394105 | + | 0.227537i | 0.683937 | − | 0.729541i | \(-0.260266\pi\) |
−0.289832 | + | 0.957078i | \(0.593599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.84802 | − | 10.6289i | 0.434318 | − | 1.62090i | −0.308374 | − | 0.951265i | \(-0.599785\pi\) |
0.742692 | − | 0.669633i | \(-0.233549\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.63772 | − | 1.83255i | −0.691351 | − | 0.273181i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.61716 | + | 7.99715i | 0.673482 | + | 1.16650i | 0.976910 | + | 0.213650i | \(0.0685352\pi\) |
−0.303429 | + | 0.952854i | \(0.598131\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.27308 | − | 9.13324i | 0.753297 | − | 1.30475i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.52186 | − | 1.16341i | −0.493159 | − | 0.162910i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.17892 | + | 1.17892i | 0.161937 | + | 0.161937i | 0.783424 | − | 0.621487i | \(-0.213471\pi\) |
−0.621487 | + | 0.783424i | \(0.713471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.97171i | − | 1.07491i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.25698 | + | 1.13611i | −0.298944 | + | 0.150481i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.48185 | − | 0.397061i | 0.192921 | − | 0.0516930i | −0.161065 | − | 0.986944i | \(-0.551493\pi\) |
0.353986 | + | 0.935251i | \(0.384826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.53224 | + | 2.01826i | 0.964404 | + | 0.258411i | 0.706464 | − | 0.707749i | \(-0.250289\pi\) |
0.257941 | + | 0.966161i | \(0.416956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.4841 | − | 1.43585i | −1.57285 | − | 0.180900i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.82498 | + | 4.89300i | 0.350395 | + | 0.606902i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.63252 | − | 9.82470i | −0.321614 | − | 1.20028i | −0.917673 | − | 0.397338i | \(-0.869934\pi\) |
0.596059 | − | 0.802941i | \(-0.296732\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.540220 | + | 0.605914i | 0.0650348 | + | 0.0729434i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.27863i | 0.982493i | 0.871021 | + | 0.491246i | \(0.163458\pi\) | ||||
−0.871021 | + | 0.491246i | \(0.836542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.16641i | 0.955806i | 0.878413 | + | 0.477903i | \(0.158603\pi\) | ||||
−0.878413 | + | 0.477903i | \(0.841397\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.79388 | + | 0.787022i | −0.438079 | + | 0.0908775i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.19937 | − | 19.4043i | −0.592523 | − | 2.21133i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.63065 | − | 6.28847i | −0.408480 | − | 0.707508i | 0.586240 | − | 0.810138i | \(-0.300608\pi\) |
−0.994720 | + | 0.102630i | \(0.967274\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.61302 | + | 8.61232i | 0.290336 | + | 0.956925i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.59149 | + | 2.03413i | 0.833274 | + | 0.223275i | 0.650142 | − | 0.759813i | \(-0.274710\pi\) |
0.183133 | + | 0.983088i | \(0.441376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.43821 | − | 0.921267i | 0.372927 | − | 0.0999254i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.82166 | + | 6.44684i | 1.05299 | + | 0.691174i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.1968i | 1.18686i | 0.804886 | + | 0.593429i | \(0.202226\pi\) | ||||
−0.804886 | + | 0.593429i | \(0.797774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0678 | + | 10.0678i | 1.05539 | + | 1.05539i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.22376 | + | 7.33213i | −0.852764 | + | 0.760306i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.21246 | − | 2.10004i | 0.124396 | − | 0.215460i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.67759 | − | 9.83387i | −0.576472 | − | 0.998479i | −0.995880 | − | 0.0906808i | \(-0.971096\pi\) |
0.419408 | − | 0.907798i | \(-0.362238\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.2693 | + | 8.94443i | −1.13261 | + | 0.898949i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.777558 | − | 2.90189i | 0.0773699 | − | 0.288749i | −0.916390 | − | 0.400286i | \(-0.868911\pi\) |
0.993760 | + | 0.111537i | \(0.0355775\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.24824 | + | 0.720669i | 0.122992 | + | 0.0710096i | 0.560234 | − | 0.828334i | \(-0.310711\pi\) |
−0.437242 | + | 0.899344i | \(0.644045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.7720 | − | 5.42236i | 1.05124 | − | 0.529168i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.85602 | − | 5.85602i | −0.566123 | − | 0.566123i | 0.364917 | − | 0.931040i | \(-0.381097\pi\) |
−0.931040 | + | 0.364917i | \(0.881097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.05249 | + | 2.05249i | −0.196593 | + | 0.196593i | −0.798538 | − | 0.601945i | \(-0.794393\pi\) |
0.601945 | + | 0.798538i | \(0.294393\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.802042 | − | 1.59333i | −0.0761265 | − | 0.151232i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.12726 | + | 7.14862i | −0.388260 | + | 0.672486i | −0.992216 | − | 0.124532i | \(-0.960257\pi\) |
0.603956 | + | 0.797018i | \(0.293590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.752495 | − | 0.201630i | −0.0701705 | − | 0.0188021i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.74736 | − | 9.48361i | 0.346443 | − | 0.876760i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.76824 | − | 4.48500i | 0.712114 | − | 0.411139i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3923 | − | 5.99998i | −0.944752 | − | 0.545453i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.35871 | + | 3.76715i | 0.302845 | + | 0.339672i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.50616 | − | 8.50616i | 0.760814 | − | 0.760814i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.68483 | 0.149504 | 0.0747521 | − | 0.997202i | \(-0.476183\pi\) | ||||
0.0747521 | + | 0.997202i | \(0.476183\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4586 | − | 15.9335i | 0.920825 | − | 1.40286i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.97334 | − | 7.36461i | −0.172412 | − | 0.643449i | −0.996978 | − | 0.0776838i | \(-0.975248\pi\) |
0.824566 | − | 0.565765i | \(-0.191419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.58160 | − | 5.90261i | 0.137142 | − | 0.511821i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.63177 | − | 5.53352i | −0.570772 | − | 0.476249i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.26806 | − | 4.77357i | 0.706388 | − | 0.407833i | −0.103334 | − | 0.994647i | \(-0.532951\pi\) |
0.809722 | + | 0.586813i | \(0.199618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9684 | − | 3.74281i | 1.18478 | − | 0.317461i | 0.387960 | − | 0.921676i | \(-0.373180\pi\) |
0.796821 | + | 0.604215i | \(0.206513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.24877 | + | 15.6609i | 0.273596 | + | 1.31888i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.3012 | 1.36318 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.2748 | −0.936321 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.6343 | − | 12.1561i | 1.12454 | − | 1.00261i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.66249 | + | 0.445462i | −0.136196 | + | 0.0364937i | −0.326273 | − | 0.945276i | \(-0.605793\pi\) |
0.190077 | + | 0.981769i | \(0.439126\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.5071 | + | 10.6851i | −1.50609 | + | 0.869542i | −0.506115 | + | 0.862466i | \(0.668919\pi\) |
−0.999975 | + | 0.00707596i | \(0.997748\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.16011 | − | 3.82678i | −0.417170 | − | 0.309377i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.73663 | − | 10.2132i | 0.219811 | − | 0.820346i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.74550 | + | 10.2463i | 0.219114 | + | 0.817746i | 0.984677 | + | 0.174385i | \(0.0557938\pi\) |
−0.765563 | + | 0.643361i | \(0.777539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.29840 | + | 2.57939i | 0.102970 | + | 0.204559i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.96319 | −0.154721 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.47621 | − | 3.47621i | 0.272278 | − | 0.272278i | −0.557739 | − | 0.830017i | \(-0.688331\pi\) |
0.830017 | + | 0.557739i | \(0.188331\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.33096 | − | 13.1106i | 0.337165 | − | 1.02066i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.277442 | − | 0.160181i | −0.0214691 | − | 0.0123952i | 0.489227 | − | 0.872156i | \(-0.337279\pi\) |
−0.510696 | + | 0.859761i | \(0.670612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.25270 | − | 0.723245i | 0.0963613 | − | 0.0556342i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.32915 | + | 0.642287i | −0.331059 | + | 0.0491169i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.6901 | + | 3.13236i | 0.888784 | + | 0.238149i | 0.674193 | − | 0.738555i | \(-0.264491\pi\) |
0.214591 | + | 0.976704i | \(0.431158\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.68525 | − | 8.11510i | 0.354172 | − | 0.613444i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.65283 | + | 0.152055i | 0.199399 | + | 0.0114291i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.6780 | + | 18.6780i | −1.39606 | + | 1.39606i | −0.585104 | + | 0.810958i | \(0.698946\pi\) |
−0.810958 | + | 0.585104i | \(0.801054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.10527 | + | 4.10527i | 0.305143 | + | 0.305143i | 0.843022 | − | 0.537879i | \(-0.180774\pi\) |
−0.537879 | + | 0.843022i | \(0.680774\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2913 | + | 7.41150i | 0.834677 | + | 0.547874i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.48254 | + | 0.855945i | 0.108998 | + | 0.0629303i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.65804 | − | 9.91993i | 0.194375 | − | 0.725417i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.7518 | − | 9.14397i | −1.43673 | − | 0.665126i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.60099 | − | 14.8974i | −0.622346 | − | 1.07793i | −0.989048 | − | 0.147596i | \(-0.952846\pi\) |
0.366702 | − | 0.930338i | \(-0.380487\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.17459 | − | 15.8909i | 0.660402 | − | 1.14385i | −0.320108 | − | 0.947381i | \(-0.603719\pi\) |
0.980510 | − | 0.196468i | \(-0.0629473\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.98774 | + | 9.58201i | 0.142345 | + | 0.686182i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.80431 | + | 8.80431i | 0.627281 | + | 0.627281i | 0.947383 | − | 0.320102i | \(-0.103717\pi\) |
−0.320102 | + | 0.947383i | \(0.603717\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.0277i | − | 0.710847i | −0.934705 | − | 0.355423i | \(-0.884337\pi\) | ||
0.934705 | − | 0.355423i | \(-0.115663\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00813 | − | 17.5883i | 0.0711077 | − | 1.24058i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −27.4445 | + | 7.35374i | −1.92623 | + | 0.516131i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.67849 | − | 1.25360i | −0.326760 | − | 0.0875550i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.559278 | + | 1.29001i | 0.0388725 | + | 0.0896616i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.49819 | − | 6.05904i | −0.241975 | − | 0.419112i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.14678 | + | 19.2080i | 0.354319 | + | 1.32234i | 0.881340 | + | 0.472483i | \(0.156642\pi\) |
−0.527021 | + | 0.849852i | \(0.676691\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.49770 | + | 13.6154i | −0.308178 | + | 0.932908i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.2909i | 1.24743i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 26.6454i | − | 1.80881i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.43674 | + | 13.4308i | −0.299807 | + | 0.907569i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.88389 | + | 7.03076i | 0.126724 | + | 0.472940i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.96587 | + | 12.0652i | 0.466469 | + | 0.807948i | 0.999266 | − | 0.0382947i | \(-0.0121926\pi\) |
−0.532797 | + | 0.846243i | \(0.678859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.66714 | − | 0.766813i | −0.444476 | − | 0.0511209i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.32092 | + | 1.96164i | 0.485907 | + | 0.130198i | 0.493452 | − | 0.869773i | \(-0.335735\pi\) |
−0.00754492 | + | 0.999972i | \(0.502402\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4637 | + | 4.94734i | −1.22012 | + | 0.326930i | −0.810724 | − | 0.585428i | \(-0.800926\pi\) |
−0.409394 | + | 0.912358i | \(0.634260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.99110 | − | 34.7378i | 0.131005 | − | 2.28558i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7647i | 0.705216i | 0.935771 | + | 0.352608i | \(0.114705\pi\) | ||||
−0.935771 | + | 0.352608i | \(0.885295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.8537 | − | 10.8537i | −0.708017 | − | 0.708017i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.55464 | − | 12.3147i | −0.165941 | − | 0.799929i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.1429 | − | 19.3001i | 0.720774 | − | 1.24842i | −0.239916 | − | 0.970794i | \(-0.577120\pi\) |
0.960690 | − | 0.277624i | \(-0.0895469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7285 | + | 23.7785i | 0.884332 | + | 1.53171i | 0.846478 | + | 0.532424i | \(0.178719\pi\) |
0.0378540 | + | 0.999283i | \(0.487948\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.381525 | + | 15.5838i | −0.0244748 | + | 0.999700i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.53710 | + | 16.9327i | −0.289865 | + | 1.08179i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.29435 | + | 2.47934i | 0.273243 | + | 0.157757i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.3801 | + | 7.46980i | 0.721186 | + | 0.473379i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.4125 | − | 11.4125i | −0.720350 | − | 0.720350i | 0.248326 | − | 0.968676i | \(-0.420119\pi\) |
−0.968676 | + | 0.248326i | \(0.920119\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.58935 | + | 1.58935i | −0.0999217 | + | 0.0999217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.15514 | + | 0.352800i | 0.385450 | + | 0.0220932i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.930384 | + | 1.61147i | −0.0580357 | + | 0.100521i | −0.893584 | − | 0.448897i | \(-0.851817\pi\) |
0.835548 | + | 0.549418i | \(0.185150\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.16699 | + | 1.11654i | 0.258924 | + | 0.0693785i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.6506 | + | 15.9387i | 0.783051 | + | 0.986583i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.0414842 | + | 0.0239509i | −0.00255802 | + | 0.00147687i | −0.501278 | − | 0.865286i | \(-0.667137\pi\) |
0.498720 | + | 0.866763i | \(0.333803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.40003 | − | 1.38566i | −0.147433 | − | 0.0851203i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.08312 | + | 18.4147i | −0.372281 | + | 1.12696i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.5681 | + | 14.5681i | −0.888235 | + | 0.888235i | −0.994354 | − | 0.106118i | \(-0.966158\pi\) |
0.106118 | + | 0.994354i | \(0.466158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.7807 | 0.958607 | 0.479304 | − | 0.877649i | \(-0.340889\pi\) | ||||
0.479304 | + | 0.877649i | \(0.340889\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.0881 | + | 22.0275i | 0.671083 | + | 1.33317i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.77672 | − | 10.3629i | −0.167442 | − | 0.624904i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.93294 | + | 7.21383i | −0.116139 | + | 0.433437i | −0.999370 | − | 0.0355022i | \(-0.988697\pi\) |
0.883231 | + | 0.468939i | \(0.155364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.5086 | + | 7.59080i | −1.04821 | + | 0.454449i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.84440 | + | 3.37427i | −0.348648 | + | 0.201292i | −0.664089 | − | 0.747653i | \(-0.731181\pi\) |
0.315442 | + | 0.948945i | \(0.397847\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4414 | + | 3.33366i | −0.739563 | + | 0.198165i | −0.608884 | − | 0.793259i | \(-0.708383\pi\) |
−0.130679 | + | 0.991425i | \(0.541716\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.13499 | − | 2.79509i | 0.185701 | − | 0.165567i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.2058 | −0.720483 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.4143 | −0.730255 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.99493 | − | 19.2577i | −0.234187 | − | 1.12891i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.8785 | − | 3.71874i | 0.810792 | − | 0.217251i | 0.170475 | − | 0.985362i | \(-0.445470\pi\) |
0.640317 | + | 0.768111i | \(0.278803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.20841 | + | 1.27503i | −0.128579 | + | 0.0742349i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.3933 | + | 8.58785i | −1.35742 | + | 0.498318i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.412311 | − | 1.53877i | 0.0238446 | − | 0.0889891i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9298 | + | 44.5226i | 0.687622 | + | 2.56624i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.85537 | − | 4.35011i | 0.164037 | − | 0.249907i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.9619 | −0.742196 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.2394 | + | 12.2394i | −0.698539 | + | 0.698539i | −0.964095 | − | 0.265556i | \(-0.914444\pi\) |
0.265556 | + | 0.964095i | \(0.414444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.66136 | + | 1.86339i | 0.0945116 | + | 0.106005i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.742777 | + | 0.428842i | 0.0421190 | + | 0.0243174i | 0.520912 | − | 0.853611i | \(-0.325592\pi\) |
−0.478793 | + | 0.877928i | \(0.658925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8984 | + | 9.17895i | −0.898631 | + | 0.518825i | −0.876756 | − | 0.480936i | \(-0.840297\pi\) |
−0.0218755 | + | 0.999761i | \(0.506964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.6620 | − | 3.06548i | 1.16417 | − | 0.172720i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.02641 | − | 1.07887i | −0.226146 | − | 0.0605956i | 0.143967 | − | 0.989583i | \(-0.454014\pi\) |
−0.370112 | + | 0.928987i | \(0.620681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.2650 | + | 28.1718i | −0.910666 | + | 1.57732i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.44952 | − | 12.8126i | −0.359977 | − | 0.715128i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.20900 | − | 2.20900i | 0.122912 | − | 0.122912i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.37668 | + | 5.37668i | 0.298244 | + | 0.298244i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.49070 | + | 2.26050i | −0.248336 | + | 0.125006i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −33.4986 | − | 19.3404i | −1.84684 | − | 1.06627i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.33734 | + | 4.99103i | −0.0735070 | + | 0.274332i | −0.992891 | − | 0.119030i | \(-0.962021\pi\) |
0.919384 | + | 0.393362i | \(0.128688\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.453427 | − | 3.05620i | −0.0248476 | − | 0.167478i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.45344 | + | 14.6418i | 0.461861 | + | 0.799966i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.94762 | − | 3.37338i | 0.106094 | − | 0.183760i | −0.808091 | − | 0.589058i | \(-0.799499\pi\) |
0.914185 | + | 0.405298i | \(0.132832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.6716 | + | 9.51459i | −0.579603 | + | 0.516762i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.5715 | − | 21.5715i | −1.16816 | − | 1.16816i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.8542i | 0.802049i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.12804 | − | 0.740433i | −0.0607315 | − | 0.0398635i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.04812 | − | 0.816741i | 0.163632 | − | 0.0438449i | −0.176073 | − | 0.984377i | \(-0.556340\pi\) |
0.339705 | + | 0.940532i | \(0.389673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.39893 | + | 0.374843i | 0.0748831 | + | 0.0200649i | 0.296066 | − | 0.955167i | \(-0.404325\pi\) |
−0.221183 | + | 0.975232i | \(0.570992\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3154 | − | 13.5612i | 0.603972 | − | 0.723844i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.73892 | + | 13.4042i | 0.411901 | + | 0.713434i | 0.995098 | − | 0.0988971i | \(-0.0315315\pi\) |
−0.583196 | + | 0.812331i | \(0.698198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.56158 | − | 13.2920i | −0.189029 | − | 0.705466i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.2126 | − | 3.15578i | 0.805137 | − | 0.167022i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4.78775i | − | 0.252688i | −0.991987 | − | 0.126344i | \(-0.959676\pi\) | ||
0.991987 | − | 0.126344i | \(-0.0403242\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.8718i | 0.887988i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.8318 | − | 15.5138i | −0.725981 | − | 0.814264i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.51330 | − | 13.1118i | −0.183895 | − | 0.686304i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.93807 | + | 17.2133i | 0.518763 | + | 0.898524i | 0.999762 | + | 0.0218032i | \(0.00694073\pi\) |
−0.480999 | + | 0.876721i | \(0.659726\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.47720 | + | 8.02035i | 0.181016 | + | 0.417523i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.74579 | − | 1.80753i | −0.350224 | − | 0.0938422i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.427591 | + | 0.114573i | −0.0221398 | + | 0.00593235i | −0.269872 | − | 0.962896i | \(-0.586981\pi\) |
0.247732 | + | 0.968829i | \(0.420315\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.6109 | − | 9.36823i | 0.961061 | − | 0.483774i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 23.0557i | − | 1.18743i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.18132 | + | 6.18132i | 0.317513 | + | 0.317513i | 0.847811 | − | 0.530298i | \(-0.177920\pi\) |
−0.530298 | + | 0.847811i | \(0.677920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.77093 | + | 0.915351i | 0.141959 | + | 0.0468949i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.46708 | + | 11.2013i | −0.330452 | + | 0.572360i | −0.982601 | − | 0.185731i | \(-0.940535\pi\) |
0.652148 | + | 0.758091i | \(0.273868\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.6960 | + | 28.9183i | 0.850907 | + | 1.47381i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.8571 | − | 20.5227i | 1.31439 | − | 1.04323i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.08096 | − | 26.4265i | 0.359019 | − | 1.33988i | −0.516331 | − | 0.856389i | \(-0.672703\pi\) |
0.875351 | − | 0.483489i | \(-0.160631\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.869168 | − | 0.501814i | −0.0439557 | − | 0.0253778i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.755693 | − | 13.1842i | 0.0381197 | − | 0.665056i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.53468 | + | 8.53468i | 0.429426 | + | 0.429426i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9741 | − | 21.9741i | 1.10285 | − | 1.10285i | 0.108781 | − | 0.994066i | \(-0.465305\pi\) |
0.994066 | − | 0.108781i | \(-0.0346948\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.80799 | − | 8.84839i | 0.290763 | − | 0.442974i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4970 | − | 23.3775i | 0.674009 | − | 1.16742i | −0.302749 | − | 0.953070i | \(-0.597904\pi\) |
0.976758 | − | 0.214347i | \(-0.0687624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.8849 | + | 5.59609i | 1.04035 | + | 0.278761i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.90055 | − | 12.7036i | −0.392581 | − | 0.631248i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.27742 | − | 2.46957i | 0.212024 | − | 0.122412i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.1537 | + | 6.43957i | 0.551513 | + | 0.318416i | 0.749732 | − | 0.661741i | \(-0.230182\pi\) |
−0.198219 | + | 0.980158i | \(0.563516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.1914 | − | 3.35883i | 0.798663 | − | 0.165679i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.54399 | + | 4.54399i | −0.223595 | + | 0.223595i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.0638 | −0.641279 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.0063 | + | 1.43331i | 1.22457 | + | 0.0701896i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.0545100 | + | 0.203434i | 0.00266299 | + | 0.00993841i | 0.967245 | − | 0.253846i | \(-0.0816958\pi\) |
−0.964582 | + | 0.263785i | \(0.915029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.17194 | − | 34.2301i | 0.447013 | − | 1.66827i | −0.263554 | − | 0.964645i | \(-0.584895\pi\) |
0.710567 | − | 0.703630i | \(-0.248439\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.16535 | + | 27.5215i | −0.153905 | + | 1.33814i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.14862 | − | 2.39521i | 0.201238 | − | 0.116185i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.5511 | + | 8.45410i | −1.52687 | + | 0.409123i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.8096 | + | 8.85631i | 1.29438 | + | 0.427587i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.5339 | −1.61527 | −0.807635 | − | 0.589683i | \(-0.799253\pi\) | ||||
−0.807635 | + | 0.589683i | \(0.799253\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.9691 | −1.39217 | −0.696083 | − | 0.717962i | \(-0.745075\pi\) | ||||
−0.696083 | + | 0.717962i | \(0.745075\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.5430 | − | 6.12550i | −0.889067 | − | 0.293695i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.660427 | + | 0.176961i | −0.0315925 | + | 0.00846519i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.6656 | − | 8.46718i | 0.699950 | − | 0.404116i | −0.107379 | − | 0.994218i | \(-0.534246\pi\) |
0.807329 | + | 0.590102i | \(0.200912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.0278 | − | 12.5849i | 1.38227 | − | 0.599282i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.826654 | + | 3.08511i | −0.0392755 | + | 0.146578i | −0.982779 | − | 0.184784i | \(-0.940841\pi\) |
0.943504 | + | 0.331362i | \(0.107508\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.81702 | − | 17.9773i | −0.228348 | − | 0.852208i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.97621 | − | 0.170590i | −0.140770 | − | 0.00806863i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −41.9192 | −1.97829 | −0.989145 | − | 0.146944i | \(-0.953056\pi\) | ||||
−0.989145 | + | 0.146944i | \(0.953056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.88149 | + | 9.88149i | −0.465301 | + | 0.465301i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −36.2427 | + | 7.51837i | −1.70283 | + | 0.353244i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.4959 | − | 11.8333i | −0.960862 | − | 0.554754i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.93980 | − | 2.85199i | 0.231074 | − | 0.133411i | −0.379993 | − | 0.924989i | \(-0.624074\pi\) |
0.611067 | + | 0.791579i | \(0.290740\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.40745 | − | 9.09712i | −0.299074 | − | 0.424617i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.3338 | − | 10.2715i | −1.78538 | − | 0.478392i | −0.793834 | − | 0.608135i | \(-0.791918\pi\) |
−0.991548 | + | 0.129743i | \(0.958585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.28293 | − | 10.8824i | 0.291992 | − | 0.505746i | −0.682288 | − | 0.731083i | \(-0.739015\pi\) |
0.974281 | + | 0.225337i | \(0.0723485\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.0495 | − | 15.3103i | 0.466035 | − | 0.709997i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.1784 | + | 12.1784i | −0.563550 | + | 0.563550i | −0.930314 | − | 0.366764i | \(-0.880466\pi\) |
0.366764 | + | 0.930314i | \(0.380466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.1267 | + | 30.1267i | 1.39112 | + | 1.39112i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.05139 | + | 18.3431i | −0.0484455 | + | 0.845206i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 45.7025 | + | 26.3864i | 2.10140 | + | 1.21325i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.844652 | − | 3.15228i | 0.0387553 | − | 0.144637i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.734036 | + | 4.94756i | 0.0336092 | + | 0.226533i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.6864 | + | 18.5094i | 0.488275 | + | 0.845717i | 0.999909 | − | 0.0134862i | \(-0.00429292\pi\) |
−0.511634 | + | 0.859204i | \(0.670960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.75031 | + | 3.03162i | −0.0798072 | + | 0.138230i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.22874 | − | 1.06658i | −0.146913 | − | 0.0485313i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.3465 | + | 13.3465i | 0.606033 | + | 0.606033i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 39.3716i | − | 1.78410i | −0.451939 | − | 0.892049i | \(-0.649268\pi\) | ||
0.451939 | − | 0.892049i | \(-0.350732\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.60570 | − | 3.82851i | 0.343942 | − | 0.173131i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.8903 | − | 9.08087i | 1.52945 | − | 0.409814i | 0.606608 | − | 0.795001i | \(-0.292530\pi\) |
0.922839 | + | 0.385187i | \(0.125863\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.0303 | − | 3.75940i | −0.631891 | − | 0.169315i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.2457 | − | 19.2092i | 0.640297 | − | 0.863389i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.3388 | − | 30.0317i | −0.777752 | − | 1.34711i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.38889 | − | 12.6475i | −0.151708 | − | 0.566181i | −0.999365 | − | 0.0356364i | \(-0.988654\pi\) |
0.847657 | − | 0.530544i | \(-0.178012\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.369267 | − | 0.414172i | −0.0164976 | − | 0.0185039i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.93881i | 0.131035i | 0.997851 | + | 0.0655175i | \(0.0208698\pi\) | ||||
−0.997851 | + | 0.0655175i | \(0.979130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.99373i | 0.222218i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.45317 | − | 0.508897i | 0.108949 | − | 0.0226009i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.11461 | + | 15.3559i | 0.182377 | + | 0.680640i | 0.995177 | + | 0.0980972i | \(0.0312756\pi\) |
−0.812800 | + | 0.582543i | \(0.802058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.1038 | − | 29.6246i | −0.756627 | − | 1.31052i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.46884 | − | 1.29566i | −0.329757 | − | 0.0572048i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.31418 | − | 0.620083i | −0.101975 | − | 0.0273241i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.7772 | + | 11.4621i | −1.88134 | + | 0.504103i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.5243 | + | 11.5027i | 0.769230 | + | 0.504914i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.2119i | 0.841689i | 0.907133 | + | 0.420844i | \(0.138266\pi\) | ||||
−0.907133 | + | 0.420844i | \(0.861734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0495 | + | 10.0495i | 0.439436 | + | 0.439436i | 0.891822 | − | 0.452386i | \(-0.149427\pi\) |
−0.452386 | + | 0.891822i | \(0.649427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.1144 | − | 10.8009i | 0.528716 | − | 0.471392i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.81087 | − | 11.7968i | 0.296686 | − | 0.513875i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3902 | − | 19.7284i | −0.495225 | − | 0.857755i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.28034 | + | 1.69133i | 0.185751 | + | 0.0733976i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.56346 | − | 9.56697i | 0.111036 | − | 0.414392i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.9217 | + | 6.88297i | 0.515418 | + | 0.297577i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −40.8662 | + | 20.5710i | −1.76351 | + | 0.887705i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35.7637 | + | 35.7637i | 1.54045 | + | 1.54045i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.3802 | − | 15.3802i | 0.661246 | − | 0.661246i | −0.294428 | − | 0.955674i | \(-0.595129\pi\) |
0.955674 | + | 0.294428i | \(0.0951290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.52133 | + | 8.98205i | 0.194029 | + | 0.385457i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.41243 | − | 4.17844i | 0.103337 | − | 0.178985i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.1362 | + | 6.19933i | 0.989233 | + | 0.265064i | 0.716928 | − | 0.697147i | \(-0.245548\pi\) |
0.272304 | + | 0.962211i | \(0.412214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.5435 | + | 18.3237i | 0.620702 | + | 0.782036i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.56961 | + | 4.94767i | −0.365078 | + | 0.210778i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.3412 | + | 15.2081i | 1.12014 | + | 0.646714i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.97321 | + | 2.21317i | 0.0837583 | + | 0.0939438i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.932077 | − | 0.932077i | 0.0394934 | − | 0.0394934i | −0.687084 | − | 0.726578i | \(-0.741110\pi\) |
0.726578 | + | 0.687084i | \(0.241110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.4027 | −1.58197 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.76092 | − | 14.8706i | 0.412106 | − | 0.627838i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.71390 | + | 6.39635i | 0.0722321 | + | 0.269574i | 0.992591 | − | 0.121500i | \(-0.0387704\pi\) |
−0.920359 | + | 0.391074i | \(0.872104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.55121 | − | 13.2533i | 0.149400 | − | 0.557570i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.5167 | − | 25.7695i | −1.15559 | − | 1.08222i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.84553 | − | 4.52962i | 0.328902 | − | 0.189892i | −0.326452 | − | 0.945214i | \(-0.605853\pi\) |
0.655353 | + | 0.755322i | \(0.272520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9078 | − | 4.79838i | 0.749417 | − | 0.200806i | 0.136158 | − | 0.990687i | \(-0.456525\pi\) |
0.613260 | + | 0.789881i | \(0.289858\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.05192 | − | 29.1736i | −0.252823 | − | 1.21874i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.04844 | −0.0437230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.3455 | 1.80450 | 0.902248 | − | 0.431217i | \(-0.141916\pi\) | ||||
0.902248 | + | 0.431217i | \(0.141916\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.7223 | − | 21.1502i | 0.985863 | − | 0.878974i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.7993 | + | 8.52060i | −1.31926 | + | 0.353494i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.92456 | + | 3.99790i | −0.286786 | + | 0.165576i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.93670 | + | 16.8389i | −0.0800727 | + | 0.696201i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.81553 | − | 25.4359i | 0.281307 | − | 1.04985i | −0.670189 | − | 0.742191i | \(-0.733787\pi\) |
0.951496 | − | 0.307662i | \(-0.0995465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.40180 | − | 8.96364i | −0.0989645 | − | 0.369341i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.69660 | + | 19.2632i | 0.398865 | + | 0.792382i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.9274 | 1.72175 | 0.860876 | − | 0.508814i | \(-0.169916\pi\) | ||||
0.860876 | + | 0.508814i | \(0.169916\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.5430 | + | 10.5430i | −0.432222 | + | 0.432222i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.44797 | − | 16.4920i | 0.222971 | − | 0.674972i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.1742 | + | 12.2249i | 0.865154 | + | 0.499497i | 0.865735 | − | 0.500503i | \(-0.166852\pi\) |
−0.000580933 | 1.00000i | \(0.500185\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7521 | − | 14.2906i | 1.00966 | − | 0.582928i | 0.0985682 | − | 0.995130i | \(-0.468574\pi\) |
0.911092 | + | 0.412203i | \(0.135240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.2136 | − | 28.3787i | 0.456652 | − | 1.15567i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.2669 | + | 5.16255i | 0.783310 | + | 0.209887i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.32245 | − | 16.1470i | 0.378387 | − | 0.655385i | −0.612441 | − | 0.790516i | \(-0.709812\pi\) |
0.990828 | + | 0.135131i | \(0.0431456\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −49.1315 | − | 2.81612i | −1.99091 | − | 0.114115i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.1946 | − | 22.1946i | 0.897896 | − | 0.897896i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.3177 | − | 13.3177i | −0.537896 | − | 0.537896i | 0.385014 | − | 0.922911i | \(-0.374196\pi\) |
−0.922911 | + | 0.385014i | \(0.874196\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.01335 | − | 4.60349i | −0.282806 | − | 0.185631i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.1035 | − | 8.72003i | −0.608045 | − | 0.351055i | 0.164155 | − | 0.986435i | \(-0.447510\pi\) |
−0.772200 | + | 0.635379i | \(0.780844\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.84959 | + | 21.8310i | −0.235115 | + | 0.877461i | 0.742982 | + | 0.669311i | \(0.233411\pi\) |
−0.978097 | + | 0.208150i | \(0.933256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.218963 | + | 2.42544i | 0.00878667 | + | 0.0973297i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.4506 | − | 40.6177i | −0.939530 | − | 1.62731i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.40527 | + | 7.63015i | −0.176211 | + | 0.305206i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.46143 | − | 11.8655i | −0.0983001 | − | 0.473861i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.55946 | + | 1.55946i | 0.0621797 | + | 0.0621797i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8510i | 0.790254i | 0.918627 | + | 0.395127i | \(0.129299\pi\) | ||||
−0.918627 | + | 0.395127i | \(0.870701\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.97096 | + | 34.3865i | −0.0783387 | + | 1.36674i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.70512 | + | 0.724836i | −0.107350 | + | 0.0287642i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.6254 | − | 9.27785i | −1.37191 | − | 0.367602i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.7942 | + | 19.9488i | −0.585249 | + | 0.789161i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.5842 | + | 35.6529i | 0.813026 | + | 1.40820i | 0.910736 | + | 0.412988i | \(0.135515\pi\) |
−0.0977099 | + | 0.995215i | \(0.531152\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.73128 | − | 25.1215i | −0.265456 | − | 0.990694i | −0.961971 | − | 0.273152i | \(-0.911934\pi\) |
0.696515 | − | 0.717542i | \(-0.254733\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.93726 | + | 30.0818i | −0.391279 | + | 1.18447i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 40.3426i | − | 1.58603i | −0.609201 | − | 0.793016i | \(-0.708510\pi\) | ||
0.609201 | − | 0.793016i | \(-0.291490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.35741i | 0.288803i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.4762 | − | 43.8220i | 0.567367 | − | 1.71752i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.68547 | + | 6.29024i | 0.0659574 | + | 0.246156i | 0.991031 | − | 0.133631i | \(-0.0426638\pi\) |
−0.925074 | + | 0.379787i | \(0.875997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.33671 | + | 10.9755i | 0.247596 | + | 0.428849i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.5937 | + | 19.6784i | −0.569353 | + | 0.767726i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.0887093 | − | 0.0237696i | −0.00345562 | − | 0.000925932i | 0.257091 | − | 0.966387i | \(-0.417236\pi\) |
−0.260546 | + | 0.965461i | \(0.583903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.0157 | − | 7.23883i | 1.05079 | − | 0.281558i | 0.308211 | − | 0.951318i | \(-0.400270\pi\) |
0.742578 | + | 0.669760i | \(0.233603\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.721435 | + | 12.5865i | −0.0280182 | + | 0.488821i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.1575i | 0.393892i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.24790 | + | 2.24790i | 0.0870392 | + | 0.0870392i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.90140 | + | 23.6274i | 0.189499 | + | 0.913490i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.6988 | + | 32.3873i | −0.721859 | + | 1.25030i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.48158 | + | 4.29822i | 0.0956578 | + | 0.165684i | 0.909883 | − | 0.414865i | \(-0.136171\pi\) |
−0.814225 | + | 0.580549i | \(0.802838\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.5484 | − | 4.88333i | −0.406009 | − | 0.187959i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.77876 | − | 6.63841i | 0.0683632 | − | 0.255135i | −0.923283 | − | 0.384119i | \(-0.874505\pi\) |
0.991647 | + | 0.128985i | \(0.0411718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.1923 | + | 23.7824i | 1.58081 | + | 0.912683i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.9745 | + | 7.20357i | 0.420545 | + | 0.276041i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.7192 | − | 20.7192i | −0.792797 | − | 0.792797i | 0.189151 | − | 0.981948i | \(-0.439426\pi\) |
−0.981948 | + | 0.189151i | \(0.939426\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2214 | + | 11.2214i | −0.428747 | + | 0.428747i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.0540 | − | 1.89459i | −1.26109 | − | 0.0722831i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.83351 | − | 4.90779i | 0.107948 | − | 0.186972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.31450 | + | 1.42402i | 0.202173 | + | 0.0541721i | 0.358484 | − | 0.933536i | \(-0.383294\pi\) |
−0.156311 | + | 0.987708i | \(0.549960\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.1474 | − | 56.0494i | 0.841310 | − | 2.12914i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.8171 | + | 12.0188i | −0.789638 | + | 0.455898i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.40388 | − | 3.11993i | −0.204687 | − | 0.118176i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.84834 | + | 17.7040i | −0.221205 | + | 0.669626i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.06232 | + | 1.06232i | −0.0401233 | + | 0.0401233i | −0.726884 | − | 0.686760i | \(-0.759032\pi\) |
0.686760 | + | 0.726884i | \(0.259032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.50244 | 0.0566656 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.9537 | − | 23.7471i | −0.450202 | − | 0.894368i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.25705 | + | 12.1555i | 0.122494 | + | 0.457153i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.50159 | + | 35.4604i | −0.356840 | + | 1.33174i | 0.521314 | + | 0.853365i | \(0.325442\pi\) |
−0.878153 | + | 0.478379i | \(0.841224\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.48904 | − | 21.6412i | 0.0933463 | − | 0.811609i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.58187 | + | 1.49064i | −0.0966916 | + | 0.0558249i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.1729 | + | 7.01301i | −0.978812 | + | 0.262272i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.8116 | − | 25.6878i | 1.07599 | − | 0.959328i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.37513 | 0.275046 | 0.137523 | − | 0.990499i | \(-0.456086\pi\) | ||||
0.137523 | + | 0.990499i | \(0.456086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.03749 | −0.224848 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.65981 | + | 46.5656i | 0.359252 | + | 1.73179i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.6567 | + | 3.92726i | −0.544337 | + | 0.145855i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.80127 | + | 3.34936i | −0.215157 | + | 0.124221i | −0.603706 | − | 0.797207i | \(-0.706310\pi\) |
0.388549 | + | 0.921428i | \(0.372977\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.09400 | + | 25.4224i | −0.336815 | + | 0.941571i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.09879 | + | 22.7610i | −0.225572 | + | 0.841846i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.28281 | − | 34.6439i | −0.342868 | − | 1.27960i | −0.895083 | − | 0.445900i | \(-0.852884\pi\) |
0.552214 | − | 0.833702i | \(-0.313783\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.6613 | + | 25.3832i | −0.614560 | + | 0.936272i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.7797 | 1.79682 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.01107 | + | 4.01107i | −0.147549 | + | 0.147549i | −0.777022 | − | 0.629473i | \(-0.783271\pi\) |
0.629473 | + | 0.777022i | \(0.283271\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.71564 | + | 6.41070i | 0.209969 | + | 0.235503i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.1551 | − | 11.0592i | −0.702734 | − | 0.405724i | 0.105631 | − | 0.994405i | \(-0.466314\pi\) |
−0.808365 | + | 0.588682i | \(0.799647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.47761 | − | 1.43045i | 0.0907726 | − | 0.0524076i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.6579 | + | 18.4678i | 0.536305 | + | 0.675703i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.5083 | + | 8.97853i | 1.22437 | + | 0.328068i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.05672 | − | 10.4905i | 0.221013 | − | 0.382805i | −0.734103 | − | 0.679038i | \(-0.762397\pi\) |
0.955116 | + | 0.296233i | \(0.0957304\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.5691 | − | 24.9697i | −0.458044 | − | 0.909947i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.1178 | − | 25.1178i | 0.914131 | − | 0.914131i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.9365 | − | 19.9365i | −0.724604 | − | 0.724604i | 0.244935 | − | 0.969539i | \(-0.421233\pi\) |
−0.969539 | + | 0.244935i | \(0.921233\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.47739 | + | 1.75043i | −0.126221 | + | 0.0635366i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.1681 | − | 21.4590i | −1.34734 | − | 0.777889i | −0.359471 | − | 0.933156i | \(-0.617043\pi\) |
−0.987873 | + | 0.155267i | \(0.950376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.14690 | − | 11.7444i | 0.113925 | − | 0.425176i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.93130 | + | 3.92426i | 0.359067 | + | 0.141882i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.60728 | − | 4.51595i | −0.0941435 | − | 0.163061i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.7618 | + | 23.8361i | −0.496263 | + | 0.859553i | −0.999991 | − | 0.00430961i | \(-0.998628\pi\) |
0.503728 | + | 0.863863i | \(0.331962\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.40564 | + | 2.14482i | −0.0866371 | + | 0.0772438i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.4688 | − | 11.4688i | −0.412504 | − | 0.412504i | 0.470106 | − | 0.882610i | \(-0.344216\pi\) |
−0.882610 | + | 0.470106i | \(0.844216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 14.2300i | − | 0.511155i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.24658 | + | 4.10019i | 0.224095 | + | 0.147094i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.10608 | + | 1.10022i | −0.147115 | + | 0.0394195i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.3500 | − | 10.2759i | −1.37227 | − | 0.367699i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.1462 | + | 33.0864i | 0.434071 | + | 1.18241i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.81622 | − | 15.2701i | −0.314664 | − | 0.545015i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.4753 | − | 42.8263i | −0.409049 | − | 1.52659i | −0.796463 | − | 0.604687i | \(-0.793298\pi\) |
0.387414 | − | 0.921906i | \(-0.373368\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.0812387 | + | 0.0168526i | −0.00289217 | + | 0.000599968i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 34.5766i | − | 1.22940i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 26.5056i | − | 0.941241i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.19437 | − | 3.58282i | −0.113292 | − | 0.127070i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.68647 | + | 28.6863i | 0.272269 | + | 1.01612i | 0.957650 | + | 0.287936i | \(0.0929690\pi\) |
−0.685381 | + | 0.728185i | \(0.740364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.88726 | − | 17.1252i | −0.349786 | − | 0.605847i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.0091 | + | 26.9806i | −0.706985 | + | 0.953312i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.8302 | − | 10.1366i | −1.33500 | − | 0.357712i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.15206 | − | 0.844592i | 0.111096 | − | 0.0297679i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.8741 | + | 16.0446i | −1.12202 | + | 0.564796i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 16.7474i | − | 0.588806i | −0.955681 | − | 0.294403i | \(-0.904879\pi\) | ||
0.955681 | − | 0.294403i | \(-0.0951209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.60619 | + | 7.60619i | 0.267090 | + | 0.267090i | 0.827926 | − | 0.560837i | \(-0.189520\pi\) |
−0.560837 | + | 0.827926i | \(0.689520\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.9535 | + | 8.57349i | 0.910229 | + | 0.300685i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.08582 | + | 7.07684i | −0.143120 | + | 0.247891i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.02649 | + | 13.9023i | 0.280811 | + | 0.486379i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.26855 | + | 42.2514i | 0.219041 | + | 1.47638i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.99074 | + | 37.2860i | −0.348679 | + | 1.30129i | 0.539575 | + | 0.841937i | \(0.318585\pi\) |
−0.888255 | + | 0.459351i | \(0.848082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.9783 | + | 13.8439i | 0.835831 | + | 0.482567i | 0.855845 | − | 0.517233i | \(-0.173038\pi\) |
−0.0200141 | + | 0.999800i | \(0.506371\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.06335 | − | 18.5517i | 0.0370210 | − | 0.645888i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.6025 | + | 27.6025i | 0.959833 | + | 0.959833i | 0.999224 | − | 0.0393907i | \(-0.0125417\pi\) |
−0.0393907 | + | 0.999224i | \(0.512542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.8542 | − | 14.8542i | 0.515908 | − | 0.515908i | −0.400423 | − | 0.916330i | \(-0.631137\pi\) |
0.916330 | + | 0.400423i | \(0.131137\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.09819 | + | 10.8140i | −0.246234 | + | 0.375133i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.2919 | + | 19.5581i | −0.391240 | + | 0.677647i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.514368 | + | 0.137824i | 0.0178004 | + | 0.00476961i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.9193 | + | 2.97187i | −1.13786 | + | 0.102723i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.0413 | − | 25.4272i | 1.52047 | − | 0.877846i | 0.520766 | − | 0.853700i | \(-0.325647\pi\) |
0.999708 | − | 0.0241463i | \(-0.00768676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.7301 | + | 8.50445i | 0.507936 | + | 0.293257i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.4451 | + | 2.37424i | −0.394191 | + | 0.0817731i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.70015 | + | 1.70015i | −0.0584871 | + | 0.0584871i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.2656 | 1.72715 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.2727 | − | 1.27663i | −0.764398 | − | 0.0438137i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.124927 | − | 0.466233i | −0.00428244 | − | 0.0159823i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.65390 | − | 13.6365i | 0.125107 | − | 0.466906i | −0.874736 | − | 0.484599i | \(-0.838966\pi\) |
0.999843 | + | 0.0176931i | \(0.00563219\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.67448 | − | 2.89370i | 0.228262 | − | 0.0989625i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.7618 | − | 8.52275i | 0.504255 | − | 0.291132i | −0.226214 | − | 0.974078i | \(-0.572635\pi\) |
0.730469 | + | 0.682946i | \(0.239302\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.9255 | + | 6.67877i | −0.850448 | + | 0.227877i | −0.657614 | − | 0.753355i | \(-0.728434\pi\) |
−0.192833 | + | 0.981232i | \(0.561768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.0741 | − | 6.63128i | −0.684122 | − | 0.225993i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.8217 | 0.640698 | 0.320349 | − | 0.947300i | \(-0.396200\pi\) | ||||
0.320349 | + | 0.947300i | \(0.396200\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.1170 | −0.683999 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.4171 | − | 6.74459i | −0.693401 | − | 0.229058i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.6373 | − | 9.01309i | 1.14107 | − | 0.305748i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.9408 | + | 17.2863i | −1.01450 | + | 0.585725i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.89235 | − | 33.8424i | 0.131736 | − | 1.14539i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.0417 | + | 48.6724i | −0.440891 | + | 1.64543i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.80014 | + | 10.4503i | 0.0945540 | + | 0.352880i | 0.996951 | − | 0.0780244i | \(-0.0248612\pi\) |
−0.902397 | + | 0.430905i | \(0.858195\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.8455 | + | 1.42409i | 0.838018 | + | 0.0480335i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.1658 | 1.35322 | 0.676610 | − | 0.736342i | \(-0.263448\pi\) | ||||
0.676610 | + | 0.736342i | \(0.263448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.5617 | − | 16.5617i | 0.557346 | − | 0.557346i | −0.371205 | − | 0.928551i | \(-0.621055\pi\) |
0.928551 | + | 0.371205i | \(0.121055\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.32475 | + | 0.897148i | −0.145375 | + | 0.0301573i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.1259 | + | 7.57822i | 0.440723 | + | 0.254452i | 0.703904 | − | 0.710295i | \(-0.251438\pi\) |
−0.263181 | + | 0.964746i | \(0.584772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.11191 | + | 3.52871i | −0.204987 | + | 0.118349i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −43.1393 | + | 1.41453i | −1.44522 | + | 0.0473885i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0124 | − | 3.48667i | −0.435444 | − | 0.116677i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.9535 | − | 38.0246i | 0.733826 | − | 1.27102i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.51410 | − | 2.30671i | 0.0505543 | − | 0.0770187i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.5097 | + | 30.5097i | −1.01755 | + | 1.01755i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.52455 | − | 2.52455i | −0.0841050 | − | 0.0841050i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.56853 | + | 79.7050i | −0.152031 | + | 2.65242i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.35749 | − | 4.82520i | −0.277812 | − | 0.160395i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.61434 | − | 9.75684i | 0.0868077 | − | 0.323971i | −0.908843 | − | 0.417139i | \(-0.863033\pi\) |
0.995650 | + | 0.0931683i | \(0.0296995\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.05943 | − | 5.60307i | 0.234146 | − | 0.185842i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.2358 | + | 43.7097i | 0.836099 | + | 1.44817i | 0.893132 | + | 0.449794i | \(0.148503\pi\) |
−0.0570332 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.8459 | + | 32.6420i | −0.623708 | + | 1.08029i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.3176 | − | 7.04208i | −0.704739 | − | 0.232804i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.5830 | + | 22.5830i | 0.745757 | + | 0.745757i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.7422i | − | 0.552274i | −0.961118 | − | 0.276137i | \(-0.910946\pi\) | ||
0.961118 | − | 0.276137i | \(-0.0890544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.7789 | + | 13.4798i | −0.882396 | + | 0.444175i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.1806 | − | 7.28302i | 0.894661 | − | 0.239724i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.22538 | + | 0.596288i | 0.0731699 | + | 0.0196058i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.71998 | + | 3.96721i | 0.0564914 | + | 0.130300i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.92665 | + | 17.1935i | 0.325683 | + | 0.564099i | 0.981650 | − | 0.190690i | \(-0.0610725\pi\) |
−0.655967 | + | 0.754789i | \(0.727739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.98199 | + | 14.8610i | 0.130504 | + | 0.487049i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.988613 | + | 1.10883i | 0.0323657 | + | 0.0363016i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.0708i | 0.558273i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.05876i | 0.0999253i | 0.998751 | + | 0.0499626i | \(0.0159102\pi\) | ||||
−0.998751 | + | 0.0499626i | \(0.984090\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.1340 | + | 6.45859i | −1.01602 | + | 0.210768i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.07424 | + | 11.4732i | 0.100217 | + | 0.374016i | 0.997759 | − | 0.0669140i | \(-0.0213153\pi\) |
−0.897541 | + | 0.440930i | \(0.854649\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.682835 | + | 1.18270i | 0.0222362 | + | 0.0385141i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 35.6470 | + | 6.18387i | 1.15960 | + | 0.201161i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55.6732 | + | 14.9176i | 1.80914 | + | 0.484757i | 0.995343 | − | 0.0963965i | \(-0.0307317\pi\) |
0.813794 | + | 0.581153i | \(0.197398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.8122 | − | 7.18430i | 0.870360 | − | 0.233212i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.03585 | − | 3.96187i | −0.195726 | − | 0.128472i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.2546i | − | 1.43355i | −0.697306 | − | 0.716774i | \(-0.745618\pi\) | ||
0.697306 | − | 0.716774i | \(-0.254382\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.2186 | + | 20.2186i | 0.654259 | + | 0.654259i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −42.0556 | + | 37.4958i | −1.35946 | + | 1.21207i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.9956 | + | 34.6334i | −0.645691 | + | 1.11837i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.73171 | − | 8.19557i | −0.152636 | − | 0.264373i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.64617 | − | 24.5760i | −0.117496 | − | 0.791951i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.89407 | + | 29.4611i | −0.254119 | + | 0.948386i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.7930 | − | 21.2424i | −1.18318 | − | 0.683110i | −0.226433 | − | 0.974027i | \(-0.572706\pi\) |
−0.956748 | + | 0.290916i | \(0.906040\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.83314 | − | 2.43288i | 0.155263 | − | 0.0781552i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.1469 | − | 11.1469i | −0.357720 | − | 0.357720i | 0.505252 | − | 0.862972i | \(-0.331400\pi\) |
−0.862972 | + | 0.505252i | \(0.831400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.8329 | + | 42.8329i | −1.37316 | + | 1.37316i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.92159 | + | 11.7638i | 0.189643 | + | 0.376743i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.47430 | + | 4.28561i | −0.0791598 | + | 0.137109i | −0.902888 | − | 0.429877i | \(-0.858557\pi\) |
0.823728 | + | 0.566985i | \(0.191890\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.8682 | − | 13.8980i | −1.65771 | − | 0.444183i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.61369 | + | 1.27795i | −0.275014 | + | 0.0408019i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.6831 | + | 24.0658i | −1.32948 | + | 0.767578i | −0.985220 | − | 0.171294i | \(-0.945205\pi\) |
−0.344265 | + | 0.938873i | \(0.611872\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.9237 | − | 10.3483i | −0.571098 | − | 0.329724i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −44.5856 | − | 50.0074i | −1.41917 | − | 1.59175i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.64672 | − | 3.64672i | 0.115959 | − | 0.115959i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.90020 | 0.282724 | 0.141362 | − | 0.989958i | \(-0.454852\pi\) | ||||
0.141362 | + | 0.989958i | \(0.454852\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.91103 | + | 7.48188i | −0.155847 | + | 0.237430i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.31407 | + | 16.1003i | 0.136765 | + | 0.510414i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.66586 | − | 24.8773i | 0.211110 | − | 0.787873i | −0.776390 | − | 0.630253i | \(-0.782951\pi\) |
0.987500 | − | 0.157620i | \(-0.0503822\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.914680 | − | 5.27268i | 0.0289392 | − | 0.166820i |
(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 | 576.2.bb.e.49.16 | 72 | ||
3.2 | odd | 2 | 1728.2.bc.e.1009.13 | 72 | |||
4.3 | odd | 2 | 144.2.x.e.85.7 | yes | 72 | ||
9.2 | odd | 6 | 1728.2.bc.e.1585.6 | 72 | |||
9.7 | even | 3 | inner | 576.2.bb.e.241.8 | 72 | ||
12.11 | even | 2 | 432.2.y.e.37.12 | 72 | |||
16.3 | odd | 4 | 144.2.x.e.13.18 | ✓ | 72 | ||
16.13 | even | 4 | inner | 576.2.bb.e.337.8 | 72 | ||
36.7 | odd | 6 | 144.2.x.e.133.18 | yes | 72 | ||
36.11 | even | 6 | 432.2.y.e.181.1 | 72 | |||
48.29 | odd | 4 | 1728.2.bc.e.145.6 | 72 | |||
48.35 | even | 4 | 432.2.y.e.253.1 | 72 | |||
144.29 | odd | 12 | 1728.2.bc.e.721.13 | 72 | |||
144.61 | even | 12 | inner | 576.2.bb.e.529.16 | 72 | ||
144.83 | even | 12 | 432.2.y.e.397.12 | 72 | |||
144.115 | odd | 12 | 144.2.x.e.61.7 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.18 | ✓ | 72 | 16.3 | odd | 4 | ||
144.2.x.e.61.7 | yes | 72 | 144.115 | odd | 12 | ||
144.2.x.e.85.7 | yes | 72 | 4.3 | odd | 2 | ||
144.2.x.e.133.18 | yes | 72 | 36.7 | odd | 6 | ||
432.2.y.e.37.12 | 72 | 12.11 | even | 2 | |||
432.2.y.e.181.1 | 72 | 36.11 | even | 6 | |||
432.2.y.e.253.1 | 72 | 48.35 | even | 4 | |||
432.2.y.e.397.12 | 72 | 144.83 | even | 12 | |||
576.2.bb.e.49.16 | 72 | 1.1 | even | 1 | trivial | ||
576.2.bb.e.241.8 | 72 | 9.7 | even | 3 | inner | ||
576.2.bb.e.337.8 | 72 | 16.13 | even | 4 | inner | ||
576.2.bb.e.529.16 | 72 | 144.61 | even | 12 | inner | ||
1728.2.bc.e.145.6 | 72 | 48.29 | odd | 4 | |||
1728.2.bc.e.721.13 | 72 | 144.29 | odd | 12 | |||
1728.2.bc.e.1009.13 | 72 | 3.2 | odd | 2 | |||
1728.2.bc.e.1585.6 | 72 | 9.2 | odd | 6 |