Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1000,2,Mod(149,1000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1000.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.o (of order \(10\), degree \(4\), 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: | \(7.98504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(112\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 149.10 | ||
Character | \(\chi\) | \(=\) | 1000.149 |
Dual form | 1000.2.o.a.349.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times\).
\(n\) | \(377\) | \(501\) | \(751\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.658957 | − | 1.25131i | −0.465953 | − | 0.884810i | ||||
\(3\) | 2.03813 | + | 1.48079i | 1.17671 | + | 0.854932i | 0.991797 | − | 0.127822i | \(-0.0407986\pi\) |
0.184916 | + | 0.982754i | \(0.440799\pi\) | |||||||
\(4\) | −1.13155 | + | 1.64912i | −0.565776 | + | 0.824559i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.509884 | − | 3.52610i | 0.208159 | − | 1.43953i | ||||
\(7\) | − | 3.58786i | − | 1.35608i | −0.735024 | − | 0.678042i | \(-0.762829\pi\) | ||
0.735024 | − | 0.678042i | \(-0.237171\pi\) | |||||||
\(8\) | 2.80920 | + | 0.329223i | 0.993203 | + | 0.116398i | ||||
\(9\) | 1.03418 | + | 3.18289i | 0.344728 | + | 1.06096i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.49567 | + | 0.810891i | 0.752472 | + | 0.244493i | 0.660044 | − | 0.751227i | \(-0.270537\pi\) |
0.0924272 | + | 0.995719i | \(0.470537\pi\) | |||||||
\(12\) | −4.74824 | + | 1.68553i | −1.37070 | + | 0.486570i | ||||
\(13\) | −2.11444 | − | 6.50757i | −0.586440 | − | 1.80488i | −0.593410 | − | 0.804900i | \(-0.702219\pi\) |
0.00697033 | − | 0.999976i | \(-0.497781\pi\) | |||||||
\(14\) | −4.48952 | + | 2.36424i | −1.19988 | + | 0.631871i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.43918 | − | 3.73212i | −0.359796 | − | 0.933031i | ||||
\(17\) | 1.14335 | + | 1.57369i | 0.277304 | + | 0.381677i | 0.924839 | − | 0.380360i | \(-0.124200\pi\) |
−0.647534 | + | 0.762036i | \(0.724200\pi\) | |||||||
\(18\) | 3.30130 | − | 3.39148i | 0.778124 | − | 0.799378i | ||||
\(19\) | −3.00859 | − | 4.14097i | −0.690218 | − | 0.950003i | 0.309782 | − | 0.950808i | \(-0.399744\pi\) |
−1.00000 | 0.000804663i | \(0.999744\pi\) | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.31285 | − | 7.31251i | 1.15936 | − | 1.59572i | ||||
\(22\) | −0.629861 | − | 3.65719i | −0.134287 | − | 0.779716i | ||||
\(23\) | 0.737902 | + | 0.239759i | 0.153863 | + | 0.0499932i | 0.384936 | − | 0.922943i | \(-0.374224\pi\) |
−0.231073 | + | 0.972936i | \(0.574224\pi\) | |||||||
\(24\) | 5.23800 | + | 4.83083i | 1.06920 | + | 0.986088i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.74966 | + | 6.93403i | −1.32372 | + | 1.35987i | ||||
\(27\) | −0.269899 | + | 0.830663i | −0.0519421 | + | 0.159861i | ||||
\(28\) | 5.91680 | + | 4.05985i | 1.11817 | + | 0.767239i | ||||
\(29\) | 3.28631 | − | 4.52322i | 0.610252 | − | 0.839940i | −0.386346 | − | 0.922354i | \(-0.626263\pi\) |
0.996598 | + | 0.0824137i | \(0.0262629\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.72253 | − | 1.25149i | 0.309376 | − | 0.224775i | −0.422253 | − | 0.906478i | \(-0.638761\pi\) |
0.731629 | + | 0.681704i | \(0.238761\pi\) | |||||||
\(32\) | −3.72168 | + | 4.26017i | −0.657907 | + | 0.753099i | ||||
\(33\) | 3.88573 | + | 5.34825i | 0.676419 | + | 0.931010i | ||||
\(34\) | 1.21576 | − | 2.46769i | 0.208500 | − | 0.423205i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.41920 | − | 1.89612i | −1.06987 | − | 0.316019i | ||||
\(37\) | 2.73986 | + | 8.43241i | 0.450430 | + | 1.38628i | 0.876418 | + | 0.481551i | \(0.159926\pi\) |
−0.425988 | + | 0.904729i | \(0.640074\pi\) | |||||||
\(38\) | −3.19910 | + | 6.49339i | −0.518963 | + | 1.05337i | ||||
\(39\) | 5.32683 | − | 16.3943i | 0.852975 | − | 2.62519i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.12308 | + | 3.45647i | 0.175395 | + | 0.539811i | 0.999651 | − | 0.0264065i | \(-0.00840642\pi\) |
−0.824256 | + | 0.566217i | \(0.808406\pi\) | |||||||
\(42\) | −12.6512 | − | 1.82939i | −1.95212 | − | 0.282281i | ||||
\(43\) | −0.652170 | −0.0994550 | −0.0497275 | − | 0.998763i | \(-0.515835\pi\) | ||||
−0.0497275 | + | 0.998763i | \(0.515835\pi\) | |||||||
\(44\) | −4.16123 | + | 3.19808i | −0.627329 | + | 0.482129i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.186233 | − | 1.08133i | −0.0274585 | − | 0.159434i | ||||
\(47\) | −0.541317 | + | 0.745059i | −0.0789592 | + | 0.108678i | −0.846670 | − | 0.532119i | \(-0.821396\pi\) |
0.767710 | + | 0.640797i | \(0.221396\pi\) | |||||||
\(48\) | 2.59324 | − | 9.73767i | 0.374302 | − | 1.40551i | ||||
\(49\) | −5.87273 | −0.838962 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.90045i | 0.686201i | ||||||||
\(52\) | 13.1244 | + | 3.87669i | 1.82002 | + | 0.537601i | ||||
\(53\) | −1.48529 | − | 1.07913i | −0.204020 | − | 0.148229i | 0.481084 | − | 0.876675i | \(-0.340243\pi\) |
−0.685104 | + | 0.728445i | \(0.740243\pi\) | |||||||
\(54\) | 1.21727 | − | 0.209644i | 0.165649 | − | 0.0285290i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.18121 | − | 10.0790i | 0.157845 | − | 1.34687i | ||||
\(57\) | − | 12.8949i | − | 1.70797i | ||||||
\(58\) | −7.82548 | − | 1.13159i | −1.02754 | − | 0.148584i | ||||
\(59\) | 3.74706 | − | 1.21749i | 0.487826 | − | 0.158504i | −0.0547685 | − | 0.998499i | \(-0.517442\pi\) |
0.542594 | + | 0.839995i | \(0.317442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.21266 | − | 2.01862i | −0.795449 | − | 0.258457i | −0.117027 | − | 0.993129i | \(-0.537336\pi\) |
−0.678423 | + | 0.734672i | \(0.737336\pi\) | |||||||
\(62\) | −2.70108 | − | 1.33074i | −0.343037 | − | 0.169004i | ||||
\(63\) | 11.4198 | − | 3.71051i | 1.43876 | − | 0.467480i | ||||
\(64\) | 7.78322 | + | 1.84971i | 0.972903 | + | 0.231214i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.13179 | − | 8.38651i | 0.508588 | − | 1.03231i | ||||
\(67\) | −3.97847 | + | 2.89052i | −0.486047 | + | 0.353134i | −0.803662 | − | 0.595086i | \(-0.797118\pi\) |
0.317615 | + | 0.948220i | \(0.397118\pi\) | |||||||
\(68\) | −3.88897 | + | 0.104813i | −0.471607 | + | 0.0127104i | ||||
\(69\) | 1.14891 | + | 1.58133i | 0.138312 | + | 0.190370i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.48762 | + | 3.26045i | 0.532582 | + | 0.386944i | 0.821323 | − | 0.570464i | \(-0.193236\pi\) |
−0.288740 | + | 0.957407i | \(0.593236\pi\) | |||||||
\(72\) | 1.85735 | + | 9.28187i | 0.218891 | + | 1.09388i | ||||
\(73\) | 14.1026 | + | 4.58222i | 1.65059 | + | 0.536309i | 0.978868 | − | 0.204496i | \(-0.0655554\pi\) |
0.671721 | + | 0.740804i | \(0.265555\pi\) | |||||||
\(74\) | 8.74611 | − | 8.98500i | 1.01671 | − | 1.04449i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.2333 | − | 0.275801i | 1.17384 | − | 0.0316365i | ||||
\(77\) | 2.90936 | − | 8.95410i | 0.331553 | − | 1.02041i | ||||
\(78\) | −24.0245 | + | 4.13762i | −2.72024 | + | 0.468493i | ||||
\(79\) | 7.65406 | + | 5.56100i | 0.861148 | + | 0.625661i | 0.928197 | − | 0.372089i | \(-0.121358\pi\) |
−0.0670487 | + | 0.997750i | \(0.521358\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.34247 | − | 4.60807i | 0.704719 | − | 0.512008i | ||||
\(82\) | 3.58506 | − | 3.68298i | 0.395904 | − | 0.406718i | ||||
\(83\) | 6.50869 | − | 4.72884i | 0.714422 | − | 0.519058i | −0.170176 | − | 0.985414i | \(-0.554433\pi\) |
0.884597 | + | 0.466356i | \(0.154433\pi\) | |||||||
\(84\) | 6.04743 | + | 17.0360i | 0.659829 | + | 1.85878i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.429752 | + | 0.816067i | 0.0463414 | + | 0.0879988i | ||||
\(87\) | 13.3958 | − | 4.35257i | 1.43618 | − | 0.466645i | ||||
\(88\) | 6.74386 | + | 3.09959i | 0.718898 | + | 0.330417i | ||||
\(89\) | 3.35636 | − | 10.3298i | 0.355773 | − | 1.09496i | −0.599787 | − | 0.800160i | \(-0.704748\pi\) |
0.955560 | − | 0.294797i | \(-0.0952521\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.3483 | + | 7.58631i | −2.44756 | + | 0.795261i | ||||
\(92\) | −1.23036 | + | 0.945588i | −0.128274 | + | 0.0985843i | ||||
\(93\) | 5.36393 | 0.556213 | ||||||||
\(94\) | 1.28900 | + | 0.186393i | 0.132951 | + | 0.0192250i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −13.8937 | + | 3.17175i | −1.41802 | + | 0.323716i | ||||
\(97\) | 3.31560 | − | 4.56353i | 0.336648 | − | 0.463356i | −0.606811 | − | 0.794846i | \(-0.707551\pi\) |
0.943459 | + | 0.331490i | \(0.107551\pi\) | |||||||
\(98\) | 3.86988 | + | 7.34861i | 0.390917 | + | 0.742321i | ||||
\(99\) | 8.78205i | 0.882629i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.202935i | 0.0201928i | 0.999949 | + | 0.0100964i | \(0.00321383\pi\) | ||||
−0.999949 | + | 0.0100964i | \(0.996786\pi\) | |||||||
\(102\) | 6.13198 | − | 3.22919i | 0.607157 | − | 0.319737i | ||||
\(103\) | −7.76000 | + | 10.6807i | −0.764616 | + | 1.05240i | 0.232201 | + | 0.972668i | \(0.425407\pi\) |
−0.996816 | + | 0.0797351i | \(0.974593\pi\) | |||||||
\(104\) | −3.79744 | − | 18.9772i | −0.372369 | − | 1.86087i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.371579 | + | 2.56966i | −0.0360910 | + | 0.249587i | ||||
\(107\) | −14.9185 | −1.44222 | −0.721111 | − | 0.692819i | \(-0.756368\pi\) | ||||
−0.721111 | + | 0.692819i | \(0.756368\pi\) | |||||||
\(108\) | −1.06446 | − | 1.38503i | −0.102427 | − | 0.133275i | ||||
\(109\) | −8.22423 | + | 2.67221i | −0.787738 | + | 0.255952i | −0.675141 | − | 0.737689i | \(-0.735917\pi\) |
−0.112598 | + | 0.993641i | \(0.535917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.90242 | + | 21.2435i | −0.655149 | + | 2.01634i | ||||
\(112\) | −13.3903 | + | 5.16358i | −1.26527 | + | 0.487913i | ||||
\(113\) | −5.61964 | + | 1.82593i | −0.528652 | + | 0.171769i | −0.561168 | − | 0.827702i | \(-0.689648\pi\) |
0.0325164 | + | 0.999471i | \(0.489648\pi\) | |||||||
\(114\) | −16.1355 | + | 8.49718i | −1.51123 | + | 0.795834i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.74069 | + | 10.5378i | 0.347314 | + | 0.978407i | ||||
\(117\) | 18.5262 | − | 13.4601i | 1.71275 | − | 1.24438i | ||||
\(118\) | −3.99261 | − | 3.88646i | −0.367550 | − | 0.357778i | ||||
\(119\) | 5.64619 | − | 4.10220i | 0.517585 | − | 0.376048i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.32838 | − | 2.41821i | −0.302580 | − | 0.219837i | ||||
\(122\) | 1.56796 | + | 9.10414i | 0.141957 | + | 0.824250i | ||||
\(123\) | −2.82933 | + | 8.70777i | −0.255112 | + | 0.785153i | ||||
\(124\) | 0.114726 | + | 4.25678i | 0.0103027 | + | 0.382270i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.1681 | − | 11.8446i | −1.08402 | − | 1.05520i | ||||
\(127\) | −3.36061 | − | 1.09193i | −0.298206 | − | 0.0968930i | 0.156093 | − | 0.987742i | \(-0.450110\pi\) |
−0.454299 | + | 0.890849i | \(0.650110\pi\) | |||||||
\(128\) | −2.81425 | − | 10.9581i | −0.248747 | − | 0.968569i | ||||
\(129\) | −1.32921 | − | 0.965725i | −0.117030 | − | 0.0850273i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.96559 | + | 5.45817i | 0.346475 | + | 0.476883i | 0.946319 | − | 0.323235i | \(-0.104770\pi\) |
−0.599843 | + | 0.800118i | \(0.704770\pi\) | |||||||
\(132\) | −13.2168 | + | 0.356209i | −1.15037 | + | 0.0310040i | ||||
\(133\) | −14.8572 | + | 10.7944i | −1.28828 | + | 0.935992i | ||||
\(134\) | 6.23858 | + | 3.07356i | 0.538931 | + | 0.265515i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.69382 | + | 4.79724i | 0.230993 | + | 0.411360i | ||||
\(137\) | −7.83872 | + | 2.54696i | −0.669707 | + | 0.217601i | −0.624084 | − | 0.781358i | \(-0.714528\pi\) |
−0.0456237 | + | 0.998959i | \(0.514528\pi\) | |||||||
\(138\) | 1.22166 | − | 2.47967i | 0.103994 | − | 0.211083i | ||||
\(139\) | −1.29543 | − | 0.420910i | −0.109877 | − | 0.0357011i | 0.253563 | − | 0.967319i | \(-0.418398\pi\) |
−0.363439 | + | 0.931618i | \(0.618398\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.20655 | + | 0.716950i | −0.185825 | + | 0.0603781i | ||||
\(142\) | 1.12268 | − | 7.76389i | 0.0942132 | − | 0.651531i | ||||
\(143\) | − | 17.9553i | − | 1.50150i | ||||||
\(144\) | 10.3906 | − | 8.44047i | 0.865881 | − | 0.703373i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.55925 | − | 20.6663i | −0.294565 | − | 1.71035i | ||||
\(147\) | −11.9694 | − | 8.69626i | −0.987218 | − | 0.717256i | ||||
\(148\) | −17.0063 | − | 5.02336i | −1.39791 | − | 0.412918i | ||||
\(149\) | − | 9.46274i | − | 0.775218i | −0.921824 | − | 0.387609i | \(-0.873301\pi\) | ||
0.921824 | − | 0.387609i | \(-0.126699\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.99542 | 0.650658 | 0.325329 | − | 0.945601i | \(-0.394525\pi\) | ||||
0.325329 | + | 0.945601i | \(0.394525\pi\) | |||||||
\(152\) | −7.08843 | − | 12.6233i | −0.574947 | − | 1.02389i | ||||
\(153\) | −3.82646 | + | 5.26667i | −0.309351 | + | 0.425785i | ||||
\(154\) | −13.1215 | + | 2.25985i | −1.05736 | + | 0.182104i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21.0086 | + | 27.3356i | 1.68203 | + | 2.18860i | ||||
\(157\) | −7.78075 | −0.620971 | −0.310486 | − | 0.950578i | \(-0.600492\pi\) | ||||
−0.310486 | + | 0.950578i | \(0.600492\pi\) | |||||||
\(158\) | 1.91484 | − | 13.2421i | 0.152336 | − | 1.05348i | ||||
\(159\) | −1.42926 | − | 4.39880i | −0.113347 | − | 0.348847i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.860221 | − | 2.64749i | 0.0677949 | − | 0.208651i | ||||
\(162\) | −9.94554 | − | 4.89987i | −0.781396 | − | 0.384970i | ||||
\(163\) | 7.10008 | + | 21.8518i | 0.556121 | + | 1.71157i | 0.692964 | + | 0.720973i | \(0.256305\pi\) |
−0.136842 | + | 0.990593i | \(0.543695\pi\) | |||||||
\(164\) | −6.97095 | − | 2.05909i | −0.544340 | − | 0.160788i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.2062 | − | 5.02828i | −0.792154 | − | 0.390271i | ||||
\(167\) | 7.10896 | + | 9.78464i | 0.550108 | + | 0.757158i | 0.990027 | − | 0.140879i | \(-0.0449929\pi\) |
−0.439919 | + | 0.898037i | \(0.644993\pi\) | |||||||
\(168\) | 17.3323 | − | 18.7932i | 1.33722 | − | 1.44993i | ||||
\(169\) | −27.3604 | + | 19.8785i | −2.10465 | + | 1.52912i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.0688 | − | 13.8585i | 0.769982 | − | 1.05979i | ||||
\(172\) | 0.737964 | − | 1.07551i | 0.0562692 | − | 0.0820065i | ||||
\(173\) | 4.88649 | − | 15.0391i | 0.371513 | − | 1.14340i | −0.574288 | − | 0.818653i | \(-0.694721\pi\) |
0.945801 | − | 0.324747i | \(-0.105279\pi\) | |||||||
\(174\) | −14.2737 | − | 13.8942i | −1.08209 | − | 1.05332i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.565371 | − | 10.4812i | −0.0426165 | − | 0.790047i | ||||
\(177\) | 9.43984 | + | 3.06719i | 0.709542 | + | 0.230544i | ||||
\(178\) | −15.1375 | + | 2.60705i | −1.13460 | + | 0.195407i | ||||
\(179\) | −8.68076 | + | 11.9480i | −0.648830 | + | 0.893038i | −0.999048 | − | 0.0436301i | \(-0.986108\pi\) |
0.350217 | + | 0.936668i | \(0.386108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.16443 | + | 4.35546i | 0.235210 | + | 0.323739i | 0.910263 | − | 0.414030i | \(-0.135879\pi\) |
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(182\) | 24.8783 | + | 24.2168i | 1.84410 | + | 1.79507i | ||||
\(183\) | −9.67305 | − | 13.3138i | −0.715053 | − | 0.984186i | ||||
\(184\) | 1.99398 | + | 0.916465i | 0.146998 | + | 0.0675627i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.53460 | − | 6.71194i | −0.259169 | − | 0.492143i | ||||
\(187\) | 1.57734 | + | 4.85455i | 0.115346 | + | 0.355000i | ||||
\(188\) | −0.616162 | − | 1.73577i | −0.0449382 | − | 0.126594i | ||||
\(189\) | 2.98030 | + | 0.968359i | 0.216785 | + | 0.0704378i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.20367 | + | 9.85988i | 0.231809 | + | 0.713436i | 0.997529 | + | 0.0702610i | \(0.0223832\pi\) |
−0.765719 | + | 0.643175i | \(0.777617\pi\) | |||||||
\(192\) | 13.1242 | + | 15.2952i | 0.947156 | + | 1.10384i | ||||
\(193\) | 0.720451i | 0.0518592i | 0.999664 | + | 0.0259296i | \(0.00825458\pi\) | ||||
−0.999664 | + | 0.0259296i | \(0.991745\pi\) | |||||||
\(194\) | −7.89523 | − | 1.14167i | −0.566844 | − | 0.0819672i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.64530 | − | 9.68483i | 0.474664 | − | 0.691774i | ||||
\(197\) | −4.83357 | − | 3.51179i | −0.344377 | − | 0.250205i | 0.402129 | − | 0.915583i | \(-0.368270\pi\) |
−0.746506 | + | 0.665378i | \(0.768270\pi\) | |||||||
\(198\) | 10.9891 | − | 5.78699i | 0.780959 | − | 0.411264i | ||||
\(199\) | −13.1660 | −0.933311 | −0.466655 | − | 0.884439i | \(-0.654541\pi\) | ||||
−0.466655 | + | 0.884439i | \(0.654541\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.3889 | −0.873843 | ||||||||
\(202\) | 0.253934 | − | 0.133725i | 0.0178668 | − | 0.00940888i | ||||
\(203\) | −16.2287 | − | 11.7908i | −1.13903 | − | 0.827553i | ||||
\(204\) | −8.08142 | − | 5.54511i | −0.565813 | − | 0.388236i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.4784 | + | 2.67203i | 1.28745 | + | 0.186169i | ||||
\(207\) | 2.59662i | 0.180477i | ||||||||
\(208\) | −21.2440 | + | 17.2569i | −1.47301 | + | 1.19655i | ||||
\(209\) | −4.15056 | − | 12.7741i | −0.287100 | − | 0.883603i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.22662 | + | 1.69823i | 0.359816 | + | 0.116911i | 0.483346 | − | 0.875430i | \(-0.339421\pi\) |
−0.123530 | + | 0.992341i | \(0.539421\pi\) | |||||||
\(212\) | 3.46029 | − | 1.22833i | 0.237654 | − | 0.0843622i | ||||
\(213\) | 4.31832 | + | 13.2904i | 0.295886 | + | 0.910644i | ||||
\(214\) | 9.83063 | + | 18.6676i | 0.672008 | + | 1.27609i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.03167 | + | 2.24464i | −0.0701965 | + | 0.152729i | ||||
\(217\) | −4.49018 | − | 6.18020i | −0.304813 | − | 0.419539i | ||||
\(218\) | 8.76318 | + | 8.53018i | 0.593517 | + | 0.577737i | ||||
\(219\) | 21.9577 | + | 30.2221i | 1.48376 | + | 2.04222i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.82337 | − | 10.7679i | 0.526257 | − | 0.724330i | ||||
\(222\) | 31.1306 | − | 5.36147i | 2.08935 | − | 0.359838i | ||||
\(223\) | 19.3706 | + | 6.29390i | 1.29715 | + | 0.421471i | 0.874590 | − | 0.484862i | \(-0.161130\pi\) |
0.422564 | + | 0.906333i | \(0.361130\pi\) | |||||||
\(224\) | 15.2849 | + | 13.3529i | 1.02127 | + | 0.892177i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.98791 | + | 5.82870i | 0.398310 | + | 0.387720i | ||||
\(227\) | −4.89137 | + | 15.0541i | −0.324652 | + | 0.999175i | 0.646946 | + | 0.762536i | \(0.276046\pi\) |
−0.971598 | + | 0.236639i | \(0.923954\pi\) | |||||||
\(228\) | 21.2652 | + | 14.5912i | 1.40832 | + | 0.966328i | ||||
\(229\) | −3.76598 | + | 5.18342i | −0.248863 | + | 0.342530i | −0.915113 | − | 0.403198i | \(-0.867898\pi\) |
0.666250 | + | 0.745729i | \(0.267898\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.1888 | − | 13.9414i | 1.26253 | − | 0.917280i | ||||
\(232\) | 10.7211 | − | 11.6247i | 0.703872 | − | 0.763199i | ||||
\(233\) | 10.3375 | + | 14.2284i | 0.677234 | + | 0.932133i | 0.999897 | − | 0.0143813i | \(-0.00457787\pi\) |
−0.322662 | + | 0.946514i | \(0.604578\pi\) | |||||||
\(234\) | −29.0507 | − | 14.3124i | −1.89910 | − | 0.935631i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.23220 | + | 7.55701i | −0.145304 | + | 0.491919i | ||||
\(237\) | 7.36529 | + | 22.6680i | 0.478427 | + | 1.47245i | ||||
\(238\) | −8.85371 | − | 4.36196i | −0.573901 | − | 0.282744i | ||||
\(239\) | −2.60748 | + | 8.02498i | −0.168664 | + | 0.519093i | −0.999288 | − | 0.0377406i | \(-0.987984\pi\) |
0.830624 | + | 0.556834i | \(0.187984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.07674 | + | 3.31387i | 0.0693591 | + | 0.213465i | 0.979728 | − | 0.200332i | \(-0.0642022\pi\) |
−0.910369 | + | 0.413797i | \(0.864202\pi\) | |||||||
\(242\) | −0.832671 | + | 5.75834i | −0.0535261 | + | 0.370160i | ||||
\(243\) | 22.3706 | 1.43507 | ||||||||
\(244\) | 10.3589 | − | 7.96124i | 0.663159 | − | 0.509666i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.7605 | − | 2.19768i | 0.813581 | − | 0.140119i | ||||
\(247\) | −20.5862 | + | 28.3344i | −1.30987 | + | 1.80288i | ||||
\(248\) | 5.25096 | − | 2.94859i | 0.333436 | − | 0.187236i | ||||
\(249\) | 20.2679 | 1.28443 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.8769i | 1.06526i | 0.846347 | + | 0.532632i | \(0.178797\pi\) | ||||
−0.846347 | + | 0.532632i | \(0.821203\pi\) | |||||||
\(252\) | −6.80299 | + | 23.0312i | −0.428548 | + | 1.45083i | ||||
\(253\) | 1.64714 | + | 1.19672i | 0.103555 | + | 0.0752369i | ||||
\(254\) | 0.848157 | + | 4.92470i | 0.0532181 | + | 0.309003i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.8575 | + | 10.7424i | −0.741094 | + | 0.671401i | ||||
\(257\) | − | 4.42621i | − | 0.276099i | −0.990425 | − | 0.138050i | \(-0.955917\pi\) | ||
0.990425 | − | 0.138050i | \(-0.0440833\pi\) | |||||||
\(258\) | −0.332531 | + | 2.29962i | −0.0207025 | + | 0.143168i | ||||
\(259\) | 30.2543 | − | 9.83022i | 1.87991 | − | 0.610820i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.7956 | + | 5.78213i | 1.10152 | + | 0.357905i | ||||
\(262\) | 4.21671 | − | 8.55888i | 0.260509 | − | 0.528770i | ||||
\(263\) | 11.6771 | − | 3.79412i | 0.720041 | − | 0.233956i | 0.0740002 | − | 0.997258i | \(-0.476423\pi\) |
0.646041 | + | 0.763303i | \(0.276423\pi\) | |||||||
\(264\) | 9.15503 | + | 16.3036i | 0.563453 | + | 1.00342i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 23.2974 | + | 11.4779i | 1.42845 | + | 0.703757i | ||||
\(267\) | 22.1369 | − | 16.0834i | 1.35476 | − | 0.984289i | ||||
\(268\) | −0.264978 | − | 9.83174i | −0.0161861 | − | 0.600569i | ||||
\(269\) | −16.8702 | − | 23.2198i | −1.02859 | − | 1.41573i | −0.906000 | − | 0.423277i | \(-0.860880\pi\) |
−0.122591 | − | 0.992457i | \(-0.539120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.96640 | − | 2.15522i | −0.180196 | − | 0.130920i | 0.494031 | − | 0.869444i | \(-0.335523\pi\) |
−0.674227 | + | 0.738524i | \(0.735523\pi\) | |||||||
\(272\) | 4.22772 | − | 6.53197i | 0.256343 | − | 0.396059i | ||||
\(273\) | −58.8204 | − | 19.1119i | −3.55997 | − | 1.15671i | ||||
\(274\) | 8.35241 | + | 8.13034i | 0.504588 | + | 0.491172i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.90785 | + | 0.105322i | −0.235225 | + | 0.00633961i | ||||
\(277\) | −1.23158 | + | 3.79042i | −0.0739986 | + | 0.227744i | −0.981214 | − | 0.192922i | \(-0.938204\pi\) |
0.907216 | + | 0.420666i | \(0.138204\pi\) | |||||||
\(278\) | 0.326942 | + | 1.89834i | 0.0196087 | + | 0.113855i | ||||
\(279\) | 5.76478 | + | 4.18836i | 0.345128 | + | 0.250750i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.0045 | + | 16.7138i | −1.37234 | + | 0.997060i | −0.374785 | + | 0.927112i | \(0.622283\pi\) |
−0.997551 | + | 0.0699483i | \(0.977717\pi\) | |||||||
\(282\) | 2.35115 | + | 2.28863i | 0.140009 | + | 0.136286i | ||||
\(283\) | 10.5601 | − | 7.67233i | 0.627730 | − | 0.456073i | −0.227883 | − | 0.973689i | \(-0.573180\pi\) |
0.855613 | + | 0.517616i | \(0.173180\pi\) | |||||||
\(284\) | −10.4548 | + | 3.71125i | −0.620380 | + | 0.220222i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.4676 | + | 11.8318i | −1.32854 | + | 0.699627i | ||||
\(287\) | 12.4013 | − | 4.02944i | 0.732028 | − | 0.237850i | ||||
\(288\) | −17.4086 | − | 7.43992i | −1.02581 | − | 0.438402i | ||||
\(289\) | 4.08404 | − | 12.5694i | 0.240238 | − | 0.739375i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.5152 | − | 4.39136i | 0.792277 | − | 0.257426i | ||||
\(292\) | −23.5145 | + | 18.0719i | −1.37608 | + | 1.05758i | ||||
\(293\) | −27.0373 | −1.57954 | −0.789769 | − | 0.613404i | \(-0.789800\pi\) | ||||
−0.789769 | + | 0.613404i | \(0.789800\pi\) | |||||||
\(294\) | −2.99441 | + | 20.7079i | −0.174638 | + | 1.20771i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.92066 | + | 24.5904i | 0.286008 | + | 1.42929i | ||||
\(297\) | −1.34715 | + | 1.85420i | −0.0781698 | + | 0.107592i | ||||
\(298\) | −11.8408 | + | 6.23554i | −0.685920 | + | 0.361215i | ||||
\(299\) | − | 5.30890i | − | 0.307022i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.33989i | 0.134869i | ||||||||
\(302\) | −5.26864 | − | 10.0047i | −0.303176 | − | 0.575708i | ||||
\(303\) | −0.300503 | + | 0.413607i | −0.0172635 | + | 0.0237611i | ||||
\(304\) | −11.1247 | + | 17.1880i | −0.638045 | + | 0.985801i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.11170 | + | 1.31758i | 0.520881 | + | 0.0753208i | ||||
\(307\) | 23.1194 | 1.31949 | 0.659747 | − | 0.751488i | \(-0.270664\pi\) | ||||
0.659747 | + | 0.751488i | \(0.270664\pi\) | |||||||
\(308\) | 11.4743 | + | 14.9299i | 0.653807 | + | 0.850710i | ||||
\(309\) | −31.6317 | + | 10.2778i | −1.79947 | + | 0.584682i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.30515 | − | 10.1722i | 0.187418 | − | 0.576813i | −0.812564 | − | 0.582872i | \(-0.801929\pi\) |
0.999982 | + | 0.00605932i | \(0.00192875\pi\) | |||||||
\(312\) | 20.3615 | − | 44.3012i | 1.15274 | − | 2.50806i | ||||
\(313\) | −6.62056 | + | 2.15115i | −0.374216 | + | 0.121590i | −0.490086 | − | 0.871674i | \(-0.663035\pi\) |
0.115870 | + | 0.993264i | \(0.463035\pi\) | |||||||
\(314\) | 5.12718 | + | 9.73613i | 0.289343 | + | 0.549441i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.8317 | + | 6.32989i | −1.00311 | + | 0.356084i | ||||
\(317\) | −2.26671 | + | 1.64686i | −0.127311 | + | 0.0924971i | −0.649619 | − | 0.760260i | \(-0.725071\pi\) |
0.522307 | + | 0.852757i | \(0.325071\pi\) | |||||||
\(318\) | −4.56244 | + | 4.68706i | −0.255849 | + | 0.262837i | ||||
\(319\) | 11.8694 | − | 8.62360i | 0.664557 | − | 0.482829i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.4057 | − | 22.0911i | −1.69708 | − | 1.23300i | ||||
\(322\) | −3.87967 | + | 0.668177i | −0.216206 | + | 0.0372361i | ||||
\(323\) | 3.07673 | − | 9.46919i | 0.171194 | − | 0.526880i | ||||
\(324\) | 0.422428 | + | 15.6738i | 0.0234682 | + | 0.870764i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.6647 | − | 23.2838i | 1.25528 | − | 1.28957i | ||||
\(327\) | −20.7190 | − | 6.73201i | −1.14576 | − | 0.372281i | ||||
\(328\) | 2.01700 | + | 10.0797i | 0.111370 | + | 0.556557i | ||||
\(329\) | 2.67317 | + | 1.94217i | 0.147376 | + | 0.107075i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6066 | − | 21.4807i | −0.857819 | − | 1.18069i | −0.982085 | − | 0.188437i | \(-0.939658\pi\) |
0.124266 | − | 0.992249i | \(-0.460342\pi\) | |||||||
\(332\) | 0.433498 | + | 16.0845i | 0.0237913 | + | 0.882753i | ||||
\(333\) | −24.0060 | + | 17.4413i | −1.31552 | + | 0.955780i | ||||
\(334\) | 7.55912 | − | 15.3432i | 0.413616 | − | 0.839540i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −34.9374 | − | 9.30419i | −1.90599 | − | 0.507585i | ||||
\(337\) | 18.1528 | − | 5.89820i | 0.988845 | − | 0.321295i | 0.230446 | − | 0.973085i | \(-0.425982\pi\) |
0.758400 | + | 0.651790i | \(0.225982\pi\) | |||||||
\(338\) | 42.9035 | + | 21.1373i | 2.33364 | + | 1.14972i | ||||
\(339\) | −14.1574 | − | 4.60001i | −0.768923 | − | 0.249838i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.31368 | − | 1.72652i | 0.287752 | − | 0.0934963i | ||||
\(342\) | −23.9762 | − | 3.46703i | −1.29649 | − | 0.187475i | ||||
\(343\) | − | 4.04448i | − | 0.218381i | ||||||
\(344\) | −1.83208 | − | 0.214710i | −0.0987790 | − | 0.0115764i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.0385 | + | 3.79559i | −1.18480 | + | 0.204052i | ||||
\(347\) | 15.5716 | + | 11.3134i | 0.835926 | + | 0.607336i | 0.921230 | − | 0.389019i | \(-0.127186\pi\) |
−0.0853039 | + | 0.996355i | \(0.527186\pi\) | |||||||
\(348\) | −7.98018 | + | 27.0165i | −0.427782 | + | 1.44824i | ||||
\(349\) | − | 0.0595710i | − | 0.00318876i | −0.999999 | − | 0.00159438i | \(-0.999492\pi\) | ||
0.999999 | − | 0.00159438i | \(-0.000507507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.97629 | 0.318991 | ||||||||
\(352\) | −12.7426 | + | 7.61408i | −0.679184 | + | 0.405832i | ||||
\(353\) | 11.4459 | − | 15.7539i | 0.609203 | − | 0.838497i | −0.387308 | − | 0.921950i | \(-0.626595\pi\) |
0.996512 | + | 0.0834537i | \(0.0265951\pi\) | |||||||
\(354\) | −2.38244 | − | 13.8333i | −0.126625 | − | 0.735232i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.2372 | + | 17.2237i | 0.701569 | + | 0.912856i | ||||
\(357\) | 17.5821 | 0.930545 | ||||||||
\(358\) | 20.6709 | + | 2.98907i | 1.09249 | + | 0.157977i | ||||
\(359\) | 7.90364 | + | 24.3249i | 0.417138 | + | 1.28382i | 0.910324 | + | 0.413896i | \(0.135832\pi\) |
−0.493186 | + | 0.869924i | \(0.664168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.22468 | + | 6.84685i | −0.117088 | + | 0.360361i | ||||
\(362\) | 3.36481 | − | 6.82974i | 0.176850 | − | 0.358963i | ||||
\(363\) | −3.20281 | − | 9.85725i | −0.168104 | − | 0.517371i | ||||
\(364\) | 13.9090 | − | 47.0883i | 0.729032 | − | 2.46810i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.2856 | + | 20.8772i | −0.537636 | + | 1.09127i | ||||
\(367\) | 16.9820 | + | 23.3737i | 0.886453 | + | 1.22010i | 0.974592 | + | 0.223990i | \(0.0719082\pi\) |
−0.0881385 | + | 0.996108i | \(0.528092\pi\) | |||||||
\(368\) | −0.167165 | − | 3.09900i | −0.00871409 | − | 0.161546i | ||||
\(369\) | −9.84012 | + | 7.14927i | −0.512256 | + | 0.372176i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.87175 | + | 5.32901i | −0.201011 | + | 0.276669i | ||||
\(372\) | −6.06956 | + | 8.84575i | −0.314692 | + | 0.458631i | ||||
\(373\) | 7.68840 | − | 23.6625i | 0.398090 | − | 1.22520i | −0.528438 | − | 0.848972i | \(-0.677222\pi\) |
0.926529 | − | 0.376224i | \(-0.122778\pi\) | |||||||
\(374\) | 5.03514 | − | 5.17268i | 0.260361 | − | 0.267473i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.76596 | + | 1.91481i | −0.0910724 | + | 0.0987486i | ||||
\(377\) | −36.3839 | − | 11.8218i | −1.87386 | − | 0.608855i | ||||
\(378\) | −0.752174 | − | 4.36739i | −0.0386877 | − | 0.224634i | ||||
\(379\) | −3.80553 | + | 5.23786i | −0.195477 | + | 0.269051i | −0.895492 | − | 0.445077i | \(-0.853176\pi\) |
0.700016 | + | 0.714128i | \(0.253176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.23244 | − | 7.20183i | −0.268066 | − | 0.368961i | ||||
\(382\) | 10.2267 | − | 10.5060i | 0.523243 | − | 0.537535i | ||||
\(383\) | −1.79838 | − | 2.47525i | −0.0918928 | − | 0.126480i | 0.760595 | − | 0.649227i | \(-0.224907\pi\) |
−0.852488 | + | 0.522747i | \(0.824907\pi\) | |||||||
\(384\) | 10.4908 | − | 26.5013i | 0.535357 | − | 1.35239i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.901508 | − | 0.474746i | 0.0458855 | − | 0.0241640i | ||||
\(387\) | −0.674465 | − | 2.07579i | −0.0342850 | − | 0.105518i | ||||
\(388\) | 3.77403 | + | 10.6317i | 0.191597 | + | 0.539742i | ||||
\(389\) | 26.7250 | + | 8.68349i | 1.35501 | + | 0.440270i | 0.894375 | − | 0.447318i | \(-0.147621\pi\) |
0.460637 | + | 0.887588i | \(0.347621\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.466377 | + | 1.43536i | 0.0235857 | + | 0.0725893i | ||||
\(392\) | −16.4977 | − | 1.93344i | −0.833259 | − | 0.0976535i | ||||
\(393\) | 16.9966i | 0.857367i | ||||||||
\(394\) | −1.20923 | + | 8.36241i | −0.0609200 | + | 0.421292i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −14.4826 | − | 9.93734i | −0.727780 | − | 0.499370i | ||||
\(397\) | −28.3014 | − | 20.5622i | −1.42041 | − | 1.03199i | −0.991704 | − | 0.128539i | \(-0.958971\pi\) |
−0.428701 | − | 0.903446i | \(-0.641029\pi\) | |||||||
\(398\) | 8.67581 | + | 16.4747i | 0.434879 | + | 0.825802i | ||||
\(399\) | −46.2651 | −2.31615 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3727 | 0.667799 | 0.333900 | − | 0.942609i | \(-0.391635\pi\) | ||||
0.333900 | + | 0.942609i | \(0.391635\pi\) | |||||||
\(402\) | 8.16373 | + | 15.5023i | 0.407170 | + | 0.773185i | ||||
\(403\) | −11.7864 | − | 8.56329i | −0.587120 | − | 0.426568i | ||||
\(404\) | −0.334663 | − | 0.229631i | −0.0166501 | − | 0.0114246i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.05997 | + | 28.0767i | −0.201493 | + | 1.39342i | ||||
\(407\) | 23.2662i | 1.15326i | ||||||||
\(408\) | −1.61334 | + | 13.7664i | −0.0798724 | + | 0.681536i | ||||
\(409\) | 8.50186 | + | 26.1660i | 0.420390 | + | 1.29383i | 0.907340 | + | 0.420397i | \(0.138109\pi\) |
−0.486950 | + | 0.873430i | \(0.661891\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.7478 | − | 6.41645i | −0.974088 | − | 0.316500i | ||||
\(412\) | −8.83294 | − | 24.8829i | −0.435168 | − | 1.22589i | ||||
\(413\) | −4.36820 | − | 13.4439i | −0.214945 | − | 0.661533i | ||||
\(414\) | 3.24917 | − | 1.71106i | 0.159688 | − | 0.0840940i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 35.5927 | + | 15.2113i | 1.74507 | + | 0.745793i | ||||
\(417\) | −2.01697 | − | 2.77612i | −0.0987713 | − | 0.135947i | ||||
\(418\) | −13.2493 | + | 13.6112i | −0.648046 | + | 0.665746i | ||||
\(419\) | −23.3551 | − | 32.1455i | −1.14097 | − | 1.57041i | −0.765321 | − | 0.643648i | \(-0.777420\pi\) |
−0.375649 | − | 0.926762i | \(-0.622580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.75042 | − | 3.78563i | 0.134047 | − | 0.184500i | −0.736717 | − | 0.676202i | \(-0.763625\pi\) |
0.870764 | + | 0.491701i | \(0.163625\pi\) | |||||||
\(422\) | −1.31910 | − | 7.65919i | −0.0642130 | − | 0.372843i | ||||
\(423\) | −2.93127 | − | 0.952426i | −0.142523 | − | 0.0463085i | ||||
\(424\) | −3.81721 | − | 3.52048i | −0.185380 | − | 0.170969i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.7848 | − | 14.1614i | 0.667877 | − | 0.686120i | ||||
\(427\) | −7.24251 | + | 22.2901i | −0.350489 | + | 1.07870i | ||||
\(428\) | 16.8810 | − | 24.6023i | 0.815975 | − | 1.18920i | ||||
\(429\) | 26.5880 | − | 36.5952i | 1.28368 | − | 1.76683i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.2735 | + | 11.8234i | −0.783869 | + | 0.569514i | −0.906138 | − | 0.422983i | \(-0.860983\pi\) |
0.122269 | + | 0.992497i | \(0.460983\pi\) | |||||||
\(432\) | 3.48857 | − | 0.188180i | 0.167844 | − | 0.00905379i | ||||
\(433\) | 0.827085 | + | 1.13838i | 0.0397472 | + | 0.0547073i | 0.828428 | − | 0.560096i | \(-0.189236\pi\) |
−0.788681 | + | 0.614803i | \(0.789236\pi\) | |||||||
\(434\) | −4.77451 | + | 9.69108i | −0.229184 | + | 0.465187i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.89934 | − | 16.5865i | 0.234636 | − | 0.794348i | ||||
\(437\) | −1.22721 | − | 3.77696i | −0.0587054 | − | 0.180677i | ||||
\(438\) | 23.3481 | − | 47.3909i | 1.11562 | − | 2.26443i | ||||
\(439\) | −4.33963 | + | 13.3560i | −0.207119 | + | 0.637447i | 0.792500 | + | 0.609871i | \(0.208779\pi\) |
−0.999620 | + | 0.0275762i | \(0.991221\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.07349 | − | 18.6923i | −0.289214 | − | 0.890109i | ||||
\(442\) | −18.6293 | − | 2.69385i | −0.886105 | − | 0.128133i | ||||
\(443\) | 9.37158 | 0.445257 | 0.222629 | − | 0.974903i | \(-0.428536\pi\) | ||||
0.222629 | + | 0.974903i | \(0.428536\pi\) | |||||||
\(444\) | −27.2226 | − | 35.4210i | −1.29193 | − | 1.68101i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.88880 | − | 28.3861i | −0.231491 | − | 1.34412i | ||||
\(447\) | 14.0123 | − | 19.2863i | 0.662759 | − | 0.912210i | ||||
\(448\) | 6.63650 | − | 27.9251i | 0.313545 | − | 1.31934i | ||||
\(449\) | 27.0993 | 1.27889 | 0.639447 | − | 0.768835i | \(-0.279163\pi\) | ||||
0.639447 | + | 0.768835i | \(0.279163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.53690i | 0.449075i | ||||||||
\(452\) | 3.34774 | − | 11.3336i | 0.157464 | − | 0.533088i | ||||
\(453\) | 16.2957 | + | 11.8395i | 0.765638 | + | 0.556269i | ||||
\(454\) | 22.0605 | − | 3.79938i | 1.03535 | − | 0.178314i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.24530 | − | 36.2244i | 0.198804 | − | 1.69636i | ||||
\(457\) | 32.1890i | 1.50574i | 0.658170 | + | 0.752869i | \(0.271331\pi\) | ||||
−0.658170 | + | 0.752869i | \(0.728669\pi\) | |||||||
\(458\) | 8.96768 | + | 1.29675i | 0.419032 | + | 0.0605932i | ||||
\(459\) | −1.61580 | + | 0.525005i | −0.0754190 | + | 0.0245051i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.49963 | + | 0.812178i | 0.116419 | + | 0.0378269i | 0.366647 | − | 0.930360i | \(-0.380506\pi\) |
−0.250228 | + | 0.968187i | \(0.580506\pi\) | |||||||
\(462\) | −30.0896 | − | 14.8243i | −1.39990 | − | 0.689687i | ||||
\(463\) | −28.7725 | + | 9.34875i | −1.33717 | + | 0.434473i | −0.888358 | − | 0.459152i | \(-0.848153\pi\) |
−0.448814 | + | 0.893625i | \(0.648153\pi\) | |||||||
\(464\) | −21.6108 | − | 5.75518i | −1.00326 | − | 0.267178i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.9921 | − | 22.3113i | 0.509201 | − | 1.03355i | ||||
\(467\) | 33.3692 | − | 24.2441i | 1.54414 | − | 1.12188i | 0.596471 | − | 0.802635i | \(-0.296569\pi\) |
0.947671 | − | 0.319250i | \(-0.103431\pi\) | |||||||
\(468\) | 1.23390 | + | 45.7826i | 0.0570371 | + | 2.11630i | ||||
\(469\) | 10.3708 | + | 14.2742i | 0.478879 | + | 0.659120i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.8582 | − | 11.5216i | −0.730705 | − | 0.530889i | ||||
\(472\) | 10.9271 | − | 2.18657i | 0.502960 | − | 0.100645i | ||||
\(473\) | −1.62760 | − | 0.528839i | −0.0748371 | − | 0.0243160i | ||||
\(474\) | 23.5113 | − | 24.1535i | 1.07991 | − | 1.10941i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.376053 | + | 13.9531i | 0.0172364 | + | 0.639538i | ||||
\(477\) | 1.89868 | − | 5.84354i | 0.0869346 | − | 0.267557i | ||||
\(478\) | 11.7600 | − | 2.02536i | 0.537888 | − | 0.0926378i | ||||
\(479\) | 12.7715 | + | 9.27902i | 0.583544 | + | 0.423969i | 0.840000 | − | 0.542586i | \(-0.182555\pi\) |
−0.256456 | + | 0.966556i | \(0.582555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.0813 | − | 35.6596i | 2.23791 | − | 1.62594i | ||||
\(482\) | 3.43715 | − | 3.53104i | 0.156558 | − | 0.160834i | ||||
\(483\) | 5.67360 | − | 4.12211i | 0.258158 | − | 0.187563i | ||||
\(484\) | 7.75416 | − | 2.75257i | 0.352462 | − | 0.125117i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.7412 | − | 27.9925i | −0.668676 | − | 1.26977i | ||||
\(487\) | −34.0773 | + | 11.0724i | −1.54419 | + | 0.501738i | −0.952529 | − | 0.304449i | \(-0.901528\pi\) |
−0.591661 | + | 0.806187i | \(0.701528\pi\) | |||||||
\(488\) | −16.7880 | − | 7.71605i | −0.759959 | − | 0.349289i | ||||
\(489\) | −17.8870 | + | 55.0505i | −0.808877 | + | 2.48947i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.10672 | + | 2.30911i | −0.320722 | + | 0.104209i | −0.464954 | − | 0.885335i | \(-0.653929\pi\) |
0.144232 | + | 0.989544i | \(0.453929\pi\) | |||||||
\(492\) | −11.1586 | − | 14.5192i | −0.503069 | − | 0.654575i | ||||
\(493\) | 10.8756 | 0.489811 | ||||||||
\(494\) | 49.0205 | + | 7.08850i | 2.20554 | + | 0.318927i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.14976 | − | 4.62757i | −0.321034 | − | 0.207784i | ||||
\(497\) | 11.6980 | − | 16.1009i | 0.524728 | − | 0.722226i | ||||
\(498\) | −13.3557 | − | 25.3615i | −0.598483 | − | 1.13647i | ||||
\(499\) | 1.61567i | 0.0723272i | 0.999346 | + | 0.0361636i | \(0.0115137\pi\) | ||||
−0.999346 | + | 0.0361636i | \(0.988486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.4692i | 1.36126i | ||||||||
\(502\) | 21.1183 | − | 11.1212i | 0.942555 | − | 0.496363i | ||||
\(503\) | −17.4576 | + | 24.0283i | −0.778395 | + | 1.07137i | 0.217062 | + | 0.976158i | \(0.430353\pi\) |
−0.995457 | + | 0.0952114i | \(0.969647\pi\) | |||||||
\(504\) | 33.3020 | − | 6.66391i | 1.48339 | − | 0.296834i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.412069 | − | 2.84966i | 0.0183187 | − | 0.126683i | ||||
\(507\) | −85.1999 | −3.78386 | ||||||||
\(508\) | 5.60342 | − | 4.30647i | 0.248612 | − | 0.191069i | ||||
\(509\) | −1.21315 | + | 0.394177i | −0.0537721 | + | 0.0174716i | −0.335780 | − | 0.941941i | \(-0.609000\pi\) |
0.282007 | + | 0.959412i | \(0.409000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.4404 | − | 50.5983i | 0.727279 | − | 2.23834i | ||||
\(512\) | 21.2557 | + | 7.75863i | 0.939377 | + | 0.342886i | ||||
\(513\) | 4.25176 | − | 1.38148i | 0.187720 | − | 0.0609939i | ||||
\(514\) | −5.53856 | + | 2.91668i | −0.244295 | + | 0.128649i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.09666 | − | 1.09925i | 0.136323 | − | 0.0483918i | ||||
\(517\) | −1.95511 | + | 1.42047i | −0.0859855 | + | 0.0624722i | ||||
\(518\) | −32.2369 | − | 31.3798i | −1.41641 | − | 1.37875i | ||||
\(519\) | 32.2290 | − | 23.4157i | 1.41469 | − | 1.02784i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.44563 | + | 6.86265i | 0.413821 | + | 0.300658i | 0.775147 | − | 0.631781i | \(-0.217676\pi\) |
−0.361326 | + | 0.932440i | \(0.617676\pi\) | |||||||
\(522\) | −4.49128 | − | 26.0779i | −0.196578 | − | 1.14140i | ||||
\(523\) | −6.21617 | + | 19.1314i | −0.271814 | + | 0.836558i | 0.718230 | + | 0.695805i | \(0.244952\pi\) |
−0.990045 | + | 0.140753i | \(0.955048\pi\) | |||||||
\(524\) | −13.4884 | + | 0.363531i | −0.589245 | + | 0.0158809i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.4423 | − | 12.1115i | −0.542512 | − | 0.528087i | ||||
\(527\) | 3.93893 | + | 1.27984i | 0.171582 | + | 0.0557505i | ||||
\(528\) | 14.3681 | − | 22.1991i | 0.625289 | − | 0.966093i | ||||
\(529\) | −18.1204 | − | 13.1652i | −0.787842 | − | 0.572401i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.75031 | + | 10.6674i | 0.336335 | + | 0.462925i | ||||
\(532\) | −0.989534 | − | 36.7157i | −0.0429018 | − | 1.59183i | ||||
\(533\) | 20.1186 | − | 14.6170i | 0.871432 | − | 0.633133i | ||||
\(534\) | −34.7126 | − | 17.1019i | −1.50216 | − | 0.740070i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.1279 | + | 6.81026i | −0.523847 | + | 0.294158i | ||||
\(537\) | −35.3850 | + | 11.4973i | −1.52697 | + | 0.496144i | ||||
\(538\) | −17.9384 | + | 36.4106i | −0.773380 | + | 1.56977i | ||||
\(539\) | −14.6564 | − | 4.76215i | −0.631295 | − | 0.205120i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0637 | + | 6.19417i | −0.819612 | + | 0.266308i | −0.688664 | − | 0.725081i | \(-0.741802\pi\) |
−0.130949 | + | 0.991389i | \(0.541802\pi\) | |||||||
\(542\) | −0.742113 | + | 5.13208i | −0.0318765 | + | 0.220442i | ||||
\(543\) | 13.5628i | 0.582036i | ||||||||
\(544\) | −10.9594 | − | 0.985901i | −0.469881 | − | 0.0422701i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.8452 | + | 86.1965i | 0.635316 | + | 3.68887i | ||||
\(547\) | −31.1058 | − | 22.5997i | −1.32999 | − | 0.966293i | −0.999749 | − | 0.0223953i | \(-0.992871\pi\) |
−0.330239 | − | 0.943897i | \(-0.607129\pi\) | |||||||
\(548\) | 4.66969 | − | 15.8090i | 0.199479 | − | 0.675327i | ||||
\(549\) | − | 21.8619i | − | 0.933041i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.6176 | −1.21915 | ||||||||
\(552\) | 2.70690 | + | 4.82053i | 0.115213 | + | 0.205175i | ||||
\(553\) | 19.9521 | − | 27.4617i | 0.848448 | − | 1.16779i | ||||
\(554\) | 5.55455 | − | 0.956633i | 0.235990 | − | 0.0406434i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.15997 | − | 1.66003i | 0.0916032 | − | 0.0704010i | ||||
\(557\) | 10.9707 | 0.464844 | 0.232422 | − | 0.972615i | \(-0.425335\pi\) | ||||
0.232422 | + | 0.972615i | \(0.425335\pi\) | |||||||
\(558\) | 1.44219 | − | 9.97347i | 0.0610528 | − | 0.422211i | ||||
\(559\) | 1.37897 | + | 4.24405i | 0.0583244 | + | 0.179504i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.97373 | + | 12.2299i | −0.167771 | + | 0.516346i | ||||
\(562\) | 36.0731 | + | 17.7721i | 1.52165 | + | 0.749672i | ||||
\(563\) | −0.325391 | − | 1.00145i | −0.0137136 | − | 0.0422061i | 0.943966 | − | 0.330044i | \(-0.107064\pi\) |
−0.957679 | + | 0.287838i | \(0.907064\pi\) | |||||||
\(564\) | 1.31448 | − | 4.45012i | 0.0553498 | − | 0.187384i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.5591 | − | 8.15816i | −0.696030 | − | 0.342913i | ||||
\(567\) | −16.5331 | − | 22.7559i | −0.694326 | − | 0.955658i | ||||
\(568\) | 11.5332 | + | 10.6367i | 0.483923 | + | 0.446305i | ||||
\(569\) | 16.4403 | − | 11.9446i | 0.689213 | − | 0.500743i | −0.187188 | − | 0.982324i | \(-0.559937\pi\) |
0.876401 | + | 0.481581i | \(0.159937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.81803 | − | 12.1370i | 0.369023 | − | 0.507917i | −0.583612 | − | 0.812033i | \(-0.698361\pi\) |
0.952635 | + | 0.304116i | \(0.0983610\pi\) | |||||||
\(572\) | 29.6104 | + | 20.3174i | 1.23807 | + | 0.849511i | ||||
\(573\) | −8.07089 | + | 24.8396i | −0.337166 | + | 1.03769i | ||||
\(574\) | −13.2140 | − | 12.8627i | −0.551543 | − | 0.536878i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.16186 | + | 26.6861i | 0.0900776 | + | 1.11192i | ||||
\(577\) | 27.0844 | + | 8.80026i | 1.12754 | + | 0.366360i | 0.812640 | − | 0.582765i | \(-0.198029\pi\) |
0.314899 | + | 0.949125i | \(0.398029\pi\) | |||||||
\(578\) | −18.4194 | + | 3.17228i | −0.766146 | + | 0.131950i | ||||
\(579\) | −1.06683 | + | 1.46837i | −0.0443361 | + | 0.0610235i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.9664 | − | 23.3523i | −0.703885 | − | 0.968815i | ||||
\(582\) | −14.4009 | − | 14.0180i | −0.596937 | − | 0.581065i | ||||
\(583\) | −2.83173 | − | 3.89755i | −0.117278 | − | 0.161420i | ||||
\(584\) | 38.1086 | + | 17.5153i | 1.57694 | + | 0.724789i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.8164 | + | 33.8321i | 0.735990 | + | 1.39759i | ||||
\(587\) | 10.7007 | + | 32.9333i | 0.441664 | + | 1.35930i | 0.886101 | + | 0.463491i | \(0.153403\pi\) |
−0.444438 | + | 0.895810i | \(0.646597\pi\) | |||||||
\(588\) | 27.8851 | − | 9.89865i | 1.14996 | − | 0.408213i | ||||
\(589\) | −10.3648 | − | 3.36772i | −0.427073 | − | 0.138764i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.65121 | − | 14.3150i | −0.191325 | − | 0.588839i | ||||
\(592\) | 27.5277 | − | 22.3613i | 1.13138 | − | 0.919042i | ||||
\(593\) | − | 34.9925i | − | 1.43697i | −0.695543 | − | 0.718484i | \(-0.744836\pi\) | ||
0.695543 | − | 0.718484i | \(-0.255164\pi\) | |||||||
\(594\) | 3.20789 | + | 0.463870i | 0.131621 | + | 0.0190328i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.6052 | + | 10.7076i | 0.639213 | + | 0.438600i | ||||
\(597\) | −26.8339 | − | 19.4960i | −1.09824 | − | 0.797918i | ||||
\(598\) | −6.64308 | + | 3.49834i | −0.271656 | + | 0.143058i | ||||
\(599\) | 17.7341 | 0.724596 | 0.362298 | − | 0.932062i | \(-0.381992\pi\) | ||||
0.362298 | + | 0.932062i | \(0.381992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.01505 | −0.0821957 | −0.0410979 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0410979 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(602\) | 2.92793 | − | 1.54189i | 0.119334 | − | 0.0628427i | ||||
\(603\) | −13.3147 | − | 9.67370i | −0.542217 | − | 0.393943i | ||||
\(604\) | −9.04723 | + | 13.1854i | −0.368127 | + | 0.536506i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.715569 | + | 0.103473i | 0.0290680 | + | 0.00420331i | ||||
\(607\) | − | 39.1971i | − | 1.59096i | −0.605979 | − | 0.795481i | \(-0.707218\pi\) | ||
0.605979 | − | 0.795481i | \(-0.292782\pi\) | |||||||
\(608\) | 28.8382 | + | 2.59427i | 1.16955 | + | 0.105211i | ||||
\(609\) | −15.6164 | − | 48.0624i | −0.632809 | − | 1.94759i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.99311 | + | 1.94728i | 0.242455 | + | 0.0787785i | ||||
\(612\) | −4.35552 | − | 12.2698i | −0.176062 | − | 0.495977i | ||||
\(613\) | −6.65786 | − | 20.4908i | −0.268909 | − | 0.827615i | −0.990767 | − | 0.135575i | \(-0.956712\pi\) |
0.721859 | − | 0.692041i | \(-0.243288\pi\) | |||||||
\(614\) | −15.2347 | − | 28.9295i | −0.614822 | − | 1.16750i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1209 | − | 24.1960i | 0.448073 | − | 0.974886i | ||||
\(617\) | −17.5267 | − | 24.1235i | −0.705600 | − | 0.971175i | −0.999881 | − | 0.0154563i | \(-0.995080\pi\) |
0.294280 | − | 0.955719i | \(-0.404920\pi\) | |||||||
\(618\) | 33.7046 | + | 32.8085i | 1.35580 | + | 1.31975i | ||||
\(619\) | 2.86875 | + | 3.94849i | 0.115305 | + | 0.158703i | 0.862768 | − | 0.505599i | \(-0.168729\pi\) |
−0.747464 | + | 0.664303i | \(0.768729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.398318 | + | 0.548237i | −0.0159839 | + | 0.0220000i | ||||
\(622\) | −14.9065 | + | 2.56728i | −0.597698 | + | 0.102939i | ||||
\(623\) | −37.0619 | − | 12.0421i | −1.48485 | − | 0.482458i | ||||
\(624\) | −68.8518 | + | 3.71399i | −2.75628 | + | 0.148678i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.05442 | + | 6.86685i | 0.281951 | + | 0.274455i | ||||
\(627\) | 10.4564 | − | 32.1813i | 0.417587 | − | 1.28520i | ||||
\(628\) | 8.80432 | − | 12.8314i | 0.351331 | − | 0.512028i | ||||
\(629\) | −10.1374 | + | 13.9529i | −0.404205 | + | 0.556340i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.3860 | + | 8.99897i | −0.493080 | + | 0.358243i | −0.806367 | − | 0.591415i | \(-0.798570\pi\) |
0.313288 | + | 0.949658i | \(0.398570\pi\) | |||||||
\(632\) | 19.6710 | + | 18.1419i | 0.782469 | + | 0.721644i | ||||
\(633\) | 8.13781 | + | 11.2007i | 0.323449 | + | 0.445189i | ||||
\(634\) | 3.55441 | + | 1.75115i | 0.141163 | + | 0.0695470i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.87141 | + | 2.62045i | 0.351774 | + | 0.103908i | ||||
\(637\) | 12.4175 | + | 38.2172i | 0.492001 | + | 1.51422i | ||||
\(638\) | −18.6122 | − | 9.16967i | −0.736864 | − | 0.363031i | ||||
\(639\) | −5.73663 | + | 17.6555i | −0.226937 | + | 0.698442i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.46226 | − | 7.57805i | −0.0972533 | − | 0.299315i | 0.890581 | − | 0.454825i | \(-0.150298\pi\) |
−0.987834 | + | 0.155510i | \(0.950298\pi\) | |||||||
\(642\) | −7.60669 | + | 52.6041i | −0.300212 | + | 2.07612i | ||||
\(643\) | −6.46830 | −0.255085 | −0.127542 | − | 0.991833i | \(-0.540709\pi\) | ||||
−0.127542 | + | 0.991833i | \(0.540709\pi\) | |||||||
\(644\) | 3.39263 | + | 4.41437i | 0.133689 | + | 0.173951i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.8763 | + | 2.38985i | −0.545956 | + | 0.0940274i | ||||
\(647\) | 8.81321 | − | 12.1303i | 0.346483 | − | 0.476893i | −0.599838 | − | 0.800122i | \(-0.704768\pi\) |
0.946321 | + | 0.323229i | \(0.104768\pi\) | |||||||
\(648\) | 19.3344 | − | 10.8569i | 0.759526 | − | 0.426500i | ||||
\(649\) | 10.3387 | 0.405828 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 19.2450i | − | 0.754272i | ||||||
\(652\) | −44.0703 | − | 13.0176i | −1.72593 | − | 0.509807i | ||||
\(653\) | 31.2404 | + | 22.6975i | 1.22253 | + | 0.888220i | 0.996308 | − | 0.0858552i | \(-0.0273622\pi\) |
0.226223 | + | 0.974076i | \(0.427362\pi\) | |||||||
\(654\) | 5.22910 | + | 30.3620i | 0.204474 | + | 1.18725i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.2837 | − | 9.16596i | 0.440554 | − | 0.357870i | ||||
\(657\) | 49.6261i | 1.93610i | ||||||||
\(658\) | 0.668753 | − | 4.62476i | 0.0260707 | − | 0.180292i | ||||
\(659\) | 32.1885 | − | 10.4587i | 1.25389 | − | 0.407412i | 0.394574 | − | 0.918864i | \(-0.370892\pi\) |
0.859312 | + | 0.511452i | \(0.170892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.06103 | − | 0.344750i | −0.0412693 | − | 0.0134092i | 0.288310 | − | 0.957537i | \(-0.406907\pi\) |
−0.329579 | + | 0.944128i | \(0.606907\pi\) | |||||||
\(662\) | −16.5949 | + | 33.6836i | −0.644979 | + | 1.30915i | ||||
\(663\) | 31.8900 | − | 10.3617i | 1.23851 | − | 0.402415i | ||||
\(664\) | 19.8411 | − | 11.1415i | 0.769983 | − | 0.432372i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 37.6434 | + | 18.5458i | 1.45865 | + | 0.718635i | ||||
\(667\) | 3.50945 | − | 2.54977i | 0.135887 | − | 0.0987274i | ||||
\(668\) | −24.1802 | + | 0.651686i | −0.935559 | + | 0.0252145i | ||||
\(669\) | 30.1599 | + | 41.5116i | 1.16605 | + | 1.60493i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8678 | − | 10.0756i | −0.535362 | − | 0.388963i | ||||
\(672\) | 11.3798 | + | 49.8485i | 0.438986 | + | 1.92295i | ||||
\(673\) | 25.0129 | + | 8.12719i | 0.964177 | + | 0.313280i | 0.748463 | − | 0.663177i | \(-0.230792\pi\) |
0.215714 | + | 0.976457i | \(0.430792\pi\) | |||||||
\(674\) | −19.3424 | − | 18.8281i | −0.745040 | − | 0.725231i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.82229 | − | 67.6142i | −0.0700880 | − | 2.60054i | ||||
\(677\) | −5.47038 | + | 16.8361i | −0.210244 | + | 0.647064i | 0.789213 | + | 0.614119i | \(0.210489\pi\) |
−0.999457 | + | 0.0329450i | \(0.989511\pi\) | |||||||
\(678\) | 3.57306 | + | 20.7465i | 0.137223 | + | 0.796763i | ||||
\(679\) | −16.3733 | − | 11.8959i | −0.628350 | − | 0.456523i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.2611 | + | 23.4391i | −1.23625 | + | 0.898188i | ||||
\(682\) | −5.66190 | − | 5.51136i | −0.216805 | − | 0.211041i | ||||
\(683\) | −37.0207 | + | 26.8971i | −1.41656 | + | 1.02919i | −0.424230 | + | 0.905554i | \(0.639455\pi\) |
−0.992328 | + | 0.123635i | \(0.960545\pi\) | |||||||
\(684\) | 11.4610 | + | 32.2863i | 0.438222 | + | 1.23450i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.06089 | + | 2.66514i | −0.193226 | + | 0.101755i | ||||
\(687\) | −15.3511 | + | 4.98787i | −0.585680 | + | 0.190299i | ||||
\(688\) | 0.938592 | + | 2.43398i | 0.0357835 | + | 0.0927946i | ||||
\(689\) | −3.88194 | + | 11.9474i | −0.147890 | + | 0.455159i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.90130 | + | 1.91745i | −0.224496 | + | 0.0729432i | −0.419105 | − | 0.907938i | \(-0.637656\pi\) |
0.194609 | + | 0.980881i | \(0.437656\pi\) | |||||||
\(692\) | 19.2719 | + | 25.0759i | 0.732608 | + | 0.953243i | ||||
\(693\) | 31.5088 | 1.19692 | ||||||||
\(694\) | 3.89558 | − | 26.9399i | 0.147874 | − | 1.02262i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 39.0646 | − | 7.81702i | 1.48074 | − | 0.296304i | ||||
\(697\) | −4.15535 | + | 5.71935i | −0.157395 | + | 0.216636i | ||||
\(698\) | −0.0745417 | + | 0.0392547i | −0.00282145 | + | 0.00148581i | ||||
\(699\) | 44.3069i | 1.67584i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.2933i | − | 0.804238i | −0.915587 | − | 0.402119i | \(-0.868274\pi\) | ||
0.915587 | − | 0.402119i | \(-0.131726\pi\) | |||||||
\(702\) | −3.93812 | − | 7.47818i | −0.148635 | − | 0.282246i | ||||
\(703\) | 26.6752 | − | 36.7153i | 1.00608 | − | 1.38474i | ||||
\(704\) | 17.9244 | + | 10.9276i | 0.675552 | + | 0.411850i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.2554 | − | 3.94120i | −1.02577 | − | 0.148329i | ||||
\(707\) | 0.728101 | 0.0273831 | ||||||||
\(708\) | −15.7398 | + | 12.0967i | −0.591539 | + | 0.454623i | ||||
\(709\) | −10.0050 | + | 3.25084i | −0.375747 | + | 0.122088i | −0.490801 | − | 0.871272i | \(-0.663296\pi\) |
0.115054 | + | 0.993359i | \(0.463296\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.78435 | + | 30.1131i | −0.366942 | + | 1.12933i | ||||
\(712\) | 12.8295 | − | 27.9135i | 0.480806 | − | 1.04610i | ||||
\(713\) | 1.57111 | − | 0.510486i | 0.0588387 | − | 0.0191178i | ||||
\(714\) | −11.5859 | − | 22.0007i | −0.433590 | − | 0.823355i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.88100 | − | 27.8354i | −0.369270 | − | 1.04026i | ||||
\(717\) | −17.1977 | + | 12.4948i | −0.642258 | + | 0.466628i | ||||
\(718\) | 25.2298 | − | 25.9190i | 0.941569 | − | 0.967287i | ||||
\(719\) | 5.42565 | − | 3.94197i | 0.202343 | − | 0.147011i | −0.482000 | − | 0.876171i | \(-0.660089\pi\) |
0.684342 | + | 0.729161i | \(0.260089\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.3209 | + | 27.8418i | 1.42715 | + | 1.03688i | ||||
\(722\) | 10.0335 | − | 1.72802i | 0.373408 | − | 0.0643103i | ||||
\(723\) | −2.71260 | + | 8.34852i | −0.100883 | + | 0.310485i | ||||
\(724\) | −10.7634 | + | 0.290087i | −0.400018 | + | 0.0107810i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.2240 | + | 10.5032i | −0.379447 | + | 0.389811i | ||||
\(727\) | 40.2119 | + | 13.0656i | 1.49138 | + | 0.484578i | 0.937490 | − | 0.348013i | \(-0.113143\pi\) |
0.553888 | + | 0.832591i | \(0.313143\pi\) | |||||||
\(728\) | −68.0875 | + | 13.6247i | −2.52349 | + | 0.504964i | ||||
\(729\) | 26.5667 | + | 19.3018i | 0.983951 | + | 0.714882i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.745662 | − | 1.02632i | −0.0275793 | − | 0.0379597i | ||||
\(732\) | 32.9016 | − | 0.886740i | 1.21608 | − | 0.0327749i | ||||
\(733\) | 21.7381 | − | 15.7936i | 0.802914 | − | 0.583351i | −0.108854 | − | 0.994058i | \(-0.534718\pi\) |
0.911768 | + | 0.410707i | \(0.134718\pi\) | |||||||
\(734\) | 18.0573 | − | 36.6520i | 0.666509 | − | 1.35285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.76765 | + | 2.25128i | −0.138877 | + | 0.0829833i | ||||
\(737\) | −12.2728 | + | 3.98768i | −0.452075 | + | 0.146888i | ||||
\(738\) | 15.4302 | + | 7.60198i | 0.567992 | + | 0.279833i | ||||
\(739\) | −13.3854 | − | 4.34919i | −0.492391 | − | 0.159988i | 0.0522881 | − | 0.998632i | \(-0.483349\pi\) |
−0.544679 | + | 0.838644i | \(0.683349\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −83.9145 | + | 27.2655i | −3.08268 | + | 1.00162i | ||||
\(742\) | 9.21956 | + | 1.33317i | 0.338461 | + | 0.0489423i | ||||
\(743\) | 43.2190i | 1.58555i | 0.609513 | + | 0.792776i | \(0.291365\pi\) | ||||
−0.609513 | + | 0.792776i | \(0.708635\pi\) | |||||||
\(744\) | 15.0684 | + | 1.76593i | 0.552433 | + | 0.0647422i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34.6754 | + | 5.97197i | −1.26956 | + | 0.218650i | ||||
\(747\) | 21.7826 | + | 15.8260i | 0.796983 | + | 0.579042i | ||||
\(748\) | −9.79056 | − | 2.89195i | −0.357978 | − | 0.105740i | ||||
\(749\) | 53.5254i | 1.95577i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.24240 | −0.118317 | −0.0591584 | − | 0.998249i | \(-0.518842\pi\) | ||||
−0.0591584 | + | 0.998249i | \(0.518842\pi\) | |||||||
\(752\) | 3.55971 | + | 0.947987i | 0.129809 | + | 0.0345695i | ||||
\(753\) | −24.9912 | + | 34.3974i | −0.910728 | + | 1.25351i | ||||
\(754\) | 9.18262 | + | 53.3176i | 0.334411 | + | 1.94171i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.96930 | + | 3.81912i | −0.180732 | + | 0.138900i | ||||
\(757\) | −25.4279 | −0.924193 | −0.462096 | − | 0.886830i | \(-0.652903\pi\) | ||||
−0.462096 | + | 0.886830i | \(0.652903\pi\) | |||||||
\(758\) | 9.06187 | + | 1.31037i | 0.329142 | + | 0.0475948i | ||||
\(759\) | 1.58500 | + | 4.87812i | 0.0575317 | + | 0.177064i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.54324 | − | 17.0603i | 0.200942 | − | 0.618437i | −0.798913 | − | 0.601446i | \(-0.794591\pi\) |
0.999856 | − | 0.0169909i | \(-0.00540862\pi\) | |||||||
\(762\) | −5.56377 | + | 11.2931i | −0.201554 | + | 0.409106i | ||||
\(763\) | 9.58753 | + | 29.5074i | 0.347092 | + | 1.06824i | ||||
\(764\) | −19.8852 | − | 5.87373i | −0.719422 | − | 0.212504i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.91226 | + | 3.88141i | −0.0690926 | + | 0.140241i | ||||
\(767\) | −15.8459 | − | 21.8100i | −0.572161 | − | 0.787512i | ||||
\(768\) | −40.0743 | + | 4.33597i | −1.44606 | + | 0.156461i | ||||
\(769\) | −9.85987 | + | 7.16362i | −0.355556 | + | 0.258327i | −0.751196 | − | 0.660079i | \(-0.770523\pi\) |
0.395640 | + | 0.918406i | \(0.370523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.55427 | − | 9.02118i | 0.236046 | − | 0.324890i | ||||
\(772\) | −1.18811 | − | 0.815228i | −0.0427610 | − | 0.0293407i | ||||
\(773\) | −6.29718 | + | 19.3807i | −0.226494 | + | 0.697076i | 0.771643 | + | 0.636056i | \(0.219435\pi\) |
−0.998137 | + | 0.0610199i | \(0.980565\pi\) | |||||||
\(774\) | −2.15301 | + | 2.21182i | −0.0773884 | + | 0.0795022i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.8166 | − | 11.7283i | 0.388294 | − | 0.421022i | ||||
\(777\) | 76.2186 | + | 24.7649i | 2.73433 | + | 0.888437i | ||||
\(778\) | −6.74491 | − | 39.1633i | −0.241817 | − | 1.40407i | ||||
\(779\) | 10.9343 | − | 15.0497i | 0.391761 | − | 0.539213i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.55573 | + | 11.7760i | 0.306148 | + | 0.421377i | ||||
\(782\) | 1.48876 | − | 1.52942i | 0.0532379 | − | 0.0546920i | ||||
\(783\) | 2.87030 | + | 3.95063i | 0.102576 | + | 0.141184i | ||||
\(784\) | 8.45193 | + | 21.9178i | 0.301855 | + | 0.782777i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 21.2681 | − | 11.2001i | 0.758607 | − | 0.399493i | ||||
\(787\) | −0.608835 | − | 1.87380i | −0.0217026 | − | 0.0667938i | 0.939619 | − | 0.342223i | \(-0.111180\pi\) |
−0.961321 | + | 0.275430i | \(0.911180\pi\) | |||||||
\(788\) | 11.2608 | − | 3.99735i | 0.401149 | − | 0.142400i | ||||
\(789\) | 29.4177 | + | 9.55840i | 1.04730 | + | 0.340288i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.55119 | + | 20.1625i | 0.232934 | + | 0.716896i | ||||
\(792\) | −2.89126 | + | 24.6705i | −0.102736 | + | 0.876630i | ||||
\(793\) | 44.6976i | 1.58726i | ||||||||
\(794\) | −7.08024 | + | 48.9634i | −0.251268 | + | 1.73765i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.8980 | − | 21.7122i | 0.528045 | − | 0.769570i | ||||
\(797\) | 18.3873 | + | 13.3592i | 0.651313 | + | 0.473206i | 0.863718 | − | 0.503975i | \(-0.168130\pi\) |
−0.212405 | + | 0.977182i | \(0.568130\pi\) | |||||||
\(798\) | 30.4867 | + | 57.8919i | 1.07922 | + | 2.04935i | ||||
\(799\) | −1.79141 | −0.0633756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.3498 | 1.28436 | ||||||||
\(802\) | −8.81201 | − | 16.7334i | −0.311163 | − | 0.590875i | ||||
\(803\) | 31.4798 | + | 22.8714i | 1.11090 | + | 0.807114i | ||||
\(804\) | 14.0186 | − | 20.4307i | 0.494399 | − | 0.720536i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.94863 | + | 20.3912i | −0.103861 | + | 0.718250i | ||||
\(807\) | − | 72.3059i | − | 2.54529i | ||||||
\(808\) | −0.0668109 | + | 0.570085i | −0.00235040 | + | 0.0200555i | ||||
\(809\) | −15.7618 | − | 48.5099i | −0.554156 | − | 1.70552i | −0.698163 | − | 0.715939i | \(-0.745999\pi\) |
0.144007 | − | 0.989577i | \(-0.454001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.6096 | + | 13.8447i | 1.49622 | + | 0.486153i | 0.938914 | − | 0.344152i | \(-0.111834\pi\) |
0.557310 | + | 0.830305i | \(0.311834\pi\) | |||||||
\(812\) | 37.8080 | − | 13.4211i | 1.32680 | − | 0.470987i | ||||
\(813\) | −2.85449 | − | 8.78521i | −0.100111 | − | 0.308111i | ||||
\(814\) | 29.1132 | − | 15.3314i | 1.02042 | − | 0.537366i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 18.2891 | − | 7.05264i | 0.640246 | − | 0.246892i | ||||
\(817\) | 1.96211 | + | 2.70061i | 0.0686456 | + | 0.0944826i | ||||
\(818\) | 27.1395 | − | 27.8808i | 0.948909 | − | 0.974828i | ||||
\(819\) | −48.2928 | − | 66.4694i | −1.68749 | − | 2.32263i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5666 | − | 22.8020i | 0.578180 | − | 0.795796i | −0.415314 | − | 0.909678i | \(-0.636328\pi\) |
0.993494 | + | 0.113881i | \(0.0363284\pi\) | |||||||
\(822\) | 4.98399 | + | 28.9388i | 0.173837 | + | 1.00936i | ||||
\(823\) | 3.43957 | + | 1.11758i | 0.119896 | + | 0.0389565i | 0.368350 | − | 0.929687i | \(-0.379923\pi\) |
−0.248455 | + | 0.968644i | \(0.579923\pi\) | |||||||
\(824\) | −25.3157 | + | 27.4495i | −0.881916 | + | 0.956250i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.9441 | + | 14.3249i | −0.485176 | + | 0.498428i | ||||
\(827\) | −8.71857 | + | 26.8330i | −0.303174 | + | 0.933075i | 0.677178 | + | 0.735819i | \(0.263203\pi\) |
−0.980352 | + | 0.197255i | \(0.936797\pi\) | |||||||
\(828\) | −4.28213 | − | 2.93821i | −0.148814 | − | 0.102110i | ||||
\(829\) | −31.0042 | + | 42.6736i | −1.07682 | + | 1.48212i | −0.213846 | + | 0.976867i | \(0.568599\pi\) |
−0.862974 | + | 0.505248i | \(0.831401\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.12292 | + | 5.90165i | −0.281781 | + | 0.204726i | ||||
\(832\) | −4.42003 | − | 54.5610i | −0.153237 | − | 1.89156i | ||||
\(833\) | −6.71462 | − | 9.24188i | −0.232648 | − | 0.320212i | ||||
\(834\) | −2.14469 | + | 4.35319i | −0.0742645 | + | 0.150739i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 25.7626 | + | 7.60980i | 0.891018 | + | 0.263190i | ||||
\(837\) | 0.574659 | + | 1.76862i | 0.0198631 | + | 0.0611324i | ||||
\(838\) | −24.8340 | + | 50.4069i | −0.857876 | + | 1.74128i | ||||
\(839\) | 2.76644 | − | 8.51422i | 0.0955081 | − | 0.293944i | −0.891878 | − | 0.452277i | \(-0.850612\pi\) |
0.987386 | + | 0.158333i | \(0.0506120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.698169 | − | 2.14874i | −0.0240748 | − | 0.0740946i | ||||
\(842\) | −6.54940 | − | 0.947061i | −0.225707 | − | 0.0326379i | ||||
\(843\) | −71.6357 | −2.46726 | ||||||||
\(844\) | −8.71478 | + | 6.69768i | −0.299975 | + | 0.230544i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.739798 | + | 4.29553i | 0.0254348 | + | 0.147683i | ||||
\(847\) | −8.67620 | + | 11.9418i | −0.298118 | + | 0.410324i | ||||
\(848\) | −1.88983 | + | 7.09635i | −0.0648971 | + | 0.243690i | ||||
\(849\) | 32.8838 | 1.12857 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.87919i | 0.235816i | ||||||||
\(852\) | −26.8039 | − | 7.91737i | −0.918285 | − | 0.271245i | ||||
\(853\) | −25.4769 | − | 18.5100i | −0.872312 | − | 0.633772i | 0.0588942 | − | 0.998264i | \(-0.481243\pi\) |
−0.931206 | + | 0.364492i | \(0.881243\pi\) | |||||||
\(854\) | 32.6644 | − | 5.62563i | 1.11775 | − | 0.192505i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41.9090 | − | 4.91151i | −1.43242 | − | 0.167872i | ||||
\(857\) | 47.9238i | 1.63705i | 0.574473 | + | 0.818523i | \(0.305207\pi\) | ||||
−0.574473 | + | 0.818523i | \(0.694793\pi\) | |||||||
\(858\) | −63.3123 | − | 9.15512i | −2.16145 | − | 0.312551i | ||||
\(859\) | −25.9430 | + | 8.42940i | −0.885164 | + | 0.287607i | −0.716100 | − | 0.697998i | \(-0.754075\pi\) |
−0.169064 | + | 0.985605i | \(0.554075\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.2423 | + | 10.1512i | 1.06473 | + | 0.345953i | ||||
\(862\) | 25.5183 | + | 12.5721i | 0.869157 | + | 0.428208i | ||||
\(863\) | −40.6471 | + | 13.2070i | −1.38364 | + | 0.449573i | −0.903865 | − | 0.427817i | \(-0.859283\pi\) |
−0.479778 | + | 0.877390i | \(0.659283\pi\) | |||||||
\(864\) | −2.53429 | − | 4.24128i | −0.0862183 | − | 0.144291i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.879458 | − | 1.78509i | 0.0298852 | − | 0.0606597i | ||||
\(867\) | 26.9364 | − | 19.5704i | 0.914807 | − | 0.664646i | ||||
\(868\) | 15.2727 | − | 0.411620i | 0.518391 | − | 0.0139713i | ||||
\(869\) | 14.5926 | + | 20.0850i | 0.495020 | + | 0.681337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.2225 | + | 19.7783i | 0.922400 | + | 0.670163i | ||||
\(872\) | −23.9833 | + | 4.79918i | −0.812176 | + | 0.162521i | ||||
\(873\) | 17.9542 | + | 5.83367i | 0.607657 | + | 0.197440i | ||||
\(874\) | −3.91747 | + | 4.02447i | −0.132510 | + | 0.136130i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −74.6861 | + | 2.01289i | −2.52341 | + | 0.0680091i | ||||
\(877\) | 17.9202 | − | 55.1526i | 0.605121 | − | 1.86237i | 0.109168 | − | 0.994023i | \(-0.465181\pi\) |
0.495953 | − | 0.868349i | \(-0.334819\pi\) | |||||||
\(878\) | 19.5721 | − | 3.37081i | 0.660527 | − | 0.113759i | ||||
\(879\) | −55.1055 | − | 40.0365i | −1.85866 | − | 1.35040i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.3649 | − | 10.4367i | 0.483965 | − | 0.351621i | −0.318894 | − | 0.947790i | \(-0.603311\pi\) |
0.802859 | + | 0.596169i | \(0.203311\pi\) | |||||||
\(882\) | −19.3877 | + | 19.9172i | −0.652817 | + | 0.670648i | ||||
\(883\) | 34.4318 | − | 25.0162i | 1.15872 | − | 0.841861i | 0.169107 | − | 0.985598i | \(-0.445912\pi\) |
0.989616 | + | 0.143736i | \(0.0459118\pi\) | |||||||
\(884\) | 8.90507 | + | 25.0861i | 0.299510 | + | 0.843738i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.17547 | − | 11.7267i | −0.207469 | − | 0.393968i | ||||
\(887\) | 37.7360 | − | 12.2612i | 1.26705 | − | 0.411689i | 0.403048 | − | 0.915179i | \(-0.367951\pi\) |
0.864001 | + | 0.503489i | \(0.167951\pi\) | |||||||
\(888\) | −26.3841 | + | 57.4047i | −0.885394 | + | 1.92638i | ||||
\(889\) | −3.91768 | + | 12.0574i | −0.131395 | + | 0.404392i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.5653 | − | 6.35716i | 0.655463 | − | 0.212973i | ||||
\(892\) | −32.2983 | + | 24.8226i | −1.08143 | + | 0.831122i | ||||
\(893\) | 4.71386 | 0.157743 | ||||||||
\(894\) | −33.3666 | − | 4.82490i | −1.11595 | − | 0.161369i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −39.3161 | + | 10.0971i | −1.31346 | + | 0.337321i | ||||
\(897\) | 7.86135 | − | 10.8202i | 0.262483 | − | 0.361277i | ||||
\(898\) | −17.8573 | − | 33.9096i | −0.595904 | − | 1.13158i | ||||
\(899\) | − | 11.9042i | − | 0.397026i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.57122i | − | 0.118974i | ||||||
\(902\) | 11.9336 | − | 6.28440i | 0.397346 | − | 0.209248i | ||||
\(903\) | −3.46488 | + | 4.76900i | −0.115304 | + | 0.158703i | ||||
\(904\) | −16.3879 | + | 3.27930i | −0.545052 | + | 0.109068i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.07674 | − | 28.1927i | 0.135440 | − | 0.936639i | ||||
\(907\) | 34.9093 | 1.15914 | 0.579571 | − | 0.814921i | \(-0.303220\pi\) | ||||
0.579571 | + | 0.814921i | \(0.303220\pi\) | |||||||
\(908\) | −19.2911 | − | 25.1009i | −0.640199 | − | 0.833004i | ||||
\(909\) | −0.645920 | + | 0.209872i | −0.0214238 | + | 0.00696102i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.05588 | + | 21.7158i | −0.233772 | + | 0.719476i | 0.763510 | + | 0.645796i | \(0.223474\pi\) |
−0.997282 | + | 0.0736799i | \(0.976526\pi\) | |||||||
\(912\) | −48.1254 | + | 18.5581i | −1.59359 | + | 0.614520i | ||||
\(913\) | 20.0781 | − | 6.52377i | 0.664488 | − | 0.215905i | ||||
\(914\) | 40.2784 | − | 21.2112i | 1.33229 | − | 0.701603i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.28668 | − | 12.0758i | −0.141636 | − | 0.398997i | ||||
\(917\) | 19.5831 | − | 14.2280i | 0.646692 | − | 0.469850i | ||||
\(918\) | 1.72169 | + | 1.67591i | 0.0568241 | + | 0.0553133i | ||||
\(919\) | −44.3337 | + | 32.2104i | −1.46244 | + | 1.06252i | −0.479715 | + | 0.877424i | \(0.659260\pi\) |
−0.982720 | + | 0.185097i | \(0.940740\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 47.1203 | + | 34.2349i | 1.55267 | + | 1.12808i | ||||
\(922\) | −0.630861 | − | 3.66300i | −0.0207763 | − | 0.120634i | ||||
\(923\) | 11.7288 | − | 36.0975i | 0.386058 | − | 1.18816i | ||||
\(924\) | 1.27803 | + | 47.4200i | 0.0420441 | + | 1.56000i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.6580 | + | 29.8429i | 1.00748 | + | 0.980698i | ||||
\(927\) | −42.0209 | − | 13.6534i | −1.38015 | − | 0.448437i | ||||
\(928\) | 7.03907 | + | 30.8342i | 0.231069 | + | 1.01218i | ||||
\(929\) | −26.3740 | − | 19.1618i | −0.865301 | − | 0.628678i | 0.0640206 | − | 0.997949i | \(-0.479608\pi\) |
−0.929322 | + | 0.369270i | \(0.879608\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.6686 | + | 24.3188i | 0.579066 | + | 0.797016i | ||||
\(932\) | −35.1617 | + | 0.947653i | −1.15176 | + | 0.0310414i | ||||
\(933\) | 21.7992 | − | 15.8380i | 0.713673 | − | 0.518514i | ||||
\(934\) | −52.3258 | − | 25.7793i | −1.71215 | − | 0.843526i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 56.4752 | − | 31.7128i | 1.84595 | − | 1.03656i | ||||
\(937\) | −7.69340 | + | 2.49974i | −0.251332 | + | 0.0816628i | −0.431974 | − | 0.901886i | \(-0.642183\pi\) |
0.180641 | + | 0.983549i | \(0.442183\pi\) | |||||||
\(938\) | 11.0275 | − | 22.3831i | 0.360061 | − | 0.730835i | ||||
\(939\) | −16.6789 | − | 5.41932i | −0.544297 | − | 0.176853i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.7042 | − | 11.2761i | 1.13133 | − | 0.367590i | 0.317246 | − | 0.948343i | \(-0.397242\pi\) |
0.814080 | + | 0.580753i | \(0.197242\pi\) | |||||||
\(942\) | −3.96728 | + | 27.4357i | −0.129261 | + | 0.893904i | ||||
\(943\) | 2.81981i | 0.0918255i | ||||||||
\(944\) | −9.93655 | − | 12.2323i | −0.323407 | − | 0.398128i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.410776 | + | 2.38511i | 0.0133555 | + | 0.0775467i | ||||
\(947\) | 12.2602 | + | 8.90757i | 0.398404 | + | 0.289457i | 0.768890 | − | 0.639380i | \(-0.220809\pi\) |
−0.370487 | + | 0.928838i | \(0.620809\pi\) | |||||||
\(948\) | −45.7165 | − | 13.5038i | −1.48480 | − | 0.438584i | ||||
\(949\) | − | 101.463i | − | 3.29362i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.05851 | −0.228888 | ||||||||
\(952\) | 17.2118 | − | 9.66504i | 0.557838 | − | 0.313246i | ||||
\(953\) | 32.0176 | − | 44.0685i | 1.03715 | − | 1.42752i | 0.137714 | − | 0.990472i | \(-0.456024\pi\) |
0.899439 | − | 0.437047i | \(-0.143976\pi\) | |||||||
\(954\) | −8.56323 | + | 1.47480i | −0.277245 | + | 0.0477485i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.2837 | − | 13.3807i | −0.332597 | − | 0.432763i | ||||
\(957\) | 36.9610 | 1.19478 | ||||||||
\(958\) | 3.19508 | − | 22.0956i | 0.103228 | − | 0.713875i | ||||
\(959\) | 9.13812 | + | 28.1242i | 0.295085 | + | 0.908179i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.17865 | + | 25.1713i | −0.263827 | + | 0.811977i | ||||
\(962\) | −76.9637 | − | 37.9177i | −2.48141 | − | 1.22252i | ||||
\(963\) | −15.4285 | − | 47.4839i | −0.497175 | − | 1.53015i | ||||
\(964\) | −6.68335 | − | 1.97414i | −0.215256 | − | 0.0635828i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.89670 | − | 4.38314i | −0.286247 | − | 0.141025i | ||||
\(967\) | 12.9780 | + | 17.8627i | 0.417344 | + | 0.574424i | 0.964990 | − | 0.262285i | \(-0.0844762\pi\) |
−0.547647 | + | 0.836710i | \(0.684476\pi\) | |||||||
\(968\) | −8.55397 | − | 7.88903i | −0.274935 | − | 0.253563i | ||||
\(969\) | 20.2926 | − | 14.7434i | 0.651892 | − | 0.473628i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.05516 | + | 6.95783i | −0.162228 | + | 0.223287i | −0.882390 | − | 0.470518i | \(-0.844067\pi\) |
0.720163 | + | 0.693805i | \(0.244067\pi\) | |||||||
\(972\) | −25.3135 | + | 36.8917i | −0.811930 | + | 1.18330i | ||||
\(973\) | −1.51016 | + | 4.64781i | −0.0484137 | + | 0.149002i | ||||
\(974\) | 36.3105 | + | 35.3450i | 1.16346 | + | 1.13253i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.40742 | + | 26.0916i | 0.0450505 | + | 0.835171i | ||||
\(977\) | 18.1117 | + | 5.88484i | 0.579444 | + | 0.188273i | 0.584052 | − | 0.811717i | \(-0.301467\pi\) |
−0.00460737 | + | 0.999989i | \(0.501467\pi\) | |||||||
\(978\) | 80.6719 | − | 13.8937i | 2.57960 | − | 0.444273i | ||||
\(979\) | 16.7527 | − | 23.0581i | 0.535418 | − | 0.736940i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.0107 | − | 23.4133i | −0.543111 | − | 0.747529i | ||||
\(982\) | 7.57244 | + | 7.37111i | 0.241646 | + | 0.235221i | ||||
\(983\) | −12.0848 | − | 16.6333i | −0.385446 | − | 0.530521i | 0.571571 | − | 0.820553i | \(-0.306334\pi\) |
−0.957017 | + | 0.290032i | \(0.906334\pi\) | |||||||
\(984\) | −10.8150 | + | 23.5304i | −0.344768 | + | 0.750122i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.16653 | − | 13.6087i | −0.228229 | − | 0.433390i | ||||
\(987\) | 2.57232 | + | 7.91678i | 0.0818777 | + | 0.251994i | ||||
\(988\) | −23.4325 | − | 66.0109i | −0.745488 | − | 2.10009i | ||||
\(989\) | −0.481237 | − | 0.156364i | −0.0153025 | − | 0.00497207i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.98983 | − | 24.5902i | −0.253805 | − | 0.781132i | −0.994063 | − | 0.108809i | \(-0.965296\pi\) |
0.740258 | − | 0.672323i | \(-0.234704\pi\) | |||||||
\(992\) | −1.07915 | + | 11.9959i | −0.0342629 | + | 0.380871i | ||||
\(993\) | − | 66.8905i | − | 2.12271i | ||||||
\(994\) | −27.8558 | − | 4.02802i | −0.883531 | − | 0.127761i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −22.9342 | + | 33.4242i | −0.726699 | + | 1.05909i | ||||
\(997\) | 15.5099 | + | 11.2686i | 0.491204 | + | 0.356881i | 0.805647 | − | 0.592396i | \(-0.201818\pi\) |
−0.314443 | + | 0.949276i | \(0.601818\pi\) | |||||||
\(998\) | 2.02170 | − | 1.06466i | 0.0639958 | − | 0.0337011i | ||||
\(999\) | −7.74398 | −0.245009 |
(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 | 1000.2.o.a.149.10 | 112 | ||
5.2 | odd | 4 | 1000.2.t.b.101.48 | 224 | |||
5.3 | odd | 4 | 1000.2.t.b.101.9 | 224 | |||
5.4 | even | 2 | 200.2.o.a.29.19 | ✓ | 112 | ||
8.5 | even | 2 | inner | 1000.2.o.a.149.5 | 112 | ||
20.19 | odd | 2 | 800.2.be.a.529.25 | 112 | |||
25.6 | even | 5 | 200.2.o.a.69.24 | yes | 112 | ||
25.8 | odd | 20 | 1000.2.t.b.901.37 | 224 | |||
25.17 | odd | 20 | 1000.2.t.b.901.20 | 224 | |||
25.19 | even | 10 | inner | 1000.2.o.a.349.5 | 112 | ||
40.13 | odd | 4 | 1000.2.t.b.101.37 | 224 | |||
40.19 | odd | 2 | 800.2.be.a.529.4 | 112 | |||
40.29 | even | 2 | 200.2.o.a.29.24 | yes | 112 | ||
40.37 | odd | 4 | 1000.2.t.b.101.20 | 224 | |||
100.31 | odd | 10 | 800.2.be.a.369.4 | 112 | |||
200.69 | even | 10 | inner | 1000.2.o.a.349.10 | 112 | ||
200.117 | odd | 20 | 1000.2.t.b.901.48 | 224 | |||
200.131 | odd | 10 | 800.2.be.a.369.25 | 112 | |||
200.133 | odd | 20 | 1000.2.t.b.901.9 | 224 | |||
200.181 | even | 10 | 200.2.o.a.69.19 | yes | 112 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.o.a.29.19 | ✓ | 112 | 5.4 | even | 2 | ||
200.2.o.a.29.24 | yes | 112 | 40.29 | even | 2 | ||
200.2.o.a.69.19 | yes | 112 | 200.181 | even | 10 | ||
200.2.o.a.69.24 | yes | 112 | 25.6 | even | 5 | ||
800.2.be.a.369.4 | 112 | 100.31 | odd | 10 | |||
800.2.be.a.369.25 | 112 | 200.131 | odd | 10 | |||
800.2.be.a.529.4 | 112 | 40.19 | odd | 2 | |||
800.2.be.a.529.25 | 112 | 20.19 | odd | 2 | |||
1000.2.o.a.149.5 | 112 | 8.5 | even | 2 | inner | ||
1000.2.o.a.149.10 | 112 | 1.1 | even | 1 | trivial | ||
1000.2.o.a.349.5 | 112 | 25.19 | even | 10 | inner | ||
1000.2.o.a.349.10 | 112 | 200.69 | even | 10 | inner | ||
1000.2.t.b.101.9 | 224 | 5.3 | odd | 4 | |||
1000.2.t.b.101.20 | 224 | 40.37 | odd | 4 | |||
1000.2.t.b.101.37 | 224 | 40.13 | odd | 4 | |||
1000.2.t.b.101.48 | 224 | 5.2 | odd | 4 | |||
1000.2.t.b.901.9 | 224 | 200.133 | odd | 20 | |||
1000.2.t.b.901.20 | 224 | 25.17 | odd | 20 | |||
1000.2.t.b.901.37 | 224 | 25.8 | odd | 20 | |||
1000.2.t.b.901.48 | 224 | 200.117 | odd | 20 |