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: | \(1\) |
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 | 379.2 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.379 |
Dual form | 405.2.j.a.109.2 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.686141 | + | 0.396143i | 0.485175 | + | 0.280116i | 0.722570 | − | 0.691297i | \(-0.242960\pi\) |
−0.237396 | + | 0.971413i | \(0.576294\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.686141 | − | 1.18843i | −0.343070 | − | 0.594215i | ||||
\(5\) | −1.50000 | + | 1.65831i | −0.670820 | + | 0.741620i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | − | 1.73205i | −1.13389 | − | 0.654654i | −0.188982 | − | 0.981981i | \(-0.560519\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | − | 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 | 0.321691 | + | 0.946845i | \(0.395749\pi\) |
−0.980837 | + | 0.194830i | \(0.937584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.05842 | + | 2.92048i | −1.40295 | + | 0.809996i | −0.994695 | − | 0.102870i | \(-0.967197\pi\) |
−0.408259 | + | 0.912866i | \(0.633864\pi\) | |||||||
\(14\) | −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 | \(-0.969370\pi\) | ||
0.995374 | − | 0.0960789i | \(-0.0306301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.372281 | 0.0854072 | 0.0427036 | − | 0.999088i | \(-0.486403\pi\) | ||||
0.0427036 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(20\) | 3.00000 | + | 0.644810i | 0.670820 | + | 0.144184i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | + | 1.73205i | −0.639602 | + | 0.369274i | ||||
\(23\) | 1.37228 | − | 0.792287i | 0.286140 | − | 0.165203i | −0.350060 | − | 0.936727i | \(-0.613839\pi\) |
0.636200 | + | 0.771524i | \(0.280505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 4.97494i | −0.100000 | − | 0.994987i | ||||
\(26\) | −4.62772 | −0.907570 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.75372i | 0.898369i | ||||||||
\(29\) | 2.87228 | − | 4.97494i | 0.533369 | − | 0.923823i | −0.465871 | − | 0.884853i | \(-0.654259\pi\) |
0.999240 | − | 0.0389701i | \(-0.0124077\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.18614 | − | 5.51856i | −0.572248 | − | 0.991162i | −0.996335 | − | 0.0855407i | \(-0.972738\pi\) |
0.424087 | − | 0.905621i | \(-0.360595\pi\) | |||||||
\(32\) | −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 | ||||||||
\(40\) | 4.43070 | + | 4.00772i | 0.700556 | + | 0.633676i | ||||
\(41\) | 2.18614 | + | 3.78651i | 0.341418 | + | 0.591353i | 0.984696 | − | 0.174279i | \(-0.0557596\pi\) |
−0.643278 | + | 0.765632i | \(0.722426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | − | 1.73205i | −0.457496 | − | 0.264135i | 0.253495 | − | 0.967337i | \(-0.418420\pi\) |
−0.710991 | + | 0.703201i | \(0.751753\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25544 | 0.185104 | ||||||||
\(47\) | 1.62772 | + | 0.939764i | 0.237427 | + | 0.137079i | 0.613994 | − | 0.789311i | \(-0.289562\pi\) |
−0.376566 | + | 0.926390i | \(0.622895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.50000 | + | 4.33013i | 0.357143 | + | 0.618590i | ||||
\(50\) | 1.62772 | − | 3.61158i | 0.230194 | − | 0.510754i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.94158 | + | 4.00772i | 0.962624 | + | 0.555771i | ||||
\(53\) | 11.9769i | 1.64515i | 0.568656 | + | 0.822575i | \(0.307464\pi\) | ||||
−0.568656 | + | 0.822575i | \(0.692536\pi\) | |||||||
\(54\) | 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 | \(-0.200457\pi\) |
−0.914128 | + | 0.405425i | \(0.867123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.68614 | + | 8.11663i | −0.599999 | + | 1.03923i | 0.392822 | + | 0.919615i | \(0.371499\pi\) |
−0.992820 | + | 0.119614i | \(0.961834\pi\) | |||||||
\(62\) | − | 5.04868i | − | 0.641182i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.37228 | −0.421535 | ||||||||
\(65\) | 2.74456 | − | 12.7692i | 0.340421 | − | 1.58382i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1168 | − | 5.84096i | 1.23597 | − | 0.713587i | 0.267701 | − | 0.963502i | \(-0.413736\pi\) |
0.968268 | + | 0.249915i | \(0.0804026\pi\) | |||||||
\(68\) | −0.941578 | + | 0.543620i | −0.114183 | + | 0.0659236i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | + | 1.28962i | 0.717137 | + | 0.154139i | ||||
\(71\) | −13.1168 | −1.55668 | −0.778341 | − | 0.627841i | \(-0.783939\pi\) | ||||
−0.778341 | + | 0.627841i | \(0.783939\pi\) | |||||||
\(72\) | 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 | −0.611565 | − | 0.791194i | \(-0.709460\pi\) |
0.990977 | + | 0.134034i | \(0.0427932\pi\) | |||||||
\(80\) | −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 | −0.192446 | − | 0.981308i | \(-0.561642\pi\) |
−0.946060 | + | 0.323991i | \(0.894975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.31386 | + | 1.18843i | 0.142508 | + | 0.128903i | ||||
\(86\) | −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 | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 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 | ||||
\(95\) | −0.558422 | + | 0.617359i | −0.0572929 | + | 0.0633397i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.11684 | + | 0.644810i | 0.113398 | + | 0.0654706i | 0.555626 | − | 0.831432i | \(-0.312478\pi\) |
−0.442228 | + | 0.896903i | \(0.645812\pi\) | |||||||
\(98\) | 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 | 0.0950981 | + | 0.995468i | \(0.469684\pi\) |
−0.909650 | + | 0.415377i | \(0.863650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | − | 3.46410i | 0.591198 | − | 0.341328i | −0.174373 | − | 0.984680i | \(-0.555790\pi\) |
0.765571 | + | 0.643352i | \(0.222457\pi\) | |||||||
\(104\) | 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 | \(0.221588\pi\) | ||||
−0.767323 | + | 0.641260i | \(0.778412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.74456 | −0.933360 | −0.466680 | − | 0.884426i | \(-0.654550\pi\) | ||||
−0.466680 | + | 0.884426i | \(0.654550\pi\) | |||||||
\(110\) | 1.62772 | − | 7.57301i | 0.155197 | − | 0.722058i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.88316 | − | 1.08724i | 0.177942 | − | 0.102735i | ||||
\(113\) | 5.31386 | − | 3.06796i | 0.499886 | − | 0.288609i | −0.228781 | − | 0.973478i | \(-0.573474\pi\) |
0.728666 | + | 0.684869i | \(0.240140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.744563 | + | 3.46410i | −0.0694308 | + | 0.323029i | ||||
\(116\) | −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 | ||||||||
\(130\) | 6.94158 | − | 7.67420i | 0.608817 | − | 0.673072i | ||||
\(131\) | 2.18614 | + | 3.78651i | 0.191004 | + | 0.330829i | 0.945583 | − | 0.325380i | \(-0.105492\pi\) |
−0.754579 | + | 0.656209i | \(0.772159\pi\) | |||||||
\(132\) | 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 | −0.136034 | − | 0.990704i | \(-0.543436\pi\) |
−0.925992 | + | 0.377543i | \(0.876769\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.55842 | + | 9.62747i | 0.471459 | + | 0.816591i | 0.999467 | − | 0.0326483i | \(-0.0103941\pi\) |
−0.528008 | + | 0.849240i | \(0.677061\pi\) | |||||||
\(140\) | −7.88316 | − | 7.13058i | −0.666248 | − | 0.602644i | ||||
\(141\) | 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 | \(-0.310034\pi\) |
−0.997322 | + | 0.0731305i | \(0.976701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.441578 | + | 0.764836i | −0.0359351 | + | 0.0622414i | −0.883434 | − | 0.468556i | \(-0.844774\pi\) |
0.847499 | + | 0.530798i | \(0.178108\pi\) | |||||||
\(152\) | − | 0.994667i | − | 0.0806781i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | 0.966988 | ||||||||
\(155\) | 13.9307 | + | 2.99422i | 1.11894 | + | 0.240502i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.94158 | + | 5.73977i | −0.793424 | + | 0.458084i | −0.841167 | − | 0.540776i | \(-0.818131\pi\) |
0.0477424 | + | 0.998860i | \(0.484797\pi\) | |||||||
\(158\) | 4.62772 | − | 2.67181i | 0.368162 | − | 0.212558i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.74456 | − | 12.7692i | 0.216977 | − | 1.00949i | ||||
\(161\) | −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 | −0.880052 | − | 0.474878i | \(-0.842492\pi\) |
−0.0287697 | + | 0.999586i | \(0.509159\pi\) | |||||||
\(168\) | 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 | 0.820768 | − | 0.571262i | \(-0.193546\pi\) |
−0.0843439 | + | 0.996437i | \(0.526879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.11684 | + | 15.7908i | −0.537983 | + | 1.19368i | ||||
\(176\) | −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 | \(-0.558416\pi\) | ||||
−0.182492 | + | 0.983207i | \(0.558416\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | 3.94158 | + | 3.56529i | 0.289791 | + | 0.262125i | ||||
\(186\) | 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 | \(-0.744337\pi\) |
0.970377 | + | 0.241595i | \(0.0776705\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.94158 | + | 5.73977i | −0.715610 | + | 0.413158i | −0.813135 | − | 0.582075i | \(-0.802241\pi\) |
0.0975245 | + | 0.995233i | \(0.468908\pi\) | |||||||
\(194\) | 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 | \(-0.926425\pi\) | ||
0.973405 | − | 0.229090i | \(-0.0735751\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | −13.2921 | + | 1.33591i | −0.939894 | + | 0.0944629i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.2337 | + | 6.48577i | −0.790400 | + | 0.456337i | ||||
\(203\) | −17.2337 | + | 9.94987i | −1.20957 | + | 0.698344i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.55842 | − | 2.05446i | −0.667589 | − | 0.143489i | ||||
\(206\) | 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 | 0.896282 | − | 0.443484i | \(-0.146258\pi\) |
−0.832210 | + | 0.554461i | \(0.812925\pi\) | |||||||
\(212\) | 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 | ||||||||
\(220\) | −9.00000 | + | 9.94987i | −0.606780 | + | 0.670820i | ||||
\(221\) | 2.31386 | + | 4.00772i | 0.155647 | + | 0.269589i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.1168 | − | 9.30506i | −1.07926 | − | 0.623113i | −0.148566 | − | 0.988902i | \(-0.547466\pi\) |
−0.930698 | + | 0.365789i | \(0.880799\pi\) | |||||||
\(224\) | 20.2337 | 1.35192 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.86141 | 0.323376 | ||||||||
\(227\) | 11.7446 | + | 6.78073i | 0.779514 | + | 0.450053i | 0.836258 | − | 0.548336i | \(-0.184739\pi\) |
−0.0567440 | + | 0.998389i | \(0.518072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.80298 | − | 15.2472i | −0.581718 | − | 1.00756i | −0.995276 | − | 0.0970868i | \(-0.969048\pi\) |
0.413558 | − | 0.910478i | \(-0.364286\pi\) | |||||||
\(230\) | −1.88316 | + | 2.08191i | −0.124172 | + | 0.137277i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.2921 | − | 7.67420i | −0.872670 | − | 0.503836i | ||||
\(233\) | 6.13592i | 0.401977i | 0.979594 | + | 0.200989i | \(0.0644154\pi\) | ||||
−0.979594 | + | 0.200989i | \(0.935585\pi\) | |||||||
\(234\) | 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 | −0.951045 | − | 0.309052i | \(-0.899988\pi\) |
0.207875 | − | 0.978155i | \(-0.433345\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.755437 | − | 1.30846i | 0.0486620 | − | 0.0842851i | −0.840668 | − | 0.541550i | \(-0.817838\pi\) |
0.889330 | + | 0.457265i | \(0.151171\pi\) | |||||||
\(242\) | − | 6.43087i | − | 0.413392i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.8614 | 0.823367 | ||||||||
\(245\) | −10.9307 | − | 2.34941i | −0.698337 | − | 0.150098i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.88316 | + | 1.08724i | −0.119822 | + | 0.0691795i | ||||
\(248\) | −14.7446 | + | 8.51278i | −0.936281 | + | 0.540562i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.54755 | + | 8.11663i | 0.224367 | + | 0.513341i | ||||
\(251\) | 20.2337 | 1.27714 | 0.638570 | − | 0.769564i | \(-0.279526\pi\) | ||||
0.638570 | + | 0.769564i | \(0.279526\pi\) | |||||||
\(252\) | 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 | −0.663541 | − | 0.748140i | \(-0.730947\pi\) |
0.316138 | + | 0.948713i | \(0.397614\pi\) | |||||||
\(258\) | 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 | 0.996025 | − | 0.0890715i | \(-0.0283900\pi\) |
0.420874 | + | 0.907119i | \(0.361723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.8614 | − | 17.9653i | −1.22008 | − | 1.10360i | ||||
\(266\) | −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 | \(-0.850139\pi\) | ||||
−0.891205 | + | 0.453601i | \(0.850139\pi\) | |||||||
\(270\) | 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 | ||||
\(275\) | 19.9307 | + | 8.98266i | 1.20187 | + | 0.541675i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.1168 | + | 11.0371i | 1.14862 | + | 0.663156i | 0.948551 | − | 0.316626i | \(-0.102550\pi\) |
0.200069 | + | 0.979782i | \(0.435883\pi\) | |||||||
\(278\) | 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 | \(-0.846366\pi\) |
0.844834 | + | 0.535029i | \(0.179699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.0000 | − | 13.8564i | 1.42665 | − | 0.823678i | 0.429797 | − | 0.902926i | \(-0.358585\pi\) |
0.996855 | + | 0.0792477i | \(0.0252518\pi\) | |||||||
\(284\) | 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 | ||||||||
\(290\) | −2.13859 | + | 9.94987i | −0.125583 | + | 0.584277i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.82473 | − | 1.63086i | 0.165305 | − | 0.0954389i | ||||
\(293\) | −0.686141 | + | 0.396143i | −0.0400848 | + | 0.0231430i | −0.519908 | − | 0.854222i | \(-0.674034\pi\) |
0.479824 | + | 0.877365i | \(0.340701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.55842 | + | 0.764836i | 0.207179 | + | 0.0445304i | ||||
\(296\) | −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 | ||||||||
\(310\) | 8.37228 | + | 7.57301i | 0.475514 | + | 0.430118i | ||||
\(311\) | −7.93070 | − | 13.7364i | −0.449709 | − | 0.778919i | 0.548658 | − | 0.836047i | \(-0.315139\pi\) |
−0.998367 | + | 0.0571282i | \(0.981806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1753 | + | 12.2255i | 1.19690 | + | 0.691029i | 0.959862 | − | 0.280472i | \(-0.0904911\pi\) |
0.237035 | + | 0.971501i | \(0.423824\pi\) | |||||||
\(314\) | −9.09509 | −0.513266 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.25544 | −0.520659 | ||||||||
\(317\) | −25.5475 | − | 14.7499i | −1.43489 | − | 0.828436i | −0.437405 | − | 0.899265i | \(-0.644102\pi\) |
−0.997488 | + | 0.0708288i | \(0.977436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5584 | + | 21.7518i | 0.703137 | + | 1.21787i | ||||
\(320\) | 5.05842 | − | 5.59230i | 0.282774 | − | 0.312619i | ||||
\(321\) | 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 | −0.963678 | − | 0.267066i | \(-0.913946\pi\) |
0.713125 | + | 0.701037i | \(0.247279\pi\) | |||||||
\(332\) | 16.4356i | 0.902023i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.7446 | −0.587916 | ||||||||
\(335\) | −5.48913 | + | 25.5383i | −0.299903 | + | 1.39531i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | − | 3.46410i | 0.326841 | − | 0.188702i | −0.327597 | − | 0.944818i | \(-0.606239\pi\) |
0.654438 | + | 0.756116i | \(0.272905\pi\) | |||||||
\(338\) | 14.4891 | − | 8.36530i | 0.788105 | − | 0.455012i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.510875 | − | 2.37686i | 0.0277061 | − | 0.128903i | ||||
\(341\) | 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 | −0.431698 | − | 0.902018i | \(-0.642085\pi\) |
0.565321 | + | 0.824871i | \(0.308752\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.3030 | + | 23.0414i | −0.712092 | + | 1.23338i | 0.251978 | + | 0.967733i | \(0.418919\pi\) |
−0.964070 | + | 0.265647i | \(0.914414\pi\) | |||||||
\(350\) | −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 | 0.542692 | − | 0.839932i | \(-0.317405\pi\) |
−0.456057 | + | 0.889951i | \(0.650739\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.6753 | − | 21.7518i | 1.04425 | − | 1.15447i | ||||
\(356\) | 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 | \(-0.592723\pi\) | ||||
−0.287196 | + | 0.957872i | \(0.592723\pi\) | |||||||
\(360\) | 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 | ||||
\(365\) | −3.94158 | − | 3.56529i | −0.206312 | − | 0.186616i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2337 | + | 8.21782i | 0.742992 | + | 0.428967i | 0.823156 | − | 0.567815i | \(-0.192211\pi\) |
−0.0801639 | + | 0.996782i | \(0.525544\pi\) | |||||||
\(368\) | 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 | \(-0.734909\pi\) |
0.304305 | + | 0.952575i | \(0.401576\pi\) | |||||||
\(374\) | 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 | \(0.487823\pi\) | |||||||
\(380\) | 1.11684 | + | 0.240051i | 0.0572929 | + | 0.0123143i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.23369 | − | 3.02167i | 0.267779 | − | 0.154602i | ||||
\(383\) | 9.60597 | − | 5.54601i | 0.490842 | − | 0.283388i | −0.234082 | − | 0.972217i | \(-0.575208\pi\) |
0.724924 | + | 0.688829i | \(0.241875\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.11684 | + | 33.1113i | −0.362708 | + | 1.68751i | ||||
\(386\) | −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 | \(-0.829211\pi\) |
0.872428 | + | 0.488742i | \(0.162544\pi\) | |||||||
\(390\) | 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 | ||||||||
\(400\) | 2.86141 | + | 1.28962i | 0.143070 | + | 0.0644810i | ||||
\(401\) | 12.6861 | + | 21.9730i | 0.633516 | + | 1.09728i | 0.986828 | + | 0.161776i | \(0.0517221\pi\) |
−0.353312 | + | 0.935506i | \(0.614945\pi\) | |||||||
\(402\) | 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 | 0.997030 | + | 0.0770150i | \(0.0245389\pi\) |
−0.431818 | + | 0.901961i | \(0.642128\pi\) | |||||||
\(410\) | −5.74456 | − | 5.19615i | −0.283704 | − | 0.256620i | ||||
\(411\) | 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 | \(-0.0261667\pi\) |
−0.569423 | + | 0.822045i | \(0.692833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.8723 | − | 18.8313i | 0.529883 | − | 0.917784i | −0.469510 | − | 0.882927i | \(-0.655569\pi\) |
0.999392 | − | 0.0348563i | \(-0.0110973\pi\) | |||||||
\(422\) | 1.47477i | 0.0717906i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 32.0000 | 1.55406 | ||||||||
\(425\) | −3.94158 | + | 0.396143i | −0.191195 | + | 0.0192158i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.1168 | − | 16.2333i | 1.36067 | − | 0.785583i | ||||
\(428\) | 15.7663 | − | 9.10268i | 0.762093 | − | 0.439995i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.00000 | + | 1.28962i | 0.289346 | + | 0.0621910i | ||||
\(431\) | 33.3505 | 1.60644 | 0.803219 | − | 0.595683i | \(-0.203119\pi\) | ||||
0.803219 | + | 0.595683i | \(0.203119\pi\) | |||||||
\(432\) | 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 | −0.182349 | − | 0.983234i | \(-0.558370\pi\) |
0.942680 | − | 0.333698i | \(-0.108297\pi\) | |||||||
\(440\) | −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 | −0.0120223 | − | 0.999928i | \(-0.503827\pi\) |
−0.871974 | + | 0.489552i | \(0.837160\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.50000 | − | 4.97494i | 0.213320 | − | 0.235835i | ||||
\(446\) | −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 | \(-0.582669\pi\) | ||||
−0.256804 | + | 0.966464i | \(0.582669\pi\) | |||||||
\(450\) | 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 | ||||
\(455\) | −30.3505 | + | 33.5538i | −1.42285 | + | 1.57303i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.1753 | − | 10.4935i | −0.850203 | − | 0.490865i | 0.0105163 | − | 0.999945i | \(-0.496652\pi\) |
−0.860719 | + | 0.509080i | \(0.829986\pi\) | |||||||
\(458\) | − | 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 | −0.436290 | − | 0.899806i | \(-0.643708\pi\) |
0.997400 | − | 0.0720652i | \(-0.0229590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.0000 | + | 6.92820i | −0.557687 | + | 0.321981i | −0.752217 | − | 0.658916i | \(-0.771015\pi\) |
0.194529 | + | 0.980897i | \(0.437682\pi\) | |||||||
\(464\) | 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 | \(-0.860709\pi\) | ||
0.905773 | − | 0.423763i | \(-0.139291\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.4674 | −1.86861 | ||||||||
\(470\) | −3.25544 | − | 0.699713i | −0.150162 | − | 0.0322754i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.76631 | + | 2.17448i | −0.173359 | + | 0.100089i | ||||
\(473\) | 13.1168 | − | 7.57301i | 0.603113 | − | 0.348208i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.186141 | − | 1.85208i | −0.00854072 | − | 0.0849791i | ||||
\(476\) | 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 | \(-0.973082\pi\) |
0.571362 | + | 0.820698i | \(0.306415\pi\) | |||||||
\(480\) | 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 | ||||||||
\(490\) | −6.56930 | − | 5.94215i | −0.296771 | − | 0.268439i | ||||
\(491\) | −15.8139 | − | 27.3904i | −0.713669 | − | 1.23611i | −0.963470 | − | 0.267815i | \(-0.913699\pi\) |
0.249801 | − | 0.968297i | \(-0.419635\pi\) | |||||||
\(492\) | 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 | −0.998574 | − | 0.0533931i | \(-0.982996\pi\) |
0.453047 | − | 0.891487i | \(-0.350337\pi\) | |||||||
\(500\) | 1.70789 | − | 15.2472i | 0.0763792 | − | 0.681876i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.8832 | + | 8.01544i | 0.619636 | + | 0.357747i | ||||
\(503\) | − | 3.16915i | − | 0.141305i | −0.997501 | − | 0.0706527i | \(-0.977492\pi\) | ||
0.997501 | − | 0.0706527i | \(-0.0225082\pi\) | |||||||
\(504\) | 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 | \(-0.170271\pi\) |
−0.871631 | + | 0.490163i | \(0.836937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.11684 | − | 7.13058i | 0.182118 | − | 0.315438i | ||||
\(512\) | − | 7.02078i | − | 0.310277i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.09509 | −0.224735 | ||||||||
\(515\) | −3.25544 | + | 15.1460i | −0.143452 | + | 0.667414i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.11684 | + | 4.10891i | −0.312998 | + | 0.180710i | ||||
\(518\) | −5.64947 | + | 3.26172i | −0.248223 | + | 0.143312i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −34.1168 | − | 7.33296i | −1.49612 | − | 0.321572i | ||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 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 | ||||||||
\(535\) | −22.0000 | − | 19.8997i | −0.951143 | − | 0.860341i | ||||
\(536\) | −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 | ||||
\(545\) | 14.6168 | − | 16.1595i | 0.626117 | − | 0.692198i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.00000 | + | 3.46410i | 0.256541 | + | 0.148114i | 0.622756 | − | 0.782416i | \(-0.286013\pi\) |
−0.366214 | + | 0.930531i | \(0.619346\pi\) | |||||||
\(548\) | 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 | \(-0.822000\pi\) | ||
0.847678 | − | 0.530511i | \(-0.178000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.2337 | 0.855794 | ||||||||
\(560\) | −1.02175 | + | 4.75372i | −0.0431768 | + | 0.200881i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.941578 | + | 0.543620i | −0.0397181 | + | 0.0229312i | ||||
\(563\) | −27.8614 | + | 16.0858i | −1.17422 | + | 0.677935i | −0.954670 | − | 0.297666i | \(-0.903792\pi\) |
−0.219548 | + | 0.975602i | \(0.570458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.88316 | + | 13.4140i | −0.121295 | + | 0.564330i | ||||
\(566\) | 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 | \(-0.974634\pi\) |
0.567352 | + | 0.823475i | \(0.307968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.06930 | − | 3.58413i | −0.0865974 | − | 0.149991i | 0.819473 | − | 0.573117i | \(-0.194266\pi\) |
−0.906071 | + | 0.423126i | \(0.860933\pi\) | |||||||
\(572\) | −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 | ||||||||
\(580\) | 11.8247 | − | 13.0727i | 0.490995 | − | 0.542816i | ||||
\(581\) | 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 | 0.170236 | − | 0.985403i | \(-0.445547\pi\) |
−0.768266 | + | 0.640130i | \(0.778880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.18614 | − | 2.05446i | −0.0488741 | − | 0.0846524i | ||||
\(590\) | 2.13859 | + | 1.93443i | 0.0880445 | + | 0.0796392i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.29211 | + | 0.746000i | 0.0531054 | + | 0.0306604i | ||||
\(593\) | − | 1.67715i | − | 0.0688722i | −0.999407 | − | 0.0344361i | \(-0.989036\pi\) | ||
0.999407 | − | 0.0344361i | \(-0.0109635\pi\) | |||||||
\(594\) | 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 | \(-0.177254\pi\) |
−0.882173 | + | 0.470925i | \(0.843920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.98913 | − | 15.5696i | 0.366674 | − | 0.635098i | −0.622369 | − | 0.782724i | \(-0.713830\pi\) |
0.989043 | + | 0.147626i | \(0.0471631\pi\) | |||||||
\(602\) | 9.50744i | 0.387494i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.21194 | 0.0493131 | ||||||||
\(605\) | 17.7446 | + | 3.81396i | 0.721419 | + | 0.155059i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.4674 | + | 21.6318i | −1.52075 | + | 0.878008i | −0.521054 | + | 0.853524i | \(0.674461\pi\) |
−0.999700 | + | 0.0244837i | \(0.992206\pi\) | |||||||
\(608\) | −1.88316 | + | 1.08724i | −0.0763721 | + | 0.0440934i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.48913 | − | 16.2333i | 0.141271 | − | 0.657266i | ||||
\(611\) | −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 | −0.815277 | − | 0.579071i | \(-0.803415\pi\) |
0.0938519 | + | 0.995586i | \(0.470082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00000 | − | 3.46410i | 0.0803868 | − | 0.139234i | −0.823029 | − | 0.567999i | \(-0.807718\pi\) |
0.903416 | + | 0.428765i | \(0.141051\pi\) | |||||||
\(620\) | −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 | ||||||||
\(625\) | −24.5000 | + | 4.97494i | −0.980000 | + | 0.198997i | ||||
\(626\) | 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 | ||||
\(635\) | 17.2337 | + | 15.5885i | 0.683898 | + | 0.618609i | ||||
\(636\) | 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 | \(-0.782970\pi\) |
0.933989 | + | 0.357303i | \(0.116304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.11684 | − | 0.644810i | 0.0440440 | − | 0.0254288i | −0.477816 | − | 0.878460i | \(-0.658572\pi\) |
0.521860 | + | 0.853031i | \(0.325238\pi\) | |||||||
\(644\) | 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 | \(-0.809145\pi\) | ||
0.825567 | − | 0.564304i | \(-0.190855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.11684 | 0.279361 | ||||||||
\(650\) | 2.31386 | + | 23.0226i | 0.0907570 | + | 0.903021i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.0000 | + | 10.3923i | −0.704934 | + | 0.406994i | ||||
\(653\) | 5.48913 | − | 3.16915i | 0.214806 | − | 0.124018i | −0.388737 | − | 0.921349i | \(-0.627089\pi\) |
0.603543 | + | 0.797330i | \(0.293755\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.55842 | − | 2.05446i | −0.373478 | − | 0.0802742i | ||||
\(656\) | −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 | \(-0.969201\pi\) |
0.581325 | + | 0.813671i | \(0.302534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.61684 | + | 13.1928i | 0.296261 | + | 0.513139i | 0.975277 | − | 0.220984i | \(-0.0709269\pi\) |
−0.679017 | + | 0.734123i | \(0.737594\pi\) | |||||||
\(662\) | −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 | ||||||||
\(670\) | −13.8832 | + | 15.3484i | −0.536353 | + | 0.592961i | ||||
\(671\) | −20.4891 | − | 35.4882i | −0.790974 | − | 1.37001i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.17527 | − | 5.29734i | −0.353681 | − | 0.204198i | 0.312625 | − | 0.949877i | \(-0.398792\pi\) |
−0.666305 | + | 0.745679i | \(0.732125\pi\) | |||||||
\(674\) | 5.48913 | 0.211433 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.9783 | −1.11455 | ||||||||
\(677\) | 22.9783 | + | 13.2665i | 0.883126 | + | 0.509873i | 0.871688 | − | 0.490062i | \(-0.163026\pi\) |
0.0114381 | + | 0.999935i | \(0.496359\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.23369 | − | 3.86886i | −0.0857211 | − | 0.148473i | ||||
\(680\) | 3.17527 | − | 3.51039i | 0.121766 | − | 0.134617i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.1168 | + | 11.0371i | 0.732022 | + | 0.422633i | ||||
\(683\) | 27.1229i | 1.03783i | 0.854826 | + | 0.518915i | \(0.173664\pi\) | ||||
−0.854826 | + | 0.518915i | \(0.826336\pi\) | |||||||
\(684\) | 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 | −0.00737407 | + | 0.999973i | \(0.502347\pi\) |
−0.862315 | + | 0.506373i | \(0.830986\pi\) | |||||||
\(692\) | − | 15.3484i | − | 0.583459i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.27719 | 0.0864408 | ||||||||
\(695\) | −24.3030 | − | 5.22360i | −0.921865 | − | 0.198143i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | − | 1.73205i | 0.113633 | − | 0.0656061i | ||||
\(698\) | −18.2554 | + | 10.5398i | −0.690978 | + | 0.398937i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 23.6495 | − | 2.37686i | 0.893866 | − | 0.0898369i | ||||
\(701\) | −17.2337 | −0.650907 | −0.325454 | − | 0.945558i | \(-0.605517\pi\) | ||||
−0.325454 | + | 0.945558i | \(0.605517\pi\) | |||||||
\(702\) | 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 | 0.332661 | − | 0.943046i | \(-0.392053\pi\) |
0.650372 | − | 0.759616i | \(-0.274613\pi\) | |||||||
\(710\) | 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 | ||||||||
\(715\) | 42.3505 | + | 38.3075i | 1.58382 | + | 1.43262i | ||||
\(716\) | 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 | \(-0.434951\pi\) | ||||
0.202937 | + | 0.979192i | \(0.434951\pi\) | |||||||
\(720\) | 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 | ||||
\(725\) | −26.1861 | − | 11.8020i | −0.972529 | − | 0.438313i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.3505 | − | 24.4511i | −1.57069 | − | 0.906841i | −0.996084 | − | 0.0884137i | \(-0.971820\pi\) |
−0.574610 | − | 0.818427i | \(-0.694846\pi\) | |||||||
\(728\) | − | 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 | \(-0.568501\pi\) |
0.739277 | + | 0.673401i | \(0.235167\pi\) | |||||||
\(734\) | 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 | \(0.533007\pi\) | |||||||
\(740\) | 1.53262 | − | 7.13058i | 0.0563404 | − | 0.262125i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.4674 | − | 16.4356i | 1.04507 | − | 0.603372i | ||||
\(743\) | 8.13859 | − | 4.69882i | 0.298576 | − | 0.172383i | −0.343227 | − | 0.939252i | \(-0.611520\pi\) |
0.641803 | + | 0.766870i | \(0.278187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.2337 | + | 4.99377i | 0.851216 | + | 0.182958i | ||||
\(746\) | −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 | 0.596933 | − | 0.802291i | \(-0.296386\pi\) |
−0.993271 | + | 0.115813i | \(0.963053\pi\) | |||||||
\(752\) | −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 | ||||||||
\(760\) | 1.64947 | + | 1.49200i | 0.0598325 | + | 0.0541205i | ||||
\(761\) | 16.2446 | + | 28.1364i | 0.588865 | + | 1.01994i | 0.994381 | + | 0.105856i | \(0.0337583\pi\) |
−0.405517 | + | 0.914088i | \(0.632908\pi\) | |||||||
\(762\) | 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 | 0.678212 | − | 0.734866i | \(-0.262755\pi\) |
−0.975519 | + | 0.219916i | \(0.929422\pi\) | |||||||
\(770\) | −18.0000 | + | 19.8997i | −0.648675 | + | 0.717137i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.6426 | + | 7.87658i | 0.491009 | + | 0.283484i | ||||
\(773\) | − | 21.5769i | − | 0.776067i | −0.921645 | − | 0.388034i | \(-0.873154\pi\) | ||
0.921645 | − | 0.388034i | \(-0.126846\pi\) | |||||||
\(774\) | 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 | ||||||||
\(785\) | 5.39403 | − | 25.0959i | 0.192521 | − | 0.895711i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | − | 8.66025i | 0.534692 | − | 0.308705i | −0.208233 | − | 0.978079i | \(-0.566771\pi\) |
0.742925 | + | 0.669375i | \(0.233438\pi\) | |||||||
\(788\) | −7.64264 | + | 4.41248i | −0.272258 | + | 0.157188i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.51087 | + | 11.6819i | −0.0893329 | + | 0.415624i | ||||
\(791\) | −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 | −0.0523851 | − | 0.998627i | \(-0.516682\pi\) |
0.838644 | + | 0.544680i | \(0.183349\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 8.23369 | − | 9.10268i | 0.290199 | − | 0.320827i | ||||
\(806\) | 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 | \(-0.379645\pi\) | ||||
0.369160 | + | 0.929366i | \(0.379645\pi\) | |||||||
\(810\) | 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 | ||||
\(815\) | 25.1168 | + | 22.7190i | 0.879805 | + | 0.795813i | ||||
\(816\) | 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 | 0.254007 | + | 0.967202i | \(0.418251\pi\) |
−0.964625 | + | 0.263624i | \(0.915082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.76631 | + | 2.17448i | −0.131285 | + | 0.0757977i | −0.564204 | − | 0.825635i | \(-0.690817\pi\) |
0.432919 | + | 0.901433i | \(0.357484\pi\) | |||||||
\(824\) | −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 | \(0.127154\pi\) | ||||
−0.921269 | + | 0.388926i | \(0.872846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.3505 | 0.810997 | 0.405499 | − | 0.914096i | \(-0.367098\pi\) | ||||
0.405499 | + | 0.914096i | \(0.367098\pi\) | |||||||
\(830\) | 20.7446 | + | 4.45877i | 0.720054 | + | 0.154766i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17.0584 | − | 9.84868i | 0.591394 | − | 0.341442i | ||||
\(833\) | 3.43070 | − | 1.98072i | 0.118867 | − | 0.0686278i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.37228 | − | 29.6472i | 0.220522 | − | 1.02599i | ||||
\(836\) | 2.23369 | 0.0772537 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.8564i | 0.478662i | ||||||||
\(839\) | 22.9307 | − | 39.7171i | 0.791656 | − | 1.37119i | −0.133285 | − | 0.991078i | \(-0.542553\pi\) |
0.924941 | − | 0.380110i | \(-0.124114\pi\) | |||||||
\(840\) | 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 | ||||||||
\(850\) | −2.86141 | − | 1.28962i | −0.0981454 | − | 0.0442336i | ||||
\(851\) | −1.88316 | − | 3.26172i | −0.0645538 | − | 0.111810i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.35053 | + | 5.39853i | 0.320156 | + | 0.184842i | 0.651462 | − | 0.758681i | \(-0.274156\pi\) |
−0.331306 | + | 0.943523i | \(0.607489\pi\) | |||||||
\(854\) | 25.7228 | 0.880217 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.4456 | 1.21151 | ||||||||
\(857\) | −42.7812 | − | 24.6998i | −1.46138 | − | 0.843728i | −0.462304 | − | 0.886722i | \(-0.652977\pi\) |
−0.999075 | + | 0.0429939i | \(0.986310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.1644 | + | 41.8540i | 0.824478 | + | 1.42804i | 0.902317 | + | 0.431073i | \(0.141865\pi\) |
−0.0778389 | + | 0.996966i | \(0.524802\pi\) | |||||||
\(860\) | −7.88316 | − | 7.13058i | −0.268813 | − | 0.243151i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.8832 | + | 13.2116i | 0.779403 | + | 0.449989i | ||||
\(863\) | 16.7306i | 0.569516i | 0.958599 | + | 0.284758i | \(0.0919133\pi\) | ||||
−0.958599 | + | 0.284758i | \(0.908087\pi\) | |||||||
\(864\) | 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 | ||||||||
\(875\) | −15.5109 | − | 35.4882i | −0.524363 | − | 1.19972i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.941578 | + | 0.543620i | −0.0317948 | + | 0.0183568i | −0.515813 | − | 0.856701i | \(-0.672510\pi\) |
0.484018 | + | 0.875058i | \(0.339177\pi\) | |||||||
\(878\) | 21.8614 | − | 12.6217i | 0.737787 | − | 0.425961i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.00000 | + | 1.28962i | 0.202260 | + | 0.0434731i | ||||
\(881\) | −10.8832 | −0.366663 | −0.183331 | − | 0.983051i | \(-0.558688\pi\) | ||||
−0.183331 | + | 0.983051i | \(0.558688\pi\) | |||||||
\(882\) | 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 | −0.975959 | − | 0.217954i | \(-0.930062\pi\) |
−0.299226 | + | 0.954182i | \(0.596728\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | 7.32473 | − | 8.09780i | 0.244839 | − | 0.270680i | ||||
\(896\) | −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 | ||||
\(905\) | 20.7921 | − | 22.9865i | 0.691153 | − | 0.764099i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.7663 | + | 9.10268i | 0.523512 | + | 0.302250i | 0.738370 | − | 0.674396i | \(-0.235596\pi\) |
−0.214858 | + | 0.976645i | \(0.568929\pi\) | |||||||
\(908\) | − | 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 | \(-0.933067\pi\) |
0.669752 | + | 0.742585i | \(0.266401\pi\) | |||||||
\(912\) | 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 | \(0.866180\pi\) | |||||||
\(920\) | 9.25544 | + | 1.98933i | 0.305143 | + | 0.0655864i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.5326 | − | 9.54511i | 0.544473 | − | 0.314352i | ||||
\(923\) | 66.3505 | − | 38.3075i | 2.18395 | − | 1.26091i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.8247 | + | 1.18843i | −0.388795 | + | 0.0390754i | ||||
\(926\) | −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 | \(-0.814990\pi\) |
0.893385 | + | 0.449292i | \(0.148324\pi\) | |||||||
\(930\) | 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 | ||||||||
\(940\) | 4.27719 | + | 3.86886i | 0.139506 | + | 0.126188i | ||||
\(941\) | −3.43070 | − | 5.94215i | −0.111838 | − | 0.193709i | 0.804674 | − | 0.593718i | \(-0.202340\pi\) |
−0.916511 | + | 0.400009i | \(0.869007\pi\) | |||||||
\(942\) | 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 | −0.250714 | − | 0.968061i | \(-0.580665\pi\) |
−0.963722 | + | 0.266906i | \(0.913999\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.94158 | − | 12.0232i | −0.225333 | − | 0.390288i | ||||
\(950\) | 0.605969 | − | 1.34452i | 0.0196602 | − | 0.0436221i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.35053 | + | 3.66648i | 0.205822 | + | 0.118831i | ||||
\(953\) | − | 25.0410i | − | 0.811158i | −0.914060 | − | 0.405579i | \(-0.867070\pi\) | ||
0.914060 | − | 0.405579i | \(-0.132930\pi\) | |||||||
\(954\) | 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 | ||||||||
\(965\) | 5.39403 | − | 25.0959i | 0.173640 | − | 0.807866i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.4674 | + | 21.6318i | −1.20487 | + | 0.695632i | −0.961634 | − | 0.274335i | \(-0.911542\pi\) |
−0.243236 | + | 0.969967i | \(0.578209\pi\) | |||||||
\(968\) | −18.7812 | + | 10.8434i | −0.603652 | + | 0.348519i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.23369 | − | 0.480102i | −0.0717194 | − | 0.0154151i | ||||
\(971\) | −41.5842 | −1.33450 | −0.667251 | − | 0.744833i | \(-0.732529\pi\) | ||||
−0.667251 | + | 0.744833i | \(0.732529\pi\) | |||||||
\(972\) | 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 | −0.837907 | − | 0.545813i | \(-0.816221\pi\) |
0.0537346 | + | 0.998555i | \(0.482888\pi\) | |||||||
\(978\) | 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 | 0.993482 | − | 0.113987i | \(-0.0363621\pi\) |
0.398026 | + | 0.917374i | \(0.369695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6644 | + | 9.64630i | 0.339796 | + | 0.307357i | ||||
\(986\) | −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 | ||||
\(995\) | 24.0000 | − | 26.5330i | 0.760851 | − | 0.841153i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.2921 | + | 30.1909i | 1.65611 | + | 0.956154i | 0.974486 | + | 0.224450i | \(0.0720585\pi\) |
0.681622 | + | 0.731704i | \(0.261275\pi\) | |||||||
\(998\) | − | 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.a.379.2 | 4 | ||
3.2 | odd | 2 | 405.2.j.e.379.1 | 4 | |||
5.4 | even | 2 | 405.2.j.d.379.1 | 4 | |||
9.2 | odd | 6 | 405.2.b.a.244.3 | yes | 4 | ||
9.4 | even | 3 | 405.2.j.d.109.1 | 4 | |||
9.5 | odd | 6 | 405.2.j.b.109.2 | 4 | |||
9.7 | even | 3 | 405.2.b.b.244.2 | yes | 4 | ||
15.14 | odd | 2 | 405.2.j.b.379.2 | 4 | |||
45.2 | even | 12 | 2025.2.a.w.1.2 | 4 | |||
45.4 | even | 6 | inner | 405.2.j.a.109.2 | 4 | ||
45.7 | odd | 12 | 2025.2.a.x.1.3 | 4 | |||
45.14 | odd | 6 | 405.2.j.e.109.1 | 4 | |||
45.29 | odd | 6 | 405.2.b.a.244.2 | ✓ | 4 | ||
45.34 | even | 6 | 405.2.b.b.244.3 | yes | 4 | ||
45.38 | even | 12 | 2025.2.a.w.1.3 | 4 | |||
45.43 | odd | 12 | 2025.2.a.x.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.b.a.244.2 | ✓ | 4 | 45.29 | odd | 6 | ||
405.2.b.a.244.3 | yes | 4 | 9.2 | odd | 6 | ||
405.2.b.b.244.2 | yes | 4 | 9.7 | even | 3 | ||
405.2.b.b.244.3 | yes | 4 | 45.34 | even | 6 | ||
405.2.j.a.109.2 | 4 | 45.4 | even | 6 | inner | ||
405.2.j.a.379.2 | 4 | 1.1 | even | 1 | trivial | ||
405.2.j.b.109.2 | 4 | 9.5 | odd | 6 | |||
405.2.j.b.379.2 | 4 | 15.14 | odd | 2 | |||
405.2.j.d.109.1 | 4 | 9.4 | even | 3 | |||
405.2.j.d.379.1 | 4 | 5.4 | even | 2 | |||
405.2.j.e.109.1 | 4 | 45.14 | odd | 6 | |||
405.2.j.e.379.1 | 4 | 3.2 | odd | 2 | |||
2025.2.a.w.1.2 | 4 | 45.2 | even | 12 | |||
2025.2.a.w.1.3 | 4 | 45.38 | even | 12 | |||
2025.2.a.x.1.2 | 4 | 45.43 | odd | 12 | |||
2025.2.a.x.1.3 | 4 | 45.7 | odd | 12 |