Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(67,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.g (of order \(3\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.10 | ||
Character | \(\chi\) | \(=\) | 441.79 |
Dual form | 441.2.g.h.67.10 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.863305 | + | 1.49529i | 0.610449 | + | 1.05733i | 0.991165 | + | 0.132637i | \(0.0423443\pi\) |
−0.380716 | + | 0.924692i | \(0.624322\pi\) | |||||||
\(3\) | 0.615283 | − | 1.61908i | 0.355234 | − | 0.934778i | ||||
\(4\) | −0.490592 | + | 0.849731i | −0.245296 | + | 0.424865i | ||||
\(5\) | 3.51231 | 1.57075 | 0.785377 | − | 0.619018i | \(-0.212469\pi\) | ||||
0.785377 | + | 0.619018i | \(0.212469\pi\) | |||||||
\(6\) | 2.95217 | − | 0.477737i | 1.20522 | − | 0.195035i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.75910 | 0.621935 | ||||||||
\(9\) | −2.24285 | − | 1.99239i | −0.747618 | − | 0.664129i | ||||
\(10\) | 3.03220 | + | 5.25192i | 0.958865 | + | 1.66080i | ||||
\(11\) | −6.09064 | −1.83640 | −0.918199 | − | 0.396120i | \(-0.870356\pi\) | ||||
−0.918199 | + | 0.396120i | \(0.870356\pi\) | |||||||
\(12\) | 1.07393 | + | 1.31713i | 0.310017 | + | 0.380224i | ||||
\(13\) | 0.560139 | + | 0.970190i | 0.155355 | + | 0.269082i | 0.933188 | − | 0.359388i | \(-0.117015\pi\) |
−0.777833 | + | 0.628471i | \(0.783681\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.16106 | − | 5.68672i | 0.557984 | − | 1.46831i | ||||
\(16\) | 2.49982 | + | 4.32982i | 0.624956 | + | 1.08246i | ||||
\(17\) | −0.601978 | − | 1.04266i | −0.146001 | − | 0.252881i | 0.783745 | − | 0.621083i | \(-0.213307\pi\) |
−0.929746 | + | 0.368202i | \(0.879974\pi\) | |||||||
\(18\) | 1.04293 | − | 5.07375i | 0.245820 | − | 1.19589i | ||||
\(19\) | 1.10269 | − | 1.90991i | 0.252974 | − | 0.438163i | −0.711370 | − | 0.702818i | \(-0.751925\pi\) |
0.964343 | + | 0.264655i | \(0.0852581\pi\) | |||||||
\(20\) | −1.72311 | + | 2.98452i | −0.385300 | + | 0.667359i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.25808 | − | 9.10727i | −1.12103 | − | 1.94168i | ||||
\(23\) | −1.27339 | −0.265520 | −0.132760 | − | 0.991148i | \(-0.542384\pi\) | ||||
−0.132760 | + | 0.991148i | \(0.542384\pi\) | |||||||
\(24\) | 1.08234 | − | 2.84812i | 0.220932 | − | 0.581371i | ||||
\(25\) | 7.33633 | 1.46727 | ||||||||
\(26\) | −0.967143 | + | 1.67514i | −0.189672 | + | 0.328522i | ||||
\(27\) | −4.60583 | + | 2.40548i | −0.886392 | + | 0.462936i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.10262 | + | 5.37390i | −0.576142 | + | 0.997907i | 0.419774 | + | 0.907628i | \(0.362109\pi\) |
−0.995917 | + | 0.0902789i | \(0.971224\pi\) | |||||||
\(30\) | 10.3689 | − | 1.67796i | 1.89310 | − | 0.306352i | ||||
\(31\) | 0.0942019 | − | 0.163162i | 0.0169192 | − | 0.0293048i | −0.857442 | − | 0.514581i | \(-0.827948\pi\) |
0.874361 | + | 0.485276i | \(0.161281\pi\) | |||||||
\(32\) | −2.55712 | + | 4.42907i | −0.452040 | + | 0.782956i | ||||
\(33\) | −3.74747 | + | 9.86125i | −0.652350 | + | 1.71662i | ||||
\(34\) | 1.03938 | − | 1.80026i | 0.178252 | − | 0.308742i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.79332 | − | 0.928373i | 0.465553 | − | 0.154729i | ||||
\(37\) | −1.78835 | + | 3.09752i | −0.294003 | + | 0.509228i | −0.974753 | − | 0.223288i | \(-0.928321\pi\) |
0.680749 | + | 0.732516i | \(0.261654\pi\) | |||||||
\(38\) | 3.80782 | 0.617710 | ||||||||
\(39\) | 1.91546 | − | 0.309971i | 0.306719 | − | 0.0496350i | ||||
\(40\) | 6.17850 | 0.976907 | ||||||||
\(41\) | 1.68320 | + | 2.91538i | 0.262871 | + | 0.455307i | 0.967004 | − | 0.254762i | \(-0.0819972\pi\) |
−0.704132 | + | 0.710069i | \(0.748664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90276 | + | 3.29567i | −0.290168 | + | 0.502585i | −0.973849 | − | 0.227195i | \(-0.927044\pi\) |
0.683681 | + | 0.729781i | \(0.260378\pi\) | |||||||
\(44\) | 2.98802 | − | 5.17540i | 0.450461 | − | 0.780221i | ||||
\(45\) | −7.87760 | − | 6.99788i | −1.17432 | − | 1.04318i | ||||
\(46\) | −1.09932 | − | 1.90408i | −0.162086 | − | 0.280742i | ||||
\(47\) | 2.86035 | + | 4.95427i | 0.417225 | + | 0.722654i | 0.995659 | − | 0.0930746i | \(-0.0296695\pi\) |
−0.578434 | + | 0.815729i | \(0.696336\pi\) | |||||||
\(48\) | 8.54843 | − | 1.38336i | 1.23386 | − | 0.199670i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.33349 | + | 10.9699i | 0.895691 | + | 1.55138i | ||||
\(51\) | −2.05853 | + | 0.333123i | −0.288252 | + | 0.0466466i | ||||
\(52\) | −1.09920 | −0.152432 | ||||||||
\(53\) | 4.16913 | + | 7.22115i | 0.572675 | + | 0.991901i | 0.996290 | + | 0.0860593i | \(0.0274275\pi\) |
−0.423615 | + | 0.905842i | \(0.639239\pi\) | |||||||
\(54\) | −7.57313 | − | 4.81037i | −1.03057 | − | 0.654609i | ||||
\(55\) | −21.3922 | −2.88453 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.41384 | − | 2.96047i | −0.319720 | − | 0.392124i | ||||
\(58\) | −10.7140 | −1.40682 | ||||||||
\(59\) | 5.63427 | − | 9.75883i | 0.733519 | − | 1.27049i | −0.221851 | − | 0.975081i | \(-0.571210\pi\) |
0.955370 | − | 0.295411i | \(-0.0954567\pi\) | |||||||
\(60\) | 3.77198 | + | 4.62618i | 0.486960 | + | 0.597238i | ||||
\(61\) | −6.00109 | − | 10.3942i | −0.768361 | − | 1.33084i | −0.938451 | − | 0.345411i | \(-0.887739\pi\) |
0.170091 | − | 0.985428i | \(-0.445594\pi\) | |||||||
\(62\) | 0.325300 | 0.0413131 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.16898 | 0.146123 | ||||||||
\(65\) | 1.96738 | + | 3.40761i | 0.244024 | + | 0.422662i | ||||
\(66\) | −17.9806 | + | 2.90972i | −2.21326 | + | 0.358162i | ||||
\(67\) | 3.95652 | − | 6.85289i | 0.483366 | − | 0.837214i | −0.516452 | − | 0.856316i | \(-0.672748\pi\) |
0.999818 | + | 0.0191025i | \(0.00608088\pi\) | |||||||
\(68\) | 1.18130 | 0.143254 | ||||||||
\(69\) | −0.783494 | + | 2.06172i | −0.0943217 | + | 0.248202i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2052 | −1.44850 | −0.724248 | − | 0.689540i | \(-0.757813\pi\) | ||||
−0.724248 | + | 0.689540i | \(0.757813\pi\) | |||||||
\(72\) | −3.94540 | − | 3.50480i | −0.464970 | − | 0.413045i | ||||
\(73\) | 2.65737 | + | 4.60269i | 0.311021 | + | 0.538704i | 0.978584 | − | 0.205849i | \(-0.0659957\pi\) |
−0.667563 | + | 0.744554i | \(0.732662\pi\) | |||||||
\(74\) | −6.17557 | −0.717896 | ||||||||
\(75\) | 4.51392 | − | 11.8781i | 0.521222 | − | 1.37157i | ||||
\(76\) | 1.08194 | + | 1.87397i | 0.124107 | + | 0.214959i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.11712 | + | 2.59657i | 0.239717 | + | 0.294003i | ||||
\(79\) | −4.60855 | − | 7.98225i | −0.518503 | − | 0.898073i | −0.999769 | − | 0.0214988i | \(-0.993156\pi\) |
0.481266 | − | 0.876575i | \(-0.340177\pi\) | |||||||
\(80\) | 8.78016 | + | 15.2077i | 0.981651 | + | 1.70027i | ||||
\(81\) | 1.06079 | + | 8.93727i | 0.117866 | + | 0.993030i | ||||
\(82\) | −2.90623 | + | 5.03373i | −0.320939 | + | 0.555883i | ||||
\(83\) | 0.624950 | − | 1.08245i | 0.0685972 | − | 0.118814i | −0.829687 | − | 0.558229i | \(-0.811481\pi\) |
0.898284 | + | 0.439415i | \(0.144814\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.11433 | − | 3.66213i | −0.229332 | − | 0.397214i | ||||
\(86\) | −6.57064 | −0.708531 | ||||||||
\(87\) | 6.79179 | + | 8.32986i | 0.728156 | + | 0.893055i | ||||
\(88\) | −10.7140 | −1.14212 | ||||||||
\(89\) | −2.77066 | + | 4.79892i | −0.293689 | + | 0.508684i | −0.974679 | − | 0.223608i | \(-0.928216\pi\) |
0.680990 | + | 0.732293i | \(0.261550\pi\) | |||||||
\(90\) | 3.66308 | − | 17.8206i | 0.386122 | − | 1.87846i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.624715 | − | 1.08204i | 0.0651310 | − | 0.112810i | ||||
\(93\) | −0.206213 | − | 0.252912i | −0.0213832 | − | 0.0262257i | ||||
\(94\) | −4.93871 | + | 8.55409i | −0.509389 | + | 0.882287i | ||||
\(95\) | 3.87298 | − | 6.70820i | 0.397359 | − | 0.688246i | ||||
\(96\) | 5.59767 | + | 6.86532i | 0.571310 | + | 0.700689i | ||||
\(97\) | 8.24277 | − | 14.2769i | 0.836926 | − | 1.44960i | −0.0555261 | − | 0.998457i | \(-0.517684\pi\) |
0.892452 | − | 0.451142i | \(-0.148983\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.6604 | + | 12.1349i | 1.37292 | + | 1.21960i | ||||
\(100\) | −3.59915 | + | 6.23391i | −0.359915 | + | 0.623391i | ||||
\(101\) | −12.9638 | −1.28995 | −0.644975 | − | 0.764203i | \(-0.723132\pi\) | ||||
−0.644975 | + | 0.764203i | \(0.723132\pi\) | |||||||
\(102\) | −2.27526 | − | 2.79051i | −0.225284 | − | 0.276302i | ||||
\(103\) | 2.70182 | 0.266218 | 0.133109 | − | 0.991101i | \(-0.457504\pi\) | ||||
0.133109 | + | 0.991101i | \(0.457504\pi\) | |||||||
\(104\) | 0.985340 | + | 1.70666i | 0.0966205 | + | 0.167352i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.19847 | + | 12.4681i | −0.699177 | + | 1.21101i | ||||
\(107\) | 0.0892402 | − | 0.154569i | 0.00862718 | − | 0.0149427i | −0.861680 | − | 0.507453i | \(-0.830587\pi\) |
0.870307 | + | 0.492510i | \(0.163921\pi\) | |||||||
\(108\) | 0.215569 | − | 5.09382i | 0.0207431 | − | 0.490153i | ||||
\(109\) | −4.67927 | − | 8.10473i | −0.448192 | − | 0.776292i | 0.550076 | − | 0.835115i | \(-0.314599\pi\) |
−0.998268 | + | 0.0588226i | \(0.981265\pi\) | |||||||
\(110\) | −18.4680 | − | 31.9876i | −1.76086 | − | 3.04989i | ||||
\(111\) | 3.91479 | + | 4.80134i | 0.371575 | + | 0.455723i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.21019 | + | 7.29226i | 0.396061 | + | 0.685998i | 0.993236 | − | 0.116113i | \(-0.0370434\pi\) |
−0.597175 | + | 0.802111i | \(0.703710\pi\) | |||||||
\(114\) | 2.34289 | − | 6.16517i | 0.219431 | − | 0.577422i | ||||
\(115\) | −4.47254 | −0.417067 | ||||||||
\(116\) | −3.04424 | − | 5.27278i | −0.282651 | − | 0.489565i | ||||
\(117\) | 0.676682 | − | 3.29201i | 0.0625593 | − | 0.304346i | ||||
\(118\) | 19.4564 | 1.79110 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.80152 | − | 10.0035i | 0.347030 | − | 0.913190i | ||||
\(121\) | 26.0959 | 2.37235 | ||||||||
\(122\) | 10.3615 | − | 17.9467i | 0.938090 | − | 1.62482i | ||||
\(123\) | 5.75589 | − | 0.931450i | 0.518991 | − | 0.0839861i | ||||
\(124\) | 0.0924294 | + | 0.160092i | 0.00830040 | + | 0.0143767i | ||||
\(125\) | 8.20593 | 0.733960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.92438 | −0.880647 | −0.440323 | − | 0.897839i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897839i | \(0.645136\pi\) | |||||||
\(128\) | 6.12343 | + | 10.6061i | 0.541240 | + | 0.937455i | ||||
\(129\) | 4.16523 | + | 5.10849i | 0.366728 | + | 0.449778i | ||||
\(130\) | −3.39691 | + | 5.88361i | −0.297928 | + | 0.516027i | ||||
\(131\) | −15.2467 | −1.33211 | −0.666055 | − | 0.745902i | \(-0.732019\pi\) | ||||
−0.666055 | + | 0.745902i | \(0.732019\pi\) | |||||||
\(132\) | −6.54093 | − | 8.02219i | −0.569314 | − | 0.698242i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.6627 | 1.18028 | ||||||||
\(135\) | −16.1771 | + | 8.44881i | −1.39230 | + | 0.727158i | ||||
\(136\) | −1.05894 | − | 1.83413i | −0.0908032 | − | 0.157276i | ||||
\(137\) | 6.14700 | 0.525174 | 0.262587 | − | 0.964908i | \(-0.415424\pi\) | ||||
0.262587 | + | 0.964908i | \(0.415424\pi\) | |||||||
\(138\) | −3.75926 | + | 0.608345i | −0.320010 | + | 0.0517858i | ||||
\(139\) | 0.438687 | + | 0.759829i | 0.0372090 | + | 0.0644478i | 0.884030 | − | 0.467430i | \(-0.154820\pi\) |
−0.846821 | + | 0.531878i | \(0.821487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.78129 | − | 1.58286i | 0.823733 | − | 0.133301i | ||||
\(142\) | −10.5368 | − | 18.2504i | −0.884233 | − | 1.53154i | ||||
\(143\) | −3.41161 | − | 5.90908i | −0.285293 | − | 0.494142i | ||||
\(144\) | 3.01994 | − | 14.6918i | 0.251661 | − | 1.22431i | ||||
\(145\) | −10.8974 | + | 18.8748i | −0.904977 | + | 1.56747i | ||||
\(146\) | −4.58824 | + | 7.94706i | −0.379725 | + | 0.657703i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.75470 | − | 3.03923i | −0.144236 | − | 0.249823i | ||||
\(149\) | 5.77553 | 0.473150 | 0.236575 | − | 0.971613i | \(-0.423975\pi\) | ||||
0.236575 | + | 0.971613i | \(0.423975\pi\) | |||||||
\(150\) | 21.6581 | − | 3.50484i | 1.76838 | − | 0.286169i | ||||
\(151\) | −2.02643 | −0.164908 | −0.0824541 | − | 0.996595i | \(-0.526276\pi\) | ||||
−0.0824541 | + | 0.996595i | \(0.526276\pi\) | |||||||
\(152\) | 1.93973 | − | 3.35972i | 0.157333 | − | 0.272509i | ||||
\(153\) | −0.727226 | + | 3.53790i | −0.0587927 | + | 0.286022i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.330866 | − | 0.573077i | 0.0265758 | − | 0.0460307i | ||||
\(156\) | −0.676319 | + | 1.77969i | −0.0541488 | + | 0.142490i | ||||
\(157\) | 1.52378 | − | 2.63927i | 0.121611 | − | 0.210636i | −0.798792 | − | 0.601607i | \(-0.794527\pi\) |
0.920403 | + | 0.390971i | \(0.127861\pi\) | |||||||
\(158\) | 7.95718 | − | 13.7822i | 0.633039 | − | 1.09646i | ||||
\(159\) | 14.2568 | − | 2.30712i | 1.13064 | − | 0.182967i | ||||
\(160\) | −8.98141 | + | 15.5563i | −0.710043 | + | 1.22983i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.4480 | + | 9.30178i | −0.978008 | + | 0.730817i | ||||
\(163\) | 2.69445 | − | 4.66693i | 0.211046 | − | 0.365542i | −0.740996 | − | 0.671509i | \(-0.765646\pi\) |
0.952042 | + | 0.305967i | \(0.0989797\pi\) | |||||||
\(164\) | −3.30306 | −0.257925 | ||||||||
\(165\) | −13.1623 | + | 34.6358i | −1.02468 | + | 2.69639i | ||||
\(166\) | 2.15809 | 0.167500 | ||||||||
\(167\) | −8.30480 | − | 14.3843i | −0.642645 | − | 1.11309i | −0.984840 | − | 0.173464i | \(-0.944504\pi\) |
0.342196 | − | 0.939629i | \(-0.388829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.87249 | − | 10.1714i | 0.451730 | − | 0.782419i | ||||
\(170\) | 3.65063 | − | 6.32308i | 0.279991 | − | 0.484958i | ||||
\(171\) | −6.27844 | + | 2.08667i | −0.480125 | + | 0.159572i | ||||
\(172\) | −1.86696 | − | 3.23366i | −0.142354 | − | 0.246564i | ||||
\(173\) | 8.82516 | + | 15.2856i | 0.670965 | + | 1.16214i | 0.977631 | + | 0.210328i | \(0.0674531\pi\) |
−0.306666 | + | 0.951817i | \(0.599214\pi\) | |||||||
\(174\) | −6.59216 | + | 17.3469i | −0.499750 | + | 1.31507i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −15.2255 | − | 26.3714i | −1.14767 | − | 1.98782i | ||||
\(177\) | −12.3337 | − | 15.1268i | −0.927057 | − | 1.13700i | ||||
\(178\) | −9.56769 | −0.717128 | ||||||||
\(179\) | −1.31422 | − | 2.27630i | −0.0982294 | − | 0.170138i | 0.812722 | − | 0.582651i | \(-0.197985\pi\) |
−0.910952 | + | 0.412513i | \(0.864651\pi\) | |||||||
\(180\) | 9.81100 | − | 3.26073i | 0.731269 | − | 0.243041i | ||||
\(181\) | 3.97391 | 0.295378 | 0.147689 | − | 0.989034i | \(-0.452816\pi\) | ||||
0.147689 | + | 0.989034i | \(0.452816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.5214 | + | 3.32089i | −1.51699 | + | 0.245487i | ||||
\(184\) | −2.24002 | −0.165136 | ||||||||
\(185\) | −6.28125 | + | 10.8794i | −0.461806 | + | 0.799872i | ||||
\(186\) | 0.200151 | − | 0.526687i | 0.0146758 | − | 0.0386186i | ||||
\(187\) | 3.66643 | + | 6.35045i | 0.268116 | + | 0.464391i | ||||
\(188\) | −5.61306 | −0.409374 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.3743 | 0.970270 | ||||||||
\(191\) | 9.10295 | + | 15.7668i | 0.658666 | + | 1.14084i | 0.980961 | + | 0.194204i | \(0.0622125\pi\) |
−0.322295 | + | 0.946639i | \(0.604454\pi\) | |||||||
\(192\) | 0.719254 | − | 1.89268i | 0.0519077 | − | 0.136592i | ||||
\(193\) | 0.101193 | − | 0.175271i | 0.00728401 | − | 0.0126163i | −0.862360 | − | 0.506295i | \(-0.831015\pi\) |
0.869644 | + | 0.493679i | \(0.164348\pi\) | |||||||
\(194\) | 28.4641 | 2.04360 | ||||||||
\(195\) | 6.72770 | − | 1.08871i | 0.481780 | − | 0.0779644i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.63136 | −0.116229 | −0.0581147 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581147 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(198\) | −6.35208 | + | 30.9024i | −0.451423 | + | 2.19614i | ||||
\(199\) | −3.14605 | − | 5.44912i | −0.223018 | − | 0.386278i | 0.732705 | − | 0.680546i | \(-0.238257\pi\) |
−0.955723 | + | 0.294268i | \(0.904924\pi\) | |||||||
\(200\) | 12.9053 | 0.912544 | ||||||||
\(201\) | −8.66101 | − | 10.6224i | −0.610901 | − | 0.749246i | ||||
\(202\) | −11.1918 | − | 19.3847i | −0.787449 | − | 1.36390i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.726835 | − | 1.91263i | 0.0508886 | − | 0.133911i | ||||
\(205\) | 5.91192 | + | 10.2397i | 0.412906 | + | 0.715174i | ||||
\(206\) | 2.33249 | + | 4.04000i | 0.162512 | + | 0.281480i | ||||
\(207\) | 2.85603 | + | 2.53708i | 0.198508 | + | 0.176340i | ||||
\(208\) | −2.80050 | + | 4.85061i | −0.194180 | + | 0.336329i | ||||
\(209\) | −6.71607 | + | 11.6326i | −0.464560 | + | 0.804642i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.14368 | + | 14.1053i | 0.560634 | + | 0.971046i | 0.997441 | + | 0.0714912i | \(0.0227758\pi\) |
−0.436807 | + | 0.899555i | \(0.643891\pi\) | |||||||
\(212\) | −8.18138 | −0.561899 | ||||||||
\(213\) | −7.50967 | + | 19.7613i | −0.514554 | + | 1.35402i | ||||
\(214\) | 0.308166 | 0.0210658 | ||||||||
\(215\) | −6.68308 | + | 11.5754i | −0.455782 | + | 0.789438i | ||||
\(216\) | −8.10210 | + | 4.23148i | −0.551278 | + | 0.287916i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.07927 | − | 13.9937i | 0.547197 | − | 0.947773i | ||||
\(219\) | 9.08717 | − | 1.47054i | 0.614054 | − | 0.0993696i | ||||
\(220\) | 10.4949 | − | 18.1776i | 0.707563 | − | 1.22554i | ||||
\(221\) | 0.674383 | − | 1.16807i | 0.0453639 | − | 0.0785726i | ||||
\(222\) | −3.79972 | + | 9.99876i | −0.255021 | + | 0.671073i | ||||
\(223\) | −9.98472 | + | 17.2940i | −0.668626 | + | 1.15809i | 0.309662 | + | 0.950847i | \(0.399784\pi\) |
−0.978288 | + | 0.207248i | \(0.933549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.4543 | − | 14.6168i | −1.09695 | − | 0.974454i | ||||
\(226\) | −7.26936 | + | 12.5909i | −0.483551 | + | 0.837534i | ||||
\(227\) | 3.61283 | 0.239792 | 0.119896 | − | 0.992786i | \(-0.461744\pi\) | ||||
0.119896 | + | 0.992786i | \(0.461744\pi\) | |||||||
\(228\) | 3.69981 | − | 0.598725i | 0.245026 | − | 0.0396515i | ||||
\(229\) | 13.7147 | 0.906290 | 0.453145 | − | 0.891437i | \(-0.350302\pi\) | ||||
0.453145 | + | 0.891437i | \(0.350302\pi\) | |||||||
\(230\) | −3.86117 | − | 6.68774i | −0.254598 | − | 0.440976i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.45781 | + | 9.45321i | −0.358323 | + | 0.620634i | ||||
\(233\) | 12.6271 | − | 21.8707i | 0.827227 | − | 1.43280i | −0.0729776 | − | 0.997334i | \(-0.523250\pi\) |
0.900205 | − | 0.435466i | \(-0.143417\pi\) | |||||||
\(234\) | 5.50669 | − | 1.83017i | 0.359983 | − | 0.119642i | ||||
\(235\) | 10.0464 | + | 17.4009i | 0.655357 | + | 1.13511i | ||||
\(236\) | 5.52825 | + | 9.57521i | 0.359859 | + | 0.623293i | ||||
\(237\) | −15.7595 | + | 2.55029i | −1.02369 | + | 0.165659i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.49495 | − | 7.78549i | −0.290754 | − | 0.503601i | 0.683234 | − | 0.730200i | \(-0.260573\pi\) |
−0.973988 | + | 0.226598i | \(0.927240\pi\) | |||||||
\(240\) | 30.0248 | − | 4.85877i | 1.93809 | − | 0.313633i | ||||
\(241\) | 9.25724 | 0.596311 | 0.298156 | − | 0.954517i | \(-0.403629\pi\) | ||||
0.298156 | + | 0.954517i | \(0.403629\pi\) | |||||||
\(242\) | 22.5287 | + | 39.0209i | 1.44820 | + | 2.50836i | ||||
\(243\) | 15.1229 | + | 3.78144i | 0.970132 | + | 0.242579i | ||||
\(244\) | 11.7763 | 0.753903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.36188 | + | 7.80259i | 0.405619 | + | 0.497475i | ||||
\(247\) | 2.47063 | 0.157203 | ||||||||
\(248\) | 0.165710 | − | 0.287019i | 0.0105226 | − | 0.0182257i | ||||
\(249\) | −1.36805 | − | 1.67786i | −0.0866965 | − | 0.106330i | ||||
\(250\) | 7.08422 | + | 12.2702i | 0.448045 | + | 0.776037i | ||||
\(251\) | 20.6517 | 1.30353 | 0.651763 | − | 0.758422i | \(-0.274030\pi\) | ||||
0.651763 | + | 0.758422i | \(0.274030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.75576 | 0.487600 | ||||||||
\(254\) | −8.56777 | − | 14.8398i | −0.537590 | − | 0.931133i | ||||
\(255\) | −7.23021 | + | 1.17003i | −0.452773 | + | 0.0732703i | ||||
\(256\) | −9.40380 | + | 16.2879i | −0.587738 | + | 1.01799i | ||||
\(257\) | −2.44579 | −0.152564 | −0.0762819 | − | 0.997086i | \(-0.524305\pi\) | ||||
−0.0762819 | + | 0.997086i | \(0.524305\pi\) | |||||||
\(258\) | −4.04280 | + | 10.6384i | −0.251694 | + | 0.662318i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.86073 | −0.239432 | ||||||||
\(261\) | 17.6656 | − | 5.87125i | 1.09347 | − | 0.363421i | ||||
\(262\) | −13.1626 | − | 22.7982i | −0.813186 | − | 1.40848i | ||||
\(263\) | −24.5628 | −1.51460 | −0.757302 | − | 0.653065i | \(-0.773483\pi\) | ||||
−0.757302 | + | 0.653065i | \(0.773483\pi\) | |||||||
\(264\) | −6.59216 | + | 17.3469i | −0.405719 | + | 1.06763i | ||||
\(265\) | 14.6433 | + | 25.3629i | 0.899531 | + | 1.55803i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.06510 | + | 7.43861i | 0.371178 | + | 0.455236i | ||||
\(268\) | 3.88207 | + | 6.72395i | 0.237135 | + | 0.410730i | ||||
\(269\) | 14.7851 | + | 25.6086i | 0.901466 | + | 1.56139i | 0.825592 | + | 0.564268i | \(0.190842\pi\) |
0.0758746 | + | 0.997117i | \(0.475825\pi\) | |||||||
\(270\) | −26.5992 | − | 16.8955i | −1.61877 | − | 1.02823i | ||||
\(271\) | 12.3958 | − | 21.4701i | 0.752989 | − | 1.30421i | −0.193380 | − | 0.981124i | \(-0.561945\pi\) |
0.946368 | − | 0.323090i | \(-0.104722\pi\) | |||||||
\(272\) | 3.00968 | − | 5.21291i | 0.182488 | − | 0.316079i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.30674 | + | 9.19154i | 0.320592 | + | 0.555281i | ||||
\(275\) | −44.6830 | −2.69448 | ||||||||
\(276\) | −1.36753 | − | 1.67722i | −0.0823157 | − | 0.100957i | ||||
\(277\) | 1.87850 | 0.112868 | 0.0564340 | − | 0.998406i | \(-0.482027\pi\) | ||||
0.0564340 | + | 0.998406i | \(0.482027\pi\) | |||||||
\(278\) | −0.757442 | + | 1.31193i | −0.0454284 | + | 0.0786842i | ||||
\(279\) | −0.536364 | + | 0.178263i | −0.0321113 | + | 0.0106723i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.03965 | − | 10.4610i | 0.360295 | − | 0.624049i | −0.627714 | − | 0.778444i | \(-0.716009\pi\) |
0.988009 | + | 0.154395i | \(0.0493427\pi\) | |||||||
\(282\) | 10.8111 | + | 13.2594i | 0.643790 | + | 0.789583i | ||||
\(283\) | 13.9859 | − | 24.2244i | 0.831378 | − | 1.43999i | −0.0655680 | − | 0.997848i | \(-0.520886\pi\) |
0.896946 | − | 0.442140i | \(-0.145781\pi\) | |||||||
\(284\) | 5.98779 | − | 10.3712i | 0.355310 | − | 0.615415i | ||||
\(285\) | −8.47814 | − | 10.3981i | −0.502202 | − | 0.615931i | ||||
\(286\) | 5.89052 | − | 10.2027i | 0.348314 | − | 0.603297i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 14.5597 | − | 4.83897i | 0.857937 | − | 0.285139i | ||||
\(289\) | 7.77524 | − | 13.4671i | 0.457367 | − | 0.792183i | ||||
\(290\) | −37.6310 | −2.20977 | ||||||||
\(291\) | −18.0438 | − | 22.1300i | −1.05775 | − | 1.29729i | ||||
\(292\) | −5.21473 | −0.305169 | ||||||||
\(293\) | −4.41163 | − | 7.64117i | −0.257730 | − | 0.446402i | 0.707903 | − | 0.706309i | \(-0.249641\pi\) |
−0.965634 | + | 0.259908i | \(0.916308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.7893 | − | 34.2761i | 1.15218 | − | 1.99563i | ||||
\(296\) | −3.14589 | + | 5.44883i | −0.182851 | + | 0.316707i | ||||
\(297\) | 28.0524 | − | 14.6509i | 1.62777 | − | 0.850134i | ||||
\(298\) | 4.98604 | + | 8.63608i | 0.288834 | + | 0.500275i | ||||
\(299\) | −0.713276 | − | 1.23543i | −0.0412498 | − | 0.0714467i | ||||
\(300\) | 7.87871 | + | 9.66293i | 0.454878 | + | 0.557889i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.74942 | − | 3.03009i | −0.100668 | − | 0.174362i | ||||
\(303\) | −7.97643 | + | 20.9895i | −0.458234 | + | 1.20582i | ||||
\(304\) | 11.0261 | 0.632389 | ||||||||
\(305\) | −21.0777 | − | 36.5076i | −1.20691 | − | 2.09042i | ||||
\(306\) | −5.91800 | + | 1.96687i | −0.338309 | + | 0.112439i | ||||
\(307\) | 1.05532 | 0.0602304 | 0.0301152 | − | 0.999546i | \(-0.490413\pi\) | ||||
0.0301152 | + | 0.999546i | \(0.490413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.66238 | − | 4.37446i | 0.0945696 | − | 0.248855i | ||||
\(310\) | 1.14255 | 0.0648927 | ||||||||
\(311\) | −1.53608 | + | 2.66056i | −0.0871029 | + | 0.150867i | −0.906285 | − | 0.422666i | \(-0.861094\pi\) |
0.819182 | + | 0.573533i | \(0.194428\pi\) | |||||||
\(312\) | 3.36948 | − | 0.545269i | 0.190759 | − | 0.0308698i | ||||
\(313\) | −14.0810 | − | 24.3891i | −0.795907 | − | 1.37855i | −0.922262 | − | 0.386566i | \(-0.873661\pi\) |
0.126355 | − | 0.991985i | \(-0.459672\pi\) | |||||||
\(314\) | 5.26196 | 0.296949 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.04368 | 0.508747 | ||||||||
\(317\) | −6.42324 | − | 11.1254i | −0.360765 | − | 0.624863i | 0.627322 | − | 0.778760i | \(-0.284151\pi\) |
−0.988087 | + | 0.153897i | \(0.950818\pi\) | |||||||
\(318\) | 15.7578 | + | 19.3263i | 0.883654 | + | 1.08377i | ||||
\(319\) | 18.8969 | − | 32.7305i | 1.05803 | − | 1.83255i | ||||
\(320\) | 4.10582 | 0.229523 | ||||||||
\(321\) | −0.195351 | − | 0.239591i | −0.0109034 | − | 0.0133726i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.65517 | −0.147738 | ||||||||
\(324\) | −8.11468 | − | 3.48317i | −0.450816 | − | 0.193509i | ||||
\(325\) | 4.10937 | + | 7.11763i | 0.227947 | + | 0.394815i | ||||
\(326\) | 9.30454 | 0.515331 | ||||||||
\(327\) | −16.0013 | + | 2.58942i | −0.884873 | + | 0.143195i | ||||
\(328\) | 2.96091 | + | 5.12845i | 0.163489 | + | 0.283171i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −63.1535 | + | 10.2199i | −3.47649 | + | 0.562585i | ||||
\(331\) | 10.7780 | + | 18.6681i | 0.592413 | + | 1.02609i | 0.993906 | + | 0.110228i | \(0.0351581\pi\) |
−0.401493 | + | 0.915862i | \(0.631509\pi\) | |||||||
\(332\) | 0.613191 | + | 1.06208i | 0.0336532 | + | 0.0582891i | ||||
\(333\) | 10.1825 | − | 3.38419i | 0.557995 | − | 0.185452i | ||||
\(334\) | 14.3392 | − | 24.8361i | 0.784604 | − | 1.35897i | ||||
\(335\) | 13.8965 | − | 24.0695i | 0.759248 | − | 1.31506i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.30340 | + | 10.9178i | 0.343368 | + | 0.594731i | 0.985056 | − | 0.172235i | \(-0.0550989\pi\) |
−0.641688 | + | 0.766966i | \(0.721766\pi\) | |||||||
\(338\) | 20.2790 | 1.10303 | ||||||||
\(339\) | 14.3972 | − | 2.32984i | 0.781950 | − | 0.126540i | ||||
\(340\) | 4.14910 | 0.225017 | ||||||||
\(341\) | −0.573750 | + | 0.993764i | −0.0310703 | + | 0.0538153i | ||||
\(342\) | −8.54039 | − | 7.58665i | −0.461811 | − | 0.410239i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.34714 | + | 5.79741i | −0.180466 | + | 0.312575i | ||||
\(345\) | −2.75188 | + | 7.24141i | −0.148156 | + | 0.389864i | ||||
\(346\) | −15.2376 | + | 26.3923i | −0.819179 | + | 1.41886i | ||||
\(347\) | −11.5683 | + | 20.0369i | −0.621020 | + | 1.07564i | 0.368276 | + | 0.929716i | \(0.379948\pi\) |
−0.989296 | + | 0.145922i | \(0.953385\pi\) | |||||||
\(348\) | −10.4101 | + | 1.68463i | −0.558042 | + | 0.0903055i | ||||
\(349\) | 8.24346 | − | 14.2781i | 0.441262 | − | 0.764289i | −0.556521 | − | 0.830833i | \(-0.687864\pi\) |
0.997783 | + | 0.0665448i | \(0.0211975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.91368 | − | 3.12112i | −0.262273 | − | 0.166593i | ||||
\(352\) | 15.5745 | − | 26.9759i | 0.830124 | − | 1.43782i | ||||
\(353\) | −24.4875 | −1.30334 | −0.651669 | − | 0.758503i | \(-0.725931\pi\) | ||||
−0.651669 | + | 0.758503i | \(0.725931\pi\) | |||||||
\(354\) | 11.9712 | − | 31.5015i | 0.636260 | − | 1.67428i | ||||
\(355\) | −42.8686 | −2.27523 | ||||||||
\(356\) | −2.71852 | − | 4.70862i | −0.144081 | − | 0.249556i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.26915 | − | 3.93028i | 0.119928 | − | 0.207722i | ||||
\(359\) | −10.2389 | + | 17.7342i | −0.540386 | + | 0.935977i | 0.458495 | + | 0.888697i | \(0.348389\pi\) |
−0.998882 | + | 0.0472797i | \(0.984945\pi\) | |||||||
\(360\) | −13.8575 | − | 12.3100i | −0.730353 | − | 0.648792i | ||||
\(361\) | 7.06816 | + | 12.2424i | 0.372009 | + | 0.644338i | ||||
\(362\) | 3.43070 | + | 5.94214i | 0.180313 | + | 0.312312i | ||||
\(363\) | 16.0564 | − | 42.2514i | 0.842740 | − | 2.21762i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.33349 | + | 16.1661i | 0.488537 | + | 0.846172i | ||||
\(366\) | −22.6819 | − | 27.8185i | −1.18560 | − | 1.45410i | ||||
\(367\) | 22.2539 | 1.16164 | 0.580821 | − | 0.814031i | \(-0.302732\pi\) | ||||
0.580821 | + | 0.814031i | \(0.302732\pi\) | |||||||
\(368\) | −3.18325 | − | 5.51355i | −0.165938 | − | 0.287414i | ||||
\(369\) | 2.03341 | − | 9.89237i | 0.105855 | − | 0.514976i | ||||
\(370\) | −21.6905 | −1.12764 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.316073 | − | 0.0511487i | 0.0163876 | − | 0.00265194i | ||||
\(373\) | −32.5369 | −1.68469 | −0.842347 | − | 0.538935i | \(-0.818827\pi\) | ||||
−0.842347 | + | 0.538935i | \(0.818827\pi\) | |||||||
\(374\) | −6.33050 | + | 10.9647i | −0.327342 | + | 0.566974i | ||||
\(375\) | 5.04896 | − | 13.2861i | 0.260727 | − | 0.686090i | ||||
\(376\) | 5.03163 | + | 8.71504i | 0.259487 | + | 0.449444i | ||||
\(377\) | −6.95160 | −0.358026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54440 | 0.0793306 | 0.0396653 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396653 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(380\) | 3.80011 | + | 6.58198i | 0.194941 | + | 0.337648i | ||||
\(381\) | −6.10630 | + | 16.0684i | −0.312835 | + | 0.823209i | ||||
\(382\) | −15.7173 | + | 27.2231i | −0.804165 | + | 1.39285i | ||||
\(383\) | 31.6294 | 1.61619 | 0.808093 | − | 0.589055i | \(-0.200500\pi\) | ||||
0.808093 | + | 0.589055i | \(0.200500\pi\) | |||||||
\(384\) | 20.9398 | − | 3.38859i | 1.06858 | − | 0.172923i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.349441 | 0.0177861 | ||||||||
\(387\) | 10.8339 | − | 3.60068i | 0.550716 | − | 0.183033i | ||||
\(388\) | 8.08767 | + | 14.0083i | 0.410589 | + | 0.711162i | ||||
\(389\) | −5.24626 | −0.265996 | −0.132998 | − | 0.991116i | \(-0.542460\pi\) | ||||
−0.132998 | + | 0.991116i | \(0.542460\pi\) | |||||||
\(390\) | 7.43600 | + | 9.11996i | 0.376536 | + | 0.461807i | ||||
\(391\) | 0.766552 | + | 1.32771i | 0.0387662 | + | 0.0671451i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.38103 | + | 24.6857i | −0.473210 | + | 1.24523i | ||||
\(394\) | −1.40836 | − | 2.43935i | −0.0709521 | − | 0.122893i | ||||
\(395\) | −16.1867 | − | 28.0362i | −0.814440 | − | 1.41065i | ||||
\(396\) | −17.0131 | + | 5.65438i | −0.854940 | + | 0.284143i | ||||
\(397\) | −0.0138175 | + | 0.0239325i | −0.000693478 | + | 0.00120114i | −0.866372 | − | 0.499399i | \(-0.833554\pi\) |
0.865678 | + | 0.500600i | \(0.166887\pi\) | |||||||
\(398\) | 5.43201 | − | 9.40851i | 0.272282 | − | 0.471606i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.3395 | + | 31.7650i | 0.916977 | + | 1.58825i | ||||
\(401\) | 12.1377 | 0.606127 | 0.303064 | − | 0.952970i | \(-0.401991\pi\) | ||||
0.303064 | + | 0.952970i | \(0.401991\pi\) | |||||||
\(402\) | 8.40644 | − | 22.1211i | 0.419275 | − | 1.10330i | ||||
\(403\) | 0.211065 | 0.0105139 | ||||||||
\(404\) | 6.35996 | − | 11.0158i | 0.316420 | − | 0.548055i | ||||
\(405\) | 3.72583 | + | 31.3905i | 0.185138 | + | 1.55980i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.8922 | − | 18.8659i | 0.539907 | − | 0.935146i | ||||
\(408\) | −3.62116 | + | 0.585997i | −0.179274 | + | 0.0290112i | ||||
\(409\) | −15.6726 | + | 27.1458i | −0.774963 | + | 1.34227i | 0.159853 | + | 0.987141i | \(0.448898\pi\) |
−0.934816 | + | 0.355134i | \(0.884435\pi\) | |||||||
\(410\) | −10.2076 | + | 17.6800i | −0.504116 | + | 0.873155i | ||||
\(411\) | 3.78214 | − | 9.95250i | 0.186559 | − | 0.490921i | ||||
\(412\) | −1.32549 | + | 2.29582i | −0.0653022 | + | 0.113107i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.32805 | + | 6.46086i | −0.0652701 | + | 0.317534i | ||||
\(415\) | 2.19502 | − | 3.80189i | 0.107749 | − | 0.186627i | ||||
\(416\) | −5.72938 | −0.280906 | ||||||||
\(417\) | 1.50014 | − | 0.242761i | 0.0734623 | − | 0.0118881i | ||||
\(418\) | −23.1921 | −1.13436 | ||||||||
\(419\) | 7.44319 | + | 12.8920i | 0.363623 | + | 0.629814i | 0.988554 | − | 0.150866i | \(-0.0482061\pi\) |
−0.624931 | + | 0.780680i | \(0.714873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.54213 | + | 7.86721i | −0.221370 | + | 0.383424i | −0.955224 | − | 0.295883i | \(-0.904386\pi\) |
0.733854 | + | 0.679307i | \(0.237720\pi\) | |||||||
\(422\) | −14.0610 | + | 24.3543i | −0.684477 | + | 1.18555i | ||||
\(423\) | 3.45547 | − | 16.8106i | 0.168011 | − | 0.817360i | ||||
\(424\) | 7.33392 | + | 12.7027i | 0.356166 | + | 0.616898i | ||||
\(425\) | −4.41631 | − | 7.64927i | −0.214223 | − | 0.371044i | ||||
\(426\) | −36.0320 | + | 5.83089i | −1.74575 | + | 0.282508i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.0875611 | + | 0.151660i | 0.00423243 | + | 0.00733078i | ||||
\(429\) | −11.6664 | + | 1.88792i | −0.563258 | + | 0.0911496i | ||||
\(430\) | −23.0781 | −1.11293 | ||||||||
\(431\) | 8.31776 | + | 14.4068i | 0.400652 | + | 0.693950i | 0.993805 | − | 0.111140i | \(-0.0354502\pi\) |
−0.593152 | + | 0.805090i | \(0.702117\pi\) | |||||||
\(432\) | −21.9291 | − | 13.9291i | −1.05506 | − | 0.670165i | ||||
\(433\) | 19.7423 | 0.948756 | 0.474378 | − | 0.880321i | \(-0.342673\pi\) | ||||
0.474378 | + | 0.880321i | \(0.342673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.8549 | + | 29.2571i | 1.14375 | + | 1.40277i | ||||
\(436\) | 9.18244 | 0.439759 | ||||||||
\(437\) | −1.40415 | + | 2.43206i | −0.0671696 | + | 0.116341i | ||||
\(438\) | 10.0439 | + | 12.3184i | 0.479915 | + | 0.588597i | ||||
\(439\) | 3.36757 | + | 5.83280i | 0.160725 | + | 0.278384i | 0.935129 | − | 0.354307i | \(-0.115283\pi\) |
−0.774404 | + | 0.632692i | \(0.781950\pi\) | |||||||
\(440\) | −37.6310 | −1.79399 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.32879 | 0.110769 | ||||||||
\(443\) | −14.3202 | − | 24.8033i | −0.680372 | − | 1.17844i | −0.974867 | − | 0.222786i | \(-0.928485\pi\) |
0.294496 | − | 0.955653i | \(-0.404848\pi\) | |||||||
\(444\) | −6.00041 | + | 0.971019i | −0.284767 | + | 0.0460825i | ||||
\(445\) | −9.73141 | + | 16.8553i | −0.461313 | + | 0.799017i | ||||
\(446\) | −34.4794 | −1.63265 | ||||||||
\(447\) | 3.55358 | − | 9.35105i | 0.168079 | − | 0.442290i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.66872 | −0.314716 | −0.157358 | − | 0.987542i | \(-0.550298\pi\) | ||||
−0.157358 | + | 0.987542i | \(0.550298\pi\) | |||||||
\(450\) | 7.65124 | − | 37.2227i | 0.360683 | − | 1.75470i | ||||
\(451\) | −10.2518 | − | 17.7566i | −0.482736 | − | 0.836124i | ||||
\(452\) | −8.26194 | −0.388609 | ||||||||
\(453\) | −1.24683 | + | 3.28095i | −0.0585810 | + | 0.154153i | ||||
\(454\) | 3.11898 | + | 5.40223i | 0.146381 | + | 0.253539i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.24617 | − | 5.20776i | −0.198845 | − | 0.243876i | ||||
\(457\) | 14.3287 | + | 24.8180i | 0.670266 | + | 1.16093i | 0.977829 | + | 0.209407i | \(0.0671533\pi\) |
−0.307563 | + | 0.951528i | \(0.599513\pi\) | |||||||
\(458\) | 11.8399 | + | 20.5074i | 0.553244 | + | 0.958246i | ||||
\(459\) | 5.28070 | + | 3.35425i | 0.246482 | + | 0.156563i | ||||
\(460\) | 2.19419 | − | 3.80045i | 0.102305 | − | 0.177197i | ||||
\(461\) | −10.0087 | + | 17.3355i | −0.466150 | + | 0.807395i | −0.999253 | − | 0.0386554i | \(-0.987693\pi\) |
0.533103 | + | 0.846050i | \(0.321026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.95789 | − | 8.58731i | −0.230413 | − | 0.399086i | 0.727517 | − | 0.686090i | \(-0.240674\pi\) |
−0.957930 | + | 0.287003i | \(0.907341\pi\) | |||||||
\(464\) | −31.0240 | −1.44025 | ||||||||
\(465\) | −0.724283 | − | 0.888304i | −0.0335878 | − | 0.0411941i | ||||
\(466\) | 43.6041 | 2.01992 | ||||||||
\(467\) | 8.04035 | − | 13.9263i | 0.372063 | − | 0.644432i | −0.617820 | − | 0.786320i | \(-0.711984\pi\) |
0.989883 | + | 0.141888i | \(0.0453172\pi\) | |||||||
\(468\) | 2.46535 | + | 2.19003i | 0.113961 | + | 0.101234i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17.3463 | + | 30.0446i | −0.800124 | + | 1.38586i | ||||
\(471\) | −3.33563 | − | 4.09102i | −0.153698 | − | 0.188504i | ||||
\(472\) | 9.91123 | − | 17.1667i | 0.456201 | − | 0.790164i | ||||
\(473\) | 11.5890 | − | 20.0728i | 0.532863 | − | 0.922946i | ||||
\(474\) | −17.4187 | − | 21.3633i | −0.800066 | − | 0.981249i | ||||
\(475\) | 8.08967 | − | 14.0117i | 0.371180 | − | 0.642902i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.03657 | − | 24.5025i | 0.230609 | − | 1.12189i | ||||
\(478\) | 7.76103 | − | 13.4425i | 0.354981 | − | 0.614846i | ||||
\(479\) | 8.20255 | 0.374784 | 0.187392 | − | 0.982285i | \(-0.439997\pi\) | ||||
0.187392 | + | 0.982285i | \(0.439997\pi\) | |||||||
\(480\) | 19.6608 | + | 24.1131i | 0.897387 | + | 1.10061i | ||||
\(481\) | −4.00690 | −0.182699 | ||||||||
\(482\) | 7.99183 | + | 13.8423i | 0.364018 | + | 0.630497i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.8024 | + | 22.1745i | −0.581929 | + | 1.00793i | ||||
\(485\) | 28.9512 | − | 50.1449i | 1.31460 | − | 2.27696i | ||||
\(486\) | 7.40130 | + | 25.8776i | 0.335730 | + | 1.17383i | ||||
\(487\) | −1.36840 | − | 2.37014i | −0.0620081 | − | 0.107401i | 0.833355 | − | 0.552738i | \(-0.186417\pi\) |
−0.895363 | + | 0.445337i | \(0.853084\pi\) | |||||||
\(488\) | −10.5565 | − | 18.2844i | −0.477871 | − | 0.827696i | ||||
\(489\) | −5.89829 | − | 7.23402i | −0.266730 | − | 0.327134i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.85482 | + | 17.0690i | 0.444742 | + | 0.770315i | 0.998034 | − | 0.0626719i | \(-0.0199622\pi\) |
−0.553293 | + | 0.832987i | \(0.686629\pi\) | |||||||
\(492\) | −2.03231 | + | 5.34792i | −0.0916237 | + | 0.241103i | ||||
\(493\) | 7.47084 | 0.336470 | ||||||||
\(494\) | 2.13291 | + | 3.69431i | 0.0959642 | + | 0.166215i | ||||
\(495\) | 47.9796 | + | 42.6216i | 2.15652 | + | 1.91570i | ||||
\(496\) | 0.941952 | 0.0422949 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.32784 | − | 3.49413i | 0.0595018 | − | 0.156576i | ||||
\(499\) | −33.0960 | −1.48158 | −0.740789 | − | 0.671737i | \(-0.765548\pi\) | ||||
−0.740789 | + | 0.671737i | \(0.765548\pi\) | |||||||
\(500\) | −4.02576 | + | 6.97283i | −0.180038 | + | 0.311834i | ||||
\(501\) | −28.3992 | + | 4.59572i | −1.26878 | + | 0.205322i | ||||
\(502\) | 17.8288 | + | 30.8803i | 0.795737 | + | 1.37826i | ||||
\(503\) | −12.1860 | −0.543346 | −0.271673 | − | 0.962390i | \(-0.587577\pi\) | ||||
−0.271673 | + | 0.962390i | \(0.587577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.5331 | −2.02619 | ||||||||
\(506\) | 6.69559 | + | 11.5971i | 0.297655 | + | 0.515554i | ||||
\(507\) | −12.8552 | − | 15.7664i | −0.570918 | − | 0.700208i | ||||
\(508\) | 4.86882 | − | 8.43305i | 0.216019 | − | 0.374156i | ||||
\(509\) | −13.6393 | −0.604551 | −0.302276 | − | 0.953221i | \(-0.597746\pi\) | ||||
−0.302276 | + | 0.953221i | \(0.597746\pi\) | |||||||
\(510\) | −7.99142 | − | 9.80116i | −0.353866 | − | 0.434002i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.97968 | −0.352656 | ||||||||
\(513\) | −0.484527 | + | 11.4492i | −0.0213924 | + | 0.505495i | ||||
\(514\) | −2.11146 | − | 3.65715i | −0.0931325 | − | 0.161310i | ||||
\(515\) | 9.48962 | 0.418163 | ||||||||
\(516\) | −6.38427 | + | 1.03314i | −0.281052 | + | 0.0454814i | ||||
\(517\) | −17.4214 | − | 30.1747i | −0.766190 | − | 1.32708i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.1787 | − | 4.88368i | 1.32470 | − | 0.214370i | ||||
\(520\) | 3.46082 | + | 5.99432i | 0.151767 | + | 0.262868i | ||||
\(521\) | −17.7745 | − | 30.7863i | −0.778714 | − | 1.34877i | −0.932683 | − | 0.360697i | \(-0.882539\pi\) |
0.153969 | − | 0.988076i | \(-0.450794\pi\) | |||||||
\(522\) | 24.0300 | + | 21.3465i | 1.05177 | + | 0.934311i | ||||
\(523\) | 13.3593 | − | 23.1391i | 0.584163 | − | 1.01180i | −0.410816 | − | 0.911718i | \(-0.634756\pi\) |
0.994979 | − | 0.100082i | \(-0.0319105\pi\) | |||||||
\(524\) | 7.47991 | − | 12.9556i | 0.326761 | − | 0.565967i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2052 | − | 36.7284i | −0.924589 | − | 1.60143i | ||||
\(527\) | −0.226830 | −0.00988086 | ||||||||
\(528\) | −52.0654 | + | 8.42552i | −2.26586 | + | 0.366674i | ||||
\(529\) | −21.3785 | −0.929499 | ||||||||
\(530\) | −25.2833 | + | 43.7919i | −1.09824 | + | 1.90220i | ||||
\(531\) | −32.0802 | + | 10.6620i | −1.39216 | + | 0.462692i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.88565 | + | 3.26604i | −0.0816766 | + | 0.141468i | ||||
\(534\) | −5.88683 | + | 15.4909i | −0.254748 | + | 0.670356i | ||||
\(535\) | 0.313440 | − | 0.542893i | 0.0135512 | − | 0.0234713i | ||||
\(536\) | 6.95990 | − | 12.0549i | 0.300622 | − | 0.520693i | ||||
\(537\) | −4.49413 | + | 0.727265i | −0.193936 | + | 0.0313838i | ||||
\(538\) | −25.5282 | + | 44.2161i | −1.10060 | + | 1.90629i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.757146 | − | 17.8911i | 0.0325824 | − | 0.769910i | ||||
\(541\) | −18.7927 | + | 32.5500i | −0.807963 | + | 1.39943i | 0.106309 | + | 0.994333i | \(0.466097\pi\) |
−0.914272 | + | 0.405100i | \(0.867237\pi\) | |||||||
\(542\) | 42.8053 | 1.83864 | ||||||||
\(543\) | 2.44508 | − | 6.43408i | 0.104928 | − | 0.276113i | ||||
\(544\) | 6.15733 | 0.263993 | ||||||||
\(545\) | −16.4350 | − | 28.4663i | −0.704000 | − | 1.21936i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.13381 | + | 15.8202i | −0.390533 | + | 0.676424i | −0.992520 | − | 0.122082i | \(-0.961043\pi\) |
0.601986 | + | 0.798506i | \(0.294376\pi\) | |||||||
\(548\) | −3.01567 | + | 5.22329i | −0.128823 | + | 0.223128i | ||||
\(549\) | −7.24968 | + | 35.2691i | −0.309409 | + | 1.50525i | ||||
\(550\) | −38.5750 | − | 66.8139i | −1.64485 | − | 2.84896i | ||||
\(551\) | 6.84243 | + | 11.8514i | 0.291498 | + | 0.504889i | ||||
\(552\) | −1.37824 | + | 3.62677i | −0.0586619 | + | 0.154366i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.62172 | + | 2.80890i | 0.0689002 | + | 0.119339i | ||||
\(555\) | 13.7500 | + | 16.8638i | 0.583653 | + | 0.715828i | ||||
\(556\) | −0.860866 | −0.0365089 | ||||||||
\(557\) | 1.94636 | + | 3.37119i | 0.0824698 | + | 0.142842i | 0.904310 | − | 0.426876i | \(-0.140386\pi\) |
−0.821840 | + | 0.569718i | \(0.807053\pi\) | |||||||
\(558\) | −0.729600 | − | 0.648123i | −0.0308864 | − | 0.0274372i | ||||
\(559\) | −4.26324 | −0.180316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.5378 | − | 2.02893i | 0.529346 | − | 0.0856617i | ||||
\(562\) | 20.8562 | 0.879767 | ||||||||
\(563\) | −1.66428 | + | 2.88261i | −0.0701409 | + | 0.121488i | −0.898963 | − | 0.438025i | \(-0.855678\pi\) |
0.828822 | + | 0.559512i | \(0.189012\pi\) | |||||||
\(564\) | −3.45362 | + | 9.08800i | −0.145424 | + | 0.382674i | ||||
\(565\) | 14.7875 | + | 25.6127i | 0.622115 | + | 1.07753i | ||||
\(566\) | 48.2965 | 2.03006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.4702 | −0.900870 | ||||||||
\(569\) | 18.3122 | + | 31.7177i | 0.767688 | + | 1.32967i | 0.938814 | + | 0.344425i | \(0.111926\pi\) |
−0.171126 | + | 0.985249i | \(0.554741\pi\) | |||||||
\(570\) | 8.22895 | − | 21.6540i | 0.344673 | − | 0.906987i | ||||
\(571\) | 11.2912 | − | 19.5569i | 0.472522 | − | 0.818432i | −0.526984 | − | 0.849875i | \(-0.676677\pi\) |
0.999506 | + | 0.0314435i | \(0.0100104\pi\) | |||||||
\(572\) | 6.69483 | 0.279925 | ||||||||
\(573\) | 31.1286 | − | 5.03740i | 1.30042 | − | 0.210441i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.34201 | −0.389589 | ||||||||
\(576\) | −2.62185 | − | 2.32906i | −0.109244 | − | 0.0970442i | ||||
\(577\) | −11.2725 | − | 19.5245i | −0.469279 | − | 0.812815i | 0.530104 | − | 0.847932i | \(-0.322153\pi\) |
−0.999383 | + | 0.0351177i | \(0.988819\pi\) | |||||||
\(578\) | 26.8496 | 1.11680 | ||||||||
\(579\) | −0.221516 | − | 0.271680i | −0.00920588 | − | 0.0112906i | ||||
\(580\) | −10.6923 | − | 18.5197i | −0.443975 | − | 0.768987i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.5135 | − | 46.0857i | 0.725957 | − | 1.91031i | ||||
\(583\) | −25.3927 | − | 43.9814i | −1.05166 | − | 1.82152i | ||||
\(584\) | 4.67457 | + | 8.09659i | 0.193435 | + | 0.335039i | ||||
\(585\) | 2.37672 | − | 11.5626i | 0.0982652 | − | 0.478053i | ||||
\(586\) | 7.61717 | − | 13.1933i | 0.314662 | − | 0.545011i | ||||
\(587\) | −12.1198 | + | 20.9921i | −0.500237 | + | 0.866436i | 0.499763 | + | 0.866162i | \(0.333421\pi\) |
−1.00000 | 0.000273884i | \(0.999913\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.207750 | − | 0.359834i | −0.00856020 | − | 0.0148267i | ||||
\(590\) | 68.3368 | 2.81338 | ||||||||
\(591\) | −1.00375 | + | 2.64130i | −0.0412886 | + | 0.108649i | ||||
\(592\) | −17.8822 | −0.734956 | ||||||||
\(593\) | 22.8663 | − | 39.6056i | 0.939007 | − | 1.62641i | 0.171680 | − | 0.985153i | \(-0.445081\pi\) |
0.767328 | − | 0.641255i | \(-0.221586\pi\) | |||||||
\(594\) | 46.1252 | + | 29.2983i | 1.89254 | + | 1.20212i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.83343 | + | 4.90764i | −0.116062 | + | 0.201025i | ||||
\(597\) | −10.7583 | + | 1.74097i | −0.440308 | + | 0.0712530i | ||||
\(598\) | 1.23155 | − | 2.13311i | 0.0503618 | − | 0.0872292i | ||||
\(599\) | 15.0834 | − | 26.1252i | 0.616290 | − | 1.06745i | −0.373866 | − | 0.927483i | \(-0.621968\pi\) |
0.990157 | − | 0.139963i | \(-0.0446985\pi\) | |||||||
\(600\) | 7.94042 | − | 20.8948i | 0.324166 | − | 0.853026i | ||||
\(601\) | 7.36933 | − | 12.7641i | 0.300601 | − | 0.520657i | −0.675671 | − | 0.737203i | \(-0.736146\pi\) |
0.976272 | + | 0.216547i | \(0.0694794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.5275 | + | 7.48712i | −0.917391 | + | 0.304899i | ||||
\(604\) | 0.994149 | − | 1.72192i | 0.0404513 | − | 0.0700638i | ||||
\(605\) | 91.6569 | 3.72638 | ||||||||
\(606\) | −38.2715 | + | 6.19331i | −1.55467 | + | 0.251586i | ||||
\(607\) | −6.07836 | −0.246713 | −0.123356 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123356 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(608\) | 5.63941 | + | 9.76774i | 0.228708 | + | 0.396134i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.3930 | − | 63.0345i | 1.47351 | − | 2.55219i | ||||
\(611\) | −3.20439 | + | 5.55016i | −0.129636 | + | 0.224535i | ||||
\(612\) | −2.64949 | − | 2.35361i | −0.107099 | − | 0.0951391i | ||||
\(613\) | −5.88668 | − | 10.1960i | −0.237761 | − | 0.411814i | 0.722311 | − | 0.691569i | \(-0.243080\pi\) |
−0.960071 | + | 0.279755i | \(0.909747\pi\) | |||||||
\(614\) | 0.911065 | + | 1.57801i | 0.0367676 | + | 0.0636833i | ||||
\(615\) | 20.2165 | − | 3.27154i | 0.815207 | − | 0.131921i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.0319 | − | 27.7680i | −0.645418 | − | 1.11790i | −0.984205 | − | 0.177034i | \(-0.943350\pi\) |
0.338786 | − | 0.940863i | \(-0.389984\pi\) | |||||||
\(618\) | 7.97623 | − | 1.29076i | 0.320851 | − | 0.0519219i | ||||
\(619\) | −12.5518 | −0.504498 | −0.252249 | − | 0.967662i | \(-0.581170\pi\) | ||||
−0.252249 | + | 0.967662i | \(0.581170\pi\) | |||||||
\(620\) | 0.324641 | + | 0.562294i | 0.0130379 | + | 0.0225823i | ||||
\(621\) | 5.86501 | − | 3.06312i | 0.235355 | − | 0.122919i | ||||
\(622\) | −5.30441 | −0.212688 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.13043 | + | 7.51873i | 0.245414 | + | 0.300990i | ||||
\(625\) | −7.85989 | −0.314396 | ||||||||
\(626\) | 24.3125 | − | 42.1104i | 0.971721 | − | 1.68307i | ||||
\(627\) | 14.7018 | + | 18.0312i | 0.587134 | + | 0.720096i | ||||
\(628\) | 1.49511 | + | 2.58961i | 0.0596614 | + | 0.103337i | ||||
\(629\) | 4.30619 | 0.171699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4642 | 1.33219 | 0.666095 | − | 0.745867i | \(-0.267964\pi\) | ||||
0.666095 | + | 0.745867i | \(0.267964\pi\) | |||||||
\(632\) | −8.10690 | − | 14.0416i | −0.322475 | − | 0.558543i | ||||
\(633\) | 27.8482 | − | 4.50656i | 1.10687 | − | 0.179120i | ||||
\(634\) | 11.0904 | − | 19.2092i | 0.440457 | − | 0.762894i | ||||
\(635\) | −34.8575 | −1.38328 | ||||||||
\(636\) | −5.03386 | + | 13.2463i | −0.199606 | + | 0.525251i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 65.2553 | 2.58348 | ||||||||
\(639\) | 27.3746 | + | 24.3176i | 1.08292 | + | 0.961988i | ||||
\(640\) | 21.5074 | + | 37.2519i | 0.850155 | + | 1.47251i | ||||
\(641\) | −18.9837 | −0.749809 | −0.374905 | − | 0.927063i | \(-0.622325\pi\) | ||||
−0.374905 | + | 0.927063i | \(0.622325\pi\) | |||||||
\(642\) | 0.189609 | − | 0.498947i | 0.00748329 | − | 0.0196918i | ||||
\(643\) | 4.81347 | + | 8.33718i | 0.189825 | + | 0.328786i | 0.945192 | − | 0.326516i | \(-0.105875\pi\) |
−0.755367 | + | 0.655302i | \(0.772541\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.6296 | + | 17.9426i | 0.576039 | + | 0.706490i | ||||
\(646\) | −2.29222 | − | 3.97025i | −0.0901864 | − | 0.156207i | ||||
\(647\) | 3.90607 | + | 6.76551i | 0.153564 | + | 0.265980i | 0.932535 | − | 0.361079i | \(-0.117592\pi\) |
−0.778972 | + | 0.627059i | \(0.784258\pi\) | |||||||
\(648\) | 1.86604 | + | 15.7215i | 0.0733048 | + | 0.617600i | ||||
\(649\) | −34.3163 | + | 59.4375i | −1.34703 | + | 2.33313i | ||||
\(650\) | −7.09528 | + | 12.2894i | −0.278300 | + | 0.482029i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.64376 | + | 4.57912i | 0.103537 | + | 0.179332i | ||||
\(653\) | 31.7429 | 1.24219 | 0.621097 | − | 0.783734i | \(-0.286687\pi\) | ||||
0.621097 | + | 0.783734i | \(0.286687\pi\) | |||||||
\(654\) | −17.6859 | − | 21.6911i | −0.691574 | − | 0.848189i | ||||
\(655\) | −53.5512 | −2.09242 | ||||||||
\(656\) | −8.41540 | + | 14.5759i | −0.328566 | + | 0.569093i | ||||
\(657\) | 3.21026 | − | 15.6177i | 0.125244 | − | 0.609303i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.10685 | − | 5.38122i | 0.121026 | − | 0.209623i | −0.799147 | − | 0.601136i | \(-0.794715\pi\) |
0.920172 | + | 0.391513i | \(0.128048\pi\) | |||||||
\(660\) | −22.9738 | − | 28.1764i | −0.894253 | − | 1.09677i | ||||
\(661\) | −13.7631 | + | 23.8384i | −0.535324 | + | 0.927208i | 0.463824 | + | 0.885927i | \(0.346477\pi\) |
−0.999148 | + | 0.0412802i | \(0.986856\pi\) | |||||||
\(662\) | −18.6094 | + | 32.2325i | −0.723276 | + | 1.25275i | ||||
\(663\) | −1.47626 | − | 1.81057i | −0.0573331 | − | 0.0703168i | ||||
\(664\) | 1.09935 | − | 1.90413i | 0.0426630 | − | 0.0738945i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.8509 | + | 12.3041i | 0.536712 | + | 0.476775i | ||||
\(667\) | 3.95084 | − | 6.84306i | 0.152977 | − | 0.264964i | ||||
\(668\) | 16.2971 | 0.630553 | ||||||||
\(669\) | 21.8570 | + | 26.8068i | 0.845042 | + | 1.03641i | ||||
\(670\) | 47.9878 | 1.85393 | ||||||||
\(671\) | 36.5505 | + | 63.3073i | 1.41102 | + | 2.44395i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.10894 | + | 14.0451i | −0.312577 | + | 0.541399i | −0.978919 | − | 0.204247i | \(-0.934526\pi\) |
0.666343 | + | 0.745646i | \(0.267859\pi\) | |||||||
\(674\) | −10.8835 | + | 18.8508i | −0.419217 | + | 0.726106i | ||||
\(675\) | −33.7899 | + | 17.6474i | −1.30057 | + | 0.679250i | ||||
\(676\) | 5.76199 | + | 9.98006i | 0.221615 | + | 0.383849i | ||||
\(677\) | 10.2545 | + | 17.7613i | 0.394112 | + | 0.682623i | 0.992987 | − | 0.118220i | \(-0.0377188\pi\) |
−0.598875 | + | 0.800842i | \(0.704385\pi\) | |||||||
\(678\) | 15.9130 | + | 19.5167i | 0.611135 | + | 0.749532i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.71932 | − | 6.44205i | −0.142629 | − | 0.247041i | ||||
\(681\) | 2.22291 | − | 5.84947i | 0.0851822 | − | 0.224152i | ||||
\(682\) | −1.98128 | −0.0758673 | ||||||||
\(683\) | 0.0561542 | + | 0.0972618i | 0.00214868 | + | 0.00372162i | 0.867098 | − | 0.498138i | \(-0.165983\pi\) |
−0.864949 | + | 0.501860i | \(0.832649\pi\) | |||||||
\(684\) | 1.30705 | − | 6.35869i | 0.0499762 | − | 0.243131i | ||||
\(685\) | 21.5902 | 0.824918 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.43839 | − | 22.2052i | 0.321945 | − | 0.847179i | ||||
\(688\) | −19.0262 | −0.725368 | ||||||||
\(689\) | −4.67059 | + | 8.08970i | −0.177935 | + | 0.308193i | ||||
\(690\) | −13.2037 | + | 2.13670i | −0.502657 | + | 0.0813427i | ||||
\(691\) | −9.43351 | − | 16.3393i | −0.358868 | − | 0.621577i | 0.628904 | − | 0.777483i | \(-0.283504\pi\) |
−0.987772 | + | 0.155906i | \(0.950170\pi\) | |||||||
\(692\) | −17.3182 | −0.658340 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.9480 | −1.51640 | ||||||||
\(695\) | 1.54081 | + | 2.66876i | 0.0584461 | + | 0.101232i | ||||
\(696\) | 11.9474 | + | 14.6530i | 0.452866 | + | 0.555422i | ||||
\(697\) | 2.02650 | − | 3.51000i | 0.0767590 | − | 0.132951i | ||||
\(698\) | 28.4665 | 1.07747 | ||||||||
\(699\) | −27.6413 | − | 33.9010i | −1.04549 | − | 1.28225i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.16006 | −0.119354 | −0.0596770 | − | 0.998218i | \(-0.519007\pi\) | ||||
−0.0596770 | + | 0.998218i | \(0.519007\pi\) | |||||||
\(702\) | 0.424968 | − | 10.0419i | 0.0160394 | − | 0.379005i | ||||
\(703\) | 3.94398 | + | 6.83118i | 0.148750 | + | 0.257643i | ||||
\(704\) | −7.11984 | −0.268339 | ||||||||
\(705\) | 34.3549 | − | 5.55951i | 1.29388 | − | 0.209383i | ||||
\(706\) | −21.1402 | − | 36.6159i | −0.795622 | − | 1.37806i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.9045 | − | 3.05923i | 0.710475 | − | 0.114973i | ||||
\(709\) | 10.7606 | + | 18.6378i | 0.404121 | + | 0.699959i | 0.994219 | − | 0.107373i | \(-0.0342440\pi\) |
−0.590097 | + | 0.807332i | \(0.700911\pi\) | |||||||
\(710\) | −37.0087 | − | 64.1009i | −1.38891 | − | 2.40567i | ||||
\(711\) | −5.56741 | + | 27.0850i | −0.208794 | + | 1.01577i | ||||
\(712\) | −4.87385 | + | 8.44176i | −0.182655 | + | 0.316368i | ||||
\(713\) | −0.119956 | + | 0.207769i | −0.00449237 | + | 0.00778102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.9826 | − | 20.7545i | −0.448125 | − | 0.776175i | ||||
\(716\) | 2.57898 | 0.0963812 | ||||||||
\(717\) | −15.3710 | + | 2.48742i | −0.574041 | + | 0.0928945i | ||||
\(718\) | −35.3570 | −1.31951 | ||||||||
\(719\) | 9.41508 | − | 16.3074i | 0.351123 | − | 0.608163i | −0.635323 | − | 0.772246i | \(-0.719133\pi\) |
0.986447 | + | 0.164083i | \(0.0524665\pi\) | |||||||
\(720\) | 10.6070 | − | 51.6021i | 0.395298 | − | 1.92310i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.2040 | + | 21.1379i | −0.454185 | + | 0.786671i | ||||
\(723\) | 5.69582 | − | 14.9882i | 0.211830 | − | 0.557419i | ||||
\(724\) | −1.94957 | + | 3.37675i | −0.0724551 | + | 0.125496i | ||||
\(725\) | −22.7618 | + | 39.4247i | −0.845354 | + | 1.46420i | ||||
\(726\) | 77.0396 | − | 12.4670i | 2.85921 | − | 0.462693i | ||||
\(727\) | −19.5426 | + | 33.8489i | −0.724797 | + | 1.25538i | 0.234261 | + | 0.972174i | \(0.424733\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.4273 | − | 22.1585i | 0.571381 | − | 0.820685i | ||||
\(730\) | −16.1153 | + | 27.9125i | −0.596454 | + | 1.03309i | ||||
\(731\) | 4.58167 | 0.169459 | ||||||||
\(732\) | 7.24578 | − | 19.0669i | 0.267812 | − | 0.704732i | ||||
\(733\) | 18.5985 | 0.686951 | 0.343475 | − | 0.939162i | \(-0.388396\pi\) | ||||
0.343475 | + | 0.939162i | \(0.388396\pi\) | |||||||
\(734\) | 19.2119 | + | 33.2759i | 0.709123 | + | 1.22824i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.25621 | − | 5.63993i | 0.120026 | − | 0.207890i | ||||
\(737\) | −24.0977 | + | 41.7385i | −0.887651 | + | 1.53746i | ||||
\(738\) | 16.5474 | − | 5.49960i | 0.609118 | − | 0.202443i | ||||
\(739\) | −2.75068 | − | 4.76432i | −0.101185 | − | 0.175258i | 0.810988 | − | 0.585063i | \(-0.198930\pi\) |
−0.912173 | + | 0.409805i | \(0.865597\pi\) | |||||||
\(740\) | −6.16306 | − | 10.6747i | −0.226559 | − | 0.392411i | ||||
\(741\) | 1.52014 | − | 4.00016i | 0.0558436 | − | 0.146949i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2326 | + | 17.7234i | 0.375399 | + | 0.650210i | 0.990387 | − | 0.138327i | \(-0.0441725\pi\) |
−0.614988 | + | 0.788537i | \(0.710839\pi\) | |||||||
\(744\) | −0.362748 | − | 0.444896i | −0.0132990 | − | 0.0163107i | ||||
\(745\) | 20.2855 | 0.743201 | ||||||||
\(746\) | −28.0892 | − | 48.6520i | −1.02842 | − | 1.78128i | ||||
\(747\) | −3.55832 | + | 1.18262i | −0.130192 | + | 0.0432700i | ||||
\(748\) | −7.19489 | −0.263071 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 24.2253 | − | 3.92027i | 0.884583 | − | 0.143148i | ||||
\(751\) | 38.0460 | 1.38832 | 0.694159 | − | 0.719822i | \(-0.255777\pi\) | ||||
0.694159 | + | 0.719822i | \(0.255777\pi\) | |||||||
\(752\) | −14.3007 | + | 24.7696i | −0.521494 | + | 0.903254i | ||||
\(753\) | 12.7067 | − | 33.4369i | 0.463057 | − | 1.21851i | ||||
\(754\) | −6.00135 | − | 10.3946i | −0.218556 | − | 0.378551i | ||||
\(755\) | −7.11744 | −0.259030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.0780 | −1.85646 | −0.928230 | − | 0.372006i | \(-0.878670\pi\) | ||||
−0.928230 | + | 0.372006i | \(0.878670\pi\) | |||||||
\(758\) | 1.33329 | + | 2.30933i | 0.0484273 | + | 0.0838786i | ||||
\(759\) | 4.77198 | − | 12.5572i | 0.173212 | − | 0.455798i | ||||
\(760\) | 6.81295 | − | 11.8004i | 0.247132 | − | 0.428045i | ||||
\(761\) | −40.0749 | −1.45271 | −0.726357 | − | 0.687317i | \(-0.758788\pi\) | ||||
−0.726357 | + | 0.687317i | \(0.758788\pi\) | |||||||
\(762\) | −29.2985 | + | 4.74124i | −1.06137 | + | 0.171757i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.8633 | −0.646273 | ||||||||
\(765\) | −2.55424 | + | 12.4262i | −0.0923489 | + | 0.449270i | ||||
\(766\) | 27.3058 | + | 47.2951i | 0.986599 | + | 1.70884i | ||||
\(767\) | 12.6239 | 0.455822 | ||||||||
\(768\) | 20.5854 | + | 25.2472i | 0.742812 | + | 0.911029i | ||||
\(769\) | 22.4828 | + | 38.9414i | 0.810751 | + | 1.40426i | 0.912339 | + | 0.409436i | \(0.134274\pi\) |
−0.101587 | + | 0.994827i | \(0.532392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.50485 | + | 3.95993i | −0.0541958 | + | 0.142613i | ||||
\(772\) | 0.0992886 | + | 0.171973i | 0.00357348 | + | 0.00618944i | ||||
\(773\) | 12.1781 | + | 21.0930i | 0.438014 | + | 0.758663i | 0.997536 | − | 0.0701524i | \(-0.0223485\pi\) |
−0.559522 | + | 0.828816i | \(0.689015\pi\) | |||||||
\(774\) | 14.7370 | + | 13.0913i | 0.529710 | + | 0.470556i | ||||
\(775\) | 0.691096 | − | 1.19701i | 0.0248249 | − | 0.0429980i | ||||
\(776\) | 14.4998 | − | 25.1145i | 0.520514 | − | 0.901556i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.52913 | − | 7.84468i | −0.162377 | − | 0.281245i | ||||
\(779\) | 7.42416 | 0.265998 | ||||||||
\(780\) | −2.37544 | + | 6.25084i | −0.0850545 | + | 0.223816i | ||||
\(781\) | 74.3377 | 2.66001 | ||||||||
\(782\) | −1.32354 | + | 2.29243i | −0.0473296 | + | 0.0819773i | ||||
\(783\) | 1.36331 | − | 32.2145i | 0.0487207 | − | 1.15125i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.35200 | − | 9.26993i | 0.191021 | − | 0.330858i | ||||
\(786\) | −45.0109 | + | 7.28391i | −1.60549 | + | 0.259809i | ||||
\(787\) | −20.7617 | + | 35.9603i | −0.740073 | + | 1.28184i | 0.212388 | + | 0.977185i | \(0.431876\pi\) |
−0.952461 | + | 0.304659i | \(0.901457\pi\) | |||||||
\(788\) | 0.800331 | − | 1.38621i | 0.0285106 | − | 0.0493818i | ||||
\(789\) | −15.1130 | + | 39.7691i | −0.538038 | + | 1.41582i | ||||
\(790\) | 27.9481 | − | 48.4075i | 0.994349 | − | 1.72226i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 24.0300 | + | 21.3465i | 0.853869 | + | 0.758515i | ||||
\(793\) | 6.72289 | − | 11.6444i | 0.238737 | − | 0.413504i | ||||
\(794\) | −0.0477147 | −0.00169333 | ||||||||
\(795\) | 50.0744 | − | 8.10333i | 1.77596 | − | 0.287395i | ||||
\(796\) | 6.17372 | 0.218822 | ||||||||
\(797\) | −17.3018 | − | 29.9676i | −0.612861 | − | 1.06151i | −0.990756 | − | 0.135657i | \(-0.956685\pi\) |
0.377895 | − | 0.925848i | \(-0.376648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.44373 | − | 5.96472i | 0.121831 | − | 0.211017i | ||||
\(800\) | −18.7599 | + | 32.4931i | −0.663263 | + | 1.14880i | ||||
\(801\) | 15.7755 | − | 5.24305i | 0.557399 | − | 0.185254i | ||||
\(802\) | 10.4785 | + | 18.1494i | 0.370010 | + | 0.640876i | ||||
\(803\) | −16.1851 | − | 28.0333i | −0.571158 | − | 0.989275i | ||||
\(804\) | 13.2752 | − | 2.14827i | 0.468180 | − | 0.0757635i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.182213 | + | 0.315603i | 0.00641819 | + | 0.0111166i | ||||
\(807\) | 50.5595 | − | 8.18182i | 1.77978 | − | 0.288014i | ||||
\(808\) | −22.8047 | −0.802266 | ||||||||
\(809\) | 5.62597 | + | 9.74446i | 0.197799 | + | 0.342597i | 0.947814 | − | 0.318823i | \(-0.103287\pi\) |
−0.750016 | + | 0.661420i | \(0.769954\pi\) | |||||||
\(810\) | −43.7213 | + | 32.6707i | −1.53621 | + | 1.14793i | ||||
\(811\) | −29.6803 | −1.04222 | −0.521108 | − | 0.853491i | \(-0.674481\pi\) | ||||
−0.521108 | + | 0.853491i | \(0.674481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.1349 | − | 33.2799i | −0.951664 | − | 1.16718i | ||||
\(814\) | 37.6132 | 1.31834 | ||||||||
\(815\) | 9.46376 | − | 16.3917i | 0.331501 | − | 0.574177i | ||||
\(816\) | −6.58833 | − | 8.08033i | −0.230638 | − | 0.282868i | ||||
\(817\) | 4.19629 | + | 7.26819i | 0.146810 | + | 0.254282i | ||||
\(818\) | −54.1211 | −1.89230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.6014 | −0.405137 | ||||||||
\(821\) | −17.3215 | − | 30.0018i | −0.604526 | − | 1.04707i | −0.992126 | − | 0.125242i | \(-0.960029\pi\) |
0.387600 | − | 0.921828i | \(-0.373304\pi\) | |||||||
\(822\) | 18.1470 | − | 2.93665i | 0.632949 | − | 0.102427i | ||||
\(823\) | −18.1935 | + | 31.5121i | −0.634186 | + | 1.09844i | 0.352501 | + | 0.935811i | \(0.385331\pi\) |
−0.986687 | + | 0.162631i | \(0.948002\pi\) | |||||||
\(824\) | 4.75276 | 0.165570 | ||||||||
\(825\) | −27.4927 | + | 72.3454i | −0.957171 | + | 2.51874i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.3576 | −0.846997 | −0.423498 | − | 0.905897i | \(-0.639198\pi\) | ||||
−0.423498 | + | 0.905897i | \(0.639198\pi\) | |||||||
\(828\) | −3.55698 | + | 1.18218i | −0.123614 | + | 0.0410836i | ||||
\(829\) | −19.5851 | − | 33.9224i | −0.680219 | − | 1.17817i | −0.974914 | − | 0.222583i | \(-0.928551\pi\) |
0.294694 | − | 0.955592i | \(-0.404782\pi\) | |||||||
\(830\) | 7.57989 | 0.263102 | ||||||||
\(831\) | 1.15581 | − | 3.04144i | 0.0400945 | − | 0.105506i | ||||
\(832\) | 0.654792 | + | 1.13413i | 0.0227008 | + | 0.0393190i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.65808 | + | 2.03357i | 0.0574146 | + | 0.0704167i | ||||
\(835\) | −29.1690 | − | 50.5223i | −1.00944 | − | 1.74839i | ||||
\(836\) | −6.58970 | − | 11.4137i | −0.227910 | − | 0.394751i | ||||
\(837\) | −0.0413928 | + | 0.978099i | −0.00143075 | + | 0.0338080i | ||||
\(838\) | −12.8515 | + | 22.2594i | −0.443947 | + | 0.768939i | ||||
\(839\) | −17.1739 | + | 29.7460i | −0.592907 | + | 1.02695i | 0.400931 | + | 0.916108i | \(0.368687\pi\) |
−0.993839 | + | 0.110838i | \(0.964647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.75250 | − | 8.23157i | −0.163879 | − | 0.283847i | ||||
\(842\) | −15.6850 | −0.540541 | ||||||||
\(843\) | −13.2211 | − | 16.2151i | −0.455358 | − | 0.558479i | ||||
\(844\) | −15.9809 | −0.550085 | ||||||||
\(845\) | 20.6260 | − | 35.7253i | 0.709556 | − | 1.22899i | ||||
\(846\) | 28.1199 | − | 9.34577i | 0.966781 | − | 0.321314i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.8442 | + | 36.1032i | −0.715793 | + | 1.23979i | ||||
\(849\) | −30.6159 | − | 37.5492i | −1.05074 | − | 1.28869i | ||||
\(850\) | 7.62525 | − | 13.2073i | 0.261544 | − | 0.453007i | ||||
\(851\) | 2.27727 | − | 3.94434i | 0.0780637 | − | 0.135210i | ||||
\(852\) | −13.1076 | − | 16.0759i | −0.449058 | − | 0.550752i | ||||
\(853\) | −16.3371 | + | 28.2967i | −0.559373 | + | 0.968862i | 0.438176 | + | 0.898889i | \(0.355625\pi\) |
−0.997549 | + | 0.0699730i | \(0.977709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0518 | + | 7.32904i | −0.754157 | + | 0.250648i | ||||
\(856\) | 0.156982 | − | 0.271901i | 0.00536555 | − | 0.00929340i | ||||
\(857\) | −57.6679 | −1.96990 | −0.984950 | − | 0.172841i | \(-0.944705\pi\) | ||||
−0.984950 | + | 0.172841i | \(0.944705\pi\) | |||||||
\(858\) | −12.8946 | − | 15.8148i | −0.440216 | − | 0.539907i | ||||
\(859\) | 29.9768 | 1.02279 | 0.511397 | − | 0.859344i | \(-0.329128\pi\) | ||||
0.511397 | + | 0.859344i | \(0.329128\pi\) | |||||||
\(860\) | −6.55733 | − | 11.3576i | −0.223603 | − | 0.387292i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.3615 | + | 24.8749i | −0.489156 | + | 0.847243i | ||||
\(863\) | 11.5888 | − | 20.0724i | 0.394487 | − | 0.683272i | −0.598548 | − | 0.801087i | \(-0.704256\pi\) |
0.993036 | + | 0.117815i | \(0.0375889\pi\) | |||||||
\(864\) | 1.12361 | − | 26.5506i | 0.0382261 | − | 0.903271i | ||||
\(865\) | 30.9967 | + | 53.6879i | 1.05392 | + | 1.82544i | ||||
\(866\) | 17.0437 | + | 29.5205i | 0.579167 | + | 1.00315i | ||||
\(867\) | −17.0204 | − | 20.8748i | −0.578043 | − | 0.708947i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.0690 | + | 48.6170i | 0.952177 | + | 1.64922i | ||||
\(870\) | −23.1537 | + | 60.9277i | −0.784985 | + | 2.06564i | ||||
\(871\) | 8.86480 | 0.300372 | ||||||||
\(872\) | −8.23129 | − | 14.2570i | −0.278747 | − | 0.482803i | ||||
\(873\) | −46.9324 | + | 15.5982i | −1.58842 | + | 0.527919i | ||||
\(874\) | −4.84884 | −0.164014 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.20853 | + | 8.44308i | −0.108406 | + | 0.285265i | ||||
\(877\) | −0.739956 | −0.0249865 | −0.0124933 | − | 0.999922i | \(-0.503977\pi\) | ||||
−0.0124933 | + | 0.999922i | \(0.503977\pi\) | |||||||
\(878\) | −5.81448 | + | 10.0710i | −0.196229 | + | 0.339879i | ||||
\(879\) | −15.0861 | + | 2.44131i | −0.508841 | + | 0.0823435i | ||||
\(880\) | −53.4768 | − | 92.6245i | −1.80270 | − | 3.12237i | ||||
\(881\) | −18.0285 | −0.607395 | −0.303697 | − | 0.952769i | \(-0.598221\pi\) | ||||
−0.303697 | + | 0.952769i | \(0.598221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0928 | 1.45019 | 0.725095 | − | 0.688649i | \(-0.241796\pi\) | ||||
0.725095 | + | 0.688649i | \(0.241796\pi\) | |||||||
\(884\) | 0.661694 | + | 1.14609i | 0.0222552 | + | 0.0385471i | ||||
\(885\) | −43.3198 | − | 53.1300i | −1.45618 | − | 1.78594i | ||||
\(886\) | 24.7254 | − | 42.8256i | 0.830664 | − | 1.43875i | ||||
\(887\) | −30.9527 | −1.03929 | −0.519645 | − | 0.854382i | \(-0.673936\pi\) | ||||
−0.519645 | + | 0.854382i | \(0.673936\pi\) | |||||||
\(888\) | 6.88650 | + | 8.44602i | 0.231096 | + | 0.283430i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −33.6047 | −1.12643 | ||||||||
\(891\) | −6.46090 | − | 54.4337i | −0.216448 | − | 1.82360i | ||||
\(892\) | −9.79685 | − | 16.9686i | −0.328023 | − | 0.568152i | ||||
\(893\) | 12.6163 | 0.422187 | ||||||||
\(894\) | 17.0504 | − | 2.75918i | 0.570249 | − | 0.0922809i | ||||
\(895\) | −4.61595 | − | 7.99506i | −0.154294 | − | 0.267245i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.43913 | + | 0.394713i | −0.0814401 | + | 0.0131791i | ||||
\(898\) | −5.75714 | − | 9.97165i | −0.192118 | − | 0.332758i | ||||
\(899\) | 0.584545 | + | 1.01246i | 0.0194957 | + | 0.0337675i | ||||
\(900\) | 20.4927 | − | 6.81085i | 0.683090 | − | 0.227028i | ||||
\(901\) | 5.01945 | − | 8.69395i | 0.167222 | − | 0.289637i | ||||
\(902\) | 17.7008 | − | 30.6587i | 0.589372 | − | 1.02082i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.40614 | + | 12.8278i | 0.246324 | + | 0.426646i | ||||
\(905\) | 13.9576 | 0.463966 | ||||||||
\(906\) | −5.98236 | + | 0.968099i | −0.198751 | + | 0.0321629i | ||||
\(907\) | −42.8083 | −1.42143 | −0.710714 | − | 0.703481i | \(-0.751628\pi\) | ||||
−0.710714 | + | 0.703481i | \(0.751628\pi\) | |||||||
\(908\) | −1.77243 | + | 3.06993i | −0.0588200 | + | 0.101879i | ||||
\(909\) | 29.0760 | + | 25.8290i | 0.964391 | + | 0.856694i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.04869 | − | 5.28049i | 0.101008 | − | 0.174950i | −0.811092 | − | 0.584918i | \(-0.801127\pi\) |
0.912100 | + | 0.409968i | \(0.134460\pi\) | |||||||
\(912\) | 6.78416 | − | 17.8521i | 0.224646 | − | 0.591143i | ||||
\(913\) | −3.80635 | + | 6.59278i | −0.125972 | + | 0.218189i | ||||
\(914\) | −24.7400 | + | 42.8509i | −0.818327 | + | 1.41738i | ||||
\(915\) | −72.0776 | + | 11.6640i | −2.38281 | + | 0.385600i | ||||
\(916\) | −6.72830 | + | 11.6538i | −0.222309 | + | 0.385051i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.456710 | + | 10.7919i | −0.0150737 | + | 0.356186i | ||||
\(919\) | −12.4307 | + | 21.5305i | −0.410050 | + | 0.710227i | −0.994895 | − | 0.100918i | \(-0.967822\pi\) |
0.584845 | + | 0.811145i | \(0.301155\pi\) | |||||||
\(920\) | −7.86764 | −0.259388 | ||||||||
\(921\) | 0.649321 | − | 1.70865i | 0.0213959 | − | 0.0563020i | ||||
\(922\) | −34.5621 | −1.13824 | ||||||||
\(923\) | −6.83664 | − | 11.8414i | −0.225031 | − | 0.389764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1199 | + | 22.7244i | −0.431381 | + | 0.747174i | ||||
\(926\) | 8.56034 | − | 14.8269i | 0.281310 | − | 0.487244i | ||||
\(927\) | −6.05978 | − | 5.38306i | −0.199029 | − | 0.176803i | ||||
\(928\) | −15.8676 | − | 27.4834i | −0.520878 | − | 0.902188i | ||||
\(929\) | 20.9201 | + | 36.2347i | 0.686366 | + | 1.18882i | 0.973005 | + | 0.230783i | \(0.0741287\pi\) |
−0.286639 | + | 0.958039i | \(0.592538\pi\) | |||||||
\(930\) | 0.702994 | − | 1.84989i | 0.0230521 | − | 0.0606603i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.3895 | + | 21.4592i | 0.405831 | + | 0.702920i | ||||
\(933\) | 3.36255 | + | 4.12403i | 0.110085 | + | 0.135015i | ||||
\(934\) | 27.7651 | 0.908502 | ||||||||
\(935\) | 12.8776 | + | 22.3047i | 0.421144 | + | 0.729443i | ||||
\(936\) | 1.19035 | − | 5.79097i | 0.0389078 | − | 0.189284i | ||||
\(937\) | −29.2537 | −0.955676 | −0.477838 | − | 0.878448i | \(-0.658579\pi\) | ||||
−0.477838 | + | 0.878448i | \(0.658579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.1517 | + | 7.79218i | −1.57137 | + | 0.254288i | ||||
\(940\) | −19.7148 | −0.643026 | ||||||||
\(941\) | 1.67869 | − | 2.90757i | 0.0547236 | − | 0.0947841i | −0.837366 | − | 0.546643i | \(-0.815906\pi\) |
0.892090 | + | 0.451859i | \(0.149239\pi\) | |||||||
\(942\) | 3.23759 | − | 8.51954i | 0.105486 | − | 0.277582i | ||||
\(943\) | −2.14337 | − | 3.71242i | −0.0697976 | − | 0.120893i | ||||
\(944\) | 56.3387 | 1.83367 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0194 | 1.30114 | ||||||||
\(947\) | −2.63300 | − | 4.56050i | −0.0855612 | − | 0.148196i | 0.820069 | − | 0.572265i | \(-0.193935\pi\) |
−0.905630 | + | 0.424068i | \(0.860602\pi\) | |||||||
\(948\) | 5.56442 | − | 14.6425i | 0.180724 | − | 0.475565i | ||||
\(949\) | −2.97699 | + | 5.15630i | −0.0966372 | + | 0.167381i | ||||
\(950\) | 27.9354 | 0.906345 | ||||||||
\(951\) | −21.9650 | + | 3.55450i | −0.712264 | + | 0.115263i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.2520 | 1.82218 | 0.911090 | − | 0.412208i | \(-0.135242\pi\) | ||||
0.911090 | + | 0.412208i | \(0.135242\pi\) | |||||||
\(954\) | 40.9864 | − | 13.6220i | 1.32698 | − | 0.441030i | ||||
\(955\) | 31.9724 | + | 55.3778i | 1.03460 | + | 1.79198i | ||||
\(956\) | 8.82075 | 0.285284 | ||||||||
\(957\) | −41.3663 | − | 50.7342i | −1.33718 | − | 1.64000i | ||||
\(958\) | 7.08131 | + | 12.2652i | 0.228787 | + | 0.396270i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.52624 | − | 6.64767i | 0.0815341 | − | 0.214553i | ||||
\(961\) | 15.4823 | + | 26.8160i | 0.499427 | + | 0.865034i | ||||
\(962\) | −3.45918 | − | 5.99148i | −0.111528 | − | 0.193173i | ||||
\(963\) | −0.508113 | + | 0.168874i | −0.0163737 | + | 0.00544188i | ||||
\(964\) | −4.54153 | + | 7.86616i | −0.146273 | + | 0.253352i | ||||
\(965\) | 0.355420 | − | 0.615606i | 0.0114414 | − | 0.0198171i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.88641 | − | 11.9276i | −0.221452 | − | 0.383566i | 0.733797 | − | 0.679369i | \(-0.237746\pi\) |
−0.955249 | + | 0.295803i | \(0.904413\pi\) | |||||||
\(968\) | 45.9052 | 1.47545 | ||||||||
\(969\) | −1.63368 | + | 4.29894i | −0.0524814 | + | 0.138102i | ||||
\(970\) | 99.9748 | 3.21000 | ||||||||
\(971\) | −25.6627 | + | 44.4491i | −0.823555 | + | 1.42644i | 0.0794635 | + | 0.996838i | \(0.474679\pi\) |
−0.903019 | + | 0.429602i | \(0.858654\pi\) | |||||||
\(972\) | −10.6324 | + | 10.9952i | −0.341033 | + | 0.352671i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.36269 | − | 4.09230i | 0.0757055 | − | 0.131126i | ||||
\(975\) | 14.0525 | − | 2.27405i | 0.450039 | − | 0.0728278i | ||||
\(976\) | 30.0033 | − | 51.9673i | 0.960383 | − | 1.66343i | ||||
\(977\) | −8.84252 | + | 15.3157i | −0.282897 | + | 0.489992i | −0.972097 | − | 0.234579i | \(-0.924629\pi\) |
0.689200 | + | 0.724571i | \(0.257962\pi\) | |||||||
\(978\) | 5.72492 | − | 15.0648i | 0.183063 | − | 0.481720i | ||||
\(979\) | 16.8751 | − | 29.2285i | 0.539329 | − | 0.934146i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.65284 | + | 27.5006i | −0.180481 | + | 0.878027i | ||||
\(982\) | −17.0154 | + | 29.4716i | −0.542984 | + | 0.940476i | ||||
\(983\) | 16.0041 | 0.510453 | 0.255226 | − | 0.966881i | \(-0.417850\pi\) | ||||
0.255226 | + | 0.966881i | \(0.417850\pi\) | |||||||
\(984\) | 10.1252 | − | 1.63851i | 0.322779 | − | 0.0522339i | ||||
\(985\) | −5.72984 | −0.182568 | ||||||||
\(986\) | 6.44961 | + | 11.1711i | 0.205397 | + | 0.355759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.21207 | + | 2.09937i | −0.0385612 | + | 0.0667899i | ||||
\(989\) | 2.42295 | − | 4.19667i | 0.0770454 | − | 0.133446i | ||||
\(990\) | −22.3105 | + | 108.539i | −0.709074 | + | 3.44959i | ||||
\(991\) | 5.43319 | + | 9.41055i | 0.172591 | + | 0.298936i | 0.939325 | − | 0.343029i | \(-0.111453\pi\) |
−0.766734 | + | 0.641965i | \(0.778120\pi\) | |||||||
\(992\) | 0.481771 | + | 0.834453i | 0.0152963 | + | 0.0264939i | ||||
\(993\) | 36.8567 | − | 5.96435i | 1.16961 | − | 0.189273i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.0499 | − | 19.1390i | −0.350306 | − | 0.606748i | ||||
\(996\) | 2.09688 | − | 0.339329i | 0.0664421 | − | 0.0107520i | ||||
\(997\) | −41.0375 | −1.29967 | −0.649835 | − | 0.760075i | \(-0.725162\pi\) | ||||
−0.649835 | + | 0.760075i | \(0.725162\pi\) | |||||||
\(998\) | −28.5719 | − | 49.4880i | −0.904428 | − | 1.56652i | ||||
\(999\) | 0.785812 | − | 18.5685i | 0.0248620 | − | 0.587480i |
(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 | 441.2.g.h.79.10 | 24 | ||
3.2 | odd | 2 | 1323.2.g.h.667.3 | 24 | |||
7.2 | even | 3 | 441.2.f.h.295.10 | yes | 24 | ||
7.3 | odd | 6 | 441.2.h.h.214.4 | 24 | |||
7.4 | even | 3 | 441.2.h.h.214.3 | 24 | |||
7.5 | odd | 6 | 441.2.f.h.295.9 | yes | 24 | ||
7.6 | odd | 2 | inner | 441.2.g.h.79.9 | 24 | ||
9.4 | even | 3 | 441.2.h.h.373.3 | 24 | |||
9.5 | odd | 6 | 1323.2.h.h.226.9 | 24 | |||
21.2 | odd | 6 | 1323.2.f.h.883.4 | 24 | |||
21.5 | even | 6 | 1323.2.f.h.883.3 | 24 | |||
21.11 | odd | 6 | 1323.2.h.h.802.9 | 24 | |||
21.17 | even | 6 | 1323.2.h.h.802.10 | 24 | |||
21.20 | even | 2 | 1323.2.g.h.667.4 | 24 | |||
63.2 | odd | 6 | 3969.2.a.bi.1.9 | 12 | |||
63.4 | even | 3 | inner | 441.2.g.h.67.10 | 24 | ||
63.5 | even | 6 | 1323.2.f.h.442.3 | 24 | |||
63.13 | odd | 6 | 441.2.h.h.373.4 | 24 | |||
63.16 | even | 3 | 3969.2.a.bh.1.4 | 12 | |||
63.23 | odd | 6 | 1323.2.f.h.442.4 | 24 | |||
63.31 | odd | 6 | inner | 441.2.g.h.67.9 | 24 | ||
63.32 | odd | 6 | 1323.2.g.h.361.3 | 24 | |||
63.40 | odd | 6 | 441.2.f.h.148.9 | ✓ | 24 | ||
63.41 | even | 6 | 1323.2.h.h.226.10 | 24 | |||
63.47 | even | 6 | 3969.2.a.bi.1.10 | 12 | |||
63.58 | even | 3 | 441.2.f.h.148.10 | yes | 24 | ||
63.59 | even | 6 | 1323.2.g.h.361.4 | 24 | |||
63.61 | odd | 6 | 3969.2.a.bh.1.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.9 | ✓ | 24 | 63.40 | odd | 6 | ||
441.2.f.h.148.10 | yes | 24 | 63.58 | even | 3 | ||
441.2.f.h.295.9 | yes | 24 | 7.5 | odd | 6 | ||
441.2.f.h.295.10 | yes | 24 | 7.2 | even | 3 | ||
441.2.g.h.67.9 | 24 | 63.31 | odd | 6 | inner | ||
441.2.g.h.67.10 | 24 | 63.4 | even | 3 | inner | ||
441.2.g.h.79.9 | 24 | 7.6 | odd | 2 | inner | ||
441.2.g.h.79.10 | 24 | 1.1 | even | 1 | trivial | ||
441.2.h.h.214.3 | 24 | 7.4 | even | 3 | |||
441.2.h.h.214.4 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.373.3 | 24 | 9.4 | even | 3 | |||
441.2.h.h.373.4 | 24 | 63.13 | odd | 6 | |||
1323.2.f.h.442.3 | 24 | 63.5 | even | 6 | |||
1323.2.f.h.442.4 | 24 | 63.23 | odd | 6 | |||
1323.2.f.h.883.3 | 24 | 21.5 | even | 6 | |||
1323.2.f.h.883.4 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.361.3 | 24 | 63.32 | odd | 6 | |||
1323.2.g.h.361.4 | 24 | 63.59 | even | 6 | |||
1323.2.g.h.667.3 | 24 | 3.2 | odd | 2 | |||
1323.2.g.h.667.4 | 24 | 21.20 | even | 2 | |||
1323.2.h.h.226.9 | 24 | 9.5 | odd | 6 | |||
1323.2.h.h.226.10 | 24 | 63.41 | even | 6 | |||
1323.2.h.h.802.9 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.802.10 | 24 | 21.17 | even | 6 | |||
3969.2.a.bh.1.3 | 12 | 63.61 | odd | 6 | |||
3969.2.a.bh.1.4 | 12 | 63.16 | even | 3 | |||
3969.2.a.bi.1.9 | 12 | 63.2 | odd | 6 | |||
3969.2.a.bi.1.10 | 12 | 63.47 | even | 6 |