Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(309,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.309");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 309.9 | ||
Character | \(\chi\) | \(=\) | 572.309 |
Dual form | 572.2.p.a.485.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.716368 | + | 1.24079i | 0.413595 | + | 0.716368i | 0.995280 | − | 0.0970463i | \(-0.0309395\pi\) |
−0.581684 | + | 0.813415i | \(0.697606\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.80197i | − | 1.25308i | −0.779390 | − | 0.626539i | \(-0.784471\pi\) | ||
0.779390 | − | 0.626539i | \(-0.215529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.48758 | + | 2.59090i | 1.69614 | + | 0.979269i | 0.949353 | + | 0.314211i | \(0.101740\pi\) |
0.746791 | + | 0.665058i | \(0.231593\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.473633 | − | 0.820357i | 0.157878 | − | 0.273452i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.866025 | + | 0.500000i | −0.261116 | + | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.99912 | − | 3.00059i | −0.554456 | − | 0.832213i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.47664 | − | 2.00724i | 0.897665 | − | 0.518267i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.08476 | − | 1.87887i | 0.263094 | − | 0.455692i | −0.703969 | − | 0.710231i | \(-0.748590\pi\) |
0.967062 | + | 0.254539i | \(0.0819237\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.69474 | − | 0.978461i | −0.388801 | − | 0.224474i | 0.292840 | − | 0.956162i | \(-0.405400\pi\) |
−0.681640 | + | 0.731687i | \(0.738733\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.42416i | 1.62009i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.85806 | + | 4.95030i | 0.595946 | + | 1.03221i | 0.993413 | + | 0.114592i | \(0.0365561\pi\) |
−0.397467 | + | 0.917617i | \(0.630111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.85102 | −0.570205 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65539 | 1.08838 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.78406 | − | 4.82213i | −0.516986 | − | 0.895446i | −0.999805 | − | 0.0197262i | \(-0.993721\pi\) |
0.482819 | − | 0.875720i | \(-0.339613\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.69366i | 0.843007i | 0.906827 | + | 0.421503i | \(0.138497\pi\) | ||||
−0.906827 | + | 0.421503i | \(0.861503\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.24079 | − | 0.716368i | −0.215993 | − | 0.124704i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.25963 | − | 12.5740i | 1.22710 | − | 2.12540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.30742 | − | 2.48689i | 0.708135 | − | 0.408842i | −0.102235 | − | 0.994760i | \(-0.532599\pi\) |
0.810370 | + | 0.585918i | \(0.199266\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.29098 | − | 4.63000i | 0.366851 | − | 0.741394i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.64181 | − | 2.10260i | 0.568755 | − | 0.328371i | −0.187897 | − | 0.982189i | \(-0.560167\pi\) |
0.756652 | + | 0.653818i | \(0.226834\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.38594 | + | 9.32871i | −0.821348 | + | 1.42262i | 0.0833315 | + | 0.996522i | \(0.473444\pi\) |
−0.904679 | + | 0.426094i | \(0.859889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.29861 | − | 1.32710i | −0.342657 | − | 0.197833i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.57836i | 0.667822i | 0.942605 | + | 0.333911i | \(0.108368\pi\) | ||||
−0.942605 | + | 0.333911i | \(0.891632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.92556 | + | 17.1916i | 1.41794 | + | 2.45594i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.10836 | 0.435258 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.56839 | 0.215435 | 0.107717 | − | 0.994182i | \(-0.465646\pi\) | ||||
0.107717 | + | 0.994182i | \(0.465646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.40098 | + | 2.42658i | 0.188909 | + | 0.327199i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.80375i | − | 0.371366i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.3947 | − | 6.57871i | −1.48346 | − | 0.856475i | −0.483634 | − | 0.875270i | \(-0.660683\pi\) |
−0.999823 | + | 0.0187956i | \(0.994017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.29341 | + | 10.9005i | −0.805788 | + | 1.39567i | 0.109969 | + | 0.993935i | \(0.464925\pi\) |
−0.915758 | + | 0.401731i | \(0.868409\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.25093 | − | 2.45428i | 0.535567 | − | 0.309210i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.40755 | + | 5.60146i | −1.04283 | + | 0.694776i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.44028 | − | 3.71830i | 0.786806 | − | 0.454262i | −0.0520311 | − | 0.998645i | \(-0.516569\pi\) |
0.838837 | + | 0.544383i | \(0.183236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.09484 | + | 7.09247i | −0.492961 | + | 0.853834i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.51196 | − | 4.33703i | −0.891505 | − | 0.514711i | −0.0170707 | − | 0.999854i | \(-0.505434\pi\) |
−0.874435 | + | 0.485143i | \(0.838767\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.25882i | 0.264375i | 0.991225 | + | 0.132187i | \(0.0422001\pi\) | ||||
−0.991225 | + | 0.132187i | \(0.957800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.04238 | − | 3.53751i | −0.235834 | − | 0.408477i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.18181 | −0.590522 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.15778 | −0.692805 | −0.346402 | − | 0.938086i | \(-0.612597\pi\) | ||||
−0.346402 | + | 0.938086i | \(0.612597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.63044 | + | 4.55606i | 0.292272 | + | 0.506229i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.08702i | − | 0.668138i | −0.942549 | − | 0.334069i | \(-0.891578\pi\) | ||
0.942549 | − | 0.334069i | \(-0.108422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.26452 | − | 3.03947i | −0.571018 | − | 0.329677i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.98882 | − | 6.90884i | 0.427646 | − | 0.740705i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.80742 | − | 1.62086i | 0.297586 | − | 0.171811i | −0.343772 | − | 0.939053i | \(-0.611705\pi\) |
0.641358 | + | 0.767242i | \(0.278371\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.19696 | − | 18.6449i | −0.125476 | − | 1.95452i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.82383 | + | 3.36239i | −0.603903 | + | 0.348664i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.74162 | + | 4.74862i | −0.281284 | + | 0.487198i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.75096 | − | 2.16562i | −0.380853 | − | 0.219885i | 0.297337 | − | 0.954773i | \(-0.403902\pi\) |
−0.678189 | + | 0.734887i | \(0.737235\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.947266i | 0.0952038i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.96564 | − | 8.60075i | −0.494100 | − | 0.855806i | 0.505877 | − | 0.862606i | \(-0.331169\pi\) |
−0.999977 | + | 0.00679942i | \(0.997836\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.4194 | −1.81492 | −0.907459 | − | 0.420140i | \(-0.861981\pi\) | ||||
−0.907459 | + | 0.420140i | \(0.861981\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20.8023 | 2.03009 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.06092 | + | 7.03373i | 0.392584 | + | 0.679976i | 0.992790 | − | 0.119870i | \(-0.0382478\pi\) |
−0.600205 | + | 0.799846i | \(0.704914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3837i | 1.09036i | 0.838319 | + | 0.545180i | \(0.183539\pi\) | ||||
−0.838319 | + | 0.545180i | \(0.816461\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.17139 | + | 3.56306i | 0.585763 | + | 0.338190i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.34636 | − | 10.9922i | 0.597016 | − | 1.03406i | −0.396243 | − | 0.918146i | \(-0.629686\pi\) |
0.993259 | − | 0.115916i | \(-0.0369803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8706 | − | 8.00818i | 1.29344 | − | 0.746767i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.40840 | + | 0.218812i | −0.315107 | + | 0.0202291i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.73592 | − | 5.62104i | 0.892491 | − | 0.515280i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.21775 | + | 3.01247i | 0.470469 | + | 0.271625i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.02136i | − | 0.538567i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.23859 | − | 16.0017i | −0.819792 | − | 1.41992i | −0.905835 | − | 0.423630i | \(-0.860756\pi\) |
0.0860433 | − | 0.996291i | \(-0.472578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.4333 | −1.35882 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3887 | −1.51925 | −0.759627 | − | 0.650359i | \(-0.774618\pi\) | ||||
−0.759627 | + | 0.650359i | \(0.774618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.07020 | − | 8.78184i | −0.439642 | − | 0.761482i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 15.8462i | − | 1.36383i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.14707 | + | 4.12636i | 0.610615 | + | 0.352539i | 0.773206 | − | 0.634155i | \(-0.218652\pi\) |
−0.162591 | + | 0.986694i | \(0.551985\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.24005 | + | 9.07604i | −0.444456 | + | 0.769820i | −0.998014 | − | 0.0629905i | \(-0.979936\pi\) |
0.553558 | + | 0.832810i | \(0.313270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.68076 | + | 3.27979i | −0.478406 | + | 0.276208i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.23158 | + | 1.59903i | 0.270238 | + | 0.133717i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5114 | + | 7.80083i | −1.12206 | + | 0.647824i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.2207 | + | 24.6310i | −1.17290 | + | 2.03153i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.22926 | − | 1.86441i | −0.264551 | − | 0.152739i | 0.361858 | − | 0.932233i | \(-0.382143\pi\) |
−0.626409 | + | 0.779495i | \(0.715476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.82121i | − | 0.717860i | −0.933364 | − | 0.358930i | \(-0.883142\pi\) | ||
0.933364 | − | 0.358930i | \(-0.116858\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.02756 | − | 1.77979i | −0.0830733 | − | 0.143887i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.1515 | 1.05635 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.769573 | 0.0614186 | 0.0307093 | − | 0.999528i | \(-0.490223\pi\) | ||||
0.0307093 | + | 0.999528i | \(0.490223\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.12354 | + | 1.94603i | 0.0891028 | + | 0.154331i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 29.6198i | 2.33437i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.774673 | − | 0.447257i | −0.0606770 | − | 0.0350319i | 0.469355 | − | 0.883010i | \(-0.344487\pi\) |
−0.530032 | + | 0.847978i | \(0.677820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00724 | + | 3.47664i | −0.156263 | + | 0.270656i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.69289 | + | 3.86414i | −0.517912 | + | 0.299016i | −0.736080 | − | 0.676895i | \(-0.763325\pi\) |
0.218168 | + | 0.975911i | \(0.429992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00706 | + | 11.9971i | −0.385158 | + | 0.922851i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.60537 | + | 0.926863i | −0.122766 | + | 0.0708790i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.8369 | + | 20.5022i | −0.899945 | + | 1.55875i | −0.0723835 | + | 0.997377i | \(0.523061\pi\) |
−0.827562 | + | 0.561374i | \(0.810273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.7942 | − | 7.38673i | −0.967150 | − | 0.558384i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 18.8511i | − | 1.41694i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.5758 | + | 20.0498i | 0.865213 | + | 1.49859i | 0.866836 | + | 0.498594i | \(0.166150\pi\) |
−0.00162312 | + | 0.999999i | \(0.500517\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.19953 | 0.237820 | 0.118910 | − | 0.992905i | \(-0.462060\pi\) | ||||
0.118910 | + | 0.992905i | \(0.462060\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.0336 | −1.33308 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.96818 | − | 12.0692i | −0.512311 | − | 0.887348i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.16953i | 0.158652i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.3790 | + | 14.6526i | 1.84605 | + | 1.06582i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.55499 | + | 2.69332i | −0.112515 | + | 0.194882i | −0.916784 | − | 0.399384i | \(-0.869224\pi\) |
0.804269 | + | 0.594266i | \(0.202557\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.04569 | − | 0.603729i | 0.0752704 | − | 0.0434574i | −0.461892 | − | 0.886936i | \(-0.652829\pi\) |
0.537163 | + | 0.843479i | \(0.319496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.9731 | − | 6.41926i | −0.929025 | − | 0.459693i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.89615 | − | 2.24944i | 0.277589 | − | 0.160266i | −0.354742 | − | 0.934964i | \(-0.615431\pi\) |
0.632331 | + | 0.774698i | \(0.282098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.88849 | + | 6.73506i | −0.275648 | + | 0.477436i | −0.970298 | − | 0.241911i | \(-0.922226\pi\) |
0.694651 | + | 0.719347i | \(0.255559\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.22723 | + | 5.32734i | 0.650838 | + | 0.375762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 28.8529i | − | 2.02507i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.89142 | − | 10.2042i | −0.411474 | − | 0.712694i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.41468 | 0.376346 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.95692 | 0.135363 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.33166 | + | 16.1629i | 0.642418 | + | 1.11270i | 0.984891 | + | 0.173173i | \(0.0554019\pi\) |
−0.342474 | + | 0.939527i | \(0.611265\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 12.4276i | − | 0.851528i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.1388 | + | 15.0912i | 1.78265 | + | 1.02921i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.1608 | + | 21.0632i | −0.825531 | + | 1.42986i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.80271 | + | 1.61815i | −0.189390 | + | 0.109344i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.80628 | + | 0.501145i | −0.525107 | + | 0.0337107i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.81019 | − | 1.62246i | 0.188184 | − | 0.108648i | −0.402948 | − | 0.915223i | \(-0.632014\pi\) |
0.591132 | + | 0.806575i | \(0.298681\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.35034 | + | 2.33886i | −0.0900226 | + | 0.155924i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.5533 | + | 7.82501i | 0.899565 | + | 0.519364i | 0.877059 | − | 0.480383i | \(-0.159502\pi\) |
0.0225060 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 20.9070i | − | 1.38157i | −0.723058 | − | 0.690787i | \(-0.757264\pi\) | ||
0.723058 | − | 0.690787i | \(-0.242736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.71208 | − | 6.42951i | −0.244237 | − | 0.423031i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.3007 | −0.674818 | −0.337409 | − | 0.941358i | \(-0.609551\pi\) | ||||
−0.337409 | + | 0.941358i | \(0.609551\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8284 | 0.836833 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.41124 | − | 7.64049i | −0.286541 | − | 0.496303i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.22766i | − | 0.532203i | −0.963945 | − | 0.266101i | \(-0.914264\pi\) | ||
0.963945 | − | 0.266101i | \(-0.0857356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.41266 | − | 0.815602i | −0.0909977 | − | 0.0525375i | 0.453811 | − | 0.891098i | \(-0.350064\pi\) |
−0.544808 | + | 0.838561i | \(0.683398\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.71436 | − | 8.16550i | 0.302426 | − | 0.523817i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 48.1702 | − | 27.8111i | 3.07748 | − | 1.77679i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.452035 | + | 7.04129i | 0.0287623 | + | 0.448026i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.55270 | − | 4.36055i | 0.478633 | − | 0.276339i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.15846 | − | 3.73857i | 0.136241 | − | 0.235976i | −0.789830 | − | 0.613326i | \(-0.789831\pi\) |
0.926071 | + | 0.377350i | \(0.123165\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.95030 | − | 2.85806i | −0.311223 | − | 0.179684i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 8.70953i | − | 0.545412i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.45856 | − | 9.45451i | −0.340496 | − | 0.589756i | 0.644029 | − | 0.765001i | \(-0.277262\pi\) |
−0.984525 | + | 0.175245i | \(0.943928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.7732 | 1.60147 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.27448 | −0.326482 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.40732 | − | 7.63370i | −0.271767 | − | 0.470714i | 0.697547 | − | 0.716539i | \(-0.254275\pi\) |
−0.969314 | + | 0.245825i | \(0.920941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.39457i | − | 0.269956i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.02229 | + | 2.32227i | 0.246160 | + | 0.142121i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3739 | − | 19.7002i | 0.693480 | − | 1.20114i | −0.277210 | − | 0.960809i | \(-0.589410\pi\) |
0.970690 | − | 0.240333i | \(-0.0772567\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0882364 | − | 0.0509433i | 0.00535998 | − | 0.00309458i | −0.497318 | − | 0.867569i | \(-0.665682\pi\) |
0.502678 | + | 0.864474i | \(0.332348\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.2769 | − | 14.8418i | 1.34826 | − | 0.898265i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.46906 | − | 1.42551i | 0.148890 | − | 0.0859616i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2604 | − | 17.7715i | 0.616486 | − | 1.06779i | −0.373636 | − | 0.927576i | \(-0.621889\pi\) |
0.990122 | − | 0.140210i | \(-0.0447777\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.85048 | + | 2.22307i | 0.230522 | + | 0.133092i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.6740i | 1.59124i | 0.605798 | + | 0.795619i | \(0.292854\pi\) | ||||
−0.605798 | + | 0.795619i | \(0.707146\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.70388 | + | 15.0756i | 0.517392 | + | 0.896149i | 0.999796 | + | 0.0202004i | \(0.00643043\pi\) |
−0.482404 | + | 0.875949i | \(0.660236\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.85603 | −0.465351 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.7905 | 1.28625 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.14657 | + | 10.6462i | 0.361563 | + | 0.626246i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.20552i | − | 0.363774i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.29450 | + | 3.05678i | 0.309308 | + | 0.178579i | 0.646617 | − | 0.762815i | \(-0.276183\pi\) |
−0.337309 | + | 0.941394i | \(0.609517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.4333 | + | 31.9275i | −1.07323 | + | 1.85889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.89771 | + | 2.82770i | −0.284194 | + | 0.164080i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.14022 | − | 18.4721i | 0.528592 | − | 1.06827i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −48.3396 | + | 27.9089i | −2.78625 | + | 1.60864i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.11446 | − | 12.3226i | 0.408715 | − | 0.707915i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 30.5429 | + | 17.6339i | 1.74888 | + | 1.00972i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.3633i | − | 0.876832i | −0.898772 | − | 0.438416i | \(-0.855540\pi\) | ||
0.898772 | − | 0.438416i | \(-0.144460\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.1951 | − | 22.8546i | −0.750642 | − | 1.30015i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.2427 | −0.864337 | −0.432169 | − | 0.901793i | \(-0.642251\pi\) | ||||
−0.432169 | + | 0.901793i | \(0.642251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.4800 | 1.60978 | 0.804891 | − | 0.593422i | \(-0.202224\pi\) | ||||
0.804891 | + | 0.593422i | \(0.202224\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.87680 | − | 11.9110i | −0.387464 | − | 0.671107i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.0223i | 1.46156i | 0.682615 | + | 0.730779i | \(0.260843\pi\) | ||||
−0.682615 | + | 0.730779i | \(0.739157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.82213 | + | 2.78406i | 0.269987 | + | 0.155877i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.81823 | + | 10.0775i | −0.324742 | + | 0.562470i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.67680 | + | 2.12280i | −0.204582 | + | 0.118116i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.69953 | + | 8.55475i | 0.316153 | + | 0.474532i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.1247 | + | 8.15492i | −0.781099 | + | 0.450968i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.8621 | + | 20.5457i | −0.653977 | + | 1.13272i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.51765 | − | 3.18562i | −0.303277 | − | 0.175097i | 0.340637 | − | 0.940195i | \(-0.389357\pi\) |
−0.643914 | + | 0.765098i | \(0.722691\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 4.71149i | − | 0.258188i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.4186 | − | 18.0455i | −0.569226 | − | 0.985929i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.1004 | −1.20388 | −0.601942 | − | 0.798540i | \(-0.705606\pi\) | ||||
−0.601942 | + | 0.798540i | \(0.705606\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.1853 | 0.987692 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.34683 | − | 4.06483i | −0.127088 | − | 0.220123i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 66.5920i | 3.59563i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.8729 | + | 11.4736i | 1.06992 | + | 0.617719i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.42631 | + | 9.39864i | −0.291299 | + | 0.504545i | −0.974117 | − | 0.226043i | \(-0.927421\pi\) |
0.682818 | + | 0.730589i | \(0.260754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.1946 | − | 12.2367i | 1.13452 | − | 0.655017i | 0.189454 | − | 0.981890i | \(-0.439328\pi\) |
0.945068 | + | 0.326873i | \(0.105995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.3058 | − | 16.9695i | −0.603459 | − | 0.905765i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.1279 | − | 7.57938i | 0.698726 | − | 0.403410i | −0.108147 | − | 0.994135i | \(-0.534492\pi\) |
0.806873 | + | 0.590725i | \(0.201158\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.1522 | + | 21.0483i | −0.644973 | + | 1.11713i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.9490 | + | 8.05347i | 0.738260 | + | 0.426235i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.4827i | − | 1.39771i | −0.715265 | − | 0.698853i | \(-0.753694\pi\) | ||
0.715265 | − | 0.698853i | \(-0.246306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.58523 | − | 13.1380i | −0.399223 | − | 0.691474i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.43274 | 0.0751992 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.32914 | 0.331283 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.314518 | − | 0.544762i | −0.0164177 | − | 0.0284363i | 0.857700 | − | 0.514151i | \(-0.171893\pi\) |
−0.874118 | + | 0.485714i | \(0.838559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 3.98344i | − | 0.207370i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.03826 | + | 4.06354i | 0.365408 | + | 0.210969i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00503 | + | 12.1331i | −0.362707 | + | 0.628227i | −0.988405 | − | 0.151838i | \(-0.951481\pi\) |
0.625698 | + | 0.780065i | \(0.284814\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.47122 | − | 4.31351i | 0.385812 | − | 0.222749i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.90356 | + | 17.9938i | −0.458557 | + | 0.926728i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.7847 | − | 18.3509i | 1.63267 | − | 0.942623i | 0.649406 | − | 0.760442i | \(-0.275018\pi\) |
0.983265 | − | 0.182181i | \(-0.0583157\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.2365 | − | 22.9262i | 0.678124 | − | 1.17455i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.0246 | − | 9.25179i | −0.818817 | − | 0.472744i | 0.0311911 | − | 0.999513i | \(-0.490070\pi\) |
−0.850008 | + | 0.526769i | \(0.823403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.5193i | 0.739970i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.10192 | + | 8.83678i | 0.259345 | + | 0.449199i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.42893 | 0.376662 | 0.188331 | − | 0.982106i | \(-0.439692\pi\) | ||||
0.188331 | + | 0.982106i | \(0.439692\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.4013 | 0.627159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.4567 | − | 21.5756i | −0.628356 | − | 1.08835i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.2539i | 0.868139i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.98398 | − | 2.87750i | −0.250139 | − | 0.144418i | 0.369689 | − | 0.929156i | \(-0.379464\pi\) |
−0.619828 | + | 0.784738i | \(0.712798\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.26425 | − | 12.5821i | 0.363668 | − | 0.629891i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0290 | − | 6.94494i | 0.600699 | − | 0.346814i | −0.168617 | − | 0.985682i | \(-0.553930\pi\) |
0.769317 | + | 0.638868i | \(0.220597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.0838 | − | 9.38319i | 0.701562 | − | 0.467410i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.7659 | − | 7.37042i | 0.634345 | − | 0.366239i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.48689 | + | 4.30742i | −0.123270 | + | 0.213511i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0622 | − | 6.38679i | −0.546993 | − | 0.315806i | 0.200916 | − | 0.979609i | \(-0.435608\pi\) |
−0.747908 | + | 0.663802i | \(0.768942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8240i | 0.583234i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.0896 | − | 59.0449i | −1.67744 | − | 2.90541i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.0556 | −0.837229 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.0152 | −0.735299 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.5615 | + | 33.8815i | 0.955642 | + | 1.65522i | 0.732892 | + | 0.680345i | \(0.238170\pi\) |
0.222750 | + | 0.974875i | \(0.428496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2666i | 0.597836i | 0.954279 | + | 0.298918i | \(0.0966256\pi\) | ||||
−0.954279 | + | 0.298918i | \(0.903374\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.75588 | + | 2.16846i | 0.182617 | + | 0.105434i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.09269 | + | 5.35669i | −0.150017 | + | 0.259838i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −56.4843 | + | 32.6112i | −2.73347 | + | 1.57817i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.330952 | + | 5.15519i | 0.0159785 | + | 0.248895i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.5866 | − | 17.6592i | 1.47330 | − | 0.850612i | 0.473755 | − | 0.880657i | \(-0.342898\pi\) |
0.999549 | + | 0.0300446i | \(0.00956494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.33151 | − | 5.77034i | 0.160102 | − | 0.277305i | −0.774803 | − | 0.632203i | \(-0.782151\pi\) |
0.934905 | + | 0.354898i | \(0.115484\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.3583 | − | 11.1765i | −0.928161 | − | 0.535874i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 11.1860i | − | 0.535098i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7212 | + | 28.9620i | 0.798060 | + | 1.38228i | 0.920878 | + | 0.389851i | \(0.127474\pi\) |
−0.122818 | + | 0.992429i | \(0.539193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.8043 | 0.895443 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.6425 | −1.31333 | −0.656667 | − | 0.754181i | \(-0.728034\pi\) | ||||
−0.656667 | + | 0.754181i | \(0.728034\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.54161 | − | 7.86629i | −0.215293 | − | 0.372898i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 5.34243i | − | 0.252688i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.8470 | + | 8.57190i | 0.700672 | + | 0.404533i | 0.807598 | − | 0.589734i | \(-0.200767\pi\) |
−0.106926 | + | 0.994267i | \(0.534101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.10260 | + | 3.64181i | −0.0990075 | + | 0.171486i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.9452 | − | 6.31924i | 0.514252 | − | 0.296904i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −52.2424 | + | 3.35384i | −2.44916 | + | 0.157231i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.5138 | − | 17.6172i | 1.42738 | − | 0.824096i | 0.430462 | − | 0.902609i | \(-0.358351\pi\) |
0.996913 | + | 0.0785130i | \(0.0250172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.13477 | − | 10.6257i | 0.286346 | − | 0.495967i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.9831 | − | 14.4240i | −1.16358 | − | 0.671793i | −0.211421 | − | 0.977395i | \(-0.567809\pi\) |
−0.952159 | + | 0.305602i | \(0.901142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.0607i | 1.30409i | 0.758180 | + | 0.652046i | \(0.226089\pi\) | ||||
−0.758180 | + | 0.652046i | \(0.773911\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.42131 | + | 16.3182i | 0.436903 | + | 0.756738i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.8923 | −1.89227 | −0.946136 | − | 0.323769i | \(-0.895050\pi\) | ||||
−0.946136 | + | 0.323769i | \(0.895050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.5350 | 1.77938 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.551298 | + | 0.954875i | 0.0254025 | + | 0.0439983i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.7719i | − | 0.495291i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.83176 | + | 2.78962i | 0.221696 | + | 0.127996i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.742840 | − | 1.28664i | 0.0340123 | − | 0.0589111i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.2896 | + | 6.51805i | −0.515835 | + | 0.297817i | −0.735229 | − | 0.677819i | \(-0.762925\pi\) |
0.219394 | + | 0.975636i | \(0.429592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0732 | − | 7.95320i | −0.732873 | − | 0.362635i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −36.7518 | + | 21.2187i | −1.67227 | + | 0.965483i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.06800 | + | 10.5101i | −0.275533 | + | 0.477238i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4433 | + | 6.60677i | 0.518543 | + | 0.299381i | 0.736339 | − | 0.676613i | \(-0.236553\pi\) |
−0.217795 | + | 0.975995i | \(0.569886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.28160i | − | 0.0579561i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7078 | − | 34.1349i | −0.889399 | − | 1.54048i | −0.840587 | − | 0.541676i | \(-0.817790\pi\) |
−0.0488119 | − | 0.998808i | \(-0.515543\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0802 | −0.544064 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.65421 | 0.119298 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.4737 | − | 38.9255i | −1.00808 | − | 1.74605i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.09468i | − | 0.183303i | −0.995791 | − | 0.0916515i | \(-0.970785\pi\) | ||
0.995791 | − | 0.0916515i | \(-0.0292146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.58915 | − | 5.53630i | −0.428412 | − | 0.247344i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.04613 | − | 7.00810i | 0.180408 | − | 0.312476i | −0.761612 | − | 0.648034i | \(-0.775592\pi\) |
0.942019 | + | 0.335558i | \(0.108925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0990 | + | 13.9136i | −1.07239 | + | 0.619146i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.4727 | + | 2.38162i | −0.820400 | + | 0.105772i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.8371 | − | 10.8756i | 0.834941 | − | 0.482053i | −0.0206004 | − | 0.999788i | \(-0.506558\pi\) |
0.855541 | + | 0.517734i | \(0.173224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.85239 | + | 10.1366i | −0.258894 | + | 0.448418i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.58444 | − | 5.53358i | −0.423163 | − | 0.244314i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 51.6106i | 2.27424i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.28918 | − | 3.96497i | −0.100678 | − | 0.174379i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −33.9184 | −1.48885 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.4837 | 1.77362 | 0.886812 | − | 0.462130i | \(-0.152915\pi\) | ||||
0.886812 | + | 0.462130i | \(0.152915\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.78756 | + | 8.29230i | 0.209345 | + | 0.362597i | 0.951508 | − | 0.307623i | \(-0.0995334\pi\) |
−0.742163 | + | 0.670219i | \(0.766200\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 21.1665i | − | 0.923780i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.81877 | + | 5.09152i | 0.384152 | + | 0.221790i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.83697 | + | 8.37789i | −0.210303 | + | 0.364256i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.7938 | + | 6.23179i | −0.468410 | + | 0.270436i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.5894 | − | 6.72422i | −0.588624 | − | 0.291258i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.7083 | − | 11.3786i | 0.852063 | − | 0.491939i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.5850 | + | 28.7261i | −0.715696 | + | 1.23962i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.1916 | − | 9.92556i | −0.740494 | − | 0.427524i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.03711i | − | 0.130576i | −0.997866 | − | 0.0652878i | \(-0.979203\pi\) | ||
0.997866 | − | 0.0652878i | \(-0.0207965\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.29205 | + | 3.96994i | 0.0983611 | + | 0.170366i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.8967 | 1.36631 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.8042 | 0.504711 | 0.252356 | − | 0.967635i | \(-0.418795\pi\) | ||||
0.252356 | + | 0.967635i | \(0.418795\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.96153 | + | 10.3257i | 0.254432 | + | 0.440689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8964i | 0.464200i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.6335 | − | 15.9542i | −1.17510 | − | 0.678443i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.98357 | − | 17.2920i | 0.423779 | − | 0.734006i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.1966 | + | 16.2793i | −1.19473 | + | 0.689777i | −0.959375 | − | 0.282133i | \(-0.908958\pi\) |
−0.235353 | + | 0.971910i | \(0.575625\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.7587 | − | 2.48822i | 1.63932 | − | 0.105241i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.69192 | + | 1.55418i | −0.113653 | + | 0.0656176i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.809155 | + | 1.40150i | −0.0341018 | + | 0.0590661i | −0.882573 | − | 0.470176i | \(-0.844190\pi\) |
0.848471 | + | 0.529242i | \(0.177524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.7999 | − | 17.7823i | −1.29576 | − | 0.748107i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 27.2609i | 1.14485i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.50400 | + | 14.7294i | 0.356506 | + | 0.617487i | 0.987375 | − | 0.158403i | \(-0.0506345\pi\) |
−0.630868 | + | 0.775890i | \(0.717301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8556 | 0.579840 | 0.289920 | − | 0.957051i | \(-0.406371\pi\) | ||||
0.289920 | + | 0.957051i | \(0.406371\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.45578 | −0.186143 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.14839 | − | 14.1134i | −0.339811 | − | 0.588570i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.25714i | − | 0.177227i | −0.996066 | − | 0.0886134i | \(-0.971756\pi\) | ||
0.996066 | − | 0.0886134i | \(-0.0282436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.49820 | + | 0.864985i | 0.0622630 | + | 0.0359475i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.7709 | − | 27.3160i | 0.654287 | − | 1.13326i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.35826 | + | 0.784194i | −0.0562535 | + | 0.0324780i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.613103 | + | 9.55023i | 0.0253487 | + | 0.394853i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0717203 | − | 0.0414077i | 0.00296021 | − | 0.00170908i | −0.498519 | − | 0.866879i | \(-0.666123\pi\) |
0.501479 | + | 0.865170i | \(0.332789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.59257 | − | 7.95456i | 0.189233 | − | 0.327762i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.58215 | + | 3.22286i | 0.229619 | + | 0.132571i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.3010i | 0.587271i | 0.955917 | + | 0.293636i | \(0.0948652\pi\) | ||||
−0.955917 | + | 0.293636i | \(0.905135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.7500 | − | 27.2797i | −0.645686 | − | 1.11836i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.1424 | −0.456027 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.97772 | 0.203384 | 0.101692 | − | 0.994816i | \(-0.467574\pi\) | ||||
0.101692 | + | 0.994816i | \(0.467574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.4440 | − | 25.0177i | −0.589182 | − | 1.02049i | −0.994340 | − | 0.106247i | \(-0.966117\pi\) |
0.405158 | − | 0.914247i | \(-0.367217\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7.04444i | − | 0.286872i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.42658 | − | 1.40098i | −0.0986543 | − | 0.0569581i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.36749 | − | 11.0288i | 0.258448 | − | 0.447646i | −0.707378 | − | 0.706835i | \(-0.750122\pi\) |
0.965826 | + | 0.259190i | \(0.0834555\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 35.8003 | − | 20.6693i | 1.45070 | − | 0.837562i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.7378 | − | 9.15267i | 0.555770 | − | 0.370277i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6240 | + | 6.71111i | −0.469488 | + | 0.271059i | −0.716026 | − | 0.698074i | \(-0.754041\pi\) |
0.246537 | + | 0.969133i | \(0.420707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.44085 | − | 14.6200i | 0.340368 | − | 0.589534i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.7276 | + | 11.9671i | 0.834462 | + | 0.481777i | 0.855378 | − | 0.518004i | \(-0.173325\pi\) |
−0.0209160 | + | 0.999781i | \(0.506658\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23.8252i | − | 0.957614i | −0.877920 | − | 0.478807i | \(-0.841069\pi\) | ||
0.877920 | − | 0.478807i | \(-0.158931\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.1634 | + | 27.9959i | 0.648616 | + | 1.12344i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.7980 | 0.672998 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1268 | −1.24507 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.40188 | + | 2.42812i | 0.0559856 | + | 0.0969698i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 10.7908i | − | 0.430255i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0986 | − | 5.83041i | −0.402018 | − | 0.232105i | 0.285337 | − | 0.958427i | \(-0.407895\pi\) |
−0.687354 | + | 0.726322i | \(0.741228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.3698 | + | 23.1572i | −0.531402 | + | 0.920415i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −44.8363 | + | 25.8862i | −1.77927 | + | 1.02726i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.7425 | − | 64.1505i | 1.25768 | − | 2.54174i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.11582 | + | 4.10832i | −0.281498 | + | 0.162523i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.6700 | + | 32.3373i | −0.737419 | + | 1.27725i | 0.216235 | + | 0.976341i | \(0.430622\pi\) |
−0.953654 | + | 0.300906i | \(0.902711\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.9097 | + | 9.18548i | 0.627418 | + | 0.362240i | 0.779751 | − | 0.626089i | \(-0.215345\pi\) |
−0.152333 | + | 0.988329i | \(0.548679\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 43.2435i | 1.70271i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.697205 | + | 1.20759i | 0.0274099 | + | 0.0474754i | 0.879405 | − | 0.476074i | \(-0.157941\pi\) |
−0.851995 | + | 0.523550i | \(0.824607\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1574 | 0.516474 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34.8465 | −1.36574 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.7695 | + | 23.8495i | 0.538844 | + | 0.933305i | 0.998967 | + | 0.0454496i | \(0.0144720\pi\) |
−0.460123 | + | 0.887855i | \(0.652195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.7225i | 1.90374i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.85304 | + | 1.06985i | 0.0722939 | + | 0.0417389i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.16810 | + | 5.48731i | −0.123412 | + | 0.213755i | −0.921111 | − | 0.389300i | \(-0.872717\pi\) |
0.797699 | + | 0.603055i | \(0.206050\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.7039 | − | 12.5307i | 0.844184 | − | 0.487390i | −0.0145005 | − | 0.999895i | \(-0.504616\pi\) |
0.858684 | + | 0.512505i | \(0.171282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.21398 | − | 9.32691i | −0.241331 | − | 0.362227i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.6064 | + | 14.2065i | −0.954196 | + | 0.550905i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.9140 | − | 27.5638i | 0.616192 | − | 1.06728i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.02626 | + | 2.32456i | 0.155664 | + | 0.0898727i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 12.5868i | − | 0.485909i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.60132 | − | 7.96972i | −0.177368 | − | 0.307210i | 0.763610 | − | 0.645677i | \(-0.223425\pi\) |
−0.940978 | + | 0.338467i | \(0.890092\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.1237 | −0.620600 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.8987 | 0.572604 | 0.286302 | − | 0.958139i | \(-0.407574\pi\) | ||||
0.286302 | + | 0.958139i | \(0.407574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.2218 | − | 19.4368i | −0.430654 | − | 0.745915i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.4224i | 0.859226i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.8390 | − | 10.2993i | −0.682590 | − | 0.394093i | 0.118240 | − | 0.992985i | \(-0.462275\pi\) |
−0.800830 | + | 0.598892i | \(0.795608\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.5619 | − | 20.0258i | 0.441759 | − | 0.765148i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.9411 | − | 14.9771i | 0.989716 | − | 0.571413i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.13539 | − | 4.70609i | −0.119449 | − | 0.179288i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.5382 | − | 23.9821i | 1.58019 | − | 0.912321i | 0.585355 | − | 0.810777i | \(-0.300955\pi\) |
0.994831 | − | 0.101544i | \(-0.0323782\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.45428 | + | 4.25093i | −0.0932302 | + | 0.161479i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.4308 | + | 14.6825i | 0.964644 | + | 0.556938i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.12330i | − | 0.345570i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.37906 | − | 12.7809i | −0.279102 | − | 0.483418i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.08062 | −0.305201 | −0.152600 | − | 0.988288i | \(-0.548765\pi\) | ||||
−0.152600 | + | 0.988288i | \(0.548765\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.73329 | −0.367098 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.18986 | + | 15.9173i | 0.346110 | + | 0.599480i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 51.4620i | − | 1.93543i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.27537 | − | 2.46838i | −0.160565 | − | 0.0927021i | 0.417565 | − | 0.908647i | \(-0.362884\pi\) |
−0.578129 | + | 0.815945i | \(0.696217\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.91653 | + | 5.05158i | −0.109378 | + | 0.189449i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.2350 | + | 13.4148i | −0.870159 | + | 0.502387i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.48042 | − | 9.05479i | 0.167558 | − | 0.338630i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.2088 | − | 5.89403i | 0.381253 | − | 0.220117i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.0204414 | − | 0.0354055i | 0.000762335 | − | 0.00132040i | −0.865644 | − | 0.500660i | \(-0.833091\pi\) |
0.866406 | + | 0.499340i | \(0.166424\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −82.6585 | − | 47.7229i | −3.07836 | − | 1.77729i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2.33708i | − | 0.0869171i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.93741 | + | 13.7480i | 0.294788 | + | 0.510588i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.3751 | −0.941112 | −0.470556 | − | 0.882370i | \(-0.655947\pi\) | ||||
−0.470556 | + | 0.882370i | \(0.655947\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.2915 | 1.08487 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.6849 | + | 20.2389i | 0.432183 | + | 0.748563i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.7943i | 1.24822i | 0.781336 | + | 0.624111i | \(0.214539\pi\) | ||||
−0.781336 | + | 0.624111i | \(0.785461\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 69.0153 | + | 39.8460i | 2.54567 | + | 1.46974i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.71830 | + | 6.44028i | −0.136965 | + | 0.237231i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.5447 | + | 21.6764i | −1.38110 | + | 0.797380i | −0.992290 | − | 0.123936i | \(-0.960448\pi\) |
−0.388813 | + | 0.921317i | \(0.627115\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.41291 | + | 5.60503i | −0.309056 | + | 0.205906i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.6616 | − | 6.73281i | 0.427822 | − | 0.247003i | −0.270597 | − | 0.962693i | \(-0.587221\pi\) |
0.698418 | + | 0.715690i | \(0.253888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.22403 | + | 9.04828i | −0.191394 | + | 0.331503i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.99353 | − | 2.88302i | −0.182704 | − | 0.105484i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.0858i | 1.53778i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.89892 | + | 17.1454i | 0.361217 | + | 0.625646i | 0.988161 | − | 0.153418i | \(-0.0490282\pi\) |
−0.626945 | + | 0.779064i | \(0.715695\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.18502 | 0.225395 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.7168 | −0.899535 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.5987 | − | 32.2138i | −0.675980 | − | 1.17083i | −0.976181 | − | 0.216956i | \(-0.930387\pi\) |
0.300202 | − | 0.953876i | \(-0.402946\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 8.18968i | − | 0.297267i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.3204 | − | 16.9281i | −1.06286 | − | 0.613645i | −0.136641 | − | 0.990621i | \(-0.543631\pi\) |
−0.926223 | + | 0.376976i | \(0.876964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.4940 | + | 51.0852i | −1.06776 | + | 1.84941i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.98691 | + | 2.87919i | −0.180302 | + | 0.104097i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.03927 | + | 47.3423i | 0.109742 | + | 1.70943i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.7689 | − | 7.94946i | 0.496518 | − | 0.286665i | −0.230756 | − | 0.973012i | \(-0.574120\pi\) |
0.727275 | + | 0.686347i | \(0.240787\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.82068 | − | 13.5458i | 0.281655 | − | 0.487841i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.0728 | − | 26.6002i | −1.65712 | − | 0.956741i | −0.974033 | − | 0.226408i | \(-0.927302\pi\) |
−0.683091 | − | 0.730333i | \(-0.739365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 13.3817i | − | 0.480687i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.4631 | + | 31.9790i | 0.662359 | + | 1.14724i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.22925 | −0.294843 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.67406 | 0.310382 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.7449 | − | 27.2710i | −0.562678 | − | 0.974586i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.15632i | − | 0.0769623i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.2310 | − | 11.6803i | −0.721156 | − | 0.416359i | 0.0940223 | − | 0.995570i | \(-0.470028\pi\) |
−0.815178 | + | 0.579211i | \(0.803361\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.31452 | − | 10.9371i | 0.224803 | − | 0.389370i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.9596 | − | 32.8856i | 2.02525 | − | 1.16928i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.2892 | − | 2.90746i | 1.60827 | − | 0.103247i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.45272 | − | 3.14813i | 0.193388 | − | 0.111653i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.6403 | + | 23.6258i | −0.483166 | + | 0.836868i | −0.999813 | − | 0.0193307i | \(-0.993846\pi\) |
0.516647 | + | 0.856198i | \(0.327180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.60212 | + | 4.96644i | 0.304321 | + | 0.175700i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.07078i | − | 0.108501i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.12941 | − | 1.95620i | −0.0398560 | − | 0.0690327i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 82.9937 | 2.92514 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.5917 | 1.14728 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.7886 | + | 32.5428i | 0.660573 | + | 1.14415i | 0.980465 | + | 0.196692i | \(0.0630198\pi\) |
−0.319893 | + | 0.947454i | \(0.603647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.1264i | 0.355586i | 0.984068 | + | 0.177793i | \(0.0568957\pi\) | ||||
−0.984068 | + | 0.177793i | \(0.943104\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.126419 | + | 0.0729883i | 0.00443372 | + | 0.00255981i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.25320 | + | 2.17061i | −0.0438977 | + | 0.0760331i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.2556 | − | 10.5399i | 0.638681 | − | 0.368743i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.8624 | − | 7.84890i | −0.554276 | − | 0.274263i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.8787 | + | 14.9411i | −0.903174 | + | 0.521448i | −0.878229 | − | 0.478241i | \(-0.841274\pi\) |
−0.0249452 | + | 0.999689i | \(0.507941\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.11768 | + | 5.39999i | −0.108676 | + | 0.188232i | −0.915234 | − | 0.402923i | \(-0.867994\pi\) |
0.806558 | + | 0.591155i | \(0.201328\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.53751 | + | 2.04238i | 0.123160 | + | 0.0711066i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 49.0708i | − | 1.70636i | −0.521617 | − | 0.853180i | \(-0.674671\pi\) | ||
0.521617 | − | 0.853180i | \(-0.325329\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.77989 | − | 4.81491i | −0.0965496 | − | 0.167229i | 0.813705 | − | 0.581279i | \(-0.197447\pi\) |
−0.910254 | + | 0.414050i | \(0.864114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.4008 | 1.01990 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.0676 | 1.49220 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.8272 | + | 18.7533i | 0.374691 | + | 0.648984i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.5445i | 0.917513i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.60576 | + | 5.54589i | 0.331628 | + | 0.191465i | 0.656564 | − | 0.754271i | \(-0.272009\pi\) |
−0.324936 | + | 0.945736i | \(0.605343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00193 | + | 1.73539i | −0.0345493 | + | 0.0598412i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −33.0967 | + | 19.1084i | −1.13991 | + | 0.658128i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33.6154 | + | 14.0296i | 1.15640 | + | 0.482633i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.48758 | − | 2.59090i | 0.154195 | − | 0.0890245i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.4704 | + | 21.5993i | −0.427982 | + | 0.741286i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.6217 | + | 14.2153i | 0.844020 | + | 0.487295i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.8585i | − | 0.371788i | −0.982570 | − | 0.185894i | \(-0.940482\pi\) | ||
0.982570 | − | 0.185894i | \(-0.0595181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.59704 | + | 4.49821i | 0.0888169 | + | 0.153835i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.3654 | 0.968942 | 0.484471 | − | 0.874807i | \(-0.339012\pi\) | ||||
0.484471 | + | 0.874807i | \(0.339012\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.4665 | 0.630068 | 0.315034 | − | 0.949080i | \(-0.397984\pi\) | ||||
0.315034 | + | 0.949080i | \(0.397984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.6100 | + | 27.0374i | 0.531989 | + | 0.921432i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 29.0321i | − | 0.988263i | −0.869387 | − | 0.494131i | \(-0.835486\pi\) | ||
0.869387 | − | 0.494131i | \(-0.164514\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57.4464 | + | 33.1667i | 1.95324 | + | 1.12770i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.80642 | + | 15.2532i | −0.299082 | + | 0.518025i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.33280 | − | 3.07889i | 0.180903 | − | 0.104444i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0320 | − | 11.8913i | −0.814292 | − | 0.402922i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.55316 | + | 2.05142i | −0.120256 | + | 0.0694300i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.6008 | − | 27.0213i | 0.527402 | − | 0.913487i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.9577 | + | 6.32644i | 0.370016 | + | 0.213629i | 0.673465 | − | 0.739219i | \(-0.264805\pi\) |
−0.303450 | + | 0.952847i | \(0.598138\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.75912i | 0.295438i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.52114 | + | 4.36674i | 0.0849393 | + | 0.147119i | 0.905365 | − | 0.424634i | \(-0.139597\pi\) |
−0.820426 | + | 0.571753i | \(0.806264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.8609 | 1.81256 | 0.906281 | − | 0.422675i | \(-0.138909\pi\) | ||||
0.906281 | + | 0.422675i | \(0.138909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −52.8202 | −1.77553 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.45147 | + | 5.97813i | 0.115889 | + | 0.200726i | 0.918135 | − | 0.396268i | \(-0.129695\pi\) |
−0.802246 | + | 0.596994i | \(0.796362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 95.7451i | − | 3.21119i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.55606 | − | 2.63044i | −0.152634 | − | 0.0881232i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.47974 | − | 7.75914i | 0.149909 | − | 0.259650i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 56.1789 | − | 32.4349i | 1.87785 | − | 1.08418i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.4677 | − | 1.89176i | 0.983897 | − | 0.0631640i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.6334 | − | 13.0674i | 0.754867 | − | 0.435823i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.70133 | − | 2.94679i | 0.0566795 | − | 0.0981719i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −69.2579 | − | 39.9861i | −2.30476 | − | 1.33065i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.96499i | − | 0.298006i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.56474 | + | 4.44226i | 0.0851607 | + | 0.147503i | 0.905460 | − | 0.424432i | \(-0.139526\pi\) |
−0.820299 | + | 0.571935i | \(0.806193\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.40757 | −0.312029 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.9426 | −1.35649 | −0.678245 | − | 0.734836i | \(-0.737259\pi\) | ||||
−0.678245 | + | 0.734836i | \(0.737259\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.04351 | + | 5.27152i | 0.100726 | + | 0.174462i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 50.5295i | 1.67045i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −78.0329 | − | 45.0523i | −2.57687 | − | 1.48776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.9026 | + | 27.5441i | −0.524579 | + | 0.908597i | 0.475012 | + | 0.879979i | \(0.342444\pi\) |
−0.999590 | + | 0.0286174i | \(0.990890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.0626 | − | 11.0058i | 0.628134 | − | 0.362654i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.00365 | + | 31.2105i | 0.0659508 | + | 1.02731i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.2805 | + | 7.09018i | −0.403782 | + | 0.233124i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.72405 | + | 15.1105i | −0.286535 | + | 0.496294i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.4977 | + | 22.8040i | 1.29588 | + | 0.748175i | 0.979689 | − | 0.200522i | \(-0.0642638\pi\) |
0.316187 | + | 0.948697i | \(0.397597\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 38.8471i | − | 1.27316i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.9194 | − | 18.9130i | −0.357486 | − | 0.619184i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.07895 | 0.198803 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.54956 | −0.279302 | −0.139651 | − | 0.990201i | \(-0.544598\pi\) | ||||
−0.139651 | + | 0.990201i | \(0.544598\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.4021 | + | 35.3375i | 0.665799 | + | 1.15320i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.66537i | 0.0868885i | 0.999056 | + | 0.0434443i | \(0.0138331\pi\) | ||||
−0.999056 | + | 0.0434443i | \(0.986167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.8170 | + | 12.0187i | 0.677895 | + | 0.391383i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.0560 | − | 71.1112i | 1.33555 | − | 2.31325i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.6122 | − | 25.7569i | 1.44970 | − | 0.836986i | 0.451239 | − | 0.892403i | \(-0.350982\pi\) |
0.998463 | + | 0.0554169i | \(0.0176488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.77779 | − | 4.51565i | 0.220016 | − | 0.146584i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.2881 | + | 18.6415i | −1.04701 | + | 0.604493i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.7208 | + | 51.4780i | −0.962752 | + | 1.66753i | −0.247214 | + | 0.968961i | \(0.579515\pi\) |
−0.715538 | + | 0.698574i | \(0.753818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.54659 | + | 4.35703i | 0.244202 | + | 0.140990i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.97764i | 0.257880i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.3820 | + | 37.0347i | 0.690461 | + | 1.19591i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.96952 | 0.289339 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.69355 | 0.247921 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.69163 | − | 2.92999i | −0.0544555 | − | 0.0943196i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.6572i | − | 1.62903i | −0.580144 | − | 0.814514i | \(-0.697004\pi\) | ||
0.580144 | − | 0.814514i | \(-0.302996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.26788 | − | 3.04141i | −0.169229 | − | 0.0977042i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.8999 | − | 32.7356i | 0.606527 | − | 1.05054i | −0.385281 | − | 0.922799i | \(-0.625896\pi\) |
0.991808 | − | 0.127736i | \(-0.0407711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −47.0303 | + | 27.1530i | −1.50772 | + | 0.870484i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.53165 | + | 13.2003i | −0.209180 | + | 0.422746i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.2681 | − | 11.7018i | 0.648433 | − | 0.374373i | −0.139422 | − | 0.990233i | \(-0.544525\pi\) |
0.787856 | + | 0.615860i | \(0.211191\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.62086 | + | 2.80742i | −0.0518030 | + | 0.0897254i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.33869 | + | 5.39169i | 0.298161 | + | 0.172144i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 30.3104i | − | 0.966752i | −0.875413 | − | 0.483376i | \(-0.839410\pi\) | ||
0.875413 | − | 0.483376i | \(-0.160590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.30286 | − | 10.9169i | −0.200826 | − | 0.347841i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33.9905 | −1.08193 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −61.5732 | −1.95792 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.25812 | + | 12.5714i | 0.230562 | + | 0.399345i | 0.957974 | − | 0.286856i | \(-0.0926103\pi\) |
−0.727412 | + | 0.686201i | \(0.759277\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.12830i | − | 0.289678i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.8714 | + | 10.8954i | 0.598265 | + | 0.345408i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0246062 | + | 0.0426191i | −0.000779285 | + | 0.00134976i | −0.866415 | − | 0.499325i | \(-0.833581\pi\) |
0.865635 | + | 0.500675i | \(0.166915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.3601 | − | 14.0643i | 0.770721 | − | 0.444976i |
(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 | 572.2.p.a.309.9 | ✓ | 24 | |
13.2 | odd | 12 | 7436.2.a.v.1.4 | 12 | |||
13.4 | even | 6 | inner | 572.2.p.a.485.9 | yes | 24 | |
13.11 | odd | 12 | 7436.2.a.u.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.p.a.309.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
572.2.p.a.485.9 | yes | 24 | 13.4 | even | 6 | inner | |
7436.2.a.u.1.4 | 12 | 13.11 | odd | 12 | |||
7436.2.a.v.1.4 | 12 | 13.2 | odd | 12 |