Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(109,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.j (of order \(6\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.109 |
Dual form | 405.2.j.b.379.2 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.686141 | − | 0.396143i | 0.485175 | − | 0.280116i | −0.237396 | − | 0.971413i | \(-0.576294\pi\) |
0.722570 | + | 0.691297i | \(0.242960\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.686141 | + | 1.18843i | −0.343070 | + | 0.594215i | ||||
\(5\) | −2.18614 | − | 0.469882i | −0.977672 | − | 0.210138i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | − | 1.73205i | 1.13389 | − | 0.654654i | 0.188982 | − | 0.981981i | \(-0.439481\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | 2.67181i | 0.944629i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.68614 | + | 0.543620i | −0.533204 | + | 0.171908i | ||||
\(11\) | 2.18614 | + | 3.78651i | 0.659146 | + | 1.14167i | 0.980837 | + | 0.194830i | \(0.0624155\pi\) |
−0.321691 | + | 0.946845i | \(0.604251\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.05842 | + | 2.92048i | 1.40295 | + | 0.809996i | 0.994695 | − | 0.102870i | \(-0.0328027\pi\) |
0.408259 | + | 0.912866i | \(0.366136\pi\) | |||||||
\(14\) | 1.37228 | − | 2.37686i | 0.366758 | − | 0.635243i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.313859 | − | 0.543620i | −0.0784648 | − | 0.135905i | ||||
\(17\) | 0.792287i | 0.192158i | 0.995374 | + | 0.0960789i | \(0.0306301\pi\) | ||||
−0.995374 | + | 0.0960789i | \(0.969370\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.372281 | 0.0854072 | 0.0427036 | − | 0.999088i | \(-0.486403\pi\) | ||||
0.0427036 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(20\) | 2.05842 | − | 2.27567i | 0.460277 | − | 0.508856i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | + | 1.73205i | 0.639602 | + | 0.369274i | ||||
\(23\) | 1.37228 | + | 0.792287i | 0.286140 | + | 0.165203i | 0.636200 | − | 0.771524i | \(-0.280505\pi\) |
−0.350060 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.55842 | + | 2.05446i | 0.911684 | + | 0.410891i | ||||
\(26\) | 4.62772 | 0.907570 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.75372i | 0.898369i | ||||||||
\(29\) | −2.87228 | − | 4.97494i | −0.533369 | − | 0.923823i | −0.999240 | − | 0.0389701i | \(-0.987592\pi\) |
0.465871 | − | 0.884853i | \(-0.345741\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.18614 | + | 5.51856i | −0.572248 | + | 0.991162i | 0.424087 | + | 0.905621i | \(0.360595\pi\) |
−0.996335 | + | 0.0855407i | \(0.972738\pi\) | |||||||
\(32\) | −5.05842 | − | 2.92048i | −0.894211 | − | 0.516273i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.313859 | + | 0.543620i | 0.0538264 | + | 0.0932301i | ||||
\(35\) | −7.37228 | + | 2.37686i | −1.24614 | + | 0.401763i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.37686i | − | 0.390754i | −0.980728 | − | 0.195377i | \(-0.937407\pi\) | ||
0.980728 | − | 0.195377i | \(-0.0625930\pi\) | |||||||
\(38\) | 0.255437 | − | 0.147477i | 0.0414374 | − | 0.0239239i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.25544 | − | 5.84096i | 0.198502 | − | 0.923537i | ||||
\(41\) | −2.18614 | + | 3.78651i | −0.341418 | + | 0.591353i | −0.984696 | − | 0.174279i | \(-0.944240\pi\) |
0.643278 | + | 0.765632i | \(0.277574\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00000 | − | 1.73205i | 0.457496 | − | 0.264135i | −0.253495 | − | 0.967337i | \(-0.581580\pi\) |
0.710991 | + | 0.703201i | \(0.248247\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25544 | 0.185104 | ||||||||
\(47\) | 1.62772 | − | 0.939764i | 0.237427 | − | 0.137079i | −0.376566 | − | 0.926390i | \(-0.622895\pi\) |
0.613994 | + | 0.789311i | \(0.289562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.50000 | − | 4.33013i | 0.357143 | − | 0.618590i | ||||
\(50\) | 3.94158 | − | 0.396143i | 0.557423 | − | 0.0560232i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.94158 | + | 4.00772i | −0.962624 | + | 0.555771i | ||||
\(53\) | − | 11.9769i | − | 1.64515i | −0.568656 | − | 0.822575i | \(-0.692536\pi\) | ||
0.568656 | − | 0.822575i | \(-0.307464\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | − | 9.30506i | −0.404520 | − | 1.25469i | ||||
\(56\) | 4.62772 | + | 8.01544i | 0.618405 | + | 1.07111i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.94158 | − | 2.27567i | −0.517555 | − | 0.298810i | ||||
\(59\) | 0.813859 | − | 1.40965i | 0.105955 | − | 0.183520i | −0.808173 | − | 0.588946i | \(-0.799543\pi\) |
0.914128 | + | 0.405425i | \(0.132877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.68614 | − | 8.11663i | −0.599999 | − | 1.03923i | −0.992820 | − | 0.119614i | \(-0.961834\pi\) |
0.392822 | − | 0.919615i | \(-0.371499\pi\) | |||||||
\(62\) | 5.04868i | 0.641182i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.37228 | −0.421535 | ||||||||
\(65\) | −9.68614 | − | 8.76144i | −1.20142 | − | 1.08672i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1168 | − | 5.84096i | −1.23597 | − | 0.713587i | −0.267701 | − | 0.963502i | \(-0.586264\pi\) |
−0.968268 | + | 0.249915i | \(0.919597\pi\) | |||||||
\(68\) | −0.941578 | − | 0.543620i | −0.114183 | − | 0.0659236i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.11684 | + | 4.55134i | −0.492057 | + | 0.543989i | ||||
\(71\) | 13.1168 | 1.55668 | 0.778341 | − | 0.627841i | \(-0.216061\pi\) | ||||
0.778341 | + | 0.627841i | \(0.216061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.37686i | 0.278191i | 0.990279 | + | 0.139095i | \(0.0444194\pi\) | ||||
−0.990279 | + | 0.139095i | \(0.955581\pi\) | |||||||
\(74\) | −0.941578 | − | 1.63086i | −0.109456 | − | 0.189584i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.255437 | + | 0.442430i | −0.0293007 | + | 0.0507503i | ||||
\(77\) | 13.1168 | + | 7.57301i | 1.49480 | + | 0.863025i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.37228 | + | 5.84096i | 0.379411 | + | 0.657160i | 0.990977 | − | 0.134034i | \(-0.0427932\pi\) |
−0.611565 | + | 0.791194i | \(0.709460\pi\) | |||||||
\(80\) | 0.430703 | + | 1.33591i | 0.0481541 | + | 0.149359i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.46410i | 0.382546i | ||||||||
\(83\) | −10.3723 | + | 5.98844i | −1.13851 | + | 0.657317i | −0.946060 | − | 0.323991i | \(-0.894975\pi\) |
−0.192446 | + | 0.981308i | \(0.561642\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.372281 | − | 1.73205i | 0.0403796 | − | 0.187867i | ||||
\(86\) | 1.37228 | − | 2.37686i | 0.147977 | − | 0.256304i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.1168 | + | 5.84096i | −1.07846 | + | 0.622649i | ||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.2337 | 2.12107 | ||||||||
\(92\) | −1.88316 | + | 1.08724i | −0.196333 | + | 0.113353i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.744563 | − | 1.28962i | 0.0767958 | − | 0.133014i | ||||
\(95\) | −0.813859 | − | 0.174928i | −0.0835002 | − | 0.0179473i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.11684 | + | 0.644810i | −0.113398 | + | 0.0654706i | −0.555626 | − | 0.831432i | \(-0.687522\pi\) |
0.442228 | + | 0.896903i | \(0.354188\pi\) | |||||||
\(98\) | − | 3.96143i | − | 0.400165i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.56930 | + | 4.00772i | −0.556930 | + | 0.400772i | ||||
\(101\) | 8.18614 | + | 14.1788i | 0.814551 | + | 1.41084i | 0.909650 | + | 0.415377i | \(0.136350\pi\) |
−0.0950981 | + | 0.995468i | \(0.530316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | − | 3.46410i | −0.591198 | − | 0.341328i | 0.174373 | − | 0.984680i | \(-0.444210\pi\) |
−0.765571 | + | 0.643352i | \(0.777543\pi\) | |||||||
\(104\) | −7.80298 | + | 13.5152i | −0.765146 | + | 1.32527i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.74456 | − | 8.21782i | −0.460833 | − | 0.798186i | ||||
\(107\) | − | 13.2665i | − | 1.28252i | −0.767323 | − | 0.641260i | \(-0.778412\pi\) | ||
0.767323 | − | 0.641260i | \(-0.221588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.74456 | −0.933360 | −0.466680 | − | 0.884426i | \(-0.654550\pi\) | ||||
−0.466680 | + | 0.884426i | \(0.654550\pi\) | |||||||
\(110\) | −5.74456 | − | 5.19615i | −0.547723 | − | 0.495434i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.88316 | − | 1.08724i | −0.177942 | − | 0.102735i | ||||
\(113\) | 5.31386 | + | 3.06796i | 0.499886 | + | 0.288609i | 0.728666 | − | 0.684869i | \(-0.240140\pi\) |
−0.228781 | + | 0.973478i | \(0.573474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.62772 | − | 2.37686i | −0.245036 | − | 0.221643i | ||||
\(116\) | 7.88316 | 0.731933 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.28962i | − | 0.118719i | ||||||
\(119\) | 1.37228 | + | 2.37686i | 0.125797 | + | 0.217886i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.05842 | + | 7.02939i | −0.368947 | + | 0.639036i | ||||
\(122\) | −6.43070 | − | 3.71277i | −0.582209 | − | 0.336138i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.37228 | − | 7.57301i | −0.392642 | − | 0.680077i | ||||
\(125\) | −9.00000 | − | 6.63325i | −0.804984 | − | 0.593296i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 7.80298 | − | 4.50506i | 0.689693 | − | 0.398194i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.1168 | − | 2.17448i | −0.887306 | − | 0.190715i | ||||
\(131\) | −2.18614 | + | 3.78651i | −0.191004 | + | 0.330829i | −0.945583 | − | 0.325380i | \(-0.894508\pi\) |
0.754579 | + | 0.656209i | \(0.227841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.11684 | − | 0.644810i | 0.0968427 | − | 0.0559121i | ||||
\(134\) | −9.25544 | −0.799548 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.11684 | −0.181518 | ||||||||
\(137\) | −12.4307 | + | 7.17687i | −1.06203 | + | 0.613161i | −0.925992 | − | 0.377543i | \(-0.876769\pi\) |
−0.136034 | + | 0.990704i | \(0.543436\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.55842 | − | 9.62747i | 0.471459 | − | 0.816591i | −0.528008 | − | 0.849240i | \(-0.677061\pi\) |
0.999467 | + | 0.0326483i | \(0.0103941\pi\) | |||||||
\(140\) | 2.23369 | − | 10.3923i | 0.188781 | − | 0.878310i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.00000 | − | 5.19615i | 0.755263 | − | 0.436051i | ||||
\(143\) | 25.5383i | 2.13562i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.94158 | + | 12.2255i | 0.327330 | + | 1.01528i | ||||
\(146\) | 0.941578 | + | 1.63086i | 0.0779256 | + | 0.134971i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.82473 | + | 1.63086i | 0.232192 | + | 0.134056i | ||||
\(149\) | 5.31386 | − | 9.20387i | 0.435328 | − | 0.754011i | −0.561994 | − | 0.827141i | \(-0.689966\pi\) |
0.997322 | + | 0.0731305i | \(0.0232990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.441578 | − | 0.764836i | −0.0359351 | − | 0.0622414i | 0.847499 | − | 0.530798i | \(-0.178108\pi\) |
−0.883434 | + | 0.468556i | \(0.844774\pi\) | |||||||
\(152\) | 0.994667i | 0.0806781i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | 0.966988 | ||||||||
\(155\) | 9.55842 | − | 10.5672i | 0.767751 | − | 0.848781i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.94158 | + | 5.73977i | 0.793424 | + | 0.458084i | 0.841167 | − | 0.540776i | \(-0.181869\pi\) |
−0.0477424 | + | 0.998860i | \(0.515203\pi\) | |||||||
\(158\) | 4.62772 | + | 2.67181i | 0.368162 | + | 0.212558i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.68614 | + | 8.76144i | 0.765757 | + | 0.692653i | ||||
\(161\) | 5.48913 | 0.432604 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.1460i | − | 1.18633i | −0.805082 | − | 0.593164i | \(-0.797878\pi\) | ||
0.805082 | − | 0.593164i | \(-0.202122\pi\) | |||||||
\(164\) | −3.00000 | − | 5.19615i | −0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.74456 | + | 8.21782i | −0.368249 | + | 0.637827i | ||||
\(167\) | −11.7446 | − | 6.78073i | −0.908822 | − | 0.524708i | −0.0287697 | − | 0.999586i | \(-0.509159\pi\) |
−0.880052 | + | 0.474878i | \(0.842492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5584 | + | 18.2877i | 0.812186 | + | 1.40675i | ||||
\(170\) | −0.430703 | − | 1.33591i | −0.0330334 | − | 0.102459i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.75372i | 0.362468i | ||||||||
\(173\) | 9.68614 | − | 5.59230i | 0.736424 | − | 0.425174i | −0.0843439 | − | 0.996437i | \(-0.526879\pi\) |
0.820768 | + | 0.571262i | \(0.193546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.2337 | − | 1.73205i | 1.30274 | − | 0.130931i | ||||
\(176\) | 1.37228 | − | 2.37686i | 0.103440 | − | 0.179163i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.05842 | − | 1.18843i | 0.154285 | − | 0.0890766i | ||||
\(179\) | 4.88316 | 0.364984 | 0.182492 | − | 0.983207i | \(-0.441584\pi\) | ||||
0.182492 | + | 0.983207i | \(0.441584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8614 | −1.03031 | −0.515155 | − | 0.857097i | \(-0.672266\pi\) | ||||
−0.515155 | + | 0.857097i | \(0.672266\pi\) | |||||||
\(182\) | 13.8832 | − | 8.01544i | 1.02909 | − | 0.594144i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.11684 | + | 3.66648i | −0.156056 | + | 0.270297i | ||||
\(185\) | −1.11684 | + | 5.19615i | −0.0821120 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00000 | + | 1.73205i | −0.219382 | + | 0.126660i | ||||
\(188\) | 2.57924i | 0.188110i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.627719 | + | 0.202380i | −0.0455395 | + | 0.0146822i | ||||
\(191\) | −3.81386 | − | 6.60580i | −0.275961 | − | 0.477979i | 0.694416 | − | 0.719574i | \(-0.255663\pi\) |
−0.970377 | + | 0.241595i | \(0.922329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.94158 | + | 5.73977i | 0.715610 | + | 0.413158i | 0.813135 | − | 0.582075i | \(-0.197759\pi\) |
−0.0975245 | + | 0.995233i | \(0.531092\pi\) | |||||||
\(194\) | −0.510875 | + | 0.884861i | −0.0366787 | + | 0.0635293i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.43070 | + | 5.94215i | 0.245050 | + | 0.424439i | ||||
\(197\) | 6.43087i | 0.458181i | 0.973405 | + | 0.229090i | \(0.0735751\pi\) | ||||
−0.973405 | + | 0.229090i | \(0.926425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | −5.48913 | + | 12.1793i | −0.388140 | + | 0.861204i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.2337 | + | 6.48577i | 0.790400 | + | 0.456337i | ||||
\(203\) | −17.2337 | − | 9.94987i | −1.20957 | − | 0.698344i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.55842 | − | 7.25061i | 0.458060 | − | 0.506404i | ||||
\(206\) | −5.48913 | −0.382445 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.66648i | − | 0.254225i | ||||||
\(209\) | 0.813859 | + | 1.40965i | 0.0562958 | + | 0.0975072i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.930703 | − | 1.61203i | 0.0640723 | − | 0.110976i | −0.832210 | − | 0.554461i | \(-0.812925\pi\) |
0.896282 | + | 0.443484i | \(0.146258\pi\) | |||||||
\(212\) | 14.2337 | + | 8.21782i | 0.977574 | + | 0.564402i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.25544 | − | 9.10268i | −0.359254 | − | 0.622247i | ||||
\(215\) | −7.37228 | + | 2.37686i | −0.502785 | + | 0.162101i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.0742i | 1.49850i | ||||||||
\(218\) | −6.68614 | + | 3.86025i | −0.452843 | + | 0.261449i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 13.1168 | + | 2.81929i | 0.884337 | + | 0.190077i | ||||
\(221\) | −2.31386 | + | 4.00772i | −0.155647 | + | 0.269589i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1168 | − | 9.30506i | 1.07926 | − | 0.623113i | 0.148566 | − | 0.988902i | \(-0.452534\pi\) |
0.930698 | + | 0.365789i | \(0.119201\pi\) | |||||||
\(224\) | −20.2337 | −1.35192 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.86141 | 0.323376 | ||||||||
\(227\) | 11.7446 | − | 6.78073i | 0.779514 | − | 0.450053i | −0.0567440 | − | 0.998389i | \(-0.518072\pi\) |
0.836258 | + | 0.548336i | \(0.184739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.80298 | + | 15.2472i | −0.581718 | + | 1.00756i | 0.413558 | + | 0.910478i | \(0.364286\pi\) |
−0.995276 | + | 0.0970868i | \(0.969048\pi\) | |||||||
\(230\) | −2.74456 | − | 0.589907i | −0.180971 | − | 0.0388973i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.2921 | − | 7.67420i | 0.872670 | − | 0.503836i | ||||
\(233\) | − | 6.13592i | − | 0.401977i | −0.979594 | − | 0.200989i | \(-0.935585\pi\) | ||
0.979594 | − | 0.200989i | \(-0.0644154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 1.28962i | −0.260931 | + | 0.0841256i | ||||
\(236\) | 1.11684 | + | 1.93443i | 0.0727004 | + | 0.125921i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.88316 | + | 1.08724i | 0.122067 | + | 0.0704753i | ||||
\(239\) | 11.4891 | − | 19.8997i | 0.743170 | − | 1.28721i | −0.207875 | − | 0.978155i | \(-0.566655\pi\) |
0.951045 | − | 0.309052i | \(-0.100012\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.755437 | + | 1.30846i | 0.0486620 | + | 0.0842851i | 0.889330 | − | 0.457265i | \(-0.151171\pi\) |
−0.840668 | + | 0.541550i | \(0.817838\pi\) | |||||||
\(242\) | 6.43087i | 0.413392i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.8614 | 0.823367 | ||||||||
\(245\) | −7.50000 | + | 8.29156i | −0.479157 | + | 0.529728i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.88316 | + | 1.08724i | 0.119822 | + | 0.0691795i | ||||
\(248\) | −14.7446 | − | 8.51278i | −0.936281 | − | 0.540562i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.80298 | − | 0.986051i | −0.556750 | − | 0.0623633i | ||||
\(251\) | −20.2337 | −1.27714 | −0.638570 | − | 0.769564i | \(-0.720474\pi\) | ||||
−0.638570 | + | 0.769564i | \(0.720474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.92820i | 0.435572i | ||||||||
\(254\) | −4.11684 | − | 7.13058i | −0.258314 | − | 0.447413i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.94158 | − | 12.0232i | 0.433849 | − | 0.751448i | ||||
\(257\) | −5.56930 | − | 3.21543i | −0.347403 | − | 0.200573i | 0.316138 | − | 0.948713i | \(-0.397614\pi\) |
−0.663541 | + | 0.748140i | \(0.730947\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.11684 | − | 7.13058i | −0.255808 | − | 0.443073i | ||||
\(260\) | 17.0584 | − | 5.49972i | 1.05792 | − | 0.341078i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.46410i | 0.214013i | ||||||||
\(263\) | 22.9783 | − | 13.2665i | 1.41690 | − | 0.818047i | 0.420874 | − | 0.907119i | \(-0.361723\pi\) |
0.996025 | + | 0.0890715i | \(0.0283900\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.62772 | + | 26.1831i | −0.345708 | + | 1.60842i | ||||
\(266\) | 0.510875 | − | 0.884861i | 0.0313237 | − | 0.0542543i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.8832 | − | 8.01544i | 0.848049 | − | 0.489621i | ||||
\(269\) | 29.2337 | 1.78241 | 0.891205 | − | 0.453601i | \(-0.149861\pi\) | ||||
0.891205 | + | 0.453601i | \(0.149861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.25544 | 0.319245 | 0.159623 | − | 0.987178i | \(-0.448972\pi\) | ||||
0.159623 | + | 0.987178i | \(0.448972\pi\) | |||||||
\(272\) | 0.430703 | − | 0.248667i | 0.0261152 | − | 0.0150776i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.68614 | + | 9.84868i | −0.343512 | + | 0.594981i | ||||
\(275\) | 2.18614 | + | 21.7518i | 0.131829 | + | 1.31168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.1168 | + | 11.0371i | −1.14862 | + | 0.663156i | −0.948551 | − | 0.316626i | \(-0.897450\pi\) |
−0.200069 | + | 0.979782i | \(0.564117\pi\) | |||||||
\(278\) | − | 8.80773i | − | 0.528253i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.35053 | − | 19.6974i | −0.379517 | − | 1.17714i | ||||
\(281\) | 0.686141 | + | 1.18843i | 0.0409317 | + | 0.0708958i | 0.885765 | − | 0.464133i | \(-0.153634\pi\) |
−0.844834 | + | 0.535029i | \(0.820301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.0000 | − | 13.8564i | −1.42665 | − | 0.823678i | −0.429797 | − | 0.902926i | \(-0.641415\pi\) |
−0.996855 | + | 0.0792477i | \(0.974748\pi\) | |||||||
\(284\) | −9.00000 | + | 15.5885i | −0.534052 | + | 0.925005i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.1168 | + | 17.5229i | 0.598222 | + | 1.03615i | ||||
\(287\) | 15.1460i | 0.894042i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3723 | 0.963075 | ||||||||
\(290\) | 7.54755 | + | 6.82701i | 0.443207 | + | 0.400896i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.82473 | − | 1.63086i | −0.165305 | − | 0.0954389i | ||||
\(293\) | −0.686141 | − | 0.396143i | −0.0400848 | − | 0.0231430i | 0.479824 | − | 0.877365i | \(-0.340701\pi\) |
−0.519908 | + | 0.854222i | \(0.674034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.44158 | + | 2.69927i | −0.142154 | + | 0.157157i | ||||
\(296\) | 6.35053 | 0.369117 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 8.42020i | − | 0.487769i | ||||||
\(299\) | 4.62772 | + | 8.01544i | 0.267628 | + | 0.463545i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | − | 10.3923i | 0.345834 | − | 0.599002i | ||||
\(302\) | −0.605969 | − | 0.349857i | −0.0348696 | − | 0.0201320i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.116844 | − | 0.202380i | −0.00670146 | − | 0.0116073i | ||||
\(305\) | 6.43070 | + | 19.9460i | 0.368221 | + | 1.14211i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.1460i | − | 0.864429i | −0.901771 | − | 0.432215i | \(-0.857732\pi\) | ||
0.901771 | − | 0.432215i | \(-0.142268\pi\) | |||||||
\(308\) | −18.0000 | + | 10.3923i | −1.02565 | + | 0.592157i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.37228 | − | 11.0371i | 0.134737 | − | 0.626866i | ||||
\(311\) | 7.93070 | − | 13.7364i | 0.449709 | − | 0.778919i | −0.548658 | − | 0.836047i | \(-0.684861\pi\) |
0.998367 | + | 0.0571282i | \(0.0181944\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.1753 | + | 12.2255i | −1.19690 | + | 0.691029i | −0.959862 | − | 0.280472i | \(-0.909509\pi\) |
−0.237035 | + | 0.971501i | \(0.576176\pi\) | |||||||
\(314\) | 9.09509 | 0.513266 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.25544 | −0.520659 | ||||||||
\(317\) | −25.5475 | + | 14.7499i | −1.43489 | + | 0.828436i | −0.997488 | − | 0.0708288i | \(-0.977436\pi\) |
−0.437405 | + | 0.899265i | \(0.644102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5584 | − | 21.7518i | 0.703137 | − | 1.21787i | ||||
\(320\) | 7.37228 | + | 1.58457i | 0.412123 | + | 0.0885804i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.76631 | − | 2.17448i | 0.209888 | − | 0.121179i | ||||
\(323\) | 0.294954i | 0.0164117i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.0584 | + | 23.7051i | 0.946231 | + | 1.31492i | ||||
\(326\) | −6.00000 | − | 10.3923i | −0.332309 | − | 0.575577i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.1168 | − | 5.84096i | −0.558609 | − | 0.322513i | ||||
\(329\) | 3.25544 | − | 5.63858i | 0.179478 | − | 0.310865i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.55842 | − | 7.89542i | −0.250554 | − | 0.433971i | 0.713125 | − | 0.701037i | \(-0.247279\pi\) |
−0.963678 | + | 0.267066i | \(0.913946\pi\) | |||||||
\(332\) | − | 16.4356i | − | 0.902023i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.7446 | −0.587916 | ||||||||
\(335\) | 19.3723 | + | 17.5229i | 1.05842 | + | 0.957378i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00000 | − | 3.46410i | −0.326841 | − | 0.188702i | 0.327597 | − | 0.944818i | \(-0.393761\pi\) |
−0.654438 | + | 0.756116i | \(0.727095\pi\) | |||||||
\(338\) | 14.4891 | + | 8.36530i | 0.788105 | + | 0.455012i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.80298 | + | 1.63086i | 0.0977806 | + | 0.0884459i | ||||
\(341\) | −27.8614 | −1.50878 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820i | 0.374088i | ||||||||
\(344\) | 4.62772 | + | 8.01544i | 0.249510 | + | 0.432164i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.43070 | − | 7.67420i | 0.238196 | − | 0.412568i | ||||
\(347\) | 2.48913 | + | 1.43710i | 0.133623 | + | 0.0771474i | 0.565321 | − | 0.824871i | \(-0.308752\pi\) |
−0.431698 | + | 0.902018i | \(0.642085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.3030 | − | 23.0414i | −0.712092 | − | 1.23338i | −0.964070 | − | 0.265647i | \(-0.914414\pi\) |
0.251978 | − | 0.967733i | \(-0.418919\pi\) | |||||||
\(350\) | 11.1386 | − | 8.01544i | 0.595383 | − | 0.428443i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 25.5383i | − | 1.36120i | ||||||
\(353\) | 1.62772 | − | 0.939764i | 0.0866347 | − | 0.0500186i | −0.456057 | − | 0.889951i | \(-0.650739\pi\) |
0.542692 | + | 0.839932i | \(0.317405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.6753 | − | 6.16337i | −1.52193 | − | 0.327118i | ||||
\(356\) | −2.05842 | + | 3.56529i | −0.109096 | + | 0.188960i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.35053 | − | 1.93443i | 0.177081 | − | 0.102238i | ||||
\(359\) | 10.8832 | 0.574391 | 0.287196 | − | 0.957872i | \(-0.407277\pi\) | ||||
0.287196 | + | 0.957872i | \(0.407277\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8614 | −0.992706 | ||||||||
\(362\) | −9.51087 | + | 5.49111i | −0.499880 | + | 0.288606i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.8832 | + | 24.0463i | −0.727675 | + | 1.26037i | ||||
\(365\) | 1.11684 | − | 5.19615i | 0.0584583 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.2337 | + | 8.21782i | −0.742992 | + | 0.428967i | −0.823156 | − | 0.567815i | \(-0.807789\pi\) |
0.0801639 | + | 0.996782i | \(0.474456\pi\) | |||||||
\(368\) | − | 0.994667i | − | 0.0518506i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.29211 | + | 4.00772i | 0.0671736 | + | 0.208352i | ||||
\(371\) | −20.7446 | − | 35.9306i | −1.07700 | − | 1.86543i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.11684 | + | 4.10891i | 0.368496 | + | 0.212751i | 0.672801 | − | 0.739823i | \(-0.265091\pi\) |
−0.304305 | + | 0.952575i | \(0.598424\pi\) | |||||||
\(374\) | −1.37228 | + | 2.37686i | −0.0709590 | + | 0.122905i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.51087 | + | 4.34896i | 0.129488 | + | 0.224281i | ||||
\(377\) | − | 33.5538i | − | 1.72811i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.48913 | 0.0764912 | 0.0382456 | − | 0.999268i | \(-0.487823\pi\) | ||||
0.0382456 | + | 0.999268i | \(0.487823\pi\) | |||||||
\(380\) | 0.766312 | − | 0.847190i | 0.0393110 | − | 0.0434599i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.23369 | − | 3.02167i | −0.267779 | − | 0.154602i | ||||
\(383\) | 9.60597 | + | 5.54601i | 0.490842 | + | 0.283388i | 0.724924 | − | 0.688829i | \(-0.241875\pi\) |
−0.234082 | + | 0.972217i | \(0.575208\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.1168 | − | 22.7190i | −1.28007 | − | 1.15787i | ||||
\(386\) | 9.09509 | 0.462928 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.76972i | − | 0.0898440i | ||||||
\(389\) | −0.255437 | − | 0.442430i | −0.0129512 | − | 0.0224321i | 0.859477 | − | 0.511174i | \(-0.170789\pi\) |
−0.872428 | + | 0.488742i | \(0.837456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.627719 | + | 1.08724i | −0.0317451 | + | 0.0549841i | ||||
\(392\) | 11.5693 | + | 6.67954i | 0.584338 | + | 0.337368i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.54755 | + | 4.41248i | 0.128344 | + | 0.222298i | ||||
\(395\) | −4.62772 | − | 14.3537i | −0.232846 | − | 0.722215i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.5229i | 0.879449i | 0.898133 | + | 0.439724i | \(0.144924\pi\) | ||||
−0.898133 | + | 0.439724i | \(0.855076\pi\) | |||||||
\(398\) | −10.9783 | + | 6.33830i | −0.550290 | + | 0.317710i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.313859 | − | 3.12286i | −0.0156930 | − | 0.156143i | ||||
\(401\) | −12.6861 | + | 21.9730i | −0.633516 | + | 1.09728i | 0.353312 | + | 0.935506i | \(0.385055\pi\) |
−0.986828 | + | 0.161776i | \(0.948278\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.2337 | + | 18.6101i | −1.60567 | + | 0.927037i | ||||
\(404\) | −22.4674 | −1.11779 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.7663 | −0.782469 | ||||||||
\(407\) | 9.00000 | − | 5.19615i | 0.446113 | − | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.4307 | − | 19.7986i | 0.565212 | − | 0.978976i | −0.431818 | − | 0.901961i | \(-0.642128\pi\) |
0.997030 | − | 0.0770150i | \(-0.0245389\pi\) | |||||||
\(410\) | 1.62772 | − | 7.57301i | 0.0803873 | − | 0.374004i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.23369 | − | 4.75372i | 0.405645 | − | 0.234199i | ||||
\(413\) | − | 5.63858i | − | 0.277457i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.4891 | − | 8.21782i | 1.25121 | − | 0.403397i | ||||
\(416\) | −17.0584 | − | 29.5461i | −0.836358 | − | 1.44861i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.11684 | + | 0.644810i | 0.0546266 | + | 0.0315387i | ||||
\(419\) | −8.74456 | + | 15.1460i | −0.427200 | + | 0.739932i | −0.996623 | − | 0.0821127i | \(-0.973833\pi\) |
0.569423 | + | 0.822045i | \(0.307167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.8723 | + | 18.8313i | 0.529883 | + | 0.917784i | 0.999392 | + | 0.0348563i | \(0.0110973\pi\) |
−0.469510 | + | 0.882927i | \(0.655569\pi\) | |||||||
\(422\) | − | 1.47477i | − | 0.0717906i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 32.0000 | 1.55406 | ||||||||
\(425\) | −1.62772 | + | 3.61158i | −0.0789560 | + | 0.175187i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.1168 | − | 16.2333i | −1.36067 | − | 0.785583i | ||||
\(428\) | 15.7663 | + | 9.10268i | 0.762093 | + | 0.439995i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.11684 | + | 4.55134i | −0.198532 | + | 0.219485i | ||||
\(431\) | −33.3505 | −1.60644 | −0.803219 | − | 0.595683i | \(-0.796881\pi\) | ||||
−0.803219 | + | 0.595683i | \(0.796881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7692i | 0.613647i | 0.951766 | + | 0.306823i | \(0.0992661\pi\) | ||||
−0.951766 | + | 0.306823i | \(0.900734\pi\) | |||||||
\(434\) | 8.74456 | + | 15.1460i | 0.419752 | + | 0.727033i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.68614 | − | 11.5807i | 0.320208 | − | 0.554617i | ||||
\(437\) | 0.510875 | + | 0.294954i | 0.0244385 | + | 0.0141095i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.9307 | + | 27.5928i | 0.760331 | + | 1.31693i | 0.942680 | + | 0.333698i | \(0.108297\pi\) |
−0.182349 | + | 0.983234i | \(0.558370\pi\) | |||||||
\(440\) | 24.8614 | − | 8.01544i | 1.18522 | − | 0.382121i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.66648i | 0.174397i | ||||||||
\(443\) | −18.6060 | + | 10.7422i | −0.883996 | + | 0.510375i | −0.871974 | − | 0.489552i | \(-0.837160\pi\) |
−0.0120223 | + | 0.999928i | \(0.503827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.55842 | − | 1.40965i | −0.310899 | − | 0.0668236i | ||||
\(446\) | 7.37228 | − | 12.7692i | 0.349088 | − | 0.604638i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.1168 | + | 5.84096i | −0.477976 | + | 0.275960i | ||||
\(449\) | 10.8832 | 0.513608 | 0.256804 | − | 0.966464i | \(-0.417331\pi\) | ||||
0.256804 | + | 0.966464i | \(0.417331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.1168 | −0.900177 | ||||||||
\(452\) | −7.29211 | + | 4.21010i | −0.342992 | + | 0.198027i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.37228 | − | 9.30506i | 0.252134 | − | 0.436708i | ||||
\(455\) | −44.2337 | − | 9.50744i | −2.07371 | − | 0.445716i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1753 | − | 10.4935i | 0.850203 | − | 0.490865i | −0.0105163 | − | 0.999945i | \(-0.503348\pi\) |
0.860719 | + | 0.509080i | \(0.170014\pi\) | |||||||
\(458\) | 13.9490i | 0.651793i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.62772 | − | 1.49200i | 0.215768 | − | 0.0695649i | ||||
\(461\) | −12.0475 | − | 20.8670i | −0.561110 | − | 0.971871i | −0.997400 | − | 0.0720652i | \(-0.977041\pi\) |
0.436290 | − | 0.899806i | \(-0.356292\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0000 | + | 6.92820i | 0.557687 | + | 0.321981i | 0.752217 | − | 0.658916i | \(-0.228985\pi\) |
−0.194529 | + | 0.980897i | \(0.562318\pi\) | |||||||
\(464\) | −1.80298 | + | 3.12286i | −0.0837015 | + | 0.144975i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.43070 | − | 4.21010i | −0.112600 | − | 0.195029i | ||||
\(467\) | 18.3152i | 0.847525i | 0.905773 | + | 0.423763i | \(0.139291\pi\) | ||||
−0.905773 | + | 0.423763i | \(0.860709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.4674 | −1.86861 | ||||||||
\(470\) | −2.23369 | + | 2.46943i | −0.103032 | + | 0.113907i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.76631 | + | 2.17448i | 0.173359 | + | 0.100089i | ||||
\(473\) | 13.1168 | + | 7.57301i | 0.603113 | + | 0.348208i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.69702 | + | 0.764836i | 0.0778644 | + | 0.0350931i | ||||
\(476\) | −3.76631 | −0.172629 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 18.2054i | − | 0.832694i | ||||||
\(479\) | 9.30298 | + | 16.1132i | 0.425064 | + | 0.736233i | 0.996426 | − | 0.0844652i | \(-0.0269182\pi\) |
−0.571362 | + | 0.820698i | \(0.693585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.94158 | − | 12.0232i | 0.316509 | − | 0.548209i | ||||
\(482\) | 1.03667 | + | 0.598523i | 0.0472191 | + | 0.0272620i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.56930 | − | 9.64630i | −0.253150 | − | 0.438468i | ||||
\(485\) | 2.74456 | − | 0.884861i | 0.124624 | − | 0.0401795i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.50744i | − | 0.430823i | −0.976523 | − | 0.215412i | \(-0.930891\pi\) | ||
0.976523 | − | 0.215412i | \(-0.0691093\pi\) | |||||||
\(488\) | 21.6861 | − | 12.5205i | 0.981685 | − | 0.566776i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.86141 | + | 8.66025i | −0.0840898 | + | 0.391230i | ||||
\(491\) | 15.8139 | − | 27.3904i | 0.713669 | − | 1.23611i | −0.249801 | − | 0.968297i | \(-0.580365\pi\) |
0.963470 | − | 0.267815i | \(-0.0863015\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.94158 | − | 2.27567i | 0.177520 | − | 0.102491i | ||||
\(494\) | 1.72281 | 0.0775130 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 39.3505 | − | 22.7190i | 1.76511 | − | 1.01909i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1861 | + | 21.1070i | −0.545527 | + | 0.944880i | 0.453047 | + | 0.891487i | \(0.350337\pi\) |
−0.998574 | + | 0.0533931i | \(0.982996\pi\) | |||||||
\(500\) | 14.0584 | − | 6.14453i | 0.628712 | − | 0.274792i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.8832 | + | 8.01544i | −0.619636 | + | 0.357747i | ||||
\(503\) | 3.16915i | 0.141305i | 0.997501 | + | 0.0706527i | \(0.0225082\pi\) | ||||
−0.997501 | + | 0.0706527i | \(0.977492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.2337 | − | 34.8434i | −0.499893 | − | 1.55051i | ||||
\(506\) | 2.74456 | + | 4.75372i | 0.122011 | + | 0.211329i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.3505 | + | 7.13058i | 0.547966 | + | 0.316368i | ||||
\(509\) | 0.255437 | − | 0.442430i | 0.0113221 | − | 0.0196104i | −0.860309 | − | 0.509773i | \(-0.829729\pi\) |
0.871631 | + | 0.490163i | \(0.163063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.11684 | + | 7.13058i | 0.182118 | + | 0.315438i | ||||
\(512\) | 7.02078i | 0.310277i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.09509 | −0.224735 | ||||||||
\(515\) | 11.4891 | + | 10.3923i | 0.506271 | + | 0.457940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.11684 | + | 4.10891i | 0.312998 | + | 0.180710i | ||||
\(518\) | −5.64947 | − | 3.26172i | −0.248223 | − | 0.143312i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.4090 | − | 25.8796i | 1.02655 | − | 1.13489i | ||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.75372i | 0.207866i | 0.994584 | + | 0.103933i | \(0.0331427\pi\) | ||||
−0.994584 | + | 0.103933i | \(0.966857\pi\) | |||||||
\(524\) | −3.00000 | − | 5.19615i | −0.131056 | − | 0.226995i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.5109 | − | 18.2054i | 0.458296 | − | 0.793792i | ||||
\(527\) | −4.37228 | − | 2.52434i | −0.190460 | − | 0.109962i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2446 | − | 17.7441i | −0.445416 | − | 0.771483i | ||||
\(530\) | 6.51087 | + | 20.1947i | 0.282814 | + | 0.877202i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.76972i | 0.0767272i | ||||||||
\(533\) | −22.1168 | + | 12.7692i | −0.957987 | + | 0.553094i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.23369 | + | 29.0024i | −0.269506 | + | 1.25388i | ||||
\(536\) | 15.6060 | − | 27.0303i | 0.674075 | − | 1.16753i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.0584 | − | 11.5807i | 0.864780 | − | 0.499281i | ||||
\(539\) | 21.8614 | 0.941637 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.2337 | 0.826921 | 0.413460 | − | 0.910522i | \(-0.364320\pi\) | ||||
0.413460 | + | 0.910522i | \(0.364320\pi\) | |||||||
\(542\) | 3.60597 | − | 2.08191i | 0.154890 | − | 0.0894256i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.31386 | − | 4.00772i | 0.0992059 | − | 0.171830i | ||||
\(545\) | 21.3030 | + | 4.57879i | 0.912520 | + | 0.196134i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.00000 | + | 3.46410i | −0.256541 | + | 0.148114i | −0.622756 | − | 0.782416i | \(-0.713987\pi\) |
0.366214 | + | 0.930531i | \(0.380654\pi\) | |||||||
\(548\) | − | 19.6974i | − | 0.841430i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.1168 | + | 14.0588i | 0.431384 | + | 0.599469i | ||||
\(551\) | −1.06930 | − | 1.85208i | −0.0455536 | − | 0.0789011i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.2337 | + | 11.6819i | 0.860424 | + | 0.496766i | ||||
\(554\) | −8.74456 | + | 15.1460i | −0.371521 | + | 0.643493i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.62772 | + | 13.2116i | 0.323487 | + | 0.560296i | ||||
\(557\) | 25.0410i | 1.06102i | 0.847678 | + | 0.530511i | \(0.178000\pi\) | ||||
−0.847678 | + | 0.530511i | \(0.822000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.2337 | 0.855794 | ||||||||
\(560\) | 3.60597 | + | 3.26172i | 0.152380 | + | 0.137833i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.941578 | + | 0.543620i | 0.0397181 | + | 0.0229312i | ||||
\(563\) | −27.8614 | − | 16.0858i | −1.17422 | − | 0.677935i | −0.219548 | − | 0.975602i | \(-0.570458\pi\) |
−0.954670 | + | 0.297666i | \(0.903792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1753 | − | 9.20387i | −0.428077 | − | 0.387210i | ||||
\(566\) | −21.9565 | −0.922901 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 35.0458i | 1.47049i | ||||||||
\(569\) | 10.2446 | + | 17.7441i | 0.429474 | + | 0.743871i | 0.996827 | − | 0.0796038i | \(-0.0253655\pi\) |
−0.567352 | + | 0.823475i | \(0.692032\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.06930 | + | 3.58413i | −0.0865974 | + | 0.149991i | −0.906071 | − | 0.423126i | \(-0.860933\pi\) |
0.819473 | + | 0.573117i | \(0.194266\pi\) | |||||||
\(572\) | −30.3505 | − | 17.5229i | −1.26902 | − | 0.732669i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.00000 | + | 10.3923i | 0.250435 | + | 0.433766i | ||||
\(575\) | 4.62772 | + | 6.43087i | 0.192989 | + | 0.268186i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4077i | 0.766325i | 0.923681 | + | 0.383162i | \(0.125165\pi\) | ||||
−0.923681 | + | 0.383162i | \(0.874835\pi\) | |||||||
\(578\) | 11.2337 | − | 6.48577i | 0.467260 | − | 0.269773i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.2337 | − | 3.70415i | −0.715590 | − | 0.153807i | ||||
\(581\) | −20.7446 | + | 35.9306i | −0.860629 | + | 1.49065i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.3505 | − | 26.1831i | 1.87823 | − | 1.08439i | ||||
\(584\) | −6.35053 | −0.262787 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.627719 | −0.0259308 | ||||||||
\(587\) | −14.4891 | + | 8.36530i | −0.598030 | + | 0.345273i | −0.768266 | − | 0.640130i | \(-0.778880\pi\) |
0.170236 | + | 0.985403i | \(0.445547\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.18614 | + | 2.05446i | −0.0488741 | + | 0.0846524i | ||||
\(590\) | −0.605969 | + | 2.81929i | −0.0249474 | + | 0.116068i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.29211 | + | 0.746000i | −0.0531054 | + | 0.0306604i | ||||
\(593\) | 1.67715i | 0.0688722i | 0.999407 | + | 0.0344361i | \(0.0109635\pi\) | ||||
−0.999407 | + | 0.0344361i | \(0.989036\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.88316 | − | 5.84096i | −0.0772019 | − | 0.239456i | ||||
\(596\) | 7.29211 | + | 12.6303i | 0.298696 | + | 0.517357i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.35053 | + | 3.66648i | 0.259693 | + | 0.149934i | ||||
\(599\) | 0.813859 | − | 1.40965i | 0.0332534 | − | 0.0575966i | −0.848920 | − | 0.528522i | \(-0.822746\pi\) |
0.882173 | + | 0.470925i | \(0.156080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.98913 | + | 15.5696i | 0.366674 | + | 0.635098i | 0.989043 | − | 0.147626i | \(-0.0471631\pi\) |
−0.622369 | + | 0.782724i | \(0.713830\pi\) | |||||||
\(602\) | − | 9.50744i | − | 0.387494i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.21194 | 0.0493131 | ||||||||
\(605\) | 12.1753 | − | 13.4603i | 0.494995 | − | 0.547238i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.4674 | + | 21.6318i | 1.52075 | + | 0.878008i | 0.999700 | + | 0.0244837i | \(0.00779419\pi\) |
0.521054 | + | 0.853524i | \(0.325539\pi\) | |||||||
\(608\) | −1.88316 | − | 1.08724i | −0.0763721 | − | 0.0440934i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.3139 | + | 11.1383i | 0.498574 | + | 0.450977i | ||||
\(611\) | 10.9783 | 0.444132 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.2921i | 1.22348i | 0.791057 | + | 0.611742i | \(0.209531\pi\) | ||||
−0.791057 | + | 0.611742i | \(0.790469\pi\) | |||||||
\(614\) | −6.00000 | − | 10.3923i | −0.242140 | − | 0.419399i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.2337 | + | 35.0458i | −0.815239 | + | 1.41203i | ||||
\(617\) | −17.9198 | − | 10.3460i | −0.721425 | − | 0.416515i | 0.0938519 | − | 0.995586i | \(-0.470082\pi\) |
−0.815277 | + | 0.579071i | \(0.803415\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00000 | + | 3.46410i | 0.0803868 | + | 0.139234i | 0.903416 | − | 0.428765i | \(-0.141051\pi\) |
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(620\) | 6.00000 | + | 18.6101i | 0.240966 | + | 0.747401i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 12.5668i | − | 0.503882i | ||||||
\(623\) | 9.00000 | − | 5.19615i | 0.360577 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.5584 | + | 18.7302i | 0.662337 | + | 0.749206i | ||||
\(626\) | −9.68614 | + | 16.7769i | −0.387136 | + | 0.670539i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.6426 | + | 7.87658i | −0.544401 | + | 0.314310i | ||||
\(629\) | 1.88316 | 0.0750863 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.37228 | 0.253677 | 0.126838 | − | 0.991923i | \(-0.459517\pi\) | ||||
0.126838 | + | 0.991923i | \(0.459517\pi\) | |||||||
\(632\) | −15.6060 | + | 9.01011i | −0.620772 | + | 0.358403i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.6861 | + | 20.2410i | −0.464116 | + | 0.803872i | ||||
\(635\) | −4.88316 | + | 22.7190i | −0.193782 | + | 0.901578i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.2921 | − | 14.6024i | 1.00211 | − | 0.578568i | ||||
\(638\) | − | 19.8997i | − | 0.787839i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.1753 | + | 6.18220i | −0.757969 | + | 0.244373i | ||||
\(641\) | −3.98913 | − | 6.90937i | −0.157561 | − | 0.272904i | 0.776428 | − | 0.630206i | \(-0.217030\pi\) |
−0.933989 | + | 0.357303i | \(0.883696\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.11684 | − | 0.644810i | −0.0440440 | − | 0.0254288i | 0.477816 | − | 0.878460i | \(-0.341428\pi\) |
−0.521860 | + | 0.853031i | \(0.674762\pi\) | |||||||
\(644\) | −3.76631 | + | 6.52344i | −0.148413 | + | 0.257060i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.116844 | + | 0.202380i | 0.00459716 | + | 0.00796252i | ||||
\(647\) | 28.7075i | 1.12861i | 0.825567 | + | 0.564304i | \(0.190855\pi\) | ||||
−0.825567 | + | 0.564304i | \(0.809145\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.11684 | 0.279361 | ||||||||
\(650\) | 21.0951 | + | 9.50744i | 0.827418 | + | 0.372913i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.0000 | + | 10.3923i | 0.704934 | + | 0.406994i | ||||
\(653\) | 5.48913 | + | 3.16915i | 0.214806 | + | 0.124018i | 0.603543 | − | 0.797330i | \(-0.293755\pi\) |
−0.388737 | + | 0.921349i | \(0.627089\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.55842 | − | 7.25061i | 0.256259 | − | 0.283305i | ||||
\(656\) | 2.74456 | 0.107157 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 5.15848i | − | 0.201099i | ||||||
\(659\) | 10.6277 | + | 18.4077i | 0.413997 | + | 0.717064i | 0.995323 | − | 0.0966070i | \(-0.0307990\pi\) |
−0.581325 | + | 0.813671i | \(0.697466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.61684 | − | 13.1928i | 0.296261 | − | 0.513139i | −0.679017 | − | 0.734123i | \(-0.737594\pi\) |
0.975277 | + | 0.220984i | \(0.0709269\pi\) | |||||||
\(662\) | −6.25544 | − | 3.61158i | −0.243124 | − | 0.140368i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.0000 | − | 27.7128i | −0.620920 | − | 1.07547i | ||||
\(665\) | −2.74456 | + | 0.884861i | −0.106430 | + | 0.0343134i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 9.10268i | − | 0.352457i | ||||||
\(668\) | 16.1168 | − | 9.30506i | 0.623579 | − | 0.360024i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.2337 | + | 4.34896i | 0.781696 | + | 0.168015i | ||||
\(671\) | 20.4891 | − | 35.4882i | 0.790974 | − | 1.37001i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.17527 | − | 5.29734i | 0.353681 | − | 0.204198i | −0.312625 | − | 0.949877i | \(-0.601208\pi\) |
0.666305 | + | 0.745679i | \(0.267875\pi\) | |||||||
\(674\) | −5.48913 | −0.211433 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.9783 | −1.11455 | ||||||||
\(677\) | 22.9783 | − | 13.2665i | 0.883126 | − | 0.509873i | 0.0114381 | − | 0.999935i | \(-0.496359\pi\) |
0.871688 | + | 0.490062i | \(0.163026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.23369 | + | 3.86886i | −0.0857211 | + | 0.148473i | ||||
\(680\) | 4.62772 | + | 0.994667i | 0.177465 | + | 0.0381437i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.1168 | + | 11.0371i | −0.732022 | + | 0.422633i | ||||
\(683\) | − | 27.1229i | − | 1.03783i | −0.854826 | − | 0.518915i | \(-0.826336\pi\) | ||
0.854826 | − | 0.518915i | \(-0.173664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.5475 | − | 9.84868i | 1.16716 | − | 0.376299i | ||||
\(686\) | 2.74456 | + | 4.75372i | 0.104788 | + | 0.181498i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.88316 | − | 1.08724i | −0.0717947 | − | 0.0414507i | ||||
\(689\) | 34.9783 | − | 60.5841i | 1.33257 | − | 2.30807i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.8614 | − | 39.5971i | −0.869689 | − | 1.50635i | −0.862315 | − | 0.506373i | \(-0.830986\pi\) |
−0.00737407 | − | 0.999973i | \(-0.502347\pi\) | |||||||
\(692\) | 15.3484i | 0.583459i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.27719 | 0.0864408 | ||||||||
\(695\) | −16.6753 | + | 18.4352i | −0.632529 | + | 0.699287i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.00000 | − | 1.73205i | −0.113633 | − | 0.0656061i | ||||
\(698\) | −18.2554 | − | 10.5398i | −0.690978 | − | 0.398937i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.76631 | + | 21.6695i | −0.369132 | + | 0.819029i | ||||
\(701\) | 17.2337 | 0.650907 | 0.325454 | − | 0.945558i | \(-0.394483\pi\) | ||||
0.325454 | + | 0.945558i | \(0.394483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.884861i | − | 0.0333732i | ||||||
\(704\) | −7.37228 | − | 12.7692i | −0.277853 | − | 0.481256i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.744563 | − | 1.28962i | 0.0280220 | − | 0.0485355i | ||||
\(707\) | 49.1168 | + | 28.3576i | 1.84723 | + | 1.06650i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.1753 | + | 45.3369i | 0.983033 | + | 1.70266i | 0.650372 | + | 0.759616i | \(0.274613\pi\) |
0.332661 | + | 0.943046i | \(0.392053\pi\) | |||||||
\(710\) | −22.1168 | + | 7.13058i | −0.830030 | + | 0.267606i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.01544i | 0.300391i | ||||||||
\(713\) | −8.74456 | + | 5.04868i | −0.327486 | + | 0.189074i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | − | 55.8304i | 0.448775 | − | 2.08794i | ||||
\(716\) | −3.35053 | + | 5.80329i | −0.125215 | + | 0.216879i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.46738 | − | 4.31129i | 0.278680 | − | 0.160896i | ||||
\(719\) | −10.8832 | −0.405873 | −0.202937 | − | 0.979192i | \(-0.565049\pi\) | ||||
−0.202937 | + | 0.979192i | \(0.565049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | −12.9416 | + | 7.47182i | −0.481636 | + | 0.278072i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.51087 | − | 16.4733i | 0.353469 | − | 0.612226i | ||||
\(725\) | −2.87228 | − | 28.5788i | −0.106674 | − | 1.06139i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.3505 | − | 24.4511i | 1.57069 | − | 0.906841i | 0.574610 | − | 0.818427i | \(-0.305154\pi\) |
0.996084 | − | 0.0884137i | \(-0.0281798\pi\) | |||||||
\(728\) | 54.0607i | 2.00362i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.29211 | − | 4.00772i | −0.0478231 | − | 0.148332i | ||||
\(731\) | 1.37228 | + | 2.37686i | 0.0507557 | + | 0.0879114i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.2337 | − | 8.21782i | −0.525733 | − | 0.303532i | 0.213544 | − | 0.976933i | \(-0.431499\pi\) |
−0.739277 | + | 0.673401i | \(0.764833\pi\) | |||||||
\(734\) | −6.51087 | + | 11.2772i | −0.240321 | + | 0.416248i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.62772 | − | 8.01544i | −0.170580 | − | 0.295453i | ||||
\(737\) | − | 51.0767i | − | 1.88143i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.62772 | −0.207019 | −0.103509 | − | 0.994628i | \(-0.533007\pi\) | ||||
−0.103509 | + | 0.994628i | \(0.533007\pi\) | |||||||
\(740\) | −5.40895 | − | 4.89258i | −0.198837 | − | 0.179855i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.4674 | − | 16.4356i | −1.04507 | − | 0.603372i | ||||
\(743\) | 8.13859 | + | 4.69882i | 0.298576 | + | 0.172383i | 0.641803 | − | 0.766870i | \(-0.278187\pi\) |
−0.343227 | + | 0.939252i | \(0.611520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9416 | + | 17.6241i | −0.584054 | + | 0.645696i | ||||
\(746\) | 6.51087 | 0.238380 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4.75372i | − | 0.173813i | ||||||
\(749\) | −22.9783 | − | 39.7995i | −0.839607 | − | 1.45424i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8614 | + | 18.8125i | −0.396338 | + | 0.686478i | −0.993271 | − | 0.115813i | \(-0.963053\pi\) |
0.596933 | + | 0.802291i | \(0.296386\pi\) | |||||||
\(752\) | −1.02175 | − | 0.589907i | −0.0372594 | − | 0.0215117i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.2921 | − | 23.0226i | −0.484070 | − | 0.838434i | ||||
\(755\) | 0.605969 | + | 1.87953i | 0.0220535 | + | 0.0684030i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 41.5692i | − | 1.51086i | −0.655230 | − | 0.755429i | \(-0.727428\pi\) | ||
0.655230 | − | 0.755429i | \(-0.272572\pi\) | |||||||
\(758\) | 1.02175 | − | 0.589907i | 0.0371116 | − | 0.0214264i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.467376 | − | 2.17448i | 0.0169535 | − | 0.0788767i | ||||
\(761\) | −16.2446 | + | 28.1364i | −0.588865 | + | 1.01994i | 0.405517 | + | 0.914088i | \(0.367092\pi\) |
−0.994381 | + | 0.105856i | \(0.966242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.2337 | + | 16.8781i | −1.05833 | + | 0.611027i | ||||
\(764\) | 10.4674 | 0.378696 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.78806 | 0.317526 | ||||||||
\(767\) | 8.23369 | − | 4.75372i | 0.297301 | − | 0.171647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.24456 | + | 14.2800i | −0.297307 | + | 0.514950i | −0.975519 | − | 0.219916i | \(-0.929422\pi\) |
0.678212 | + | 0.734866i | \(0.262755\pi\) | |||||||
\(770\) | −26.2337 | − | 5.63858i | −0.945396 | − | 0.203200i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.6426 | + | 7.87658i | −0.491009 | + | 0.283484i | ||||
\(773\) | 21.5769i | 0.776067i | 0.921645 | + | 0.388034i | \(0.126846\pi\) | ||||
−0.921645 | + | 0.388034i | \(0.873154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.8614 | + | 18.6101i | −0.928969 | + | 0.668496i | ||||
\(776\) | −1.72281 | − | 2.98400i | −0.0618454 | − | 0.107119i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.350532 | − | 0.202380i | −0.0125672 | − | 0.00725566i | ||||
\(779\) | −0.813859 | + | 1.40965i | −0.0291595 | + | 0.0505058i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.6753 | + | 49.6670i | 1.02608 | + | 1.77723i | ||||
\(782\) | 0.994667i | 0.0355692i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.13859 | −0.112093 | ||||||||
\(785\) | −19.0367 | − | 17.2193i | −0.679448 | − | 0.614584i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.0000 | − | 8.66025i | −0.534692 | − | 0.308705i | 0.208233 | − | 0.978079i | \(-0.433229\pi\) |
−0.742925 | + | 0.669375i | \(0.766562\pi\) | |||||||
\(788\) | −7.64264 | − | 4.41248i | −0.272258 | − | 0.157188i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.86141 | − | 8.01544i | −0.315275 | − | 0.285177i | ||||
\(791\) | 21.2554 | 0.755756 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 54.7431i | − | 1.94399i | ||||||
\(794\) | 6.94158 | + | 12.0232i | 0.246347 | + | 0.426686i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.9783 | − | 19.0149i | 0.389114 | − | 0.673965i | ||||
\(797\) | 22.1970 | + | 12.8155i | 0.786259 | + | 0.453947i | 0.838644 | − | 0.544680i | \(-0.183349\pi\) |
−0.0523851 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.744563 | + | 1.28962i | 0.0263407 | + | 0.0456235i | ||||
\(800\) | −17.0584 | − | 23.7051i | −0.603106 | − | 0.838102i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.1021i | 0.709831i | ||||||||
\(803\) | −9.00000 | + | 5.19615i | −0.317603 | + | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | − | 2.57924i | −0.422944 | − | 0.0909063i | ||||
\(806\) | −14.7446 | + | 25.5383i | −0.519355 | + | 0.899549i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −37.8832 | + | 21.8719i | −1.33272 | + | 0.769449i | ||||
\(809\) | −21.0000 | −0.738321 | −0.369160 | − | 0.929366i | \(-0.620355\pi\) | ||||
−0.369160 | + | 0.929366i | \(0.620355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.8832 | 0.873766 | 0.436883 | − | 0.899518i | \(-0.356082\pi\) | ||||
0.436883 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(812\) | 23.6495 | − | 13.6540i | 0.829934 | − | 0.479162i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.11684 | − | 7.13058i | 0.144295 | − | 0.249927i | ||||
\(815\) | −7.11684 | + | 33.1113i | −0.249292 | + | 1.15984i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.11684 | − | 0.644810i | 0.0390734 | − | 0.0225591i | ||||
\(818\) | − | 18.1128i | − | 0.633299i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.11684 | + | 12.7692i | 0.143766 | + | 0.445919i | ||||
\(821\) | 20.3614 | + | 35.2670i | 0.710618 | + | 1.23083i | 0.964625 | + | 0.263624i | \(0.0849179\pi\) |
−0.254007 | + | 0.967202i | \(0.581749\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.76631 | + | 2.17448i | 0.131285 | + | 0.0757977i | 0.564204 | − | 0.825635i | \(-0.309183\pi\) |
−0.432919 | + | 0.901433i | \(0.642516\pi\) | |||||||
\(824\) | 9.25544 | − | 16.0309i | 0.322428 | − | 0.558462i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.23369 | − | 3.86886i | −0.0777199 | − | 0.134615i | ||||
\(827\) | − | 22.3692i | − | 0.777853i | −0.921269 | − | 0.388926i | \(-0.872846\pi\) | ||
0.921269 | − | 0.388926i | \(-0.127154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.3505 | 0.810997 | 0.405499 | − | 0.914096i | \(-0.367098\pi\) | ||||
0.405499 | + | 0.914096i | \(0.367098\pi\) | |||||||
\(830\) | 14.2337 | − | 15.7359i | 0.494059 | − | 0.546202i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.0584 | − | 9.84868i | −0.591394 | − | 0.341442i | ||||
\(833\) | 3.43070 | + | 1.98072i | 0.118867 | + | 0.0686278i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.4891 | + | 20.3422i | 0.778268 | + | 0.703970i | ||||
\(836\) | −2.23369 | −0.0772537 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.8564i | 0.478662i | ||||||||
\(839\) | −22.9307 | − | 39.7171i | −0.791656 | − | 1.37119i | −0.924941 | − | 0.380110i | \(-0.875886\pi\) |
0.133285 | − | 0.991078i | \(-0.457447\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00000 | + | 3.46410i | −0.0689655 | + | 0.119452i | ||||
\(842\) | 14.9198 | + | 8.61397i | 0.514171 | + | 0.296857i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.27719 | + | 2.21215i | 0.0439626 | + | 0.0761454i | ||||
\(845\) | −14.4891 | − | 44.9407i | −0.498441 | − | 1.54601i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.1176i | 0.966131i | ||||||||
\(848\) | −6.51087 | + | 3.75906i | −0.223584 | + | 0.129086i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.313859 | + | 3.12286i | 0.0107653 | + | 0.107113i | ||||
\(851\) | 1.88316 | − | 3.26172i | 0.0645538 | − | 0.111810i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.35053 | + | 5.39853i | −0.320156 | + | 0.184842i | −0.651462 | − | 0.758681i | \(-0.725844\pi\) |
0.331306 | + | 0.943523i | \(0.392511\pi\) | |||||||
\(854\) | −25.7228 | −0.880217 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.4456 | 1.21151 | ||||||||
\(857\) | −42.7812 | + | 24.6998i | −1.46138 | + | 0.843728i | −0.999075 | − | 0.0429939i | \(-0.986310\pi\) |
−0.462304 | + | 0.886722i | \(0.652977\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.1644 | − | 41.8540i | 0.824478 | − | 1.42804i | −0.0778389 | − | 0.996966i | \(-0.524802\pi\) |
0.902317 | − | 0.431073i | \(-0.141865\pi\) | |||||||
\(860\) | 2.23369 | − | 10.3923i | 0.0761681 | − | 0.354375i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.8832 | + | 13.2116i | −0.779403 | + | 0.449989i | ||||
\(863\) | − | 16.7306i | − | 0.569516i | −0.958599 | − | 0.284758i | \(-0.908087\pi\) | ||
0.958599 | − | 0.284758i | \(-0.0919133\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.8030 | + | 7.67420i | −0.809326 | + | 0.260931i | ||||
\(866\) | 5.05842 | + | 8.76144i | 0.171892 | + | 0.297726i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.2337 | − | 15.1460i | −0.890429 | − | 0.514090i | ||||
\(869\) | −14.7446 | + | 25.5383i | −0.500175 | + | 0.866329i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.1168 | − | 59.0921i | −1.15601 | − | 2.00226i | ||||
\(872\) | − | 26.0357i | − | 0.881679i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.467376 | 0.0158092 | ||||||||
\(875\) | −38.4891 | − | 4.31129i | −1.30117 | − | 0.145748i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.941578 | + | 0.543620i | 0.0317948 | + | 0.0183568i | 0.515813 | − | 0.856701i | \(-0.327490\pi\) |
−0.484018 | + | 0.875058i | \(0.660823\pi\) | |||||||
\(878\) | 21.8614 | + | 12.6217i | 0.737787 | + | 0.425961i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.11684 | + | 4.55134i | −0.138779 | + | 0.153426i | ||||
\(881\) | 10.8832 | 0.366663 | 0.183331 | − | 0.983051i | \(-0.441312\pi\) | ||||
0.183331 | + | 0.983051i | \(0.441312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 54.9455i | − | 1.84906i | −0.381104 | − | 0.924532i | \(-0.624456\pi\) | ||
0.381104 | − | 0.924532i | \(-0.375544\pi\) | |||||||
\(884\) | −3.17527 | − | 5.49972i | −0.106796 | − | 0.184976i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.51087 | + | 14.7413i | −0.285928 | + | 0.495243i | ||||
\(887\) | −37.9783 | − | 21.9268i | −1.27518 | − | 0.736228i | −0.299226 | − | 0.954182i | \(-0.596728\pi\) |
−0.975959 | + | 0.217954i | \(0.930062\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | − | 31.1769i | −0.603701 | − | 1.04564i | ||||
\(890\) | −5.05842 | + | 1.63086i | −0.169559 | + | 0.0546666i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.5383i | 0.855087i | ||||||||
\(893\) | 0.605969 | − | 0.349857i | 0.0202780 | − | 0.0117075i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.6753 | − | 2.29451i | −0.356835 | − | 0.0766969i | ||||
\(896\) | 15.6060 | − | 27.0303i | 0.521359 | − | 0.903020i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.46738 | − | 4.31129i | 0.249190 | − | 0.143870i | ||||
\(899\) | 36.6060 | 1.22088 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.48913 | 0.316129 | ||||||||
\(902\) | −13.1168 | + | 7.57301i | −0.436743 | + | 0.252154i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.19702 | + | 14.1976i | −0.272629 | + | 0.472207i | ||||
\(905\) | 30.3030 | + | 6.51322i | 1.00731 | + | 0.216507i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7663 | + | 9.10268i | −0.523512 | + | 0.302250i | −0.738370 | − | 0.674396i | \(-0.764404\pi\) |
0.214858 | + | 0.976645i | \(0.431071\pi\) | |||||||
\(908\) | 18.6101i | 0.617599i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −34.1168 | + | 10.9994i | −1.13096 | + | 0.364628i | ||||
\(911\) | 9.30298 | + | 16.1132i | 0.308222 | + | 0.533856i | 0.977973 | − | 0.208730i | \(-0.0669328\pi\) |
−0.669752 | + | 0.742585i | \(0.733599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.3505 | − | 26.1831i | −1.50088 | − | 0.866536i | ||||
\(914\) | 8.31386 | − | 14.4000i | 0.274998 | − | 0.476311i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.0802 | − | 20.9235i | −0.399140 | − | 0.691331i | ||||
\(917\) | 15.1460i | 0.500166i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.3505 | −1.82585 | −0.912923 | − | 0.408132i | \(-0.866180\pi\) | ||||
−0.912923 | + | 0.408132i | \(0.866180\pi\) | |||||||
\(920\) | 6.35053 | − | 7.02078i | 0.209371 | − | 0.231468i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.5326 | − | 9.54511i | −0.544473 | − | 0.314352i | ||||
\(923\) | 66.3505 | + | 38.3075i | 2.18395 | + | 1.26091i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.88316 | − | 10.8347i | 0.160557 | − | 0.356244i | ||||
\(926\) | 10.9783 | 0.360768 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.5538i | 1.10146i | ||||||||
\(929\) | −1.75544 | − | 3.04051i | −0.0575940 | − | 0.0997558i | 0.835791 | − | 0.549048i | \(-0.185010\pi\) |
−0.893385 | + | 0.449292i | \(0.851676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.930703 | − | 1.61203i | 0.0305026 | − | 0.0528320i | ||||
\(932\) | 7.29211 | + | 4.21010i | 0.238861 | + | 0.137906i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.25544 | + | 12.5668i | 0.237405 | + | 0.411198i | ||||
\(935\) | 7.37228 | − | 2.37686i | 0.241099 | − | 0.0777317i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.2766i | − | 0.727745i | −0.931449 | − | 0.363873i | \(-0.881454\pi\) | ||
0.931449 | − | 0.363873i | \(-0.118546\pi\) | |||||||
\(938\) | −27.7663 | + | 16.0309i | −0.906602 | + | 0.523427i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.21194 | − | 5.63858i | 0.0395291 | − | 0.183910i | ||||
\(941\) | 3.43070 | − | 5.94215i | 0.111838 | − | 0.193709i | −0.804674 | − | 0.593718i | \(-0.797660\pi\) |
0.916511 | + | 0.400009i | \(0.130993\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | + | 3.46410i | −0.195387 | + | 0.112807i | ||||
\(944\) | −1.02175 | −0.0332551 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | −37.3723 | + | 21.5769i | −1.21444 | + | 0.701155i | −0.963722 | − | 0.266906i | \(-0.913999\pi\) |
−0.250714 | + | 0.968061i | \(0.580665\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.94158 | + | 12.0232i | −0.225333 | + | 0.390288i | ||||
\(950\) | 1.46738 | − | 0.147477i | 0.0476080 | − | 0.00478478i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.35053 | + | 3.66648i | −0.205822 | + | 0.118831i | ||||
\(953\) | 25.0410i | 0.811158i | 0.914060 | + | 0.405579i | \(0.132930\pi\) | ||||
−0.914060 | + | 0.405579i | \(0.867070\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.23369 | + | 16.2333i | 0.169358 | + | 0.525296i | ||||
\(956\) | 15.7663 | + | 27.3081i | 0.509919 | + | 0.883206i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.7663 | + | 7.37063i | 0.412461 | + | 0.238134i | ||||
\(959\) | −24.8614 | + | 43.0612i | −0.802817 | + | 1.39052i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.80298 | − | 8.31901i | −0.154935 | − | 0.268355i | ||||
\(962\) | − | 10.9994i | − | 0.354636i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.07335 | −0.0667780 | ||||||||
\(965\) | −19.0367 | − | 17.2193i | −0.612812 | − | 0.554309i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.4674 | + | 21.6318i | 1.20487 | + | 0.695632i | 0.961634 | − | 0.274335i | \(-0.0884579\pi\) |
0.243236 | + | 0.969967i | \(0.421791\pi\) | |||||||
\(968\) | −18.7812 | − | 10.8434i | −0.603652 | − | 0.348519i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.53262 | − | 1.69438i | 0.0492096 | − | 0.0544033i | ||||
\(971\) | 41.5842 | 1.33450 | 0.667251 | − | 0.744833i | \(-0.267471\pi\) | ||||
0.667251 | + | 0.744833i | \(0.267471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 38.5099i | − | 1.23457i | ||||||
\(974\) | −3.76631 | − | 6.52344i | −0.120680 | − | 0.209025i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.94158 | + | 5.09496i | −0.0941576 | + | 0.163086i | ||||
\(977\) | −24.5109 | − | 14.1514i | −0.784172 | − | 0.452742i | 0.0537346 | − | 0.998555i | \(-0.482888\pi\) |
−0.837907 | + | 0.545813i | \(0.816221\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.55842 | + | 11.3595i | 0.209608 | + | 0.363052i | ||||
\(980\) | −4.70789 | − | 14.6024i | −0.150388 | − | 0.466457i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 25.0582i | − | 0.799640i | ||||||
\(983\) | 43.6277 | − | 25.1885i | 1.39151 | − | 0.803388i | 0.398026 | − | 0.917374i | \(-0.369695\pi\) |
0.993482 | + | 0.113987i | \(0.0363621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.02175 | − | 14.0588i | 0.0962809 | − | 0.447950i | ||||
\(986\) | 1.80298 | − | 3.12286i | 0.0574187 | − | 0.0994522i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.58422 | + | 1.49200i | −0.0822150 | + | 0.0474668i | ||||
\(989\) | 5.48913 | 0.174544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.6060 | 1.22636 | 0.613180 | − | 0.789944i | \(-0.289890\pi\) | ||||
0.613180 | + | 0.789944i | \(0.289890\pi\) | |||||||
\(992\) | 32.2337 | − | 18.6101i | 1.02342 | − | 0.590872i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.0000 | − | 31.1769i | 0.570925 | − | 0.988872i | ||||
\(995\) | 34.9783 | + | 7.51811i | 1.10889 | + | 0.238340i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.2921 | + | 30.1909i | −1.65611 | + | 0.956154i | −0.681622 | + | 0.731704i | \(0.738725\pi\) |
−0.974486 | + | 0.224450i | \(0.927942\pi\) | |||||||
\(998\) | 19.3098i | 0.611242i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.2.j.b.109.2 | 4 | ||
3.2 | odd | 2 | 405.2.j.d.109.1 | 4 | |||
5.4 | even | 2 | 405.2.j.e.109.1 | 4 | |||
9.2 | odd | 6 | 405.2.j.a.379.2 | 4 | |||
9.4 | even | 3 | 405.2.b.a.244.3 | yes | 4 | ||
9.5 | odd | 6 | 405.2.b.b.244.2 | yes | 4 | ||
9.7 | even | 3 | 405.2.j.e.379.1 | 4 | |||
15.14 | odd | 2 | 405.2.j.a.109.2 | 4 | |||
45.4 | even | 6 | 405.2.b.a.244.2 | ✓ | 4 | ||
45.13 | odd | 12 | 2025.2.a.w.1.3 | 4 | |||
45.14 | odd | 6 | 405.2.b.b.244.3 | yes | 4 | ||
45.22 | odd | 12 | 2025.2.a.w.1.2 | 4 | |||
45.23 | even | 12 | 2025.2.a.x.1.2 | 4 | |||
45.29 | odd | 6 | 405.2.j.d.379.1 | 4 | |||
45.32 | even | 12 | 2025.2.a.x.1.3 | 4 | |||
45.34 | even | 6 | inner | 405.2.j.b.379.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.b.a.244.2 | ✓ | 4 | 45.4 | even | 6 | ||
405.2.b.a.244.3 | yes | 4 | 9.4 | even | 3 | ||
405.2.b.b.244.2 | yes | 4 | 9.5 | odd | 6 | ||
405.2.b.b.244.3 | yes | 4 | 45.14 | odd | 6 | ||
405.2.j.a.109.2 | 4 | 15.14 | odd | 2 | |||
405.2.j.a.379.2 | 4 | 9.2 | odd | 6 | |||
405.2.j.b.109.2 | 4 | 1.1 | even | 1 | trivial | ||
405.2.j.b.379.2 | 4 | 45.34 | even | 6 | inner | ||
405.2.j.d.109.1 | 4 | 3.2 | odd | 2 | |||
405.2.j.d.379.1 | 4 | 45.29 | odd | 6 | |||
405.2.j.e.109.1 | 4 | 5.4 | even | 2 | |||
405.2.j.e.379.1 | 4 | 9.7 | even | 3 | |||
2025.2.a.w.1.2 | 4 | 45.22 | odd | 12 | |||
2025.2.a.w.1.3 | 4 | 45.13 | odd | 12 | |||
2025.2.a.x.1.2 | 4 | 45.23 | even | 12 | |||
2025.2.a.x.1.3 | 4 | 45.32 | even | 12 |