Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [806,2,Mod(373,806)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(806, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("806.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 806 = 2 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 806.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.43594240292\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{29})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 8x^{2} + 7x + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 497.2 | ||
Root | \(-1.09629 + 1.89883i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 806.497 |
Dual form | 806.2.g.c.373.2 |
$q$-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 \(\left(\mathbb{Z}/806\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.19258 | 0.533339 | 0.266670 | − | 0.963788i | \(-0.414077\pi\) | ||||
0.266670 | + | 0.963788i | \(0.414077\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | 1.59629 | − | 2.76486i | 0.603341 | − | 1.04502i | −0.388970 | − | 0.921250i | \(-0.627169\pi\) |
0.992311 | − | 0.123767i | \(-0.0394977\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | −0.596291 | − | 1.03281i | −0.188564 | − | 0.326602i | ||||
\(11\) | −1.09629 | − | 1.89883i | −0.330544 | − | 0.572519i | 0.652074 | − | 0.758155i | \(-0.273899\pi\) |
−0.982619 | + | 0.185636i | \(0.940566\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.50000 | − | 2.59808i | −0.693375 | − | 0.720577i | ||||
\(14\) | −3.19258 | −0.853254 | ||||||||
\(15\) | 0.596291 | + | 1.03281i | 0.153962 | + | 0.266670i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | −2.00000 | −0.471405 | ||||||||
\(19\) | −1.09629 | + | 1.89883i | −0.251506 | + | 0.435622i | −0.963941 | − | 0.266117i | \(-0.914259\pi\) |
0.712434 | + | 0.701739i | \(0.247593\pi\) | |||||||
\(20\) | −0.596291 | + | 1.03281i | −0.133335 | + | 0.230943i | ||||
\(21\) | 3.19258 | 0.696679 | ||||||||
\(22\) | −1.09629 | + | 1.89883i | −0.233730 | + | 0.404832i | ||||
\(23\) | −1.59629 | − | 2.76486i | −0.332850 | − | 0.576513i | 0.650220 | − | 0.759746i | \(-0.274677\pi\) |
−0.983069 | + | 0.183234i | \(0.941344\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −3.57775 | −0.715549 | ||||||||
\(26\) | −1.00000 | + | 3.46410i | −0.196116 | + | 0.679366i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 1.59629 | + | 2.76486i | 0.301671 | + | 0.522509i | ||||
\(29\) | −0.903709 | − | 1.56527i | −0.167815 | − | 0.290663i | 0.769837 | − | 0.638241i | \(-0.220338\pi\) |
−0.937651 | + | 0.347578i | \(0.887004\pi\) | |||||||
\(30\) | 0.596291 | − | 1.03281i | 0.108867 | − | 0.188564i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.09629 | − | 1.89883i | 0.190840 | − | 0.330544i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.90371 | − | 3.29732i | 0.321786 | − | 0.557349i | ||||
\(36\) | 1.00000 | + | 1.73205i | 0.166667 | + | 0.288675i | ||||
\(37\) | 2.78887 | + | 4.83047i | 0.458488 | + | 0.794125i | 0.998881 | − | 0.0472880i | \(-0.0150579\pi\) |
−0.540393 | + | 0.841413i | \(0.681725\pi\) | |||||||
\(38\) | 2.19258 | 0.355684 | ||||||||
\(39\) | 1.00000 | − | 3.46410i | 0.160128 | − | 0.554700i | ||||
\(40\) | 1.19258 | 0.188564 | ||||||||
\(41\) | −0.307418 | − | 0.532463i | −0.0480106 | − | 0.0831567i | 0.841021 | − | 0.541002i | \(-0.181955\pi\) |
−0.889032 | + | 0.457845i | \(0.848621\pi\) | |||||||
\(42\) | −1.59629 | − | 2.76486i | −0.246313 | − | 0.426627i | ||||
\(43\) | 4.50000 | − | 7.79423i | 0.686244 | − | 1.18861i | −0.286801 | − | 0.957990i | \(-0.592592\pi\) |
0.973044 | − | 0.230618i | \(-0.0740749\pi\) | |||||||
\(44\) | 2.19258 | 0.330544 | ||||||||
\(45\) | 1.19258 | − | 2.06561i | 0.177780 | − | 0.307923i | ||||
\(46\) | −1.59629 | + | 2.76486i | −0.235360 | + | 0.407656i | ||||
\(47\) | −3.38516 | −0.493777 | −0.246889 | − | 0.969044i | \(-0.579408\pi\) | ||||
−0.246889 | + | 0.969044i | \(0.579408\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −1.59629 | − | 2.76486i | −0.228042 | − | 0.394980i | ||||
\(50\) | 1.78887 | + | 3.09842i | 0.252985 | + | 0.438183i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.50000 | − | 0.866025i | 0.485363 | − | 0.120096i | ||||
\(53\) | 5.19258 | 0.713256 | 0.356628 | − | 0.934246i | \(-0.383926\pi\) | ||||
0.356628 | + | 0.934246i | \(0.383926\pi\) | |||||||
\(54\) | −2.50000 | − | 4.33013i | −0.340207 | − | 0.589256i | ||||
\(55\) | −1.30742 | − | 2.26451i | −0.176292 | − | 0.305347i | ||||
\(56\) | 1.59629 | − | 2.76486i | 0.213313 | − | 0.369470i | ||||
\(57\) | −2.19258 | −0.290415 | ||||||||
\(58\) | −0.903709 | + | 1.56527i | −0.118663 | + | 0.205530i | ||||
\(59\) | 5.88516 | − | 10.1934i | 0.766183 | − | 1.32707i | −0.173436 | − | 0.984845i | \(-0.555487\pi\) |
0.939619 | − | 0.342223i | \(-0.111180\pi\) | |||||||
\(60\) | −1.19258 | −0.153962 | ||||||||
\(61\) | 1.30742 | − | 2.26451i | 0.167398 | − | 0.289941i | −0.770106 | − | 0.637915i | \(-0.779797\pi\) |
0.937504 | + | 0.347974i | \(0.113130\pi\) | |||||||
\(62\) | −0.500000 | − | 0.866025i | −0.0635001 | − | 0.109985i | ||||
\(63\) | −3.19258 | − | 5.52971i | −0.402228 | − | 0.696679i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.98146 | − | 3.09842i | −0.369804 | − | 0.384312i | ||||
\(66\) | −2.19258 | −0.269888 | ||||||||
\(67\) | 2.30742 | + | 3.99656i | 0.281896 | + | 0.488258i | 0.971852 | − | 0.235593i | \(-0.0757034\pi\) |
−0.689956 | + | 0.723852i | \(0.742370\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.59629 | − | 2.76486i | 0.192171 | − | 0.332850i | ||||
\(70\) | −3.80742 | −0.455073 | ||||||||
\(71\) | −6.28887 | + | 10.8926i | −0.746352 | + | 1.29272i | 0.203208 | + | 0.979135i | \(0.434863\pi\) |
−0.949560 | + | 0.313584i | \(0.898470\pi\) | |||||||
\(72\) | 1.00000 | − | 1.73205i | 0.117851 | − | 0.204124i | ||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | 2.78887 | − | 4.83047i | 0.324200 | − | 0.561531i | ||||
\(75\) | −1.78887 | − | 3.09842i | −0.206561 | − | 0.357775i | ||||
\(76\) | −1.09629 | − | 1.89883i | −0.125753 | − | 0.217811i | ||||
\(77\) | −7.00000 | −0.797724 | ||||||||
\(78\) | −3.50000 | + | 0.866025i | −0.396297 | + | 0.0980581i | ||||
\(79\) | 5.00000 | 0.562544 | 0.281272 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281272 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(80\) | −0.596291 | − | 1.03281i | −0.0666674 | − | 0.115471i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.307418 | + | 0.532463i | −0.0339486 | + | 0.0588007i | ||||
\(83\) | −3.61484 | −0.396780 | −0.198390 | − | 0.980123i | \(-0.563571\pi\) | ||||
−0.198390 | + | 0.980123i | \(0.563571\pi\) | |||||||
\(84\) | −1.59629 | + | 2.76486i | −0.174170 | + | 0.301671i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.00000 | −0.970495 | ||||||||
\(87\) | 0.903709 | − | 1.56527i | 0.0968878 | − | 0.167815i | ||||
\(88\) | −1.09629 | − | 1.89883i | −0.116865 | − | 0.202416i | ||||
\(89\) | 8.48146 | + | 14.6903i | 0.899033 | + | 1.55717i | 0.828733 | + | 0.559644i | \(0.189062\pi\) |
0.0702995 | + | 0.997526i | \(0.477605\pi\) | |||||||
\(90\) | −2.38516 | −0.251418 | ||||||||
\(91\) | −11.1740 | + | 2.76486i | −1.17136 | + | 0.289836i | ||||
\(92\) | 3.19258 | 0.332850 | ||||||||
\(93\) | 0.500000 | + | 0.866025i | 0.0518476 | + | 0.0898027i | ||||
\(94\) | 1.69258 | + | 2.93164i | 0.174577 | + | 0.302375i | ||||
\(95\) | −1.30742 | + | 2.26451i | −0.134138 | + | 0.232334i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −4.69258 | + | 8.12779i | −0.476460 | + | 0.825252i | −0.999636 | − | 0.0269721i | \(-0.991413\pi\) |
0.523177 | + | 0.852224i | \(0.324747\pi\) | |||||||
\(98\) | −1.59629 | + | 2.76486i | −0.161250 | + | 0.279293i | ||||
\(99\) | −4.38516 | −0.440726 | ||||||||
\(100\) | 1.78887 | − | 3.09842i | 0.178887 | − | 0.309842i | ||||
\(101\) | −0.307418 | − | 0.532463i | −0.0305892 | − | 0.0529820i | 0.850326 | − | 0.526257i | \(-0.176405\pi\) |
−0.880915 | + | 0.473275i | \(0.843072\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1555 | 1.59185 | 0.795924 | − | 0.605396i | \(-0.206985\pi\) | ||||
0.795924 | + | 0.605396i | \(0.206985\pi\) | |||||||
\(104\) | −2.50000 | − | 2.59808i | −0.245145 | − | 0.254762i | ||||
\(105\) | 3.80742 | 0.371566 | ||||||||
\(106\) | −2.59629 | − | 4.49691i | −0.252174 | − | 0.436778i | ||||
\(107\) | −1.69258 | − | 2.93164i | −0.163628 | − | 0.283412i | 0.772539 | − | 0.634967i | \(-0.218986\pi\) |
−0.936167 | + | 0.351555i | \(0.885653\pi\) | |||||||
\(108\) | −2.50000 | + | 4.33013i | −0.240563 | + | 0.416667i | ||||
\(109\) | −2.19258 | −0.210011 | −0.105006 | − | 0.994472i | \(-0.533486\pi\) | ||||
−0.105006 | + | 0.994472i | \(0.533486\pi\) | |||||||
\(110\) | −1.30742 | + | 2.26451i | −0.124657 | + | 0.215913i | ||||
\(111\) | −2.78887 | + | 4.83047i | −0.264708 | + | 0.458488i | ||||
\(112\) | −3.19258 | −0.301671 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 1.09629 | + | 1.89883i | 0.102677 | + | 0.177842i | ||||
\(115\) | −1.90371 | − | 3.29732i | −0.177522 | − | 0.307477i | ||||
\(116\) | 1.80742 | 0.167815 | ||||||||
\(117\) | −7.00000 | + | 1.73205i | −0.647150 | + | 0.160128i | ||||
\(118\) | −11.7703 | −1.08355 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.596291 | + | 1.03281i | 0.0544337 | + | 0.0942819i | ||||
\(121\) | 3.09629 | − | 5.36293i | 0.281481 | − | 0.487539i | ||||
\(122\) | −2.61484 | −0.236736 | ||||||||
\(123\) | 0.307418 | − | 0.532463i | 0.0277189 | − | 0.0480106i | ||||
\(124\) | −0.500000 | + | 0.866025i | −0.0449013 | + | 0.0777714i | ||||
\(125\) | −10.2297 | −0.914970 | ||||||||
\(126\) | −3.19258 | + | 5.52971i | −0.284418 | + | 0.492626i | ||||
\(127\) | 6.00000 | + | 10.3923i | 0.532414 | + | 0.922168i | 0.999284 | + | 0.0378419i | \(0.0120483\pi\) |
−0.466870 | + | 0.884326i | \(0.654618\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 9.00000 | 0.792406 | ||||||||
\(130\) | −1.19258 | + | 4.13123i | −0.104596 | + | 0.362333i | ||||
\(131\) | −13.1926 | −1.15264 | −0.576321 | − | 0.817224i | \(-0.695512\pi\) | ||||
−0.576321 | + | 0.817224i | \(0.695512\pi\) | |||||||
\(132\) | 1.09629 | + | 1.89883i | 0.0954199 | + | 0.165272i | ||||
\(133\) | 3.50000 | + | 6.06218i | 0.303488 | + | 0.525657i | ||||
\(134\) | 2.30742 | − | 3.99656i | 0.199331 | − | 0.345251i | ||||
\(135\) | 5.96291 | 0.513206 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.88516 | − | 3.26520i | 0.161060 | − | 0.278965i | −0.774189 | − | 0.632955i | \(-0.781842\pi\) |
0.935249 | + | 0.353990i | \(0.115175\pi\) | |||||||
\(138\) | −3.19258 | −0.271771 | ||||||||
\(139\) | 10.7889 | − | 18.6869i | 0.915100 | − | 1.58500i | 0.108346 | − | 0.994113i | \(-0.465445\pi\) |
0.806754 | − | 0.590887i | \(-0.201222\pi\) | |||||||
\(140\) | 1.90371 | + | 3.29732i | 0.160893 | + | 0.278674i | ||||
\(141\) | −1.69258 | − | 2.93164i | −0.142541 | − | 0.246889i | ||||
\(142\) | 12.5777 | 1.05550 | ||||||||
\(143\) | −2.19258 | + | 7.59533i | −0.183353 | + | 0.635153i | ||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | −1.07775 | − | 1.86671i | −0.0895020 | − | 0.155022i | ||||
\(146\) | −4.50000 | − | 7.79423i | −0.372423 | − | 0.645055i | ||||
\(147\) | 1.59629 | − | 2.76486i | 0.131660 | − | 0.228042i | ||||
\(148\) | −5.57775 | −0.458488 | ||||||||
\(149\) | −9.28887 | + | 16.0888i | −0.760974 | + | 1.31805i | 0.181375 | + | 0.983414i | \(0.441945\pi\) |
−0.942349 | + | 0.334632i | \(0.891388\pi\) | |||||||
\(150\) | −1.78887 | + | 3.09842i | −0.146061 | + | 0.252985i | ||||
\(151\) | 9.77033 | 0.795098 | 0.397549 | − | 0.917581i | \(-0.369861\pi\) | ||||
0.397549 | + | 0.917581i | \(0.369861\pi\) | |||||||
\(152\) | −1.09629 | + | 1.89883i | −0.0889210 | + | 0.154016i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.50000 | + | 6.06218i | 0.282038 | + | 0.488504i | ||||
\(155\) | 1.19258 | 0.0957905 | ||||||||
\(156\) | 2.50000 | + | 2.59808i | 0.200160 | + | 0.208013i | ||||
\(157\) | −5.57775 | −0.445153 | −0.222576 | − | 0.974915i | \(-0.571447\pi\) | ||||
−0.222576 | + | 0.974915i | \(0.571447\pi\) | |||||||
\(158\) | −2.50000 | − | 4.33013i | −0.198889 | − | 0.344486i | ||||
\(159\) | 2.59629 | + | 4.49691i | 0.205899 | + | 0.356628i | ||||
\(160\) | −0.596291 | + | 1.03281i | −0.0471410 | + | 0.0816505i | ||||
\(161\) | −10.1926 | −0.803288 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 8.90371 | − | 15.4217i | 0.697392 | − | 1.20792i | −0.271975 | − | 0.962304i | \(-0.587677\pi\) |
0.969368 | − | 0.245615i | \(-0.0789898\pi\) | |||||||
\(164\) | 0.614835 | 0.0480106 | ||||||||
\(165\) | 1.30742 | − | 2.26451i | 0.101782 | − | 0.176292i | ||||
\(166\) | 1.80742 | + | 3.13054i | 0.140283 | + | 0.242977i | ||||
\(167\) | −4.19258 | − | 7.26177i | −0.324432 | − | 0.561932i | 0.656965 | − | 0.753921i | \(-0.271840\pi\) |
−0.981397 | + | 0.191988i | \(0.938506\pi\) | |||||||
\(168\) | 3.19258 | 0.246313 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.19258 | + | 3.79766i | 0.167671 | + | 0.290415i | ||||
\(172\) | 4.50000 | + | 7.79423i | 0.343122 | + | 0.594304i | ||||
\(173\) | −6.57775 | + | 11.3930i | −0.500097 | + | 0.866193i | 0.499903 | + | 0.866081i | \(0.333369\pi\) |
−1.00000 | 0.000111848i | \(0.999964\pi\) | ||||||||
\(174\) | −1.80742 | −0.137020 | ||||||||
\(175\) | −5.71113 | + | 9.89196i | −0.431721 | + | 0.747762i | ||||
\(176\) | −1.09629 | + | 1.89883i | −0.0826361 | + | 0.143130i | ||||
\(177\) | 11.7703 | 0.884712 | ||||||||
\(178\) | 8.48146 | − | 14.6903i | 0.635712 | − | 1.10109i | ||||
\(179\) | 9.57775 | + | 16.5891i | 0.715874 | + | 1.23993i | 0.962621 | + | 0.270851i | \(0.0873050\pi\) |
−0.246747 | + | 0.969080i | \(0.579362\pi\) | |||||||
\(180\) | 1.19258 | + | 2.06561i | 0.0888898 | + | 0.153962i | ||||
\(181\) | −0.807418 | −0.0600149 | −0.0300074 | − | 0.999550i | \(-0.509553\pi\) | ||||
−0.0300074 | + | 0.999550i | \(0.509553\pi\) | |||||||
\(182\) | 7.98146 | + | 8.29457i | 0.591625 | + | 0.614835i | ||||
\(183\) | 2.61484 | 0.193294 | ||||||||
\(184\) | −1.59629 | − | 2.76486i | −0.117680 | − | 0.203828i | ||||
\(185\) | 3.32596 | + | 5.76073i | 0.244530 | + | 0.423538i | ||||
\(186\) | 0.500000 | − | 0.866025i | 0.0366618 | − | 0.0635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.69258 | − | 2.93164i | 0.123444 | − | 0.213812i | ||||
\(189\) | 7.98146 | − | 13.8243i | 0.580565 | − | 1.00557i | ||||
\(190\) | 2.61484 | 0.189700 | ||||||||
\(191\) | 1.30742 | − | 2.26451i | 0.0946014 | − | 0.163854i | −0.814841 | − | 0.579685i | \(-0.803176\pi\) |
0.909442 | + | 0.415830i | \(0.136509\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 5.48146 | + | 9.49416i | 0.394564 | + | 0.683405i | 0.993045 | − | 0.117732i | \(-0.0375624\pi\) |
−0.598482 | + | 0.801137i | \(0.704229\pi\) | |||||||
\(194\) | 9.38516 | 0.673816 | ||||||||
\(195\) | 1.19258 | − | 4.13123i | 0.0854026 | − | 0.295843i | ||||
\(196\) | 3.19258 | 0.228042 | ||||||||
\(197\) | 11.8852 | + | 20.5857i | 0.846783 | + | 1.46667i | 0.884064 | + | 0.467366i | \(0.154797\pi\) |
−0.0372809 | + | 0.999305i | \(0.511870\pi\) | |||||||
\(198\) | 2.19258 | + | 3.79766i | 0.155820 | + | 0.269888i | ||||
\(199\) | 0.0962912 | − | 0.166781i | 0.00682590 | − | 0.0118228i | −0.862592 | − | 0.505900i | \(-0.831161\pi\) |
0.869418 | + | 0.494077i | \(0.164494\pi\) | |||||||
\(200\) | −3.57775 | −0.252985 | ||||||||
\(201\) | −2.30742 | + | 3.99656i | −0.162753 | + | 0.281896i | ||||
\(202\) | −0.307418 | + | 0.532463i | −0.0216298 | + | 0.0374640i | ||||
\(203\) | −5.77033 | −0.404998 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.366621 | − | 0.635006i | −0.0256059 | − | 0.0443507i | ||||
\(206\) | −8.07775 | − | 13.9911i | −0.562803 | − | 0.974804i | ||||
\(207\) | −6.38516 | −0.443800 | ||||||||
\(208\) | −1.00000 | + | 3.46410i | −0.0693375 | + | 0.240192i | ||||
\(209\) | 4.80742 | 0.332536 | ||||||||
\(210\) | −1.90371 | − | 3.29732i | −0.131368 | − | 0.227537i | ||||
\(211\) | 1.78887 | + | 3.09842i | 0.123151 | + | 0.213304i | 0.921009 | − | 0.389542i | \(-0.127367\pi\) |
−0.797858 | + | 0.602846i | \(0.794033\pi\) | |||||||
\(212\) | −2.59629 | + | 4.49691i | −0.178314 | + | 0.308849i | ||||
\(213\) | −12.5777 | −0.861813 | ||||||||
\(214\) | −1.69258 | + | 2.93164i | −0.115703 | + | 0.200403i | ||||
\(215\) | 5.36662 | − | 9.29526i | 0.366001 | − | 0.633931i | ||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 1.59629 | − | 2.76486i | 0.108363 | − | 0.187691i | ||||
\(218\) | 1.09629 | + | 1.89883i | 0.0742502 | + | 0.128605i | ||||
\(219\) | 4.50000 | + | 7.79423i | 0.304082 | + | 0.526685i | ||||
\(220\) | 2.61484 | 0.176292 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.57775 | 0.374354 | ||||||||
\(223\) | 3.78887 | + | 6.56252i | 0.253722 | + | 0.439459i | 0.964548 | − | 0.263909i | \(-0.0850119\pi\) |
−0.710826 | + | 0.703368i | \(0.751679\pi\) | |||||||
\(224\) | 1.59629 | + | 2.76486i | 0.106657 | + | 0.184735i | ||||
\(225\) | −3.57775 | + | 6.19684i | −0.238516 | + | 0.413123i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | 1.09629 | − | 1.89883i | 0.0726037 | − | 0.125753i | ||||
\(229\) | 3.38516 | 0.223698 | 0.111849 | − | 0.993725i | \(-0.464323\pi\) | ||||
0.111849 | + | 0.993725i | \(0.464323\pi\) | |||||||
\(230\) | −1.90371 | + | 3.29732i | −0.125527 | + | 0.217419i | ||||
\(231\) | −3.50000 | − | 6.06218i | −0.230283 | − | 0.398862i | ||||
\(232\) | −0.903709 | − | 1.56527i | −0.0593314 | − | 0.102765i | ||||
\(233\) | −13.3852 | −0.876891 | −0.438446 | − | 0.898758i | \(-0.644471\pi\) | ||||
−0.438446 | + | 0.898758i | \(0.644471\pi\) | |||||||
\(234\) | 5.00000 | + | 5.19615i | 0.326860 | + | 0.339683i | ||||
\(235\) | −4.03709 | −0.263351 | ||||||||
\(236\) | 5.88516 | + | 10.1934i | 0.383092 | + | 0.663534i | ||||
\(237\) | 2.50000 | + | 4.33013i | 0.162392 | + | 0.281272i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9629 | −1.42066 | −0.710331 | − | 0.703867i | \(-0.751455\pi\) | ||||
−0.710331 | + | 0.703867i | \(0.751455\pi\) | |||||||
\(240\) | 0.596291 | − | 1.03281i | 0.0384904 | − | 0.0666674i | ||||
\(241\) | −8.77033 | + | 15.1907i | −0.564947 | + | 0.978516i | 0.432108 | + | 0.901822i | \(0.357770\pi\) |
−0.997055 | + | 0.0766944i | \(0.975563\pi\) | |||||||
\(242\) | −6.19258 | −0.398074 | ||||||||
\(243\) | 8.00000 | − | 13.8564i | 0.513200 | − | 0.888889i | ||||
\(244\) | 1.30742 | + | 2.26451i | 0.0836988 | + | 0.144971i | ||||
\(245\) | −1.90371 | − | 3.29732i | −0.121623 | − | 0.210658i | ||||
\(246\) | −0.614835 | −0.0392005 | ||||||||
\(247\) | 7.67404 | − | 1.89883i | 0.488287 | − | 0.120820i | ||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −1.80742 | − | 3.13054i | −0.114540 | − | 0.198390i | ||||
\(250\) | 5.11484 | + | 8.85915i | 0.323491 | + | 0.560302i | ||||
\(251\) | 5.38516 | − | 9.32738i | 0.339909 | − | 0.588739i | −0.644507 | − | 0.764599i | \(-0.722937\pi\) |
0.984415 | + | 0.175860i | \(0.0562705\pi\) | |||||||
\(252\) | 6.38516 | 0.402228 | ||||||||
\(253\) | −3.50000 | + | 6.06218i | −0.220043 | + | 0.381126i | ||||
\(254\) | 6.00000 | − | 10.3923i | 0.376473 | − | 0.652071i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 9.09629 | + | 15.7552i | 0.567411 | + | 0.982785i | 0.996821 | + | 0.0796750i | \(0.0253883\pi\) |
−0.429410 | + | 0.903110i | \(0.641278\pi\) | |||||||
\(258\) | −4.50000 | − | 7.79423i | −0.280158 | − | 0.485247i | ||||
\(259\) | 17.8074 | 1.10650 | ||||||||
\(260\) | 4.17404 | − | 1.03281i | 0.258863 | − | 0.0640519i | ||||
\(261\) | −3.61484 | −0.223753 | ||||||||
\(262\) | 6.59629 | + | 11.4251i | 0.407520 | + | 0.705846i | ||||
\(263\) | −4.48146 | − | 7.76211i | −0.276338 | − | 0.478632i | 0.694134 | − | 0.719846i | \(-0.255788\pi\) |
−0.970472 | + | 0.241214i | \(0.922454\pi\) | |||||||
\(264\) | 1.09629 | − | 1.89883i | 0.0674721 | − | 0.116865i | ||||
\(265\) | 6.19258 | 0.380407 | ||||||||
\(266\) | 3.50000 | − | 6.06218i | 0.214599 | − | 0.371696i | ||||
\(267\) | −8.48146 | + | 14.6903i | −0.519057 | + | 0.899033i | ||||
\(268\) | −4.61484 | −0.281896 | ||||||||
\(269\) | 3.59629 | − | 6.22896i | 0.219270 | − | 0.379786i | −0.735315 | − | 0.677725i | \(-0.762966\pi\) |
0.954585 | + | 0.297939i | \(0.0962992\pi\) | |||||||
\(270\) | −2.98146 | − | 5.16403i | −0.181446 | − | 0.314273i | ||||
\(271\) | 2.00000 | + | 3.46410i | 0.121491 | + | 0.210429i | 0.920356 | − | 0.391082i | \(-0.127899\pi\) |
−0.798865 | + | 0.601511i | \(0.794566\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.98146 | − | 8.29457i | −0.483060 | − | 0.502010i | ||||
\(274\) | −3.77033 | −0.227774 | ||||||||
\(275\) | 3.92225 | + | 6.79354i | 0.236521 | + | 0.409666i | ||||
\(276\) | 1.59629 | + | 2.76486i | 0.0960854 | + | 0.166425i | ||||
\(277\) | 2.28887 | − | 3.96445i | 0.137525 | − | 0.238200i | −0.789034 | − | 0.614349i | \(-0.789419\pi\) |
0.926559 | + | 0.376149i | \(0.122752\pi\) | |||||||
\(278\) | −21.5777 | −1.29415 | ||||||||
\(279\) | 1.00000 | − | 1.73205i | 0.0598684 | − | 0.103695i | ||||
\(280\) | 1.90371 | − | 3.29732i | 0.113768 | − | 0.197053i | ||||
\(281\) | −19.7703 | −1.17940 | −0.589699 | − | 0.807623i | \(-0.700754\pi\) | ||||
−0.589699 | + | 0.807623i | \(0.700754\pi\) | |||||||
\(282\) | −1.69258 | + | 2.93164i | −0.100792 | + | 0.174577i | ||||
\(283\) | 0.981456 | + | 1.69993i | 0.0583415 | + | 0.101050i | 0.893721 | − | 0.448623i | \(-0.148085\pi\) |
−0.835380 | + | 0.549674i | \(0.814752\pi\) | |||||||
\(284\) | −6.28887 | − | 10.8926i | −0.373176 | − | 0.646360i | ||||
\(285\) | −2.61484 | −0.154889 | ||||||||
\(286\) | 7.67404 | − | 1.89883i | 0.453775 | − | 0.112280i | ||||
\(287\) | −1.96291 | −0.115867 | ||||||||
\(288\) | 1.00000 | + | 1.73205i | 0.0589256 | + | 0.102062i | ||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | −1.07775 | + | 1.86671i | −0.0632875 | + | 0.109617i | ||||
\(291\) | −9.38516 | −0.550168 | ||||||||
\(292\) | −4.50000 | + | 7.79423i | −0.263343 | + | 0.456123i | ||||
\(293\) | 7.59629 | − | 13.1572i | 0.443780 | − | 0.768650i | −0.554186 | − | 0.832393i | \(-0.686970\pi\) |
0.997966 | + | 0.0637431i | \(0.0203038\pi\) | |||||||
\(294\) | −3.19258 | −0.186195 | ||||||||
\(295\) | 7.01854 | − | 12.1565i | 0.408635 | − | 0.707777i | ||||
\(296\) | 2.78887 | + | 4.83047i | 0.162100 | + | 0.280765i | ||||
\(297\) | −5.48146 | − | 9.49416i | −0.318066 | − | 0.550907i | ||||
\(298\) | 18.5777 | 1.07618 | ||||||||
\(299\) | −3.19258 | + | 11.0594i | −0.184632 | + | 0.639583i | ||||
\(300\) | 3.57775 | 0.206561 | ||||||||
\(301\) | −14.3666 | − | 24.8837i | −0.828078 | − | 1.43427i | ||||
\(302\) | −4.88516 | − | 8.46135i | −0.281110 | − | 0.486896i | ||||
\(303\) | 0.307418 | − | 0.532463i | 0.0176607 | − | 0.0305892i | ||||
\(304\) | 2.19258 | 0.125753 | ||||||||
\(305\) | 1.55920 | − | 2.70062i | 0.0892797 | − | 0.154637i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.0000 | −0.856095 | −0.428048 | − | 0.903756i | \(-0.640798\pi\) | ||||
−0.428048 | + | 0.903756i | \(0.640798\pi\) | |||||||
\(308\) | 3.50000 | − | 6.06218i | 0.199431 | − | 0.345425i | ||||
\(309\) | 8.07775 | + | 13.9911i | 0.459527 | + | 0.795924i | ||||
\(310\) | −0.596291 | − | 1.03281i | −0.0338671 | − | 0.0586595i | ||||
\(311\) | −22.1555 | −1.25632 | −0.628161 | − | 0.778083i | \(-0.716192\pi\) | ||||
−0.628161 | + | 0.778083i | \(0.716192\pi\) | |||||||
\(312\) | 1.00000 | − | 3.46410i | 0.0566139 | − | 0.196116i | ||||
\(313\) | −12.5777 | −0.710936 | −0.355468 | − | 0.934688i | \(-0.615679\pi\) | ||||
−0.355468 | + | 0.934688i | \(0.615679\pi\) | |||||||
\(314\) | 2.78887 | + | 4.83047i | 0.157385 | + | 0.272599i | ||||
\(315\) | −3.80742 | − | 6.59464i | −0.214524 | − | 0.371566i | ||||
\(316\) | −2.50000 | + | 4.33013i | −0.140636 | + | 0.243589i | ||||
\(317\) | −13.5407 | −0.760519 | −0.380260 | − | 0.924880i | \(-0.624165\pi\) | ||||
−0.380260 | + | 0.924880i | \(0.624165\pi\) | |||||||
\(318\) | 2.59629 | − | 4.49691i | 0.145593 | − | 0.252174i | ||||
\(319\) | −1.98146 | + | 3.43198i | −0.110940 | + | 0.192154i | ||||
\(320\) | 1.19258 | 0.0666674 | ||||||||
\(321\) | 1.69258 | − | 2.93164i | 0.0944707 | − | 0.163628i | ||||
\(322\) | 5.09629 | + | 8.82704i | 0.284005 | + | 0.491911i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 8.94437 | + | 9.29526i | 0.496144 | + | 0.515608i | ||||
\(326\) | −17.8074 | −0.986262 | ||||||||
\(327\) | −1.09629 | − | 1.89883i | −0.0606250 | − | 0.105006i | ||||
\(328\) | −0.307418 | − | 0.532463i | −0.0169743 | − | 0.0294003i | ||||
\(329\) | −5.40371 | + | 9.35950i | −0.297916 | + | 0.516006i | ||||
\(330\) | −2.61484 | −0.143942 | ||||||||
\(331\) | 2.50000 | − | 4.33013i | 0.137412 | − | 0.238005i | −0.789104 | − | 0.614260i | \(-0.789455\pi\) |
0.926516 | + | 0.376254i | \(0.122788\pi\) | |||||||
\(332\) | 1.80742 | − | 3.13054i | 0.0991949 | − | 0.171811i | ||||
\(333\) | 11.1555 | 0.611317 | ||||||||
\(334\) | −4.19258 | + | 7.26177i | −0.229408 | + | 0.397346i | ||||
\(335\) | 2.75179 | + | 4.76623i | 0.150346 | + | 0.260407i | ||||
\(336\) | −1.59629 | − | 2.76486i | −0.0870848 | − | 0.150835i | ||||
\(337\) | 14.1555 | 0.771099 | 0.385549 | − | 0.922687i | \(-0.374012\pi\) | ||||
0.385549 | + | 0.922687i | \(0.374012\pi\) | |||||||
\(338\) | 11.5000 | − | 6.06218i | 0.625518 | − | 0.329739i | ||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.09629 | − | 1.89883i | −0.0593675 | − | 0.102828i | ||||
\(342\) | 2.19258 | − | 3.79766i | 0.118561 | − | 0.205354i | ||||
\(343\) | 12.1555 | 0.656335 | ||||||||
\(344\) | 4.50000 | − | 7.79423i | 0.242624 | − | 0.420237i | ||||
\(345\) | 1.90371 | − | 3.29732i | 0.102492 | − | 0.177522i | ||||
\(346\) | 13.1555 | 0.707244 | ||||||||
\(347\) | 7.21113 | − | 12.4900i | 0.387114 | − | 0.670500i | −0.604946 | − | 0.796266i | \(-0.706805\pi\) |
0.992060 | + | 0.125766i | \(0.0401388\pi\) | |||||||
\(348\) | 0.903709 | + | 1.56527i | 0.0484439 | + | 0.0839073i | ||||
\(349\) | −8.19258 | − | 14.1900i | −0.438539 | − | 0.759572i | 0.559038 | − | 0.829142i | \(-0.311171\pi\) |
−0.997577 | + | 0.0695703i | \(0.977837\pi\) | |||||||
\(350\) | 11.4223 | 0.610545 | ||||||||
\(351\) | −12.5000 | − | 12.9904i | −0.667201 | − | 0.693375i | ||||
\(352\) | 2.19258 | 0.116865 | ||||||||
\(353\) | 4.78887 | + | 8.29457i | 0.254886 | + | 0.441476i | 0.964865 | − | 0.262748i | \(-0.0846287\pi\) |
−0.709979 | + | 0.704223i | \(0.751295\pi\) | |||||||
\(354\) | −5.88516 | − | 10.1934i | −0.312793 | − | 0.541773i | ||||
\(355\) | −7.50000 | + | 12.9904i | −0.398059 | + | 0.689458i | ||||
\(356\) | −16.9629 | −0.899033 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.57775 | − | 16.5891i | 0.506200 | − | 0.876764i | ||||
\(359\) | −21.7703 | −1.14899 | −0.574497 | − | 0.818507i | \(-0.694802\pi\) | ||||
−0.574497 | + | 0.818507i | \(0.694802\pi\) | |||||||
\(360\) | 1.19258 | − | 2.06561i | 0.0628546 | − | 0.108867i | ||||
\(361\) | 7.09629 | + | 12.2911i | 0.373489 | + | 0.646902i | ||||
\(362\) | 0.403709 | + | 0.699244i | 0.0212185 | + | 0.0367515i | ||||
\(363\) | 6.19258 | 0.325026 | ||||||||
\(364\) | 3.19258 | − | 11.0594i | 0.167337 | − | 0.579672i | ||||
\(365\) | 10.7332 | 0.561804 | ||||||||
\(366\) | −1.30742 | − | 2.26451i | −0.0683398 | − | 0.118368i | ||||
\(367\) | 9.07775 | + | 15.7231i | 0.473855 | + | 0.820740i | 0.999552 | − | 0.0299315i | \(-0.00952891\pi\) |
−0.525697 | + | 0.850672i | \(0.676196\pi\) | |||||||
\(368\) | −1.59629 | + | 2.76486i | −0.0832124 | + | 0.144128i | ||||
\(369\) | −1.22967 | −0.0640141 | ||||||||
\(370\) | 3.32596 | − | 5.76073i | 0.172909 | − | 0.299486i | ||||
\(371\) | 8.28887 | − | 14.3568i | 0.430337 | − | 0.745365i | ||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | −6.57775 | + | 11.3930i | −0.340583 | + | 0.589907i | −0.984541 | − | 0.175154i | \(-0.943958\pi\) |
0.643958 | + | 0.765061i | \(0.277291\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.11484 | − | 8.85915i | −0.264129 | − | 0.457485i | ||||
\(376\) | −3.38516 | −0.174577 | ||||||||
\(377\) | −1.80742 | + | 6.26108i | −0.0930867 | + | 0.322462i | ||||
\(378\) | −15.9629 | −0.821044 | ||||||||
\(379\) | −18.8666 | − | 32.6779i | −0.969113 | − | 1.67855i | −0.698133 | − | 0.715969i | \(-0.745985\pi\) |
−0.270981 | − | 0.962585i | \(-0.587348\pi\) | |||||||
\(380\) | −1.30742 | − | 2.26451i | −0.0670691 | − | 0.116167i | ||||
\(381\) | −6.00000 | + | 10.3923i | −0.307389 | + | 0.532414i | ||||
\(382\) | −2.61484 | −0.133787 | ||||||||
\(383\) | −2.11484 | + | 3.66300i | −0.108063 | + | 0.187171i | −0.914986 | − | 0.403487i | \(-0.867798\pi\) |
0.806922 | + | 0.590657i | \(0.201131\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −8.34808 | −0.425457 | ||||||||
\(386\) | 5.48146 | − | 9.49416i | 0.278999 | − | 0.483240i | ||||
\(387\) | −9.00000 | − | 15.5885i | −0.457496 | − | 0.792406i | ||||
\(388\) | −4.69258 | − | 8.12779i | −0.238230 | − | 0.412626i | ||||
\(389\) | 11.1926 | 0.567486 | 0.283743 | − | 0.958900i | \(-0.408424\pi\) | ||||
0.283743 | + | 0.958900i | \(0.408424\pi\) | |||||||
\(390\) | −4.17404 | + | 1.03281i | −0.211361 | + | 0.0522982i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.59629 | − | 2.76486i | −0.0806249 | − | 0.139646i | ||||
\(393\) | −6.59629 | − | 11.4251i | −0.332739 | − | 0.576321i | ||||
\(394\) | 11.8852 | − | 20.5857i | 0.598766 | − | 1.03709i | ||||
\(395\) | 5.96291 | 0.300027 | ||||||||
\(396\) | 2.19258 | − | 3.79766i | 0.110181 | − | 0.190840i | ||||
\(397\) | −6.80742 | + | 11.7908i | −0.341654 | + | 0.591763i | −0.984740 | − | 0.174031i | \(-0.944321\pi\) |
0.643086 | + | 0.765794i | \(0.277654\pi\) | |||||||
\(398\) | −0.192582 | −0.00965328 | ||||||||
\(399\) | −3.50000 | + | 6.06218i | −0.175219 | + | 0.303488i | ||||
\(400\) | 1.78887 | + | 3.09842i | 0.0894437 | + | 0.154921i | ||||
\(401\) | −9.30742 | − | 16.1209i | −0.464790 | − | 0.805040i | 0.534402 | − | 0.845231i | \(-0.320537\pi\) |
−0.999192 | + | 0.0401902i | \(0.987204\pi\) | |||||||
\(402\) | 4.61484 | 0.230167 | ||||||||
\(403\) | −2.50000 | − | 2.59808i | −0.124534 | − | 0.129419i | ||||
\(404\) | 0.614835 | 0.0305892 | ||||||||
\(405\) | −0.596291 | − | 1.03281i | −0.0296299 | − | 0.0513206i | ||||
\(406\) | 2.88516 | + | 4.99725i | 0.143188 | + | 0.248009i | ||||
\(407\) | 6.11484 | − | 10.5912i | 0.303101 | − | 0.524987i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.2889 | − | 29.9452i | 0.854880 | − | 1.48070i | −0.0218767 | − | 0.999761i | \(-0.506964\pi\) |
0.876757 | − | 0.480935i | \(-0.159703\pi\) | |||||||
\(410\) | −0.366621 | + | 0.635006i | −0.0181061 | + | 0.0313607i | ||||
\(411\) | 3.77033 | 0.185977 | ||||||||
\(412\) | −8.07775 | + | 13.9911i | −0.397962 | + | 0.689290i | ||||
\(413\) | −18.7889 | − | 32.5433i | −0.924540 | − | 1.60135i | ||||
\(414\) | 3.19258 | + | 5.52971i | 0.156907 | + | 0.271771i | ||||
\(415\) | −4.31099 | −0.211618 | ||||||||
\(416\) | 3.50000 | − | 0.866025i | 0.171602 | − | 0.0424604i | ||||
\(417\) | 21.5777 | 1.05667 | ||||||||
\(418\) | −2.40371 | − | 4.16335i | −0.117569 | − | 0.203636i | ||||
\(419\) | −7.09629 | − | 12.2911i | −0.346677 | − | 0.600461i | 0.638980 | − | 0.769223i | \(-0.279356\pi\) |
−0.985657 | + | 0.168762i | \(0.946023\pi\) | |||||||
\(420\) | −1.90371 | + | 3.29732i | −0.0928915 | + | 0.160893i | ||||
\(421\) | −19.3852 | −0.944775 | −0.472388 | − | 0.881391i | \(-0.656608\pi\) | ||||
−0.472388 | + | 0.881391i | \(0.656608\pi\) | |||||||
\(422\) | 1.78887 | − | 3.09842i | 0.0870810 | − | 0.150829i | ||||
\(423\) | −3.38516 | + | 5.86328i | −0.164592 | + | 0.285082i | ||||
\(424\) | 5.19258 | 0.252174 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.28887 | + | 10.8926i | 0.304697 | + | 0.527751i | ||||
\(427\) | −4.17404 | − | 7.22965i | −0.201996 | − | 0.349867i | ||||
\(428\) | 3.38516 | 0.163628 | ||||||||
\(429\) | −7.67404 | + | 1.89883i | −0.370506 | + | 0.0916765i | ||||
\(430\) | −10.7332 | −0.517603 | ||||||||
\(431\) | −2.30742 | − | 3.99656i | −0.111144 | − | 0.192508i | 0.805088 | − | 0.593156i | \(-0.202118\pi\) |
−0.916232 | + | 0.400648i | \(0.868785\pi\) | |||||||
\(432\) | −2.50000 | − | 4.33013i | −0.120281 | − | 0.208333i | ||||
\(433\) | −8.78887 | + | 15.2228i | −0.422366 | + | 0.731560i | −0.996170 | − | 0.0874327i | \(-0.972134\pi\) |
0.573804 | + | 0.818993i | \(0.305467\pi\) | |||||||
\(434\) | −3.19258 | −0.153249 | ||||||||
\(435\) | 1.07775 | − | 1.86671i | 0.0516740 | − | 0.0895020i | ||||
\(436\) | 1.09629 | − | 1.89883i | 0.0525028 | − | 0.0909376i | ||||
\(437\) | 7.00000 | 0.334855 | ||||||||
\(438\) | 4.50000 | − | 7.79423i | 0.215018 | − | 0.372423i | ||||
\(439\) | −3.50000 | − | 6.06218i | −0.167046 | − | 0.289332i | 0.770334 | − | 0.637641i | \(-0.220089\pi\) |
−0.937380 | + | 0.348309i | \(0.886756\pi\) | |||||||
\(440\) | −1.30742 | − | 2.26451i | −0.0623287 | − | 0.107956i | ||||
\(441\) | −6.38516 | −0.304055 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5407 | 0.643336 | 0.321668 | − | 0.946852i | \(-0.395756\pi\) | ||||
0.321668 | + | 0.946852i | \(0.395756\pi\) | |||||||
\(444\) | −2.78887 | − | 4.83047i | −0.132354 | − | 0.229244i | ||||
\(445\) | 10.1148 | + | 17.5194i | 0.479489 | + | 0.830500i | ||||
\(446\) | 3.78887 | − | 6.56252i | 0.179408 | − | 0.310744i | ||||
\(447\) | −18.5777 | −0.878697 | ||||||||
\(448\) | 1.59629 | − | 2.76486i | 0.0754177 | − | 0.130627i | ||||
\(449\) | 2.51854 | − | 4.36225i | 0.118857 | − | 0.205867i | −0.800458 | − | 0.599389i | \(-0.795410\pi\) |
0.919315 | + | 0.393522i | \(0.128744\pi\) | |||||||
\(450\) | 7.15549 | 0.337313 | ||||||||
\(451\) | −0.674038 | + | 1.16747i | −0.0317392 | + | 0.0549740i | ||||
\(452\) | −3.00000 | − | 5.19615i | −0.141108 | − | 0.244406i | ||||
\(453\) | 4.88516 | + | 8.46135i | 0.229525 | + | 0.397549i | ||||
\(454\) | −3.00000 | −0.140797 | ||||||||
\(455\) | −13.3260 | + | 3.29732i | −0.624731 | + | 0.154581i | ||||
\(456\) | −2.19258 | −0.102677 | ||||||||
\(457\) | 13.2889 | + | 23.0170i | 0.621627 | + | 1.07669i | 0.989183 | + | 0.146688i | \(0.0468615\pi\) |
−0.367555 | + | 0.930002i | \(0.619805\pi\) | |||||||
\(458\) | −1.69258 | − | 2.93164i | −0.0790892 | − | 0.136986i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.80742 | 0.177522 | ||||||||
\(461\) | −1.59629 | + | 2.76486i | −0.0743467 | + | 0.128772i | −0.900802 | − | 0.434230i | \(-0.857020\pi\) |
0.826455 | + | 0.563002i | \(0.190354\pi\) | |||||||
\(462\) | −3.50000 | + | 6.06218i | −0.162835 | + | 0.282038i | ||||
\(463\) | −20.7332 | −0.963555 | −0.481778 | − | 0.876293i | \(-0.660009\pi\) | ||||
−0.481778 | + | 0.876293i | \(0.660009\pi\) | |||||||
\(464\) | −0.903709 | + | 1.56527i | −0.0419536 | + | 0.0726658i | ||||
\(465\) | 0.596291 | + | 1.03281i | 0.0276523 | + | 0.0478953i | ||||
\(466\) | 6.69258 | + | 11.5919i | 0.310028 | + | 0.536984i | ||||
\(467\) | −8.61484 | −0.398647 | −0.199324 | − | 0.979934i | \(-0.563874\pi\) | ||||
−0.199324 | + | 0.979934i | \(0.563874\pi\) | |||||||
\(468\) | 2.00000 | − | 6.92820i | 0.0924500 | − | 0.320256i | ||||
\(469\) | 14.7332 | 0.680318 | ||||||||
\(470\) | 2.01854 | + | 3.49622i | 0.0931085 | + | 0.161269i | ||||
\(471\) | −2.78887 | − | 4.83047i | −0.128505 | − | 0.222576i | ||||
\(472\) | 5.88516 | − | 10.1934i | 0.270887 | − | 0.469189i | ||||
\(473\) | −19.7332 | −0.907335 | ||||||||
\(474\) | 2.50000 | − | 4.33013i | 0.114829 | − | 0.198889i | ||||
\(475\) | 3.92225 | − | 6.79354i | 0.179965 | − | 0.311709i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.19258 | − | 8.99382i | 0.237752 | − | 0.411799i | ||||
\(478\) | 10.9815 | + | 19.0204i | 0.502280 | + | 0.869975i | ||||
\(479\) | −4.77033 | − | 8.26245i | −0.217962 | − | 0.377521i | 0.736223 | − | 0.676739i | \(-0.236608\pi\) |
−0.954185 | + | 0.299218i | \(0.903274\pi\) | |||||||
\(480\) | −1.19258 | −0.0544337 | ||||||||
\(481\) | 5.57775 | − | 19.3219i | 0.254323 | − | 0.881002i | ||||
\(482\) | 17.5407 | 0.798955 | ||||||||
\(483\) | −5.09629 | − | 8.82704i | −0.231889 | − | 0.401644i | ||||
\(484\) | 3.09629 | + | 5.36293i | 0.140741 | + | 0.243770i | ||||
\(485\) | −5.59629 | + | 9.69306i | −0.254114 | + | 0.440139i | ||||
\(486\) | −16.0000 | −0.725775 | ||||||||
\(487\) | −9.07775 | + | 15.7231i | −0.411352 | + | 0.712483i | −0.995038 | − | 0.0994970i | \(-0.968277\pi\) |
0.583686 | + | 0.811980i | \(0.301610\pi\) | |||||||
\(488\) | 1.30742 | − | 2.26451i | 0.0591840 | − | 0.102510i | ||||
\(489\) | 17.8074 | 0.805279 | ||||||||
\(490\) | −1.90371 | + | 3.29732i | −0.0860008 | + | 0.148958i | ||||
\(491\) | −10.1740 | − | 17.6220i | −0.459148 | − | 0.795268i | 0.539768 | − | 0.841814i | \(-0.318512\pi\) |
−0.998916 | + | 0.0465461i | \(0.985179\pi\) | |||||||
\(492\) | 0.307418 | + | 0.532463i | 0.0138595 | + | 0.0240053i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −5.48146 | − | 5.69650i | −0.246622 | − | 0.256297i | ||||
\(495\) | −5.22967 | −0.235056 | ||||||||
\(496\) | −0.500000 | − | 0.866025i | −0.0224507 | − | 0.0388857i | ||||
\(497\) | 20.0777 | + | 34.7757i | 0.900610 | + | 1.55990i | ||||
\(498\) | −1.80742 | + | 3.13054i | −0.0809923 | + | 0.140283i | ||||
\(499\) | 22.1555 | 0.991816 | 0.495908 | − | 0.868375i | \(-0.334835\pi\) | ||||
0.495908 | + | 0.868375i | \(0.334835\pi\) | |||||||
\(500\) | 5.11484 | − | 8.85915i | 0.228742 | − | 0.396193i | ||||
\(501\) | 4.19258 | − | 7.26177i | 0.187311 | − | 0.324432i | ||||
\(502\) | −10.7703 | −0.480703 | ||||||||
\(503\) | 21.3481 | − | 36.9760i | 0.951864 | − | 1.64868i | 0.210476 | − | 0.977599i | \(-0.432499\pi\) |
0.741387 | − | 0.671077i | \(-0.234168\pi\) | |||||||
\(504\) | −3.19258 | − | 5.52971i | −0.142209 | − | 0.246313i | ||||
\(505\) | −0.366621 | − | 0.635006i | −0.0163144 | − | 0.0282574i | ||||
\(506\) | 7.00000 | 0.311188 | ||||||||
\(507\) | −11.5000 | + | 6.06218i | −0.510733 | + | 0.269231i | ||||
\(508\) | −12.0000 | −0.532414 | ||||||||
\(509\) | −16.1926 | − | 28.0464i | −0.717724 | − | 1.24313i | −0.961900 | − | 0.273403i | \(-0.911851\pi\) |
0.244176 | − | 0.969731i | \(-0.421483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.3666 | − | 24.8837i | 0.635542 | − | 1.10079i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.48146 | + | 9.49416i | −0.242012 | + | 0.419177i | ||||
\(514\) | 9.09629 | − | 15.7552i | 0.401220 | − | 0.694934i | ||||
\(515\) | 19.2668 | 0.848995 | ||||||||
\(516\) | −4.50000 | + | 7.79423i | −0.198101 | + | 0.343122i | ||||
\(517\) | 3.71113 | + | 6.42786i | 0.163215 | + | 0.282697i | ||||
\(518\) | −8.90371 | − | 15.4217i | −0.391207 | − | 0.677590i | ||||
\(519\) | −13.1555 | −0.577462 | ||||||||
\(520\) | −2.98146 | − | 3.09842i | −0.130745 | − | 0.135875i | ||||
\(521\) | 19.3481 | 0.847655 | 0.423827 | − | 0.905743i | \(-0.360686\pi\) | ||||
0.423827 | + | 0.905743i | \(0.360686\pi\) | |||||||
\(522\) | 1.80742 | + | 3.13054i | 0.0791085 | + | 0.137020i | ||||
\(523\) | 13.5000 | + | 23.3827i | 0.590314 | + | 1.02245i | 0.994190 | + | 0.107640i | \(0.0343293\pi\) |
−0.403876 | + | 0.914814i | \(0.632337\pi\) | |||||||
\(524\) | 6.59629 | − | 11.4251i | 0.288160 | − | 0.499108i | ||||
\(525\) | −11.4223 | −0.498508 | ||||||||
\(526\) | −4.48146 | + | 7.76211i | −0.195401 | + | 0.338444i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.19258 | −0.0954199 | ||||||||
\(529\) | 6.40371 | − | 11.0915i | 0.278422 | − | 0.482241i | ||||
\(530\) | −3.09629 | − | 5.36293i | −0.134494 | − | 0.232951i | ||||
\(531\) | −11.7703 | − | 20.3868i | −0.510789 | − | 0.884712i | ||||
\(532\) | −7.00000 | −0.303488 | ||||||||
\(533\) | −0.614835 | + | 2.12985i | −0.0266315 | + | 0.0922541i | ||||
\(534\) | 16.9629 | 0.734057 | ||||||||
\(535\) | −2.01854 | − | 3.49622i | −0.0872693 | − | 0.151155i | ||||
\(536\) | 2.30742 | + | 3.99656i | 0.0996653 | + | 0.172625i | ||||
\(537\) | −9.57775 | + | 16.5891i | −0.413310 | + | 0.715874i | ||||
\(538\) | −7.19258 | −0.310094 | ||||||||
\(539\) | −3.50000 | + | 6.06218i | −0.150756 | + | 0.261116i | ||||
\(540\) | −2.98146 | + | 5.16403i | −0.128301 | + | 0.222225i | ||||
\(541\) | 36.3110 | 1.56113 | 0.780566 | − | 0.625074i | \(-0.214931\pi\) | ||||
0.780566 | + | 0.625074i | \(0.214931\pi\) | |||||||
\(542\) | 2.00000 | − | 3.46410i | 0.0859074 | − | 0.148796i | ||||
\(543\) | −0.403709 | − | 0.699244i | −0.0173248 | − | 0.0300074i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.61484 | −0.112007 | ||||||||
\(546\) | −3.19258 | + | 11.0594i | −0.136630 | + | 0.473300i | ||||
\(547\) | −26.8074 | −1.14620 | −0.573101 | − | 0.819485i | \(-0.694260\pi\) | ||||
−0.573101 | + | 0.819485i | \(0.694260\pi\) | |||||||
\(548\) | 1.88516 | + | 3.26520i | 0.0805302 | + | 0.139482i | ||||
\(549\) | −2.61484 | − | 4.52903i | −0.111598 | − | 0.193294i | ||||
\(550\) | 3.92225 | − | 6.79354i | 0.167245 | − | 0.289678i | ||||
\(551\) | 3.96291 | 0.168826 | ||||||||
\(552\) | 1.59629 | − | 2.76486i | 0.0679427 | − | 0.117680i | ||||
\(553\) | 7.98146 | − | 13.8243i | 0.339406 | − | 0.587868i | ||||
\(554\) | −4.57775 | −0.194490 | ||||||||
\(555\) | −3.32596 | + | 5.76073i | −0.141179 | + | 0.244530i | ||||
\(556\) | 10.7889 | + | 18.6869i | 0.457550 | + | 0.792500i | ||||
\(557\) | 15.5777 | + | 26.9814i | 0.660050 | + | 1.14324i | 0.980602 | + | 0.196010i | \(0.0627984\pi\) |
−0.320552 | + | 0.947231i | \(0.603868\pi\) | |||||||
\(558\) | −2.00000 | −0.0846668 | ||||||||
\(559\) | −31.5000 | + | 7.79423i | −1.33231 | + | 0.329661i | ||||
\(560\) | −3.80742 | −0.160893 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.88516 | + | 17.1216i | 0.416981 | + | 0.722231i | ||||
\(563\) | −4.38516 | + | 7.59533i | −0.184813 | + | 0.320105i | −0.943513 | − | 0.331334i | \(-0.892501\pi\) |
0.758701 | + | 0.651439i | \(0.225835\pi\) | |||||||
\(564\) | 3.38516 | 0.142541 | ||||||||
\(565\) | −3.57775 | + | 6.19684i | −0.150517 | + | 0.260703i | ||||
\(566\) | 0.981456 | − | 1.69993i | 0.0412537 | − | 0.0714535i | ||||
\(567\) | −3.19258 | −0.134076 | ||||||||
\(568\) | −6.28887 | + | 10.8926i | −0.263875 | + | 0.457045i | ||||
\(569\) | 3.61484 | + | 6.26108i | 0.151542 | + | 0.262478i | 0.931794 | − | 0.362986i | \(-0.118243\pi\) |
−0.780253 | + | 0.625464i | \(0.784910\pi\) | |||||||
\(570\) | 1.30742 | + | 2.26451i | 0.0547617 | + | 0.0948500i | ||||
\(571\) | 40.3110 | 1.68696 | 0.843481 | − | 0.537159i | \(-0.180502\pi\) | ||||
0.843481 | + | 0.537159i | \(0.180502\pi\) | |||||||
\(572\) | −5.48146 | − | 5.69650i | −0.229191 | − | 0.238182i | ||||
\(573\) | 2.61484 | 0.109236 | ||||||||
\(574\) | 0.981456 | + | 1.69993i | 0.0409652 | + | 0.0709538i | ||||
\(575\) | 5.71113 | + | 9.89196i | 0.238170 | + | 0.412523i | ||||
\(576\) | 1.00000 | − | 1.73205i | 0.0416667 | − | 0.0721688i | ||||
\(577\) | 13.6148 | 0.566793 | 0.283397 | − | 0.959003i | \(-0.408539\pi\) | ||||
0.283397 | + | 0.959003i | \(0.408539\pi\) | |||||||
\(578\) | 8.50000 | − | 14.7224i | 0.353553 | − | 0.612372i | ||||
\(579\) | −5.48146 | + | 9.49416i | −0.227802 | + | 0.394564i | ||||
\(580\) | 2.15549 | 0.0895020 | ||||||||
\(581\) | −5.77033 | + | 9.99450i | −0.239394 | + | 0.414642i | ||||
\(582\) | 4.69258 | + | 8.12779i | 0.194514 | + | 0.336908i | ||||
\(583\) | −5.69258 | − | 9.85984i | −0.235763 | − | 0.408353i | ||||
\(584\) | 9.00000 | 0.372423 | ||||||||
\(585\) | −8.34808 | + | 2.06561i | −0.345150 | + | 0.0854026i | ||||
\(586\) | −15.1926 | −0.627600 | ||||||||
\(587\) | 16.7518 | + | 29.0149i | 0.691420 | + | 1.19757i | 0.971373 | + | 0.237561i | \(0.0763480\pi\) |
−0.279952 | + | 0.960014i | \(0.590319\pi\) | |||||||
\(588\) | 1.59629 | + | 2.76486i | 0.0658299 | + | 0.114021i | ||||
\(589\) | −1.09629 | + | 1.89883i | −0.0451719 | + | 0.0782400i | ||||
\(590\) | −14.0371 | −0.577898 | ||||||||
\(591\) | −11.8852 | + | 20.5857i | −0.488890 | + | 0.846783i | ||||
\(592\) | 2.78887 | − | 4.83047i | 0.114622 | − | 0.198531i | ||||
\(593\) | 33.5407 | 1.37735 | 0.688675 | − | 0.725070i | \(-0.258193\pi\) | ||||
0.688675 | + | 0.725070i | \(0.258193\pi\) | |||||||
\(594\) | −5.48146 | + | 9.49416i | −0.224907 | + | 0.389550i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.28887 | − | 16.0888i | −0.380487 | − | 0.659023i | ||||
\(597\) | 0.192582 | 0.00788187 | ||||||||
\(598\) | 11.1740 | − | 2.76486i | 0.456940 | − | 0.113063i | ||||
\(599\) | −6.77033 | −0.276628 | −0.138314 | − | 0.990388i | \(-0.544168\pi\) | ||||
−0.138314 | + | 0.990388i | \(0.544168\pi\) | |||||||
\(600\) | −1.78887 | − | 3.09842i | −0.0730305 | − | 0.126492i | ||||
\(601\) | 1.30742 | + | 2.26451i | 0.0533307 | + | 0.0923714i | 0.891458 | − | 0.453103i | \(-0.149683\pi\) |
−0.838128 | + | 0.545474i | \(0.816350\pi\) | |||||||
\(602\) | −14.3666 | + | 24.8837i | −0.585540 | + | 1.01418i | ||||
\(603\) | 9.22967 | 0.375861 | ||||||||
\(604\) | −4.88516 | + | 8.46135i | −0.198775 | + | 0.344288i | ||||
\(605\) | 3.69258 | − | 6.39574i | 0.150125 | − | 0.260024i | ||||
\(606\) | −0.614835 | −0.0249760 | ||||||||
\(607\) | 16.9444 | − | 29.3485i | 0.687751 | − | 1.19122i | −0.284813 | − | 0.958583i | \(-0.591932\pi\) |
0.972564 | − | 0.232636i | \(-0.0747351\pi\) | |||||||
\(608\) | −1.09629 | − | 1.89883i | −0.0444605 | − | 0.0770078i | ||||
\(609\) | −2.88516 | − | 4.99725i | −0.116913 | − | 0.202499i | ||||
\(610\) | −3.11841 | −0.126261 | ||||||||
\(611\) | 8.46291 | + | 8.79492i | 0.342373 | + | 0.355804i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.48146 | − | 6.03006i | −0.140615 | − | 0.243552i | 0.787114 | − | 0.616808i | \(-0.211575\pi\) |
−0.927728 | + | 0.373256i | \(0.878241\pi\) | |||||||
\(614\) | 7.50000 | + | 12.9904i | 0.302675 | + | 0.524249i | ||||
\(615\) | 0.366621 | − | 0.635006i | 0.0147836 | − | 0.0256059i | ||||
\(616\) | −7.00000 | −0.282038 | ||||||||
\(617\) | −21.8481 | + | 37.8420i | −0.879570 | + | 1.52346i | −0.0277575 | + | 0.999615i | \(0.508837\pi\) |
−0.851813 | + | 0.523846i | \(0.824497\pi\) | |||||||
\(618\) | 8.07775 | − | 13.9911i | 0.324935 | − | 0.562803i | ||||
\(619\) | 27.9629 | 1.12392 | 0.561962 | − | 0.827163i | \(-0.310047\pi\) | ||||
0.561962 | + | 0.827163i | \(0.310047\pi\) | |||||||
\(620\) | −0.596291 | + | 1.03281i | −0.0239476 | + | 0.0414785i | ||||
\(621\) | −7.98146 | − | 13.8243i | −0.320285 | − | 0.554750i | ||||
\(622\) | 11.0777 | + | 19.1872i | 0.444177 | + | 0.769337i | ||||
\(623\) | 54.1555 | 2.16969 | ||||||||
\(624\) | −3.50000 | + | 0.866025i | −0.140112 | + | 0.0346688i | ||||
\(625\) | 5.68901 | 0.227560 | ||||||||
\(626\) | 6.28887 | + | 10.8926i | 0.251354 | + | 0.435358i | ||||
\(627\) | 2.40371 | + | 4.16335i | 0.0959949 | + | 0.166268i | ||||
\(628\) | 2.78887 | − | 4.83047i | 0.111288 | − | 0.192757i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −3.80742 | + | 6.59464i | −0.151691 | + | 0.262737i | ||||
\(631\) | −21.8666 | + | 37.8741i | −0.870496 | + | 1.50774i | −0.00901240 | + | 0.999959i | \(0.502869\pi\) |
−0.861484 | + | 0.507785i | \(0.830465\pi\) | |||||||
\(632\) | 5.00000 | 0.198889 | ||||||||
\(633\) | −1.78887 | + | 3.09842i | −0.0711013 | + | 0.123151i | ||||
\(634\) | 6.77033 | + | 11.7266i | 0.268884 | + | 0.465721i | ||||
\(635\) | 7.15549 | + | 12.3937i | 0.283957 | + | 0.491828i | ||||
\(636\) | −5.19258 | −0.205899 | ||||||||
\(637\) | −3.19258 | + | 11.0594i | −0.126495 | + | 0.438191i | ||||
\(638\) | 3.96291 | 0.156893 | ||||||||
\(639\) | 12.5777 | + | 21.7853i | 0.497568 | + | 0.861813i | ||||
\(640\) | −0.596291 | − | 1.03281i | −0.0235705 | − | 0.0408253i | ||||
\(641\) | −3.28887 | + | 5.69650i | −0.129903 | + | 0.224998i | −0.923639 | − | 0.383264i | \(-0.874800\pi\) |
0.793736 | + | 0.608262i | \(0.208133\pi\) | |||||||
\(642\) | −3.38516 | −0.133602 | ||||||||
\(643\) | 4.09629 | − | 7.09498i | 0.161542 | − | 0.279799i | −0.773880 | − | 0.633332i | \(-0.781687\pi\) |
0.935422 | + | 0.353533i | \(0.115020\pi\) | |||||||
\(644\) | 5.09629 | − | 8.82704i | 0.200822 | − | 0.347834i | ||||
\(645\) | 10.7332 | 0.422621 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0963 | + | 20.9514i | 0.475554 | + | 0.823684i | 0.999608 | − | 0.0280011i | \(-0.00891419\pi\) |
−0.524054 | + | 0.851685i | \(0.675581\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −25.8074 | −1.01303 | ||||||||
\(650\) | 3.57775 | − | 12.3937i | 0.140331 | − | 0.486120i | ||||
\(651\) | 3.19258 | 0.125127 | ||||||||
\(652\) | 8.90371 | + | 15.4217i | 0.348696 | + | 0.603959i | ||||
\(653\) | 13.1926 | + | 22.8502i | 0.516266 | + | 0.894198i | 0.999822 | + | 0.0188849i | \(0.00601161\pi\) |
−0.483556 | + | 0.875313i | \(0.660655\pi\) | |||||||
\(654\) | −1.09629 | + | 1.89883i | −0.0428684 | + | 0.0742502i | ||||
\(655\) | −15.7332 | −0.614749 | ||||||||
\(656\) | −0.307418 | + | 0.532463i | −0.0120026 | + | 0.0207892i | ||||
\(657\) | 9.00000 | − | 15.5885i | 0.351123 | − | 0.608164i | ||||
\(658\) | 10.8074 | 0.421317 | ||||||||
\(659\) | 15.8852 | − | 27.5139i | 0.618798 | − | 1.07179i | −0.370907 | − | 0.928670i | \(-0.620953\pi\) |
0.989705 | − | 0.143120i | \(-0.0457135\pi\) | |||||||
\(660\) | 1.30742 | + | 2.26451i | 0.0508912 | + | 0.0881461i | ||||
\(661\) | −17.1740 | − | 29.7463i | −0.667993 | − | 1.15700i | −0.978465 | − | 0.206415i | \(-0.933820\pi\) |
0.310472 | − | 0.950583i | \(-0.399513\pi\) | |||||||
\(662\) | −5.00000 | −0.194331 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.61484 | −0.140283 | ||||||||
\(665\) | 4.17404 | + | 7.22965i | 0.161862 | + | 0.280354i | ||||
\(666\) | −5.57775 | − | 9.66094i | −0.216133 | − | 0.374354i | ||||
\(667\) | −2.88516 | + | 4.99725i | −0.111714 | + | 0.193494i | ||||
\(668\) | 8.38516 | 0.324432 | ||||||||
\(669\) | −3.78887 | + | 6.56252i | −0.146486 | + | 0.253722i | ||||
\(670\) | 2.75179 | − | 4.76623i | 0.106311 | − | 0.184136i | ||||
\(671\) | −5.73324 | −0.221329 | ||||||||
\(672\) | −1.59629 | + | 2.76486i | −0.0615783 | + | 0.106657i | ||||
\(673\) | 6.00000 | + | 10.3923i | 0.231283 | + | 0.400594i | 0.958186 | − | 0.286146i | \(-0.0923743\pi\) |
−0.726903 | + | 0.686740i | \(0.759041\pi\) | |||||||
\(674\) | −7.07775 | − | 12.2590i | −0.272625 | − | 0.472200i | ||||
\(675\) | −17.8887 | −0.688538 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | −12.9258 | −0.496780 | −0.248390 | − | 0.968660i | \(-0.579901\pi\) | ||||
−0.248390 | + | 0.968660i | \(0.579901\pi\) | |||||||
\(678\) | 3.00000 | + | 5.19615i | 0.115214 | + | 0.199557i | ||||
\(679\) | 14.9815 | + | 25.9486i | 0.574936 | + | 0.995818i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | −1.09629 | + | 1.89883i | −0.0419792 | + | 0.0727100i | ||||
\(683\) | 5.17404 | − | 8.96170i | 0.197979 | − | 0.342910i | −0.749894 | − | 0.661558i | \(-0.769896\pi\) |
0.947873 | + | 0.318648i | \(0.103229\pi\) | |||||||
\(684\) | −4.38516 | −0.167671 | ||||||||
\(685\) | 2.24821 | − | 3.89402i | 0.0858999 | − | 0.148783i | ||||
\(686\) | −6.07775 | − | 10.5270i | −0.232049 | − | 0.401921i | ||||
\(687\) | 1.69258 | + | 2.93164i | 0.0645760 | + | 0.111849i | ||||
\(688\) | −9.00000 | −0.343122 | ||||||||
\(689\) | −12.9815 | − | 13.4907i | −0.494554 | − | 0.513956i | ||||
\(690\) | −3.80742 | −0.144946 | ||||||||
\(691\) | 22.2703 | + | 38.5733i | 0.847203 | + | 1.46740i | 0.883694 | + | 0.468065i | \(0.155049\pi\) |
−0.0364907 | + | 0.999334i | \(0.511618\pi\) | |||||||
\(692\) | −6.57775 | − | 11.3930i | −0.250048 | − | 0.433097i | ||||
\(693\) | −7.00000 | + | 12.1244i | −0.265908 | + | 0.460566i | ||||
\(694\) | −14.4223 | −0.547461 | ||||||||
\(695\) | 12.8666 | − | 22.2856i | 0.488059 | − | 0.845343i | ||||
\(696\) | 0.903709 | − | 1.56527i | 0.0342550 | − | 0.0593314i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −8.19258 | + | 14.1900i | −0.310094 | + | 0.537098i | ||||
\(699\) | −6.69258 | − | 11.5919i | −0.253137 | − | 0.438446i | ||||
\(700\) | −5.71113 | − | 9.89196i | −0.215860 | − | 0.373881i | ||||
\(701\) | −12.8074 | −0.483729 | −0.241865 | − | 0.970310i | \(-0.577759\pi\) | ||||
−0.241865 | + | 0.970310i | \(0.577759\pi\) | |||||||
\(702\) | −5.00000 | + | 17.3205i | −0.188713 | + | 0.653720i | ||||
\(703\) | −12.2297 | −0.461251 | ||||||||
\(704\) | −1.09629 | − | 1.89883i | −0.0413180 | − | 0.0715649i | ||||
\(705\) | −2.01854 | − | 3.49622i | −0.0760228 | − | 0.131675i | ||||
\(706\) | 4.78887 | − | 8.29457i | 0.180232 | − | 0.312170i | ||||
\(707\) | −1.96291 | −0.0738229 | ||||||||
\(708\) | −5.88516 | + | 10.1934i | −0.221178 | + | 0.383092i | ||||
\(709\) | −23.8852 | + | 41.3703i | −0.897026 | + | 1.55369i | −0.0657495 | + | 0.997836i | \(0.520944\pi\) |
−0.831277 | + | 0.555859i | \(0.812390\pi\) | |||||||
\(710\) | 15.0000 | 0.562940 | ||||||||
\(711\) | 5.00000 | − | 8.66025i | 0.187515 | − | 0.324785i | ||||
\(712\) | 8.48146 | + | 14.6903i | 0.317856 | + | 0.550543i | ||||
\(713\) | −1.59629 | − | 2.76486i | −0.0597816 | − | 0.103545i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.61484 | + | 9.05805i | −0.0977893 | + | 0.338752i | ||||
\(716\) | −19.1555 | −0.715874 | ||||||||
\(717\) | −10.9815 | − | 19.0204i | −0.410110 | − | 0.710331i | ||||
\(718\) | 10.8852 | + | 18.8537i | 0.406231 | + | 0.703612i | ||||
\(719\) | 9.28887 | − | 16.0888i | 0.346417 | − | 0.600011i | −0.639194 | − | 0.769046i | \(-0.720732\pi\) |
0.985610 | + | 0.169035i | \(0.0540651\pi\) | |||||||
\(720\) | −2.38516 | −0.0888898 | ||||||||
\(721\) | 25.7889 | − | 44.6676i | 0.960428 | − | 1.66351i | ||||
\(722\) | 7.09629 | − | 12.2911i | 0.264097 | − | 0.457429i | ||||
\(723\) | −17.5407 | −0.652344 | ||||||||
\(724\) | 0.403709 | − | 0.699244i | 0.0150037 | − | 0.0259872i | ||||
\(725\) | 3.23324 | + | 5.60014i | 0.120080 | + | 0.207984i | ||||
\(726\) | −3.09629 | − | 5.36293i | −0.114914 | − | 0.199037i | ||||
\(727\) | −27.7703 | −1.02994 | −0.514972 | − | 0.857207i | \(-0.672198\pi\) | ||||
−0.514972 | + | 0.857207i | \(0.672198\pi\) | |||||||
\(728\) | −11.1740 | + | 2.76486i | −0.414137 | + | 0.102472i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −5.36662 | − | 9.29526i | −0.198628 | − | 0.344033i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.30742 | + | 2.26451i | −0.0483235 | + | 0.0836988i | ||||
\(733\) | 1.84451 | 0.0681284 | 0.0340642 | − | 0.999420i | \(-0.489155\pi\) | ||||
0.0340642 | + | 0.999420i | \(0.489155\pi\) | |||||||
\(734\) | 9.07775 | − | 15.7231i | 0.335066 | − | 0.580351i | ||||
\(735\) | 1.90371 | − | 3.29732i | 0.0702194 | − | 0.121623i | ||||
\(736\) | 3.19258 | 0.117680 | ||||||||
\(737\) | 5.05920 | − | 8.76280i | 0.186358 | − | 0.322782i | ||||
\(738\) | 0.614835 | + | 1.06493i | 0.0226324 | + | 0.0392005i | ||||
\(739\) | 10.9815 | + | 19.0204i | 0.403959 | + | 0.699678i | 0.994200 | − | 0.107549i | \(-0.0343004\pi\) |
−0.590240 | + | 0.807228i | \(0.700967\pi\) | |||||||
\(740\) | −6.65192 | −0.244530 | ||||||||
\(741\) | 5.48146 | + | 5.69650i | 0.201366 | + | 0.209266i | ||||
\(742\) | −16.5777 | −0.608588 | ||||||||
\(743\) | 7.32596 | + | 12.6889i | 0.268763 | + | 0.465512i | 0.968543 | − | 0.248847i | \(-0.0800517\pi\) |
−0.699779 | + | 0.714359i | \(0.746718\pi\) | |||||||
\(744\) | 0.500000 | + | 0.866025i | 0.0183309 | + | 0.0317500i | ||||
\(745\) | −11.0777 | + | 19.1872i | −0.405857 | + | 0.702965i | ||||
\(746\) | 13.1555 | 0.481657 | ||||||||
\(747\) | −3.61484 | + | 6.26108i | −0.132260 | + | 0.229081i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.8074 | −0.394894 | ||||||||
\(750\) | −5.11484 | + | 8.85915i | −0.186767 | + | 0.323491i | ||||
\(751\) | −2.32596 | − | 4.02868i | −0.0848755 | − | 0.147009i | 0.820463 | − | 0.571700i | \(-0.193716\pi\) |
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(752\) | 1.69258 | + | 2.93164i | 0.0617221 | + | 0.106906i | ||||
\(753\) | 10.7703 | 0.392493 | ||||||||
\(754\) | 6.32596 | − | 1.56527i | 0.230378 | − | 0.0570038i | ||||
\(755\) | 11.6519 | 0.424057 | ||||||||
\(756\) | 7.98146 | + | 13.8243i | 0.290283 | + | 0.502784i | ||||
\(757\) | 9.71113 | + | 16.8202i | 0.352957 | + | 0.611339i | 0.986766 | − | 0.162150i | \(-0.0518429\pi\) |
−0.633809 | + | 0.773489i | \(0.718510\pi\) | |||||||
\(758\) | −18.8666 | + | 32.6779i | −0.685267 | + | 1.18692i | ||||
\(759\) | −7.00000 | −0.254084 | ||||||||
\(760\) | −1.30742 | + | 2.26451i | −0.0474250 | + | 0.0821425i | ||||
\(761\) | 8.42225 | − | 14.5878i | 0.305306 | − | 0.528806i | −0.672023 | − | 0.740530i | \(-0.734574\pi\) |
0.977330 | + | 0.211724i | \(0.0679078\pi\) | |||||||
\(762\) | 12.0000 | 0.434714 | ||||||||
\(763\) | −3.50000 | + | 6.06218i | −0.126709 | + | 0.219466i | ||||
\(764\) | 1.30742 | + | 2.26451i | 0.0473007 | + | 0.0819272i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.22967 | 0.152824 | ||||||||
\(767\) | −41.1962 | + | 10.1934i | −1.48751 | + | 0.368063i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −27.3481 | − | 47.3683i | −0.986197 | − | 1.70814i | −0.636492 | − | 0.771283i | \(-0.719615\pi\) |
−0.349705 | − | 0.936860i | \(-0.613718\pi\) | |||||||
\(770\) | 4.17404 | + | 7.22965i | 0.150422 | + | 0.260538i | ||||
\(771\) | −9.09629 | + | 15.7552i | −0.327595 | + | 0.567411i | ||||
\(772\) | −10.9629 | −0.394564 | ||||||||
\(773\) | −3.88516 | + | 6.72930i | −0.139740 | + | 0.242036i | −0.927398 | − | 0.374076i | \(-0.877960\pi\) |
0.787658 | + | 0.616112i | \(0.211293\pi\) | |||||||
\(774\) | −9.00000 | + | 15.5885i | −0.323498 | + | 0.560316i | ||||
\(775\) | −3.57775 | −0.128516 | ||||||||
\(776\) | −4.69258 | + | 8.12779i | −0.168454 | + | 0.291771i | ||||
\(777\) | 8.90371 | + | 15.4217i | 0.319419 | + | 0.553250i | ||||
\(778\) | −5.59629 | − | 9.69306i | −0.200637 | − | 0.347513i | ||||
\(779\) | 1.34808 | 0.0482999 | ||||||||
\(780\) | 2.98146 | + | 3.09842i | 0.106753 | + | 0.110941i | ||||
\(781\) | 27.5777 | 0.986809 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.51854 | − | 7.82635i | −0.161480 | − | 0.279691i | ||||
\(784\) | −1.59629 | + | 2.76486i | −0.0570104 | + | 0.0987449i | ||||
\(785\) | −6.65192 | −0.237417 | ||||||||
\(786\) | −6.59629 | + | 11.4251i | −0.235282 | + | 0.407520i | ||||
\(787\) | 8.57775 | − | 14.8571i | 0.305764 | − | 0.529598i | −0.671667 | − | 0.740853i | \(-0.734422\pi\) |
0.977431 | + | 0.211255i | \(0.0677549\pi\) | |||||||
\(788\) | −23.7703 | −0.846783 | ||||||||
\(789\) | 4.48146 | − | 7.76211i | 0.159544 | − | 0.276338i | ||||
\(790\) | −2.98146 | − | 5.16403i | −0.106075 | − | 0.183728i | ||||
\(791\) | 9.57775 | + | 16.5891i | 0.340545 | + | 0.589842i | ||||
\(792\) | −4.38516 | −0.155820 | ||||||||
\(793\) | −9.15192 | + | 2.26451i | −0.324994 | + | 0.0804152i | ||||
\(794\) | 13.6148 | 0.483172 | ||||||||
\(795\) | 3.09629 | + | 5.36293i | 0.109814 | + | 0.190204i | ||||
\(796\) | 0.0962912 | + | 0.166781i | 0.00341295 | + | 0.00591140i | ||||
\(797\) | 18.6370 | − | 32.2801i | 0.660155 | − | 1.14342i | −0.320420 | − | 0.947276i | \(-0.603824\pi\) |
0.980575 | − | 0.196146i | \(-0.0628426\pi\) | |||||||
\(798\) | 7.00000 | 0.247797 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.78887 | − | 3.09842i | 0.0632462 | − | 0.109546i | ||||
\(801\) | 33.9258 | 1.19871 | ||||||||
\(802\) | −9.30742 | + | 16.1209i | −0.328656 | + | 0.569249i | ||||
\(803\) | −9.86662 | − | 17.0895i | −0.348185 | − | 0.603075i | ||||
\(804\) | −2.30742 | − | 3.99656i | −0.0813763 | − | 0.140948i | ||||
\(805\) | −12.1555 | −0.428425 | ||||||||
\(806\) | −1.00000 | + | 3.46410i | −0.0352235 | + | 0.122018i | ||||
\(807\) | 7.19258 | 0.253191 | ||||||||
\(808\) | −0.307418 | − | 0.532463i | −0.0108149 | − | 0.0187320i | ||||
\(809\) | 2.67404 | + | 4.63157i | 0.0940142 | + | 0.162837i | 0.909197 | − | 0.416367i | \(-0.136697\pi\) |
−0.815183 | + | 0.579204i | \(0.803363\pi\) | |||||||
\(810\) | −0.596291 | + | 1.03281i | −0.0209515 | + | 0.0362891i | ||||
\(811\) | 13.3852 | 0.470017 | 0.235008 | − | 0.971993i | \(-0.424488\pi\) | ||||
0.235008 | + | 0.971993i | \(0.424488\pi\) | |||||||
\(812\) | 2.88516 | − | 4.99725i | 0.101249 | − | 0.175369i | ||||
\(813\) | −2.00000 | + | 3.46410i | −0.0701431 | + | 0.121491i | ||||
\(814\) | −12.2297 | −0.428650 | ||||||||
\(815\) | 10.6184 | − | 18.3916i | 0.371947 | − | 0.644230i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.86662 | + | 17.0895i | 0.345189 | + | 0.597886i | ||||
\(818\) | −34.5777 | −1.20898 | ||||||||
\(819\) | −6.38516 | + | 22.1189i | −0.223116 | + | 0.772896i | ||||
\(820\) | 0.733242 | 0.0256059 | ||||||||
\(821\) | −18.1740 | − | 31.4784i | −0.634278 | − | 1.09860i | −0.986668 | − | 0.162749i | \(-0.947964\pi\) |
0.352389 | − | 0.935854i | \(-0.385369\pi\) | |||||||
\(822\) | −1.88516 | − | 3.26520i | −0.0657527 | − | 0.113887i | ||||
\(823\) | 19.2518 | − | 33.3451i | 0.671075 | − | 1.16234i | −0.306525 | − | 0.951863i | \(-0.599166\pi\) |
0.977600 | − | 0.210473i | \(-0.0675005\pi\) | |||||||
\(824\) | 16.1555 | 0.562803 | ||||||||
\(825\) | −3.92225 | + | 6.79354i | −0.136555 | + | 0.236521i | ||||
\(826\) | −18.7889 | + | 32.5433i | −0.653749 | + | 1.13233i | ||||
\(827\) | 2.19258 | 0.0762436 | 0.0381218 | − | 0.999273i | \(-0.487863\pi\) | ||||
0.0381218 | + | 0.999273i | \(0.487863\pi\) | |||||||
\(828\) | 3.19258 | − | 5.52971i | 0.110950 | − | 0.192171i | ||||
\(829\) | −23.8481 | − | 41.3061i | −0.828278 | − | 1.43462i | −0.899388 | − | 0.437151i | \(-0.855988\pi\) |
0.0711102 | − | 0.997468i | \(-0.477346\pi\) | |||||||
\(830\) | 2.15549 | + | 3.73343i | 0.0748183 | + | 0.129589i | ||||
\(831\) | 4.57775 | 0.158800 | ||||||||
\(832\) | −2.50000 | − | 2.59808i | −0.0866719 | − | 0.0900721i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −10.7889 | − | 18.6869i | −0.373588 | − | 0.647074i | ||||
\(835\) | −5.00000 | − | 8.66025i | −0.173032 | − | 0.299700i | ||||
\(836\) | −2.40371 | + | 4.16335i | −0.0831340 | + | 0.143992i | ||||
\(837\) | 5.00000 | 0.172825 | ||||||||
\(838\) | −7.09629 | + | 12.2911i | −0.245137 | + | 0.424590i | ||||
\(839\) | −11.9629 | + | 20.7204i | −0.413006 | + | 0.715347i | −0.995217 | − | 0.0976909i | \(-0.968854\pi\) |
0.582211 | + | 0.813038i | \(0.302188\pi\) | |||||||
\(840\) | 3.80742 | 0.131368 | ||||||||
\(841\) | 12.8666 | − | 22.2856i | 0.443677 | − | 0.768470i | ||||
\(842\) | 9.69258 | + | 16.7880i | 0.334028 | + | 0.578554i | ||||
\(843\) | −9.88516 | − | 17.1216i | −0.340463 | − | 0.589699i | ||||
\(844\) | −3.57775 | −0.123151 | ||||||||
\(845\) | −0.596291 | + | 15.4921i | −0.0205130 | + | 0.532944i | ||||
\(846\) | 6.77033 | 0.232769 | ||||||||
\(847\) | −9.88516 | − | 17.1216i | −0.339658 | − | 0.588305i | ||||
\(848\) | −2.59629 | − | 4.49691i | −0.0891570 | − | 0.154424i | ||||
\(849\) | −0.981456 | + | 1.69993i | −0.0336835 | + | 0.0583415i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.90371 | − | 15.4217i | 0.305215 | − | 0.528648i | ||||
\(852\) | 6.28887 | − | 10.8926i | 0.215453 | − | 0.373176i | ||||
\(853\) | 1.26676 | 0.0433730 | 0.0216865 | − | 0.999765i | \(-0.493096\pi\) | ||||
0.0216865 | + | 0.999765i | \(0.493096\pi\) | |||||||
\(854\) | −4.17404 | + | 7.22965i | −0.142833 | + | 0.247393i | ||||
\(855\) | 2.61484 | + | 4.52903i | 0.0894255 | + | 0.154889i | ||||
\(856\) | −1.69258 | − | 2.93164i | −0.0578513 | − | 0.100201i | ||||
\(857\) | 54.2739 | 1.85396 | 0.926981 | − | 0.375109i | \(-0.122395\pi\) | ||||
0.926981 | + | 0.375109i | \(0.122395\pi\) | |||||||
\(858\) | 5.48146 | + | 5.69650i | 0.187134 | + | 0.194475i | ||||
\(859\) | −44.5777 | −1.52097 | −0.760487 | − | 0.649354i | \(-0.775040\pi\) | ||||
−0.760487 | + | 0.649354i | \(0.775040\pi\) | |||||||
\(860\) | 5.36662 | + | 9.29526i | 0.183000 | + | 0.316966i | ||||
\(861\) | −0.981456 | − | 1.69993i | −0.0334479 | − | 0.0579335i | ||||
\(862\) | −2.30742 | + | 3.99656i | −0.0785910 | + | 0.136124i | ||||
\(863\) | 27.7703 | 0.945313 | 0.472657 | − | 0.881247i | \(-0.343295\pi\) | ||||
0.472657 | + | 0.881247i | \(0.343295\pi\) | |||||||
\(864\) | −2.50000 | + | 4.33013i | −0.0850517 | + | 0.147314i | ||||
\(865\) | −7.84451 | + | 13.5871i | −0.266721 | + | 0.461975i | ||||
\(866\) | 17.5777 | 0.597316 | ||||||||
\(867\) | −8.50000 | + | 14.7224i | −0.288675 | + | 0.500000i | ||||
\(868\) | 1.59629 | + | 2.76486i | 0.0541817 | + | 0.0938454i | ||||
\(869\) | −5.48146 | − | 9.49416i | −0.185946 | − | 0.322067i | ||||
\(870\) | −2.15549 | −0.0730781 | ||||||||
\(871\) | 4.61484 | − | 15.9863i | 0.156368 | − | 0.541674i | ||||
\(872\) | −2.19258 | −0.0742502 | ||||||||
\(873\) | 9.38516 | + | 16.2556i | 0.317640 | + | 0.550168i | ||||
\(874\) | −3.50000 | − | 6.06218i | −0.118389 | − | 0.205056i | ||||
\(875\) | −16.3295 | + | 28.2836i | −0.552039 | + | 0.956160i | ||||
\(876\) | −9.00000 | −0.304082 | ||||||||
\(877\) | −20.3666 | + | 35.2760i | −0.687732 | + | 1.19119i | 0.284838 | + | 0.958576i | \(0.408060\pi\) |
−0.972570 | + | 0.232611i | \(0.925273\pi\) | |||||||
\(878\) | −3.50000 | + | 6.06218i | −0.118119 | + | 0.204589i | ||||
\(879\) | 15.1926 | 0.512433 | ||||||||
\(880\) | −1.30742 | + | 2.26451i | −0.0440730 | + | 0.0763367i | ||||
\(881\) | −8.98146 | − | 15.5563i | −0.302593 | − | 0.524106i | 0.674130 | − | 0.738613i | \(-0.264519\pi\) |
−0.976723 | + | 0.214507i | \(0.931186\pi\) | |||||||
\(882\) | 3.19258 | + | 5.52971i | 0.107500 | + | 0.186195i | ||||
\(883\) | −26.7332 | −0.899645 | −0.449823 | − | 0.893118i | \(-0.648513\pi\) | ||||
−0.449823 | + | 0.893118i | \(0.648513\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.0371 | 0.471852 | ||||||||
\(886\) | −6.77033 | − | 11.7266i | −0.227454 | − | 0.393961i | ||||
\(887\) | 10.5185 | + | 18.2187i | 0.353178 | + | 0.611722i | 0.986804 | − | 0.161917i | \(-0.0517676\pi\) |
−0.633626 | + | 0.773639i | \(0.718434\pi\) | |||||||
\(888\) | −2.78887 | + | 4.83047i | −0.0935885 | + | 0.162100i | ||||
\(889\) | 38.3110 | 1.28491 | ||||||||
\(890\) | 10.1148 | − | 17.5194i | 0.339050 | − | 0.587252i | ||||
\(891\) | −1.09629 | + | 1.89883i | −0.0367271 | + | 0.0636133i | ||||
\(892\) | −7.57775 | −0.253722 | ||||||||
\(893\) | 3.71113 | − | 6.42786i | 0.124188 | − | 0.215100i | ||||
\(894\) | 9.28887 | + | 16.0888i | 0.310666 | + | 0.538090i | ||||
\(895\) | 11.4223 | + | 19.7839i | 0.381804 | + | 0.661304i | ||||
\(896\) | −3.19258 | −0.106657 | ||||||||
\(897\) | −11.1740 | + | 2.76486i | −0.373090 | + | 0.0923159i | ||||
\(898\) | −5.03709 | −0.168090 | ||||||||
\(899\) | −0.903709 | − | 1.56527i | −0.0301404 | − | 0.0522047i | ||||
\(900\) | −3.57775 | − | 6.19684i | −0.119258 | − | 0.206561i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.34808 | 0.0448860 | ||||||||
\(903\) | 14.3666 | − | 24.8837i | 0.478091 | − | 0.828078i | ||||
\(904\) | −3.00000 | + | 5.19615i | −0.0997785 | + | 0.172821i | ||||
\(905\) | −0.962912 | −0.0320083 | ||||||||
\(906\) | 4.88516 | − | 8.46135i | 0.162299 | − | 0.281110i | ||||
\(907\) | −25.8295 | − | 44.7381i | −0.857656 | − | 1.48550i | −0.874159 | − | 0.485639i | \(-0.838587\pi\) |
0.0165038 | − | 0.999864i | \(-0.494746\pi\) | |||||||
\(908\) | 1.50000 | + | 2.59808i | 0.0497792 | + | 0.0862202i | ||||
\(909\) | −1.22967 | −0.0407856 | ||||||||
\(910\) | 9.51854 | + | 9.89196i | 0.315537 | + | 0.327915i | ||||
\(911\) | −1.77033 | −0.0586536 | −0.0293268 | − | 0.999570i | \(-0.509336\pi\) | ||||
−0.0293268 | + | 0.999570i | \(0.509336\pi\) | |||||||
\(912\) | 1.09629 | + | 1.89883i | 0.0363018 | + | 0.0628766i | ||||
\(913\) | 3.96291 | + | 6.86396i | 0.131153 | + | 0.227164i | ||||
\(914\) | 13.2889 | − | 23.0170i | 0.439557 | − | 0.761335i | ||||
\(915\) | 3.11841 | 0.103091 | ||||||||
\(916\) | −1.69258 | + | 2.93164i | −0.0559245 | + | 0.0968641i | ||||
\(917\) | −21.0592 | + | 36.4756i | −0.695436 | + | 1.20453i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.0777 | − | 22.6513i | 0.431395 | − | 0.747198i | −0.565599 | − | 0.824681i | \(-0.691355\pi\) |
0.996994 | + | 0.0774825i | \(0.0246882\pi\) | |||||||
\(920\) | −1.90371 | − | 3.29732i | −0.0627634 | − | 0.108709i | ||||
\(921\) | −7.50000 | − | 12.9904i | −0.247133 | − | 0.428048i | ||||
\(922\) | 3.19258 | 0.105142 | ||||||||
\(923\) | 44.0221 | − | 10.8926i | 1.44901 | − | 0.358536i | ||||
\(924\) | 7.00000 | 0.230283 | ||||||||
\(925\) | −9.97788 | − | 17.2822i | −0.328071 | − | 0.568235i | ||||
\(926\) | 10.3666 | + | 17.9555i | 0.340668 | + | 0.590055i | ||||
\(927\) | 16.1555 | − | 27.9821i | 0.530616 | − | 0.919054i | ||||
\(928\) | 1.80742 | 0.0593314 | ||||||||
\(929\) | −29.7518 | + | 51.5316i | −0.976124 | + | 1.69070i | −0.299951 | + | 0.953955i | \(0.596970\pi\) |
−0.676173 | + | 0.736742i | \(0.736363\pi\) | |||||||
\(930\) | 0.596291 | − | 1.03281i | 0.0195532 | − | 0.0338671i | ||||
\(931\) | 7.00000 | 0.229416 | ||||||||
\(932\) | 6.69258 | − | 11.5919i | 0.219223 | − | 0.379705i | ||||
\(933\) | −11.0777 | − | 19.1872i | −0.362669 | − | 0.628161i | ||||
\(934\) | 4.30742 | + | 7.46067i | 0.140943 | + | 0.244120i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.00000 | + | 1.73205i | −0.228802 | + | 0.0566139i | ||||
\(937\) | −7.96291 | −0.260137 | −0.130068 | − | 0.991505i | \(-0.541520\pi\) | ||||
−0.130068 | + | 0.991505i | \(0.541520\pi\) | |||||||
\(938\) | −7.36662 | − | 12.7594i | −0.240529 | − | 0.416608i | ||||
\(939\) | −6.28887 | − | 10.8926i | −0.205230 | − | 0.355468i | ||||
\(940\) | 2.01854 | − | 3.49622i | 0.0658376 | − | 0.114034i | ||||
\(941\) | −41.3481 | −1.34791 | −0.673954 | − | 0.738773i | \(-0.735406\pi\) | ||||
−0.673954 | + | 0.738773i | \(0.735406\pi\) | |||||||
\(942\) | −2.78887 | + | 4.83047i | −0.0908664 | + | 0.157385i | ||||
\(943\) | −0.981456 | + | 1.69993i | −0.0319606 | + | 0.0553574i | ||||
\(944\) | −11.7703 | −0.383092 | ||||||||
\(945\) | 9.51854 | − | 16.4866i | 0.309638 | − | 0.536309i | ||||
\(946\) | 9.86662 | + | 17.0895i | 0.320792 | + | 0.555627i | ||||
\(947\) | 17.6926 | + | 30.6445i | 0.574932 | + | 0.995811i | 0.996049 | + | 0.0888047i | \(0.0283047\pi\) |
−0.421117 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(948\) | −5.00000 | −0.162392 | ||||||||
\(949\) | −22.5000 | − | 23.3827i | −0.730381 | − | 0.759034i | ||||
\(950\) | −7.84451 | −0.254509 | ||||||||
\(951\) | −6.77033 | − | 11.7266i | −0.219543 | − | 0.380260i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.2703 | + | 47.2336i | −0.883373 | + | 1.53005i | −0.0358050 | + | 0.999359i | \(0.511400\pi\) |
−0.847568 | + | 0.530687i | \(0.821934\pi\) | |||||||
\(954\) | −10.3852 | −0.336232 | ||||||||
\(955\) | 1.55920 | − | 2.70062i | 0.0504546 | − | 0.0873900i | ||||
\(956\) | 10.9815 | − | 19.0204i | 0.355166 | − | 0.615165i | ||||
\(957\) | −3.96291 | −0.128103 | ||||||||
\(958\) | −4.77033 | + | 8.26245i | −0.154122 | + | 0.266948i | ||||
\(959\) | −6.01854 | − | 10.4244i | −0.194349 | − | 0.336622i | ||||
\(960\) | 0.596291 | + | 1.03281i | 0.0192452 | + | 0.0333337i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −19.5221 | + | 4.83047i | −0.629418 | + | 0.155741i | ||||
\(963\) | −6.77033 | −0.218171 | ||||||||
\(964\) | −8.77033 | − | 15.1907i | −0.282473 | − | 0.489258i | ||||
\(965\) | 6.53709 | + | 11.3226i | 0.210436 | + | 0.364486i | ||||
\(966\) | −5.09629 | + | 8.82704i | −0.163970 | + | 0.284005i | ||||
\(967\) | 37.3110 | 1.19984 | 0.599920 | − | 0.800060i | \(-0.295199\pi\) | ||||
0.599920 | + | 0.800060i | \(0.295199\pi\) | |||||||
\(968\) | 3.09629 | − | 5.36293i | 0.0995186 | − | 0.172371i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.1926 | 0.359372 | ||||||||
\(971\) | −14.5963 | + | 25.2815i | −0.468417 | + | 0.811323i | −0.999348 | − | 0.0360924i | \(-0.988509\pi\) |
0.530931 | + | 0.847415i | \(0.321842\pi\) | |||||||
\(972\) | 8.00000 | + | 13.8564i | 0.256600 | + | 0.444444i | ||||
\(973\) | −34.4444 | − | 59.6594i | −1.10424 | − | 1.91259i | ||||
\(974\) | 18.1555 | 0.581740 | ||||||||
\(975\) | −3.57775 | + | 12.3937i | −0.114580 | + | 0.396915i | ||||
\(976\) | −2.61484 | −0.0836988 | ||||||||
\(977\) | 5.42225 | + | 9.39162i | 0.173473 | + | 0.300464i | 0.939632 | − | 0.342187i | \(-0.111168\pi\) |
−0.766159 | + | 0.642652i | \(0.777834\pi\) | |||||||
\(978\) | −8.90371 | − | 15.4217i | −0.284709 | − | 0.493131i | ||||
\(979\) | 18.5963 | − | 32.2097i | 0.594340 | − | 1.02943i | ||||
\(980\) | 3.80742 | 0.121623 | ||||||||
\(981\) | −2.19258 | + | 3.79766i | −0.0700038 | + | 0.121250i | ||||
\(982\) | −10.1740 | + | 17.6220i | −0.324667 | + | 0.562339i | ||||
\(983\) | 11.8074 | 0.376598 | 0.188299 | − | 0.982112i | \(-0.439703\pi\) | ||||
0.188299 | + | 0.982112i | \(0.439703\pi\) | |||||||
\(984\) | 0.307418 | − | 0.532463i | 0.00980012 | − | 0.0169743i | ||||
\(985\) | 14.1740 | + | 24.5502i | 0.451622 | + | 0.782233i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.8074 | −0.344004 | ||||||||
\(988\) | −2.19258 | + | 7.59533i | −0.0697553 | + | 0.241640i | ||||
\(989\) | −28.7332 | −0.913664 | ||||||||
\(990\) | 2.61484 | + | 4.52903i | 0.0831049 | + | 0.143942i | ||||
\(991\) | −0.462912 | − | 0.801787i | −0.0147049 | − | 0.0254696i | 0.858579 | − | 0.512681i | \(-0.171348\pi\) |
−0.873284 | + | 0.487211i | \(0.838014\pi\) | |||||||
\(992\) | −0.500000 | + | 0.866025i | −0.0158750 | + | 0.0274963i | ||||
\(993\) | 5.00000 | 0.158670 | ||||||||
\(994\) | 20.0777 | − | 34.7757i | 0.636827 | − | 1.10302i | ||||
\(995\) | 0.114835 | − | 0.198900i | 0.00364052 | − | 0.00630557i | ||||
\(996\) | 3.61484 | 0.114540 | ||||||||
\(997\) | −3.00000 | + | 5.19615i | −0.0950110 | + | 0.164564i | −0.909613 | − | 0.415456i | \(-0.863622\pi\) |
0.814602 | + | 0.580020i | \(0.196955\pi\) | |||||||
\(998\) | −11.0777 | − | 19.1872i | −0.350660 | − | 0.607361i | ||||
\(999\) | 13.9444 | + | 24.1524i | 0.441180 | + | 0.764147i |
(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 | 806.2.g.c.497.2 | yes | 4 | |
13.9 | even | 3 | inner | 806.2.g.c.373.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
806.2.g.c.373.2 | ✓ | 4 | 13.9 | even | 3 | inner | |
806.2.g.c.497.2 | yes | 4 | 1.1 | even | 1 | trivial |