Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.2 | ||
Root | \(0.597828 + 1.03547i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.508 |
Dual form | 1183.2.e.f.170.2 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0978281 | − | 0.169443i | −0.0691749 | − | 0.119815i | 0.829363 | − | 0.558710i | \(-0.188703\pi\) |
−0.898538 | + | 0.438895i | \(0.855370\pi\) | |||||||
\(3\) | 0.129894 | − | 0.224983i | 0.0749945 | − | 0.129894i | −0.826089 | − | 0.563539i | \(-0.809439\pi\) |
0.901084 | + | 0.433645i | \(0.142773\pi\) | |||||||
\(4\) | 0.980859 | − | 1.69890i | 0.490430 | − | 0.849449i | ||||
\(5\) | 1.96625 | + | 3.40565i | 0.879336 | + | 1.52305i | 0.852071 | + | 0.523426i | \(0.175346\pi\) |
0.0272650 | + | 0.999628i | \(0.491320\pi\) | |||||||
\(6\) | −0.0508292 | −0.0207509 | ||||||||
\(7\) | −1.12324 | − | 2.39548i | −0.424546 | − | 0.905406i | ||||
\(8\) | −0.775135 | −0.274052 | ||||||||
\(9\) | 1.46625 | + | 2.53963i | 0.488752 | + | 0.846543i | ||||
\(10\) | 0.384710 | − | 0.666337i | 0.121656 | − | 0.210714i | ||||
\(11\) | 2.25314 | − | 3.90255i | 0.679346 | − | 1.17666i | −0.295832 | − | 0.955240i | \(-0.595597\pi\) |
0.975178 | − | 0.221422i | \(-0.0710699\pi\) | |||||||
\(12\) | −0.254816 | − | 0.441354i | −0.0735590 | − | 0.127408i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.296013 | + | 0.424671i | −0.0791129 | + | 0.113498i | ||||
\(15\) | 1.02162 | 0.263781 | ||||||||
\(16\) | −1.88589 | − | 3.26645i | −0.471472 | − | 0.816614i | ||||
\(17\) | 1.14070 | − | 1.97576i | 0.276661 | − | 0.479192i | −0.693891 | − | 0.720080i | \(-0.744105\pi\) |
0.970553 | + | 0.240888i | \(0.0774386\pi\) | |||||||
\(18\) | 0.286882 | − | 0.496894i | 0.0676187 | − | 0.117119i | ||||
\(19\) | −0.893841 | − | 1.54818i | −0.205061 | − | 0.355177i | 0.745091 | − | 0.666963i | \(-0.232406\pi\) |
−0.950152 | + | 0.311786i | \(0.899073\pi\) | |||||||
\(20\) | 7.71448 | 1.72501 | ||||||||
\(21\) | −0.684846 | − | 0.0584481i | −0.149446 | − | 0.0127544i | ||||
\(22\) | −0.881681 | −0.187975 | ||||||||
\(23\) | −0.870106 | − | 1.50707i | −0.181430 | − | 0.314245i | 0.760938 | − | 0.648825i | \(-0.224739\pi\) |
−0.942368 | + | 0.334579i | \(0.891406\pi\) | |||||||
\(24\) | −0.100686 | + | 0.174393i | −0.0205524 | + | 0.0355977i | ||||
\(25\) | −5.23232 | + | 9.06264i | −1.04646 | + | 1.81253i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.54120 | 0.296604 | ||||||||
\(28\) | −5.17142 | − | 0.441354i | −0.977307 | − | 0.0834081i | ||||
\(29\) | 1.65110 | 0.306602 | 0.153301 | − | 0.988180i | \(-0.451010\pi\) | ||||
0.153301 | + | 0.988180i | \(0.451010\pi\) | |||||||
\(30\) | −0.0999432 | − | 0.173107i | −0.0182471 | − | 0.0316048i | ||||
\(31\) | 2.80262 | − | 4.85427i | 0.503365 | − | 0.871853i | −0.496628 | − | 0.867964i | \(-0.665429\pi\) |
0.999992 | − | 0.00388953i | \(-0.00123808\pi\) | |||||||
\(32\) | −1.14412 | + | 1.98168i | −0.202254 | + | 0.350314i | ||||
\(33\) | −0.585339 | − | 1.01384i | −0.101894 | − | 0.176486i | ||||
\(34\) | −0.446372 | −0.0765522 | ||||||||
\(35\) | 5.94959 | − | 8.53550i | 1.00566 | − | 1.44276i | ||||
\(36\) | 5.75276 | 0.958793 | ||||||||
\(37\) | 3.57204 | + | 6.18695i | 0.587239 | + | 1.01713i | 0.994592 | + | 0.103857i | \(0.0331185\pi\) |
−0.407353 | + | 0.913271i | \(0.633548\pi\) | |||||||
\(38\) | −0.174886 | + | 0.302911i | −0.0283702 | + | 0.0491386i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.52411 | − | 2.63984i | −0.240983 | − | 0.417396i | ||||
\(41\) | 8.11574 | 1.26746 | 0.633732 | − | 0.773552i | \(-0.281522\pi\) | ||||
0.633732 | + | 0.773552i | \(0.281522\pi\) | |||||||
\(42\) | 0.0570936 | + | 0.121760i | 0.00880973 | + | 0.0187880i | ||||
\(43\) | 6.81353 | 1.03905 | 0.519527 | − | 0.854454i | \(-0.326108\pi\) | ||||
0.519527 | + | 0.854454i | \(0.326108\pi\) | |||||||
\(44\) | −4.42002 | − | 7.65570i | −0.666343 | − | 1.15414i | ||||
\(45\) | −5.76606 | + | 9.98711i | −0.859554 | + | 1.48879i | ||||
\(46\) | −0.170242 | + | 0.294867i | −0.0251008 | + | 0.0434758i | ||||
\(47\) | 1.77271 | + | 3.07043i | 0.258577 | + | 0.447868i | 0.965861 | − | 0.259061i | \(-0.0834131\pi\) |
−0.707284 | + | 0.706929i | \(0.750080\pi\) | |||||||
\(48\) | −0.979864 | −0.141431 | ||||||||
\(49\) | −4.47665 | + | 5.38141i | −0.639522 | + | 0.768773i | ||||
\(50\) | 2.04747 | 0.289556 | ||||||||
\(51\) | −0.296342 | − | 0.513279i | −0.0414962 | − | 0.0718735i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.64483 | + | 2.84892i | −0.225934 | + | 0.391330i | −0.956599 | − | 0.291406i | \(-0.905877\pi\) |
0.730665 | + | 0.682736i | \(0.239210\pi\) | |||||||
\(54\) | −0.150772 | − | 0.261146i | −0.0205175 | − | 0.0355374i | ||||
\(55\) | 17.7210 | 2.38949 | ||||||||
\(56\) | 0.870665 | + | 1.85682i | 0.116347 | + | 0.248128i | ||||
\(57\) | −0.464419 | −0.0615138 | ||||||||
\(58\) | −0.161524 | − | 0.279768i | −0.0212092 | − | 0.0367353i | ||||
\(59\) | 2.25314 | − | 3.90255i | 0.293333 | − | 0.508068i | −0.681262 | − | 0.732039i | \(-0.738569\pi\) |
0.974596 | + | 0.223971i | \(0.0719021\pi\) | |||||||
\(60\) | 1.00207 | − | 1.73563i | 0.129366 | − | 0.224069i | ||||
\(61\) | −3.77234 | − | 6.53388i | −0.482998 | − | 0.836577i | 0.516811 | − | 0.856099i | \(-0.327119\pi\) |
−0.999809 | + | 0.0195220i | \(0.993786\pi\) | |||||||
\(62\) | −1.09670 | −0.139281 | ||||||||
\(63\) | 4.43667 | − | 6.36500i | 0.558968 | − | 0.801915i | ||||
\(64\) | −7.09585 | −0.886981 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.114525 | + | 0.198364i | −0.0140971 | + | 0.0244169i | ||||
\(67\) | −6.33263 | + | 10.9684i | −0.773653 | + | 1.34001i | 0.161895 | + | 0.986808i | \(0.448239\pi\) |
−0.935548 | + | 0.353199i | \(0.885094\pi\) | |||||||
\(68\) | −2.23774 | − | 3.87588i | −0.271366 | − | 0.470020i | ||||
\(69\) | −0.452087 | −0.0544249 | ||||||||
\(70\) | −2.02832 | − | 0.173107i | −0.242431 | − | 0.0206902i | ||||
\(71\) | −9.54869 | −1.13322 | −0.566610 | − | 0.823986i | \(-0.691746\pi\) | ||||
−0.566610 | + | 0.823986i | \(0.691746\pi\) | |||||||
\(72\) | −1.13655 | − | 1.96855i | −0.133943 | − | 0.231996i | ||||
\(73\) | 0.540019 | − | 0.935340i | 0.0632044 | − | 0.109473i | −0.832692 | − | 0.553737i | \(-0.813201\pi\) |
0.895896 | + | 0.444264i | \(0.146535\pi\) | |||||||
\(74\) | 0.698891 | − | 1.21052i | 0.0812445 | − | 0.140720i | ||||
\(75\) | 1.35930 | + | 2.35437i | 0.156958 | + | 0.271859i | ||||
\(76\) | −3.50693 | −0.402273 | ||||||||
\(77\) | −11.8793 | − | 1.01384i | −1.35377 | − | 0.115537i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.395849 | − | 0.685630i | −0.0445365 | − | 0.0771394i | 0.842898 | − | 0.538074i | \(-0.180848\pi\) |
−0.887434 | + | 0.460934i | \(0.847514\pi\) | |||||||
\(80\) | 7.41628 | − | 12.8454i | 0.829165 | − | 1.43616i | ||||
\(81\) | −4.19857 | + | 7.27214i | −0.466508 | + | 0.808016i | ||||
\(82\) | −0.793947 | − | 1.37516i | −0.0876768 | − | 0.151861i | ||||
\(83\) | 7.14643 | 0.784422 | 0.392211 | − | 0.919875i | \(-0.371710\pi\) | ||||
0.392211 | + | 0.919875i | \(0.371710\pi\) | |||||||
\(84\) | −0.771035 | + | 1.10615i | −0.0841268 | + | 0.120691i | ||||
\(85\) | 8.97166 | 0.973114 | ||||||||
\(86\) | −0.666555 | − | 1.15451i | −0.0718765 | − | 0.124494i | ||||
\(87\) | 0.214468 | − | 0.371470i | 0.0229934 | − | 0.0398258i | ||||
\(88\) | −1.74649 | + | 3.02500i | −0.186176 | + | 0.322466i | ||||
\(89\) | −5.63281 | − | 9.75631i | −0.597077 | − | 1.03417i | −0.993250 | − | 0.115992i | \(-0.962995\pi\) |
0.396174 | − | 0.918176i | \(-0.370338\pi\) | |||||||
\(90\) | 2.25633 | 0.237838 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.41381 | −0.355914 | ||||||||
\(93\) | −0.728087 | − | 1.26108i | −0.0754991 | − | 0.130768i | ||||
\(94\) | 0.346843 | − | 0.600749i | 0.0357741 | − | 0.0619625i | ||||
\(95\) | 3.51504 | − | 6.08823i | 0.360636 | − | 0.624639i | ||||
\(96\) | 0.297229 | + | 0.514816i | 0.0303358 | + | 0.0525432i | ||||
\(97\) | 8.81353 | 0.894879 | 0.447439 | − | 0.894314i | \(-0.352336\pi\) | ||||
0.447439 | + | 0.894314i | \(0.352336\pi\) | |||||||
\(98\) | 1.34979 | + | 0.232085i | 0.136349 | + | 0.0234441i | ||||
\(99\) | 13.2147 | 1.32813 | ||||||||
\(100\) | 10.2643 | + | 17.7783i | 1.02643 | + | 1.77783i | ||||
\(101\) | 7.15855 | − | 12.3990i | 0.712303 | − | 1.23374i | −0.251688 | − | 0.967808i | \(-0.580986\pi\) |
0.963991 | − | 0.265936i | \(-0.0856810\pi\) | |||||||
\(102\) | −0.0579811 | + | 0.100426i | −0.00574099 | + | 0.00994368i | ||||
\(103\) | 3.74607 | + | 6.48839i | 0.369111 | + | 0.639320i | 0.989427 | − | 0.145033i | \(-0.0463287\pi\) |
−0.620315 | + | 0.784352i | \(0.712995\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.14753 | − | 2.44727i | −0.111987 | − | 0.238829i | ||||
\(106\) | 0.643641 | 0.0625160 | ||||||||
\(107\) | −5.48919 | − | 9.50756i | −0.530660 | − | 0.919130i | −0.999360 | − | 0.0357726i | \(-0.988611\pi\) |
0.468700 | − | 0.883357i | \(-0.344723\pi\) | |||||||
\(108\) | 1.51170 | − | 2.61834i | 0.145463 | − | 0.251950i | ||||
\(109\) | −6.22314 | + | 10.7788i | −0.596068 | + | 1.03242i | 0.397327 | + | 0.917677i | \(0.369938\pi\) |
−0.993395 | + | 0.114744i | \(0.963395\pi\) | |||||||
\(110\) | −1.73361 | − | 3.00270i | −0.165293 | − | 0.286296i | ||||
\(111\) | 1.85595 | 0.176159 | ||||||||
\(112\) | −5.70642 | + | 8.18663i | −0.539206 | + | 0.773564i | ||||
\(113\) | −1.65110 | −0.155323 | −0.0776613 | − | 0.996980i | \(-0.524745\pi\) | ||||
−0.0776613 | + | 0.996980i | \(0.524745\pi\) | |||||||
\(114\) | 0.0454333 | + | 0.0786927i | 0.00425522 | + | 0.00737025i | ||||
\(115\) | 3.42170 | − | 5.92656i | 0.319075 | − | 0.552654i | ||||
\(116\) | 1.61950 | − | 2.80505i | 0.150367 | − | 0.260443i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.881681 | −0.0811653 | ||||||||
\(119\) | −6.01418 | − | 0.513279i | −0.551319 | − | 0.0470522i | ||||
\(120\) | −0.791894 | −0.0722897 | ||||||||
\(121\) | −4.65325 | − | 8.05967i | −0.423023 | − | 0.732697i | ||||
\(122\) | −0.738081 | + | 1.27839i | −0.0668227 | + | 0.115740i | ||||
\(123\) | 1.05419 | − | 1.82591i | 0.0950528 | − | 0.164636i | ||||
\(124\) | −5.49794 | − | 9.52272i | −0.493730 | − | 0.855165i | ||||
\(125\) | −21.4897 | −1.92210 | ||||||||
\(126\) | −1.51254 | − | 0.129087i | −0.134748 | − | 0.0115000i | ||||
\(127\) | −4.49297 | −0.398687 | −0.199343 | − | 0.979930i | \(-0.563881\pi\) | ||||
−0.199343 | + | 0.979930i | \(0.563881\pi\) | |||||||
\(128\) | 2.98242 | + | 5.16569i | 0.263611 | + | 0.456587i | ||||
\(129\) | 0.885039 | − | 1.53293i | 0.0779233 | − | 0.134967i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.32836 | + | 10.9610i | 0.552911 | + | 0.957670i | 0.998063 | + | 0.0622152i | \(0.0198165\pi\) |
−0.445151 | + | 0.895455i | \(0.646850\pi\) | |||||||
\(132\) | −2.29654 | −0.199888 | ||||||||
\(133\) | −2.70463 | + | 3.88016i | −0.234521 | + | 0.336453i | ||||
\(134\) | 2.47804 | 0.214070 | ||||||||
\(135\) | 3.03039 | + | 5.24878i | 0.260814 | + | 0.451743i | ||||
\(136\) | −0.884200 | + | 1.53148i | −0.0758195 | + | 0.131323i | ||||
\(137\) | −4.64321 | + | 8.04227i | −0.396696 | + | 0.687097i | −0.993316 | − | 0.115426i | \(-0.963177\pi\) |
0.596620 | + | 0.802524i | \(0.296510\pi\) | |||||||
\(138\) | 0.0442268 | + | 0.0766031i | 0.00376484 | + | 0.00652089i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −8.66523 | − | 18.4799i | −0.732346 | − | 1.56183i | ||||
\(141\) | 0.921061 | 0.0775673 | ||||||||
\(142\) | 0.934130 | + | 1.61796i | 0.0783905 | + | 0.135776i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.53039 | − | 9.57891i | 0.460866 | − | 0.798243i | ||||
\(145\) | 3.24649 | + | 5.62308i | 0.269606 | + | 0.466971i | ||||
\(146\) | −0.211316 | −0.0174887 | ||||||||
\(147\) | 0.629237 | + | 1.70619i | 0.0518986 | + | 0.140724i | ||||
\(148\) | 14.0147 | 1.15200 | ||||||||
\(149\) | −7.58243 | − | 13.1332i | −0.621177 | − | 1.07591i | −0.989267 | − | 0.146120i | \(-0.953321\pi\) |
0.368090 | − | 0.929790i | \(-0.380012\pi\) | |||||||
\(150\) | 0.265955 | − | 0.460647i | 0.0217151 | − | 0.0376117i | ||||
\(151\) | 2.57079 | − | 4.45274i | 0.209208 | − | 0.362359i | −0.742257 | − | 0.670115i | \(-0.766245\pi\) |
0.951465 | + | 0.307756i | \(0.0995780\pi\) | |||||||
\(152\) | 0.692848 | + | 1.20005i | 0.0561974 | + | 0.0973367i | ||||
\(153\) | 6.69025 | 0.540875 | ||||||||
\(154\) | 0.990341 | + | 2.11205i | 0.0798040 | + | 0.170194i | ||||
\(155\) | 22.0426 | 1.77051 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.36557 | − | 9.29344i | 0.428219 | − | 0.741697i | −0.568496 | − | 0.822686i | \(-0.692474\pi\) |
0.996715 | + | 0.0809889i | \(0.0258078\pi\) | |||||||
\(158\) | −0.0774503 | + | 0.134148i | −0.00616162 | + | 0.0106722i | ||||
\(159\) | 0.427307 | + | 0.740117i | 0.0338877 | + | 0.0586951i | ||||
\(160\) | −8.99853 | −0.711397 | ||||||||
\(161\) | −2.63281 | + | 3.77712i | −0.207495 | + | 0.297679i | ||||
\(162\) | 1.64295 | 0.129083 | ||||||||
\(163\) | 1.18620 | + | 2.05455i | 0.0929101 | + | 0.160925i | 0.908734 | − | 0.417375i | \(-0.137050\pi\) |
−0.815824 | + | 0.578300i | \(0.803716\pi\) | |||||||
\(164\) | 7.96039 | − | 13.7878i | 0.621602 | − | 1.07665i | ||||
\(165\) | 2.30185 | − | 3.98692i | 0.179199 | − | 0.310382i | ||||
\(166\) | −0.699122 | − | 1.21091i | −0.0542624 | − | 0.0939852i | ||||
\(167\) | −12.0784 | −0.934653 | −0.467327 | − | 0.884085i | \(-0.654783\pi\) | ||||
−0.467327 | + | 0.884085i | \(0.654783\pi\) | |||||||
\(168\) | 0.530848 | + | 0.0453052i | 0.0409558 | + | 0.00349537i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.877681 | − | 1.52019i | −0.0673151 | − | 0.116593i | ||||
\(171\) | 2.62120 | − | 4.54005i | 0.200448 | − | 0.347186i | ||||
\(172\) | 6.68312 | − | 11.5755i | 0.509583 | − | 0.882624i | ||||
\(173\) | 9.70485 | + | 16.8093i | 0.737846 | + | 1.27799i | 0.953463 | + | 0.301509i | \(0.0974902\pi\) |
−0.215618 | + | 0.976478i | \(0.569176\pi\) | |||||||
\(174\) | −0.0839242 | −0.00636228 | ||||||||
\(175\) | 27.5865 | + | 2.35437i | 2.08535 | + | 0.177974i | ||||
\(176\) | −16.9967 | −1.28117 | ||||||||
\(177\) | −0.585339 | − | 1.01384i | −0.0439968 | − | 0.0762046i | ||||
\(178\) | −1.10209 | + | 1.90888i | −0.0826055 | + | 0.143077i | ||||
\(179\) | −7.32219 | + | 12.6824i | −0.547286 | + | 0.947928i | 0.451173 | + | 0.892437i | \(0.351006\pi\) |
−0.998459 | + | 0.0554912i | \(0.982328\pi\) | |||||||
\(180\) | 11.3114 | + | 19.5919i | 0.843101 | + | 1.46029i | ||||
\(181\) | −9.44627 | −0.702136 | −0.351068 | − | 0.936350i | \(-0.614181\pi\) | ||||
−0.351068 | + | 0.936350i | \(0.614181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.96002 | −0.144889 | ||||||||
\(184\) | 0.674450 | + | 1.16818i | 0.0497211 | + | 0.0861194i | ||||
\(185\) | −14.0471 | + | 24.3302i | −1.03276 | + | 1.78879i | ||||
\(186\) | −0.142455 | + | 0.246739i | −0.0104453 | + | 0.0180918i | ||||
\(187\) | −5.14033 | − | 8.90331i | −0.375898 | − | 0.651074i | ||||
\(188\) | 6.95513 | 0.507255 | ||||||||
\(189\) | −1.73114 | − | 3.69191i | −0.125922 | − | 0.268547i | ||||
\(190\) | −1.37548 | −0.0997878 | ||||||||
\(191\) | −6.27687 | − | 10.8719i | −0.454179 | − | 0.786660i | 0.544462 | − | 0.838786i | \(-0.316734\pi\) |
−0.998641 | + | 0.0521252i | \(0.983401\pi\) | |||||||
\(192\) | −0.921709 | + | 1.59645i | −0.0665186 | + | 0.115214i | ||||
\(193\) | −4.68430 | + | 8.11344i | −0.337183 | + | 0.584018i | −0.983902 | − | 0.178710i | \(-0.942807\pi\) |
0.646719 | + | 0.762729i | \(0.276141\pi\) | |||||||
\(194\) | −0.862212 | − | 1.49339i | −0.0619032 | − | 0.107219i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.75151 | + | 12.8838i | 0.339393 | + | 0.920270i | ||||
\(197\) | 7.62276 | 0.543099 | 0.271550 | − | 0.962424i | \(-0.412464\pi\) | ||||
0.271550 | + | 0.962424i | \(0.412464\pi\) | |||||||
\(198\) | −1.29277 | − | 2.23914i | −0.0918731 | − | 0.159129i | ||||
\(199\) | −6.76443 | + | 11.7163i | −0.479518 | + | 0.830549i | −0.999724 | − | 0.0234914i | \(-0.992522\pi\) |
0.520206 | + | 0.854041i | \(0.325855\pi\) | |||||||
\(200\) | 4.05575 | − | 7.02477i | 0.286785 | − | 0.496726i | ||||
\(201\) | 1.64514 | + | 2.84947i | 0.116039 | + | 0.200986i | ||||
\(202\) | −2.80123 | −0.197094 | ||||||||
\(203\) | −1.85459 | − | 3.95518i | −0.130167 | − | 0.277599i | ||||
\(204\) | −1.16268 | −0.0814038 | ||||||||
\(205\) | 15.9576 | + | 27.6394i | 1.11453 | + | 1.93042i | ||||
\(206\) | 0.732942 | − | 1.26949i | 0.0510665 | − | 0.0884498i | ||||
\(207\) | 2.55159 | − | 4.41949i | 0.177348 | − | 0.307176i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.05579 | −0.557231 | ||||||||
\(210\) | −0.302413 | + | 0.433853i | −0.0208685 | + | 0.0299387i | ||||
\(211\) | −15.7995 | −1.08768 | −0.543840 | − | 0.839189i | \(-0.683030\pi\) | ||||
−0.543840 | + | 0.839189i | \(0.683030\pi\) | |||||||
\(212\) | 3.22669 | + | 5.58879i | 0.221610 | + | 0.383839i | ||||
\(213\) | −1.24032 | + | 2.14830i | −0.0849853 | + | 0.147199i | ||||
\(214\) | −1.07399 | + | 1.86021i | −0.0734167 | + | 0.127162i | ||||
\(215\) | 13.3971 | + | 23.2045i | 0.913678 | + | 1.58254i | ||||
\(216\) | −1.19464 | −0.0812847 | ||||||||
\(217\) | −14.7763 | − | 1.26108i | −1.00308 | − | 0.0856080i | ||||
\(218\) | 2.43519 | 0.164932 | ||||||||
\(219\) | −0.140291 | − | 0.242991i | −0.00947997 | − | 0.0164198i | ||||
\(220\) | 17.3818 | − | 30.1061i | 1.17188 | − | 2.02975i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.181564 | − | 0.314478i | −0.0121858 | − | 0.0211064i | ||||
\(223\) | −22.4737 | −1.50495 | −0.752474 | − | 0.658622i | \(-0.771139\pi\) | ||||
−0.752474 | + | 0.658622i | \(0.771139\pi\) | |||||||
\(224\) | 6.03219 | + | 0.514816i | 0.403043 | + | 0.0343976i | ||||
\(225\) | −30.6876 | −2.04584 | ||||||||
\(226\) | 0.161524 | + | 0.279768i | 0.0107444 | + | 0.0186099i | ||||
\(227\) | −4.60124 | + | 7.96959i | −0.305395 | + | 0.528960i | −0.977349 | − | 0.211633i | \(-0.932122\pi\) |
0.671954 | + | 0.740593i | \(0.265455\pi\) | |||||||
\(228\) | −0.455530 | + | 0.789001i | −0.0301682 | + | 0.0522529i | ||||
\(229\) | 7.64611 | + | 13.2435i | 0.505269 | + | 0.875152i | 0.999981 | + | 0.00609528i | \(0.00194020\pi\) |
−0.494712 | + | 0.869057i | \(0.664726\pi\) | |||||||
\(230\) | −1.33895 | −0.0882880 | ||||||||
\(231\) | −1.77115 | + | 2.54095i | −0.116533 | + | 0.167182i | ||||
\(232\) | −1.27983 | −0.0840247 | ||||||||
\(233\) | 4.02789 | + | 6.97652i | 0.263876 | + | 0.457047i | 0.967269 | − | 0.253755i | \(-0.0816656\pi\) |
−0.703392 | + | 0.710802i | \(0.748332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.97121 | + | 12.0745i | −0.454752 | + | 0.787653i | ||||
\(236\) | −4.42002 | − | 7.65570i | −0.287719 | − | 0.498344i | ||||
\(237\) | −0.205674 | −0.0133600 | ||||||||
\(238\) | 0.501384 | + | 1.06928i | 0.0324999 | + | 0.0693108i | ||||
\(239\) | −21.7258 | −1.40533 | −0.702663 | − | 0.711523i | \(-0.748006\pi\) | ||||
−0.702663 | + | 0.711523i | \(0.748006\pi\) | |||||||
\(240\) | −1.92666 | − | 3.33708i | −0.124366 | − | 0.215407i | ||||
\(241\) | −10.2490 | + | 17.7518i | −0.660195 | + | 1.14349i | 0.320369 | + | 0.947293i | \(0.396193\pi\) |
−0.980564 | + | 0.196199i | \(0.937140\pi\) | |||||||
\(242\) | −0.910438 | + | 1.57692i | −0.0585252 | + | 0.101369i | ||||
\(243\) | 3.40254 | + | 5.89337i | 0.218273 | + | 0.378060i | ||||
\(244\) | −14.8005 | −0.947507 | ||||||||
\(245\) | −27.1295 | − | 4.66470i | −1.73324 | − | 0.298017i | ||||
\(246\) | −0.412517 | −0.0263011 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.17241 | + | 3.76272i | −0.137948 | + | 0.238933i | ||||
\(249\) | 0.928280 | − | 1.60783i | 0.0588273 | − | 0.101892i | ||||
\(250\) | 2.10230 | + | 3.64129i | 0.132961 | + | 0.230295i | ||||
\(251\) | 2.60871 | 0.164660 | 0.0823301 | − | 0.996605i | \(-0.473764\pi\) | ||||
0.0823301 | + | 0.996605i | \(0.473764\pi\) | |||||||
\(252\) | −6.46175 | − | 13.7806i | −0.407052 | − | 0.868098i | ||||
\(253\) | −7.84187 | −0.493014 | ||||||||
\(254\) | 0.439539 | + | 0.761304i | 0.0275791 | + | 0.0477685i | ||||
\(255\) | 1.16537 | − | 2.01848i | 0.0729781 | − | 0.126402i | ||||
\(256\) | −6.51232 | + | 11.2797i | −0.407020 | + | 0.704979i | ||||
\(257\) | 4.49838 | + | 7.79142i | 0.280601 | + | 0.486016i | 0.971533 | − | 0.236904i | \(-0.0761328\pi\) |
−0.690932 | + | 0.722920i | \(0.742799\pi\) | |||||||
\(258\) | −0.346327 | −0.0215614 | ||||||||
\(259\) | 10.8084 | − | 15.5062i | 0.671604 | − | 0.963508i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.42094 | + | 4.19318i | 0.149852 | + | 0.259551i | ||||
\(262\) | 1.23818 | − | 2.14460i | 0.0764952 | − | 0.132494i | ||||
\(263\) | −0.716961 | + | 1.24181i | −0.0442097 | + | 0.0765735i | −0.887284 | − | 0.461224i | \(-0.847410\pi\) |
0.843074 | + | 0.537798i | \(0.180744\pi\) | |||||||
\(264\) | 0.453717 | + | 0.785860i | 0.0279243 | + | 0.0483664i | ||||
\(265\) | −12.9366 | −0.794689 | ||||||||
\(266\) | 0.922056 | + | 0.0786927i | 0.0565349 | + | 0.00482496i | ||||
\(267\) | −2.92668 | −0.179110 | ||||||||
\(268\) | 12.4228 | + | 21.5170i | 0.758845 | + | 1.31436i | ||||
\(269\) | 4.08416 | − | 7.07397i | 0.249016 | − | 0.431308i | −0.714237 | − | 0.699904i | \(-0.753226\pi\) |
0.963253 | + | 0.268596i | \(0.0865596\pi\) | |||||||
\(270\) | 0.592914 | − | 1.02696i | 0.0360836 | − | 0.0624986i | ||||
\(271\) | −0.106159 | − | 0.183872i | −0.00644867 | − | 0.0111694i | 0.862783 | − | 0.505574i | \(-0.168719\pi\) |
−0.869232 | + | 0.494405i | \(0.835386\pi\) | |||||||
\(272\) | −8.60497 | −0.521753 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.81695 | 0.109766 | ||||||||
\(275\) | 23.5783 | + | 40.8387i | 1.42182 | + | 2.46267i | ||||
\(276\) | −0.443434 | + | 0.768049i | −0.0266916 | + | 0.0462311i | ||||
\(277\) | −11.4875 | + | 19.8969i | −0.690215 | + | 1.19549i | 0.281552 | + | 0.959546i | \(0.409151\pi\) |
−0.971767 | + | 0.235942i | \(0.924182\pi\) | |||||||
\(278\) | 0.391313 | + | 0.677773i | 0.0234694 | + | 0.0406501i | ||||
\(279\) | 16.4374 | 0.984081 | ||||||||
\(280\) | −4.61174 | + | 6.61617i | −0.275604 | + | 0.395392i | ||||
\(281\) | 0.345228 | 0.0205946 | 0.0102973 | − | 0.999947i | \(-0.496722\pi\) | ||||
0.0102973 | + | 0.999947i | \(0.496722\pi\) | |||||||
\(282\) | −0.0901057 | − | 0.156068i | −0.00536572 | − | 0.00929369i | ||||
\(283\) | 14.4857 | − | 25.0900i | 0.861087 | − | 1.49145i | −0.00979277 | − | 0.999952i | \(-0.503117\pi\) |
0.870880 | − | 0.491495i | \(-0.163549\pi\) | |||||||
\(284\) | −9.36592 | + | 16.2222i | −0.555765 | + | 0.962613i | ||||
\(285\) | −0.913167 | − | 1.58165i | −0.0540913 | − | 0.0936889i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.11594 | − | 19.4411i | −0.538097 | − | 1.14757i | ||||
\(288\) | −6.71029 | −0.395408 | ||||||||
\(289\) | 5.89759 | + | 10.2149i | 0.346917 | + | 0.600878i | ||||
\(290\) | 0.635195 | − | 1.10019i | 0.0372999 | − | 0.0646054i | ||||
\(291\) | 1.14483 | − | 1.98290i | 0.0671109 | − | 0.116240i | ||||
\(292\) | −1.05937 | − | 1.83487i | −0.0619947 | − | 0.107378i | ||||
\(293\) | −31.5427 | −1.84274 | −0.921372 | − | 0.388682i | \(-0.872930\pi\) | ||||
−0.921372 | + | 0.388682i | \(0.872930\pi\) | |||||||
\(294\) | 0.227545 | − | 0.273533i | 0.0132707 | − | 0.0159528i | ||||
\(295\) | 17.7210 | 1.03175 | ||||||||
\(296\) | −2.76881 | − | 4.79572i | −0.160934 | − | 0.278746i | ||||
\(297\) | 3.47253 | − | 6.01460i | 0.201497 | − | 0.349002i | ||||
\(298\) | −1.48355 | + | 2.56958i | −0.0859398 | + | 0.148852i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.33311 | 0.307907 | ||||||||
\(301\) | −7.65325 | − | 16.3217i | −0.441126 | − | 0.940766i | ||||
\(302\) | −1.00598 | −0.0578879 | ||||||||
\(303\) | −1.85971 | − | 3.22111i | −0.106838 | − | 0.185048i | ||||
\(304\) | −3.37137 | + | 5.83939i | −0.193361 | + | 0.334912i | ||||
\(305\) | 14.8348 | − | 25.6945i | 0.849435 | − | 1.47127i | ||||
\(306\) | −0.654495 | − | 1.13362i | −0.0374150 | − | 0.0648047i | ||||
\(307\) | 18.1941 | 1.03839 | 0.519197 | − | 0.854655i | \(-0.326231\pi\) | ||||
0.519197 | + | 0.854655i | \(0.326231\pi\) | |||||||
\(308\) | −13.3743 | + | 19.1873i | −0.762073 | + | 1.09330i | ||||
\(309\) | 1.94637 | 0.110725 | ||||||||
\(310\) | −2.15639 | − | 3.73498i | −0.122475 | − | 0.212132i | ||||
\(311\) | 0.188312 | − | 0.326165i | 0.0106782 | − | 0.0184951i | −0.860637 | − | 0.509219i | \(-0.829934\pi\) |
0.871315 | + | 0.490724i | \(0.163268\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.49415 | − | 9.51615i | −0.310548 | − | 0.537884i | 0.667933 | − | 0.744221i | \(-0.267179\pi\) |
−0.978481 | + | 0.206337i | \(0.933846\pi\) | |||||||
\(314\) | −2.09961 | −0.118488 | ||||||||
\(315\) | 30.4006 | + | 2.59454i | 1.71288 | + | 0.146186i | ||||
\(316\) | −1.55309 | −0.0873680 | ||||||||
\(317\) | 13.0903 | + | 22.6731i | 0.735225 | + | 1.27345i | 0.954625 | + | 0.297812i | \(0.0962568\pi\) |
−0.219400 | + | 0.975635i | \(0.570410\pi\) | |||||||
\(318\) | 0.0836053 | − | 0.144809i | 0.00468835 | − | 0.00812046i | ||||
\(319\) | 3.72016 | − | 6.44350i | 0.208289 | − | 0.360767i | ||||
\(320\) | −13.9522 | − | 24.1660i | −0.779954 | − | 1.35092i | ||||
\(321\) | −2.85206 | −0.159186 | ||||||||
\(322\) | 0.897571 | + | 0.0766031i | 0.0500197 | + | 0.00426892i | ||||
\(323\) | −4.07844 | −0.226930 | ||||||||
\(324\) | 8.23642 | + | 14.2659i | 0.457579 | + | 0.792550i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.232087 | − | 0.401986i | 0.0128541 | − | 0.0222639i | ||||
\(327\) | 1.61670 | + | 2.80020i | 0.0894037 | + | 0.154852i | ||||
\(328\) | −6.29079 | −0.347351 | ||||||||
\(329\) | 5.36397 | − | 7.69534i | 0.295725 | − | 0.424258i | ||||
\(330\) | −0.900743 | −0.0495843 | ||||||||
\(331\) | −17.0466 | − | 29.5256i | −0.936967 | − | 1.62287i | −0.771089 | − | 0.636728i | \(-0.780288\pi\) |
−0.165878 | − | 0.986146i | \(-0.553046\pi\) | |||||||
\(332\) | 7.00964 | − | 12.1411i | 0.384704 | − | 0.666327i | ||||
\(333\) | −10.4750 | + | 18.1433i | −0.574028 | + | 0.994246i | ||||
\(334\) | 1.18161 | + | 2.04660i | 0.0646546 | + | 0.111985i | ||||
\(335\) | −49.8062 | −2.72120 | ||||||||
\(336\) | 1.10063 | + | 2.34725i | 0.0600440 | + | 0.128053i | ||||
\(337\) | 14.7532 | 0.803657 | 0.401829 | − | 0.915715i | \(-0.368375\pi\) | ||||
0.401829 | + | 0.915715i | \(0.368375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.214468 | + | 0.371470i | −0.0116483 | + | 0.0201755i | ||||
\(340\) | 8.79994 | − | 15.2419i | 0.477244 | − | 0.826610i | ||||
\(341\) | −12.6294 | − | 21.8747i | −0.683918 | − | 1.18458i | ||||
\(342\) | −1.02571 | −0.0554639 | ||||||||
\(343\) | 17.9194 | + | 4.67910i | 0.967558 | + | 0.252648i | ||||
\(344\) | −5.28141 | −0.284754 | ||||||||
\(345\) | −0.888918 | − | 1.53965i | −0.0478577 | − | 0.0828920i | ||||
\(346\) | 1.89881 | − | 3.28884i | 0.102081 | − | 0.176809i | ||||
\(347\) | −14.9733 | + | 25.9345i | −0.803809 | + | 1.39224i | 0.113284 | + | 0.993563i | \(0.463863\pi\) |
−0.917092 | + | 0.398675i | \(0.869470\pi\) | |||||||
\(348\) | −0.420727 | − | 0.728720i | −0.0225533 | − | 0.0390635i | ||||
\(349\) | 13.4793 | 0.721532 | 0.360766 | − | 0.932656i | \(-0.382515\pi\) | ||||
0.360766 | + | 0.932656i | \(0.382515\pi\) | |||||||
\(350\) | −2.29981 | − | 4.90468i | −0.122930 | − | 0.262166i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.15572 | + | 8.92997i | 0.274801 | + | 0.475969i | ||||
\(353\) | 0.0817659 | − | 0.141623i | 0.00435196 | − | 0.00753781i | −0.863841 | − | 0.503764i | \(-0.831948\pi\) |
0.868193 | + | 0.496226i | \(0.165281\pi\) | |||||||
\(354\) | −0.114525 | + | 0.198364i | −0.00608695 | + | 0.0105429i | ||||
\(355\) | −18.7752 | − | 32.5195i | −0.996482 | − | 1.72596i | ||||
\(356\) | −22.1000 | −1.17130 | ||||||||
\(357\) | −0.896686 | + | 1.28642i | −0.0474577 | + | 0.0680845i | ||||
\(358\) | 2.86527 | 0.151434 | ||||||||
\(359\) | 4.46065 | + | 7.72607i | 0.235424 | + | 0.407766i | 0.959396 | − | 0.282063i | \(-0.0910188\pi\) |
−0.723972 | + | 0.689830i | \(0.757685\pi\) | |||||||
\(360\) | 4.46948 | − | 7.74136i | 0.235562 | − | 0.408006i | ||||
\(361\) | 7.90209 | − | 13.6868i | 0.415900 | − | 0.720359i | ||||
\(362\) | 0.924111 | + | 1.60061i | 0.0485702 | + | 0.0841261i | ||||
\(363\) | −2.41772 | −0.126898 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.24726 | 0.222312 | ||||||||
\(366\) | 0.191745 | + | 0.332112i | 0.0100227 | + | 0.0173598i | ||||
\(367\) | −18.3276 | + | 31.7443i | −0.956693 | + | 1.65704i | −0.226248 | + | 0.974070i | \(0.572646\pi\) |
−0.730445 | + | 0.682971i | \(0.760687\pi\) | |||||||
\(368\) | −3.28185 | + | 5.68432i | −0.171078 | + | 0.296316i | ||||
\(369\) | 11.8997 | + | 20.6110i | 0.619476 | + | 1.07296i | ||||
\(370\) | 5.49679 | 0.285765 | ||||||||
\(371\) | 8.67208 | + | 0.740117i | 0.450232 | + | 0.0384250i | ||||
\(372\) | −2.85660 | −0.148108 | ||||||||
\(373\) | −13.5637 | − | 23.4930i | −0.702302 | − | 1.21642i | −0.967656 | − | 0.252271i | \(-0.918822\pi\) |
0.265355 | − | 0.964151i | \(-0.414511\pi\) | |||||||
\(374\) | −1.00574 | + | 1.74199i | −0.0520054 | + | 0.0900761i | ||||
\(375\) | −2.79139 | + | 4.83483i | −0.144147 | + | 0.249670i | ||||
\(376\) | −1.37409 | − | 2.38000i | −0.0708634 | − | 0.122739i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.456215 | + | 0.654502i | −0.0234652 | + | 0.0336640i | ||||
\(379\) | 15.8943 | 0.816434 | 0.408217 | − | 0.912885i | \(-0.366151\pi\) | ||||
0.408217 | + | 0.912885i | \(0.366151\pi\) | |||||||
\(380\) | −6.89552 | − | 11.9434i | −0.353733 | − | 0.612683i | ||||
\(381\) | −0.583611 | + | 1.01084i | −0.0298993 | + | 0.0517871i | ||||
\(382\) | −1.22811 | + | 2.12715i | −0.0628355 | + | 0.108834i | ||||
\(383\) | 0.575394 | + | 0.996611i | 0.0294013 | + | 0.0509245i | 0.880352 | − | 0.474322i | \(-0.157307\pi\) |
−0.850950 | + | 0.525246i | \(0.823973\pi\) | |||||||
\(384\) | 1.54959 | 0.0790774 | ||||||||
\(385\) | −19.9049 | − | 42.4502i | −1.01445 | − | 2.16346i | ||||
\(386\) | 1.83302 | 0.0932985 | ||||||||
\(387\) | 9.99038 | + | 17.3038i | 0.507839 | + | 0.879604i | ||||
\(388\) | 8.64484 | − | 14.9733i | 0.438875 | − | 0.760154i | ||||
\(389\) | 7.15651 | − | 12.3954i | 0.362850 | − | 0.628474i | −0.625579 | − | 0.780161i | \(-0.715137\pi\) |
0.988429 | + | 0.151687i | \(0.0484705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.97013 | −0.200778 | ||||||||
\(392\) | 3.47001 | − | 4.17132i | 0.175262 | − | 0.210684i | ||||
\(393\) | 3.28807 | 0.165861 | ||||||||
\(394\) | −0.745721 | − | 1.29163i | −0.0375689 | − | 0.0650712i | ||||
\(395\) | 1.55668 | − | 2.69625i | 0.0783251 | − | 0.135663i | ||||
\(396\) | 12.9618 | − | 22.4504i | 0.651353 | − | 1.12818i | ||||
\(397\) | −12.9588 | − | 22.4453i | −0.650383 | − | 1.12650i | −0.983030 | − | 0.183445i | \(-0.941275\pi\) |
0.332647 | − | 0.943051i | \(-0.392058\pi\) | |||||||
\(398\) | 2.64701 | 0.132682 | ||||||||
\(399\) | 0.521656 | + | 1.11251i | 0.0261154 | + | 0.0556950i | ||||
\(400\) | 39.4703 | 1.97351 | ||||||||
\(401\) | −2.14816 | − | 3.72072i | −0.107274 | − | 0.185804i | 0.807391 | − | 0.590017i | \(-0.200879\pi\) |
−0.914665 | + | 0.404213i | \(0.867545\pi\) | |||||||
\(402\) | 0.321882 | − | 0.557517i | 0.0160540 | − | 0.0278064i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0431 | − | 24.3233i | −0.698669 | − | 1.21013i | ||||
\(405\) | −33.0219 | −1.64087 | ||||||||
\(406\) | −0.488748 | + | 0.701175i | −0.0242562 | + | 0.0347987i | ||||
\(407\) | 32.1931 | 1.59575 | ||||||||
\(408\) | 0.229705 | + | 0.397861i | 0.0113721 | + | 0.0196970i | ||||
\(409\) | −12.3536 | + | 21.3970i | −0.610844 | + | 1.05801i | 0.380255 | + | 0.924882i | \(0.375836\pi\) |
−0.991098 | + | 0.133131i | \(0.957497\pi\) | |||||||
\(410\) | 3.12221 | − | 5.40782i | 0.154195 | − | 0.267073i | ||||
\(411\) | 1.20625 | + | 2.08929i | 0.0595000 | + | 0.103057i | ||||
\(412\) | 14.6975 | 0.724093 | ||||||||
\(413\) | −11.8793 | − | 1.01384i | −0.584542 | − | 0.0498876i | ||||
\(414\) | −0.998471 | −0.0490722 | ||||||||
\(415\) | 14.0517 | + | 24.3383i | 0.689771 | + | 1.19472i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.519577 | + | 0.899934i | −0.0254438 | + | 0.0440699i | ||||
\(418\) | 0.788083 | + | 1.36500i | 0.0385464 | + | 0.0667643i | ||||
\(419\) | −24.9293 | −1.21787 | −0.608937 | − | 0.793218i | \(-0.708404\pi\) | ||||
−0.608937 | + | 0.793218i | \(0.708404\pi\) | |||||||
\(420\) | −5.28323 | − | 0.450896i | −0.257795 | − | 0.0220015i | ||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 1.54563 | + | 2.67712i | 0.0752402 | + | 0.130320i | ||||
\(423\) | −5.19850 | + | 9.00407i | −0.252760 | + | 0.437793i | ||||
\(424\) | 1.27496 | − | 2.20830i | 0.0619177 | − | 0.107245i | ||||
\(425\) | 11.9371 | + | 20.6756i | 0.579032 | + | 1.00291i | ||||
\(426\) | 0.485352 | 0.0235154 | ||||||||
\(427\) | −11.4145 | + | 16.3757i | −0.552388 | + | 0.792475i | ||||
\(428\) | −21.5365 | −1.04101 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.62124 | − | 4.54011i | 0.126407 | − | 0.218944i | ||||
\(431\) | −2.84426 | + | 4.92639i | −0.137003 | + | 0.237296i | −0.926361 | − | 0.376637i | \(-0.877080\pi\) |
0.789358 | + | 0.613933i | \(0.210414\pi\) | |||||||
\(432\) | −2.90653 | − | 5.03425i | −0.139840 | − | 0.242211i | ||||
\(433\) | 12.2598 | 0.589169 | 0.294584 | − | 0.955625i | \(-0.404819\pi\) | ||||
0.294584 | + | 0.955625i | \(0.404819\pi\) | |||||||
\(434\) | 1.23186 | + | 2.62712i | 0.0591311 | + | 0.126106i | ||||
\(435\) | 1.68680 | 0.0808758 | ||||||||
\(436\) | 12.2080 | + | 21.1450i | 0.584659 | + | 1.01266i | ||||
\(437\) | −1.55547 | + | 2.69416i | −0.0744084 | + | 0.128879i | ||||
\(438\) | −0.0274487 | + | 0.0475426i | −0.00131155 | + | 0.00227167i | ||||
\(439\) | −2.51158 | − | 4.35019i | −0.119871 | − | 0.207623i | 0.799845 | − | 0.600206i | \(-0.204915\pi\) |
−0.919717 | + | 0.392583i | \(0.871582\pi\) | |||||||
\(440\) | −13.7361 | −0.654845 | ||||||||
\(441\) | −20.2307 | − | 3.47851i | −0.963367 | − | 0.165643i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.289401 | − | 0.501258i | −0.0137499 | − | 0.0238155i | 0.859069 | − | 0.511860i | \(-0.171044\pi\) |
−0.872818 | + | 0.488045i | \(0.837710\pi\) | |||||||
\(444\) | 1.82042 | − | 3.15307i | 0.0863935 | − | 0.149638i | ||||
\(445\) | 22.1511 | − | 38.3668i | 1.05006 | − | 1.81876i | ||||
\(446\) | 2.19856 | + | 3.80801i | 0.104105 | + | 0.180315i | ||||
\(447\) | −3.93966 | −0.186339 | ||||||||
\(448\) | 7.97036 | + | 16.9980i | 0.376564 | + | 0.803078i | ||||
\(449\) | 7.36359 | 0.347509 | 0.173755 | − | 0.984789i | \(-0.444410\pi\) | ||||
0.173755 | + | 0.984789i | \(0.444410\pi\) | |||||||
\(450\) | 3.00212 | + | 5.19982i | 0.141521 | + | 0.245122i | ||||
\(451\) | 18.2859 | − | 31.6720i | 0.861048 | − | 1.49138i | ||||
\(452\) | −1.61950 | + | 2.80505i | −0.0761748 | + | 0.131939i | ||||
\(453\) | −0.667862 | − | 1.15677i | −0.0313789 | − | 0.0543499i | ||||
\(454\) | 1.80052 | 0.0845028 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.359988 | 0.0168580 | ||||||||
\(457\) | 3.95912 | + | 6.85739i | 0.185200 | + | 0.320775i | 0.943644 | − | 0.330963i | \(-0.107373\pi\) |
−0.758444 | + | 0.651738i | \(0.774040\pi\) | |||||||
\(458\) | 1.49601 | − | 2.59117i | 0.0699040 | − | 0.121077i | ||||
\(459\) | 1.75805 | − | 3.04503i | 0.0820588 | − | 0.142130i | ||||
\(460\) | −6.71241 | − | 11.6262i | −0.312968 | − | 0.542076i | ||||
\(461\) | 9.53600 | 0.444136 | 0.222068 | − | 0.975031i | \(-0.428719\pi\) | ||||
0.222068 | + | 0.975031i | \(0.428719\pi\) | |||||||
\(462\) | 0.603816 | + | 0.0515325i | 0.0280920 | + | 0.00239751i | ||||
\(463\) | −2.16049 | −0.100406 | −0.0502032 | − | 0.998739i | \(-0.515987\pi\) | ||||
−0.0502032 | + | 0.998739i | \(0.515987\pi\) | |||||||
\(464\) | −3.11379 | − | 5.39325i | −0.144554 | − | 0.250375i | ||||
\(465\) | 2.86321 | − | 4.95923i | 0.132778 | − | 0.229979i | ||||
\(466\) | 0.788083 | − | 1.36500i | 0.0365072 | − | 0.0632324i | ||||
\(467\) | 4.05950 | + | 7.03126i | 0.187851 | + | 0.325368i | 0.944534 | − | 0.328415i | \(-0.106514\pi\) |
−0.756682 | + | 0.653783i | \(0.773181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.3877 | + | 2.84947i | 1.54170 | + | 0.131576i | ||||
\(470\) | 2.72792 | 0.125830 | ||||||||
\(471\) | −1.39391 | − | 2.41433i | −0.0642281 | − | 0.111246i | ||||
\(472\) | −1.74649 | + | 3.02500i | −0.0803885 | + | 0.139237i | ||||
\(473\) | 15.3518 | − | 26.5901i | 0.705878 | − | 1.22262i | ||||
\(474\) | 0.0201207 | + | 0.0348501i | 0.000924174 | + | 0.00160072i | ||||
\(475\) | 18.7074 | 0.858357 | ||||||||
\(476\) | −6.77107 | + | 9.71402i | −0.310352 | + | 0.445241i | ||||
\(477\) | −9.64694 | −0.441703 | ||||||||
\(478\) | 2.12540 | + | 3.68129i | 0.0972133 | + | 0.168378i | ||||
\(479\) | 7.27663 | − | 12.6035i | 0.332478 | − | 0.575868i | −0.650519 | − | 0.759490i | \(-0.725449\pi\) |
0.982997 | + | 0.183621i | \(0.0587820\pi\) | |||||||
\(480\) | −1.16886 | + | 2.02452i | −0.0533508 | + | 0.0924063i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.01056 | 0.182676 | ||||||||
\(483\) | 0.507803 | + | 1.08297i | 0.0231058 | + | 0.0492766i | ||||
\(484\) | −18.2567 | −0.829852 | ||||||||
\(485\) | 17.3297 | + | 30.0158i | 0.786899 | + | 1.36295i | ||||
\(486\) | 0.665728 | − | 1.15307i | 0.0301980 | − | 0.0523045i | ||||
\(487\) | −16.6295 | + | 28.8031i | −0.753554 | + | 1.30519i | 0.192536 | + | 0.981290i | \(0.438329\pi\) |
−0.946090 | + | 0.323904i | \(0.895005\pi\) | |||||||
\(488\) | 2.92407 | + | 5.06464i | 0.132366 | + | 0.229265i | ||||
\(489\) | 0.616320 | 0.0278710 | ||||||||
\(490\) | 1.86362 | + | 5.05324i | 0.0841899 | + | 0.228282i | ||||
\(491\) | −22.5563 | −1.01795 | −0.508977 | − | 0.860780i | \(-0.669976\pi\) | ||||
−0.508977 | + | 0.860780i | \(0.669976\pi\) | |||||||
\(492\) | −2.06802 | − | 3.58191i | −0.0932335 | − | 0.161485i | ||||
\(493\) | 1.88342 | − | 3.26218i | 0.0848249 | − | 0.146921i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 25.9835 | + | 45.0047i | 1.16787 | + | 2.02281i | ||||
\(496\) | −21.1417 | −0.949290 | ||||||||
\(497\) | 10.7255 | + | 22.8737i | 0.481104 | + | 1.02603i | ||||
\(498\) | −0.363248 | −0.0162775 | ||||||||
\(499\) | −5.69271 | − | 9.86007i | −0.254841 | − | 0.441397i | 0.710011 | − | 0.704190i | \(-0.248690\pi\) |
−0.964852 | + | 0.262793i | \(0.915356\pi\) | |||||||
\(500\) | −21.0784 | + | 36.5089i | −0.942655 | + | 1.63273i | ||||
\(501\) | −1.56891 | + | 2.71743i | −0.0700938 | + | 0.121406i | ||||
\(502\) | −0.255205 | − | 0.442028i | −0.0113904 | − | 0.0197287i | ||||
\(503\) | −8.81825 | −0.393186 | −0.196593 | − | 0.980485i | \(-0.562988\pi\) | ||||
−0.196593 | + | 0.980485i | \(0.562988\pi\) | |||||||
\(504\) | −3.43902 | + | 4.93374i | −0.153186 | + | 0.219766i | ||||
\(505\) | 56.3022 | 2.50541 | ||||||||
\(506\) | 0.767156 | + | 1.32875i | 0.0341042 | + | 0.0590702i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.40697 | + | 7.63310i | −0.195528 | + | 0.338664i | ||||
\(509\) | 9.64188 | + | 16.7002i | 0.427369 | + | 0.740225i | 0.996638 | − | 0.0819263i | \(-0.0261072\pi\) |
−0.569269 | + | 0.822151i | \(0.692774\pi\) | |||||||
\(510\) | −0.456023 | −0.0201930 | ||||||||
\(511\) | −2.84716 | − | 0.242991i | −0.125951 | − | 0.0107493i | ||||
\(512\) | 14.4780 | 0.639844 | ||||||||
\(513\) | −1.37759 | − | 2.38605i | −0.0608219 | − | 0.105347i | ||||
\(514\) | 0.880136 | − | 1.52444i | 0.0388211 | − | 0.0672402i | ||||
\(515\) | −14.7315 | + | 25.5156i | −0.649146 | + | 1.12435i | ||||
\(516\) | −1.73620 | − | 3.00718i | −0.0764318 | − | 0.132384i | ||||
\(517\) | 15.9767 | 0.702653 | ||||||||
\(518\) | −3.68479 | − | 0.314478i | −0.161900 | − | 0.0138174i | ||||
\(519\) | 5.04241 | 0.221337 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5584 | + | 21.7518i | −0.550193 | + | 0.952963i | 0.448067 | + | 0.894000i | \(0.352113\pi\) |
−0.998260 | + | 0.0589629i | \(0.981221\pi\) | |||||||
\(522\) | 0.473671 | − | 0.820422i | 0.0207320 | − | 0.0359089i | ||||
\(523\) | 14.9824 | + | 25.9503i | 0.655134 | + | 1.13473i | 0.981860 | + | 0.189606i | \(0.0607212\pi\) |
−0.326726 | + | 0.945119i | \(0.605946\pi\) | |||||||
\(524\) | 24.8289 | 1.08466 | ||||||||
\(525\) | 4.11303 | − | 5.90069i | 0.179507 | − | 0.257527i | ||||
\(526\) | 0.280556 | 0.0122328 | ||||||||
\(527\) | −6.39391 | − | 11.0746i | −0.278523 | − | 0.482416i | ||||
\(528\) | −2.20777 | + | 3.82397i | −0.0960808 | + | 0.166417i | ||||
\(529\) | 9.98583 | − | 17.2960i | 0.434167 | − | 0.751999i | ||||
\(530\) | 1.26556 | + | 2.19202i | 0.0549726 | + | 0.0952153i | ||||
\(531\) | 13.2147 | 0.573469 | ||||||||
\(532\) | 3.93913 | + | 8.40078i | 0.170783 | + | 0.364220i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.286311 | + | 0.495906i | 0.0123899 | + | 0.0214599i | ||||
\(535\) | 21.5863 | − | 37.3886i | 0.933257 | − | 1.61645i | ||||
\(536\) | 4.90864 | − | 8.50201i | 0.212021 | − | 0.367231i | ||||
\(537\) | 1.90222 | + | 3.29474i | 0.0820869 | + | 0.142179i | ||||
\(538\) | −1.59818 | −0.0689026 | ||||||||
\(539\) | 10.9147 | + | 29.5954i | 0.470130 | + | 1.27476i | ||||
\(540\) | 11.8895 | 0.511644 | ||||||||
\(541\) | 2.54987 | + | 4.41650i | 0.109627 | + | 0.189880i | 0.915619 | − | 0.402046i | \(-0.131701\pi\) |
−0.805992 | + | 0.591926i | \(0.798368\pi\) | |||||||
\(542\) | −0.0207706 | + | 0.0359757i | −0.000892173 | + | 0.00154529i | ||||
\(543\) | −1.22702 | + | 2.12525i | −0.0526563 | + | 0.0912034i | ||||
\(544\) | 2.61021 | + | 4.52101i | 0.111912 | + | 0.193837i | ||||
\(545\) | −48.9451 | −2.09658 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.92025 | 0.124861 | 0.0624305 | − | 0.998049i | \(-0.480115\pi\) | ||||
0.0624305 | + | 0.998049i | \(0.480115\pi\) | |||||||
\(548\) | 9.10867 | + | 15.7767i | 0.389103 | + | 0.673946i | ||||
\(549\) | 11.0624 | − | 19.1607i | 0.472132 | − | 0.817757i | ||||
\(550\) | 4.61323 | − | 7.99035i | 0.196709 | − | 0.340710i | ||||
\(551\) | −1.47582 | − | 2.55620i | −0.0628722 | − | 0.108898i | ||||
\(552\) | 0.350428 | 0.0149152 | ||||||||
\(553\) | −1.19778 | + | 1.71838i | −0.0509348 | + | 0.0730728i | ||||
\(554\) | 4.49519 | 0.190982 | ||||||||
\(555\) | 3.64927 | + | 6.32071i | 0.154903 | + | 0.268299i | ||||
\(556\) | −3.92344 | + | 6.79559i | −0.166391 | + | 0.288197i | ||||
\(557\) | 12.9937 | − | 22.5058i | 0.550561 | − | 0.953600i | −0.447673 | − | 0.894197i | \(-0.647747\pi\) |
0.998234 | − | 0.0594024i | \(-0.0189195\pi\) | |||||||
\(558\) | −1.60804 | − | 2.78521i | −0.0680738 | − | 0.117907i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −39.1011 | − | 3.33708i | −1.65232 | − | 0.141017i | ||||
\(561\) | −2.67079 | −0.112761 | ||||||||
\(562\) | −0.0337730 | − | 0.0584965i | −0.00142463 | − | 0.00246753i | ||||
\(563\) | −1.82534 | + | 3.16159i | −0.0769291 | + | 0.133245i | −0.901924 | − | 0.431896i | \(-0.857845\pi\) |
0.824994 | + | 0.565141i | \(0.191178\pi\) | |||||||
\(564\) | 0.903431 | − | 1.56479i | 0.0380413 | − | 0.0658895i | ||||
\(565\) | −3.24649 | − | 5.62308i | −0.136581 | − | 0.236565i | ||||
\(566\) | −5.66845 | −0.238263 | ||||||||
\(567\) | 22.1363 | + | 1.88922i | 0.929637 | + | 0.0793397i | ||||
\(568\) | 7.40152 | 0.310561 | ||||||||
\(569\) | 12.6766 | + | 21.9566i | 0.531432 | + | 0.920468i | 0.999327 | + | 0.0366835i | \(0.0116793\pi\) |
−0.467895 | + | 0.883784i | \(0.654987\pi\) | |||||||
\(570\) | −0.178667 | + | 0.309460i | −0.00748353 | + | 0.0129619i | ||||
\(571\) | −13.8626 | + | 24.0108i | −0.580133 | + | 1.00482i | 0.415330 | + | 0.909671i | \(0.363666\pi\) |
−0.995463 | + | 0.0951493i | \(0.969667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.26132 | −0.136244 | ||||||||
\(574\) | −2.40237 | + | 3.44652i | −0.100273 | + | 0.143855i | ||||
\(575\) | 18.2107 | 0.759438 | ||||||||
\(576\) | −10.4043 | − | 18.0208i | −0.433513 | − | 0.750867i | ||||
\(577\) | 19.7877 | − | 34.2733i | 0.823773 | − | 1.42682i | −0.0790809 | − | 0.996868i | \(-0.525199\pi\) |
0.902854 | − | 0.429948i | \(-0.141468\pi\) | |||||||
\(578\) | 1.15390 | − | 1.99861i | 0.0479959 | − | 0.0831313i | ||||
\(579\) | 1.21693 | + | 2.10778i | 0.0505737 | + | 0.0875963i | ||||
\(580\) | 12.7374 | 0.528891 | ||||||||
\(581\) | −8.02717 | − | 17.1191i | −0.333023 | − | 0.710221i | ||||
\(582\) | −0.447985 | −0.0185696 | ||||||||
\(583\) | 7.41204 | + | 12.8380i | 0.306975 | + | 0.531697i | ||||
\(584\) | −0.418588 | + | 0.725015i | −0.0173213 | + | 0.0300013i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.08576 | + | 5.34470i | 0.127472 | + | 0.220787i | ||||
\(587\) | 8.24177 | 0.340174 | 0.170087 | − | 0.985429i | \(-0.445595\pi\) | ||||
0.170087 | + | 0.985429i | \(0.445595\pi\) | |||||||
\(588\) | 3.51583 | + | 0.604519i | 0.144990 | + | 0.0249299i | ||||
\(589\) | −10.0204 | −0.412882 | ||||||||
\(590\) | −1.73361 | − | 3.00270i | −0.0713716 | − | 0.123619i | ||||
\(591\) | 0.990153 | − | 1.71500i | 0.0407295 | − | 0.0705455i | ||||
\(592\) | 13.4729 | − | 23.3358i | 0.553734 | − | 0.959095i | ||||
\(593\) | −5.96149 | − | 10.3256i | −0.244809 | − | 0.424021i | 0.717269 | − | 0.696796i | \(-0.245392\pi\) |
−0.962078 | + | 0.272775i | \(0.912059\pi\) | |||||||
\(594\) | −1.35884 | −0.0557540 | ||||||||
\(595\) | −10.0774 | − | 21.4914i | −0.413131 | − | 0.881063i | ||||
\(596\) | −29.7492 | −1.21857 | ||||||||
\(597\) | 1.75732 | + | 3.04377i | 0.0719224 | + | 0.124573i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8079 | − | 30.8442i | 0.727611 | − | 1.26026i | −0.230279 | − | 0.973125i | \(-0.573964\pi\) |
0.957890 | − | 0.287135i | \(-0.0927027\pi\) | |||||||
\(600\) | −1.05364 | − | 1.82495i | −0.0430146 | − | 0.0745034i | ||||
\(601\) | 38.9252 | 1.58779 | 0.793896 | − | 0.608054i | \(-0.208050\pi\) | ||||
0.793896 | + | 0.608054i | \(0.208050\pi\) | |||||||
\(602\) | −2.01690 | + | 2.89351i | −0.0822026 | + | 0.117931i | ||||
\(603\) | −37.1410 | −1.51250 | ||||||||
\(604\) | −5.04317 | − | 8.73503i | −0.205204 | − | 0.355423i | ||||
\(605\) | 18.2990 | − | 31.6947i | 0.743959 | − | 1.28857i | ||||
\(606\) | −0.363864 | + | 0.630231i | −0.0147810 | + | 0.0256014i | ||||
\(607\) | 6.84828 | + | 11.8616i | 0.277963 | + | 0.481446i | 0.970878 | − | 0.239573i | \(-0.0770074\pi\) |
−0.692915 | + | 0.721019i | \(0.743674\pi\) | |||||||
\(608\) | 4.09065 | 0.165898 | ||||||||
\(609\) | −1.13075 | − | 0.0965037i | −0.0458203 | − | 0.00391053i | ||||
\(610\) | −5.80502 | −0.235039 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.56220 | − | 11.3661i | 0.265261 | − | 0.459446i | ||||
\(613\) | 1.58056 | − | 2.73761i | 0.0638382 | − | 0.110571i | −0.832340 | − | 0.554266i | \(-0.812999\pi\) |
0.896178 | + | 0.443695i | \(0.146333\pi\) | |||||||
\(614\) | −1.77990 | − | 3.08287i | −0.0718308 | − | 0.124415i | ||||
\(615\) | 8.29120 | 0.334334 | ||||||||
\(616\) | 9.20806 | + | 0.785860i | 0.371003 | + | 0.0316632i | ||||
\(617\) | −20.9297 | −0.842597 | −0.421299 | − | 0.906922i | \(-0.638426\pi\) | ||||
−0.421299 | + | 0.906922i | \(0.638426\pi\) | |||||||
\(618\) | −0.190410 | − | 0.329800i | −0.00765941 | − | 0.0132665i | ||||
\(619\) | 15.4772 | − | 26.8073i | 0.622082 | − | 1.07748i | −0.367016 | − | 0.930215i | \(-0.619621\pi\) |
0.989097 | − | 0.147262i | \(-0.0470461\pi\) | |||||||
\(620\) | 21.6207 | − | 37.4482i | 0.868309 | − | 1.50396i | ||||
\(621\) | −1.34100 | − | 2.32269i | −0.0538127 | − | 0.0932063i | ||||
\(622\) | −0.0736887 | −0.00295465 | ||||||||
\(623\) | −17.0440 | + | 24.4520i | −0.682855 | + | 0.979648i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.0927 | − | 27.8734i | −0.643708 | − | 1.11494i | ||||
\(626\) | −1.07496 | + | 1.86189i | −0.0429642 | + | 0.0744162i | ||||
\(627\) | −1.04640 | + | 1.81242i | −0.0417892 | + | 0.0723810i | ||||
\(628\) | −10.5257 | − | 18.2311i | −0.420023 | − | 0.727501i | ||||
\(629\) | 16.2986 | 0.649866 | ||||||||
\(630\) | −2.53441 | − | 5.40500i | −0.100973 | − | 0.215340i | ||||
\(631\) | 15.1218 | 0.601988 | 0.300994 | − | 0.953626i | \(-0.402682\pi\) | ||||
0.300994 | + | 0.953626i | \(0.402682\pi\) | |||||||
\(632\) | 0.306836 | + | 0.531456i | 0.0122053 | + | 0.0211402i | ||||
\(633\) | −2.05226 | + | 3.55462i | −0.0815700 | + | 0.141283i | ||||
\(634\) | 2.56120 | − | 4.43613i | 0.101718 | − | 0.176181i | ||||
\(635\) | −8.83433 | − | 15.3015i | −0.350580 | − | 0.607222i | ||||
\(636\) | 1.67651 | 0.0664780 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.45574 | −0.0576335 | ||||||||
\(639\) | −14.0008 | − | 24.2501i | −0.553864 | − | 0.959320i | ||||
\(640\) | −11.7284 | + | 20.3141i | −0.463605 | + | 0.802987i | ||||
\(641\) | 23.6207 | − | 40.9123i | 0.932962 | − | 1.61594i | 0.154733 | − | 0.987956i | \(-0.450548\pi\) |
0.778229 | − | 0.627981i | \(-0.216118\pi\) | |||||||
\(642\) | 0.279011 | + | 0.483262i | 0.0110117 | + | 0.0190728i | ||||
\(643\) | −39.9249 | −1.57448 | −0.787241 | − | 0.616645i | \(-0.788491\pi\) | ||||
−0.787241 | + | 0.616645i | \(0.788491\pi\) | |||||||
\(644\) | 3.83453 | + | 8.17770i | 0.151102 | + | 0.322247i | ||||
\(645\) | 6.96085 | 0.274083 | ||||||||
\(646\) | 0.398986 | + | 0.691064i | 0.0156979 | + | 0.0271895i | ||||
\(647\) | 14.9139 | − | 25.8317i | 0.586327 | − | 1.01555i | −0.408382 | − | 0.912811i | \(-0.633907\pi\) |
0.994709 | − | 0.102736i | \(-0.0327598\pi\) | |||||||
\(648\) | 3.25446 | − | 5.63689i | 0.127847 | − | 0.221438i | ||||
\(649\) | −10.1533 | − | 17.5859i | −0.398550 | − | 0.690309i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.20308 | + | 3.16062i | −0.0863456 | + | 0.123875i | ||||
\(652\) | 4.65397 | 0.182263 | ||||||||
\(653\) | −12.5774 | − | 21.7848i | −0.492194 | − | 0.852504i | 0.507766 | − | 0.861495i | \(-0.330471\pi\) |
−0.999960 | + | 0.00899079i | \(0.997138\pi\) | |||||||
\(654\) | 0.316317 | − | 0.547878i | 0.0123690 | − | 0.0214237i | ||||
\(655\) | −24.8863 | + | 43.1044i | −0.972390 | + | 1.68423i | ||||
\(656\) | −15.3054 | − | 26.5097i | −0.597574 | − | 1.03503i | ||||
\(657\) | 3.16722 | 0.123565 | ||||||||
\(658\) | −1.82867 | − | 0.156068i | −0.0712890 | − | 0.00608415i | ||||
\(659\) | 17.3155 | 0.674517 | 0.337258 | − | 0.941412i | \(-0.390500\pi\) | ||||
0.337258 | + | 0.941412i | \(0.390500\pi\) | |||||||
\(660\) | −4.51558 | − | 7.82122i | −0.175769 | − | 0.304441i | ||||
\(661\) | −4.60037 | + | 7.96808i | −0.178934 | + | 0.309922i | −0.941516 | − | 0.336969i | \(-0.890598\pi\) |
0.762582 | + | 0.646892i | \(0.223931\pi\) | |||||||
\(662\) | −3.33528 | + | 5.77687i | −0.129629 | + | 0.224524i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.53945 | −0.214972 | ||||||||
\(665\) | −18.5325 | − | 1.58165i | −0.718659 | − | 0.0613338i | ||||
\(666\) | 4.09901 | 0.158833 | ||||||||
\(667\) | −1.43663 | − | 2.48832i | −0.0556266 | − | 0.0963482i | ||||
\(668\) | −11.8472 | + | 20.5199i | −0.458382 | + | 0.793940i | ||||
\(669\) | −2.91920 | + | 5.05620i | −0.112863 | + | 0.195484i | ||||
\(670\) | 4.87245 | + | 8.43933i | 0.188239 | + | 0.326040i | ||||
\(671\) | −33.9984 | −1.31249 | ||||||||
\(672\) | 0.899372 | − | 1.29027i | 0.0346940 | − | 0.0497733i | ||||
\(673\) | 17.3609 | 0.669212 | 0.334606 | − | 0.942358i | \(-0.391397\pi\) | ||||
0.334606 | + | 0.942358i | \(0.391397\pi\) | |||||||
\(674\) | −1.44328 | − | 2.49983i | −0.0555930 | − | 0.0962898i | ||||
\(675\) | −8.06403 | + | 13.9673i | −0.310385 | + | 0.537602i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.9913 | − | 43.2861i | −0.960492 | − | 1.66362i | −0.721267 | − | 0.692657i | \(-0.756440\pi\) |
−0.239225 | − | 0.970964i | \(-0.576893\pi\) | |||||||
\(678\) | 0.0839242 | 0.00322309 | ||||||||
\(679\) | −9.89974 | − | 21.1126i | −0.379917 | − | 0.810229i | ||||
\(680\) | −6.95425 | −0.266683 | ||||||||
\(681\) | 1.19535 | + | 2.07041i | 0.0458059 | + | 0.0793382i | ||||
\(682\) | −2.47101 | + | 4.27992i | −0.0946200 | + | 0.163887i | ||||
\(683\) | 16.8077 | − | 29.1117i | 0.643128 | − | 1.11393i | −0.341603 | − | 0.939844i | \(-0.610970\pi\) |
0.984731 | − | 0.174086i | \(-0.0556969\pi\) | |||||||
\(684\) | −5.14205 | − | 8.90630i | −0.196611 | − | 0.340541i | ||||
\(685\) | −36.5189 | −1.39532 | ||||||||
\(686\) | −0.960183 | − | 3.49408i | −0.0366599 | − | 0.133404i | ||||
\(687\) | 3.97274 | 0.151570 | ||||||||
\(688\) | −12.8496 | − | 22.2561i | −0.489885 | − | 0.848506i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.173922 | + | 0.301242i | −0.00662111 | + | 0.0114681i | ||||
\(691\) | −7.56545 | − | 13.1038i | −0.287803 | − | 0.498490i | 0.685482 | − | 0.728090i | \(-0.259592\pi\) |
−0.973285 | + | 0.229600i | \(0.926258\pi\) | |||||||
\(692\) | 38.0764 | 1.44745 | ||||||||
\(693\) | −14.8433 | − | 31.6555i | −0.563851 | − | 1.20249i | ||||
\(694\) | 5.85924 | 0.222414 | ||||||||
\(695\) | −7.86502 | − | 13.6226i | −0.298337 | − | 0.516735i | ||||
\(696\) | −0.166242 | + | 0.287940i | −0.00630139 | + | 0.0109143i | ||||
\(697\) | 9.25766 | − | 16.0347i | 0.350659 | − | 0.607359i | ||||
\(698\) | −1.31866 | − | 2.28398i | −0.0499119 | − | 0.0864500i | ||||
\(699\) | 2.09280 | 0.0791570 | ||||||||
\(700\) | 31.0583 | − | 44.5574i | 1.17390 | − | 1.68411i | ||||
\(701\) | 2.02467 | 0.0764705 | 0.0382353 | − | 0.999269i | \(-0.487826\pi\) | ||||
0.0382353 | + | 0.999269i | \(0.487826\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.38567 | − | 11.0603i | 0.240840 | − | 0.417147i | ||||
\(704\) | −15.9879 | + | 27.6919i | −0.602567 | + | 1.04368i | ||||
\(705\) | 1.81104 | + | 3.13681i | 0.0682077 | + | 0.118139i | ||||
\(706\) | −0.0319960 | −0.00120419 | ||||||||
\(707\) | −37.7423 | − | 3.22111i | −1.41945 | − | 0.121142i | ||||
\(708\) | −2.29654 | −0.0863093 | ||||||||
\(709\) | −15.2276 | − | 26.3751i | −0.571886 | − | 0.990536i | −0.996372 | − | 0.0851015i | \(-0.972879\pi\) |
0.424486 | − | 0.905434i | \(-0.360455\pi\) | |||||||
\(710\) | −3.67348 | + | 6.36265i | −0.137863 | + | 0.238786i | ||||
\(711\) | 1.16083 | − | 2.01062i | 0.0435346 | − | 0.0754041i | ||||
\(712\) | 4.36619 | + | 7.56246i | 0.163630 | + | 0.283415i | ||||
\(713\) | −9.75429 | −0.365301 | ||||||||
\(714\) | 0.305696 | + | 0.0260896i | 0.0114404 | + | 0.000976378i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.3641 | + | 24.8793i | 0.536811 | + | 0.929784i | ||||
\(717\) | −2.82206 | + | 4.88795i | −0.105392 | + | 0.182544i | ||||
\(718\) | 0.872754 | − | 1.51165i | 0.0325709 | − | 0.0564144i | ||||
\(719\) | 12.2123 | + | 21.1523i | 0.455442 | + | 0.788848i | 0.998713 | − | 0.0507089i | \(-0.0161481\pi\) |
−0.543272 | + | 0.839557i | \(0.682815\pi\) | |||||||
\(720\) | 43.4966 | 1.62102 | ||||||||
\(721\) | 11.3351 | − | 16.2617i | 0.422139 | − | 0.605616i | ||||
\(722\) | −3.09219 | −0.115079 | ||||||||
\(723\) | 2.66257 | + | 4.61170i | 0.0990220 | + | 0.171511i | ||||
\(724\) | −9.26547 | + | 16.0483i | −0.344348 | + | 0.596429i | ||||
\(725\) | −8.63908 | + | 14.9633i | −0.320848 | + | 0.555724i | ||||
\(726\) | 0.236521 | + | 0.409667i | 0.00877813 | + | 0.0152042i | ||||
\(727\) | −3.09307 | −0.114716 | −0.0573578 | − | 0.998354i | \(-0.518268\pi\) | ||||
−0.0573578 | + | 0.998354i | \(0.518268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.4236 | −0.867539 | ||||||||
\(730\) | −0.415501 | − | 0.719670i | −0.0153784 | − | 0.0266362i | ||||
\(731\) | 7.77223 | − | 13.4619i | 0.287466 | − | 0.497906i | ||||
\(732\) | −1.92250 | + | 3.32987i | −0.0710577 | + | 0.123076i | ||||
\(733\) | −4.20713 | − | 7.28697i | −0.155394 | − | 0.269150i | 0.777808 | − | 0.628501i | \(-0.216331\pi\) |
−0.933202 | + | 0.359351i | \(0.882998\pi\) | |||||||
\(734\) | 7.17182 | 0.264717 | ||||||||
\(735\) | −4.57344 | + | 5.49776i | −0.168694 | + | 0.202788i | ||||
\(736\) | 3.98203 | 0.146779 | ||||||||
\(737\) | 28.5365 | + | 49.4267i | 1.05116 | + | 1.82066i | ||||
\(738\) | 2.32826 | − | 4.03266i | 0.0857044 | − | 0.148444i | ||||
\(739\) | −3.61379 | + | 6.25927i | −0.132936 | + | 0.230251i | −0.924807 | − | 0.380437i | \(-0.875774\pi\) |
0.791871 | + | 0.610688i | \(0.209107\pi\) | |||||||
\(740\) | 27.5564 | + | 47.7291i | 1.01299 | + | 1.75456i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.722966 | − | 1.54183i | −0.0265409 | − | 0.0566024i | ||||
\(743\) | 53.9092 | 1.97774 | 0.988869 | − | 0.148791i | \(-0.0475383\pi\) | ||||
0.988869 | + | 0.148791i | \(0.0475383\pi\) | |||||||
\(744\) | 0.564366 | + | 0.977510i | 0.0206907 | + | 0.0358373i | ||||
\(745\) | 29.8180 | − | 51.6463i | 1.09245 | − | 1.89217i | ||||
\(746\) | −2.65382 | + | 4.59656i | −0.0971634 | + | 0.168292i | ||||
\(747\) | 10.4785 | + | 18.1493i | 0.383388 | + | 0.664047i | ||||
\(748\) | −20.1678 | −0.737406 | ||||||||
\(749\) | −16.6095 | + | 23.8285i | −0.606897 | + | 0.870676i | ||||
\(750\) | 1.09231 | 0.0398854 | ||||||||
\(751\) | −14.6221 | − | 25.3262i | −0.533568 | − | 0.924168i | −0.999231 | − | 0.0392053i | \(-0.987517\pi\) |
0.465663 | − | 0.884962i | \(-0.345816\pi\) | |||||||
\(752\) | 6.68628 | − | 11.5810i | 0.243824 | − | 0.422315i | ||||
\(753\) | 0.338856 | − | 0.586916i | 0.0123486 | − | 0.0213884i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.2193 | 0.735857 | ||||||||
\(756\) | −7.97018 | − | 0.680214i | −0.289873 | − | 0.0247391i | ||||
\(757\) | −22.0597 | −0.801773 | −0.400887 | − | 0.916128i | \(-0.631298\pi\) | ||||
−0.400887 | + | 0.916128i | \(0.631298\pi\) | |||||||
\(758\) | −1.55491 | − | 2.69318i | −0.0564768 | − | 0.0978206i | ||||
\(759\) | −1.01861 | + | 1.76429i | −0.0369733 | + | 0.0640397i | ||||
\(760\) | −2.72463 | + | 4.71920i | −0.0988328 | + | 0.171183i | ||||
\(761\) | 8.90805 | + | 15.4292i | 0.322917 | + | 0.559308i | 0.981089 | − | 0.193560i | \(-0.0620033\pi\) |
−0.658172 | + | 0.752868i | \(0.728670\pi\) | |||||||
\(762\) | 0.228374 | 0.00827313 | ||||||||
\(763\) | 32.8105 | + | 2.80020i | 1.18782 | + | 0.101374i | ||||
\(764\) | −24.6269 | −0.890971 | ||||||||
\(765\) | 13.1547 | + | 22.7847i | 0.475611 | + | 0.823782i | ||||
\(766\) | 0.112579 | − | 0.194993i | 0.00406766 | − | 0.00704539i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.69182 | + | 2.93033i | 0.0610485 | + | 0.105739i | ||||
\(769\) | 11.3069 | 0.407738 | 0.203869 | − | 0.978998i | \(-0.434648\pi\) | ||||
0.203869 | + | 0.978998i | \(0.434648\pi\) | |||||||
\(770\) | −5.24564 | + | 7.52559i | −0.189040 | + | 0.271203i | ||||
\(771\) | 2.33725 | 0.0841741 | ||||||||
\(772\) | 9.18927 | + | 15.9163i | 0.330729 | + | 0.572840i | ||||
\(773\) | −0.964104 | + | 1.66988i | −0.0346764 | + | 0.0600613i | −0.882843 | − | 0.469669i | \(-0.844373\pi\) |
0.848166 | + | 0.529730i | \(0.177707\pi\) | |||||||
\(774\) | 1.95468 | − | 3.38561i | 0.0702595 | − | 0.121693i | ||||
\(775\) | 29.3284 | + | 50.7982i | 1.05351 | + | 1.82472i | ||||
\(776\) | −6.83168 | −0.245243 | ||||||||
\(777\) | −2.08468 | − | 4.44588i | −0.0747875 | − | 0.159495i | ||||
\(778\) | −2.80043 | −0.100400 | ||||||||
\(779\) | −7.25418 | − | 12.5646i | −0.259908 | − | 0.450174i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.5145 | + | 37.2642i | −0.769849 | + | 1.33342i | ||||
\(782\) | 0.388391 | + | 0.672713i | 0.0138888 | + | 0.0240562i | ||||
\(783\) | 2.54467 | 0.0909392 | ||||||||
\(784\) | 26.0206 | + | 4.47404i | 0.929307 | + | 0.159787i | ||||
\(785\) | 42.2003 | 1.50619 | ||||||||
\(786\) | −0.321666 | − | 0.557141i | −0.0114734 | − | 0.0198726i | ||||
\(787\) | 2.76577 | − | 4.79046i | 0.0985892 | − | 0.170761i | −0.812512 | − | 0.582945i | \(-0.801900\pi\) |
0.911101 | + | 0.412183i | \(0.135234\pi\) | |||||||
\(788\) | 7.47686 | − | 12.9503i | 0.266352 | − | 0.461335i | ||||
\(789\) | 0.186258 | + | 0.322609i | 0.00663097 | + | 0.0114852i | ||||
\(790\) | −0.609148 | −0.0216725 | ||||||||
\(791\) | 1.85459 | + | 3.95518i | 0.0659415 | + | 0.140630i | ||||
\(792\) | −10.2432 | −0.363975 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −2.53547 | + | 4.39156i | −0.0899804 | + | 0.155851i | ||||
\(795\) | −1.68039 | + | 2.91052i | −0.0595973 | + | 0.103225i | ||||
\(796\) | 13.2699 | + | 22.9842i | 0.470340 | + | 0.814652i | ||||
\(797\) | −13.8038 | −0.488955 | −0.244477 | − | 0.969655i | \(-0.578616\pi\) | ||||
−0.244477 | + | 0.969655i | \(0.578616\pi\) | |||||||
\(798\) | 0.137474 | − | 0.197226i | 0.00486654 | − | 0.00698171i | ||||
\(799\) | 8.08857 | 0.286153 | ||||||||
\(800\) | −11.9728 | − | 20.7375i | −0.423303 | − | 0.733182i | ||||
\(801\) | 16.5183 | − | 28.6105i | 0.583644 | − | 1.01090i | ||||
\(802\) | −0.420300 | + | 0.727982i | −0.0148413 | + | 0.0257059i | ||||
\(803\) | −2.43347 | − | 4.21490i | −0.0858754 | − | 0.148741i | ||||
\(804\) | 6.45461 | 0.227637 | ||||||||
\(805\) | −18.0404 | − | 1.53965i | −0.635839 | − | 0.0542656i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.06102 | − | 1.83774i | −0.0373496 | − | 0.0646914i | ||||
\(808\) | −5.54885 | + | 9.61088i | −0.195208 | + | 0.338110i | ||||
\(809\) | −14.1498 | + | 24.5082i | −0.497480 | + | 0.861661i | −0.999996 | − | 0.00290700i | \(-0.999075\pi\) |
0.502515 | + | 0.864568i | \(0.332408\pi\) | |||||||
\(810\) | 3.23047 | + | 5.59533i | 0.113507 | + | 0.196600i | ||||
\(811\) | 12.2124 | 0.428837 | 0.214418 | − | 0.976742i | \(-0.431214\pi\) | ||||
0.214418 | + | 0.976742i | \(0.431214\pi\) | |||||||
\(812\) | −8.53854 | − | 0.728720i | −0.299644 | − | 0.0255731i | ||||
\(813\) | −0.0551575 | −0.00193446 | ||||||||
\(814\) | −3.14940 | − | 5.45491i | −0.110386 | − | 0.191195i | ||||
\(815\) | −4.66473 | + | 8.07955i | −0.163398 | + | 0.283014i | ||||
\(816\) | −1.11774 | + | 1.93597i | −0.0391286 | + | 0.0677727i | ||||
\(817\) | −6.09022 | − | 10.5486i | −0.213070 | − | 0.369048i | ||||
\(818\) | 4.83410 | 0.169020 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 62.6087 | 2.18639 | ||||||||
\(821\) | −20.7005 | − | 35.8544i | −0.722453 | − | 1.25133i | −0.960014 | − | 0.279953i | \(-0.909681\pi\) |
0.237560 | − | 0.971373i | \(-0.423652\pi\) | |||||||
\(822\) | 0.236011 | − | 0.408782i | 0.00823182 | − | 0.0142579i | ||||
\(823\) | −23.5876 | + | 40.8550i | −0.822213 | + | 1.42411i | 0.0818184 | + | 0.996647i | \(0.473927\pi\) |
−0.904031 | + | 0.427467i | \(0.859406\pi\) | |||||||
\(824\) | −2.90371 | − | 5.02938i | −0.101156 | − | 0.175207i | ||||
\(825\) | 12.2507 | 0.426515 | ||||||||
\(826\) | 0.990341 | + | 2.11205i | 0.0344584 | + | 0.0734876i | ||||
\(827\) | −21.1124 | −0.734150 | −0.367075 | − | 0.930191i | \(-0.619641\pi\) | ||||
−0.367075 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(828\) | −5.00551 | − | 8.66980i | −0.173953 | − | 0.301296i | ||||
\(829\) | 0.318376 | − | 0.551444i | 0.0110577 | − | 0.0191524i | −0.860444 | − | 0.509546i | \(-0.829813\pi\) |
0.871501 | + | 0.490393i | \(0.163147\pi\) | |||||||
\(830\) | 2.74930 | − | 4.76193i | 0.0954297 | − | 0.165289i | ||||
\(831\) | 2.98431 | + | 5.16898i | 0.103525 | + | 0.179310i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.52583 | + | 14.9834i | 0.191459 | + | 0.519143i | ||||
\(834\) | 0.203317 | 0.00704029 | ||||||||
\(835\) | −23.7492 | − | 41.1348i | −0.821874 | − | 1.42353i | ||||
\(836\) | −7.90160 | + | 13.6860i | −0.273282 | + | 0.473339i | ||||
\(837\) | 4.31938 | − | 7.48139i | 0.149300 | − | 0.258595i | ||||
\(838\) | 2.43878 | + | 4.22410i | 0.0842464 | + | 0.145919i | ||||
\(839\) | 26.9432 | 0.930183 | 0.465092 | − | 0.885263i | \(-0.346021\pi\) | ||||
0.465092 | + | 0.885263i | \(0.346021\pi\) | |||||||
\(840\) | 0.889489 | + | 1.89697i | 0.0306903 | + | 0.0654516i | ||||
\(841\) | −26.2739 | −0.905995 | ||||||||
\(842\) | −0.978281 | − | 1.69443i | −0.0337138 | − | 0.0583940i | ||||
\(843\) | 0.0448431 | − | 0.0776705i | 0.00154448 | − | 0.00267511i | ||||
\(844\) | −15.4971 | + | 26.8417i | −0.533431 | + | 0.923929i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.03424 | 0.0699386 | ||||||||
\(847\) | −14.0800 | + | 20.1997i | −0.483796 | + | 0.694071i | ||||
\(848\) | 12.4078 | 0.426087 | ||||||||
\(849\) | −3.76323 | − | 6.51810i | −0.129154 | − | 0.223701i | ||||
\(850\) | 2.33556 | − | 4.04531i | 0.0801090 | − | 0.138753i | ||||
\(851\) | 6.21610 | − | 10.7666i | 0.213085 | − | 0.369074i | ||||
\(852\) | 2.43316 | + | 4.21435i | 0.0833586 | + | 0.144381i | ||||
\(853\) | −6.74784 | −0.231042 | −0.115521 | − | 0.993305i | \(-0.536854\pi\) | ||||
−0.115521 | + | 0.993305i | \(0.536854\pi\) | |||||||
\(854\) | 3.89141 | + | 0.332112i | 0.133161 | + | 0.0113646i | ||||
\(855\) | 20.6158 | 0.705045 | ||||||||
\(856\) | 4.25486 | + | 7.36964i | 0.145428 | + | 0.251889i | ||||
\(857\) | 22.5134 | − | 38.9943i | 0.769043 | − | 1.33202i | −0.169040 | − | 0.985609i | \(-0.554067\pi\) |
0.938082 | − | 0.346412i | \(-0.112600\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3635 | + | 31.8065i | 0.626554 | + | 1.08522i | 0.988238 | + | 0.152923i | \(0.0488687\pi\) |
−0.361684 | + | 0.932301i | \(0.617798\pi\) | |||||||
\(860\) | 52.5629 | 1.79238 | ||||||||
\(861\) | −5.55803 | − | 0.474349i | −0.189417 | − | 0.0161658i | ||||
\(862\) | 1.11299 | 0.0379087 | ||||||||
\(863\) | −21.7137 | − | 37.6093i | −0.739144 | − | 1.28024i | −0.952881 | − | 0.303344i | \(-0.901897\pi\) |
0.213737 | − | 0.976891i | \(-0.431437\pi\) | |||||||
\(864\) | −1.76332 | + | 3.05415i | −0.0599892 | + | 0.103904i | ||||
\(865\) | −38.1644 | + | 66.1027i | −1.29763 | + | 2.24756i | ||||
\(866\) | −1.19935 | − | 2.07734i | −0.0407557 | − | 0.0705910i | ||||
\(867\) | 3.06425 | 0.104067 | ||||||||
\(868\) | −16.6360 | + | 23.8665i | −0.564661 | + | 0.810083i | ||||
\(869\) | −3.56761 | −0.121023 | ||||||||
\(870\) | −0.165016 | − | 0.285817i | −0.00559458 | − | 0.00969010i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.82377 | − | 8.35502i | 0.163354 | − | 0.282937i | ||||
\(873\) | 12.9229 | + | 22.3831i | 0.437373 | + | 0.757553i | ||||
\(874\) | 0.608676 | 0.0205888 | ||||||||
\(875\) | 24.1382 | + | 51.4782i | 0.816020 | + | 1.74028i | ||||
\(876\) | −0.550422 | −0.0185970 | ||||||||
\(877\) | 20.0040 | + | 34.6480i | 0.675488 | + | 1.16998i | 0.976326 | + | 0.216304i | \(0.0694004\pi\) |
−0.300838 | + | 0.953675i | \(0.597266\pi\) | |||||||
\(878\) | −0.491407 | + | 0.851142i | −0.0165842 | + | 0.0287247i | ||||
\(879\) | −4.09721 | + | 7.09658i | −0.138196 | + | 0.239362i | ||||
\(880\) | −33.4198 | − | 57.8847i | −1.12658 | − | 1.95129i | ||||
\(881\) | 35.4308 | 1.19370 | 0.596848 | − | 0.802355i | \(-0.296420\pi\) | ||||
0.596848 | + | 0.802355i | \(0.296420\pi\) | |||||||
\(882\) | 1.38972 | + | 3.76825i | 0.0467944 | + | 0.126884i | ||||
\(883\) | 22.6654 | 0.762751 | 0.381375 | − | 0.924420i | \(-0.375451\pi\) | ||||
0.381375 | + | 0.924420i | \(0.375451\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.30185 | − | 3.98692i | 0.0773759 | − | 0.134019i | ||||
\(886\) | −0.0566232 | + | 0.0980742i | −0.00190229 | + | 0.00329487i | ||||
\(887\) | −22.3440 | − | 38.7010i | −0.750240 | − | 1.29945i | −0.947706 | − | 0.319144i | \(-0.896605\pi\) |
0.197467 | − | 0.980310i | \(-0.436729\pi\) | |||||||
\(888\) | −1.43861 | −0.0482766 | ||||||||
\(889\) | 5.04670 | + | 10.7628i | 0.169261 | + | 0.360974i | ||||
\(890\) | −8.66800 | −0.290552 | ||||||||
\(891\) | 18.9199 | + | 32.7703i | 0.633841 | + | 1.09784i | ||||
\(892\) | −22.0435 | + | 38.1804i | −0.738071 | + | 1.27838i | ||||
\(893\) | 3.16905 | − | 5.48896i | 0.106048 | − | 0.183681i | ||||
\(894\) | 0.385409 | + | 0.667548i | 0.0128900 | + | 0.0223262i | ||||
\(895\) | −57.5892 | −1.92499 | ||||||||
\(896\) | 9.02434 | − | 12.9466i | 0.301482 | − | 0.432517i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.720366 | − | 1.24771i | −0.0240389 | − | 0.0416366i | ||||
\(899\) | 4.62740 | − | 8.01489i | 0.154332 | − | 0.267312i | ||||
\(900\) | −30.1003 | + | 52.1352i | −1.00334 | + | 1.73784i | ||||
\(901\) | 3.75252 | + | 6.49956i | 0.125015 | + | 0.216532i | ||||
\(902\) | −7.15549 | −0.238252 | ||||||||
\(903\) | −4.66622 | − | 0.398238i | −0.155282 | − | 0.0132525i | ||||
\(904\) | 1.27983 | 0.0425664 | ||||||||
\(905\) | −18.5738 | − | 32.1707i | −0.617413 | − | 1.06939i | ||||
\(906\) | −0.130671 | + | 0.226330i | −0.00434127 | + | 0.00751930i | ||||
\(907\) | −27.2374 | + | 47.1766i | −0.904403 | + | 1.56647i | −0.0826860 | + | 0.996576i | \(0.526350\pi\) |
−0.821717 | + | 0.569896i | \(0.806983\pi\) | |||||||
\(908\) | 9.02635 | + | 15.6341i | 0.299550 | + | 0.518836i | ||||
\(909\) | 41.9851 | 1.39256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.4793 | −0.910431 | −0.455215 | − | 0.890381i | \(-0.650438\pi\) | ||||
−0.455215 | + | 0.890381i | \(0.650438\pi\) | |||||||
\(912\) | 0.875843 | + | 1.51700i | 0.0290021 | + | 0.0502330i | ||||
\(913\) | 16.1019 | − | 27.8893i | 0.532895 | − | 0.923000i | ||||
\(914\) | 0.774626 | − | 1.34169i | 0.0256224 | − | 0.0443792i | ||||
\(915\) | −3.85390 | − | 6.67514i | −0.127406 | − | 0.220673i | ||||
\(916\) | 29.9990 | 0.991196 | ||||||||
\(917\) | 19.1487 | − | 27.4714i | 0.632345 | − | 0.907184i | ||||
\(918\) | −0.687947 | −0.0227056 | ||||||||
\(919\) | 24.1440 | + | 41.8186i | 0.796437 | + | 1.37947i | 0.921923 | + | 0.387374i | \(0.126618\pi\) |
−0.125486 | + | 0.992095i | \(0.540049\pi\) | |||||||
\(920\) | −2.65228 | + | 4.59388i | −0.0874431 | + | 0.151456i | ||||
\(921\) | 2.36331 | − | 4.09337i | 0.0778737 | − | 0.134881i | ||||
\(922\) | −0.932889 | − | 1.61581i | −0.0307231 | − | 0.0532139i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.57957 | + | 5.50132i | 0.0848617 | + | 0.180980i | ||||
\(925\) | −74.7601 | −2.45810 | ||||||||
\(926\) | 0.211356 | + | 0.366080i | 0.00694560 | + | 0.0120301i | ||||
\(927\) | −10.9854 | + | 19.0273i | −0.360808 | + | 0.624937i | ||||
\(928\) | −1.88906 | + | 3.27195i | −0.0620114 | + | 0.107407i | ||||
\(929\) | 21.6577 | + | 37.5122i | 0.710566 | + | 1.23074i | 0.964645 | + | 0.263553i | \(0.0848943\pi\) |
−0.254079 | + | 0.967183i | \(0.581772\pi\) | |||||||
\(930\) | −1.12041 | −0.0367397 | ||||||||
\(931\) | 12.3328 | + | 2.12053i | 0.404191 | + | 0.0694975i | ||||
\(932\) | 15.8032 | 0.517651 | ||||||||
\(933\) | −0.0489212 | − | 0.0847339i | −0.00160161 | − | 0.00277406i | ||||
\(934\) | 0.794266 | − | 1.37571i | 0.0259892 | − | 0.0450146i | ||||
\(935\) | 20.2144 | − | 35.0123i | 0.661081 | − | 1.14503i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.2211 | −1.21596 | −0.607980 | − | 0.793952i | \(-0.708020\pi\) | ||||
−0.607980 | + | 0.793952i | \(0.708020\pi\) | |||||||
\(938\) | −2.78344 | − | 5.93609i | −0.0908824 | − | 0.193820i | ||||
\(939\) | −2.85463 | −0.0931574 | ||||||||
\(940\) | 13.6756 | + | 23.6868i | 0.446048 | + | 0.772577i | ||||
\(941\) | 7.98754 | − | 13.8348i | 0.260386 | − | 0.451002i | −0.705958 | − | 0.708253i | \(-0.749483\pi\) |
0.966345 | + | 0.257251i | \(0.0828167\pi\) | |||||||
\(942\) | −0.272728 | + | 0.472378i | −0.00888595 | + | 0.0153909i | ||||
\(943\) | −7.06155 | − | 12.2310i | −0.229956 | − | 0.398295i | ||||
\(944\) | −16.9967 | −0.553194 | ||||||||
\(945\) | 9.16950 | − | 13.1549i | 0.298284 | − | 0.427929i | ||||
\(946\) | −6.00736 | −0.195316 | ||||||||
\(947\) | 13.8786 | + | 24.0384i | 0.450994 | + | 0.781144i | 0.998448 | − | 0.0556912i | \(-0.0177363\pi\) |
−0.547454 | + | 0.836836i | \(0.684403\pi\) | |||||||
\(948\) | −0.201737 | + | 0.349419i | −0.00655212 | + | 0.0113486i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.83011 | − | 3.16985i | −0.0593768 | − | 0.102844i | ||||
\(951\) | 6.80142 | 0.220551 | ||||||||
\(952\) | 4.66180 | + | 0.397861i | 0.151090 | + | 0.0128947i | ||||
\(953\) | 12.0303 | 0.389700 | 0.194850 | − | 0.980833i | \(-0.437578\pi\) | ||||
0.194850 | + | 0.980833i | \(0.437578\pi\) | |||||||
\(954\) | 0.943742 | + | 1.63461i | 0.0305548 | + | 0.0529224i | ||||
\(955\) | 24.6839 | − | 42.7537i | 0.798751 | − | 1.38348i | ||||
\(956\) | −21.3100 | + | 36.9099i | −0.689213 | + | 1.19375i | ||||
\(957\) | −0.966454 | − | 1.67395i | −0.0312410 | − | 0.0541110i | ||||
\(958\) | −2.84744 | −0.0919965 | ||||||||
\(959\) | 24.4805 | + | 2.08929i | 0.790518 | + | 0.0674666i | ||||
\(960\) | −7.24926 | −0.233969 | ||||||||
\(961\) | −0.209310 | − | 0.362536i | −0.00675194 | − | 0.0116947i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.0971 | − | 27.8810i | 0.518722 | − | 0.898453i | ||||
\(964\) | 20.1056 | + | 34.8240i | 0.647559 | + | 1.12160i | ||||
\(965\) | −36.8421 | −1.18599 | ||||||||
\(966\) | 0.133824 | − | 0.191988i | 0.00430571 | − | 0.00617712i | ||||
\(967\) | −5.40788 | −0.173906 | −0.0869528 | − | 0.996212i | \(-0.527713\pi\) | ||||
−0.0869528 | + | 0.996212i | \(0.527713\pi\) | |||||||
\(968\) | 3.60690 | + | 6.24733i | 0.115930 | + | 0.200797i | ||||
\(969\) | −0.529765 | + | 0.917580i | −0.0170185 | + | 0.0294769i | ||||
\(970\) | 3.39066 | − | 5.87279i | 0.108867 | − | 0.188564i | ||||
\(971\) | −21.1376 | − | 36.6114i | −0.678338 | − | 1.17492i | −0.975481 | − | 0.220083i | \(-0.929367\pi\) |
0.297143 | − | 0.954833i | \(-0.403966\pi\) | |||||||
\(972\) | 13.3496 | 0.428190 | ||||||||
\(973\) | 4.49297 | + | 9.58192i | 0.144038 | + | 0.307182i | ||||
\(974\) | 6.50733 | 0.208508 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.2284 | + | 24.6443i | −0.455440 | + | 0.788846i | ||||
\(977\) | −5.41508 | + | 9.37920i | −0.173244 | + | 0.300067i | −0.939552 | − | 0.342406i | \(-0.888758\pi\) |
0.766308 | + | 0.642473i | \(0.222092\pi\) | |||||||
\(978\) | −0.0602935 | − | 0.104431i | −0.00192797 | − | 0.00333935i | ||||
\(979\) | −50.7660 | −1.62249 | ||||||||
\(980\) | −34.5350 | + | 41.5148i | −1.10318 | + | 1.32614i | ||||
\(981\) | −36.4988 | −1.16532 | ||||||||
\(982\) | 2.20664 | + | 3.82202i | 0.0704169 | + | 0.121966i | ||||
\(983\) | 10.7805 | − | 18.6723i | 0.343844 | − | 0.595555i | −0.641299 | − | 0.767291i | \(-0.721604\pi\) |
0.985143 | + | 0.171736i | \(0.0549375\pi\) | |||||||
\(984\) | −0.817137 | + | 1.41532i | −0.0260494 | + | 0.0451189i | ||||
\(985\) | 14.9883 | + | 25.9605i | 0.477567 | + | 0.827170i | ||||
\(986\) | −0.737005 | −0.0234710 | ||||||||
\(987\) | −1.03458 | − | 2.20638i | −0.0329309 | − | 0.0702300i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.92850 | − | 10.2685i | −0.188515 | − | 0.326518i | ||||
\(990\) | 5.08383 | − | 8.80545i | 0.161575 | − | 0.279855i | ||||
\(991\) | −4.31312 | + | 7.47054i | −0.137011 | + | 0.237310i | −0.926364 | − | 0.376630i | \(-0.877083\pi\) |
0.789353 | + | 0.613940i | \(0.210416\pi\) | |||||||
\(992\) | 6.41306 | + | 11.1078i | 0.203615 | + | 0.352671i | ||||
\(993\) | −8.85703 | −0.281069 | ||||||||
\(994\) | 2.82654 | − | 4.05505i | 0.0896524 | − | 0.128618i | ||||
\(995\) | −53.2024 | −1.68663 | ||||||||
\(996\) | −1.82102 | − | 3.15411i | −0.0577013 | − | 0.0999417i | ||||
\(997\) | −10.8484 | + | 18.7899i | −0.343571 | + | 0.595082i | −0.985093 | − | 0.172022i | \(-0.944970\pi\) |
0.641522 | + | 0.767105i | \(0.278303\pi\) | |||||||
\(998\) | −1.11381 | + | 1.92918i | −0.0352572 | + | 0.0610672i | ||||
\(999\) | 5.50521 | + | 9.53531i | 0.174177 | + | 0.301684i |
(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 | 1183.2.e.f.508.2 | 10 | ||
7.2 | even | 3 | inner | 1183.2.e.f.170.2 | 10 | ||
7.3 | odd | 6 | 8281.2.a.bx.1.4 | 5 | |||
7.4 | even | 3 | 8281.2.a.bw.1.4 | 5 | |||
13.12 | even | 2 | 91.2.e.c.53.4 | ✓ | 10 | ||
39.38 | odd | 2 | 819.2.j.h.235.2 | 10 | |||
52.51 | odd | 2 | 1456.2.r.p.417.3 | 10 | |||
91.12 | odd | 6 | 637.2.e.m.79.4 | 10 | |||
91.25 | even | 6 | 637.2.a.l.1.2 | 5 | |||
91.38 | odd | 6 | 637.2.a.k.1.2 | 5 | |||
91.51 | even | 6 | 91.2.e.c.79.4 | yes | 10 | ||
91.90 | odd | 2 | 637.2.e.m.508.4 | 10 | |||
273.38 | even | 6 | 5733.2.a.bm.1.4 | 5 | |||
273.116 | odd | 6 | 5733.2.a.bl.1.4 | 5 | |||
273.233 | odd | 6 | 819.2.j.h.352.2 | 10 | |||
364.51 | odd | 6 | 1456.2.r.p.625.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.4 | ✓ | 10 | 13.12 | even | 2 | ||
91.2.e.c.79.4 | yes | 10 | 91.51 | even | 6 | ||
637.2.a.k.1.2 | 5 | 91.38 | odd | 6 | |||
637.2.a.l.1.2 | 5 | 91.25 | even | 6 | |||
637.2.e.m.79.4 | 10 | 91.12 | odd | 6 | |||
637.2.e.m.508.4 | 10 | 91.90 | odd | 2 | |||
819.2.j.h.235.2 | 10 | 39.38 | odd | 2 | |||
819.2.j.h.352.2 | 10 | 273.233 | odd | 6 | |||
1183.2.e.f.170.2 | 10 | 7.2 | even | 3 | inner | ||
1183.2.e.f.508.2 | 10 | 1.1 | even | 1 | trivial | ||
1456.2.r.p.417.3 | 10 | 52.51 | odd | 2 | |||
1456.2.r.p.625.3 | 10 | 364.51 | odd | 6 | |||
5733.2.a.bl.1.4 | 5 | 273.116 | odd | 6 | |||
5733.2.a.bm.1.4 | 5 | 273.38 | even | 6 | |||
8281.2.a.bw.1.4 | 5 | 7.4 | even | 3 | |||
8281.2.a.bx.1.4 | 5 | 7.3 | odd | 6 |