Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(28,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([44]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.g (of order \(27\), degree \(18\), 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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{27})\) |
Twist minimal: | no (minimal twist has level 81) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{27}]$ |
Embedding invariants
Embedding label | 28.7 | ||
Character | \(\chi\) | \(=\) | 729.28 |
Dual form | 729.2.g.b.703.7 |
$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{22}{27}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29056 | − | 0.848814i | 0.912563 | − | 0.600202i | −0.00404373 | − | 0.999992i | \(-0.501287\pi\) |
0.916607 | + | 0.399790i | \(0.130917\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.152898 | − | 0.354458i | 0.0764491 | − | 0.177229i | ||||
\(5\) | −0.349244 | + | 0.370177i | −0.156187 | + | 0.165548i | −0.800742 | − | 0.599010i | \(-0.795561\pi\) |
0.644555 | + | 0.764558i | \(0.277043\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.96148 | − | 0.463031i | −1.49730 | − | 0.175009i | −0.672358 | − | 0.740226i | \(-0.734718\pi\) |
−0.824942 | + | 0.565217i | \(0.808793\pi\) | |||||||
\(8\) | 0.432916 | + | 2.45519i | 0.153059 | + | 0.868041i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.136509 | + | 0.774179i | −0.0431678 | + | 0.244817i | ||||
\(11\) | −1.09805 | + | 3.66773i | −0.331074 | + | 1.10586i | 0.616775 | + | 0.787140i | \(0.288439\pi\) |
−0.947848 | + | 0.318723i | \(0.896746\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.181020 | + | 3.10799i | −0.0502059 | + | 0.862002i | 0.875373 | + | 0.483448i | \(0.160616\pi\) |
−0.925579 | + | 0.378554i | \(0.876421\pi\) | |||||||
\(14\) | −5.50556 | + | 2.76500i | −1.47142 | + | 0.738976i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.17252 | + | 3.36268i | 0.793131 | + | 0.840669i | ||||
\(17\) | 1.41129 | − | 0.513668i | 0.342288 | − | 0.124583i | −0.165156 | − | 0.986268i | \(-0.552813\pi\) |
0.507444 | + | 0.861685i | \(0.330590\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.30242 | + | 2.29389i | 1.44587 | + | 0.526255i | 0.941436 | − | 0.337192i | \(-0.109477\pi\) |
0.504439 | + | 0.863447i | \(0.331699\pi\) | |||||||
\(20\) | 0.0778134 | + | 0.180392i | 0.0173996 | + | 0.0403368i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.69613 | + | 5.66546i | 0.361616 | + | 1.20788i | ||||
\(23\) | −1.17843 | + | 0.137739i | −0.245720 | + | 0.0287206i | −0.238062 | − | 0.971250i | \(-0.576512\pi\) |
−0.00765887 | + | 0.999971i | \(0.502438\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.275664 | + | 4.73298i | 0.0551329 | + | 0.946595i | ||||
\(26\) | 2.40449 | + | 4.16470i | 0.471559 | + | 0.816765i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.769829 | + | 1.33338i | −0.145484 | + | 0.251986i | ||||
\(29\) | −6.17988 | − | 3.10365i | −1.14757 | − | 0.576333i | −0.229722 | − | 0.973256i | \(-0.573782\pi\) |
−0.917852 | + | 0.396923i | \(0.870078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0276800 | − | 0.0371807i | −0.00497148 | − | 0.00667785i | 0.799631 | − | 0.600492i | \(-0.205029\pi\) |
−0.804602 | + | 0.593814i | \(0.797621\pi\) | |||||||
\(32\) | 2.09689 | + | 0.496972i | 0.370681 | + | 0.0878530i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.38535 | − | 1.86084i | 0.237585 | − | 0.319132i | ||||
\(35\) | 1.55493 | − | 1.30474i | 0.262831 | − | 0.220541i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.33905 | − | 1.96269i | −0.384537 | − | 0.322665i | 0.429943 | − | 0.902856i | \(-0.358533\pi\) |
−0.814481 | + | 0.580191i | \(0.802978\pi\) | |||||||
\(38\) | 10.0807 | − | 2.38918i | 1.63531 | − | 0.387576i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.06005 | − | 0.697205i | −0.167608 | − | 0.110238i | ||||
\(41\) | −4.96389 | − | 3.26480i | −0.775229 | − | 0.509876i | 0.0991780 | − | 0.995070i | \(-0.468379\pi\) |
−0.874407 | + | 0.485194i | \(0.838749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.231769 | − | 0.0549304i | 0.0353445 | − | 0.00837680i | −0.212906 | − | 0.977073i | \(-0.568293\pi\) |
0.248250 | + | 0.968696i | \(0.420145\pi\) | |||||||
\(44\) | 1.13217 | + | 0.950001i | 0.170681 | + | 0.143218i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.40392 | + | 1.17803i | −0.206997 | + | 0.173691i | ||||
\(47\) | 2.82910 | − | 3.80014i | 0.412666 | − | 0.554307i | −0.546387 | − | 0.837533i | \(-0.683997\pi\) |
0.959053 | + | 0.283226i | \(0.0914046\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.66765 | + | 2.05427i | 1.23824 | + | 0.293467i | ||||
\(50\) | 4.37318 | + | 5.87420i | 0.618461 | + | 0.830737i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.07397 | + | 0.539370i | 0.148933 | + | 0.0747972i | ||||
\(53\) | −6.81173 | + | 11.7983i | −0.935663 | + | 1.62062i | −0.162216 | + | 0.986755i | \(0.551864\pi\) |
−0.773447 | + | 0.633860i | \(0.781469\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.974224 | − | 1.68741i | −0.131364 | − | 0.227530i | ||||
\(56\) | −0.578162 | − | 9.92665i | −0.0772601 | − | 1.32650i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.6099 | + | 1.24012i | −1.39315 | + | 0.162836i | ||||
\(59\) | −0.400604 | − | 1.33811i | −0.0521543 | − | 0.174207i | 0.927944 | − | 0.372719i | \(-0.121574\pi\) |
−0.980099 | + | 0.198512i | \(0.936389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.124364 | − | 0.288308i | −0.0159232 | − | 0.0369141i | 0.910069 | − | 0.414457i | \(-0.136028\pi\) |
−0.925992 | + | 0.377543i | \(0.876769\pi\) | |||||||
\(62\) | −0.0672822 | − | 0.0244887i | −0.00854485 | − | 0.00311007i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.56048 | + | 2.02385i | −0.695060 | + | 0.252981i | ||||
\(65\) | −1.08729 | − | 1.15246i | −0.134861 | − | 0.142945i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.90826 | − | 2.46502i | 0.599639 | − | 0.301150i | −0.122966 | − | 0.992411i | \(-0.539241\pi\) |
0.722605 | + | 0.691261i | \(0.242944\pi\) | |||||||
\(68\) | 0.0337102 | − | 0.578782i | 0.00408797 | − | 0.0701877i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.899246 | − | 3.00369i | 0.107480 | − | 0.359010i | ||||
\(71\) | 2.03991 | − | 11.5689i | 0.242093 | − | 1.37298i | −0.585054 | − | 0.810994i | \(-0.698927\pi\) |
0.827147 | − | 0.561985i | \(-0.189962\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.70207 | + | 15.3242i | 0.316253 | + | 1.79356i | 0.565106 | + | 0.825019i | \(0.308835\pi\) |
−0.248853 | + | 0.968541i | \(0.580053\pi\) | |||||||
\(74\) | −4.68464 | − | 0.547556i | −0.544579 | − | 0.0636521i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.77672 | − | 1.88321i | 0.203804 | − | 0.216019i | ||||
\(77\) | 6.04817 | − | 14.0212i | 0.689253 | − | 1.59787i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6941 | − | 7.69136i | 1.31569 | − | 0.865346i | 0.319093 | − | 0.947723i | \(-0.396622\pi\) |
0.996601 | + | 0.0823774i | \(0.0262513\pi\) | |||||||
\(80\) | −2.35277 | −0.263048 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.17740 | −1.01347 | ||||||||
\(83\) | 0.587346 | − | 0.386304i | 0.0644696 | − | 0.0424023i | −0.516865 | − | 0.856067i | \(-0.672901\pi\) |
0.581335 | + | 0.813665i | \(0.302531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.302737 | + | 0.701823i | −0.0328364 | + | 0.0761234i | ||||
\(86\) | 0.252487 | − | 0.267620i | 0.0272263 | − | 0.0288582i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.48034 | − | 1.10809i | −1.01061 | − | 0.118123i | ||||
\(89\) | −2.00921 | − | 11.3948i | −0.212976 | − | 1.20785i | −0.884384 | − | 0.466760i | \(-0.845421\pi\) |
0.671408 | − | 0.741088i | \(-0.265690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.15620 | − | 12.2284i | 0.226032 | − | 1.28189i | ||||
\(92\) | −0.131358 | + | 0.438765i | −0.0136950 | + | 0.0457444i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.425507 | − | 7.30568i | 0.0438877 | − | 0.753523i | ||||
\(95\) | −3.05023 | + | 1.53188i | −0.312947 | + | 0.157168i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.92799 | + | 9.46312i | 0.906500 | + | 0.960834i | 0.999393 | − | 0.0348418i | \(-0.0110927\pi\) |
−0.0928924 | + | 0.995676i | \(0.529611\pi\) | |||||||
\(98\) | 12.9298 | − | 4.70606i | 1.30611 | − | 0.475384i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.71979 | + | 0.625952i | 0.171979 | + | 0.0625952i | ||||
\(101\) | 4.89713 | + | 11.3528i | 0.487283 | + | 1.12965i | 0.967585 | + | 0.252545i | \(0.0812677\pi\) |
−0.480302 | + | 0.877103i | \(0.659473\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.599460 | + | 2.00234i | 0.0590666 | + | 0.197296i | 0.982430 | − | 0.186631i | \(-0.0597567\pi\) |
−0.923364 | + | 0.383927i | \(0.874572\pi\) | |||||||
\(104\) | −7.70907 | + | 0.901062i | −0.755937 | + | 0.0883564i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.22359 | + | 21.0082i | 0.118846 | + | 2.04050i | ||||
\(107\) | −0.831363 | − | 1.43996i | −0.0803709 | − | 0.139207i | 0.823038 | − | 0.567986i | \(-0.192277\pi\) |
−0.903409 | + | 0.428779i | \(0.858944\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.14981 | + | 3.72357i | −0.205914 | + | 0.356654i | −0.950424 | − | 0.310958i | \(-0.899350\pi\) |
0.744510 | + | 0.667612i | \(0.232683\pi\) | |||||||
\(110\) | −2.68959 | − | 1.35076i | −0.256442 | − | 0.128790i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.0109 | − | 14.7902i | −1.04043 | − | 1.39754i | ||||
\(113\) | 13.8508 | + | 3.28270i | 1.30297 | + | 0.308810i | 0.822784 | − | 0.568354i | \(-0.192420\pi\) |
0.480189 | + | 0.877165i | \(0.340568\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.360573 | − | 0.484334i | 0.0336236 | − | 0.0451644i | ||||
\(116\) | −2.04501 | + | 1.71596i | −0.189874 | + | 0.159323i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.65281 | − | 1.38687i | −0.152154 | − | 0.127672i | ||||
\(119\) | −5.82865 | + | 1.38142i | −0.534312 | + | 0.126634i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.05618 | − | 2.01008i | −0.277834 | − | 0.182735i | ||||
\(122\) | −0.405219 | − | 0.266517i | −0.0366868 | − | 0.0241293i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0174112 | + | 0.00412654i | −0.00156357 | + | 0.000370574i | ||||
\(125\) | −3.79760 | − | 3.18657i | −0.339668 | − | 0.285015i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1754 | − | 11.8946i | 1.25787 | − | 1.05548i | 0.261961 | − | 0.965078i | \(-0.415631\pi\) |
0.995906 | − | 0.0903976i | \(-0.0288138\pi\) | |||||||
\(128\) | −8.03198 | + | 10.7888i | −0.709933 | + | 0.953606i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.38143 | − | 0.564410i | −0.208865 | − | 0.0495020i | ||||
\(131\) | 3.31614 | + | 4.45435i | 0.289732 | + | 0.389178i | 0.923029 | − | 0.384731i | \(-0.125706\pi\) |
−0.633296 | + | 0.773909i | \(0.718299\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.9048 | − | 12.0054i | −2.07281 | − | 1.04100i | ||||
\(134\) | 4.24205 | − | 7.34745i | 0.366458 | − | 0.634723i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.87212 | + | 3.24261i | 0.160533 | + | 0.278052i | ||||
\(137\) | 0.173481 | + | 2.97856i | 0.0148215 | + | 0.254475i | 0.997577 | + | 0.0695670i | \(0.0221618\pi\) |
−0.982756 | + | 0.184908i | \(0.940801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.85385 | − | 0.684217i | 0.496517 | − | 0.0580345i | 0.135851 | − | 0.990729i | \(-0.456623\pi\) |
0.360667 | + | 0.932695i | \(0.382549\pi\) | |||||||
\(140\) | −0.224730 | − | 0.750649i | −0.0189931 | − | 0.0634415i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.18724 | − | 16.6619i | −0.603140 | − | 1.39824i | ||||
\(143\) | −11.2005 | − | 4.07665i | −0.936633 | − | 0.340907i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.30719 | − | 1.20372i | 0.274647 | − | 0.0999633i | ||||
\(146\) | 16.4946 | + | 17.4832i | 1.36510 | + | 1.44692i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.05333 | + | 0.529002i | −0.0865831 | + | 0.0434837i | ||||
\(149\) | 0.316650 | − | 5.43668i | 0.0259410 | − | 0.445390i | −0.960182 | − | 0.279375i | \(-0.909873\pi\) |
0.986123 | − | 0.166015i | \(-0.0530901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.27673 | − | 14.2853i | 0.348035 | − | 1.16252i | −0.587482 | − | 0.809237i | \(-0.699881\pi\) |
0.935517 | − | 0.353281i | \(-0.114934\pi\) | |||||||
\(152\) | −2.90352 | + | 16.4667i | −0.235507 | + | 1.33563i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.09590 | − | 23.2290i | −0.330057 | − | 1.87185i | ||||
\(155\) | 0.0234305 | + | 0.00273864i | 0.00188199 | + | 0.000219973i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.75380 | + | 6.09867i | −0.459203 | + | 0.486727i | −0.915055 | − | 0.403329i | \(-0.867853\pi\) |
0.455852 | + | 0.890056i | \(0.349335\pi\) | |||||||
\(158\) | 8.56345 | − | 19.8523i | 0.681272 | − | 1.57937i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.916293 | + | 0.602656i | −0.0724394 | + | 0.0476441i | ||||
\(161\) | 4.73212 | 0.372944 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.04537 | 0.238531 | 0.119266 | − | 0.992862i | \(-0.461946\pi\) | ||||
0.119266 | + | 0.992862i | \(0.461946\pi\) | |||||||
\(164\) | −1.91620 | + | 1.26031i | −0.149630 | + | 0.0984134i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.430105 | − | 0.997096i | 0.0333826 | − | 0.0773896i | ||||
\(167\) | −14.4823 | + | 15.3503i | −1.12067 | + | 1.18785i | −0.140422 | + | 0.990092i | \(0.544846\pi\) |
−0.980252 | + | 0.197753i | \(0.936635\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.28526 | + | 0.383992i | 0.252712 | + | 0.0295378i | ||||
\(170\) | 0.205018 | + | 1.16271i | 0.0157241 | + | 0.0891760i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0159666 | − | 0.0905513i | 0.00121744 | − | 0.00690447i | ||||
\(173\) | 0.486058 | − | 1.62355i | 0.0369543 | − | 0.123436i | −0.937522 | − | 0.347925i | \(-0.886886\pi\) |
0.974477 | + | 0.224489i | \(0.0720714\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.09947 | − | 18.8773i | 0.0831125 | − | 1.42699i | ||||
\(176\) | −15.8170 | + | 7.94358i | −1.19225 | + | 0.598770i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.2651 | − | 13.0002i | −0.919307 | − | 0.974409i | ||||
\(179\) | −11.3362 | + | 4.12604i | −0.847308 | + | 0.308395i | −0.728942 | − | 0.684575i | \(-0.759988\pi\) |
−0.118366 | + | 0.992970i | \(0.537765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.09567 | − | 2.58261i | −0.527417 | − | 0.191964i | 0.0645678 | − | 0.997913i | \(-0.479433\pi\) |
−0.591985 | + | 0.805949i | \(0.701655\pi\) | |||||||
\(182\) | −7.59697 | − | 17.6117i | −0.563125 | − | 1.30547i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.848339 | − | 2.83365i | −0.0625404 | − | 0.208899i | ||||
\(185\) | 1.54344 | − | 0.180403i | 0.113476 | − | 0.0132635i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.334333 | + | 5.74027i | 0.0244488 | + | 0.419770i | ||||
\(188\) | −0.914425 | − | 1.58383i | −0.0666913 | − | 0.115513i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.63622 | + | 4.56607i | −0.191251 | + | 0.331257i | ||||
\(191\) | 11.5732 | + | 5.81226i | 0.837404 | + | 0.420560i | 0.815190 | − | 0.579193i | \(-0.196632\pi\) |
0.0222137 | + | 0.999753i | \(0.492929\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7961 | + | 14.5016i | 0.777118 | + | 1.04385i | 0.997653 | + | 0.0684715i | \(0.0218122\pi\) |
−0.220535 | + | 0.975379i | \(0.570780\pi\) | |||||||
\(194\) | 19.5545 | + | 4.63451i | 1.40393 | + | 0.332738i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.05342 | − | 2.75822i | 0.146673 | − | 0.197016i | ||||
\(197\) | −7.47510 | + | 6.27235i | −0.532579 | + | 0.446886i | −0.868991 | − | 0.494828i | \(-0.835231\pi\) |
0.336412 | + | 0.941715i | \(0.390786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.35460 | − | 5.33214i | −0.450465 | − | 0.377985i | 0.389143 | − | 0.921177i | \(-0.372771\pi\) |
−0.839609 | + | 0.543192i | \(0.817216\pi\) | |||||||
\(200\) | −11.5010 | + | 2.72579i | −0.813245 | + | 0.192743i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.9565 | + | 10.4947i | 1.12269 | + | 0.738407i | ||||
\(203\) | 23.0444 | + | 15.1565i | 1.61740 | + | 1.06378i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.94216 | − | 0.697305i | 0.205490 | − | 0.0487019i | ||||
\(206\) | 2.47325 | + | 2.07530i | 0.172320 | + | 0.144593i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.0255 | + | 9.25146i | −0.764478 | + | 0.641473i | ||||
\(209\) | −15.3337 | + | 20.5968i | −1.06066 | + | 1.42471i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0335 | − | 2.61499i | −0.759577 | − | 0.180023i | −0.167464 | − | 0.985878i | \(-0.553558\pi\) |
−0.592113 | + | 0.805855i | \(0.701706\pi\) | |||||||
\(212\) | 3.14049 | + | 4.21840i | 0.215689 | + | 0.289721i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.29519 | − | 1.15269i | −0.156896 | − | 0.0787960i | ||||
\(215\) | −0.0606102 | + | 0.104980i | −0.00413358 | + | 0.00715957i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0924381 | + | 0.160108i | 0.00627511 | + | 0.0108688i | ||||
\(218\) | 0.386170 | + | 6.63028i | 0.0261547 | + | 0.449059i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.747071 | + | 0.0873201i | −0.0503676 | + | 0.00588712i | ||||
\(221\) | 1.34100 | + | 4.47926i | 0.0902057 | + | 0.301308i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.49598 | + | 17.3776i | 0.501968 | + | 1.16369i | 0.961319 | + | 0.275438i | \(0.0888227\pi\) |
−0.459351 | + | 0.888255i | \(0.651918\pi\) | |||||||
\(224\) | −8.07667 | − | 2.93967i | −0.539646 | − | 0.196415i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.6617 | − | 7.52023i | 1.37439 | − | 0.500239i | ||||
\(227\) | −7.61638 | − | 8.07290i | −0.505517 | − | 0.535817i | 0.423479 | − | 0.905906i | \(-0.360809\pi\) |
−0.928996 | + | 0.370089i | \(0.879327\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.72124 | − | 1.36666i | 0.179825 | − | 0.0903113i | −0.356609 | − | 0.934254i | \(-0.616067\pi\) |
0.536434 | + | 0.843942i | \(0.319771\pi\) | |||||||
\(230\) | 0.0542316 | − | 0.931121i | 0.00357593 | − | 0.0613963i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.94468 | − | 16.5164i | 0.324634 | − | 1.08435i | ||||
\(233\) | 2.47370 | − | 14.0290i | 0.162057 | − | 0.919073i | −0.789989 | − | 0.613121i | \(-0.789914\pi\) |
0.952047 | − | 0.305953i | \(-0.0989750\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.418679 | + | 2.37444i | 0.0273116 | + | 0.154892i | ||||
\(236\) | −0.535556 | − | 0.0625975i | −0.0348617 | − | 0.00407475i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.34966 | + | 6.73024i | −0.411587 | + | 0.436257i | ||||
\(239\) | 3.14737 | − | 7.29642i | 0.203586 | − | 0.471966i | −0.785581 | − | 0.618759i | \(-0.787636\pi\) |
0.989167 | + | 0.146793i | \(0.0468950\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.02761 | + | 1.99129i | −0.195026 | + | 0.128270i | −0.643266 | − | 0.765643i | \(-0.722421\pi\) |
0.448241 | + | 0.893913i | \(0.352051\pi\) | |||||||
\(242\) | −5.65036 | −0.363219 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.121208 | −0.00775955 | ||||||||
\(245\) | −3.78757 | + | 2.49112i | −0.241979 | + | 0.159152i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.27026 | + | 19.1726i | −0.526224 | + | 1.21993i | ||||
\(248\) | 0.0793026 | − | 0.0840558i | 0.00503572 | − | 0.00533755i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.60584 | − | 0.888995i | −0.481035 | − | 0.0562250i | ||||
\(251\) | 0.441351 | + | 2.50303i | 0.0278578 | + | 0.157990i | 0.995563 | − | 0.0940939i | \(-0.0299954\pi\) |
−0.967706 | + | 0.252083i | \(0.918884\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.788785 | − | 4.47342i | 0.0495905 | − | 0.281242i | ||||
\(254\) | 8.19794 | − | 27.3830i | 0.514384 | − | 1.71816i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.519916 | + | 8.92662i | −0.0324948 | + | 0.557914i | ||||
\(257\) | 25.0214 | − | 12.5662i | 1.56079 | − | 0.783860i | 0.561739 | − | 0.827314i | \(-0.310133\pi\) |
0.999055 | + | 0.0434541i | \(0.0138362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.35731 | + | 8.85823i | 0.519298 | + | 0.550424i | ||||
\(260\) | −0.574742 | + | 0.209189i | −0.0356440 | + | 0.0129733i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.06059 | + | 2.93381i | 0.497985 | + | 0.181252i | ||||
\(263\) | 0.974610 | + | 2.25940i | 0.0600970 | + | 0.139321i | 0.945618 | − | 0.325278i | \(-0.105458\pi\) |
−0.885521 | + | 0.464599i | \(0.846199\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.98849 | − | 6.64202i | −0.122152 | − | 0.408016i | ||||
\(266\) | −41.0410 | + | 4.79700i | −2.51638 | + | 0.294123i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.123282 | − | 2.11667i | −0.00753064 | − | 0.129296i | ||||
\(269\) | 5.65271 | + | 9.79078i | 0.344652 | + | 0.596954i | 0.985290 | − | 0.170888i | \(-0.0546637\pi\) |
−0.640639 | + | 0.767842i | \(0.721330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.14084 | − | 3.70804i | 0.130047 | − | 0.225248i | −0.793648 | − | 0.608378i | \(-0.791821\pi\) |
0.923694 | + | 0.383130i | \(0.125154\pi\) | |||||||
\(272\) | 6.20465 | + | 3.11609i | 0.376212 | + | 0.188941i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.75213 | + | 3.69675i | 0.166262 | + | 0.223329i | ||||
\(275\) | −17.6620 | − | 4.18597i | −1.06506 | − | 0.252423i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2400 | − | 15.0980i | 0.675349 | − | 0.907151i | −0.323893 | − | 0.946094i | \(-0.604992\pi\) |
0.999241 | + | 0.0389429i | \(0.0123990\pi\) | |||||||
\(278\) | 6.97397 | − | 5.85185i | 0.418271 | − | 0.350971i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.87654 | + | 3.25280i | 0.231668 | + | 0.194392i | ||||
\(281\) | 13.2369 | − | 3.13720i | 0.789647 | − | 0.187150i | 0.184046 | − | 0.982918i | \(-0.441081\pi\) |
0.605602 | + | 0.795768i | \(0.292932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9445 | − | 9.17147i | −0.828917 | − | 0.545187i | 0.0626713 | − | 0.998034i | \(-0.480038\pi\) |
−0.891588 | + | 0.452847i | \(0.850408\pi\) | |||||||
\(284\) | −3.78880 | − | 2.49193i | −0.224824 | − | 0.147869i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.9152 | + | 4.24599i | −1.05935 | + | 0.251071i | ||||
\(287\) | 18.1527 | + | 15.2319i | 1.07152 | + | 0.899110i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.2949 | + | 9.47752i | −0.664404 | + | 0.557501i | ||||
\(290\) | 3.24639 | − | 4.36066i | 0.190634 | − | 0.256067i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.84492 | + | 1.38527i | 0.342048 | + | 0.0810669i | ||||
\(293\) | 15.1735 | + | 20.3815i | 0.886444 | + | 1.19070i | 0.980771 | + | 0.195160i | \(0.0625225\pi\) |
−0.0943276 | + | 0.995541i | \(0.530070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.635248 | + | 0.319033i | 0.0369855 | + | 0.0185748i | ||||
\(296\) | 3.80617 | − | 6.59249i | 0.221229 | − | 0.383181i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.20607 | − | 7.28513i | −0.243651 | − | 0.422016i | ||||
\(299\) | −0.214772 | − | 3.68749i | −0.0124206 | − | 0.213253i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.943585 | + | 0.110289i | −0.0543874 | + | 0.00635697i | ||||
\(302\) | −6.60616 | − | 22.0661i | −0.380142 | − | 1.26976i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.2809 | + | 28.4704i | 0.704361 | + | 1.63289i | ||||
\(305\) | 0.150158 | + | 0.0546532i | 0.00859805 | + | 0.00312943i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.43080 | + | 3.43253i | −0.538244 | + | 0.195905i | −0.596816 | − | 0.802378i | \(-0.703568\pi\) |
0.0585714 | + | 0.998283i | \(0.481345\pi\) | |||||||
\(308\) | −4.04518 | − | 4.28764i | −0.230496 | − | 0.244311i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.0325631 | − | 0.0163538i | 0.00184946 | − | 0.000928834i | ||||
\(311\) | 1.56707 | − | 26.9055i | 0.0888602 | − | 1.52567i | −0.599543 | − | 0.800342i | \(-0.704651\pi\) |
0.688403 | − | 0.725328i | \(-0.258312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.73743 | + | 12.4839i | −0.211252 | + | 0.705631i | 0.785028 | + | 0.619460i | \(0.212648\pi\) |
−0.996280 | + | 0.0861711i | \(0.972537\pi\) | |||||||
\(314\) | −2.24898 | + | 12.7546i | −0.126917 | + | 0.719784i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.938250 | − | 5.32108i | −0.0527807 | − | 0.299334i | ||||
\(317\) | 9.42954 | + | 1.10216i | 0.529616 | + | 0.0619032i | 0.376699 | − | 0.926336i | \(-0.377059\pi\) |
0.152917 | + | 0.988239i | \(0.451133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.1691 | − | 19.2582i | 1.01728 | − | 1.07825i | ||||
\(320\) | 1.19278 | − | 2.76518i | 0.0666785 | − | 0.154578i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.10709 | − | 4.01669i | 0.340335 | − | 0.223842i | ||||
\(323\) | 10.0729 | 0.560468 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.7599 | −0.818735 | ||||||||
\(326\) | 3.93023 | − | 2.58495i | 0.217675 | − | 0.143167i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.86675 | − | 13.6007i | 0.323937 | − | 0.750971i | ||||
\(329\) | −12.9670 | + | 13.7442i | −0.714894 | + | 0.757744i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.3551 | + | 2.72982i | 1.28371 | + | 0.150045i | 0.730452 | − | 0.682964i | \(-0.239309\pi\) |
0.553261 | + | 0.833008i | \(0.313383\pi\) | |||||||
\(332\) | −0.0471242 | − | 0.267255i | −0.00258628 | − | 0.0146675i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.66068 | + | 32.1033i | −0.309739 | + | 1.75661i | ||||
\(335\) | −0.801686 | + | 2.67782i | −0.0438008 | + | 0.146305i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.180721 | − | 3.10287i | 0.00984453 | − | 0.169024i | −0.989802 | − | 0.142448i | \(-0.954503\pi\) |
0.999647 | − | 0.0265759i | \(-0.00846036\pi\) | |||||||
\(338\) | 4.56576 | − | 2.29301i | 0.248344 | − | 0.124723i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.202479 | + | 0.214615i | 0.0109810 | + | 0.0116391i | ||||
\(341\) | 0.166763 | − | 0.0606967i | 0.00903071 | − | 0.00328691i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.15012 | − | 2.60243i | −0.386070 | − | 0.140518i | ||||
\(344\) | 0.235201 | + | 0.545258i | 0.0126812 | + | 0.0293983i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.750803 | − | 2.50786i | −0.0403634 | − | 0.134823i | ||||
\(347\) | −22.1439 | + | 2.58826i | −1.18875 | + | 0.138945i | −0.687386 | − | 0.726292i | \(-0.741242\pi\) |
−0.501363 | + | 0.865237i | \(0.667168\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.175177 | − | 3.00767i | −0.00937701 | − | 0.160997i | −0.999746 | − | 0.0225430i | \(-0.992824\pi\) |
0.990369 | − | 0.138454i | \(-0.0442133\pi\) | |||||||
\(350\) | −14.6043 | − | 25.2955i | −0.780635 | − | 1.35210i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.12524 | + | 7.14512i | −0.219876 | + | 0.380836i | ||||
\(353\) | −1.93406 | − | 0.971320i | −0.102939 | − | 0.0516981i | 0.396584 | − | 0.917998i | \(-0.370195\pi\) |
−0.499524 | + | 0.866300i | \(0.666492\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.57013 | + | 4.79551i | 0.189483 | + | 0.254519i | ||||
\(356\) | −4.34619 | − | 1.03007i | −0.230348 | − | 0.0545934i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.1278 | + | 14.9472i | −0.588123 | + | 0.789986i | ||||
\(359\) | 0.496794 | − | 0.416860i | 0.0262198 | − | 0.0220010i | −0.629584 | − | 0.776933i | \(-0.716774\pi\) |
0.655803 | + | 0.754932i | \(0.272330\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.9037 | + | 16.7012i | 1.04756 | + | 0.879011i | ||||
\(362\) | −11.3495 | + | 2.68989i | −0.596518 | + | 0.141377i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00479 | − | 2.63399i | −0.209908 | − | 0.138059i | ||||
\(365\) | −6.61635 | − | 4.35164i | −0.346315 | − | 0.227775i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.21403 | + | 2.18376i | −0.480968 | + | 0.113992i | −0.463946 | − | 0.885864i | \(-0.653567\pi\) |
−0.0170223 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(368\) | −4.20178 | − | 3.52571i | −0.219033 | − | 0.183790i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.83878 | − | 1.54292i | 0.0955935 | − | 0.0802124i | ||||
\(371\) | 32.4475 | − | 43.5846i | 1.68459 | − | 2.26280i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.75011 | − | 1.12580i | −0.245951 | − | 0.0582915i | 0.105791 | − | 0.994388i | \(-0.466263\pi\) |
−0.351742 | + | 0.936097i | \(0.614411\pi\) | |||||||
\(374\) | 5.30390 | + | 7.12437i | 0.274258 | + | 0.368392i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.5548 | + | 5.30083i | 0.544323 | + | 0.273369i | ||||
\(377\) | 10.7648 | − | 18.6452i | 0.554415 | − | 0.960275i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0190 | + | 22.5495i | 0.668739 | + | 1.15829i | 0.978257 | + | 0.207396i | \(0.0664989\pi\) |
−0.309518 | + | 0.950894i | \(0.600168\pi\) | |||||||
\(380\) | 0.0766134 | + | 1.31540i | 0.00393018 | + | 0.0674787i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.8694 | − | 2.32240i | 1.01661 | − | 0.118824i | ||||
\(383\) | −2.30331 | − | 7.69359i | −0.117694 | − | 0.393124i | 0.878760 | − | 0.477263i | \(-0.158371\pi\) |
−0.996454 | + | 0.0841390i | \(0.973186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.07805 | + | 7.13573i | 0.156872 | + | 0.363670i | ||||
\(386\) | 26.2422 | + | 9.55136i | 1.33569 | + | 0.486152i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.71935 | − | 1.71770i | 0.239589 | − | 0.0872032i | ||||
\(389\) | −15.6093 | − | 16.5449i | −0.791422 | − | 0.838858i | 0.198555 | − | 0.980090i | \(-0.436375\pi\) |
−0.989977 | + | 0.141231i | \(0.954894\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.59236 | + | 0.799714i | −0.0805291 | + | 0.0404433i | ||||
\(392\) | −1.29126 | + | 22.1700i | −0.0652184 | + | 1.11976i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.32300 | + | 14.4398i | −0.217789 | + | 0.727467i | ||||
\(395\) | −1.23695 | + | 7.01507i | −0.0622375 | + | 0.352967i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.29294 | + | 24.3465i | 0.215456 | + | 1.22191i | 0.880113 | + | 0.474765i | \(0.157467\pi\) |
−0.664656 | + | 0.747149i | \(0.731422\pi\) | |||||||
\(398\) | −12.7270 | − | 1.48757i | −0.637946 | − | 0.0745652i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.0409 | + | 15.9424i | −0.752046 | + | 0.797122i | ||||
\(401\) | 6.72403 | − | 15.5880i | 0.335782 | − | 0.778430i | −0.663754 | − | 0.747951i | \(-0.731038\pi\) |
0.999535 | − | 0.0304785i | \(-0.00970310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.120568 | − | 0.0792988i | 0.00600592 | − | 0.00395015i | ||||
\(404\) | 4.77286 | 0.237459 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 42.6052 | 2.11446 | ||||||||
\(407\) | 9.76702 | − | 6.42387i | 0.484133 | − | 0.318419i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.47516 | − | 10.3746i | 0.221282 | − | 0.512990i | −0.771023 | − | 0.636808i | \(-0.780255\pi\) |
0.992305 | + | 0.123818i | \(0.0395138\pi\) | |||||||
\(410\) | 3.20515 | − | 3.39726i | 0.158291 | − | 0.167779i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.801401 | + | 0.0936703i | 0.0394822 | + | 0.00461481i | ||||
\(413\) | 0.967401 | + | 5.48640i | 0.0476027 | + | 0.269968i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0621265 | + | 0.352337i | −0.00304967 | + | 0.0172955i | ||||
\(416\) | −1.92416 | + | 6.42715i | −0.0943398 | + | 0.315117i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.30625 | + | 39.5969i | −0.112803 | + | 1.93675i | ||||
\(419\) | −28.9814 | + | 14.5550i | −1.41584 | + | 0.711059i | −0.981814 | − | 0.189843i | \(-0.939202\pi\) |
−0.434021 | + | 0.900903i | \(0.642906\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.455943 | + | 0.483271i | 0.0222213 | + | 0.0235532i | 0.738389 | − | 0.674375i | \(-0.235587\pi\) |
−0.716168 | + | 0.697928i | \(0.754105\pi\) | |||||||
\(422\) | −16.4590 | + | 5.99059i | −0.801212 | + | 0.291617i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −31.9159 | − | 11.6164i | −1.54997 | − | 0.564144i | ||||
\(425\) | 2.82022 | + | 6.53801i | 0.136801 | + | 0.317140i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.359170 | + | 1.19971i | 0.0173815 | + | 0.0580581i | ||||
\(428\) | −0.637521 | + | 0.0745155i | −0.0308157 | + | 0.00360184i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0108874 | + | 0.186930i | 0.000525037 | + | 0.00901454i | ||||
\(431\) | 15.1861 | + | 26.3031i | 0.731488 | + | 1.26698i | 0.956247 | + | 0.292561i | \(0.0945073\pi\) |
−0.224759 | + | 0.974414i | \(0.572159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.68299 | − | 9.84323i | 0.273107 | − | 0.473035i | −0.696549 | − | 0.717510i | \(-0.745282\pi\) |
0.969656 | + | 0.244474i | \(0.0786153\pi\) | |||||||
\(434\) | 0.255198 | + | 0.128165i | 0.0122499 | + | 0.00615214i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.991149 | + | 1.33134i | 0.0474674 | + | 0.0637598i | ||||
\(437\) | −7.74294 | − | 1.83511i | −0.370395 | − | 0.0877853i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.28247 | + | 5.75236i | −0.204391 | + | 0.274545i | −0.892485 | − | 0.451076i | \(-0.851040\pi\) |
0.688094 | + | 0.725621i | \(0.258448\pi\) | |||||||
\(440\) | 3.72114 | − | 3.12241i | 0.177399 | − | 0.148855i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.53271 | + | 4.64249i | 0.263164 | + | 0.220821i | ||||
\(443\) | 1.69953 | − | 0.402796i | 0.0807471 | − | 0.0191374i | −0.190044 | − | 0.981776i | \(-0.560863\pi\) |
0.270791 | + | 0.962638i | \(0.412715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.91981 | + | 3.23581i | 0.233221 | + | 0.153392i | ||||
\(446\) | 24.4244 | + | 16.0642i | 1.15653 | + | 0.760661i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22.9649 | − | 5.44277i | 1.08499 | − | 0.257147i | ||||
\(449\) | −25.6694 | − | 21.5392i | −1.21142 | − | 1.01650i | −0.999229 | − | 0.0392691i | \(-0.987497\pi\) |
−0.212187 | − | 0.977229i | \(-0.568059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.4250 | − | 14.6213i | 0.820510 | − | 0.688490i | ||||
\(452\) | 3.28134 | − | 4.40761i | 0.154341 | − | 0.207316i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.6818 | − | 3.95366i | −0.782915 | − | 0.185554i | ||||
\(455\) | 3.77365 | + | 5.06889i | 0.176911 | + | 0.237633i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.2116 | + | 5.12846i | 0.477679 | + | 0.239899i | 0.671312 | − | 0.741175i | \(-0.265731\pi\) |
−0.193634 | + | 0.981074i | \(0.562027\pi\) | |||||||
\(458\) | 2.35188 | − | 4.07358i | 0.109896 | − | 0.190346i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.116545 | − | 0.201862i | −0.00543394 | − | 0.00941186i | ||||
\(461\) | 0.967981 | + | 16.6196i | 0.0450834 | + | 0.774051i | 0.942776 | + | 0.333428i | \(0.108205\pi\) |
−0.897692 | + | 0.440623i | \(0.854758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.54546 | − | 0.531288i | 0.211245 | − | 0.0246910i | −0.00981201 | − | 0.999952i | \(-0.503123\pi\) |
0.221057 | + | 0.975261i | \(0.429049\pi\) | |||||||
\(464\) | −9.16922 | − | 30.6273i | −0.425670 | − | 1.42184i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.71560 | − | 20.2050i | −0.403742 | − | 0.935980i | ||||
\(467\) | 31.8531 | + | 11.5936i | 1.47398 | + | 0.536486i | 0.949179 | − | 0.314736i | \(-0.101916\pi\) |
0.524805 | + | 0.851222i | \(0.324138\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.5854 | + | 7.49246i | −0.950544 | + | 0.345970i | ||||
\(470\) | 2.55579 | + | 2.70898i | 0.117890 | + | 0.124956i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.11189 | − | 1.56285i | 0.143236 | − | 0.0719360i | ||||
\(473\) | −0.0530238 | + | 0.910384i | −0.00243804 | + | 0.0418595i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.11959 | + | 30.4616i | −0.418436 | + | 1.39767i | ||||
\(476\) | −0.401537 | + | 2.27723i | −0.0184044 | + | 0.104377i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.13144 | − | 12.0880i | −0.0974898 | − | 0.552892i | ||||
\(479\) | 8.62453 | + | 1.00806i | 0.394065 | + | 0.0460596i | 0.310818 | − | 0.950469i | \(-0.399397\pi\) |
0.0832467 | + | 0.996529i | \(0.473471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.52345 | − | 6.91445i | 0.297444 | − | 0.315272i | ||||
\(482\) | −2.21708 | + | 5.13976i | −0.100985 | + | 0.234110i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.17977 | + | 0.775949i | −0.0536261 | + | 0.0352704i | ||||
\(485\) | −6.62108 | −0.300648 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.3432 | −0.967154 | −0.483577 | − | 0.875302i | \(-0.660663\pi\) | ||||
−0.483577 | + | 0.875302i | \(0.660663\pi\) | |||||||
\(488\) | 0.654012 | − | 0.430150i | 0.0296057 | − | 0.0194720i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.77358 | + | 6.42989i | −0.125298 | + | 0.290473i | ||||
\(491\) | 2.89262 | − | 3.06600i | 0.130542 | − | 0.138366i | −0.658805 | − | 0.752314i | \(-0.728938\pi\) |
0.789347 | + | 0.613947i | \(0.210419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3158 | − | 1.20575i | −0.464602 | − | 0.0543042i | ||||
\(494\) | 5.60073 | + | 31.7633i | 0.251989 | + | 1.42910i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0372113 | − | 0.211036i | 0.00167084 | − | 0.00947578i | ||||
\(497\) | −13.4379 | + | 44.8856i | −0.602770 | + | 2.01339i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.76905 | + | 30.3734i | −0.0791936 | + | 1.35970i | 0.691445 | + | 0.722429i | \(0.256975\pi\) |
−0.770638 | + | 0.637273i | \(0.780062\pi\) | |||||||
\(500\) | −1.71015 | + | 0.858870i | −0.0764803 | + | 0.0384098i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.69419 | + | 2.85568i | 0.120248 | + | 0.127455i | ||||
\(503\) | 11.9111 | − | 4.33528i | 0.531089 | − | 0.193301i | −0.0625356 | − | 0.998043i | \(-0.519919\pi\) |
0.593624 | + | 0.804742i | \(0.297696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.91285 | − | 2.15210i | −0.263118 | − | 0.0957673i | ||||
\(506\) | −2.77913 | − | 6.44275i | −0.123547 | − | 0.286415i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.04874 | − | 6.84326i | −0.0908981 | − | 0.303621i | ||||
\(509\) | −3.48848 | + | 0.407744i | −0.154624 | + | 0.0180730i | −0.193053 | − | 0.981188i | \(-0.561839\pi\) |
0.0384287 | + | 0.999261i | \(0.487765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.60862 | − | 61.9577i | −0.159636 | − | 2.74085i | ||||
\(512\) | −6.54427 | − | 11.3350i | −0.289219 | − | 0.500941i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.6252 | − | 37.4560i | 0.953849 | − | 1.65211i | ||||
\(515\) | −0.950578 | − | 0.477398i | −0.0418875 | − | 0.0210367i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.8314 | + | 14.5491i | 0.476364 | + | 0.639869i | ||||
\(518\) | 18.3046 | + | 4.33827i | 0.804258 | + | 0.190613i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.35880 | − | 3.16841i | 0.103440 | − | 0.138944i | ||||
\(521\) | −6.50992 | + | 5.46247i | −0.285205 | + | 0.239315i | −0.774154 | − | 0.632997i | \(-0.781825\pi\) |
0.488950 | + | 0.872312i | \(0.337380\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.72249 | − | 8.15814i | −0.425135 | − | 0.356730i | 0.404978 | − | 0.914327i | \(-0.367279\pi\) |
−0.830112 | + | 0.557596i | \(0.811724\pi\) | |||||||
\(524\) | 2.08591 | − | 0.494370i | 0.0911234 | − | 0.0215966i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.17560 | + | 2.08863i | 0.138463 | + | 0.0910685i | ||||
\(527\) | −0.0581631 | − | 0.0382545i | −0.00253362 | − | 0.00166639i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0103 | + | 4.97953i | −0.913491 | + | 0.216501i | ||||
\(530\) | −8.20411 | − | 6.88406i | −0.356364 | − | 0.299025i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.91043 | + | 6.63763i | −0.342960 | + | 0.287778i | ||||
\(533\) | 11.0455 | − | 14.8367i | 0.478435 | − | 0.642650i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.823391 | + | 0.195147i | 0.0355983 | + | 0.00843695i | ||||
\(536\) | 8.17695 | + | 10.9836i | 0.353191 | + | 0.474417i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.6057 | + | 7.83748i | 0.672810 | + | 0.337898i | ||||
\(539\) | −17.0520 | + | 29.5349i | −0.734481 | + | 1.27216i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.14520 | − | 10.6438i | −0.264203 | − | 0.457612i | 0.703152 | − | 0.711040i | \(-0.251775\pi\) |
−0.967354 | + | 0.253427i | \(0.918442\pi\) | |||||||
\(542\) | −0.384559 | − | 6.60262i | −0.0165182 | − | 0.283607i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.21460 | − | 0.375733i | 0.137825 | − | 0.0161094i | ||||
\(545\) | −0.627575 | − | 2.09625i | −0.0268824 | − | 0.0897933i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6521 | − | 24.6944i | −0.455452 | − | 1.05586i | −0.979000 | − | 0.203861i | \(-0.934651\pi\) |
0.523548 | − | 0.851996i | \(-0.324608\pi\) | |||||||
\(548\) | 1.08230 | + | 0.393924i | 0.0462335 | + | 0.0168276i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26.3469 | + | 9.58950i | −1.12344 | + | 0.408898i | ||||
\(551\) | −31.8287 | − | 33.7365i | −1.35595 | − | 1.43722i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.8875 | + | 25.0545i | −2.12143 | + | 1.06542i | ||||
\(554\) | 1.69055 | − | 29.0256i | 0.0718245 | − | 1.23318i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.652517 | − | 2.17956i | 0.0276729 | − | 0.0924339i | ||||
\(557\) | −3.81879 | + | 21.6574i | −0.161807 | + | 0.917654i | 0.790488 | + | 0.612477i | \(0.209827\pi\) |
−0.952296 | + | 0.305177i | \(0.901284\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.128768 | + | 0.730281i | 0.00544631 | + | 0.0308876i | ||||
\(560\) | 9.32047 | + | 1.08941i | 0.393862 | + | 0.0460358i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.4201 | − | 15.2844i | 0.608275 | − | 0.644734i | ||||
\(563\) | −18.7536 | + | 43.4757i | −0.790370 | + | 1.83228i | −0.333505 | + | 0.942748i | \(0.608232\pi\) |
−0.456865 | + | 0.889536i | \(0.651028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.05249 | + | 3.98079i | −0.254630 | + | 0.167473i | ||||
\(566\) | −25.7811 | −1.08366 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.2870 | 1.22886 | ||||||||
\(569\) | −14.4816 | + | 9.52469i | −0.607099 | + | 0.399296i | −0.815508 | − | 0.578746i | \(-0.803542\pi\) |
0.208408 | + | 0.978042i | \(0.433172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1217 | − | 32.7377i | 0.590973 | − | 1.37003i | −0.315967 | − | 0.948770i | \(-0.602329\pi\) |
0.906940 | − | 0.421260i | \(-0.138412\pi\) | |||||||
\(572\) | −3.15754 | + | 3.34680i | −0.132023 | + | 0.139937i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 36.3561 | + | 4.24942i | 1.51747 | + | 0.177367i | ||||
\(575\) | −0.976768 | − | 5.53953i | −0.0407341 | − | 0.231014i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.228884 | + | 1.29807i | −0.00952858 | + | 0.0540393i | −0.989201 | − | 0.146563i | \(-0.953179\pi\) |
0.979673 | + | 0.200602i | \(0.0642899\pi\) | |||||||
\(578\) | −6.53204 | + | 21.8185i | −0.271697 | + | 0.907532i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.0789958 | − | 1.35630i | 0.00328012 | − | 0.0563175i | ||||
\(581\) | −2.50563 | + | 1.25838i | −0.103951 | + | 0.0522063i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.7933 | − | 37.9386i | −1.48241 | − | 1.57126i | ||||
\(584\) | −36.4540 | + | 13.2682i | −1.50848 | + | 0.549041i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.8824 | + | 13.4241i | 1.52360 | + | 0.554544i | ||||
\(587\) | −1.99538 | − | 4.62581i | −0.0823582 | − | 0.190928i | 0.872061 | − | 0.489397i | \(-0.162783\pi\) |
−0.954419 | + | 0.298469i | \(0.903524\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0891625 | − | 0.297824i | −0.00367388 | − | 0.0122716i | ||||
\(590\) | 1.09062 | − | 0.127476i | 0.0449003 | − | 0.00524809i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.820774 | − | 14.0922i | −0.0337336 | − | 0.579184i | ||||
\(593\) | −13.0012 | − | 22.5187i | −0.533895 | − | 0.924732i | −0.999216 | − | 0.0395907i | \(-0.987395\pi\) |
0.465321 | − | 0.885142i | \(-0.345939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.52425 | − | 2.64009i | 0.0624883 | − | 0.108233i | ||||
\(596\) | −1.87866 | − | 0.943497i | −0.0769528 | − | 0.0386472i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.40717 | − | 4.57663i | −0.139330 | − | 0.187152i | ||||
\(599\) | 17.4587 | + | 4.13779i | 0.713344 | + | 0.169066i | 0.571236 | − | 0.820786i | \(-0.306464\pi\) |
0.142108 | + | 0.989851i | \(0.454612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.4833 | + | 27.5138i | −0.835531 | + | 1.12231i | 0.155389 | + | 0.987853i | \(0.450337\pi\) |
−0.990919 | + | 0.134459i | \(0.957070\pi\) | |||||||
\(602\) | −1.12414 | + | 0.943264i | −0.0458164 | + | 0.0384446i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.40962 | − | 3.70011i | −0.179425 | − | 0.150555i | ||||
\(605\) | 1.81144 | − | 0.429319i | 0.0736455 | − | 0.0174543i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.64151 | + | 1.07964i | 0.0666267 | + | 0.0438211i | 0.582385 | − | 0.812913i | \(-0.302120\pi\) |
−0.515759 | + | 0.856734i | \(0.672490\pi\) | |||||||
\(608\) | 12.0755 | + | 7.94216i | 0.489725 | + | 0.322097i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.240179 | − | 0.0569234i | 0.00972456 | − | 0.00230476i | ||||
\(611\) | 11.2987 | + | 9.48071i | 0.457095 | + | 0.383549i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.60067 | + | 1.34312i | −0.0646505 | + | 0.0542482i | −0.674540 | − | 0.738238i | \(-0.735658\pi\) |
0.609890 | + | 0.792486i | \(0.291214\pi\) | |||||||
\(614\) | −9.25743 | + | 12.4349i | −0.373599 | + | 0.501831i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 37.0431 | + | 8.77938i | 1.49251 | + | 0.353731i | ||||
\(617\) | 24.8220 | + | 33.3418i | 0.999298 | + | 1.34229i | 0.938928 | + | 0.344113i | \(0.111820\pi\) |
0.0603694 | + | 0.998176i | \(0.480772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.28378 | − | 3.15583i | −0.252567 | − | 0.126844i | 0.318012 | − | 0.948087i | \(-0.396985\pi\) |
−0.570579 | + | 0.821243i | \(0.693281\pi\) | |||||||
\(620\) | 0.00455322 | − | 0.00788641i | 0.000182862 | − | 0.000316726i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.8154 | − | 36.0533i | −0.834620 | − | 1.44561i | ||||
\(623\) | 2.68331 | + | 46.0707i | 0.107505 | + | 1.84578i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.0388 | + | 2.45908i | −0.841553 | + | 0.0983634i | ||||
\(626\) | 5.77312 | + | 19.2836i | 0.230740 | + | 0.770727i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.28198 | + | 2.97195i | 0.0511564 | + | 0.118594i | ||||
\(629\) | −4.30925 | − | 1.56844i | −0.171821 | − | 0.0625378i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.32771 | − | 2.30310i | 0.251902 | − | 0.0916848i | −0.212983 | − | 0.977056i | \(-0.568318\pi\) |
0.464885 | + | 0.885371i | \(0.346096\pi\) | |||||||
\(632\) | 23.9463 | + | 25.3816i | 0.952534 | + | 1.00963i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.1049 | − | 6.58153i | 0.520463 | − | 0.261386i | ||||
\(635\) | −0.547578 | + | 9.40155i | −0.0217300 | + | 0.373089i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.95367 | + | 26.5671i | −0.315136 | + | 1.05263i | ||||
\(638\) | 7.10175 | − | 40.2760i | 0.281161 | − | 1.59454i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.18865 | − | 6.74119i | −0.0469857 | − | 0.266469i | ||||
\(641\) | 12.9949 | + | 1.51889i | 0.513270 | + | 0.0599926i | 0.368786 | − | 0.929515i | \(-0.379774\pi\) |
0.144484 | + | 0.989507i | \(0.453848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.79987 | − | 1.90775i | 0.0709800 | − | 0.0752344i | −0.690910 | − | 0.722941i | \(-0.742790\pi\) |
0.761890 | + | 0.647706i | \(0.224272\pi\) | |||||||
\(644\) | 0.723533 | − | 1.67734i | 0.0285112 | − | 0.0660964i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.9996 | − | 8.54998i | 0.511463 | − | 0.336394i | ||||
\(647\) | −2.94663 | −0.115844 | −0.0579219 | − | 0.998321i | \(-0.518447\pi\) | ||||
−0.0579219 | + | 0.998321i | \(0.518447\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.34772 | 0.209916 | ||||||||
\(650\) | −19.0486 | + | 12.5285i | −0.747147 | + | 0.491406i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.465631 | − | 1.07945i | 0.0182355 | − | 0.0422747i | ||||
\(653\) | 24.1758 | − | 25.6248i | 0.946071 | − | 1.00278i | −0.0539200 | − | 0.998545i | \(-0.517172\pi\) |
0.999991 | − | 0.00423147i | \(-0.00134692\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.80704 | − | 0.328096i | −0.109680 | − | 0.0128198i | ||||
\(656\) | −4.76957 | − | 27.0496i | −0.186221 | − | 1.05611i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.06840 | + | 28.7443i | −0.197587 | + | 1.12057i | ||||
\(659\) | 4.81941 | − | 16.0979i | 0.187738 | − | 0.627087i | −0.811357 | − | 0.584550i | \(-0.801271\pi\) |
0.999095 | − | 0.0425366i | \(-0.0135439\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.169220 | − | 2.90540i | 0.00658190 | − | 0.113007i | −0.993417 | − | 0.114555i | \(-0.963456\pi\) |
0.999999 | + | 0.00154821i | \(0.000492812\pi\) | |||||||
\(662\) | 32.4583 | − | 16.3012i | 1.26153 | − | 0.633562i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.20272 | + | 1.27481i | 0.0466746 | + | 0.0494722i | ||||
\(665\) | 12.7928 | − | 4.65618i | 0.496082 | − | 0.180559i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.71007 | + | 2.80623i | 0.298535 | + | 0.108658i | ||||
\(668\) | 3.22673 | + | 7.48041i | 0.124846 | + | 0.289426i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.23835 | + | 4.13637i | 0.0478415 | + | 0.159802i | ||||
\(671\) | 1.19399 | − | 0.139558i | 0.0460936 | − | 0.00538757i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.176906 | − | 3.03736i | −0.00681923 | − | 0.117082i | −1.00000 | 0.000496017i | \(-0.999842\pi\) | |
0.993181 | − | 0.116586i | \(-0.0371949\pi\) | |||||||
\(674\) | −2.40053 | − | 4.15783i | −0.0924648 | − | 0.160154i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.638419 | − | 1.10577i | 0.0245546 | − | 0.0425298i | ||||
\(677\) | −33.4519 | − | 16.8002i | −1.28566 | − | 0.645684i | −0.331072 | − | 0.943605i | \(-0.607410\pi\) |
−0.954590 | + | 0.297921i | \(0.903707\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.9864 | − | 41.6219i | −1.18915 | − | 1.59730i | ||||
\(680\) | −1.85417 | − | 0.439446i | −0.0711042 | − | 0.0168520i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.163697 | − | 0.219883i | 0.00626829 | − | 0.00841977i | ||||
\(683\) | 23.8512 | − | 20.0135i | 0.912641 | − | 0.765797i | −0.0599783 | − | 0.998200i | \(-0.519103\pi\) |
0.972620 | + | 0.232403i | \(0.0746587\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.16318 | − | 0.976025i | −0.0444429 | − | 0.0372920i | ||||
\(686\) | −11.4366 | + | 2.71053i | −0.436653 | + | 0.103489i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.920007 | + | 0.605098i | 0.0350749 | + | 0.0230691i | ||||
\(689\) | −35.4358 | − | 23.3065i | −1.35000 | − | 0.887907i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4258 | − | 2.47095i | 0.396615 | − | 0.0939995i | −0.0274683 | − | 0.999623i | \(-0.508745\pi\) |
0.424083 | + | 0.905623i | \(0.360596\pi\) | |||||||
\(692\) | −0.501162 | − | 0.420525i | −0.0190513 | − | 0.0159859i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.3811 | + | 22.1364i | −1.00141 | + | 0.840286i | ||||
\(695\) | −1.79114 | + | 2.40592i | −0.0679419 | + | 0.0912618i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.68251 | − | 2.05779i | −0.328874 | − | 0.0779445i | ||||
\(698\) | −2.77903 | − | 3.73289i | −0.105188 | − | 0.141292i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.52308 | − | 3.27602i | −0.246549 | − | 0.123822i | ||||
\(701\) | 10.3580 | − | 17.9406i | 0.391216 | − | 0.677607i | −0.601394 | − | 0.798953i | \(-0.705388\pi\) |
0.992610 | + | 0.121346i | \(0.0387210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.2395 | − | 17.7353i | −0.386188 | − | 0.668898i | ||||
\(704\) | −1.31727 | − | 22.6166i | −0.0496464 | − | 0.852396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.32048 | + | 0.388109i | −0.124968 | + | 0.0146067i | ||||
\(707\) | −14.1432 | − | 47.2416i | −0.531910 | − | 1.77670i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.20452 | − | 16.7019i | −0.270571 | − | 0.627255i | 0.727708 | − | 0.685887i | \(-0.240585\pi\) |
−0.998280 | + | 0.0586319i | \(0.981326\pi\) | |||||||
\(710\) | 8.67796 | + | 3.15852i | 0.325678 | + | 0.118537i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.1066 | − | 9.86600i | 1.01586 | − | 0.369744i | ||||
\(713\) | 0.0377403 | + | 0.0400024i | 0.00141339 | + | 0.00149810i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.42080 | − | 2.72243i | 0.202726 | − | 0.101813i | ||||
\(716\) | −0.270778 | + | 4.64907i | −0.0101194 | + | 0.173744i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.287306 | − | 0.959668i | 0.0107222 | − | 0.0358145i | ||||
\(719\) | 5.53156 | − | 31.3710i | 0.206292 | − | 1.16994i | −0.689101 | − | 0.724666i | \(-0.741994\pi\) |
0.895393 | − | 0.445277i | \(-0.146895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.44761 | − | 8.20980i | −0.0539118 | − | 0.305749i | ||||
\(722\) | 39.8631 | + | 4.65933i | 1.48355 | + | 0.173402i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.00034 | + | 2.12024i | −0.0743421 | + | 0.0787981i | ||||
\(725\) | 12.9859 | − | 30.1048i | 0.482285 | − | 1.11806i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.91945 | + | 5.20870i | −0.293716 | + | 0.193180i | −0.687811 | − | 0.725890i | \(-0.741428\pi\) |
0.394095 | + | 0.919070i | \(0.371058\pi\) | |||||||
\(728\) | 30.9566 | 1.14733 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.2325 | −0.452746 | ||||||||
\(731\) | 0.298878 | − | 0.196575i | 0.0110544 | − | 0.00727060i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.6921 | + | 38.6967i | −0.616538 | + | 1.42930i | 0.268271 | + | 0.963343i | \(0.413548\pi\) |
−0.884809 | + | 0.465953i | \(0.845712\pi\) | |||||||
\(734\) | −10.0376 | + | 10.6393i | −0.370496 | + | 0.392703i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.53950 | − | 0.296824i | −0.0936070 | − | 0.0109411i | ||||
\(737\) | 3.65153 | + | 20.7089i | 0.134506 | + | 0.762821i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.32565 | − | 47.2171i | 0.306264 | − | 1.73691i | −0.311232 | − | 0.950334i | \(-0.600742\pi\) |
0.617496 | − | 0.786574i | \(-0.288147\pi\) | |||||||
\(740\) | 0.172045 | − | 0.574669i | 0.00632449 | − | 0.0211253i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.88024 | − | 83.7904i | 0.179159 | − | 3.07604i | ||||
\(743\) | 9.21372 | − | 4.62730i | 0.338019 | − | 0.169759i | −0.271690 | − | 0.962385i | \(-0.587583\pi\) |
0.609709 | + | 0.792625i | \(0.291286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.90195 | + | 2.01594i | 0.0696819 | + | 0.0738585i | ||||
\(746\) | −7.08589 | + | 2.57905i | −0.259433 | + | 0.0944258i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.08580 | + | 0.759170i | 0.0762645 | + | 0.0277580i | ||||
\(749\) | 2.62669 | + | 6.08934i | 0.0959770 | + | 0.222500i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.18583 | − | 24.0023i | −0.262215 | − | 0.875858i | −0.983141 | − | 0.182847i | \(-0.941469\pi\) |
0.720927 | − | 0.693011i | \(-0.243716\pi\) | |||||||
\(752\) | 21.7540 | − | 2.54268i | 0.793287 | − | 0.0927220i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.93368 | − | 33.2000i | −0.0704205 | − | 1.20907i | ||||
\(755\) | 3.79446 | + | 6.57219i | 0.138094 | + | 0.239187i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.05875 | − | 5.29791i | 0.111172 | − | 0.192556i | −0.805071 | − | 0.593178i | \(-0.797873\pi\) |
0.916243 | + | 0.400623i | \(0.131206\pi\) | |||||||
\(758\) | 35.9421 | + | 18.0508i | 1.30547 | + | 0.655634i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.08156 | − | 6.82572i | −0.184328 | − | 0.247595i | ||||
\(761\) | −43.6455 | − | 10.3442i | −1.58215 | − | 0.374976i | −0.656790 | − | 0.754073i | \(-0.728086\pi\) |
−0.925357 | + | 0.379097i | \(0.876234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.2406 | − | 13.7555i | 0.370733 | − | 0.497981i | ||||
\(764\) | 3.82972 | − | 3.21351i | 0.138554 | − | 0.116261i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.50299 | − | 7.97396i | −0.343357 | − | 0.288111i | ||||
\(767\) | 4.23136 | − | 1.00285i | 0.152785 | − | 0.0362108i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.6906 | − | 20.8432i | −1.14279 | − | 0.751626i | −0.170490 | − | 0.985359i | \(-0.554535\pi\) |
−0.972301 | + | 0.233734i | \(0.924906\pi\) | |||||||
\(770\) | 10.0293 | + | 6.59639i | 0.361431 | + | 0.237717i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.79092 | − | 1.60948i | 0.244411 | − | 0.0579264i | ||||
\(773\) | −11.7711 | − | 9.87712i | −0.423377 | − | 0.355255i | 0.406069 | − | 0.913842i | \(-0.366899\pi\) |
−0.829446 | + | 0.558587i | \(0.811344\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.168345 | − | 0.141258i | 0.00604713 | − | 0.00507415i | ||||
\(776\) | −19.3687 | + | 26.0167i | −0.695295 | + | 0.933944i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.1882 | − | 8.10276i | −1.22571 | − | 0.290498i | ||||
\(779\) | −23.7954 | − | 31.9628i | −0.852559 | − | 1.14518i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.1918 | + | 20.1851i | 1.43818 | + | 0.722279i | ||||
\(782\) | −1.37623 | + | 2.38370i | −0.0492138 | + | 0.0852408i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.5905 | + | 35.6637i | 0.735373 | + | 1.27370i | ||||
\(785\) | −0.248108 | − | 4.25985i | −0.00885535 | − | 0.152041i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.9986 | − | 5.72711i | 1.74661 | − | 0.204150i | 0.818003 | − | 0.575213i | \(-0.195081\pi\) |
0.928607 | + | 0.371064i | \(0.121007\pi\) | |||||||
\(788\) | 1.08036 | + | 3.60864i | 0.0384861 | + | 0.128552i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.35814 | + | 10.1033i | 0.155056 | + | 0.359459i | ||||
\(791\) | −53.3497 | − | 19.4177i | −1.89690 | − | 0.690414i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.918571 | − | 0.334333i | 0.0326194 | − | 0.0118725i | ||||
\(794\) | 26.2059 | + | 27.7766i | 0.930013 | + | 0.985756i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.86163 | + | 1.43716i | −0.101428 | + | 0.0509389i | ||||
\(797\) | −0.887101 | + | 15.2309i | −0.0314227 | + | 0.539507i | 0.945461 | + | 0.325736i | \(0.105612\pi\) |
−0.976884 | + | 0.213772i | \(0.931425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.04067 | − | 6.81632i | 0.0721938 | − | 0.241144i | ||||
\(800\) | −1.77412 | + | 10.0615i | −0.0627245 | + | 0.355728i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.55360 | − | 25.8247i | −0.160793 | − | 0.911903i | ||||
\(803\) | −59.1720 | − | 6.91621i | −2.08813 | − | 0.244068i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.65267 | + | 1.75172i | −0.0582489 | + | 0.0617402i | ||||
\(806\) | 0.0882902 | − | 0.204680i | 0.00310989 | − | 0.00720953i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −25.7533 | + | 16.9382i | −0.905998 | + | 0.595884i | ||||
\(809\) | −30.2451 | −1.06336 | −0.531681 | − | 0.846945i | \(-0.678439\pi\) | ||||
−0.531681 | + | 0.846945i | \(0.678439\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.7859 | −0.729892 | −0.364946 | − | 0.931029i | \(-0.618913\pi\) | ||||
−0.364946 | + | 0.931029i | \(0.618913\pi\) | |||||||
\(812\) | 8.89580 | − | 5.85086i | 0.312181 | − | 0.205325i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.15224 | − | 16.5808i | 0.250686 | − | 0.581156i | ||||
\(815\) | −1.06358 | + | 1.12733i | −0.0372555 | + | 0.0394885i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.58671 | + | 0.185460i | 0.0555121 | + | 0.00648843i | ||||
\(818\) | −3.03064 | − | 17.1876i | −0.105964 | − | 0.600950i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.202686 | − | 1.14949i | 0.00707810 | − | 0.0401419i | ||||
\(821\) | 12.5623 | − | 41.9611i | 0.438428 | − | 1.46445i | −0.398515 | − | 0.917162i | \(-0.630474\pi\) |
0.836943 | − | 0.547290i | \(-0.184340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.434717 | + | 7.46380i | −0.0151533 | + | 0.260172i | 0.982220 | + | 0.187735i | \(0.0601146\pi\) |
−0.997373 | + | 0.0724368i | \(0.976922\pi\) | |||||||
\(824\) | −4.65660 | + | 2.33863i | −0.162220 | + | 0.0814702i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.90542 | + | 6.25938i | 0.205476 | + | 0.217792i | ||||
\(827\) | 36.5331 | − | 13.2970i | 1.27038 | − | 0.462381i | 0.383142 | − | 0.923690i | \(-0.374842\pi\) |
0.887240 | + | 0.461309i | \(0.152620\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.8678 | − | 11.9629i | −1.14155 | − | 0.415489i | −0.299075 | − | 0.954230i | \(-0.596678\pi\) |
−0.842471 | + | 0.538741i | \(0.818900\pi\) | |||||||
\(830\) | 0.218890 | + | 0.507445i | 0.00759780 | + | 0.0176137i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.28355 | − | 17.6483i | −0.183174 | − | 0.611844i | ||||
\(833\) | 13.2878 | − | 1.55312i | 0.460395 | − | 0.0538124i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.624488 | − | 10.7220i | −0.0216113 | − | 0.371051i | ||||
\(836\) | 4.95619 | + | 8.58438i | 0.171413 | + | 0.296897i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.0477 | + | 43.3840i | −0.865260 | + | 1.49867i | ||||
\(839\) | −4.80771 | − | 2.41452i | −0.165980 | − | 0.0833585i | 0.363869 | − | 0.931450i | \(-0.381455\pi\) |
−0.529850 | + | 0.848091i | \(0.677752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.2406 | + | 15.0988i | 0.387608 | + | 0.520647i | ||||
\(842\) | 0.998628 | + | 0.236679i | 0.0344150 | + | 0.00815650i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.61390 | + | 3.51108i | −0.0899743 | + | 0.120856i | ||||
\(845\) | −1.28950 | + | 1.08202i | −0.0443602 | + | 0.0372227i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.1763 | + | 9.37801i | 0.384021 | + | 0.322232i | ||||
\(848\) | −61.2841 | + | 14.5246i | −2.10450 | + | 0.498777i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.18922 | + | 6.04384i | 0.315188 | + | 0.207302i | ||||
\(851\) | 3.02675 | + | 1.99073i | 0.103756 | + | 0.0682412i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.6540 | − | 4.42107i | 0.638700 | − | 0.151375i | 0.101508 | − | 0.994835i | \(-0.467633\pi\) |
0.537192 | + | 0.843460i | \(0.319485\pi\) | |||||||
\(854\) | 1.48186 | + | 1.24343i | 0.0507083 | + | 0.0425493i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.17547 | − | 2.66454i | 0.108535 | − | 0.0910721i | ||||
\(857\) | 19.0265 | − | 25.5570i | 0.649933 | − | 0.873012i | −0.347985 | − | 0.937500i | \(-0.613134\pi\) |
0.997918 | + | 0.0644883i | \(0.0205415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.3291 | + | 3.63307i | 0.523024 | + | 0.123959i | 0.483643 | − | 0.875265i | \(-0.339313\pi\) |
0.0393807 | + | 0.999224i | \(0.487462\pi\) | |||||||
\(860\) | 0.0279438 | + | 0.0375350i | 0.000952874 | + | 0.00127993i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 41.9250 | + | 21.0555i | 1.42797 | + | 0.717154i | ||||
\(863\) | −1.55618 | + | 2.69539i | −0.0529731 | + | 0.0917521i | −0.891296 | − | 0.453422i | \(-0.850203\pi\) |
0.838323 | + | 0.545174i | \(0.183536\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.431247 | + | 0.746942i | 0.0146628 | + | 0.0253968i | ||||
\(866\) | −1.02084 | − | 17.5271i | −0.0346894 | − | 0.595594i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.0708850 | − | 0.00828527i | 0.00240599 | − | 0.000281220i | ||||
\(869\) | 15.3691 | + | 51.3365i | 0.521362 | + | 1.74147i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.77277 | + | 15.7010i | 0.229486 | + | 0.532009i | ||||
\(872\) | −10.0728 | − | 3.66619i | −0.341107 | − | 0.124153i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.5504 | + | 4.20400i | −0.390698 | + | 0.142202i | ||||
\(875\) | 13.5687 | + | 14.3819i | 0.458705 | + | 0.486199i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.86701 | + | 3.44874i | −0.231882 | + | 0.116456i | −0.560947 | − | 0.827852i | \(-0.689563\pi\) |
0.329065 | + | 0.944307i | \(0.393267\pi\) | |||||||
\(878\) | −0.644100 | + | 11.0588i | −0.0217373 | + | 0.373216i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.58345 | − | 8.62933i | 0.0870882 | − | 0.290895i | ||||
\(881\) | −8.24582 | + | 46.7644i | −0.277809 | + | 1.57553i | 0.452087 | + | 0.891974i | \(0.350680\pi\) |
−0.729896 | + | 0.683558i | \(0.760432\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.38476 | + | 30.5385i | 0.181212 | + | 1.02770i | 0.930727 | + | 0.365715i | \(0.119176\pi\) |
−0.749515 | + | 0.661987i | \(0.769713\pi\) | |||||||
\(884\) | 1.79275 | + | 0.209542i | 0.0602966 | + | 0.00704767i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.85144 | − | 1.96242i | 0.0622005 | − | 0.0659287i | ||||
\(887\) | −1.20818 | + | 2.80086i | −0.0405666 | + | 0.0940438i | −0.937295 | − | 0.348538i | \(-0.886678\pi\) |
0.896728 | + | 0.442582i | \(0.145937\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61.6634 | + | 40.5566i | −2.06812 | + | 1.36023i | ||||
\(890\) | 9.09590 | 0.304895 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.30576 | 0.244615 | ||||||||
\(893\) | 26.5473 | − | 17.4604i | 0.888371 | − | 0.584291i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.43174 | − | 5.63740i | 0.0812840 | − | 0.188438i | ||||
\(896\) | 36.8141 | − | 39.0207i | 1.22987 | − | 1.30359i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −51.4107 | − | 6.00905i | −1.71560 | − | 0.200525i | ||||
\(899\) | 0.0556631 | + | 0.315681i | 0.00185647 | + | 0.0105286i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.55294 | + | 20.1497i | −0.118366 | + | 0.671285i | ||||
\(902\) | 10.0772 | − | 33.6602i | 0.335534 | − | 1.12076i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.06341 | + | 35.4275i | −0.0686282 | + | 1.17830i | ||||
\(905\) | 3.43415 | − | 1.72469i | 0.114155 | − | 0.0573307i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.1409 | − | 10.7487i | −0.336723 | − | 0.356905i | 0.536782 | − | 0.843721i | \(-0.319640\pi\) |
−0.873505 | + | 0.486816i | \(0.838158\pi\) | |||||||
\(908\) | −4.02603 | + | 1.46536i | −0.133609 | + | 0.0486296i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.17266 | + | 3.33858i | 0.304071 | + | 0.110673i | ||||
\(911\) | −11.8845 | − | 27.5515i | −0.393752 | − | 0.912820i | −0.993626 | − | 0.112726i | \(-0.964042\pi\) |
0.599874 | − | 0.800095i | \(-0.295217\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.771925 | + | 2.57841i | 0.0255470 | + | 0.0853328i | ||||
\(914\) | 17.5318 | − | 2.04917i | 0.579900 | − | 0.0677806i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0683500 | − | 1.17352i | −0.00225835 | − | 0.0387744i | ||||
\(917\) | −11.0743 | − | 19.1813i | −0.365707 | − | 0.633422i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6334 | + | 23.6138i | −0.449725 | + | 0.778947i | −0.998368 | − | 0.0571097i | \(-0.981812\pi\) |
0.548642 | + | 0.836057i | \(0.315145\pi\) | |||||||
\(920\) | 1.34523 | + | 0.675600i | 0.0443509 | + | 0.0222739i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.3562 | + | 20.6269i | 0.505729 | + | 0.679312i | ||||
\(923\) | 35.5869 | + | 8.43424i | 1.17136 | + | 0.277616i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.64459 | − | 11.6117i | 0.284232 | − | 0.381790i | ||||
\(926\) | 5.41522 | − | 4.54391i | 0.177955 | − | 0.149322i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.4161 | − | 9.57923i | −0.374751 | − | 0.314454i | ||||
\(929\) | 41.8572 | − | 9.92033i | 1.37329 | − | 0.325475i | 0.523243 | − | 0.852184i | \(-0.324722\pi\) |
0.850046 | + | 0.526708i | \(0.176574\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.9149 | + | 32.8295i | 1.63589 | + | 1.07594i | ||||
\(932\) | −4.59448 | − | 3.02184i | −0.150497 | − | 0.0989836i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 50.9491 | − | 12.0751i | 1.66710 | − | 0.395111i | ||||
\(935\) | −2.24168 | − | 1.88099i | −0.0733108 | − | 0.0615151i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.7580 | − | 30.8436i | 1.20083 | − | 1.00762i | 0.201226 | − | 0.979545i | \(-0.435507\pi\) |
0.999606 | − | 0.0280726i | \(-0.00893697\pi\) | |||||||
\(938\) | −20.2069 | + | 27.1426i | −0.659780 | + | 0.886238i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.905656 | + | 0.214644i | 0.0295392 | + | 0.00700093i | ||||
\(941\) | −17.4141 | − | 23.3912i | −0.567683 | − | 0.762530i | 0.421877 | − | 0.906653i | \(-0.361371\pi\) |
−0.989560 | + | 0.144123i | \(0.953964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.29930 | + | 3.16363i | 0.205133 | + | 0.103022i | ||||
\(944\) | 3.22871 | − | 5.59229i | 0.105086 | − | 0.182014i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.704316 | + | 1.21991i | 0.0228993 | + | 0.0396628i | ||||
\(947\) | −3.03416 | − | 52.0945i | −0.0985968 | − | 1.69284i | −0.578628 | − | 0.815591i | \(-0.696412\pi\) |
0.480032 | − | 0.877251i | \(-0.340625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.1166 | + | 5.62402i | −1.56193 | + | 0.182563i | ||||
\(950\) | 14.0868 | + | 47.0533i | 0.457037 | + | 1.52661i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.91496 | − | 13.7124i | −0.191705 | − | 0.444422i | ||||
\(953\) | −10.4942 | − | 3.81957i | −0.339940 | − | 0.123728i | 0.166409 | − | 0.986057i | \(-0.446783\pi\) |
−0.506349 | + | 0.862329i | \(0.669005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.19342 | + | 2.25422i | −0.200414 | + | 0.0729449i | ||||
\(956\) | −2.10505 | − | 2.23122i | −0.0680821 | − | 0.0721628i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.9861 | − | 6.01966i | 0.387254 | − | 0.194486i | ||||
\(959\) | 0.691921 | − | 11.8798i | 0.0223433 | − | 0.383620i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.89028 | − | 29.6956i | 0.286783 | − | 0.957923i | ||||
\(962\) | 2.54981 | − | 14.4607i | 0.0822093 | − | 0.466232i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.242913 | + | 1.37763i | 0.00782369 | + | 0.0443703i | ||||
\(965\) | −9.13864 | − | 1.06815i | −0.294183 | − | 0.0343851i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.4029 | + | 38.5848i | −1.17064 | + | 1.24081i | −0.205618 | + | 0.978632i | \(0.565921\pi\) |
−0.965021 | + | 0.262173i | \(0.915561\pi\) | |||||||
\(968\) | 3.61206 | − | 8.37369i | 0.116096 | − | 0.269141i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.54490 | + | 5.62007i | −0.274360 | + | 0.180450i | ||||
\(971\) | 45.0507 | 1.44575 | 0.722873 | − | 0.690981i | \(-0.242821\pi\) | ||||
0.722873 | + | 0.690981i | \(0.242821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.5068 | −0.753592 | ||||||||
\(974\) | −27.5447 | + | 18.1164i | −0.882589 | + | 0.580488i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.574939 | − | 1.33286i | 0.0184034 | − | 0.0426638i | ||||
\(977\) | −37.8530 | + | 40.1218i | −1.21102 | + | 1.28361i | −0.263228 | + | 0.964734i | \(0.584787\pi\) |
−0.947796 | + | 0.318877i | \(0.896694\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.9993 | + | 5.14278i | 1.40622 | + | 0.164364i | ||||
\(980\) | 0.303886 | + | 1.72342i | 0.00970728 | + | 0.0550527i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.13063 | − | 6.41214i | 0.0360800 | − | 0.204620i | ||||
\(983\) | −11.1606 | + | 37.2791i | −0.355969 | + | 1.18902i | 0.573217 | + | 0.819404i | \(0.305695\pi\) |
−0.929185 | + | 0.369614i | \(0.879490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.288753 | − | 4.95769i | 0.00920043 | − | 0.157965i | ||||
\(986\) | −14.3367 | + | 7.20015i | −0.456573 | + | 0.229299i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.53138 | + | 5.86292i | 0.175977 | + | 0.186524i | ||||
\(989\) | −0.265559 | + | 0.0966555i | −0.00844428 | + | 0.00307347i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.91069 | − | 2.87925i | −0.251291 | − | 0.0914625i | 0.213303 | − | 0.976986i | \(-0.431578\pi\) |
−0.464595 | + | 0.885523i | \(0.653800\pi\) | |||||||
\(992\) | −0.0395641 | − | 0.0917200i | −0.00125616 | − | 0.00291211i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.7572 | + | 69.3338i | 0.658377 | + | 2.19913i | ||||
\(995\) | 4.19314 | − | 0.490108i | 0.132932 | − | 0.0155375i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.84136 | + | 48.7843i | 0.0899869 | + | 1.54501i | 0.677332 | + | 0.735678i | \(0.263136\pi\) |
−0.587345 | + | 0.809337i | \(0.699827\pi\) | |||||||
\(998\) | 23.4983 | + | 40.7003i | 0.743827 | + | 1.28835i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 729.2.g.b.28.7 | 144 | ||
3.2 | odd | 2 | 729.2.g.c.28.2 | 144 | |||
9.2 | odd | 6 | 81.2.g.a.13.7 | ✓ | 144 | ||
9.4 | even | 3 | 729.2.g.a.514.7 | 144 | |||
9.5 | odd | 6 | 729.2.g.d.514.2 | 144 | |||
9.7 | even | 3 | 243.2.g.a.10.2 | 144 | |||
81.2 | odd | 54 | 81.2.g.a.25.7 | yes | 144 | ||
81.25 | even | 27 | 729.2.g.a.217.7 | 144 | |||
81.29 | odd | 54 | 729.2.g.c.703.2 | 144 | |||
81.32 | odd | 54 | 6561.2.a.c.1.56 | 72 | |||
81.49 | even | 27 | 6561.2.a.d.1.17 | 72 | |||
81.52 | even | 27 | inner | 729.2.g.b.703.7 | 144 | ||
81.56 | odd | 54 | 729.2.g.d.217.2 | 144 | |||
81.79 | even | 27 | 243.2.g.a.73.2 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.13.7 | ✓ | 144 | 9.2 | odd | 6 | ||
81.2.g.a.25.7 | yes | 144 | 81.2 | odd | 54 | ||
243.2.g.a.10.2 | 144 | 9.7 | even | 3 | |||
243.2.g.a.73.2 | 144 | 81.79 | even | 27 | |||
729.2.g.a.217.7 | 144 | 81.25 | even | 27 | |||
729.2.g.a.514.7 | 144 | 9.4 | even | 3 | |||
729.2.g.b.28.7 | 144 | 1.1 | even | 1 | trivial | ||
729.2.g.b.703.7 | 144 | 81.52 | even | 27 | inner | ||
729.2.g.c.28.2 | 144 | 3.2 | odd | 2 | |||
729.2.g.c.703.2 | 144 | 81.29 | odd | 54 | |||
729.2.g.d.217.2 | 144 | 81.56 | odd | 54 | |||
729.2.g.d.514.2 | 144 | 9.5 | odd | 6 | |||
6561.2.a.c.1.56 | 72 | 81.32 | odd | 54 | |||
6561.2.a.d.1.17 | 72 | 81.49 | even | 27 |